978-3-032-14938-1

Efficiency of Using Lime Plaster Mixture as a Finishing Layer for External Walls of Buildings
1 Introduction

Increased Bending Strength and Water Resistance of Plywood for Construction Purposes

Refinement of Stresses in Monolithic Floor Slabs of Frameless Buildings with Regard to Construction History, Loading and Rheological Properties of Concrete
1 Introduction

Multi-objective Optimization of Concrete Driven by Synergistic Effects of Smart Restoration and Nano-Enhancement

2 Materials and Methods
2.1 Materials Used
2.2 Experimental Mix Ratio Design

2.3 Evaluation Indicators and Results Analysis Method

3 Results and Discussion
3.1 Analysis of Orthogonal Experimental Results
3.2 Influence of Different Factors on 7-Day/28-Day Strength

3.3 Influence of Different Factors on Repair Rate

3.4 Influence of Different Factors on Permeability

Development of Limit State Functions for Probabilistic Analysis of Progressive Collapse in Reinforced Concrete Buildings

2 Methods and Materials
2.1 Probability of Progressive Collapse of Reinforced Concrete Structural System

2.2 Determining Probability P(C|DH) Using a Limit State Function Model

2.3 Limit State Function of the Substructure Above the Removed Column

2.4 Limit State Function
3 Results and Discussion

Experimental Determination of Shear Parameters at the Interface Between Structures and Soil

Assessment of the Influence of a Construction Joint on the Deformability of a Monolithic Reinforced Concrete Floor Slab
1 Introduction
1.1 Prerequisites for Considering the Influence of Construction Joints on Structural Systems

1.2 National and International Codes Regulating Construction Joint Implementation and Analysis

1.3 National and International Research on the Influence of Construction Joints on the Behavior of Reinforced Concrete Structures and Their Results

Calculation of the Pile Grillage Taking into Account the Nonlinear Operation of Piles in the Ground by the Method of Compensating Loads

Scientific Support for the Design of the Marine Terminal
1 Introduction

4 Experimental Studies in a Hydrowave Flume

6 Numerical Studies of the Operation of Designed Coastal Structures

Improvement of Thermal Protection and Durability of Timber Houses with Walls with Wooden Siding and Air Gap

3 Modeling of Thermal Protection of the Structure of Log External Walls with Wooden Siding and Air Gap

4 Calculation of Air Infiltration Processes Through Board Siding with Air Gap for Log Walls

Research of the Stress–Strain State of the Thread Using the Generalized Unknown Method

Application of Ray Expansions for Studying Nonstationary Motion of a Nonlinear Plate on an Elastic Half-Space
1 Introduction

2 Governing Equations for the Formulated Problem

4 Solution for a Nonlinear Elastic Plate

The Effect of Nanomodifying Additives on the Properties of Dispersed Reinforced Concrete
1 Introduction

Computer Simulation of a Spatial Rod Arch
1 Introduction

Analysis of Reinforced Concrete Beams in Road Bridge Superstructures According to Limit State Method
1 Introduction

2 Reinforced Concrete Beams and Road Bridge Superstructures

3 Analysis Methods for Reinforced Concrete Beam Calculation in Road Bridge Superstructures

Investigation of the Strength of Monolithic Reinforced Concrete Slabs with Non-removable Truncated-Pyramidal Hollow Formers
1 Introduction

Selection of a Waterproofing Solution for the Underground Part of a Building Under the Module-Based Methodology

4 Construction Geotechnical Indicators Module

5 Module of Labor-Cost Indicators for New Construction and Further Operation (Repair)

Calculations of Standard Cells of Structures Made of Film and Fabric Orthotropic Membranes
1 Introduction

Static-Dynamic Deformation and Force Resistance of a Monolithic Reinforced Concrete Frame During Brittle and Plastic Fracture

Numerical Simulation of Surface Degradation Process in Cement Granular Composite
1 Introduction

4 Calculation of Normative Wind Load
5 Design Value of the Average Wind Load Component (External Pressure on External Walls)

Development of Approaches to Assessing the Energy Efficiency of Capital Construction Facilities in the Context of Climate Change

2 Relevance and Scientific Significance with a Brief Literature Review

Ensuring Operational Resistance of Paint and Varnish Coatings Due to the Comprehensive Effect of Nano-Additives on Metal Surfaces

Transformation of Discrete Force Equations into a Unified Formula

Organomineral Mixtures for Road Foundations Based on Industrial Waste
1 Introduction

2 Relevance of the Research Topic and Problem Statement

Study of the Properties of Slag-Based Cold Asphalt Concrete Produced with a High Content of RAP Aggregates

2 Research of the Properties of Initial Components and Development of Asphalt Granulate Concrete Compositions Using Slag Fillers and RAP

3 The Study Investigates the Influence of Slag Fillers and RAP Content on the Physico-Mechanical Properties of Asphalt Granular Concretes

4 The Influence of the Modifier Based on a Secondary Product from Hydrolysis Production on the Strength and Water Resistance Indicators of the Obtained Asphalt–granular Concretes

Study of the Reduction of the Bearing Capacity of a Steel-Reinforced Concrete Floor Under the Influence of Various Factors

Analysis of the Efficiency of Pavement Structures at Automatic Weighing Stations

The Effect of Reinforced Methods for Beams with Openings
1 Introduction

2 Investigated and Validated Model in ABAQUS

3.1 The Influence of the Position of Web Opening in Normal Beam

3.2 The Influence of the Reinforced Reinforcement around the Web Openings

Kinetic Characterization of Densified Wood under an Assumed Real Fire Curve Using Thermogravimetric Analysis
1 Introduction

2 Thermogravimetric Tests
2.1 Test Pieces and Materials

2.2 Experimental Setup
2.3 Heating Condition

3 Thermogravimetric Analysis
3.1 Kinetic Modeling of Pyrolysis

3.2 Kinetic Parameter Estimation Approach
3.3 Characterization of the Kinetic Parameters

Special and Unique Structures Construction

Aerodynamics of Ultra-Flexible Structures
1 Introduction

Main Characteristics of Equal-Strength Six-Span Beam

Application of the Theory of Elasticity to the Study of Cracks in Bridge Structures

Influence of Beam and Column Cross-Section on Deflection of Monolithic Floor Slab
1 Materials and Methods

2 Influence of Concrete and Reinforcement Parameters
3 Discussion

4 Practical Recommendations
5 Conclusion

Progressive Limit States of a Flat Model of Portal Frame
1 Introduction

3.1 Frames with Simply Supported Ends (Fig. 2a)

Information Modeling Technologies for Russian Wooden Architecture Objects as a Basis for Modern Design

2 Stages of Project Development
2.1 Research and Application of Historical Analogs in the Project

2.2 Information Modeling of Wooden Buildings

2.3 Basic Principles of Modeling Wooden Elements

3 Software Used in the Project
3.1 Technological Scheme for Designing a Site with Buildings

3.2 Consolidated Project of the Tourist Complex

Architectural Aesthetics and Additive Construction in the Field of Rapid Construction
1 Introduction

3 Results
3.1 Parametricism in Architecture and Additive Manufacturing

3.2 Morphogenesis in Architecture and Additive Manufacturing

Methodology for Determining Deformations of Pile Structures with a “Solid” Reinforcement Body During Bank Protection

2 Constructive and Technological Solutions for Bank Protection Using Deep-Seated Structural Elements

Generalized Geometrically Exact Theory of Column Stability

Analysis of Belt-To-Roller Contact and Pressure Distribution in Pipe Conveyors Using Motion Simulation
1 Introduction

Urban Planning Regulation of Sustainable Development of the World Cities

3 Results and Discussion
3.1 About Sustainable Development Goals
3.2 Major World Cities and Urban Development Models

3.3 Urban Development Concepts in the World Cities at the Time the Sustainable Development Goals Were Formulated and at the Present Stage

4 Summary of Experience in Urban Planning Regulation of Sustainable Development of the World Cities
4.1 About Current Trends in Sustainable Development

4.2 Possibilities for Urban Planning Interpretation of Sustainable Development of the World Cities
5 Conclusions

2.1 “Smart urban spaces” in Russian Cities

2.2 Challenges to Developing Smart Cities and Smart Urban Spaces
3 Сonclusion

Principles and Methods of Forming the Architectural and Artistic Image of Cities and Urban High Responsibility Infrastructure Objects

5 Practical Significance, Proposals and Implementation Results

Innovations in Architectural and Construction Design of Modern Chinese Schools

3 Modern School Education Development Strategies

4 Modern Trends in Designing School Facilities

4.1 Modern School Education Development Strategies

Restoration Technologies of Wooden Architecture Monuments on the Example of the Resort Area and the Church of St. Panteleimon in Tinaki
1 Introduction

2 Historical Background and Current Status

3 Experience in Restoring Wooden Architecture Monuments in Russia

Sustainable Spatial Integration in the Housing Sector as a Strategic Entry Point to Urban Quality of Life

1 Introduction
2 Current and Future Needs for Residential Land Use in the Holy City of Karbala

3 Spatial Analysis of Housing Density Patterns in the Holy City of Karbala

3.1 Analysis of Population Density (Net and Gross)
3.2 Residential Unit Density (Units per Hectare)

4 Spatial Diversity of Housing Units in the Neighborhoods of the Holy City of Karbala
4.1 Relationship Between Residential Density and Housing Unit Diversity

5 Application of the Shannon Index in Karbala

6 Sustainable Spatial Integration Strategies for Urban Housing Development in Karbala

7 Conclusions
8 Recommendations
8.1 At the National Policy Level
8.2 At the Local Urban Planning Level

8.3 At the Social and Housing Diversity Level
References

Implementation of Pedestrian Call Buttons at the Semi-Actuated Intersection of Tulskaya Street and 50 Let VLKSM Street in Tyumen
1 Introduction

Engineering Structure Safety, Environmental Engineering and Environmental Protection

Mitigation of Risks at the Stages of the Life Cycle of Wastewater Treatment Plants
1 Introduction

Determining the Dependence of Aerosol Deposition Surface on the Conditions of Dynamic Foam Layer Formation
1 Introduction

2 Factors of Aerosol Particle Deposition

3 Evaluation of the Conditions for Implementing the Dust Removal Process in a Dynamic Foam Layer

4 Dependence of the Aerosol Deposition Surface on the Conditions of Dynamic Foam Layer Formation

Assessment of Hydro-energy Potential of Kyrgyzstan in the Context of a Green Economy

Reliability and Safety Analysis of Truck Leaf Springs Under Permafrost Conditions Using Failure Time Series

2 The Impact of Seasonal Operating Conditions in Yakutia on Reliability of Truck Suspension Springs
2.1 Road-Climatic Operation Conditions of Automobile Transport in Yakutia, Failure Databases and Their Analysis Using Time Series

2.2 Modeling the Time Series of Leaf Spring Failures

2.3 Evaluation of Service Properties of KAMAZ Trucks’ Leaf Springs Under Exploitation in Yakutia

Aggregated Complexes in the Technology of Ceramic Matrix Composites for Construction

Mathematical Modeling of Municipal Solid Waste (MSW) Incineration Ash Carbonation
1 Introduction

Parameters of a Human-Generated Aerosol Cloud
1 Introduction

Integrated Use of Land and Water Resources in the Talas Region

2 Methods and Research Methodology
3 Theoretical Background

Mixed Wastewater Treatment in the Recycling Water System of a Construction Industry Enterprise
1 Introduction

$New Approaches to Recycling Refractory Scrap$ 1 Introduction

Special Technical Conditions for Ensuring Fire Safety for Liquefied Natural Gas Terminals
1 Introduction

6 Practical Significance and Suggestions

Mathematical Modeling of Explosion-Proof Valve Loading in Ventilation Systems
1 Introduction

The Use of Polyolefin Polymer Wastes in the Production of Bituminous Materials
1 Introduction

2 Purpose, Stages and Objects of the Study

The Directions of Complex Utilization of Ash and Slag Waste of Thermal Power Plants

2 Background
2.1 Properties of Ash and Slag Waste
2.2 Alkali-Activated Materials on the Base of ASW (Milled Slag)

2.3 High Volume Fly Ash Concretes Based on the Beneficiated Ponded Ash

2.4 Application of Fly Ash Waste in Wastewater Treatment
3 Materials and Methods

4 Results and Discussion
4.1 Compressive Strength of Geopolymer-Binders Based on ASW

4.2 The Properties of Beneficiated Ponded Ash

4.3 Study of Phosphate Adsorption on Ponded Ash Surface

Study of Oxygen Transfer from Air to Water Depending on Suspended Matter Concentration in Water
1 Introduction

2 Theoretical Basics of Oxygen Transfer Dynamics in Water

Integrated Safety Design of Cable Lines and Communications for the Development of Oil and Gas Fields in Freezing Seas
1 Introduction

5 Fire Safety of Cable and Communication Systems

Development of a New Method for Extinguishing Oil Fires for Above-Ground Oil Storage Tanks
1 Introduction

5 Practical Significance and Suggestions

Hydrochemical Composition of Waters of the Jyrgalan River Basin

2 Relevance, Scientific Significance of the Issue
3 Setting the Task
4 The Theoretical Part

Radioecological Studies of the Kaji-Sai Tailings Dam

1 Introduction
2 Relevance, Scientific Significance of the Issue
3 Setting the Task

4 The Theoretical Part
5 Practical Significance, Proposals and Implementation Results

6 Isotopic Composition of the Soil Cover

Comprehensive Method of Reagent-Free Purification of Natural and Wastewater
1 Introduction

Investigation of the Dependence of Air-to-Water Oxygen Transfer on the Content of Surfactants in Water

Information and Analytical Support of Resources Degradation Risk Management of the Sport Center Fire Extinguishing Operation

ISBN: 2366-2557

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Text

Lecture Notes in Civil Engineering

Andrey A. Radionov
Vadim R. Gasiyarov Editors

Proceedings of the
9th International
Conference
on Construction,
Architecture and
Technosphere Safety
ICCATS 2025

Lecture Notes in Civil Engineering
Volume 799

Series Editors
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Sheng-Hong Chen, School of Water Resources and Hydropower Engineering,
Wuhan University, Wuhan, China
Ioannis Vayas, Institute of Steel Structures, National Technical University of
Athens, Athens, Greece
Sanjay Kumar Shukla, School of Engineering, Edith Cowan University, Joondalup,
Australia
Anuj Sharma, Iowa State University, Ames, USA
Nagesh Kumar, Department of Civil Engineering, Indian Institute of Science
Bangalore, Bengaluru, India
Chien Ming Wang, School of Civil Engineering, The University of Queensland,
Brisbane, Australia
Zhen-Dong Cui , China University of Mining and Technology, Xuzhou, China
Xinzheng Lu , Department of Civil Engineering, Tsinghua University, Beijing,
China

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Andrey A. Radionov · Vadim R. Gasiyarov
Editors

Proceedings of the 9th
International Conference
on Construction, Architecture
and Technosphere Safety
ICCATS 2025

Editors
Andrey A. Radionov
Moscow Polytechnic University
Moscow, Russia

Vadim R. Gasiyarov
Moscow Polytechnic University
Moscow, Russia

ISSN 2366-2557
ISSN 2366-2565 (electronic)
Lecture Notes in Civil Engineering
ISBN 978-3-032-14937-4
ISBN 978-3-032-14938-1 (eBook)
https://doi.org/10.1007/978-3-032-14938-1
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature
Switzerland AG 2026
This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether
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If disposing of this product, please recycle the paper.

Preface

The International Conference on Construction, Architecture and Technosphere
Safety (ICCATS-2025) was organized by Moscow Polytechnic University on 7–13
of September, 2025.
The conference program encompassed a wide range of topics and was divided into
4 parts: Industrial and Civil Engineering; Special and Unique Structures Construction; Urban Engineering and Planning; Engineering Structure Safety, Environmental
Engineering and Environmental Protection.
Participants could take part in the conference as in a traditional face-to-face format
and as format of video conference remotely.
The international program committee has selected totally 69 papers for publishing
in Lecture Notes in Civil Engineering (Springer International Publishing AG).
On behalf of the Organizing Committee we express appreciation to our colleagues
who participated in the review procedure of the papers and especially thank members
of International Program Committee, who helped us to organize this conference.
We express our gratitude to the participants for the active work at the conference
sections and look forward to meeting at ICCATS-2026 next September in Sochi,
Russia.
Moscow, Russia

Prof. Andrey A. Radionov
Prof. Vadim R. Gasiyarov

Contents

Industrial and Civil Engineering
Efficiency of Using Lime Plaster Mixture as a Finishing Layer
for External Walls of Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
M. V. Frolov, V. I. Loganina, and V. S. Pylaev

Increased Bending Strength and Water Resistance of Plywood
for Construction Purposes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
T. N. Vakhnina, A. A. Fedotov, and I. V. Susoeva

Refinement of Stresses in Monolithic Floor Slabs of Frameless
Buildings with Regard to Construction History, Loading
and Rheological Properties of Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
O. B. Zavyalova

Multi-objective Optimization of Concrete Driven by Synergistic
Effects of Smart Restoration and Nano-Enhancement . . . . . . . . . . . . . . . . .
Mingyuan Wang, Zhuxuan Xu, Li Zheng, and V. S. Rudnov

Development of Limit State Functions for Probabilistic Analysis
of Progressive Collapse in Reinforced Concrete Buildings . . . . . . . . . . . . .
Vu Ngoc Tuyen

Experimental Determination of Shear Parameters at the Interface
Between Structures and Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I. S. Alirzaev, E. I. Alirzaev, N. S. Sova, G. D. Shmelev,
and O. E. Perekalsky
Assessment of the Influence of a Construction Joint
on the Deformability of a Monolithic Reinforced Concrete Floor
Slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B. K. Dzhamuev and I. Z. Kalkan

vii

viii

Contents

Calculation of the Pile Grillage Taking into Account the Nonlinear
Operation of Piles in the Ground by the Method of Compensating
Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
M. I. Bochkov, A. V. Ignatyev, N. A. Maslennikov, I. S. Zavyalov,
and E. A. Maksyutova

Scientific Support for the Design of the Marine Terminal:
“Nakhodka Mineral Fertilizer Plant” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A. Bunov and N. Shunko

Improvement of Thermal Protection and Durability of Timber
Houses with Walls with Wooden Siding and Air Gap . . . . . . . . . . . . . . . . . . 113
N. P. Umnyakova
Research of the Stress–Strain State of the Thread Using
the Generalized Unknown Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
A. V. Ignatiev, S. A. Kalinovsky, M. I. Bochkov, and I. S. Zavyalov
Application of Ray Expansions for Studying Nonstationary Motion
of a Nonlinear Plate on an Elastic Half-Space . . . . . . . . . . . . . . . . . . . . . . . . 141
M. V. Shitikova and A. S. Bespalova
The Effect of Nanomodifying Additives on the Properties
of Dispersed Reinforced Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
V. A. Perfilov, D. A. Lyashenko, I. A. Tomareva, M. E. Nicolaev,
and V. I. Klimenko
Computer Simulation of a Spatial Rod Arch . . . . . . . . . . . . . . . . . . . . . . . . . 163
N. Tsaritova, A. Kurbanova, A. N. Korchagin, N. Raschenko,
and A. Fedorov
Analysis of Reinforced Concrete Beams in Road Bridge
Superstructures According to Limit State Method . . . . . . . . . . . . . . . . . . . . 175
N. V. Pham, T. H. Tran, T. T. V. Tran, T. B. Q. Vu, and T. Q. T. Nguyen
Investigation of the Strength of Monolithic Reinforced Concrete
Slabs with Non-removable Truncated-Pyramidal Hollow Formers . . . . . . 185
B. K. Dzhamuev and O. S. Matukhova
Selection of a Waterproofing Solution for the Underground Part
of a Building Under the Module-Based Methodology . . . . . . . . . . . . . . . . . . 197
E. G. Davletshin, Z. R. Mukhametzyanov, A. A. Yudin,
T. F. Suleymanov, and I. I. Kuznetsova
Calculations of Standard Cells of Structures Made of Film
and Fabric Orthotropic Membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
R. F. Vagapov, S. A. Gabitov, A. S. Salov, A. R. Biktasheva,
and R. K. Koksharov

Contents

Static-Dynamic Deformation and Force Resistance of a Monolithic
Reinforced Concrete Frame During Brittle and Plastic Fracture . . . . . . . 221
P. A. Korenkov, N. V. Fedorova, and S. R. Meliksetyan
Numerical Simulation of Surface Degradation Process in Cement
Granular Composite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
N. V. Makarova, M. V. Polonik, and A. A. Mantzubora
Wind Loads: Analysis of Deformations in Building Structures . . . . . . . . . 247
E. N. Egereva, A. O. Kresik, and S. A. Martyusheva
Development of Approaches to Assessing the Energy Efficiency
of Capital Construction Facilities in the Context of Climate Change . . . . 261
T. V. Dolgushev and E. A. Korol
Ensuring Operational Resistance of Paint and Varnish Coatings
Due to the Comprehensive Effect of Nano-Additives on Metal
Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
A. V. Pchelnikov, A. P. Pichugin, M. H. Iskandarov,
and A. K. Tuliaganov
Transformation of Discrete Force Equations into a Unified Formula . . . . 285
A. A. Sobakin, D. A. Nikolaeva, and D. V. Aleksandrov
Organomineral Mixtures for Road Foundations Based
on Industrial Waste . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
A. I. Leskin, S. V. Aleksikov, D. I. Gofman, L. M. Leskina,
and I. I. Glazunov
Study of the Properties of Slag-Based Cold Asphalt Concrete
Produced with a High Content of RAP Aggregates . . . . . . . . . . . . . . . . . . . . 313
A. I. Leskin, S. V. Aleksikov, D. I. Gofman, I. I. Glazunov,
and L. M. Leskina
Study of the Reduction of the Bearing Capacity
of a Steel-Reinforced Concrete Floor Under the Influence
of Various Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
Yu. A. Shaposhnikova
Analysis of the Efficiency of Pavement Structures at Automatic
Weighing Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
R. A. Tonkikh, A. O. Glazachev, R. M. Akhmetshin, D. T. Murtazin,
and V. V. Sokolova
The Effect of Reinforced Methods for Beams with Openings . . . . . . . . . . . 353
Viet-Phuong Nguyen, Van-Nam Nguyen, Cong-Vinh Pham,
and Trong-Tuan Tran

Contents

Kinetic Characterization of Densified Wood under an Assumed
Real Fire Curve Using Thermogravimetric Analysis . . . . . . . . . . . . . . . . . . 365
T. T. Tran, T. B. Q. Vu, and Viet-Phuong Nguyen
Special and Unique Structures Construction
Aerodynamics of Ultra-Flexible Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
E. F. Khrapunov, S. A. Mozhayskiy, A. N. Novikov, V. V. Sokolov,
and S. Y. Solovev
Main Characteristics of Equal-Strength Six-Span Beam . . . . . . . . . . . . . . . 389
M. V. Alexandrovsky, S. A. Martyusheva, S. V. Merkulova,
and E. S. Lazutina
Application of the Theory of Elasticity to the Study of Cracks
in Bridge Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
M. V. Alexandrovskyi, R. R. Khakimzyanov, V. A. Vyatkin,
and M. A. Denisenko
Influence of Beam and Column Cross-Section on Deflection
of Monolithic Floor Slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
D. I. Romensky, R. R. Khakimzyanov, V. A. Vyatkin, and D. R. Buev
Progressive Limit States of a Flat Model of Portal Frame . . . . . . . . . . . . . . 437
L. Yu. Stupishin, K. E. Nikitin, and M. L. Moshkevich
Information Modeling Technologies for Russian Wooden
Architecture Objects as a Basis for Modern Design . . . . . . . . . . . . . . . . . . . 449
G. Zakharova and A. Romanov
Architectural Aesthetics and Additive Construction in the Field
of Rapid Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463
M. Saleh
Methodology for Determining Deformations of Pile Structures
with a “Solid” Reinforcement Body During Bank Protection . . . . . . . . . . . 475
N. V. Kupchikova, T. V. Zolina, S. P. Strelkov, and A. S. Resnyanskaya
Generalized Geometrically Exact Theory of Column Stability . . . . . . . . . 487
V. A. Neshchadimov
Analysis of Belt-To-Roller Contact and Pressure Distribution
in Pipe Conveyors Using Motion Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 507
I. A. Magomedov, E. M. Magomedov, and A. M. Bagov
Urban Engineering and Planning
Urban Planning Regulation of Sustainable Development
of the World Cities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
V. A. Kolyasnikov, S. G. Shabiev, and I. I. Nadymov

Contents

Smart Urban Spaces: Current Situation and Insights for Future
in Russia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533
G. A. Ptichnikova and O. A. Antyufeeva
Principles and Methods of Forming the Architectural and Artistic
Image of Cities and Urban High Responsibility Infrastructure
Objects: Formation Principles Using QUANТUM CERAMIC/
QUANТUM PARUS Composite Materials (Safety, Aesthetics,
Regulations) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543
A. V. Fedorchenko, V. A. Gutnikov, P. V. Parabin, D. O. Presniakova,
and V. E. Kolpakov
Innovations in Architectural and Construction Design of Modern
Chinese Schools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559
I. N. Maltseva, Jie Liu, N. N. Kaganovich, and A. P. Isaev
Restoration Technologies of Wooden Architecture Monuments
on the Example of the Resort Area and the Church of St.
Panteleimon in Tinaki . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571
N. V. Kupchikova, T. V. Zolina, S. P. Strelkov, and A. S. Resnyanskaya
Sustainable Spatial Integration in the Housing Sector as a Strategic
Entry Point to Urban Quality of Life: A Vision for Karbala City,
Republic of Iraq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583
E. J. Al-Shebillawy, S. Korniyenko, and B. A. Al-Mossawy
Implementation of Pedestrian Call Buttons at the Semi-Actuated
Intersection of Tulskaya Street and 50 Let VLKSM Street
in Tyumen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595
R. V. Andronov and E. E. Leverents
Engineering Structure Safety, Environmental Engineering and
Environmental Protection
Mitigation of Risks at the Stages of the Life Cycle of Wastewater
Treatment Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607
N. G. Vurdova, P. Yu. Vurdov, and Yu. A. Birman
Determining the Dependence of Aerosol Deposition Surface
on the Conditions of Dynamic Foam Layer Formation . . . . . . . . . . . . . . . . 623
L. I. Khorzova, S. I. Golubeva, and O. S. Vlasova
Assessment of Hydro-energy Potential of Kyrgyzstan in the Context
of a Green Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635
E. T. Toktoraliev, R. A. Kerimbekova, T. M. Choduraev,
N. E. Zhumaliev, and Ch. D. Duishenaliev

xii

Contents

Reliability and Safety Analysis of Truck Leaf Springs Under
Permafrost Conditions Using Failure Time Series . . . . . . . . . . . . . . . . . . . . . 647
I. I. Buslaeva and S. P. Yakovleva
Aggregated Complexes in the Technology of Ceramic Matrix
Composites for Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657
O. A. Fomina and A. Yu. Stolboushkin
Mathematical Modeling of Municipal Solid Waste (MSW)
Incineration Ash Carbonation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671
K. A. Vorobyev and A. V. Nasonova
Parameters of a Human-Generated Aerosol Cloud . . . . . . . . . . . . . . . . . . . . 681
S. N. Gavrilin, N. A. Parfentyeva, E. R. Burmistrov, I. D. Bykovskaya,
and N. V. Radionov
Integrated Use of Land and Water Resources in the Talas Region . . . . . . 691
E. T. Toktoraliev, R. A. Kerimbekova, E. K. Mukanbet,
T. M. Choduraev, and N. E. Zhumaliev
Mixed Wastewater Treatment in the Recycling Water System
of a Construction Industry Enterprise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705
O. V. Sidorenko and E. I. Vialkova
New Approaches to Recycling Refractory Scrap . . . . . . . . . . . . . . . . . . . . . . 717
I. V. Shadrunova, O. E. Gorlova, E. V. Kolodezhnaya, M. S. Garkavi,
and T. V. Chekushina
Special Technical Conditions for Ensuring Fire Safety for Liquefied
Natural Gas Terminals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727
M. Medianik, N. Shunko, and A. Shunko
Mathematical Modeling of Explosion-Proof Valve Loading
in Ventilation Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739
S. A. Yaremenko, O. I. Gaidash, K. V. Garmonov, and M. N. Zherlykina
The Use of Polyolefin Polymer Wastes in the Production
of Bituminous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 751
Y. A. Bulauka, A. G. Kulbei, and A. D. Kandratsiuk
The Directions of Complex Utilization of Ash and Slag Waste
of Thermal Power Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763
N. M. Zaichenko, I. Yu. Petrik, L. G. Zaichenko, and D. Yu. Bukina
Study of Oxygen Transfer from Air to Water Depending
on Suspended Matter Concentration in Water . . . . . . . . . . . . . . . . . . . . . . . . 777
M. Dyagelev
Integrated Safety Design of Cable Lines and Communications
for the Development of Oil and Gas Fields in Freezing Seas . . . . . . . . . . . . 789
D. Korolchenko and A. Shunko

Contents

xiii

Development of a New Method for Extinguishing Oil Fires
for Above-Ground Oil Storage Tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805
D. Korolchenko and A. Shunko
Hydrochemical Composition of Waters of the Jyrgalan River Basin . . . . 819
S. K. Belekov, R. T. Akmatov, M. T. Abylgazieva,
S. M. G. B. Kadyrova, and K. E. Saypidinova
Radioecological Studies of the Kaji-Sai Tailings Dam . . . . . . . . . . . . . . . . . 831
Ch. Sultanbek kyzy, R. T. Akmatov, T. K. Kurenkeev,
A. T. Zulushova, and A. K. Esenkanova
Comprehensive Method of Reagent-Free Purification of Natural
and Wastewater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843
O. N. Medvedeva and T. N. Sautkina
Investigation of the Dependence of Air-to-Water Oxygen Transfer
on the Content of Surfactants in Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855
M. Dyagelev
Information and Analytical Support of Resources Degradation
Risk Management of the Sport Center Fire Extinguishing
Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867
O. M. Shikulskaya, T. U. Yesmagambetov, M. I. Shikulskiy,
and M. M. Yesmagambetova

Industrial and Civil Engineering

Efficiency of Using Lime Plaster Mixture
as a Finishing Layer for External Walls
of Buildings
M. V. Frolov, V. I. Loganina, and V. S. Pylaev

Abstract A formulation of a lime plaster dry building mix with polysaccharide
additives designed for exterior finishing work has been developed. The issues of the
finishing layer influence on the heat and humidity conditions of building enclosing
structures are considered using four types of dry building plaster mixes and three
types of enclosing structures as an example. The amount of condensate falling out is
analyzed depending on the type of structure and time of operation. It is established
that the presence of a finishing layer based on dry building mixes on the outer surface
of the enclosing structure contributes to the shift of the zero isotherm. It was found
that in walls made of foam blocks without insulation, condensation will fall out in the
foam concrete layer. The use of plasters based on dry building mixes Porotherm LP,
VerMix ShN50 and on the basis of the proposed lime plaster eliminates the formation
of condensate in the thickness of structures made of expanded clay concrete with
insulation and brick with insulation. The expediency of using a dry building mix based
on the developed lime composition with additives of polysaccharides is formulated.
Keywords Lime coating · Humidity conditions · Amount of condensate ·
Humidity of the structure · The zero isotherm

1 Introduction
Lime compositions are widely used for finishing external walls of buildings. Given
the low operational resistance of lime coatings, modifying additives are introduced
into the formulation [1–3]. The additives used to modify building materials vary
in chemical composition and physical characteristics. To increase the resistance of
lime solutions, highly active pozzolan materials are introduced into the formulation,
for example, metacaolinite, with a weight ratio of metacaolinite:lime 1:1 [4]. When
metakaolin is introduced into the formulation, the amount of chemically bound water
M. V. Frolov · V. I. Loganina (B) · V. S. Pylaev
Penza State University of Architecture and Construction, Penza, Russia
e-mail: loganin@mail.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_1

M. V. Frolov et al.

increases, the pore size decreases, and the compressive strength of solutions increases
to 9 MPa.
Noteworthy are the results of [5, 6], which provide data on the effect of synthesized calcium hydrosilicates on the hardening process and properties of lime solutions. The introduction of synthesized hydrosilicates and calcium hydroaluminosilicates into the formulation of lime solution helps to reduce porosity and increase
the volume of closed pores, resulting in reduced water absorption of lime stone,
increased compressive strength by 1.5–2 times.
To increase the durability of composites based on mineral binders, it was proposed
to introduce colloidal dispersions based on silicon dioxide into the formulation [7].
As a result of the interaction of silicon oxide nanoparticles with Ca(OH)2 , calcium
hydrosilicate is formed, which contributes to a significant (up to 30%) reduction in
the number of pores.
In [8], it was proposed to use an organomineral additive as a modifying additive
in lime compositions.
In [9, 10], the introduction of organic components (polysaccharides, proteins and
fatty acids) into the formulation of lime compositions is proposed. It was found that
the introduction of animal glue in the form of an additive increases the mechanical
strength of the solution and the carbonation front by 2 times, reduces porosity and
pore size. Polysaccharides, natural or derived, are commonly used as additives in
modern factory-made mortars. They are able to improve the water retention capacity
of cement-based solutions. Due to their thickening properties, polysaccharides also
improve the rheological properties of building mortars.
The additives used to modify building materials vary in chemical composition and
physical characteristics. We have proposed introducing synthetic polysaccharides
Atren Cem LV and Atren Cem HV (TU 2458-062-63121839-2014) into the formulation of the lime composition, as this contributes to obtaining a lime composite with
meso-nanostructural characteristics corresponding to calcite biominerals [11, 12].
This will significantly increase the operational durability of the restoration material.
We have developed a plaster composition that includes lime, a synthetic polysaccharide additive, ash aluminosilicate microspheres, a plasticizer, and a redispersible
powder. Lime compositions with the addition of Atren Cem LV polysaccharides are
characterized by higher crack resistance. The cohesive strength is 0.47 MPa with an
additive content of 1% of the lime weight, the thermal conductivity coefficient is
0.202 W/(m K), the vapor permeability coefficient is 0.12 mg/(m h Pa). The frost
resistance grade of the finishing layer is F35.
The presence of an organic polysaccharide additive in the lime coating formulation
helps to increase the carbonation front and form a qualitatively different structure,
which helps to improve the performance properties of the lime composite.
To assess the operating conditions of the developed plaster layer and the effectiveness of its application in comparison with other types of plaster, it is of interest to
evaluate the effect of the finishing layer based on the developed composition on the
change in the heat and humidity conditions of the enclosing structure. The need to
conduct this assessment is justified by numerous domestic and foreign studies, which

Efficiency of Using Lime Plaster Mixture as a Finishing Layer …

note the importance of designing external enclosing structures taking into account
the humidity conditions inside the enclosures [13–18].

2 Materials and Experimental Methods
To assess the influence of the plaster layer based on the developed DBM on the change
in the thermal and humidity conditions of the enclosing structures of buildings, a wall
calculation was performed. The calculation schemes of the studied wall structures
are presented in Fig. 1.
The developed composition was compared with three types of plaster mixes:
• KNAUF-Grunband cement facade plaster, vapor permeability coefficient μ =
0.01 mg/(m h Pa);
• Porotherm LP lightweight plaster, vapor permeability coefficient μ = 0.134 mg/
(m h Pa);
• VerMix SHN50 thermal insulation plaster for external work, vapor permeability
coefficient μ = 0.11 mg/(m h Pa).
The choice of these types of plasters is due to their wide application in external
finishing works.
Data on the materials used in the structures, their calculated thermal conductivity
coefficients and vapor permeability coefficients are summarized in Tables 1, 2 and
3.
All the structures under study comply with the requirements of SP 50.13330.2024
“SNiP 23-02-2003 Thermal protection of buildings”.
In the work, the humidity regime in walls of various designs for the conditions
of Irkutsk was assessed. The choice of this city is due to the fact that it is located in
the climatic subregion 1B, which is characterized by fairly cold winters. In the event

Fig. 1 Calculation schemes of enclosing structures: a wall made of foam concrete; b wall made of
expanded clay concrete with insulation; c wall made of brick with insulation

M. V. Frolov et al.

Table 1 Characteristics of materials used in foam concrete walls
Layer
number

Material

Layer
thickness δ,
m

Average
density of
material, kg/
m3

Thermal
conductivity
coefficient λA ,
W/(m K)

Vapor
permeability
coefficient µ,
mg/(m h Pa)

Plaster
cement-slag

0.01

1200

0.470

0.140

Foam concrete
D400

0.45

400

0.14

0.230

Knauf-Grunband

0.018

1100

0.35

0.1

Porotherm LP

0.018

900

0.25

0.134

VerMix SHN50

0.018

1000

0.26

0.11

Developed
composition

0.018

800

0.202

0.12

Table 2 Characteristics of the materials used in expanded clay concrete walls with insulation
Layer
number

Material

Layer
thickness δ,
m

Average
density of
material, kg/
m3

Thermal
conductivity
coefficient λA ,
W/(m K)

Vapor
permeability
coefficient µ,
mg/(m h Pa)

Plaster
cement-sand

0.01

1800

0.76

0.09

Expanded clay
concrete

0.51

1200

0.44

0.11

Mineral wool mats 0.10

125

0.041

0.40

Knauf-Grunband

0.018

1100

0.35

0.1

Porotherm LP

0.018

900

0.25

0.134

VerMix SHN50

0.018

1000

0.26

0.11

Developed
composition

0.018

800

0.202

0.12

that the research shows high efficiency of using the developed composition in the
fences under consideration, it will be possible to conclude that in a warmer climate
the humidity regime in the walls will be even more favorable. The average outside
air temperature in Irkutsk for December, January and February is t winter = –16.5 °С.
Later in the course of the research, the temperatures of the onset of condensation
tb.c. in the studied enclosures were compared with the average temperatures of the
coldest months: March t mar = − 7.9; December, t dec = − 15.7 °С; January, t jan = −
18.4 °С; February—t feb = − 15.4 °С. The calculated parameters of the internal air
were taken as equal: temperature t in = 21.0 °С, relative humidity of the internal air
φin = 50%, relative humidity of the external air φout = 79%.
The temperature of the beginning of condensation t b.c. for the considered cases was
determined by the following method. The wall in question is conventionally divided

Efficiency of Using Lime Plaster Mixture as a Finishing Layer …

Table 3 Characteristics of the materials used in clay brick walls with insulation
Layer
number

Material

Layer
thickness δ,
m

Average
density of
material, kg/
m3

Thermal
conductivity
coefficient λA ,
W/(m K)

Vapor
permeability
coefficient µ,
mg/(m h Pa)

Plaster
cement-sand

0.01

1800

0.76

0.09

Ceramic brick

0.51

1800

0.70

0.11

Mineral wool mats 0.10

Knauf-Grunband

0.018

125

0.041

0.40

1100

0.35

0.1

Porotherm LP
VerMix SHN50

0.018

900

0.25

0.134

0.018

1000

0.26

Developed
composition

0.11

0.018

800

0.202

0.12

into several vertical layers with a thickness of 0.01 m each. Then, the values of the
absolute E and partial elasticity e of water vapor in each of the layers were determined at different outdoor temperatures. In the course of the research, the outdoor
temperature was consistently lowered until the moment when the condition began to
be fulfilled in one of the layers
exi < Exi

(1)

where exi is partial value of water vapor pressure, Pa; Exi is absolute value of water
vapor pressure, Pa.
The maximum outdoor temperature at which this condition was met for this enclosure is the temperature at which condensation begins t b.c. . Thus, when the outside
temperature drops below this value, condensation will begin to accumulate in the wall
thickness. If the outside temperature is above this value, there will be no conditions
for condensation to form in the wall.
The amount of condensate falling was determined separately for each month. The
diffusion rate of water vapor after the condensation plane was determined by the
formula
h
Gcon
=

Econ − eout
ein − Econ
− 1
δi
δn
1
+
p +
p
μi
μn
α
α
in

(2)

out

where ein , eout is the actual elasticity of water vapor in indoor and outdoor air,
respectively, Pa; Econ is the maximum elasticity of water vapor in the condensation
p
p
plane, Pа; αin , αout is the coefficient of vapor permeability of the indoor and outdoor
wall surfaces, respectively, mg/m2 h Pa; δi , δn is the thickness of the layers located
respectively before and after the condensation plane, m; μi , μn is vapor permeability
of layers located respectively before and after the condensation plane, mg/m h Pa.

M. V. Frolov et al.

Taking into account the duration of each month, the amount of condensate falling
during the entire period of moisture accumulation was determined [19–22]. The
increase in weight moisture % during condensation of water vapor was determined
by the formula
W =

Gcon
100
ρ·δ

(3)

where ρ is the bulk density of the material of the moistened layer, kg/m3 ; δ is the
thickness of the condensation layer, m.

3 Results
Analysis of the data obtained as a result of the heat engineering calculation shows that
the presence of a finishing layer based on DBM on the outer surface of the enclosing
structure contributes to the displacement of the zero isotherm by 0.174–186 m from
the inner surface of the wall made of foam concrete and by 0.494–0.530 m for a
structure made of expanded clay concrete and ceramic brick (Table 4).
It has also been established that the temperature on the inner surface of the fences
in question is higher than the dew point temperature [23]. Therefore, condensation
will not form on the inner surface of the fences in question.
As an example, we will present in detail in Table 5 the results of studies to
determine the temperature of the beginning of condensation t b.c. formation for one
wall structure: walls made of ceramic bricks with insulation, finished with plaster
based on the developed composition. As we can see in the table, condensation will
begin to form at a temperature of − 19.9 °C at a distance of 64 cm from the inner
Table 4 The meaning of the zero isotherm
Type of
construction

The meaning of the zero isotherm

Walls made of
foam blocks
without
insulation

Plaster based on
the developed
composition

Knauf-Grunband

Porotherm LP

VerMix SHN50

0.180 m from the 0.186 m from the
inner surface
inner surface

0.178 m from the
inner surface

0.174 m from the
inner surface

Walls made of
expanded clay
concrete with
insulation

0.500 m from the 0.494 m from the
inner surface
inner surface

0.496 m from the
inner surface

0.500 m from the
inner surface

Ceramic brick
walls with
insulation

0.530 m from the 0.525 m from the
inner surface
inner surface

0.528 m from the
inner surface

0.522 m from the
inner surface

Efficiency of Using Lime Plaster Mixture as a Finishing Layer …

surface of the wall. This corresponds to the contact layer of the insulation and the
outer plaster coating.
The results of the studies conducted to determine the temperature of the beginning
of condensate formation for the 12 walls under study are shown in Fig. 2.
It has been established that in a wall made of foam concrete, in March there will be
no moisture condensation. However, during December-February, moisture condensation will be observed in the fence when using all four types of dry building mixtures
as a finishing layer. For structures made of expanded clay concrete with insulation and
brick with insulation, moisture condensation will be observed in January only when
using Knauf-Grunband cement facade plaster. This is due to the fact that coatings
based on this plaster have a higher thermal conductivity coefficient λA and a lower
vapor permeability coefficient µ [24, 25]. The use of plasters based on Porotherm
LP, VerMix SHN50 DBM and based on the proposed lime plaster eliminates the
formation of condensate in the thickness of the structure.
Data on the amount of condensate and the increase in moisture content in materials
over the entire period of moisture accumulation for the structures under consideration
are presented in Table 6.
The largest amount of condensate falling out over the entire period of moisture
accumulation, amounting to 0.564 kg/m2 , is typical for aerated concrete when using
the Knauf-Grunband cement facade plaster. The use of plaster based on the developed
composition allows reducing the amount of condensate falling out in foam concrete
to 0.469 kg/m2 .
During the research it was established that condensation in the walls made of
foam blocks without insulation will fall out in the layer of foam concrete. Moisture
inside the wall will move in foam concrete towards the outer surface and accumulate
under the outer plaster, in a layer about 0.05 m thick. In walls made of expanded
clay concrete and brick, when using Knauf-Grunband cement facade plaster as an
external finish, condensation will accumulate in the insulation layer in front of the
plaster, about 0.05 m thick. Therefore, to calculate moisture accumulation, the thickness of the condensation layer was taken equal to 0.05 m. The greatest increase in
humidity is also observed in foam concrete. At the same time, in all the fences under
consideration, the increase in humidity is insignificant and the accumulated moisture
in the wall will not have a significant effect on the performance characteristics and
durability of the studied structures of external walls.

4 Conclusions
A dry lime mixture with the addition of polysaccharides has been developed, intended
for exterior finishing work.
Was found that the efficiency of using the proposed lime plaster as an external
finishing layer is not inferior to the widely used DBM “KNAUF-Grunband”,
Porotherm LP, VerMix SHN50. A shift in the zero isotherm in the enclosing structure in the presence of a finishing layer was established. A decrease in the amount

M. V. Frolov et al.

Table 5 Data on the distribution of temperature and relative humidity in the wall thickness
Distance
from the
inner
surface,
cm

τxi , °C

Exi ,
Pa

exi , Pa

Exi −exi ,
Pa

Distance
from the
inner
surface,
cm

τxi , °C

Exi ,
Pa

exi , Pa

Exi −exi ,
Pa

19.80

2308

1236.9

1071.6

14.67

1668

550.9

1117.3

19.58

2277

1220.9

1056.0

14.52

1652

530.6

1121.6

19.43

2256

1200.6

1055.4

14.37

1636

510.3

1126.1

19.28

2235

1180.3

1054.9

14.22

1621

490.0

1130.7

19.13

2215

1160.0

1054.5

14.07

1605

469.7

1135.5

18.98

2194

1139.7

1054.4

13.92

1590

449.4

1140.3

18.84

2174

1119.4

1054.4

13.77

1574

429.1

1145.3

18.69

2154

1099.1

1054.5

13.62

1559

408.8

1150.5

18.54

2134

1078.8

1054.9

13.48

1544

388.5

1155.7

18.39

2114

1058.5

1055.4

13.33

1529

368.2

1161.1

18.24

2094

1038.2

1056.0

13.18

1514

347.8

1166.6

18.09

2075

1017.9

1056.8

13.03

1500

327.5

1172.3

17.94

2055

997.6

1057.8

12.88

1485

307.2

1178.0

17.79

2036

977.3

1058.9

12.73

1471

286.9

1183.9

17.64

2017

957.0

1060.2

12.58

1457

266.6

1189.9

17.50

1998

936.6

1061.7

12.43

1442

246.3

1196.0

17.35

1980

916.3

1063.3

12.28

1428

226.0

1202.3

17.20

1961

896.0

1065.0

12.14

1414

205.7

1208.7

17.05

1943

875.7

1066.9

11.99

1401

185.4

1215.2
1002.5

16.90

1924

855.4

1069.0

9.44

1182

179.8

16.75

1906

835.1

1071.2

6.90

995

174.3

820.4

16.60

1888

814.8

1073.6

4.36

834

168.7

665.0

16.45

1871

794.5

1076.1

1.82

696

163.1

533.1

16.30

1853

774.2

1078.7

− 0.72

575

157.5

417.6

16.16

1835

753.9

1081.5

− 3.27

465

151.9

313.0

16.01

1818

733.6

1084.5

− 5.81

374

146.3

228.0

15.86

1801

713.3

1087.5

− 8.35

300

140.8

159.3

15.71

1784

693.0

1090.8

− 10.89

239

135.2

104.3

15.56

1767

672.7

1094.1

− 13.43

190

129.6

60.7

15.41

1750

652.4

1097.7

− 15.98

150

124.0

26.5

15.26

1733

632.1

1101.3

− 18.52

118

118.4

− 0.4

15.11

1717

611.8

1105.1

64.9

− 18.98

113

101.7

11.6

14.96

1701

591.5

1109.0

65.8

− 19.45

108

84.9

23.4

14.82

1684

571.2

1113.1

Outside
air

− 19.90

104

82.0

21.8

Efficiency of Using Lime Plaster Mixture as a Finishing Layer …

Fig. 2 Dependences of the temperature of the onset of condensation tb.c . on the type of plaster
composition: 1—foam concrete, 2—expanded clay concrete with insulation, 3—bricks with
insulation

Table 6 The amount of condensate falling during the entire period of moisture accumulation
Type of
construction

Types of dry building mixtures
Developed
composition

Knauf-Grunband

Porotherm LP

VerMix SHN50

Walls made of
foam blocks
without
insulation

0.469*
1.53

0.564
1.88

0.448
1.49

0.513
1.71

Walls made of
expanded clay
concrete with
insulation

0.000
0.00

0.025
0.98

0.000
0.00

Ceramic brick
walls with
insulation

0.000
0.00

0.025
0.98

0.000
0.00

Note * The amount of condensate falling out in kg/m2 for the entire period of moisture accumulation
is indicated above the line; the increase in humidity in a 5 cm thick layer for the entire period of
moisture accumulation in %. is indicated below the line

of condensate was found when using the developed lime plaster as a finishing layer.
It was found that the use of plasters based on Porotherm LP, VerMix SHN50 DBM
and based on the proposed lime plaster eliminates the formation of condensation in
the thickness of the structure.

M. V. Frolov et al.

References
1. Kulikova AA, Demyanenko OV, Sorokina EA, Kopanitsa NO (2019) Complex modifying
additives for cement-based building mixtures. Bull Tomsk State Univ Arch Civ Eng 21(6):140–
148. https://doi.org/10.31675/1607-1859-2019-21-6-140-148
2. Loganina VI, Frolov MV (2022) Research and optimization of the technology for the synthesis
of a modifying additive based on a mixture of hydrosilicates and calcium aluminosilicates. Nanotechnologies Constr 14(3):190–197. https://doi.org/10.15828/2075-8545-2022-143-190-197774
3. Loganina VI, Akzhigitova ER (2023) Mineral additive for lime dry building mixtures. Mag
Civ Eng 117(1):11707. https://doi.org/10.34910/MCE.117.7
4. Bakolas A, Aggelakopoulou E, Anagnostopoulou S, Moropoulou A (2006) Evaluationof
pozzolanic activity and physico-mechanical characteristics in metakaolin–lime pastes. J Therm
Anal Calorim 84(1):157–163
5. Loganina V, Sergeeva K, Fediuk R, Uvarov V, Vatin N, Vasilev Y, Amran M, Szelag M (2021)
Increase the performances of lime finishing mixes due to modification with calcium silicate
hydrates. Crystals 11(4)4:399. https://doi.org/10.3390/cryst11040399
6. Loganina V, Zhegera K, Fediuk R, Timokhin R, Zayakhanov M, Liseitsev Y (2020) Amorphous
aluminosilicates as a structure-forming additive in cementitious systems. J Mater Civ Eng
32(5):06020004. https://doi.org/10.1061/(ASCE)MT.1943-5533.0002995
7. Loganina V, Davydova O, Fediuk R, Amran M, Klyuev S, Klyuev A, Sabitov L, Nabiullina K
(2022) Improving the durability of lime finishing mortars by modifying them with silicic acid
sol. Materials 15:2360. https://doi.org/10.3390/ma15072360
8. Loganina VI, Petukhovaa NA, Fediuk RS, Timokhin RA (2019) Polystyrene paint with reduced
contents of volatile compounds. Mag Civ Eng 88(4):25–41. https://doi.org/10.18720/MCE.88.3
9. Bokan Bosiljkov V (2001) The use of industrial and traditional limes for lime mortars. In:
Lourenco PB, Roca P (Eds) Historical constructions. University of Minho, Guimaraes, pp
343–352
10. Elert K, Ruiz-Agudo E, Jroundi F, Gonzalez-Muñoz MT, Fash BW, Fash WL, Valentin N, de
Tagle A, Rodriguez-Navarro C (2021) Degradation of ancient Maya carved tuff stone at Copan
and its bacterial bioconservation. Npj Mater Degrad 5:44. https://doi.org/10.1038/s41529-02100191-4
11. Littmann ER, Ancient (1960) Mesoamerican mortars, plasters, and stuccos: the use of bark
extracts in lime plasters. Am Antiquity 25:593–597. https://doi.org/10.2307/276642
12. Magaloni D, Pancella R, Fruh Y, Cañetas J, Castaño V (1995) Studies on the Mayan mortars
technique. MRS Online Proc Lib 352:483
13. Pokroy B, Fitch A, Zolotoyabko E (2006) The microstructure of biogenic calcite: a view by
high-resolution synchrotron powder diffraction. Adv Mater 18:2363–2368. https://doi.org/10.
1002/adma.200600714
14. Loganina V, Pylaev V (2025) Durability of lime coatings with polysaccharides additives. Lect
Notes Civ Eng 565:34–41. https://doi.org/10.1007/978-3-031-80482-3_3
15. Loganina V, Pylaev V (2024) Physical and mechanical properties of lime coatings with the
additive of polysaccharides. E3S Web Conference 533:01002. https://doi.org/10.1051/e3sconf/
202453301002
16. Kovacic I, Waltenbereger L, Gourlis G (2016) Tool for life cycle analysis of facade-systems for
industrial buildings. J Clean Prod 130:260272. https://doi.org/10.1016/j.jclepro.2015.10.063
17. Choi Y hee Song D, Seo D, Kim J (2018) Analysis of the variable heat exchange efficiency of
heat recovery ventilators and the associated heating energy demand. Energy Build 172:152158.
https://doi.org/10.1016/j.enbuild.2018.04.066
18. Loganina VI, Frolov MV, Skachkov YuP (2018) Substantiation of selection of components at
creation of thermal insulating dry building mixtures. Int J Eng Technol 7(4):43414344. https://
doi.org/10.14419/ijet.v7i4.10393

Efficiency of Using Lime Plaster Mixture as a Finishing Layer …

19. Frolov MV, Loganina VI, Zhuravleva EA (2023) Humidity conditions of aerated concrete walls
depending on the type of finishing coating. Appl Sci 13(17):9529. https://doi.org/10.3390/app
13179529
20. Evdokimov AV, Sergunenkov BB, Kotelnikov DV (2002) Selection of facade coverings taking
into account vapor permeability and water absorption. Constr Mater 11:30–31
21. Vatin NI, Gorshkov AS, Glumov AV (2011) Influence of physical, technical and geometric
characteristics of plaster coatings on the humidity regime of homogeneous walls made of
aerated concrete blocks. Eng Constr J 1:28–33. https://doi.org/10.18720/mce.19.7
22. Kupriyanov VN, Safin ISH, Shamsutdinov MR (2012) Influence of the enclosure design on
the condensation of vaporous moisture. Hous Constr 6:29–31. https://doi.org/10.52409/207
31523_2022_1_29
23. Loganina VI, Frolov MV, Klyuev AV, Sabitov LS, Solovyeva EA (2024) Hydro-physical properties of the coating for the walls of aerated concrete. Lect Notes Civ Eng 436:174–181. https://
doi.org/10.1007/978-3-031-44432-6_23
24. Harmati N, Jakšić Ž, Vatin N (2015) Energy consumption modelling via heat balance method
for energy performance of a building. Procedia Eng 1(117):791–799. https://doi.org/10.1016/
j.proeng.2015.08.238
25. Blengini GA, Di Carlo T (2010) Energy-saving policies and low-energy residential buildings:
an LCA case study to support decision makers in piedmont (Italy). Int J Life Cycle Assess
15(7):652–665. https://doi.org/10.1007/s11367-010-0190-5

Increased Bending Strength and Water
Resistance of Plywood for Construction
Purposes
T. N. Vakhnina, A. A. Fedotov, and I. V. Susoeva

Abstract The article solves the problem of substantiating the production of birch
plywood for construction purposes using phenol–formaldehyde binder at a reduced
pressing temperature and reduced consumption of phenol–formaldehyde binder
(PFB). When the pressing temperature drops to 100…105 °C, the phenol–formaldehyde binder does not reach its maximum degree of curing. With a decrease in binder
consumption to 95…98 g per square meter of veneer surface and a decrease in
pressing temperature to 105 °C, it is necessary to ensure the required mechanical
properties—the strength of plywood during static bending and chipping along the
adhesive layer, as well as a low thickness swelling after 24 h in water. To ensure the
required level of physico-mechanical properties of plywood, modifiers were used
in the work—copper acetate, resorcinol and copper resorcinate. The proportion of
the modifier additive was 1.0…2.0% by weight of the phenol–formaldehyde binder.
Using two-factor analysis of variance, the significance of the effect of the type of
modifier and the proportion of the additive in the binder on plywood performance
was mathematically verified. A regression mathematical model of the dependence of
plywood thickness swelling on technological factors of the production process has
been developed. Plywood based on a modified phenol–formaldehyde binder, manufactured with reduced binder consumption and reduced pressing temperature, has
high strength and low thickness swelling. The results obtained can be recommended
for use in the production of plywood for construction purposes.
Keywords Plywood · Phenol–formaldehyde binder · Pressing temperature ·
Modification · Strength · Static bending · Thickness swelling

T. N. Vakhnina · A. A. Fedotov (B) · I. V. Susoeva
Kostroma State University, Kostroma, Russia
e-mail: aafedotoff@yandex.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_2

T. N. Vakhnina et al.

1 Introduction
Monolithic construction technology is widely used in the construction of industrial
and residential buildings. This technology is based on the use of formwork materials,
that is, a frame that holds the mortar in a certain shape until it hardens.
In many countries, most of the plywood is used for the manufacture of building
formwork [1, 2].
Plywood formwork is subjected not only to mechanical, but also to chemical and
thermal stresses, since solidified monolithic concrete is an aggressive, highly alkaline
and self-heating medium.
A set of plywood formwork holds freshly laid concrete at the level of an entire
floor, and the formwork must be reusable, and the decision on reuse is made based
on the results of an inspection of the plywood after disassembling the formwork.
The quality of the formwork materials significantly affects the construction budget
[3, 4].
Therefore, increased requirements are applied to the performance of plywood
for formwork. All formwork sheets must have a certain set of qualities: strength,
moisture resistance and flexibility. The material should have a combination of good
strength, adaptability, reusability and price [5].
Songklod Jarusombuti and colleagues analyzed a study by Jan Sedliacik and
co-authors [6], using temperature regimes of 180, 200, 220 °C. To identify the
significance of the differences, the results were processed using analysis of variance
[7].
The choice of temperature parameters was due to the fact that reducing the pressing
temperature of plywood on phenol–formaldehyde binder without additional technological measures leads to a deterioration in physical and mechanical parameters. This
is due to the insufficient degree of curing of the phenol–formaldehyde binder at a
low temperature [8, 9].
One of the solutions to the problem is the introduction of modifying additives
into the finished phenol–formaldehyde resin during the preparation of the binder.
Domestic and foreign scientists are working in this area [10–16].
In most cases, hot pressing of plywood is carried out at a sufficiently high (from the
point of view of current production) temperature and binder consumption. In order to
reduce the cost of production, industrial enterprises producing waterproof plywood
are working to reduce the pressing temperature. Obtaining the desired complex of
physico-mechanical properties at a reduced pressing temperature can be achieved, in
particular, by modifying the phenol–formaldehyde binder with salts containing Al+3
ions, etc. In the authors’ study, the results were obtained using aluminum-ammonium
and aluminum-potassium alum [17].
In the continuation of this work, copper acetate, resorcinol, and copper resorcinate
were used to modify PFB during low-temperature pressing. Resorcinol can accelerate
the curing of PFB and reduce the curing temperature. This is explained by the fact that
there are two functional OH groups in the resorcinol molecule, which makes it a more
reactive substance than ordinary monatomic phenol, so the polycondensation reaction

Increased Bending Strength and Water Resistance of Plywood …

deepens [18]. Copper compounds were chosen as modifiers because, according to
researchers, they improve the performance of phenol–formaldehyde binders and
composites based on them [19, 20].

2 Methods
Birch plywood based on a modified phenol–formaldehyde binder was manufactured
in the laboratory of the Department of Logging and Wood Processing Industries
(KSU, Kostroma) at low temperature. The plywood was made at constant values of
the following factors: specific pressure during ore pressing = 1.4 MPa; consumption
of FFS 95 g/m2 of veneer surface, pressing temperature 105 °C. Plywood indicators
are strength under static bending, MPa; strength when chipping along the adhesive
layer after boiling for 1 h, MPa.
The experimental results for plywood strength indicators were processed using
two-factor analysis of variance.
The indicator “thickness swelling of plywood”, % after 24 h of exposure to water,
was studied by regression analysis.
Experimental factors in coded and natural terms:
Factor A is a type of modifier. Levels of factor A:
a1 —copper acetate;
a2 —resorcinol;
a3 —copper resorcinate.
Factor B is the proportion of the modifier additive. Factor B levels:
b1 —0% (control samples);
b2 —1.0%;
b3 —2.0%.
The experimental results are processed as follows.
1. At each point of the plan (for each combination of factor levels), the statistical parameters of the samples are determined—the arithmetic averages Y ij and
sample variances Sij2 .
2. The uniformity of the variances is checked. The verification is carried out
according to the Kohren criterion. The calculated value of the Kohren criterion
is determined by the formula.
km

Si2 ,

2
Gp = Smax
/

(1)

i=1

where km is the number of combinations of factor A and B levels (number of
2
is the largest of the km variances.
samples); Si2 is the variance of the i-th sample; Smax

T. N. Vakhnina et al.

The tabular value of the Kohren criterion is determined by the significance level
of q = 0.05, the number of km samples and the number of degrees of freedom of
each sample f = n − 1.
GT (q = 0.05; km; f = n − 1).

(2)

Gp ≤ GT ,

(3)

If the ratio is met

then the variances of all km samples are homogeneous.
If condition (3) is not fulfilled, the variances at the points of the plan are
heterogeneous.
3. The average for each level of factor A is determined—Y a1, Y a2, . how are the
averages across the columns.
4. The average is determined for each level of the factor in—Y b1, Y b2, . as the
average across the lines.
5. The total average of all observations is determined:
Y =

Y aj
=
k

Y bi
m

(4)

6. The sums of squares and variances are found according to the formulas presented
in Table 1.
7. The hypothesis that there is no interaction between factors A and B. The
calculated value of the Fisher criterion is determined by the formula.
Fp =

2
SAB
Sn2

(5)

Tabular value of the Fisher criterion FT (q, f3 , f4 ) It is determined by the level
of significance q = 0.05, the number of degrees of freedom of the variance of the
interaction between the factors f3 = (k − 1)(m − 1) and the number of degrees of
freedom of the residual variance f4 = km(n − 1).
If the condition is met
FP ≤ FT ,

(6)

there is no interaction between factors A and B.
If FP > FT , then the hypothesis of the absence of interaction between factors A
and B is rejected, and the analysis of variance cannot be continued. The calculation
of variance components is presented in Table 1.

Increased Bending Strength and Water Resistance of Plywood …

Table 1 Calculation of variance components
The component Sum of squares
of variance
Between the
average of the
columns

Qi = nm

k
j=1

Y aj − Y

Between the
average of the
lines

Q2 = nk

m
i=1

Y bi − Y

In the
interaction
between the
factors

Q3 =
n

k
j=1

m
i=1 (Y ij

m
i=1

Within the
Q4 =
party (residual)

k
j=1

− Ybi − Y aj
n
v=1 ·(Yijv

+ Y )2

− Y ij)2

Number of
degrees of
freedom

Variance

f1 = k − 1

SA2 =

Q1
k−1

f2 = m − 1

SB2 =

Q2
m−1

2 =
f3 =
SAB
Q3
(k − 1)(m − 1)

(k−1)(m−1)

f4 =
km(n − 1)

Q4
km(n−1)

Sn2 =
Sn2 =
k
j=1

m
2
I =1 SIJ

Full

Q = Q1 + Q2 + Q3 + Q4
=

j=1

i=1

v=1

f = kmn − 1

S2 =

Q
kmn−1

(Yijv − Y )2

8. A combined estimate of the variance is found:
S02 =

Q3 + Q4
f3 + f4

(7)

The number of degrees of freedom of the combined variance:
f0 = f3 + f4

(8)

9. The significance of the influence of factor A on the output value is checked. To
do this, the uniformity of the variance of factor A and the combined variance is
estimated. Calculated value of the Fisher criterion:
FP1 =

SA2
S02

(9)

Tabular value of the Fisher criterion FT 1 (q, f1 , f0 ) is determined by the level of
significance q = 0.05, the number of degrees of freedom of the variance of factor
A f1 = k − 1 and the number of degrees of freedom of the combined variance
f0 = f3 + f4 .
If the condition is met FP > FT , then factor A significantly affects the output
value.

T. N. Vakhnina et al.

10. The significance of the influence of factor B on the output value is checked. To
do this, the uniformity of the variance of factor B and the combined variance is
estimated. Calculated value of the Fisher criterion:
FP2 =

SB2
S02

(10)

Tabular value of the Fisher criterion FT 2 (q, f2 , f0 ) is determined by the level of
significance, the number of degrees of freedom of factor B, and the number of degrees
of freedom of the combined variance.
If the condition is met FP > FT , then factor B significantly affects the output
value.
11. The degree of influence of factors A and B on the scattering of the output value Y
is determined. The degree of influence is determined by the sample coefficients
of determination.
ρA2 = SA2 S 2 ,

(11)

ρB2 = SB2 S 2

(12)

3 Results
The results of statistical processing of experimental data on the output values “plywood strength when chipping along the adhesive layer” and “strength under static
bending” are presented in Tables 2 and 3. The results of data processing by twofactor dispersion analysis of two values are presented in Table 4. Statistically, the
absence of an interaction effect between the factors “type of modifier” and “proportion of modifier additive” was confirmed. According to the Fisher criterion, the
significance of the influence of factors on the strength of plywood when chipping
along the adhesive layer and strength under static bending was verified.
It can be noted that the proportion of modifier additives from the additives used in
this study—copper acetate, resorcinol and copper resorcinate in the range of 0.2% of
the weight of phenol–formaldehyde resin significantly affects the strength of plywood
when chipping. This is also shown by the sample coefficients of determination: for
factor A, the coefficient value is 1.74, and for factor B, pB2 = 7.36, i.e. the degree of
influence of the proportion of the modifier additive is 4.2 times greater than the type
of modifier (see Table 3). At the same time, all three types of modifiers used do not
significantly affect the strength of plywood under static bending. In our opinion, this
is due to the fact that the elasticity of plywood is more influenced by the performance
of peeled birch veneer.
The addition of two percent copper acetate to the adhesive composition (from the
weight of the resin) slightly increases the strength of plywood under static bending

Increased Bending Strength and Water Resistance of Plywood …

Table 2 The results of determining the strength of plywood when chipping on the adhesive layer
Levels of factor B

The strength of plywood samples for chipping
in tests at levels, MPa (the first line is the
arithmetic mean, the second line is the
quadratic mean, dispersion)

Row average Y bi

а1

а2

а3

1.57/0.412
0.170

1.57

1.63/0.372
0.139

1.91/0.164
0.027

2.06/0.166
0.028

1.87

1.88/0.451
0.203

2.22/0.440
0.194

1.95/0.323
0.104

2.02

Column average Y aj

1.69

1.9

1.86

1.82

Table 3 The results of determining the strength of plywood under static bending
Levels of factor B

Static bending strength of plywood samples in
Row average Y bi
tests at levels, MPa (the first line is the
arithmetic mean, the second line is the quadratic
mean, dispersion)
а1

а2

а3

124.8/12.23
149.57

124.8

123.2/4.02
16.16

124.0/9.82
96.43

135.3/8.69
75.52

127.5

125.9/9.10
82.81

126.9/8.12
65.93

121.4/7.72
59.60

124.7

Column average Y aj

124.6

125.2

127.2

125.7

by 1 MPa (0.8% in relative terms). At the same time, the adhesive strength of the
binder increases significantly—the tensile strength of plywood when chipping along
the adhesive layer increases by an average of 0.33 MPa (by 19.7%) to 1.88 MPa (see
Table 2).
When resorcinol is used as a modifier with an additive content of 2%, the strength
of plywood during chipping increases by 0.65 MPa (by 41.4%) to 2.2 MPa. The
addition of 1% copper resorcinate to the binder increases the strength of plywood
when chipping by an average of 0.49 MPa (by 31.2%) to 2.06 MPa.
All three modifiers have a comparable effect on the water resistance of the material.
The study developed a regression model of plywood thickness swelling after 24 h
of exposure to water. The experiment was conducted according to the B-plan of
the second order. The ranges of experimental factors are shown in Table 5. The
experimental plan and the results of statistical processing of experimental data are
shown in Table 6.

T. N. Vakhnina et al.

Table 4 Results of experimental data processing by the method of variance analysis
Plywood indicators

Variances

Factor A SA2
Factor В

SB2

Interactions between factors
2
SAB

Chipping strength of the
adhesive layer, MPa

Static bending strength, MPa

0.2988

7.695

1.26

22.725

0.1512

73.695

Inside the party Sn2

0.134

93.91

United S 2 о

0.135

90.23

Full S 2

0.1713

78.69

Testing the hypothesis of the absence of an interaction effect
F P ≤ F T (the condition of no interaction)
Tabular value of the Fisher
criterion F T

F T = 2.52 (by q = 0.05; f3
= 4; f4 = 63)

F T = 2.93 (by q = 0.05; f3 = 4;
f4 = 8

Calculated value of the Fisher
criterion F р

1.128
(there is no interaction)

0.785
(there is no interaction)

The significance of the influence of factors
F P > F T (significance condition)
3.11 (by q = 0.05; f1 = 2;
f0 = 67)

Tabular value of the Fisher
criterion F TА

Factor A is the calculated value 2.21
of the Fisher criterion F рА
(factor A does not
significantly affect)

3.55 (by q = 0.05; f1 = 2; f0 =
22)
0.09
(but not significant)

Tabular value of the Fisher
criterion F TВ

3.11 (by q = 0.05; f2 = 2;
f0 = 67)

3.55 (by q = 0.05; f2 = 2; f0 =
22)

Factor B calculated value of
the Fisher criterion F рВ

9.33
(factor B has a significant
effect)

0.25
(factor B does not significantly
affect)

Selective coefficients of
determination: ρA2

1.74

0.098

ρB2

7.36

0.29

Table 5 Ranges of variation of factors
Name of the factor

Designation of
the factor
Natural Coded

−1 0

1. Pressing temperature, °C

Х1

105

2. Resin consumption, g/m2

Х2

3. Modifier share, %

Х3

1.0

2.0

1.0

Levels of
variation

The range of variation,

Increased Bending Strength and Water Resistance of Plywood …

Table 6 The experimental plan in coded terms of factors and the results of statistical processing
of experimental data
X1

Experience number

The arithmetic mean of plywood
swelling in thickness У j , %

Variance S 2 1j

6.43

1.510

–

20.01

0.684

–

10.65

1.416

–

20.09

0.024

–

9.95

1.59

–

20.40

0.112

–

11.46

0.176

–

20.49

0.010

10.56

0.314

–

20.68

0.233

10,26

0.042

–

11.00

0.261

9.76

0.089

–

11.25

0.041

When processing experimental data, a regression model of plywood swelling in
thickness Y, % after 24 h in water was obtained (13)
Y = 10.725 − 5.960X1 − 0.364X2 − 0.361X3
+ 2.90X12 − 0.09X22 − 0.216X32 − 0.320X1 X2
− 0.068X1 X3 + 0.04X2 X3

(13)

Graphs of the dependence of plywood swelling on the pressing temperature (X1 ),
the consumption of phenol–formaldehyde binder (X2 ) and the proportion of copper
acetate additive (X3 ) are shown in Figs. 1, 2 and 3.

4 Conclusions
The increase in the pressing temperature has the greatest effect on reducing the
swelling of the material in thickness, this is explained by an increase in the degree
of curing of the resol phenol–formaldehyde binder with an increase in the pressing
temperature.
The influence of the factors “binder consumption” and “proportion of modifier
additive” on reducing the swelling of plywood in thickness during 24 h in water is

T. N. Vakhnina et al.

Fig. 1 Dependence of plywood thickness swelling (Y, %) on the pressing temperature (Х1 ): 1 – Х2
= 1, Х3 = 1; 2 – Х2 = − 1, Х3 = − 1; 3 – Х2 = 1, Х3 = − 1; 4 – Х2 = − 1, Х3 = 1

Fig. 2 Dependence of plywood thickness swelling (Y, %) on binder consumption (Х2 ): 1 – Х1 =
1, Х3 = 1; 2 – Х1 = − 1, Х3 = − 1; 3 – Х1 = 1, Х3 = − 1; 4 – Х1 = − 1, Х3 = 1

comparable. It should be noted that the cost of the FSF significantly exceeds the cost
of the modifier.
As part of this study, the pressing temperature of plywood has been reduced to
105 °C. Also, in order to reduce the cost of production of construction plywood,
the consumption of PFB is reduced to 95…98 g/m2 . A decrease in the thickness
of plywood to an average of 6.3% is achieved by adding 2% copper acetate to the

Increased Bending Strength and Water Resistance of Plywood …

Fig. 3 Dependence of plywood swelling in thickness (Y, %) on the proportion of copper acetate
additive (Х3 ): 1 – Х1 = 1, Х2 = 1; 2 – Х1 = − 1, Х2 = − 1; 3 – Х1 = 1, Х2 = − 1; 4 – Х1 = −
1, Х2 = 1

binder, up to 6.8% by adding 1%, while the pressing temperature is 105 °C, and the
binder consumption is 98 g/m2 .
Thus, the study solved the problem of ensuring the necessary physical and mechanical parameters of plywood based on phenol–formaldehyde binder, manufactured
under low-temperature pressing conditions. This makes it possible to produce waterproof plywood for construction purposes with the necessary range of operational
properties, and at the same time with reduced production costs due to lower binder
consumption and lower pressing temperature.
Acknowledgements The research was performed with financial support from the Russian Science
Foundation and the Kostroma Region Administration as part of scientific project No. 24-29-20157.

References
1. Li WY, Evison DC (2018) Consumption of plywood and sawn timber for concrete formwork
in the Chinese construction industry. N Z J For 62(4):30–37
2. Rustiadini M, Novianti T (2025) Comparison of plywood export competitiveness of Indonesia
and China in the Asean+3 market and its influencing factors. Jurnal Manajemen dan Agribisnis
22(1):79. https://doi.org/10.17358/jma.22.1.79
3. Balasbaneh AT, Sher W, Ibrahim MHW (2024) Life cycle assessment and economic analysis
of Reusable formwork materials considering the circular economy. Ain Shams Eng J. https://
doi.org/10.1016/j.asej.2023.102585

T. N. Vakhnina et al.

4. Worku TT (2025) Formwork material selection and optimization by a comprehensive integrated
subjective–objective criteria weighting MCDM model. Discov Mater 5:2. https://doi.org/10.
1007/s43939-024-00162-x
5. Chatzimichailidou M, Dabic D, Härkönen R (2023) Opportunities and challenges of using
plywood in data-driven parametric building construction. Prod Process Prod Evol Age Disrupt.
https://doi.org/10.1007/978-3-031-34821-1_69
6. Sedliacik J, Bekhta P, Potapova O (2010) Technology of low-temperature production of
plywood bonded with modified phenol-formaldehyde resin. Wood Res 55(4):124–130
7. Jarusombuti S et al (2022) Physical and mechanical properties of teak thermo-plywood from
plantation in Laos. Glob J Sci Front Res 22(G22):77–84
8. Fedotov AA, Vakhnina TN, Susoeva IV, Titunin AA (2024) Modeling of indicators of competitive materials for the manufacture of formwork in the construction of industrial buildings.
Build Mater 12:68–72. https://doi.org/10.31659/0585-430X-2024-831-12-68-72
9. Knob A, Knob B (1983) Phenolic resins and materials based on them: translated from English
by A.M. Vasilenko, G.M. Voskanyants. Chemistry, Moscow
10. Fitrianum F, Lubis MAR, Hadi YS et al (2023) Adhesion and cohesion strength of phenolformaldehyde resin mixed with different types and levels of catalyst for wood composites. J
Compos Sci 7:310. https://doi.org/10.3390/jcs7080310
11. Hamad SF, Nicholas THF, Teng F et al (2019) Optimizing size and distribution of voids in
phenolic resins through the choice of catalyst types. J Appl Polym Sci 136(47):48249. https://
doi.org/10.1002/app.48249
12. Kawalerczyk J, Dziurka D, Mirski R et al (2021) Microcellulose as a modifier for UF and
PF resins allowing the reduction of adhesive application in plywood manufacturing. Acta
FacultatisXylologiae 63(2):31–38. https://doi.org/10.17423/afx.2021.63.2.03
13. Kawalerczyk J, Dziurka D, Mirski R (2020) The possible reduction of phenol-formaldehyde
resin spread rate by its nanocellulose-reinforcement in plywood manufacturing process. Annals
of WULS SGGW (Forestry and Wood Technology) 111:21–26. https://doi.org/10.5604/01.
3001.0014.6420
14. Sahoo SC, Sil A (2021) Synthesis and characterization of modified low curing phenolformaldehyde resin for manufacture of wood composites. Int J Mod Agric 10:2
15. Chubinsky AN, Rusakov DS, Sokolova EG et al (2023) Innovative methods of adhesive joint
research. Proc St Petersburg For Acad 243:253–268. https://doi.org/10.21266/2079-4304.2023.
243.253-268
16. Ivanov AM, Rusakov DS, Varankina GS et al (2017) Modification with aluminosilicates of
phenol-formaldehyde resins for gluing plywood. Adhes Sealants Technol 3:13–17
17. Vakhnina T, Fedotov A, Susoeva I (2025) Use of dispersion analysis to assess significance of
effect of production process factors on construction plywood parameters. Lect Notes Civ Eng
565:64–73. https://doi.org/10.1007/978-3-031-80482-3_7
18. Plotnikov NP, Troshkin SN (2017) Justification of the choice of modifying substances for
gluing veneer with high humidity. The system. Methods Technol 1(33):107–113. https://doi.
org/10.18324/2077-5415-2017-1-107-113
19. Yeroshenko VD, Ovchinnikov AN, Efimenko AA et al (2019) Modifications of resol phenolformaldehyde resin with copper salts used as a binder. https://doi.org/10.31618/EESA.27821994
20. Li F, Ye C, Huang Y et al (2021) Incorporation of in situ synthesized nano-copper modified
phenol-formaldehyde resin to improve the mechanical properties of Chinese fir: a preliminary
study. Polymers 13(6):876. https://doi.org/10.3390/polym13060876

Refinement of Stresses in Monolithic
Floor Slabs of Frameless Buildings
with Regard to Construction History,
Loading and Rheological Properties
of Concrete
O. B. Zavyalova

Abstract The article continues the topic of taking into account the history of the
construction and loading of monolithic buildings erected in a short time. This paper
provides an analysis of the stress–strain state of monolithic disks without a single floor
covering of the 14-storey PARK INN hotel in Astrakhan. The construction stages of
the building were taken according to the schedule of work on the construction site. The
rate of monolithic work was 9 days per floor. The author defines the internal forces,
displacements and stresses in a monolithic reinforced concrete slab that occur during
the construction of a monolithic frame. Stress changes in concrete and reinforcement
are analyzed. The creep of concrete and the change in its modulus of instantaneous
elasticity are assumed based on the linear theory of creep by Harutyunyan.
Keywords Loading history · Concrete creep · Modulus of elasticity · Monolithic
plate

1 Introduction
The volume of monolithic construction has increased significantly in recent years
both in Russia and abroad. Monolithic shearless frames have become widespread,
often being erected in record time—3–5 days per floor. A reasonable question arises
as to how justified is the loading of concrete at a fairly young age, when its strength
and rigidity are still far from the design values.
In recent years, a number of studies on this subject have been carried out [1–10],
in which various aspects of the formation of design schemes and consideration of the

O. B. Zavyalova (B)
Astrakhan State University of Architecture and Civil Engineering, Astrakhan, Russia
e-mail: zavyalova_ob@aucu.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_3

O. B. Zavyalova

rheological properties of concrete, in particular, curing, creep and physical nonlinearity, have been considered. The main focus of these works was on columns of highrise buildings as the most loaded elements. Earlier in [1] the author proposed a method
of calculation and analysis of loading results of monolithic centrally loaded pylons
of the building of multi-storey hotel ‘PARK INN’ in Astrakhan taking into account
the mechanical characteristics of young age concrete changing during construction.
The stages of erection were taken according to the calendar plan of works at the
construction site. The speed of monolithic works was 9 days per floor.
Now let’s pay attention not to columns and pylons, but to the monolithic floor
slab of a typical floor taking into account the typical erection technology.
Let’s consider the method of taking into account the additional stresses in the
reinforcement of monolithic slabs caused by creep of concrete and changes in its
elastic-modulus deformation during the erection of a monolithic reinforced concrete
building of a transomless structural system. In the process of erection, the monolithic
slabs of the underlying floors serve as a support for the newly erected slabs, whose
load is transferred to the underlying structures through telescopic columns. Technological standards stipulate that at least two slabs under the newly erected slab must
support the weight of the slab through the telescopic struts. Taking into account that
the speed of concrete works is sometimes several days per floor, additional loads
on the not yet hardened concrete will cause significant unaccounted stresses in the
reinforcement of the base slabs. The calculation is made using the known formulas
of Arutyunyan N. Kh. on the example of the 14-storey hotel “PARK INN” erected
in Astrakhan. Since the object is real, the loading stages at the erection stage are
taken according to the work production log. Erection of load-bearing structures of
the building was performed in accordance with the construction schedule. The structural scheme of the building is a plate-and-barrel, transomless. Racks in the form of
pylons with dimensions 250 × 1400…1800 mm, reinforced with longitudinal rods
and transverse clamps, monolithic slabs 200 mm thick.

2 Methods
Firstly, to illustrate the methodology used, let us present the calculation of the ground
floor column considered in the author’s paper [1]. Creep and real modulus of elasticity of concrete at different ages were taken into account according to the known
dependences of Harutyunyan [11].
E(x) = E0 · 1 − e−α·x ,

(1)

where E 0 = E b = 3.24·104 MPa, α = 0.03 day−1 (designations correspond to [11]).
If the creep measure of concrete is given by Eq:
C(t, τ ) = ϕ(τ ) 1 − e−γ (t−τ ) ,

(2)

Refinement of Stresses in Monolithic Floor Slabs of Frameless …

where
ϕ(τ ) =

A1
+ C0 ,
τ

(3)

then for a centrally compressed element, the correction factor to the stress in the
reinforcement at any time t > τ is determined by the expression:
γ · Ea · ϕ(τ1 )
·
Z1 (t) := 1 +
m(τ1 ) · (1 + μ · m(τ1 ))

−

τ
τ1

Ea ·ϕ(x)
γ · 1+μ· 1+μ·m(x)
+

(

d m(x)
dx
1+μ·m(x)

μ·

)

dτ

(4)

τ1

here C 0 is the limiting value of the creep measure for the material, A1 , γ -constant
parameters of the creep measure; τ 1 —age of concrete in which the load is applied to
it; m(x) = E s /E x —ratio of elastic moduli of reinforcement and concrete (at the age
of concrete x-days); μ—reinforcement coefficient.
Let’s assume the values: C 0 = 0.09·10–7 kPa−1 ; γ = 0.026; A1 = 4.83·10–7 day/
kPa;
τ 1 = 23, 32, 41, … 140 days; μ = 8.93·10–4 ; α = 0.03 day−1 .
Here we present only the results of this calculation (Fig. 1).
As we can see, the highest stresses in the reinforcement reach the values of
70.4 MPa. For comparison, without taking into account the creep of concrete and
changes in its elastic modulus, the stresses in the reinforcement at a given load would
have reached the value of 19.6 MPa. Of course, the entire load applied here is only
a fraction of the permanent loads that will be applied to the pylon in question, and
temporary loads are not taken into account at all. However, the above calculation
shows that the real compressive stresses in the reinforcement of this element will be
50 MPa higher than those obtained in a conventional strength calculation. And when
the time limit is extended to 360 days, the increase in stresses will be 55 MPa.

Fig. 1 Graph of stress variation in pylon reinforcement (MPa) from stepwise (after 9 days) load
application in the first 260 days.

O. B. Zavyalova

Fig. 2 Resulting graph of stresses (MPa) in concrete of the 1st floor pylon after 260 days

The opposite situation is observed in concrete. Here stresses drop with time due
to creep of concrete (Fig. 2).
Let’s perform the calculation of monolithic slab taking into account creep and
hardening of concrete in the same example with a monolithic hotel. On the real
object the speed of monolithic works was 9 days per floor. The newly erected slab,
which initially had zero stiffness, transferred its entire weight through the formwork
panels and the telescopic props underneath to the underlying slab, which was 9 days
old by this time. This slab, as well as the one below it, were reinforced with the same
props, but more sparsely installed—one row in each step of the axis grid. Thus, three
bending slabs are included in the calculation:
• at the age of 9 days: takes the load from its own weight—5 kPa, the weight of
the slab being erected—5 kPa, the weight of the formwork—1 kPa. Taking into
account the large number of columns transmitting the load from the newly erected
slab, this load is assumed to be uniformly distributed;
• at the age of 18 days: it supports the load from its own weight and part of the load
from the two overlying slabs, transmitted through the erection struts installed in
one row in each column grid step;
• 27-day old slab: in addition to its own weight, it also supports the weight of the
three slabs through the erection struts. This slab does not have any additional
supports, as the erection props have already been removed underneath it. All the
underlying slabs only support their own weight for the time being.

3 Results and Discussion
The calculation of the plate-and-bar system, representing the bearing frame of the
hotel, was carried out in the MONOMAH program. The results of the calculation
are presented in Figs 3, 4, 5, 6 and 7. Figure 4 shows the displacement isopoles of
the slab at the age of 9 days, Fig. 5 shows the deflection epiphysis.

Refinement of Stresses in Monolithic Floor Slabs of Frameless …

Fig. 3 Deformed scheme of
a fragment of the bearing
frame of the hotel (the newly
erected slab is not shown)

Fig. 4 Vertical displacements (in mm) of the floor slab at the age of 9 days

The bending moments M x and M y are calculated for all slabs considered. Their
values vary from − 24.7 to + 19.11 (kNm)/m for Mx and from − 19.17 to + 10.4
(kNm)/m for M x . The different ages of concrete in the slabs (9, 18, 27 days) were

O. B. Zavyalova

Fig. 5 Slab deflection diagram. The section is drawn between the supporting pylons along the
symmetry axis of the slab (vertical in Fig. 4)

Fig. 6 Graph My in the slab at the age of 9 days, units—kNm/m cross section 4–4 was made along
the row of pylons

taken into account when specifying the modulus of elasticity Eb . The modulus of
elasticity was calculated by expression (5).
It should be noted that it was not possible to calculate the stresses in the reinforcement of the floor slab by conventional calculation according to the construction
norms due to the large thickness (20 cm) and over-reinforcement of the slab, because
in this calculation the height of the compressed zone was negative. Stresses in the
reinforcement were calculated using the methods of structural mechanics through
displacements, namely using Hooke’s law and elastic line expression:
σs = Es εs = Es · ys · y ,

(5)

Refinement of Stresses in Monolithic Floor Slabs of Frameless …

Fig.7 Graph Mx in the slab at the age of 9 days, units—kNm/m longitudinal section 5–5 is made
along the middle row of pylons

where ys is the coordinate of the center of gravity of the reinforcement in the considered section relative to the horizontal axis of the section; y —the second derivative
of the deflection in the section under consideration.
With a sufficient degree of accuracy y can be determined by the finite difference
method, knowing the deflections in the section under consideration and in two equally
spaced from it at a distance Δ:
yz =

yz−1 − 2yz + yz+1
2

(6)

To investigate the effect of creep, the section of the slab between the pylons,
working in the direction of the “y” axis, was selected. The vertical displacement
diagram is shown in Fig. 6. In the place of the largest deflection the displacement
value was 8.312 mm, in the points located 1.9 m to the left and right—the points of
inflection of the deflection curve − 7.057 mm. According to formula (6) we obtain:
y =

(−7.057 − 2 · (−8.312) − 7.057) · 10−3
= 0.695 · 10−3 M−1 .
1.92

The stresses in the reinforcement at ys = 8 cm = 0.08 m, E s = 200 GPa will be
11.2 MPa.
The analysis of bending moments in the slabs shows that the stresses in the slab
at the age of 18 days increase by 11%, at the age of 27 days—by 4.5%. At the
age of 36 days the temporary supports from the considered slab are removed and
this slab starts to work on its own load with normative value of 5.0 kPa and design
value of 5.5 kPa. The bending moments and, consequently, the stresses are reduced.
Further change of the load on the slab began at the device of partitions, floors, as
well as at the action of useful load. To calculate the elastic-instantaneous stresses
in the tensile reinforcement of the slab section under consideration, the deflection
epuple of all nodes of the finite element mesh along the line 1–1 from the action of

O. B. Zavyalova

uniformly distributed load intensity of 10 kPa (the full design load including its own
weight) was preliminarily determined. Then, by expression (5) using formula (6), the
stresses in the reinforcement were obtained, which from the specified load amounted
to 16.66 MPa. Further, at each loading stage, the initial elastic-instantaneous stresses
were calculated in proportion to the applied load, assuming elastic operation of the
reinforcing steel.
According to the work schedule, the following loading periods were adopted
(starting not from the beginning of construction, but from the moment of origin of
the slab under consideration), given in Table 1:
The influence of creep and hardening of concrete in the bending element is taken
into account according to the expression obtained by N. H. Harutyunyan for this type
of deformation, multiplying the elastic-instantaneous stresses in the reinforcement
by the coefficient:
γ Ea ϕ(τ1 )
·
Za (t) = 1 +
m(τ1 )[1 + μm(τ1 )n0 ]

−

τ
τ1

μE ϕ(x)n

μm (x)n

a
0
0 +
γ 1+ 1+μm(x)n
1+μm(x) dx
0

τ1

d τ,

(7)

where n0 = 1 + h2s · Ab Ib ,—coordinate of the reinforcement along the height of the
cross-section; Ab , Ib —area and moment of inertia of concrete in the cross-section.
The methodology for calculating stresses in the reinforcement, taking into account
hardening and creep of concrete, is similar to that given in [1] for compressed
elements. The calculation is performed in the MathCad program complex. The total
graph of stresses in the reinforcement of the slab taking into account all stages of
loading is shown in Fig. 8. The stresses decrease at the age of concrete 36 days is
explained by the fact that at this time the supports transferring the load from the
overlying slabs to the slab under consideration are removed, and it begins to work
only on its own weight.
According to the graph in Fig. 8, the stresses in the reinforcement stabilize at
the age of concrete 300 days, reaching a value of 46 MPa by this time. The design
stresses were at 16.7 MPa, an increase of 176%. Taking into account the strong
Table 1 Accepted stages of loading of monolithic reinforced concrete floor slab
Age of slab concrete, days Addition stress, MPa Total stress without taking into account creep
and hardening of concrete, MPa
9

+ 11.2

11.2

+ 1.232

12.432
12.932

+ 0.5

− 3.77

+ 1.666

98
150

9.162
10.828

+ 2.5

13.328

+ 3.332

16.66

Refinement of Stresses in Monolithic Floor Slabs of Frameless …

Fig. 8 Total stresses in the tensile reinforcement of the floor slab (MPa)

over-reinforcement of the slab, the real stress increase in its reinforcement was about
30 MPa.
In the considered example, the periodicity of floor erection was assumed to be
9 days, which was determined by the volume of work on the site and the number of
workers involved—concrete and reinforcement workers. There are known examples,
both in Russia and abroad, when the speed of erection of monolithic buildings was
3 days per floor. Various additives are used to accelerate concrete hardening and
to make the concrete mixture more manageable. In the considered example with
a multi-storey hotel it was CREAPLAST—anti-freeze plasticizer. Various authors
[12–14] investigating the creep problem, in their works note the influence of chemical
and mineral additives on the relative deformation of concrete. In particular, Brooks
[13] tested different types of chemical admixtures by comparing the creep strain
of concrete with admixtures with a control concrete composition with the same
composition but without admixtures. It was found that there were no big differences
in the effect on creep strain of concrete between different types of plasticizers and
superplasticizers. However, a 20% increase in creep strains was observed compared
to the control concrete. Another author, Ramashandran [14], in his book concluded
on concrete curing gas pedals. Calcium chloride based admixtures increase creep
strain of concrete loaded at 7 days of age by 36% and at 28 days of age by 22%.
Creep performance of concrete with triethanolamine admixture increased at early
loading age (7 days).
Thus, the effect of stress growth in the reinforcement revealed in the present work
will be even more significant when taking into account the additives: plasticisers and
concrete hardening accelerators.

O. B. Zavyalova

4 Conclusions
When calculating the stresses in the working reinforcement of monolithic slab reinforcement of monolithic slabs of trussless frames erected with accelerated construction time, the real modulus of elasticity and creep of early-age concrete should be
taken into account.
Acceleration of the construction terms of monolithic reinforced concrete structures leads to a decrease in the resource of structural safety of these buildings.
Taking into account the stage-by-stage loading allows to reveal the value of
additional stresses in the reinforcement of the most critical structural elements;
The increase of stresses in the tensile reinforcement of the considered floor slab
only from the accounted part of the constant load was 30 MPa compared to the design
stresses;
The active growth of stresses in the reinforcement caused by creep of concrete,
calculated by the formulas [11], is manifested up to the age of concrete 260–290 days,
which should be especially taken into account when determining the stress–strain
state of multi-storey monolithic structures;
The introduction of plasticisers, superplasticisers and curing accelerators into the
concrete mix will increase the creep and associated relaxation of the concrete, which
will only intensify the considered effect of the growth of additional stresses in the
reinforcement.

References
1. Zavyalova OB (2012) Taking into account the loading history of monolithic reinforced concrete
slab-and-rod systems in determining the stressed state of their elements. PGS 7:58–61
2. Shein AI, Zavyalova OB (2012) Calculation of monolithic reinforced concrete frames with
consideration of erection sequence, physical nonlinearity and creep of concrete. PGS 8:29–31
3. Kabantsev OV, Karlin AV (2012) Calculation of the bearing structures of buildings taking
into account the history of erection and step-by-step change of the main parameters of the
calculation model. PGS 7:33–35
4. Kabantsev OV, Tamrazyan AG (2014) Accounting for changes in the design scheme when
analysing the structure operation. Eng Constr J 5:15–26
5. Kim HS, Shin AK (2011) Column shortening analysis with lumped construction sequences.
Procedia Eng 14:1791–1798
6. Jayasinghe MTR, Jayasena WMVPK (2004) Effects of axial shortening of columns on design
and construction of tall reinforced concrete buildings. Pract Period Struct Des Constr, ASCE
9(2):70–78
7. Barabash MS (2012) Methods of computer modelling of the processes of erection of high-rise
buildings. Int J Comput Civ Struct Eng 8(3):58–67
8. Zavyalova OB (2018) Calculation of internal efforts in combined multystoried frames
taking into account changing settlement scheme. IOP Conf Ser Mater Sci Eng Chelyabinsk
451:012057. https://doi.org/10.1088/1757-899X/451/1/012057
9. Zavyalova O, Shein A (2019) The reinforced concrete frame calculation with allowance for
the erection sequence, physical nonlinearity and the concrete creep. ARPN J Eng Appl Sci
14(1):166–172

Refinement of Stresses in Monolithic Floor Slabs of Frameless …

10. Zavyalova OB (2020) Calculation of a multi-storey stepped pylon taking into account hardening
and creep of early age concrete. Eng Constr Bull Casp Sea 3(33):26–30
11. Arutyunyan NKH (1952) Some questions of the creep theory. Gostekhizdat, Moscow, p 323
12. Karimov ISH (2011) Mechanism of concrete creep and factors influencing it (review). Concr
Technol 3–4:61–65
13. Brooks JJ (1999) How admixtures affect shrinkage and greep. In: How admixtures affect
shrinkage and creep. Concrete international, pp 35–38
14. Ramachandran VS (1995) Concrete admixtures handbook. In: Handbook of concrete admixtures, 2nd edn. Noyes Publications, Park Ridge, New Jersey, USA, p 1153

Multi-objective Optimization of Concrete
Driven by Synergistic Effects of Smart
Restoration and Nano-Enhancement
Mingyuan Wang, Zhuxuan Xu, Li Zheng, and V. S. Rudnov

Abstract This study employed a three-factor, three-level orthogonal experimental
design (variables: water-cement ratio, microcapsules, modified graphene oxide (GO))
to investigate the synergistic optimization effects of additive dosage on multiple
performance indicators of concrete (7-day/28-day compressive strength, self-healing
rate, water penetration depth). Range analysis and analysis of variance (ANOVA)
revealed that microcapsules primarily control the self-healing rate, while GO dominates impermeability. Specifically, optimizing the water-cement ratio enhanced earlyage strength by 17.2% and improved later-age compactness. A GO dosage of 0.1%
reduced water penetration depth by 33.97%, but excessive dosage (e.g., 0.15%) inhibited self-healing (reducing the healing rate by 15.09%). A microcapsule dosage of
3% increased the self-healing rate by 25.1%, but increasing it to 5% caused a sharp
decrease of 27.09% due to premature rupture (although synergistically reducing
water penetration depth by 29.04%, it weakened early-age strength by 8.9%). The
GO/microcapsule composite concrete prepared through multi-objective optimization can simultaneously meet the requirements for strength, self-healing capability,
and durability (low permeability). However, because the optimal mix ratios for
each performance indicator conflict (early-age strength: A3B1C3, later-age strength:
A1B2C3, self-healing rate: A2B1C2, impermeability: A3B2C2), careful balancing
of the interaction effects is required based on specific engineering demands.

M. Wang (B) · Z. Xu · L. Zheng · V. S. Rudnov
Ural Federal University Named After the First President of Russia B. N. Yeltsin, Ekaterinburg,
Russia
e-mail: vanurfu@163.com
Z. Xu
e-mail: xuzhuxuan9@gmail.com
L. Zheng
e-mail: zhengli321@foxmail.com
V. S. Rudnov
e-mail: rudnovv@yandex.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_4

M. Wang et al.

Keywords Orthogonal experiment · Modified graphene oxide · Self-healing
concrete · Range analysis method

1 Introduction
Concrete, as the core substrate of building structures, faces persistent challenges
to its full-life service performance due to the evolution of microcracks and macroscopic cracking behavior [1, 2]. Traditional repair methods relying on manual intervention suffer from inherent shortcomings of insufficient timeliness and poor costeffectiveness [3]. Although self-healing technologies based on microcapsule encapsulation and microbial mineralization can achieve active responses to localized
damage [4], a single repair mechanism struggles to coordinate strength self-recovery
with functional synergy (such as durability enhancement) [5]. Nanomaterials like
graphene oxide (GO) have been demonstrated to optimize the microstructure of
concrete; however, unmodified GO is prone to agglomeration within the cementitious matrix, leading to fluctuations in enhancement efficiency and undesirable
attenuation in strength [6]. Based on literature findings [7], this study introduces
the silane coupling agent KH-560 to perform surface functionalization modification
on graphene oxide, aiming to overcome the dispersion limitation and explore its
multi-scale synergistic mechanism with self-healing components.
Current technological bottlenecks are concentrated on two aspects:
(1) The lack of a quantitative correlation model between microcapsule dosage and
repair efficacy, where excessive introduction leads to systematic deterioration
of matrix mechanical properties [8];
(2) The urgent need for precise regulation of the dispersion stability and functional
contribution rate of graphene oxide (GO) within the cement paste-aggregate
interface zone [9–11]. For the development of self-healing concrete, it is imperative to achieve "four-dimensional performance synergy" in material design:
rapid development of early-age strength and long-term performance stability;
enhanced crack repair efficiency based on autonomous response; tunable bulk
resistivity to support structural health monitoring; and barrier capabilities
against permeating media and chemical erosion.
This study proposes a “dual-functional coupling” strategy: utilizing self-made
inorganic microcapsules to establish a damage-responsive repair effect [12, 13],
while achieving matrix densification through KH-560 modified GO. A three-factor
orthogonal experiment is employed to analyze the coupling effects of water-cement
ratio, microcapsule content, and modified graphene oxide dosage on the strengthrepair-durability fields. This provides a theoretical basis and technical pathway for
the on-demand design of smart concrete.

Multi-objective Optimization of Concrete Driven by Synergistic Effects …

2 Materials and Methods
2.1 Materials Used
Cement: P·O 42.5 grade ordinary Portland cement (CEMROS Co.), average particle
size 10 μm, specific surface area 360 m2 kg−1 .
Fine aggregate: Quartz sand (apparent density 2420 kg m−3 ), particle size
distribution 0.075–0.6 mm, gradation conforming to ISO 679:2009 standard.
Coarse aggregate: Mechanically crushed granite (particle size 5–10 mm), crushing
index ≤ 8%.
Water reducer: Sodium fluorosilicate-based high-efficiency water reducer (Ural
Industrial Holding “AMK-Group”, solid content ≥ 98%).
Modified nanomaterial: Self-synthesized KH-560 functionalized graphene oxide
solution (10 mg mL−1 ), diluted with purified water, ultrasonically dispersed (40 kHz,
0.5 h), and subsequently aged for 24 h [13].
Self-healing microcapsules: Inorganic green microcapsules [12], average particle
size 120 μm, encapsulation rate ≥ 95%.

2.2 Experimental Mix Ratio Design
Orthogonal experimental design, based on the principle of orthogonality, selects
representative test points from the full factorial combination. It ensures uniform
distribution of factor levels and minimizes interference between factors, enabling the
analysis of multi-factor influence mechanisms with minimal experiments. For optimizing the mix proportion of modified graphene oxide/microcapsule concrete, the
study focuses on three key factors: Water-cement ratio (A): regulating paste rheological properties and compactness; Microcapsule dosage (B): controlling self-healing
efficiency; Graphene oxide dosage (C) (Orthogonal factor levels are presented in
Table 1). Nine experimental groups were designed using an L9 (34 ) orthogonal array.
Specimens were formed under standard curing conditions (20 ± 2 °C, RH ≥ 95%).
Table 1 Orthogonal experimental design. Level. Factor
Level

Factors
A: Microcapsules (%)

B: GO (%)

C: Water-cement ratio

0.05

0.4

0.1

0.45

0.2

0.5

M. Wang et al.

2.3 Evaluation Indicators and Results Analysis Method
Compressive strength test: After placing the specimen into the mold and positioning
it on the loading platform, set the loading rate of the testing machine to 5 KN/
s. The specimen was completely crushed on the testing machine, and the ultimate
compressive strength obtained was recorded as K0 .
Self-healing evaluation: Based on the mechanical property testing of the specimen, pre-compression was applied at 70% of the ultimate load. The mechanical
properties of the specimen after loading were then tested and recorded as K1 . The
pre-compressed specimens were subsequently cured in a constant temperature water
bath. After reaching the designed curing time, repair testing was conducted, and
the result was recorded as K2 . The healing rate and recovery rate for each group of
specimens were calculated according to “Eqs. 1–2”
Kx =

K2 − K1
× 100%
K0 − K1

(1)

K2
× 100%
K0

(2)

Kh =

Penetration Height: According to ГОСТ 12730.5-2018 “Methods for Determining
Water Resistance of Concrete”, the impermeability of concrete was evaluated using
the stepped water pressure method: Standard-cured (28d) 150 × 150 × 150 mm
cube specimens (ГОСТ 10180), with their lateral surfaces sealed with bitumen, were
placed in an HP-4.0 automatic permeameter. Water pressure was applied stepwise
from 0.2 → 0.8 MPa (increment of + 0.1 MPa/2 h, total duration 14 h).
Range Analysis Method (R-value analysis): A multi-factor experimental data
processing method based on statistical comparison principles, aiming to quantify the
significance of the influence of various factors on the target performance indicator.
The significance is assessed by calculating the mean response value of the experimental results for each factor at different levels (Eqs. 3–4), and the primary and
secondary order of the factors is determined by ranking based on the range value
(R-value).
Ki =

1
m

yij

(3)

j=1

R = max(K1 , K2 , . . . , Kk ) − min(K1 , K2 , . . . , Kk )

(4)

K i : denotes the mean value of the indicator at the i-th factor level;
yij : represents the observed value of the indicator in the j-th trial at the i-th level;
m: indicates the number of trials per factor level (in orthogonal arrays, this typically
signifies the number of level repetitions).
K: is the number of factor levels (e.g., for 3 levels, k = 3);

Multi-objective Optimization of Concrete Driven by Synergistic Effects …

R: signifies the magnitude of a factor’s effect on the result, where a higher R value
indicates a stronger influence of the factor on the outcome.
Analysis of Variance (ANOVA): A multi-factor design optimization method based
on mathematical statistical inference. Its core lies in quantifying the significant influence of various factors and their interactions by decomposing the sources of variation
(Eqs. 5–6).
n

(yi − y) =

SST =
i=1

Fi =

SSj + SSE

(5)

j=1

SSi /dfi
SSi · dfe
MSi
=
=
MSe
SSe /dfe
SSe · dfi

(6)

SST: denotes the total sum of squares;
SSj: represents the sum of squares for the effect of the j-th factor;
SSE: signifies the sum of squared errors. If the;
F i : value exceeds the critical value or the p-value is less than the significance level
(typically 0.05), it can be concluded that the effect of the given factor is statistically
significant.

3 Results and Discussion
3.1 Analysis of Orthogonal Experimental Results
The orthogonal experimental results are presented in Fig. 1. The A1 B2 C3 combination exhibited the optimal strength (7-day and 28-day compressive strengths of
35.3 MPa and 46.3 MPa, respectively). The A2 B1 C2 and A1 B1 C1 combinations
demonstrated outstanding comprehensive performance (repair rates of 25.4%-25.3%,
water seepage heights of 34.78–31.21 mm). The A3 B3 C1 and A1 B3 C2 combinations
showed the best resistivity (35,186.5 Ω cm and 36,157.1 Ω cm, respectively).
Normality tests indicated that the 28-day strength (S-W *p* = 0.646; K-S *p*
= 0.930) and water seepage performance (S-W *p* = 0.775; K-S *p* = 0.978)
conformed to a normal distribution. The 7-day strength (S-W *p* = 0.083; K-S *p*
= 0.732) and repair rate (S-W *p* = 0.053; K-S *p* = 0.380) were considered
approximately normal (skewness < 3 / kurtosis < 10).

3.2 Influence of Different Factors on 7-Day/28-Day Strength
Early-age Strength Analysis: The results in Table 2 indicate that the water-cement
ratio (W/C) is the primary factor influencing the early-age strength of concrete (range

M. Wang et al.

Fig. 1 Orthogonal experiment results a compressive strength at 7 days and 28 days; b self-healing
ratio (%) and water penetration height (mm)

R = 5.667). When the W/C increases from 0.4 → 0.50, the early-age strength
increases by 17.2%. The underlying mechanism is as follows: during the initial
concrete pouring stage, the cement hydration reaction continuously progresses, and
the strength primarily originates from the cementitious gel formed by hydration.
A lower W/C results in reduced mixing water, promoting more complete hydration of cement particles and generating more hydration products, thereby enhancing
strength. When the dosage of modified graphene oxide (MGO) increases from 0.05%
→ 0.2%, the early-age strength increases by 11.4%. This is attributed to the incorporation of graphene and the adjustment of the W/C, which effectively counteracts
the negative impact of microcapsules on early-age strength. However, increasing the
microcapsule dosage from 1 to 5% leads to an 8.9% decrease in early-age strength.
The reason is that the structural design of the microcapsules, to ensure their effective
rupture, sacrifices some mechanical performance, rendering them unable to provide
sufficient mechanical contribution to the concrete. The range analysis and analysis
of variance (ANOVA) results are consistent: the sum of squared deviations for modified graphene oxide and W/C are significantly smaller than the error term, indicating
their significant influence on data variability; the F-values for all factors are greater
than 1 (confidence in between-group differences > 50%), and the F-value for W/C is
the largest, further highlighting its most significant influence on early-age strength.
Therefore, it is concluded that the optimal mix proportion for early-age concrete
strength is A3 B1 C3 (microcapsules 5%/MGO 0.05%/W/C 0.5).
Later-Stage Strength Evolution: Upon extending the curing age to 28 days, the
order of influence of the various factors on strength transformed into C > A > B
(i.e., water-cement ratio > microcapsules > graphene). As shown in Table 2, the
range (R = 5) for the water-cement ratio is significantly larger than those for the
other factors, indicating its critical role in later-stage strength. Strength exhibited an
upward trend with increasing water-cement ratio. This is attributed to the fact that
an excessively low water-cement ratio impairs concrete workability, reduces casting
quality, and induces dry shrinkage cracks. Conversely, when the water-cement ratio is
increased, graphene effectively reduces concrete porosity and enhances its density,

Multi-objective Optimization of Concrete Driven by Synergistic Effects …

Table 2 Analysis of the effects of different factors on 7-day/28-day intensity
Range of analysis
Factors
7-day

28-day

32.67

31.67

30.33

2.33

29.00

32.33

33.33

4.33

28.67

34.33

31.67

5.67

15.57

18.17

20.33

8.17

19.77

19.57

15.83

3.17

23.73

21.33

22.90

7.07

Analysis of variance (ANOVA)

7-day

28-day

Factors

Sum of squares

Mean
square

8.18

4.09

1.231

31.49

15.75

2.892

47.10

23.55

3.333

100.07

50.03

1.612

15.11

7.55

0.243

76.78

38.39

1.236

Variance plot

Order of significance

7-day

C>B>A

28-day

C>A>B

M. Wang et al.

thereby improving strength. The effect of increasing microcapsule dosage on 28day strength manifested as an initial decrease followed by a slight rebound: when the
dosage increased from 1% → 3%, strength decreased by 5.34%; upon further increase
to 5%, strength instead increased by 2.82%. This indicates that microcapsules exert
a certain positive effect on later-stage strength, but beyond a critical value, this
improvement weakens and may even restrict strength development. The effect of
increasing modified graphene oxide dosage showed a trend of decrease, followed by
an increase, and then another decrease; when the dosage increased from 0.05% →
0.1%, strength improved by 5.12%. Therefore, the optimal mix proportion for 28-day
concrete strength is A1 B2 C3 (Microcapsules 1%/Graphene 0.1%/Water-cement ratio
0.5).

3.3 Influence of Different Factors on Repair Rate
Based on the results in Table 3, the self-healing performance of concrete was
primarily dominated by the microcapsule dosage, which exhibited the highest range
analysis value (R = 8.167). When the microcapsule dosage increased from 1%
→ 3%, the repair rate significantly improved by 25.1%. This improvement was
attributed to the effective release of the CaCO3 healing agent from the microcapsules to fill the cracks. However, when the dosage was further increased to 5%, the
repair rate sharply decreased by 27.09%. This decline occurred because excessive
microcapsules ruptured prematurely during the mixing stage, leading to the depletion
of the healing agent reserve. Although modified graphene oxide (GO) was beneficial for enhancing strength, it reduced the repair rate by 15.09%. Its mechanism of
action likely manifested as a physical barrier effect and crystallization interference,
inhibiting the self-healing process rather than promoting the hydration reaction; the
carboxyl groups on the surface of the modified GO might have interfered with the
orderly crystallization of CaCO3 . Excessive addition of modified GO would hinder
the contact between unhydrated particles and water, and lead to disordered crystallization of hydration products, thereby reducing self-healing effectiveness. The
water-cement ratio (w/c), as a secondary factor, reduced repair efficiency at higher
dosages by softening the microcapsule shell. The mean square of the microcapsule
dosage factor was significantly greater than the error mean square, indicating that this
factor had a significant influence on data variability. The primary-secondary relationship of the three factors was consistent with the range analysis results. The F-values
for both microcapsule dosage and w/c were greater than 1, indicating the reliability
of the experimental results exceeded 50%. Therefore, the optimal mix proportion
was A2 B1 C2 (microcapsule 3% / GO 0.025%/w/c 0.45), which ensured the effective
release of the healing agent while minimizing the interference of nanomaterials with
the self-healing process.

Multi-objective Optimization of Concrete Driven by Synergistic Effects …

Table 3 Analyse the impact of different factors on the repair rate
Range of analysis
Repair rate

Factors

15.57

19.77

23.73

8.17

18.17

19.57

21.33

3.17

20.33

15.83

22.90

7.07

Analysis of variance (ANOVA)
Factors
Repair rate

Mean square

100.07

2.00

50.03

1.61

15.11

2.00

7.55

0.24

2.00

38.39

1.24

Variance plot
Repair rate

Sum of squares

Order of significance
A>C>B

3.4 Influence of Different Factors on Permeability
The results in Table 4 indicate that modified graphene oxide (MGO) is the dominant
factor affecting concrete permeability (Range R = 17.363). When the MGO dosage
increased from 0.05% to 0.1%, the water penetration height significantly decreased
by 33.97%. However, when the dosage further increased from 0.1% to 0.2%, the
water penetration height instead increased by 17.54%. The mechanism by which
MGO enhances impermeability lies in its ability to undergo chemical adsorption
with cement particles, promoting tighter particle packing. This leads to densification
of the concrete structure and a reduction in permeable pores. Furthermore, its high
chemical stability helps inhibit oxidation reactions within the concrete, reducing the
risk of expansion and cracking. Concurrently, its high surface activity and chemical
stability enable it to adsorb and catalyze hydration products and pollutants, promoting
the internal self-healing process and thereby further enhancing impermeability.
When the microcapsule dosage increased from 1 to 5%, the water penetration
height also decreased by 29.04%, indicating that microcapsules can effectively
improve concrete impermeability. However, their mechanism of action differs from

M. Wang et al.

Table 4 Analyse the impact of different factors on penetration rate
Range of analysis
Permeability

Factors

48.83

37.91

38.27

10.92

51.26

39.86

33.89

17.36

49.85

38.77

36.39

13.45

Analysis of variance (ANOVA)

Permeability

Factors

Sum of squares

Mean
square

230.754

115.377

0.52

467.007

233.503

1.053

309.391

154.696

0.698

Variance plot
Permeability

Order of significance
B>C>A

that of MGO. Penetrating cracks and numerous microcracks generated after specimen fracturing provide channels for water ingress. Under the humid conditions of
the permeability test, the bentonite within the microcapsule core material rapidly
expands upon water absorption, effectively filling the fissures and blocking the path
for further water intrusion. Therefore, while microcapsules do not directly alter
the mortar matrix properties, they indirectly enhance impermeability through the
physical filling of cracks.
Additionally, as the water-cement ratio increased, the concrete’s water penetration
height also exhibited an initial substantial decrease followed by a slight rebound,
indicating that increasing the water-cement ratio can improve impermeability to
some extent. The mean square value of the MGO factor was significantly greater
than the error mean square, confirming its significant impact on data variability.
The primary and secondary relationships among the factors were consistent with the
range analysis results. The F-value for MGO was greater than 1, indicating that the
confidence level of the experimental results exceeds 50%. Consequently, the optimal
mix ratio was determined to be A3B2C2 (Microcapsule 5%/GO 0.1%/Water-cement
ratio 0.45).

Multi-objective Optimization of Concrete Driven by Synergistic Effects …

4 Summary
Based on the analysis of the orthogonal experiment with three factors and three
levels:
The water-to-cement ratio (A) is the key control parameter governing both earlystage and later-stage concrete strength. By optimizing the hydration reaction process,
it can increase early-stage strength by 17.2% and enhance later-stage compactness.
Modified graphene oxide (GO) (B) dominates impermeability. At a 0.1% dosage,
the water penetration depth was significantly reduced by 33.97%. However, excessive
incorporation (e.g., exceeding 0.1%) inhibits self-healing efficacy (resulting in a
15.09% reduction in healing rate).
Microcapsule dosage (C) significantly impacts the healing rate. At a 3% dosage,
the healing rate increased by 25.1%. However, increasing it to 5% caused premature
cracking due to interfacial stress concentration, leading to a sharp 27.09% decrease
in healing rate. While it synergistically improved impermeability (water penetration
depth reduced by 29.04%), it concurrently weakened early-stage strength by 8.9%.
The optimal mix proportions for each performance indicator differ significantly:
•
•
•
•

Early-stage strength: A3 B1 C3
Later-stage strength: A1 B2 C3
Healing rate: A2 B1 C2
Impermeability: A3 B2 C2

Therefore, achieving a balanced multi-objective performance requires coordinated optimization based on specific engineering demands, carefully weighing the
synergistic interactions among the water-to-cement ratio (A), GO dosage (B), and
microcapsule dosage (C).

References
1. Ojha A, Aggarwal P (2022) Fly ash based geopolymer concrete: a comprehensive review.
SILICON 14:2453–2472. https://doi.org/10.1007/s12633-021-01044-0
2. Chahar AS, Pal P (2023) A review on various aspects of high performance concrete. Innov
Infrastruct Solut 8:175. https://doi.org/10.1007/s41062-023-01144-3
3. Karna S, Deb P, Mondal S (2024) Consequences of fatigue in concrete structures: a state-ofthe-art review and possible remedial measures. Innov Infrastruct Solut 9:320. https://doi.org/
10.1007/s41062-024-01630-2
4. Kontiza A, Polymers IK (2025) Undefined 2024: Smart composite materials with self-healing
properties: a review on design and applications. mdpi.com. https://www.mdpi.com/2073-4360/
16/15/2115. Accessed 05 Jan 2025
5. Phogat P, Sharma S, Rai S, Thakur J (2025) Challenges and limitations in self-healing materials.
In: Self-healing materials. Engineering materials. Springer, Singapore. https://doi.org/10.1007/
978-981-96-6767-3_11
6. Singh N, Singh J (2025) Investigation on permeability characteristics and microstructural analysis of concrete made with graphene oxide. Innov Infrastruct Solut 10:280. https://doi.org/10.
1007/s41062-025-02077-9

M. Wang et al.

7. Muthu MS, Perumalla M (2024) Graphene reinforcement in cementitious materials: A comprehensive review of mechanical and durability properties. In: Jayalekshmi BR, Rao KSN, Pavan
GS (eds) Technologies for sustainable buildings and infrastructure. SIIOC 2023. Lecture notes
in civil engineering, vol 528. Springer, Singapore. https://doi.org/10.1007/978-981-97-48440_25
8. Wang M, Tang D, Rudnov VS, Bondarenko SN, Zheng L (2025) Modeling the self-healing
process of concrete. In: Radionov AA, Ulrikh DV, Gasiyarov VR (eds) Proceedings of the 8th
international conference on construction, architecture and technosphere safety. ICCATS 2024.
Lecture notes in civil engineering, vol 565. Springer, Cham. https://doi.org/10.1007/978-3031-80482-3_31
9. Lekshmi MLA, Prakash AJ, Jerlin RJ et al (2024) Graphene oxide: unveiling its chemistry and
its emerging applications (a review). Russ J Gen Chem 94:2413–2431. https://doi.org/10.1134/
S1070363224090202
10. Firoozi AA, Naji M, Dithinde M et al (2021) A review: influence of potential nanomaterials
for civil engineering projects. Iran J Sci Technol Trans Civ Eng 45:2057–2068. https://doi.org/
10.1007/s40996-020-00474-x
11. Raj PVR, Sujatha SJ (2024) Impact of graphene oxide nanoparticles on cement mortar: mechanical, microstructure and durability properties. Russ J Gen Chem 94:2945–2956. https://doi.org/
10.1134/S1070363224110173
12. Mingyuan W, Rudnov VS, Dongyang T, Xinyuan X, Zhenzhi L (2024) The efficiency of
self-healing cementing materials. In: Radionov AA, Ulrikh DV, Timofeeva SS, Alekhin VN,
Gasiyarov VR (eds) Proceedings of the 7th international conference on construction, architecture and technosphere safety. ICCATS 2023. Lecture notes in civil engineering, vol 400.
Springer, Cham. https://doi.org/10.1007/978-3-031-47810-9_9
13. Jiang H, Feng Y, Li L et al (2025) Multi-scale investigation of interfacial enhancement in
KH560-modified carbon fiber reinforced concrete. Mater Struct 58:165. https://doi.org/10.
1617/s11527-025-02689-8

Development of Limit State Functions
for Probabilistic Analysis of Progressive
Collapse in Reinforced Concrete
Buildings
Vu Ngoc Tuyen

Abstract In high-rise buildings utilizing reinforced concrete structures, the loadbearing capacity and energy absorption capability of the structure play a crucial role
in ensuring the safety, stability, and durability of the building. Operational processes
may cause local damages, altering internal forces and triggering progressive collapse
mechanisms, which can lead to the risk of total structural failure. Assessing the probability of progressive collapse is an important tool for risk mitigation, design optimization, and cost reduction in construction. Probabilistic analysis methods based
on reliability models, such as the First-Order Reliability Method (FORM), have
been widely applied but face limitations in handling nonlinear functions and nonstandard probability distributions. Recently, the Advanced First-Order Reliability
Method (AFORM) has been proposed to overcome these limitations, enabling more
accurate estimation of collapse probability in complex problems. This study focuses
on developing appropriate limit state functions to simulate the progressive collapse
process of reinforced concrete buildings, laying the groundwork for applying the
AFORM in subsequent analyses. Additionally, a Robustness Index (RI) is proposed
to measure the structure’s resistance to progressive collapse, based on the tolerance
of local damages and the risk of overall failure. The research results provide both
theoretical and practical tools to assist engineers in enhancing design efficiency, risk
management, and safety assurance for buildings and constructions.
Keywords Progressive collapse · Reinforced concrete · Structural reliability ·
Advanced first order reliability method · Robustness

V. N. Tuyen (B)
Moscow State University of Civil Engineering National Research University, Moscow, Russia
e-mail: ngoctuyennd91@gmail.com
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_5

V. N. Tuyen

1 Introduction
In high-rise buildings using reinforced concrete structures, the strength and energy
absorption capacity of the structure play a crucial role in ensuring the safety, stability,
and durability of the construction. During operation, these structures face various
damaging agents such as wind loads, earthquakes, or abnormal events like fire,
impacts, explosions, or human interventions during design, construction, and operation phases. Notably, these factors can cause local damages within the structure,
leading to a redistribution of internal forces. This redistribution is unpredictable
during the design stage and can trigger a successive failure process of adjacent
components, commonly referred to as progressive collapse [1–3].
In the design and strengthening of reinforced concrete buildings and structures,
predicting the probability of progressive collapse has become a key issue aimed
at minimizing risks, optimizing design, and reducing construction costs. Probabilistic analysis methods, particularly those based on reliability models, have been
developed and widely applied in both practice and recent research. These methods
enable the calculation of collapse probabilities of structural systems under assumed
abnormal loads, thereby assisting engineers in making informed decisions during
design, construction, and operation phases [4–6].
In previous studies, probabilistic methods based on the First-Order Reliability
Method (FORM) have been widely used to assess the risk of failure in structural
systems [7]. Bassam investigated the failure probability of multi-story buildings
subjected to extreme loads using the FORM approach [4]. Saassouh et al. employ
the FORM to model the parametric uncertainty inherent in a deterministic corrosion model for reinforced concrete structures [8]. However, this method is effective
only when dealing with linear limit state functions and standard probability distributions of basic variables. In practice, limit state functions are often nonlinear and
complex, and the basic random variables may follow non-normal distributions such
as Weibull, exponential, or mixed distributions. Therefore, the linearization of the
limit state function at the mean values of variables (x i ), by neglecting higher-order
terms, introduces significant errors in the calculations. This limitation restricts the
applicability of FORM, resulting in predictions that may be inaccurate or fail to
reflect reality [9–11].
To overcome these limitations, recent research has proposed various probabilistic analysis methods. One such method is the Advanced First-Order Reliability Method (AFORM), which provides more accurate handling of nonlinear
limit state functions and non-standard probability distributions. AFORM enables
higher precision in estimating failure probabilities, especially in complex problems
involving multiple random variables and intricate progressive collapse mechanisms
in reinforced concrete structures [12–14].
However, to effectively apply these methods, the development of limit state
functions is a prerequisite. Limit state functions represent the unsafe conditions
of structural systems under rapid deformation rates caused by the sudden failure
of a load-bearing component, reflecting the relationship among random variables

Development of Limit State Functions for Probabilistic Analysis …

such as element strength, load effects, and failure mechanisms. Accurate determination of these functions enhances the reliability of predictions, minimizing errors and
undesirable risks [15–17].
Within the scope of this paper, we focus on constructing appropriate limit state
functions to simulate the progressive collapse process of reinforced concrete buildings. The established limit state functions will serve as a foundation for applying the
AFORM in subsequent studies. The research outcomes will provide a solid theoretical basis and practical tools for structural engineers to predict, assess, and manage
the risk of progressive collapse in reinforced concrete buildings. Consequently, this
contributes to improving design efficiency, reducing losses caused by progressive
failure, and promoting standards and risk control procedures in modern construction.
Additionally, a Robustness Index (RI) has been proposed to measure the robustness against progressive collapse of multi-story reinforced concrete structures, based
on the acceptable level of local failure and the risk of structural collapse.

2 Methods and Materials
2.1 Probability of Progressive Collapse of Reinforced
Concrete Structural System
If each of the previously mentioned off-design actions is considered as a random
event, then the probability of total structural collapse can be expressed by the
following formula [18–20]:
P(C) = P(C|DH )P(D|H )P(H )

(1)

where: C is the random event representing the disproportionate collapse (progressive
collapse) of the reinforced concrete structural system; P(C) denotes the probability
of progressive collapse of the reinforced concrete structure; P(H) is the probability of
occurrence of a specific extraordinary action H; P(D|H) is the conditional probability
of local failure of a load-bearing component D caused by the extraordinary action H;
P(C|DH) is the conditional probability of progressive collapse of the entire structure
initiated by the local failure of the load-bearing component D due to the extraordinary
action H.
The assessment of the probability of progressive collapse in reinforced concrete
structural systems plays a crucial role in helping design engineers determine whether
additional measures are necessary to reduce risks to acceptable levels. Based on
Eq. (1), the probability of progressive collapse can be controlled through three main
factors:
1. Minimizing the probability of occurrence of extraordinary actions on the structure by implementing measures such as tightening building security to prevent

V. N. Tuyen

terrorist attacks, providing fire safety instructions to occupants, prohibiting
the storage of explosives in residential areas, reviewing design documents to
reduce human errors, and disseminating regulations on building operation and
maintenance.
2. Reducing the probability of local failure in key load-bearing components. Key
components are understood as load-bearing elements or connections that are
essential to the overall load-bearing capacity of the structural system. However,
in typical reinforced concrete structures where components are designed for
specific functions, it is often difficult to clearly identify which elements are key
components. This results in increased construction costs when applying measures
to reduce the probability of local failure across all load-bearing components.
3. Minimizing the probability of progressive collapse of the entire structure
following a local failure caused by extraordinary external actions. This can be
addressed during the design stage and thus receives special attention in current
progressive collapse design standards. Several methods for minimizing the probability P(C|DH) have been prescribed and proposed, such as ensuring continuity
and integrity of the structural system, considering the redistribution of internal
forces in adjacent components when local failure occurs, investigating progressive collapse resistance mechanisms often neglected in traditional design—such
as compression arch and catenary action—and accounting for high strain rate
effects of materials, geometric and material nonlinearities.

2.2 Determining Probability P(C|DH) Using a Limit State
Function Model
To determine the probability P(C|DH), it is first necessary to establish a mathematical
model of the limit state of the structure after the load-bearing column is removed.
Within the framework of reliability theory, the strength, stiffness, and stability of
a structure at any given time can be described through a set of characteristic limit
states. These states define the boundary between a safe state (normal operation) and
an unsafe state (failure), with the structure exceeding this boundary considered as
failure.
The mathematical model of the limit state is represented by a limit state function
g(x), which includes the basic variables xi required for describing the structural state.
Figure 1 illustrates the limit state in a two-dimensional case (a state function with
two basic variables). In this instance, the limit state equation (g(x) = 0) is a plane
curve.
Assuming that the limit state function g(x) can be expressed in terms of the
structural resistance (capacity) r and the load effects (Fig. 2), where r and s are
considered random variables represented through the basic variables xi , the safety
limit state will be violated if:
g(x) = r − s ≤ 0

(2)

Development of Limit State Functions for Probabilistic Analysis …

Fig. 1 Determination of the
limit state in the space of
basic variables: I—failure
region; II—safe operation
region

Fig. 2 Determination of the probability of progressive collapse of a structure based on reliability
analysis with random basic variables

where r = gR xR1 , xR2 , ... ; s = gS xS1 , xS2 , ... .
Progressive collapse of a structural system is a stochastic event, and the probability
of its occurrence is calculated as:
P(C|DH ) = P(r − s ≤ 0) = P(g(r, s) ≤ 0) < Pd

(3)

where Pd is the acceptable probability of collapse under blast load. where Pd is the
acceptable predetermined progressive collapse probability.

V. N. Tuyen

2.3 Limit State Function of the Substructure Above
the Removed Column
Experimental and numerical studies have demonstrated that, for multi-story buildings, the area most significantly affected by disproportionate collapse due to the
loss of a first-story load-bearing column is the immediate area above that column.
This indicates that internal force redistribution primarily occurs vertically. Moreover,
the floors immediately above the removed column exhibit nearly identical behavior;
therefore, researchers often propose analyzing the stress–strain state of a representative story. This representative story in a reinforced concrete frame structure is
modeled as a substructure consisting of two beams and three columns, subjected to a
concentrated force at the middle column to idealize the progressive collapse behavior
of multi-story reinforced concrete frames.
Recent experimental research provides a comprehensive overview of the behavior
of this reinforced concrete substructure. Four primary load-bearing mechanisms
have been identified during the deformation process of the structural system. The
initial mechanism to emerge is the classic flexural beam mechanism, characterized
by tensile stress in the reinforcing steel at critical sections remaining at or below
the yield strength and the maximum compressive strain in the concrete compression
zone remaining below the limit value of εc = 0.0035. The critical sections, in the
case of middle column removal, are the sections adjacent to the middle and outer
columns. At this stage, the internal forces in the beam primarily consist of bending
moment and shear force. The flexural capacity of the beam plays the dominant role
in resisting the applied load.
The second stage involves the development of a compressive arch mechanism,
where the compressive strain in the concrete reaches the limit value of εc = 0.0035
and the reinforcing steel yields at the two sections near the outer columns and the
section near the middle column. In the tensile region of the beam, cracks appear
and propagate. The compression zone of the concrete then assumes the shape of an
arch, which distributes the vertical load to the adjacent structural members through
reactions at the beam supports.
The third stage occurs when the displacement of the beam continues to increase,
reducing the effective height of the compressive arch to approximately zero. Consequently, the concrete arch no longer effectively redistributes the external load to
adjacent structural members. At this point, only the top tensile reinforcement of the
end sections remains effective, leading to a partial reduction in the load-carrying
capacity of the reinforced concrete beam.
As the displacement in the beam continues to increase, an increase in the loadcarrying capacity of the beam can be observed. The bottom reinforcement of the
end sections transitions from compression in stages 1 and 2 to tension, forming a
catenary action mechanism. The load-carrying capacity of the catenary mechanism
reaches a maximum when the stress in one of the tensile reinforcing bars reaches the
ultimate tensile strength. The catenary mechanism is the final mechanism resisting
progressive collapse. Its termination begins with the fracture of one of the reinforcing

Development of Limit State Functions for Probabilistic Analysis …

Fig. 3 Behavior of reinforced concrete substructure in progressive collapse analysis

bars, signifying the complete loss of load-carrying capacity of the reinforced concrete
beam.
Based on the aforementioned findings regarding the mechanisms resisting
progressive collapse, the behavior of a reinforced concrete structure in the event of
middle column removal can be simplified and represented by a force–displacement
diagram (Fig. 3).
Referring to Fig. 3, point A corresponds to the flexural beam mechanism at the
onset of yielding in the tensile reinforcement at the edge sections. Point B describes
the load-carrying capacity of the compressive arch mechanism, and point C represents the transition process from the compressive arch mechanism to the catenary
action mechanism. It can be observed that the load-carrying capacity of the substructure partially decreases from point B to C. Finally, point D corresponds to the full
development of the catenary action mechanism in the beam.

2.3.1

Calculating the Structural Resistance Function r (Load-Carrying
Capacity) Based on Maximum Strain Energy

We determine the load-carrying capacity of the structure through the maximum
energy it can accumulate during deformation. Based on the idealized behavior of
the substructure, represented by the polyline OABCD, the maximum stored strain
energy, denoted as Es , is the area bounded by the polyline OABCD, the horizontal
axis, and the vertical line u = uD (Fig. 3). The formula for determining Es is then:
umax

1
1
Pu du = PA uA + (PA + PB )(uB − uA )
2
2

r = Es =
0

V. N. Tuyen

1
1
+ (PC + PB )(uC − uB ) + (PC + PD )(uD − uC )
2
2

(4)

where PA , PB , PC , and PD are the load-carrying capacities of the flexural beam mechanism, compressive arch mechanism, transition mechanism, and catenary mechanism, respectively; uA , uB , uC , and uD are the corresponding displacements of these
mechanisms.

2.3.2

Calculating the Load Effect Function s Based on External Work

The load effect function s can be evaluated through the work done by the dynamic
force P0 applied at the top of the middle column during the displacement of the top
of the column. Assuming that the column loss occurs abruptly, the dynamic force
P0 applied to the system can be considered instantaneous and constant over time
(Fig. 4). The external work done by the dynamic force P0 when the displacement
reaches its maximum value uD is expressed by the following formula:
s = Wu = P0 uD

(5)

The dynamic force P0 is determined by the internal force in the middle column
before failure.

Fig. 4 Determination of external force work in progressive collapse analysis

Development of Limit State Functions for Probabilistic Analysis …

2.4 Limit State Function
From the principle of work and energy, it can be seen that the event of progressive
collapse of the structure occurs when the maximum energy that the system can
accumulate during deformation is less than the work of the dynamic force P0 when
the displacement reaches its maximum value uD . Therefore, we can represent the
limit state function g(.) through the work of the external force and the accumulated
energy using the following formula:
g(r, s) = r − s = Es − Wu
1
1
1
= PA uA + (PA + PB )(uB − uA ) + (PC + PB )(uC − uB )
2
2
2
1
+ (PC + PD )(uD − uC ) − P0 uD
2

(6)

The limit state function g(r, s) includes the following nine random variables: the
internal force in the middle column before failure, the load-carrying capacities of
the flexural beam, compressive arch, transition, and catenary mechanisms, and the
corresponding displacements.
The value of P0 depends on the boundary conditions of the beam under consideration and can be easily determined by applying traditional methods in structural
mechanics, such as the force method. If the beam is simply supported, then the value
of P0 is 5ql/8. Conversely, for a beam with fixed ends, P0 is calculated as ql/2. Where
l is the span of the beam after the middle column is removed. q is the distributed
force acting on the beam and is calculated according to the formula:
q = a(DL + 0.25LL)

(7)

where a is the spacing between the planar frames of the building structure (Fig. 5);
DL and LL are the dead load and live load, respectively.

3 Results and Discussion
In this study, to evaluate the performance of multi-story reinforced concrete buildings
under a column loss scenario, a robustness index (RI) is proposed, as defined by the
following formula:
RI =

Pacceptable − P(C)
P(C)

(8)

V. N. Tuyen

Fig. 5 Multi-story reinforced concrete frame structure with loss of load-bearing column

where Pacceptable is the acceptable probability of progressive collapse, and P(C) is
the probability of progressive collapse of the reinforced concrete structural system,
calculated according to formula (1).
Based on COST Action TU0601, the acceptable probability of failure for the
overall collapse of buildings in seismic regions of the United States is taken as 2 ×
10–5 per year. As there are currently no dedicated studies on the Pacceptable probability,
this study adopts the Pacceptable value from COST Action TU0601.
According to formula (8), the higher the RI value, the greater the robustness of
the structure against progressive collapse in a column loss scenario. The structural
robustness index can be classified into four levels, as shown in Table 1.
To further clarify the proposed calculation method, Fig. 6 presents the probabilistic
analysis procedure for progressive collapse of a multi-story reinforced concrete
building in a sudden column loss scenario in the form of a flowchart.

Table 1 Robustness levels of structures against progressive collapses
Level

Progressive
collapse

Low robustness
level

Medium
robustness level

High robustness
level

RI ≤ 0

0 < RI ≤ 1/3

1/3 < RI ≤ 2/3

2/3 < RI ≤ 1

P(C)

P(C) ≥ 2 × 10–5 /
year

1.5 × 10–5 /year <
RI ≤ 2 × 10–5 /year

1.2 × 10–5 /year <
RI ≤ 1.5 × 10–5 /
year

1 × 10–5 /year < RI
≤ 1.2 × 10–5 /year

Pacceptable

2 × 10–5 /year

Development of Limit State Functions for Probabilistic Analysis …

Fig. 6 Probabilistic analysis
procedure for progressive
collapse of a multi-story
reinforced concrete building
in a sudden column loss
scenario

4 Conclusion
In this study, we developed appropriate limit state functions to accurately simulate the progressive collapse process in reinforced concrete structures of multi-story
buildings, based on the principle of work and energy and the progressive collapse
resistance mechanisms that emerge in the substructure when a load-bearing column
is lost. Furthermore, the proposed robustness index (RI) provides a useful tool for
measuring the resistance of a structure to progressive collapse, based on the level

V. N. Tuyen

of acceptable localized damage and the risk of overall collapse. These results not
only contribute to the refinement of the theoretical framework but also offer practical
value in assisting engineers to optimize design, manage risk, and enhance the safety
of reinforced concrete building structures.
Acknowledgements This work was supported by the Russian Science Foundation grant No. 2449-10010, https://rscf.ru//project/24-49-10010/.

References
1. Kiakojouri F, De Biagi V, Chiaia B, Sheidaii MR (2020) Progressive collapse of framed building
structures: current knowledge and future prospects. Eng Struct 206:110061
2. Abdelwahed B (2019) A review on building progressive collapse, survey and discussion. Case
Stud Constr Mater. https://doi.org/10.1016/j.cscm.2019.e00264
3. Tuyen VN, Ivanovich KV, Vitalyevna FN (2024) Dynamic response model of reinforced
concrete building frame under column removal scenario. Structures 63:106356
4. Izzuddin BA, Pereira MF, Kuhlmann U, Rölle L, Vrouwenvelder T, Leira BJ (2012) Application
of probabilistic robustness framework: risk assessment of multi-storey buildings under extreme
loading. Struct Eng Int 22:79–85
5. Xu G, Ellingwood BR (2011) Probabilistic robustness assessment of pre-northridge steel
moment resisting frames. J Struct Eng 137:925–934
6. Beck AT, da Ribeiro LR, Valdebenito M (2020) Risk-based cost-benefit analysis of frame
structures considering progressive collapse under column removal scenarios. Eng Struct
225:111295
7. Abdelouafi EG, Benaissa K, Abdellatif K (2015) Reliability analysis of reinforced concrete
buildings: comparison between FORM and ISM. Procedia Eng 114:650–657
8. Saassouh B, Lounis Z (2012) Probabilistic modeling of chloride-induced corrosion in concrete
structures using first- and second-order reliability methods. Cem Concr Compos 34:1082–1093
9. Starossek U, Haberland M (2011) Approaches to measures of structural robustness. Struct
Infrastruct Eng 7:625–631
10. Shahraki H, Reyhani A (2024) Reliability based assessment of reinforced concrete columns
under eccenric loads using refined first-order reliability method. Numer Methods Civ Eng
8:63–76
11. Alibrandi U, Koh CG (2015) First-order reliability method for structural reliability analysis in
the presence of random and interval variables. ASCE-ASME J Risk Uncertain Eng Syst Part
B Mech Eng. https://doi.org/10.1115/1.4030911/447486
12. Chen CH, Zhu YF, Yao Y, Huang Y, Long X (2016) An evaluation method to predict progressive
collapse resistance of steel frame structures. J Constr Steel Res 122:238–250
13. Wang Z, Zhang Y, Song Y (2020) An adaptive first-order reliability analysis method for
nonlinear problems. Math Probl Eng 2020:3925689
14. Zhang J, Xiao T, Ji J, Zeng P, Cao Z (2023) First order reliability methods. In: Geotechnical
reliability analysis, pp 35–85
15. Ellingwood BR (2006) Mitigating risk from abnormal loads and progressive collapse. J Perform
Constr Facil 20:315–323
16. Ellingwood BR (2007) Strategies for mitigating risk to buildings from abnormal load events.
Int J Risk Assess Manag 7:828–845
17. Feng DC, Xie SC, Xu J, Qian K (2020) Robustness quantification of reinforced concrete
structures subjected to progressive collapse via the probability density evolution method. Eng
Struct 202:109877

Development of Limit State Functions for Probabilistic Analysis …

18. Feng DC, Xie SC, Li Y, Jin L (2021) Time-dependent reliability-based redundancy assessment
of deteriorated RC structures against progressive collapse considering corrosion effect. Struct
Saf 89:102061
19. El Hajj DM, Desprez C, Orcesi A, Bleyer J (2022) Structural robustness quantification through
the characterization of disproportionate collapse compared to the initial local failure. Eng Struct
255:113869
20. Zhang Q, Zhao YG, Kolozvari K, Xu L (2022) Reliability analysis of reinforced concrete
structure against progressive collapse. Reliab Eng Syst Saf 228:108831

Experimental Determination of Shear
Parameters at the Interface Between
Structures and Soil
I. S. Alirzaev, E. I. Alirzaev, N. S. Sova, G. D. Shmelev, and O. E. Perekalsky

Abstract The paper presents the results of experimental determination of shear
parameters at the contact between structures and foundation soil. In particular, the
conducted research experimentally determined the ultimate shear resistance for a
series of micropiles. The test scheme of the experimental samples was chosen so that,
on the one hand, the main features of the stress state of the prototype were reproduced,
and on the other hand, excessive difficulties in interpreting the experimental results
were avoided. The most common and perhaps the most successful method involves
testing by pulling the pile out of the soil. Based on the experimental results, the values
of the maximum uplift forces (ultimate shear resistance), the stiffness characteristics
of the interface element in the longitudinal direction (along the axis of the structure),
and the stiffness characteristics of the interface element in the normal direction
(perpendicular to the axis of the structure) were established. During the tests, it
was assumed that the uplift force is a random variable and a single experiment is
insufficient for its complete description. To ensure reliability, the data obtained in
the tests were subjected to statistical processing. To eliminate random variations,
six tests were carried out for each sample. The obtained results for the uplift forces
completely contradict the design provisions of the current regulatory documents. The
authors assume that the discrepancy between the provisions of the standards and the
test results is caused by the neglect of the behavior of the contact layer.
Keywords Structure-soil interface · Adhesion · Contact zone · Ultimate-shear
resistance · Interface element

I. S. Alirzaev (B) · N. S. Sova · G. D. Shmelev · O. E. Perekalsky
Voronezh State Technical University, Voronezh, Russia
e-mail: imranalirzaev@yandex.ru
E. I. Alirzaev
LLC StroyGeoProekt, Moscow, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_6

I. S. Alirzaev et al.

1 Introduction. Problem Statement
When solving contact problems for the “soil-structure” system, it is usually necessary
to consider the specific conditions inherent to the problem at hand: material properties, loads, and boundary conditions [1, 2]. As a result, the collection of solved
problems does not yet form a systematic body of knowledge about soil behavior in
the contact zone. There are many obstacles to such systematization: lack of information about the distribution of contact stresses, complexity of the failure mechanism
in the contact zone, and the absence of direct application of elasticity and plasticity
theory. Consequently, in geotechnical problem-solving, one of the key stages involves
assessing potential shear failure at the interface between steel, reinforced concrete,
or wooden structures and soil. This requires determination of ultimate shear resistance forces, which depend on the interface’s friction and adhesion characteristics
[3–10]. According to [1, 2], the frictional and adhesive forces at the “structure-soil”
interface should be determined based on: the soil’s strength parameters (angle of
internal friction and cohesion), hydrogeological conditions of the construction site,
structural materials, and installation technology. However, this approach remains
approximate as it disregards the stress–strain state of interacting elements. Moreover, since loading causes significant degradation of soil within the contact zone,
the system should be considered as an interaction between three components: soil,
contact layer, and structure (Fig. 1). The essence of the “soil-contact layer-structure”
model lies in identifying a contact layer comprising soil subjected to high stress
concentrations. This conceptual separation is justified by the fact that soil failure
mechanisms, particularly plastic deformations, typically develop within a narrow
zone. However, the defined contact layer parameter lacks full determinacy due to the
absence of precise thickness measurements. In reality, the contact layer thickness is
not constant and varies depending on stress conditions within the soil mass.
The requirement for defining interface elements and their determination methods
is explicitly addressed in current regulatory documents. Specifically, Clause 7.7.10
[2] stipulates that the concentration of shear deformations and plastic soil flow along
the “pile-soil” boundary should be modeled using special interface elements. For

Fig. 1 Interaction of three components: soil, contact layer and structure. a Soil-structure system;
b soil; с contact layer; d structure

Experimental Determination of Shear Parameters at the Interface …

Fig. 2 Interaction between three components: soil, interface, and structure. a Initial soil-pile
system; b soil; с interface; d pile

this purpose, a dedicated contact interface element is introduced between the soil
and structure. Consequently, the original “soil-structure” system is represented by
three components: the soil mass, interface, and structure (Fig. 2).
According to Clause B.4 of this standard, when analyzing piles and pile groups
using continuum-based numerical software, interface elements must be incorporated along pile shafts. The properties of these interface elements shall be assigned
considering the pile working condition coefficient specified in Table 7.6 [2].
Another regulatory document [1] specifies the strength parameters for interface
elements in cohesionless soils as follows:
• The adhesion component is taken as zero;
• The soil-structure friction angle is calculated as δ = γk ϕ, where ϕ—is the soil’s
internal friction angle and γk is a reduction factor according to Table 9.1 [1].
Typical values of this coefficient are provided in Table 1.
In modern software systems like Midas GTS NX and PLAXIS, the contact layer is
simulated using interface elements. These elements reduce the soil’s strength parameters at the boundary between the structural component and the soil mass [2]. The
reduction is controlled by the Rinter coefficient, with possible values ranging from
0.01 to 1.0.
The determination of Rinter proves challenging as this parameter depends on
multiple variables. Evaluating the stress–strain state of the contact zone is challenging, as it requires accounting for the characteristics of several complex interacting
processes. The main task here is to determine the type of contact (rigid or sliding)
Table 1 Values of the reduction factor γk
Material of the
structure

Installation technology and special conditions

γk

Concrete, reinforced
concrete

Cast-in-place gravity and flexible retaining walls, dry-cast.
Monolithic foundations

0.67

In fine-grained and silty water-saturated sands

Metal, wood
Any

In other soil types

0.33

When vibration loads act on the foundation

I. S. Alirzaev et al.

depending on the development of plastic deformations. So far, this problem has no
direct solution, and only approximate calculation methods and empirical formulas
are used. The development of plastic deformations in the contact zone leads to a
decrease in shear stresses, which can be regarded as a gradual transition from rigid
to sliding contact.
Consequently, geotechnical practice typically adopts Rinter values from regulatory documents [1, 2] based on: structural material, installation technique, soil type,
and loading conditions—rather than calculating them directly. These empirically
derived interface element values neglect numerous factors including contact area,
structural stiffness, depth-dependent variations in deformation/strength properties,
among other considerations.
On the other hand, the value of i Rinter s usually assumed to be constant along the
entire height for each engineering–geological element. This approach is incorrect, as
the transition of soil to the plastic stage occurs non-uniformly. The main issue here
is the variability of transverse (normal) pressure, which changes during the mutual
displacements of the soil and structures. Therefore, it is necessary to account in some
way for the non-uniform distribution of this parameter along the height.
It is not yet possible to obtain direct data on the stress–strain state of the contact
zone; therefore, one has to rely on approximate estimates based on test results.
This study focuses on refining the parameters of the “structure-soil” contact zone
under static loading conditions. The key strength and stiffness characteristics of
interface elements, as implemented in the Midas GTS NX software package, are
presented in Table 2.
The determination of the parameters listed in Table 2 is a key requirement when
solving contact problems for the “soil–structure” system. To satisfy this requirement,
the range of considered factors had to be limited (to the stiffness characteristics of the
interface element in the longitudinal and transverse directions). The physical basis
of the contact zone lies in the properties of soil in small volumes. The properties
of the contact layer are usually compared with those of concrete in standard-size
specimens intended for laboratory tests. However, the properties of soil strongly
depend on the absolute size of the specimen, and it cannot be assumed that the same
strength characteristics will be realized in the contact zone. Predictions of concrete
behavior in the contact layer should be made based on its properties in volumes with
characteristic dimensions on the order of millimeters.
In this study, the ultimate shear resistance (Ultimate Shear Force) for various
structural configurations was determined experimentally.
Table 2 Strength and stiffness characteristics of interface elements
Name

Description

Ultimate shear force

Maximum shear capacity at interface

Shear stiffness modulus Shear stiffness modulus (Tangential stiffness along the structural axis)

Experimental Determination of Shear Parameters at the Interface …

2 Experimental Procedure
The “soil–steel” contact pair is common, which makes its study important. Moreover,
due to its well-defined nature and the possibility of observing the contact surface,
friction can serve as a simplified model for studying the mechanism of soil–steel
contact, which in many respects is similar for both adhesion and friction. In addition,
the shear resistance of the “soil–steel” pair under friction has a complex dependence
on the properties of the contacting bodies, as well as on the applied normal stresses,
the contact area, and the shape of the steel elements. Experimental studies of the
contact interaction of pile foundations with soil, as with any other structure, require
at least a general understanding of the mechanism of soil contact resistance. Despite
numerous studies in this field and the investigation of friction for various material
pairs [5–8], regulatory documents treat friction as a stationary process in which the
resistance does not change during mutual displacement of the contacting bodies,
remaining proportional to the normal pressure.
The main difficulty of experimental studies for contact problems lies in the variety
of factors that influence the parameters being determined. A series of tests was
conducted to determine the ultimate shear resistance. Four pile specimens were fabricated for this investigation (Fig. 3). The test specimens consisted of steel tubes with
welded steel plates. In the experiments, the nominal contact area and the effect of
the transverse profile of the steel element surfaces were varied. The influence of the
type of surface treatment (grinding) was not investigated.
Before the tests, the strength characteristics of the soils were determined: the
internal friction angle and cohesion.
The test setup for the specimens was chosen so that, on the one hand, it reproduced
the main features of the stress state of the prototype, and on the other hand, it did not
create excessive difficulties in interpreting the test results. The most common and,
perhaps, the most effective method involves testing the pile for pullout from the soil.
The test setup is shown in Fig. 4.
During the tests, it was assumed that the pullout force is a random variable and that
a single test is insufficient for its full characterization. To ensure reliability, the data

Fig. 3 Test specimens for experimental investigation

I. S. Alirzaev et al.

Fig. 4 Schematic of the pullout test setup

obtained during the tests were subjected to statistical processing. To eliminate random
variations, six tests were carried out for each specimen. The described method will
likely be replaced in the near future by establishing direct relationships between the
pullout force and all key factors based on multifactor analysis.
The piles were subjected to pullout testing using a hydraulic jack mounted on
a beam supported by independent columns (Fig. 5). A distribution beam with tie
rods was attached to the jack, connecting to a crosshead that transferred the load
to the pile’s bearing plate. Pile displacements were measured using dial gauges.
Each pile was loaded with progressively increasing pullout forces. Load increments
were maintained until settlement stabilization was achieved, defined as displacement
increments below 0.1 mm during the final 30-min interval. All tests were continued
until pile failure (“pullout rupture”) occurred, identified by a sharp inflection point
on the load–displacement curve at critical load–displacement curve at critical load.
At critical load, the displacement gauges registered sharp, non-decelerating movement progression while the jack’s pressure gauge maintained a constant reading—the
ultimate load capacity.
The experimental results quantified the maximum pullout forces. The specimens’
geometric parameters and test outcomes are summarized in Table 3.

3 Analysis of Results
The experimental findings demonstrate fundamental discrepancies with design provisions of current regulatory standards. Specifically, Clause 7.2.7 [2] stipulates that the
ultimate tensile capacity of driven, pressed, and shell piles (installed without soil

Experimental Determination of Shear Parameters at the Interface …

Fig. 5 Specimen testing procedure
Table 3 Geometric characteristics and test results of specimens
Specimen

Critical load Specimen

Critical load

1480 Н

2630 Н

2800 Н

1620 Н

I. S. Alirzaev et al.

removal) should be calculated as:
Fdu = γc u

γRf fi hi

(1)

where γc - the pile working condition coefficient in the soil, u - the perimeter of the
pile shaft cross-section,
γRf is the soil working condition coefficient on the pile shaft surface, which
depends on the method of borehole formation and concreting conditions, fi is the
design resistance of the i-th soil layer on the pile shaft surface, and the thickness of
the i-th soil layer.
According to this formula, for example, when a pile’s perimeter is tripled, its
bearing capacity increases by the same factor (three times). However, our test results
contradict this: when we tripled the perimeter, the capacity increased by only 2800/
1480 = 1.89 times (Table 3). This shows that increasing the perimeter actually
reduces the pile’s “efficiency.” Comparing Specimens 1 and 3 (Table 3), we see that
maximum efficiency requires maintaining optimal spacing between piles. Furthermore, by comparing Specimens 1 and 4 (Table 4), we confirmed that cross-sectional
shape significantly affects pullout resistance.
In our opinion, the discrepancy between regulatory requirements and test results
is caused by not accounting for the contact layer’s behavior. To illustrate the contact
layer’s effect on bearing capacity, let’s compare the perimeters of: a single pile
with diameter d versus two piles with half the diameter (d/2). We’ll perform this
comparison twice: first without considering the contact layer, and then including it.
The contact layer thickness δ remains the same in all cases, as it depends solely on
the pile material, installation method, and soil type.
As evident from the table, the perimeter of a single pile (diameter d) equals
the combined perimeter of two half-diameter piles (d/2) when ignoring the contact
layer, whereas these values differ when accounting for the contact layer. The resulting
perimeter difference (2πδ) in the second case increases the combined bearing capacity
Table 4 Determination of pile perimeters
Configuration

Perimeter calculation
Single pile (diameter d)

Two piles (diameter d/2)

Perimeter
difference
u2 − u1 = 0

Piles without
contact layer

u1 = π d

u2 = 2π(d /2) = π d
u2 − u1 =
2π δ

Piles with
contact layer

u1 = π(d + 2δ)

u2 = 2π(d /2 + 2δ) = π(d + 4δ)

Experimental Determination of Shear Parameters at the Interface …

of two smaller piles compared to a single larger pile. Consequently, optimizing pileto-soil adhesion requires limiting the diameter of tension-loaded piles in foundation
design.
We reiterate that this phenomenon remains unaddressed in current design codes.
However, technical literature partially documents this effect. For instance, reference
[11] states: “During pile driving, high pressures create a compacted soil ‘envelope’
around the shaft that moves downward with the pile. This envelope, typically 3–
10 mm thick depending on pile material, soil type, and installation method, enhances
shaft resistance. A similar envelope forms around cast-in-situ piles due to surface
irregularities and concrete penetration into surrounding soil.”
The research presented in this paper constitutes a problem-formulating study and
does not purport to comprehensively address all aspects of soil-structure interface
behavior. The conclusion about the behavior of the contact zone made in this work
may, however, be premature. Comprehensive information on the behavior of the
contact layer will likely be obtained only after conducting full-scale tests, i.e., after
eliminating the scale factor (volume effect). The specificity of the contact problem
under consideration is that it simultaneously involves soil strength in very different
volumes, and the scale factor cannot be ignored. In addition, due to the presence of the
scale effect, caution must be exercised when using the finite element method, since
when replacing the given volume with smaller volumes, it is necessary to carefully
select the Rinter values to account for the scale effect.
It is interesting to compare the problem of soil–pile contact with the problem of
reinforcement–concrete interaction in reinforced concrete structures. At first glance,
these seem to be two different problems from entirely unrelated fields. However, the
physical nature of the phenomena in both cases is the same.
In the problem of reinforcement–concrete contact, a similar phenomenon is also
of interest—the influence of bar diameter on their bond with concrete. The answer
to this question can be found in textbook [12]: “When designing reinforced concrete
elements, the diameter of tensioned bars should be limited.”
Over time, it will probably be possible to answer these questions.

4 Conclusions
Based on the conducted research, the following conclusions can be drawn:
• Experimental results for the ultimate shear resistance of micropiles fundamentally
contradict the design provisions of current regulatory standards
• The authors conclude that this discrepancy stems from regulatory standards’
failure to account for the mechanical behavior of the contact layer at the
soil-structure interface
• For piles under tensile loading, increasing the perimeter reduces their load-transfer
efficiency. Consequently, to optimize pile-soil adhesion in foundation design, the
diameter of tension-loaded piles must be restricted.

I. S. Alirzaev et al.

References
1. SP 22.13330.2016 (2016) Foundations of buildings and structures. Moscow
2. SP 24.13330.2021 (2021) Pile foundations. Updated edition of SNiP 2.02.03-85. Moscow
3. Kotov VL, Balandin VV, Lomunov AK (2010) Evaluation of surface friction effects in nonstationary contact between structural elements and sandy soil. Probl Strength Plast 72:137–141
4. Sultanov KS (1993) Patterns of underground structure-soil interaction during relative shear.
Appl Mech 29(3):60–68
5. Ter-Martirosyan AZ, Sidorov VV, Almakaeva AS (2019) Features and challenges in determining strength at soil-structure interfaces. Geotechnics 11(4):30–40
6. Haeri H, Sarfarazi V, Zhu ZM, Fatehimarji M (2019) Investigation of shear behavior of soilconcrete interface. Smart Struct Syst 23(1):81–90
7. Eid HT, Amarasinghe R, Rabie KH, Wijewickreme D (2015) Residual shear strength of finegrained soils and soil-solid interfaces at low effective normal stresses. Can Geotech J 52(2):198–
210
8. Mohammadi A, Ebadi T, Eslami A (2017) Shear strength behavior of crude oil contaminated
sand-concrete interface. Geomech Eng 12(2):211–221
9. Isaev ON, Sharafutdinov RF (2020) Studies of soil shear resistance at structure contact surfaces.
Bases, Found Soil Mech 2:23–30
10. Kupchikova NV (2018) Experimental studies of pile groups with stepped surface enlargements.
Constr Reconstr 1:45–54
11. Glushkov GI (1977) Design of subsurface structures. Stroyizdat, Moscow, p 295
12. Baikov VN, Sigalov EE (1991) Reinforced concrete structures. Stroyizdat, Moscow, p 767

Assessment of the Influence
of a Construction Joint
on the Deformability of a Monolithic
Reinforced Concrete Floor Slab
B. K. Dzhamuev and I. Z. Kalkan

Abstract This article explores the influence of construction joints on the stress–
strain behavior of monolithic reinforced concrete floor slabs in frame buildings. A
200 mm thick slab without joints, placed within a 6 × 6 m bay frame structure, is used
as the reference model. The study is based on eleven spatial models that differ in the
location of the “cold” construction joint, while material properties remain constant:
concrete of compressive strength class B35 and A500C reinforcement with a 12 mm
diameter arranged in a 300 × 300 mm grid. The findings show that the presence of a
construction joint can increase slab deflection by up to 1.26 times, depending on its
position. The most effective joint location is in zones of minimum bending moments,
as regulated by Russian construction codes, where its impact on the stress–strain state
is minimal. The results can be applied in structural analysis and in refining regulatory
approaches to the placement of construction joints in monolithic reinforced concrete
floor slabs.
Keywords Monolithic concrete slab · Construction joint · Numerical modeling ·
Elastic modulus · LIRA-SAPR Software · Structural deformability · Vertical
deflection · Crack formation

1 Introduction
1.1 Prerequisites for Considering the Influence
of Construction Joints on Structural Systems
Modern monolithic construction practices–ranging from high-rise residential
complexes to large-scale transport infrastructure–must combine high-speed execution with enhanced reliability requirements. Under these conditions, the construction
B. K. Dzhamuev (B) · I. Z. Kalkan
National Research Moscow State University of Civil Engineering (MGSU), Moscow, Russia
e-mail: dbk-07@mail.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_7

B. K. Dzhamuev and I. Z. Kalkan

joint (CJ) becomes an essential structural element: it enables staged placement of
concrete, facilitates batching across work shifts, and ensures technological flexibility of the project. However, each concreting boundary creates a potential zone
of weakness, where bonding between the “old” and “new” concrete occurs, tensile
stresses are localized, and the risk of crack development increases. Consequently,
neglecting construction joints in structural analysis leads to an artificial underestimation of deformations and an overestimation of the structural load-bearing capacity
compared to actual conditions [1]. As a result, structures with and without CJs are
often treated identically in calculations, disregarding the negative impact of the joint
on strength and deformability.
A key milestone in the development of regulations related to construction joints
was the inclusion of specific requirements in design codes–first in SNiP III-15-76
[2], and later in SNiP 3.03.01-87 [3]. These documents clearly defined:
• permissible zones for joint placement (within 1/4 to 1/3 of the span of structural
elements);
• surface preparation methods prior to resuming concreting (cleaning, moistening,
and application of a cement slurry);
• the minimum allowable concrete strength before subsequent placement (e.g.,
achieving compressive strength sufficient to ensure proper bonding).

1.2 National and International Codes Regulating
Construction Joint Implementation and Analysis
In the subsequent decades, with the development of the regulatory framework during
the post-Soviet period, the requirements were significantly revised. The provisions
of the original SNiP were updated and incorporated into new codes of practice,
such as SP 70.13330.2012 [1] (an updated edition of SNiP 3.03.01-87 [3]) and SP
63.13330.2018 [4]. These documents not only reaffirmed the fundamental principles
but also introduced quantitative criteria for assessing concrete strength in the joint
zone (e.g., not less than 1.5 MPa), as well as outlined procedures for surface curing
during construction pauses.
Meanwhile, in international engineering practice, the approaches to the design
and implementation of construction joints have also evolved. Since 1995, the United
States has applied a specialized standard–ACI 224.3R [4]–which provides a detailed
classification and design methodology for both construction and working joints. In
the European regulatory framework, relevant provisions are found in Eurocode 2
[5] and its national annexes [6], where the influence of joints on crack resistance,
durability, and overall structural deformability is considered.
Thus, the concept of the construction joint has evolved from a forced technological necessity into a structurally and analytically significant element formally
integrated into the regulatory field. Today, the construction joint is regarded as a
potentially vulnerable zone requiring a systematic and deliberate approach at all

Assessment of the Influence of a Construction Joint …

stages of the building life cycle–from design and analysis to implementation and
quality control. The modern regulatory framework accumulates consolidated engineering experience, transforming the construction joint from a mere line on a drawing
into a critical component of structural reliability.

1.3 National and International Research on the Influence
of Construction Joints on the Behavior of Reinforced
Concrete Structures and Their Results
Experimental studies confirm that neglecting construction joints leads to a systematic
overestimation of structural stiffness. For example, in study [7], the authors observed
a 15–25% increase in actual slab deflections in the presence of vertical construction
joints and recommended reducing the modulus of elasticity to 35% of its nominal
value. A study led by A. A. Koyankin [8] demonstrated a decrease in the load-bearing
capacity of beams by nearly 50% when joint formation technology was violated,
and by 30% even when the joint was properly executed. Numerous domestic and
international articles and dissertations [9–12] report that even when a construction
joint is correctly installed, the structural strength is still significantly reduced.
In study [13], alkali-activated slag aggregates were investigated for use in beam
construction joints, enabling the mechanical characteristics of elements with joints
to approach those of fully monolithic structures. It is important to note that with
this method, stiffness was reduced by only 8%, and by 11.5% when expanded metal
mesh was used. When inclined construction joints were combined with preliminary
coating using an alkali-activated binder, the stiffness reduction was limited to just 7%.
Figure 1 presents a schematic of a construction joint formed using alkali-activated
slag mixtures.
Thus, the topic of the influence of construction joints on structural performance
remains highly relevant and significant. This is evidenced both by the existence of
codes and standards regulating their placement and treatment during construction,
and by the growing body of scientific publications by various authors dedicated to
this issue.
Fig. 1 Construction joint
formation using
alkali-activated slag
aggregates

B. K. Dzhamuev and I. Z. Kalkan

2 Models and Methods
The objective of this study is to assess the influence of construction joints on the structural analysis of a monolithic reinforced concrete floor slab in a frame building. As
part of the research, analytical models were developed and evaluated with construction joints placed outside the zones specified by the regulatory documents of the
Russian Federation [1, 4].
The subject of the study is a computational model of a monolithic reinforced
concrete slab, with construction joints positioned in various zones of the slab. The
considered model represents a slab with rigid fixity at the corners, which reflects
the actual behavior of a monolithic reinforced concrete floor slab within a frame
structure featuring a 6 × 6 m grid and four reinforced concrete columns, each with
a cross-section of 600 × 600 mm, located at the grid corners.
To ensure accurate modeling of boundary conditions, the computational domain
was extended beyond the support lines by half the span length on each side (3 m),
with appropriate constraints applied. This allowed for a more realistic simulation of
the slab’s spatial behavior.
A triangular mesh with a 300 × 300 mm step was used to construct the numerical
model. This choice is justified, as further mesh refinement was found to influence
calculation accuracy by less than 5%, making it inefficient. The triangular mesh,
element contours, mesh steps and dimensions, along with auxiliary numerical labels,
are shown in Fig. 2.
The study examines 11 variants of construction joint placement, ranging from the
central axis of the structural bay to the support axes. A slab model without a construction joint was selected as the reference configuration. This set of configurations is
sufficient due to the symmetry of the structure, which allows for generalization of
the results obtained.
The construction joints are located along the interfaces of finite elements corresponding to the upper line numbers 21–31. The lower numbers represent their
symmetric counterparts. The numbering is shown in Fig. 2. The configuration names
used in the text correspond to the position of the construction joint according to the
lower row of numbers.
The slab thickness is 200 mm. Concrete of class B35 is used as the primary
material, with reinforcement of class A500C, 12 mm in diameter, placed in a 300 ×
300 mm grid, and a concrete cover of 50 mm. All material properties were adopted
in accordance with current regulatory documents of the Russian Federation [1, 4].
The study is focused on a comparative analysis of different construction joint
layouts. Therefore, among all the normative loads, only the self-weight of the
structure was considered, as it is the most representative for evaluating the slab’s
deformability and stress–strain behavior [14].
For modeling the nonlinear properties of materials, deformation laws were applied
in accordance with the documentation of the LIRA-SAPR software package:
• for the primary material (B35 concrete with natural curing) — deformation law
No. 21;

Assessment of the Influence of a Construction Joint …

Fig. 2 Computational model with numbering

• for reinforcement—deformation law No. 14;
• for concrete in the area of construction joints—deformation law No. 11, which
allows manual adjustment of the modulus of elasticity without altering other
material properties. This enables accurate simulation of weakened zones resulting
from staged concreting.
Ultimate compressive strain of concrete ε(−) = − 0.002, ultimate tensile strain
of concrete ε(+) = 0.0001 adopted in accordance with SP 63.13330.2018 [4]. Values
σ(−) and σ(+) are assigned automatically based on the selected concrete class and
type.
For the reinforcing material, the parameters of the nonlinear deformation law
should be adopted in accordance with SP 63.13330.2018 [4] εs0 = 0.002175, εs2 =
0.025. To achieve the required strain value εs0 , it is necessary to set the yield stress σs
as close as possible to 435 MPa, to achieve the required strain value εs0 . Accordingly,
when σ s = 434.999 МПа, εs0 = 0.002175.
Particular attention was paid to the numbering of nodes and elements, as the analysis of all 11 configurations with construction joints and one reference configuration
without a joint was performed by exporting displacement values in CSV format.
In practical design, construction joints are typically placed at 1/4 to 1/3 of the span
length, which complies with the requirements of SP 70.13330.2012 [1]. Based on

B. K. Dzhamuev and I. Z. Kalkan

the analysis of the computational models developed in this study, it was confirmed
that the zones of zero bending moments indeed fall within this range.
According to scientific publications by Malakhova [15–18], as well as those by
Tamrazyan [19] and his joint work with Kabantsev [20], the reduction factor for the
modulus of elasticity of concrete in the construction joint zone may range from 0.2
to 0.4.
While further research is required to determine an accurate value of this factor, a
value close to 0.3 is used in this study as a worst-case approximation. It is also important to note that an idealized slab cell model is used, as factors such as workmanship
quality, aging of materials, and long-term property changes are not accounted for.
The maximum modulus of elasticity reduction for B35 concrete with a reduction
factor of 0.3 yields Eb35,red = 10 355 823 kN/m2 , The closest available concrete class
in terms of modulus is B5, with E b5 = 13 042 840 kN/m2 , which was adopted for the
calculations. The resulting reduction coefficient is 0.378, or 37.8% of the original
value.
For further analysis, it should be noted that under the given conditions, the nominal
configuration without a construction joint exhibited no cracking, and the maximum
deflection was 1.667 mm.

3 Research Results and Their Analysis
The analysis of results is based on key indicators of the stress–strain state, such
as crack formation and deflections. Consequently, the structural analysis must be
performed based on internal forces.
Following the calculations, deflection values were obtained for all 12 configurations, including the reference model without a construction joint. Figures 3 and
4 present diagrams that clearly illustrate the structural behavior depending on the
location of the construction joint.

Fig. 3 Structural deflections along the construction joint line, mm

Assessment of the Influence of a Construction Joint …

Fig. 4 Structural deflections perpendicular to the construction joint line, mm

According to the calculations and analysis, the farther the construction joint is
shifted from the zone of zero bending moments toward the mid-span, the greater the
deflection becomes. Among all configurations, the maximum deflection was recorded
at 2.103 mm, which is 1.26 times greater than the nominal value. Moreover, shifting
the joint closer to the supports also significantly worsens the behavior—resulting in
a deflection of 1.833 mm, which is 1.1 times higher than that of the configuration
without a joint. The smallest deviation in maximum deflection was observed along
lines 3 and 5 (corresponding to lines 28 and 26, respectively), as shown in Figs. 3
and 4.
However, when analyzing Fig. 3, it should be noted that the slightly higher deflection in configuration 4 (1.741 mm) compared to configuration 5 (1.735 mm) does not
imply that placing the joint along line 5 (26) has a more favorable effect. In fact, the
deflection pattern along the axis perpendicular to the construction joint line is more
favorable in configuration 4.
It is also important to note that the location of the zero bending moment is approximately 1.2 m from the support, which corresponds to 1/5 of the span length. However,
in this study, only the self-weight of the structure was considered among the load
types prescribed by the standards [14]. Under increased loading, the zero-moment
zone would likely shift toward the span center. In any case, the commonly applied
design rule of placing construction

B. K. Dzhamuev and I. Z. Kalkan

joints within 1/4 to 1/3 of the span in horizontal elements is indeed consistent
with Russian regulations and design practice [1, 4].
Additionally, for comparative analysis, the built-in Pearson correlation coefficient
function in MS Excel was used to quantify the total deviation in deflection values
relative to the nominal configuration. The Pearson correlation coefficient measures
the strength and direction of a linear relationship between two quantitative variables.
Its value ranges from − 1 to 1, where − 1 indicates a perfect inverse linear correlation,
0 denotes no linear relationship, and 1 represents a perfect direct linear correlation.
Table 1 presents the correlation coefficients calculated for the deflection values
shown in Fig. 4. However, using this method to track linear correlations between
deflection values from different configurations that exhibit similar deformation
behavior is not methodologically appropriate, as the correlation will be ideal or
nearly ideal.
In our case, only the position of the construction joint was varied, while all other
parameters of the model remained unchanged. This is confirmed by the nearly perfect
linear correlation observed in the deflection values across different configurations in
Fig. 3.
The crack analysis revealed the following:
• when the joint is shifted toward the supports (lines 0–2), radial cracks form along
the top surface in the support zone, while the bottom surface remains intact; see
Fig. 5a;
• within the range of 0.15–0.33L (lines 3–6), cracking is limited to short, superficial
surface cracks without visible opening, see Fig. 5b, which is nearly identical to
the results obtained from the configuration without a construction joint;
• when the joint is shifted toward the mid-span (lines 7–10), long cracks appear first
on the top surface, followed by the bottom surface; the spacing between cracks
reduces to 9–18 cm, indicating an increase in tensile stresses; see Fig. 5c.
Thus, the analysis of the 11 configurations confirms that the correct placement of
the construction joint can virtually eliminate its impact on the load-bearing capacity
and stiffness of the slab, whereas improper placement leads to a significant increase
in deflections and the development of cracks.

− 1.619

− 1.590

− 1.545

− 1.488

− 1.427

− 1.366

− 1.315

− 1.278

− 1.263

− 1.273

− 1.310

− 1.372

− 1.455

− 1.554

− 1.660

− 1.766

− 1.864

− 1.948

− 2.009

− 1.639

− 1.608

− 1.560

− 1.500

− 1.434

− 1.368

− 1.309

− 1.264

− 1.238

− 1.235

− 1.257

− 1.302

− 1.366

− 1.444

− 1.530

− 1.615

− 1.694

− 1.760

− 1.807

2 (9)

3 (8)

4 (7)

5 (6)

6 (5)

7 (4)

8 (3)

9 (2)

10 (1)

11 (0)

12 (1)

13 (2)

14 (3)

15 (4)

16 (5)

17 (6)

18 (7)

19 (8)

20 (9)

− 1.971

− 1.914

− 1.835

− 1.741

− 1.639

− 1.536

− 1.442

− 1.362

− 1.303

− 1.268

− 1.260

− 1.277

− 1.315

− 1.368

− 1.429

− 1.491

− 1.548

− 1.594

− 1.623

− 1.633

− 1.629

− 1.649

0.807

2 (29)

Deflection by line no. mm

0.787

1 (30)

1 (10)

0.844

0 (31)

Line no.

Corr. Coeff

CJ position no

Table 1 Deflections for Fig. 4, mm

− 1.713

− 1.672

− 1.614

− 1.543

− 1.467

− 1.391

− 1.322

− 1.267

− 1.230

− 1.215

− 1.225

− 1.256

− 1.305

− 1.368

− 1.437

− 1.506

− 1.568

− 1.617

− 1.649

− 1.660

0.961

3 (28)

− 1.722

− 1.683

− 1.626

− 1.556

− 1.479

− 1.402

− 1.332

− 1.275

− 1.237

− 1.221

− 1.229

− 1.259

− 1.308

− 1.370

− 1.439

− 1.507

− 1.569

− 1.617

− 1.649

− 1.659

0.964

4 (27)

− 1.713

− 1.672

− 1.614

− 1.543

− 1.467

− 1.391

− 1.322

− 1.267

− 1.230

− 1.215

− 1.225

− 1.256

− 1.305

− 1.368

− 1.437

− 1.506

− 1.568

− 1.617

− 1.649

− 1.660

0.961

5 (26)

− 1.741

− 1.692

− 1.628

− 1.553

− 1.473

− 1.394

− 1.323

− 1.266

− 1.228

− 1.212

− 1.221

− 1.252

− 1.301

− 1.363

− 1.432

− 1.501

− 1.563

− 1.612

− 1.644

− 1.654

0.844

6 (25)

− 1.800

− 1.740

− 1.666

− 1.583

− 1.495

− 1.410

− 1.333

− 1.271

− 1.230

− 1.212

− 1.218

− 1.247

− 1.295

− 1.356

− 1.424

− 1.493

− 1.554

− 1.603

− 1.634

− 1.645

0.787

7 (24)

− 1.886

− 1.813

− 1.726

− 1.631

− 1.532

− 1.438

− 1.353

− 1.284

− 1.237

− 1.214

− 1.216

− 1.242

− 1.288

− 1.348

− 1.414

− 1.481

− 1.542

− 1.590

− 1.621

− 1.631

0.807

8 (23)

− 1.982

− 1.896

− 1.797

− 1.689

− 1.580

− 1.475

− 1.381

− 1.304

− 1.250

− 1.222

− 1.220

− 1.242

− 1.285

− 1.342

− 1.407

− 1.473

− 1.532

− 1.579

− 1.610

− 1.620

0.961

9 (22)

− 2.061

− 1.967

− 1.860

− 1.744

− 1.626

− 1.512

− 1.411

− 1.327

− 1.267

− 1.233

− 1.227

− 1.246

− 1.286

− 1.340

− 1.403

− 1.467

− 1.525

− 1.572

− 1.602

− 1.612

0.964

10 (21)

(continued)

− 1.656

− 1.624

− 1.575

− 1.512

− 1.442

− 1.372

− 1.309

− 1.257

− 1.224

− 1.213

− 1.224

− 1.257

− 1.309

− 1.372

− 1.442

− 1.512

− 1.575

− 1.624

− 1.656

− 1.667

0.961

No CJ

Assessment of the Influence of a Construction Joint …
83

1 (30)

− 2.045

− 2.053

− 2.032

− 1.984

− 1.915

− 1.830

− 1.736

− 1.644

− 1.560

− 1.502

− 1.485

− 1.501

− 1.536

− 1.588

− 1.651

− 1.720

− 1.788

− 1.849

− 1.898

− 1.929

− 1.939

0 (31)

− 1.833

− 1.835

− 1.814

− 1.772

− 1.714

− 1.645

− 1.572

− 1.501

− 1.440

− 1.395

− 1.383

− 1.418

− 1.485

− 1.568

− 1.661

− 1.755

− 1.846

− 1.924

− 1.985

− 2.024

− 2.037

CJ position no

21 (10)

22 (9)

23 (8)

24 (7)

25 (6)

26 (5)

27 (4)

28 (3)

29 (2)

30 (1)

31 (0)

32 (1)

33 (2)

34 (3)

35 (4)

36 (5)

37 (6)

38 (7)

39 (8)

40 (9)

41 (10)

Table 1 (continued)

− 1.853

− 1.843

− 1.815

− 1.771

− 1.715

− 1.655

− 1.595

− 1.542

− 1.502

− 1.479

− 1.475

− 1.492

− 1.534

− 1.604

− 1.690

− 1.779

− 1.863

− 1.933

− 1.982

− 2.007

− 2.003

2 (29)

− 1.682

− 1.672

− 1.642

− 1.596

− 1.538

− 1.475

− 1.412

− 1.357

− 1.316

− 1.295

− 1.297

− 1.323

− 1.370

− 1.435

− 1.510

− 1.584

− 1.643

− 1.687

− 1.720

− 1.737

− 1.735

3 (28)

− 1.720

− 1.710

− 1.680

− 1.634

− 1.576

− 1.512

− 1.448

− 1.392

− 1.349

− 1.325

− 1.323

− 1.342

− 1.381

− 1.434

− 1.497

− 1.560

− 1.619

− 1.673

− 1.714

− 1.738

− 1.741

4 (27)

− 1.682

− 1.672

− 1.642

− 1.596

− 1.538

− 1.475

− 1.412

− 1.357

− 1.316

− 1.295

− 1.297

− 1.323

− 1.370

− 1.435

− 1.510

− 1.584

− 1.643

− 1.687

− 1.720

− 1.737

− 1.735

5 (26)

− 1.656

− 1.646

− 1.616

− 1.570

− 1.513

− 1.450

− 1.388

− 1.334

− 1.295

− 1.276

− 1.282

− 1.313

− 1.368

− 1.443

− 1.531

− 1.625

− 1.706

− 1.754

− 1.776

− 1.782

− 1.771

6 (25)

− 1.633

− 1.623

− 1.593

− 1.548

− 1.491

− 1.428

− 1.367

− 1.314

− 1.276

− 1.260

− 1.269

− 1.304

− 1.365

− 1.448

− 1.546

− 1.653

− 1.761

− 1.843

− 1.874

− 1.867

− 1.842

7 (24)

− 1.617

− 1.607

− 1.577

− 1.532

− 1.475

− 1.412

− 1.351

− 1.299

− 1.262

− 1.246

− 1.256

− 1.294

− 1.358

− 1.445

− 1.550

− 1.666

− 1.784

− 1.897

− 1.973

− 1.981

− 1.943

8 (23)

− 1.610

− 1.600

− 1.570

− 1.524

− 1.467

− 1.404

− 1.342

− 1.289

− 1.251

− 1.235

− 1.244

− 1.281

− 1.345

− 1.433

− 1.539

− 1.656

− 1.778

− 1.896

− 2.005

− 2.068

− 2.050

9 (22)

− 1.612

− 1.602

− 1.572

− 1.525

− 1.467

− 1.403

− 1.340

− 1.286

− 1.246

− 1.227

− 1.233

− 1.267

− 1.327

− 1.411

− 1.512

− 1.626

− 1.744

− 1.860

− 1.967

− 2.061

− 2.103

10 (21)

− 1.667

− 1.656

− 1.624

− 1.575

− 1.512

− 1.442

− 1.372

− 1.309

− 1.257

− 1.224

− 1.213

− 1.224

− 1.257

− 1.309

− 1.372

− 1.442

− 1.512

− 1.575

− 1.624

− 1.656

− 1.667

No CJ

84
B. K. Dzhamuev and I. Z. Kalkan

Assessment of the Influence of a Construction Joint …

Fig. 5 a—Crack pattern for the joint placed along line 0: cracks are observed on the top surface; no
cracks are present on the bottom surface; b—crack pattern for the joint placed along line 5: cracks
are observed on the top surface; no cracks are present on the bottom surface; c—crack pattern for the
joint placed along line 10: cracks are observed on the bottom surface; the top surface crack pattern
corresponds to that in Fig. 5b and d; d—crack pattern in the reference model without a construction
joint: cracks are present on the top surface; no cracks are observed on the bottom surface

References
1. Gosstroy of Russia (2012) SP 70.13330.2012 load-bearing and enclosing structures: updated
edition of SNiP 3.03.01-87. Code of Practice. Gosstroy of Russia, Moscow
2. Gosstroy of the USSR (1976) SNiP III-15-76 rules for execution and acceptance of works:
monolithic concrete and reinforced concrete structures. Gosstroy of the USSR, Moscow
3. Gosstroy of the USSR (1987) SNiP 3.03.01-87 load-bearing and enclosing structures. Gosstroy
of the USSR, Moscow
4. Ministry of Construction of Russia (2018) SP 63.13330.2018 concrete and reinforced concrete
structures: general provisions. Code of Practice. Minstroy of Russia, Moscow
5. European Committee for Standardization (2004) Eurocode 2: design of concrete structures (EN
1992). CEN, Brussels

B. K. Dzhamuev and I. Z. Kalkan

6. European Committee for Standardization (2004) National Annexes to EN 1992: additional
provisions to Eurocode 2 in EU member states. CEN, Brussels
7. Deyneko AV, Kurochkina VA, Yakovleva IU et al (2019) Design of reinforced concrete slabs
considering construction joints. Vestnik MGSU 4:45–53. https://doi.org/10.22227/1997-0935.
2019.9.1106-1120
8. Koyankin AA, Beletskaya VI, Guzhevskaya AI (2014) Influence of construction joints on
structural behavior. Vestnik MGSU 6:30–36
9. Gerges NN, Issa CA, Fawaz S (2016) The effect of construction joints on the flexural bending
capacity of singly reinforced beams. Case Stud Constr Mater 5:112–123. https://doi.org/10.
1016/j.cscm.2016.09.004
10. Gerges NN, Issa CA, Fawaz S (2015) Effect of construction joints on the splitting tensile
strength of concrete. Case Stud Constr Mater 3:83–91. https://doi.org/10.1016/j.cscm.2015.
07.001
11. Issa CA, Gerges NN, Fawaz S (2014) The effect of concrete vertical construction joints on
the modulus of rupture. Case Stud Constr Mater 1:25–32. https://doi.org/10.1016/j.cscm.2013.
12.001
12. Nawshad MJM (2004) Stress–strain behavior of monolithic reinforced concrete slabs with
defects. Dissertation, Moscow State University of Civil Engineering
13. Kagan MN, Derbentsev IS, Koval SB et al (2023) Influence of technological factors in the
formation of construction joints on the behavior of reinforced concrete structures. Bull SUSU
1:50–57
14. Ministry of Construction of Russia (2016) SP 20.13330.2016 loads and actions. Code of
practice. Minstroy of Russia, Moscow
15. Malakhova AN (2013) Behavior of monolithic beam slabs under load. Vestnik MGSU 11:50–57
16. Malakhova AN (2016) Hollow coffered slabs in monolithic multi-storey buildings. Vestnik
MGSU 6:45–52
17. Malakhova AN (2014) Reinforcement of reinforced concrete structures. MGSU, Moscow
18. Malakhova AN (2024) Accounting for defects and damage in reinforced concrete structures in
verification calculations. Struct Des Eng Syst Struct Mech Found Substr 2(1):1
19. Tamrazyan AG (2018) Reinforced concrete and masonry structures: special course, 2nd edn.
MGSU, Moscow
20. Kabantsev OV, Tamrazyan AG (2014) Considering structural scheme variations in structural
analysis. Eng Constr J 49:15–26. https://doi.org/10.5862/MCE.49.2

Calculation of the Pile Grillage Taking
into Account the Nonlinear Operation
of Piles in the Ground by the Method
of Compensating Loads
M. I. Bochkov, A. V. Ignatyev, N. A. Maslennikov, I. S. Zavyalov,
and E. A. Maksyutova

Abstract The article discusses the modification of a previously developed algorithm
by the authors for solving systems involving non-linear supports, applied to the
calculation of a pile raft foundation with a known dependency of pile settlement
on load. The dependency of pile settlement on load was obtained experimentally,
as a result of static testing of the pile in the ground. The proposed algorithm is
based on a modification of the load compensating method using the finite element
method in the form of the classical mixed method. The algorithm developed by
the authors combines the advantages of the finite element method in the form of
the classical mixed method and the load compensating method, taking into account
that the function of the pile’s elastic work in the ground is a piecewise-defined
function consisting of three sections. When performing calculations the pile raft was
loaded with a load applied according to the typical layout of load-bearing walls in
a private low-rise house. The verification of the proposed algorithm was carried out
by comparing the obtained results with the solutions of this problem obtained using
common and verified software packages based on FEM in displacements, using both
linear and nonlinear incremental calculation methods. The advantages provided by
the finite element method in the form of the classical mixed method for linear and
nonlinear calculation of a slab on piles are analyzed. The effectiveness and stability
of convergence to the result of the load compensating method are demonstrated when
using a calculation scheme with mixed unknowns.
Keywords Structural nonlinearity · Pile foundation · Raft · Load compensating
method · Finite element method · Static pile testing

M. I. Bochkov (B) · A. V. Ignatyev · I. S. Zavyalov · E. A. Maksyutova
Volgograd State Technical University, Volgograd, Russia
e-mail: maxim.bochckow@yandex.ru
N. A. Maslennikov
St. Petersburg State University, St. Petersburg, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_8

M. I. Bochkov et al.

1 Introduction
In the design of building foundations, it is necessary to consider the factors affecting
the real behavior of the soil foundation, which often leads to the use of numerous
safety factors and conditions in engineering practice. The wide application of these
factors is due to the inability to thoroughly study the properties of the soil foundation,
as well as the reliability requirements for foundation structures, the failure of which
can negatively impact the entire building’s performance.
Field testing methods of soil foundations [1, 2] are often used to refine calculations.
One such method for pile foundations involves testing the soil with static driven loads.
However, in practical engineering calculations, the results of these tests are often not
fully utilized and are limited to considering the pile behavior on linear segments of
load-settlement curves. Accounting for the nonlinear behavior of piles in soil in this
problem will refine the calculation of raft foundations and load distribution on piles.
Additionally, treating piles as structurally nonlinear supports allows for modeling
certain soil features such as frost heave, settlement, and more.
Various types of piles are used in modern design practices, and modeling pile
behavior in soil requires specific considerations taking into account: soil properties
[3–5]; interaction between piles and soil during building construction [6, 7].
This article presents a method for considering the nonlinear behavior of piles in soil
by representing piles as structurally nonlinear supports with strength characteristics
determined according to the load-settlement curve. The algorithm developed by the
authors in [8] combines the advantages of the finite element method in the form of the
classical mixed method [9] and the load compensating method [10]. Utilizing these
features allows for analyzing systems involving structurally nonlinear connections of
different types without changing the calculation scheme or intermediate calculation
steps for modeling nonlinear connection behavior.
The aim of this research is to modify the generalized algorithm developed by
the authors in [8] for calculating systems with structurally nonlinear connections
to analyze pile foundations considering the nonlinear behavior of piles in soil as
supports.
To achieve this goal, a problem of calculating a slab raft with piles was solved.
The strength characteristics of the soil under the piles are assumed to be known and
characterized by a load-settlement curve obtained based on approaches described in
[1].

2 Materials and Methods
The essence of the developed algorithm lies in modeling the nonlinear behavior of
supports by introducing loads compensating for the softening or hardening of these
supports in the directions of their actions, which allows combining the advantages
of V. P. Alyonin’s load compensating method [10] and the finite element method in

Calculation of the Pile Grillage Taking into Account the Nonlinear …

the form of the classical mixed method. The calculation algorithm in the form of a
flowchart is shown in Fig. 1. The finite element method in the form of the classical
mixed method, as applied to this algorithm, demonstrates such advantages as the
ability to conduct nonlinear iterative calculations without changing the calculation
scheme and the ability to calculate without additional computation of parameters
determining the nonlinear behavior of connections. These parameters are immediately included in the result vector, simplifying the decision-making process on
introducing compensating loads in the corresponding directions. The calculation is
carried out until the discrepancy δ(j+1) between the values of compensating loads
at the j and (j + 1) iterations of the calculation, calculated according to the formula
F
− F(j)
δ(j+1) = (j+1)
· 100%, , becomes less than δ , which is set at the beginning of
F(j+1)
the calculation.
For conducting calculations using the FEM in the form of the classical mixed
method, the algorithm for calculating a thin bending plate was implemented using
the Scilab package of applied mathematical programs.
The calculation by the load compensating method is usually carried out for
supports whose behavior is described by a bilinear law. As previously noted in [8],
the behavior of elastic–plastic connections can be accurately described by a more
complex function. As demonstrated by the results of static tests conducted according
to the methodology, this is also true for pile behavior in soil.
The application of the Finite Element Method in the form of the classical mixed
method for the calculation of building structures is detailed in a series of articles [11–
16]. Publications by other scientists [17–20] are also dedicated to the development
of the mixed form of the FEM. These articles include an algorithm for obtaining the
coefficients of the response matrix for a bending rectangular finite element of a plate.
The basic algorithm for calculating thin bending plates based on the FEM in the form
of the classical Mixed Finite Element Method (MFEM) is also described. The system
of resolving equations obtained based on the MFEM in the form of MFEM in matrix
form is formulated as (1) and consists of two groups: equations of equilibrium, which
represent the physical meaning of zero reactions in the constraints introduced into
the main system (2), and equations of compatibility of displacements (deformations)
of finite elements converging at a common node (3).
R

0
0

(1)

IV
Ri,j = RIi,j + RIIi,j + RIII
i,j + Ri,j = 0

(2)

r r̃
δ̃ δ

q
r
+ p
δp
q̃

I
II
III
IV
ϕij(x) = ϕ(x)
+ ϕ(x)
+ ϕ(x)
+ ϕ(x)
= 0;
(y)

I
II
III
IV
ϕij = ϕ(y
) + ϕ(y) + ϕ(y) + ϕ(y) = 0.

(3)

M. I. Bochkov et al.

Fig. 1 The calculation
algorithm in the form of a
flowchart

3 Results and Discussion
In this study, a diagram consisting of three linear segments, constructed based on the
results of pile testing in soil, was used to calculate the connections.
Figure 2 presents the results of a static pile test [2] according to the scheme shown
in Fig. 2a.

Calculation of the Pile Grillage Taking into Account the Nonlinear …

Fig. 2 a the results of the static pile test, b pile testing scheme

The results of the test can be represented as a piecewise-defined function (4)
describing the behavior of a pile in soil as a standalone, elastic–plastic support:
(i)

⎧
⎨

120570 · (i) , 0 ≤ (i) ≤ 0.35 · 10−3 ;
(i)
= 23115 · (i) + 34.105, 0.35 · 10−3
≤ 2.18 · 10−3 ;
⎩
(i)
(i)
+ 74.015
> 2.18 · 10−3 .
4788 ·

(4)

Behavior analysis of the function shows that the stiffness coefficient of the pile in
the ground, as a support, significantly changes under load. This clearly demonstrates
the relevance of developing methods that allow accurately describing the stress–strain
state of the structure with such stiffness properties of the foundation.

M. I. Bochkov et al.

When using the Finite Element Method in the form of the Classical Mixed Method
(FEM in CMM form), both displacements and forces are included in the response
matrix. This allows us to determine both the displacement and force that arise in a
single-node finite element at the calculation stage of the resolving equations. Such
elements will have 2 degrees of freedom—displacement along the directions of the
global axe Z and force arising in the link. The response matrix of such a finite element
can be written in the form of expression (5).
r1,1 r̃1,2
δ̃2,1 δ2,2

0 −1
1 1/CZ

(5)

where CZ —is the equivalent stiffness of the element, which corresponds to vertical
stiffness.
The response matrix of a single-node finite element includes displacement and
force arising in the elastic-flexible support. This fact eliminates the need for intermediate steps in calculating reactions required for solving problems using the method
of equivalent loads. The stiffness of the elastic-flexible support is directly included
in the response matrix as the stiffness of the pile, according to the diagram in Fig. 2b.
To verify the proposed algorithm, a calculation of a foundation slab with dimensions of 12 × 12 m was performed, as shown in Fig. 3. The loading scenario considered for this slab was a load applied around the perimeter of the slab and along the
symmetry axis in the Y direction.
The stiffness characteristics of the slab: h= 0.3 m; μx = μy = 0.2; E = 30 ·
103 MPa.
In the calculation, the slab was divided into 256 finite elements (16 × 16 mesh). To
verify the proposed algorithm, comparisons were made with calculations performed
in a verified software complex based on the principles of finite element method in
displacements. A linear calculation was carried out, assuming the stiffness of the
elastic-flexible connections to be equal to their stiffness in the first segment. Various
options for dividing the slab into finite elements were considered during calculation
with the verified software complex—mesh sizes of 16 × 16, 32 × 32, and 64 × 64.
The comparison of calculation results is presented in Table 1.
According to the obtained calculation results, the finite element method in the
form of a classical mixed method allows for accurate system calculations with linear
discrete elastic-flexible supports using fewer elements compared to verified software
complexes based on finite element method in displacements.
Further calculations were performed taking into account the nonlinear behavior
of elastic-flexible connections, following an algorithm whose flowchart is depicted
in Fig. 1.
Since according to the results of static tests on ground with piles, the function
describing its behavior is a piecewise function consisting of three intervals, the transition was conducted in two stages: firstly, all connections (i) > 0.35 · 10−3 were
transitioned to a state corresponding to the second interval of the function, and then
all connections (i) > 2.18 · 10−3 were transitioned to a state corresponding to the

Calculation of the Pile Grillage Taking into Account the Nonlinear …

Fig. 3 Foundation plate with dimensions of 12 × 12 m
Table 1 Comparison of linear calculation results
Mesh sizes

FEM in CMM form

FEM in displacements

16 × 16

32 × 32

64 × 64

w(0,b/2), mm

− 0.931

− 0.930

− 0.929

w(a/2,b/2), mm

− 1.058

− 1.059

Mx(0,b/2), tm

0.000

− 0.567

− 0.244

− 0.005

Mx(a/2,b/2), tm

5.157

4.043

4.708

4.662

− 2.725

− 0.089

− 1.043

− 2.478

My(0,b/2), tm

− 0.218

0.836

0.474

− 0.164

R(0,b/2), t

− 11.223

− 11.226

− 11.213

− 11.208

R(a/2,b/2), t

− 12.762

− 12.763

− 12.862

− 12.764

My(a/2,b/2), tm

M. I. Bochkov et al.

Fig. 4 Displacements of the foundation slab

third interval. It should be noted that the proposed method for determining compensating loads of structurally nonlinear connections is most advantageous for manual
calculations; however, future research aims at developing an automated algorithm
for determining the segment describing elastic-flexible properties of connections.
If setting the exit criterion from the algorithm as δ = 1%, solving the problem
will require 19 operations in the first stage and 8 operations in the second stage of
transition.
Verification of the proposed algorithm was performed through a non-linear calculation in a verified software complex based on the Finite Element Method in displacements. For the non-linear calculation, 50 load partitioning steps were specified. Since
the solution algorithm for non-linear problems in such complexes is usually based
on simple step-by-step loading and its specifics are not disclosed, comparing the
number of operations is inappropriate. The calculation results are presented in Fig. 4
as displacement isopoles along the z-axis. Additionally, the results of the linear
calculation are provided for comparison. It can be observed from the displacement
isopoles and result comparison.
Table 2 that considering the non-linear behavior of piles in this problem leads to
a significant increase in displacements from − 1.058 mm in the linear calculation
to − 1.887 mm in the non-linear calculation (up to 78.4%). The moment Mx also
significantly increased (by 56%), while the moment My changed sign and value
entirely (167% to the absolute value). Thus, considering the non-linear elastic–plastic
behavior of piles in the ground had a significant influence on the stress–strain state
of the structure.
In contrast, the load on the piles decreased significantly by 38%. This result is
logical as there was a more uniform redistribution of the load on the interacting and
interconnected pile field.
The proposed calculation algorithm, combining the advantages of the Finite
Element Method in the form of a classical mixed method and the method of load
compensation, showed minor discrepancies with the results obtained using verified

Calculation of the Pile Grillage Taking into Account the Nonlinear …

Table 2 Comparison of results of construction-nonlinear calculation
Mesh sizes

FEM in CMM form

FEM in displacements

16 × 16

32 × 32

64 × 64

w(0,b/2), mm

− 2.262

− 2.336

− 2.352

− 2.350

w(a/2,b/2), mm

− 1.887

− 1.850

− 1.872

− 1.879

0.000

− 1.227

− 0.578

− 0.198

Mx(0,b/2), tm
Mx(a/2,b/2), tm
My(0,b/2), tm
My(a/2,b/2), tm

8.044

5.955

7.024

7.323

− 2.250

− 0.509

− 1.079

− 2.101

0.584

0.773

0.744

0.431

R(0,b/2), t

− 8.482

− 8.515

− 8.523

− 8.522

R(a/2,b/2), t

− 7.684

− 7.796

− 7.850

− 7.867

software complexes. The discrepancies in displacements and reactions were approximately 0% for linear calculations and less than 3.9% for non-linear calculations,
possibly due to mathematical errors in calculations. The discrepancy in bending
moments decreased with a more frequent mesh division. The error may be related to
the fact that the software complex used provides moment values at the center of the
finite element rather than at nodes, leading to errors for moments close to zero.
The obtained results allow for the following conclusions:
1. The proposed algorithm, combining the advantages of FEM in the form of a
classical mixed method and the method of compensating loads, allows one to
effectively solve problems of calculating a slab foundation on piles. The algorithm
allows one to take into account the nonlinear properties of the pile in the soil and
does not require a significant number of operations to obtain results with sufficient
accuracy.
2. Considering the non-linear elastic–plastic behavior of piles in the ground significantly affects the stress–strain state of the structure and the forces transferred to
the piles themselves.
3. The use of elastic-compliant finite elements in FEM calculations in the form of a
mixed method allows determining bending moments close to the values obtained
in verified software packages, while requiring a less dense finite element mesh.
4. The use of the proposed version of switching the state of nonlinear connections
in calculations showed good convergence of the obtained results.
Acknowledgements The research was carried out at the expense of the funds of the development
program of VSTU “Priority 2030", within the framework of scientific project No. 45/654-24.

M. I. Bochkov et al.

References
1. Savinov AV (2013) Sovremennye metody ocenki nesushchej sposobnosti vdavlivaemyh svaj
po predel’nomu usiliyu pogruzheniya (Modern methods for assessing the bearing capacity
of pressed piles based on the maximum immersion force). Vestnik Volgogradskogo gosudarstvennogo arhitekturno-stroiteľnogo universiteta Seriya: Stroiteľstvo i arhitektura (Bull
Volgogr State Univ Arch Civ Eng Ser: Civ Eng Arch) 30(49):80–86
2. Basu P, Prezzi M, Basu D (2010) Drilled displacement piles—current practice and design. DFI
Journal 4(1):3–20
3. Sychkina EN Ponomarev AB (2016) Perspektivy ispol’zovaniya dannyh staticheskogo
zondirovaniya pri proektirovanii svajnyh fundamentov na argillitopodobnyh glinah (Prospects
for the use of static sensing data in the design of pile foundations on mudstone-like clays).
Vestnik Volgogradskogo gosudarstvennogo arhitekturno-stroiteľnogo universiteta Seriya:
Stroiteľstvo i arhitektura (Bull Volgogr State Univ Arch Civ Eng Ser: Civ Eng Arch)
43(62):44–54
4. Gao D, Zhao K, Ma B, Han Z, Fan J (2023) Research on the bearing behavior of single pile
in self-weight collapsible loess areas. PLoS ONE 18(8):e0290878. https://doi.org/10.1371/jou
rnal.pone.0290878
5. Yushchube SV, Podshivalov II (2020) Modelirovanie napryazhenno-deformirovannogo sostoyaniya svajno-go fundamenta s plitnym rostverkom vysotnogo zdaniya s uchetom nedopogruzheniya svaj (Modeling of the stress-strain state of a pile foundation with a slab grillage of a high-rise building, taking into account the under-loading of piles). Vеstniк tomskogo
gosudarstvennogo arkhitekturno-stroitel’nogo universiteta (Bull Tomsk State Univ Arch Civ
Eng) 22(2):145–161
6. Khoirunisaa T, Setiawan B, Purwana YM (2023) Сomparative study of axial bearing capacity
for pile foundation based on empirical, numerical method and pile driving analyzer test.
Int J Comput Civ Struct Eng 19(4):196–207. https://doi.org/10.22337/2587-9618-2023-194-196-207
7. Yuan X, Chen L, Deng J (2020) Calculation of displacements and internal forces of anchored
retaining piles. PLoS ONE 15(12):e0243659. https://doi.org/10.1371/journal.pone.0243659
8. Ignatyev AV, Bochkov MI (2023) Raschet prostyh sistem s nelinejnymi momentnymi
svyazyami metodom konechnyh elementov v forme klassicheskogo smeshannogo metoda
(Calculation of simple systems with nonlinear moment connections by the finite element
method in the form of the classical mixed method). Izvestia vuzov. Stroitelstvo (News of
Higher Educational Institutions. Construction) 11:9–14. https://doi.org/10.32683/0536-10522023-779-1-5-14
9. Ignatyev AV (2015) Metod konechnyh elementov v forme klassicheskogo smeshannogo metoda
(osobennosti i vozmozhnosti primeneniya) (The finite element method in the form of a classical mixed method (features and application possibilities)). Stroitel’naya mekhanika i raschet
sooruzhenij (Struct Mech Anal Constr) 3(260):55–60
10. Alenin VP (2002) Iterative methods for calculating systems with external and internal one-way
connections (DSc dissertation). Volgograd State Academy of Architecture and Construction,
Omsk
11. Voronkova GV, Rekunov SS (2007) Osobennosti rascheta plastinok po metodu konechnyh
elementov v smeshannoj forme (Features of calculation of plates using the finite element
method in mixed form). Vestnik Volgogradskogo gosudarstvennogo arhitekturno-stroiteľnogo
universiteta Seriya: Stroiteľstvo i arhitektura (Bull Volgogr State Univ Arch Civ Eng Ser Civ
Eng Arch) 7:74–77
12. Rekunov SS (2008) Application of the mixed form of FEM to calculations of plate systems (PhD
dissertation). Volgograd State University of Architecture and Civil Engineering, Volgograd
13. Gabova VV (2011) Application of the mixed form of FEM to calculations of core systems.
Dissertation. Volgograd State University of Architecture and Civil Engineering, Volgograd

Calculation of the Pile Grillage Taking into Account the Nonlinear …

14. Ignatyev AV, Ignatyev VA (2014) Specific features and advantages of the finite element method
in the form of classical mixed method as an alternative for the traditional finite element method.
Int J Comput Civ Struct Eng 10(4):121–124
15. Ignatyev AV, Zavyalov IS (2024) Technique for solving finite element systems of high-order
linear algebraic equations describing the stress–strain state of one-dimensional and twodimensional structures. In: Lecture notes in civil engineering 400:232–243. https://doi.org/
10.1007/978-3-031-47810-9_22
16. Zavyalov IS (2022) Sravnitel’nyj analiz tochnosti rezul’tatov rascheta tonkoj izgibaemoj plastinki s ispol’zovaniem razlichnyh form MKE (Comparative analysis of the accuracy of the calculation results of a thin bendable plate using various forms of FEM). Stroitel’naya mekhanika i
raschet sooruzhenij (Struct Mech Anal Constr) 6:8–17
17. Pierre L (2012) Nonlinear computational structural mechanics. Springer Science & Business
Media, p 230
18. Gureeva NA, Kiseleva RZ, Klochkov YuV, Nikolaev AP, Ryabukha VV (2023) O fizicheskih
uravneniyah deformiruemogo tela na shage nagruzheniya s realizaciej na osnove smeshannogo
MKE (On the physical equations of a deformable body at the loading step with implementation
based on a mixed FEM). Izvestiya Saratovskogo Universiteta. Novaya Seriya. Seriya Matematika, Mekhanika, Informatika (Izvestiya of Saratov University. Mathematics. Mechanics.
Informatics) 23(1):70–82. https://doi.org/10.18500/1816-9791-2023-23-1-70-82
19. Klochkov YV, Pshenichkina VA, Nikolaev AP, Vakhnina OV, Klochkov MYu (2023) Stressstrain state of elastic shell based on mixed finite element. Mag Civ Eng 4(120):34–47. https://
doi.org/10.34910/MCE.120.3
20. Klochkov YV, Nikolaev AP, Vakhnina OV, Sobolevskaya TA, Klochkov MY (2022) Physically nonlinear shell deformation based on three-dimensional finite elements. Mag Civ Eng
5(113):159–170. https://doi.org/10.34910/MCE.113.14

Scientific Support for the Design
of the Marine Terminal: “Nakhodka
Mineral Fertilizer Plant”
A. Bunov and N. Shunko

Abstract The main studies included in the scientific support of the project of the sea
terminal of the Nakhodka mineral fertilizer plant are presented. The project of the
plant for the production of methanol and nitrogen fertilizers in Primorsky Krai is one
of the most significant objects for the Far East region. The presented work presents
research on ensuring the selection of a rational layout and the most efficient designs
of hydraulic structures of a marine terminal, in accordance with the current regulatory
documents of the Russian Federation in the field of marine hydraulic engineering.
In addition, studies of the operation of coastal structures are presented taking into
account the nonlinear properties of foundation soils in the MIDAS GTS NX software
package and verification of the adopted design solutions for the structures under
study for compliance with current regulatory documents in the field of design and
construction of foundations and bases in the Russian Federation.
Keywords Fertilizer plant · Scientific support · Physical modeling · Numerical
modeling · Berthing structure · Wave parameters · Storm risk · Wave splash ·
Stress–strain state · Coastal protection · Retaining wall

1 Introduction
The scientific article is devoted to one of the largest investment projects in the Russian
Far East—the Nakhodka Mineral Fertilizer Plant (NZMU). The high-tech plant for
the production of methanol and urea is the largest construction project in the strategically important region of the Russian Federation, on par with the construction of
the newest infrastructure facilities on the east coast of Sakhalin: the Multifunctional
Cargo Area of the Poronaysk Sea Port [1], as well as the construction of the Northern
Sea Transit Corridor. Eastern Transport and Logistics Hub and Western Transport
and Logistics Hub [2].
A. Bunov (B) · N. Shunko
Moscow State University of Civil Engineering, Moscow, Russia
e-mail: a_bunov@mail.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_9

100

A. Bunov and N. Shunko

2 Relevance
According to the latest research, the Russian Federation is one of the largest suppliers
of fertilizers to the world market [3], which justifies the unconditional strategic
importance of this area of the national economy. The main production of NZMU is
devoted to the production of methanol from natural gas, using the reforming method
in three stages of raw material processing [4, 5]. This is the latest technology that
contributes to a significant reduction in the carbon footprint [6]. The NZMU plant
declares the principle of a closed cycle—all processed products will be used in subsequent production cycles [7–9]. Accordingly, the NZMU project received a positive
conclusion from the state environmental review.
Design and construction of NZMU lines—the transition from a raw materials
economy to the export of high-tech industrial goods. Natural gas is needed to synthesize methanol. It will be supplied to the enterprise via pipelines from the Sakhalin
gas fields, and the synthesized methanol product will be pumped into the tanks of
oil tankers and delivered by sea to end consumers. In accordance with this, a marine
terminal with modern cargo berths was designed in the sea area adjacent to the NZMU
(Fig. 1).

Fig. 1 General plan of the area under study

Scientific Support for the Design of the Marine Terminal: “Nakhodka …

101

3 Statement of the Problem
In accordance with the current regulatory documentation [10, 11], the designed cargo
berthing structures must be examined for hydrodynamic impact using the physical
modeling method. The studied wave effects on the berthing structures, which must
be taken into account at various stages of the project, include the amount of wave
splash on the berth.
Wave splash on the studied hydraulic structures determines the position of the
marks of their above-water parts above the estimated water level, so that the crest of
the estimated wave in the estimated storm system does not interfere with the normal
operation of the structures [12–14].
The main structures of the cargo berth structure of the NZMU marine terminal
include: a technological platform; mooring and fender dolphins (4 pieces) and
mooring dolphins (4 pieces). The technological platform is adjacent to the approach
ramp. Structurally, the technological platform with a bottom mark at the cordon of
minus 16.5 m is made on a pile foundation of vertical and inclined steel pipes. When
installing piles and reaching the roof of coarse-grained soil, the piles are drilled into
it. In their lower part, the piles are filled with concrete. Above the mark of the top of
the concrete of the lower part, the internal cavity of the piles is filled with sand. In the
zone of ice effects, reinforced concrete plugs are arranged in the cavity of the piles,
into which reinforcement cages are installed, connecting the pile foundation with the
reinforced concrete grillage. The bottom mark of the grillage is taken equal to plus
3.2 m BS, in accordance with the requirements of SP 350.1326000.2018 «Standards
for the technological design of seaports», clause 4.3.5.4 [15]. At berths of through
construction, the grillage bottom mark should not be lower than the 13% wave height
mark for a storm with a recurrence rate of 1 time in 25 years. The grillage thickness
is taken to be 1.3 m, and the grillage top mark is taken to be plus 4.5 m BS.
Under the grillage of the technological platform, dolphins are arranged on a pile
foundation made of steel pipes, designed to ensure mooring and parking of minimum
design vessels. Technological equipment for handling bulk cargo is installed on the
grillage surface. Bottom fastening is arranged in front of the cordon line of the
technological platform towards the water area.
When developing design solutions for the technological platform, the possibility
of installing a fire-fighting water intake was taken into account. In accordance with
the Decree of the Government of the Russian Federation dated November 2, 2013
No. 986 [16], the technological platform of the berth belongs to the III class of GTS.
In addition to the berth structures, coastal structures, which are an integral part
of the entire complex, are also subject to design. As part of scientific support, it is
necessary to carry out a set of studies confirming the bearing capacity of all coastal
structures.

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A. Bunov and N. Shunko

4 Experimental Studies in a Hydrowave Flume
The scale of the physical model used in the experiments was: 1:50.
The purpose of the experiment was to study:
• the magnitude of wave splash on the structure of the technological platform of
the cargo berth;
• determining the presence/absence of contact of the wave crest with the downstream face of the grillage of the technological platform of the cargo berth;
• the overall efficiency of the structure of the cargo berth.
The studied structure of the technological platform is shown in Figs. 2 and 3. The
experimental studies are shown in Fig. 4.
The water level of 5% probability was: H5% = − 0.29 mBS (in-kind data) [10, 11].
The parameters of the westerly storm waves, probability of 1 time in 25 years, were:
h5% = 3.3 m, Taverage = 12.5 s (in-kind data) [10, 11]. In the presented experimental
studies, a standard methodology was used, with observance of the similarity between
the full-scale design and the model according to the Froude number [10–12]. The
composition of the measuring equipment and the installation in the form of a wave
tray are also standard for conducting such studies.
The experiments used an automated system for collecting and processing experimental data in real time, including: wave recorders (resistive level meters of the rough
surface) (2 pieces); an electronic data processing unit for 8 channels; a package
of complex programs for collecting, analyzing and visualizing experimental data,

Fig. 2 View of the physical model of the technological platform of the cargo berth

Scientific Support for the Design of the Marine Terminal: “Nakhodka …

103

Fig. 3 Technological platform of the cargo berth. Section 2–2

Fig. 4 a, b experimental studies at different points in time

with the processing of statistical information displayed on the computer screen (HR
Wallingford).
Wave recorder No. 1 (B1) was installed at a distance of 10 m from the model
(Fig. 5), closer to the wave generator, to control the compliance of the generated
wave parameters with the specified.
The initial wave parameters were recorded by wave recorder No. 1, located at
a distance of 6.0 m from the base of the model. The wave parameters as the wave
approached the structure were: h5% = 3.3 m, Taverage = 12.5 s (in-kind data) (Fig. 6a).
The wave directly at the process site is shown in Fig. 6b. The wave parameters were:
h5% = 3.8 m, Taverage = 12.5 s.

5 Results of Physical Modeling
The experiments conducted to study the impact of the most wave-hazardous storm
of the western direction h5% = 3.3 m, Taverage = 12.5 s (in-kind data) on the
construction of the technological platform of the berth showed that:
• there was no wave splash on the superstructure of the structure;

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A. Bunov and N. Shunko

Fig. 5 Wave detector sensors in working position

Fig. 6 a wave surface oscillations on the approach to the construction site; b oscillations of the
wave surface at the construction site

• there was no contact of the wave crest with the bottom of the grillage of the
structure under study.
Based on the analysis of the results of the obtained experimental data, the conclusion follows that the overall efficiency of the structure of the technological platform
of the berth is acceptable, the structure is stable.

Scientific Support for the Design of the Marine Terminal: “Nakhodka …

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6 Numerical Studies of the Operation of Designed Coastal
Structures
The structures for studying their operation include: a retaining wall, an artificial relief
system, gabion fastening, bank protection and a special passage. Let us dwell in more
detail on the retaining wall structure and its calculations (Fig. 7).
The functional purpose of the retaining wall is to hold the soil from collapsing,
as well as to be used as a base for installing an external mesh fence. The external
mesh fence is made of elements from the Fensys manufacturer, according to the
manufacturer’s specifications. It consists of galvanized mesh sections with 50 ×
150 mm cells, with a rod thickness of 5.0 mm. The fence posts are made of square
pipes with a cross-section of 80 × 80 × 3.0 mm and a height of 3.0 m.
The retaining wall is designed as a monolithic reinforced concrete structure with
an angle section: the width of the base is 6.0 m, the thickness of the base is 1.0 m,
the height of the retaining wall from the base is 7 m, the height of the retaining wall
from the planning surface is 6.0 m, the width of the retaining wall at the top is 0.4 m,
the width along the base is 1.5 m, the length of the retaining wall along the axis is
86.0 m.
To increase the stability and reliability of the retaining wall, and in accordance
with the calculation, the design provides for the installation of a number of bundle
anchors in the horizontal and inclined direction. The anchors are made of A500CE
reinforcement Ø 3X32 mm. Drilling a hole for installing the anchor is performed
with a crown Ø 161 mm. Installation of horizontal and inclined (angle 30°) anchors
is performed in a staggered manner with a step of 1 m. The length of the anchors in
sections 1–1 and 2–2 is: 7.5 m, in section: 3–3, is: 15.5 m.

Fig. 7 Section of retaining wall along section 1–1

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A. Bunov and N. Shunko

Fig. 8 General finite element scheme of the structure along section 1–1

To exclude backwater from groundwater and filtered water from surface runoff on
the retaining wall, a drainage layer of rocky soil of fraction 0.15–0.3 m is arranged in
the behind-the-wall space. The slope of the drainage layer corresponds to the slope of
the retaining wall base. To eliminate suffusion phenomena, rock soil is poured onto
geotextile laid on the foundation and covered with geotextile along the perimeter of
the backfill. Backfilling is performed from local soil with the formation of the design
position of a technological passage of variable width.
Work on installing the fence is carried out only after the backfilling of the retaining
wall has been completed.
The stability of the structure to shear and overturning under the influence of
horizontal soil pressure is ensured mainly by the dead weight of the wall and the
weight of the backfill soil.
To determine the internal forces and assess the stress–strain state of structures and
soils in section 1–1, the MIDAS GTS NX software package was used [17, 18]. Three
stages of work were considered: during the construction period, during operation
of the structure in its natural state, during operation of the structure under seismic
impact.
It is known that when solving problems using the finite element method (FEM),
a continuous area is considered as a set of a finite number of elements. In this case,
tetrahedral finite elements were used, which allow modeling any spatial problems
with a sufficient degree of accuracy. The soil behavior was described by the ideal
elastic–plastic Mohr–Coulomb model. The figures below show the results of calculations of the coastal slope along section 1–1, taking into account the fortifications,
as well as the internal forces in the retaining wall structure under the worst operating
condition (Figs. 8, 9, 10 and 11).

7 Results of Numerical Studies
The analysis of the obtained results on slope stability is presented in Table 1. The
stability coefficient exceeds the minimum permissible value.

Scientific Support for the Design of the Marine Terminal: “Nakhodka …

107

Fig. 9 a position of the sliding prism during construction with kstab. = 2.29; b position of the
sliding prism during operation of the structure in its natural state with kstab. = 2.75

Fig. 10 a position of the sliding prism during operation of the structure under seismic impact of
the PZ level with kstab. = 2.1; b position of the sliding prism during operation of the structure under
seismic impact of the MRZ level with kstab. = 1.9

The results of the checks of the retaining wall along section 1–1 are given in
Table 2. The coefficient of utilization of elements by bearing capacity does not
exceed 1.
The calculated sections along the retaining wall are shown in Fig. 12.

Fig. 11 a diagram of transverse forces in the structure of a retaining wall under the main combination of loads; b diagram of longitudinal forces in the structure
of a retaining wall under the main combination of loads; c bending moment diagram in the retaining wall structure under the main combination of loads

108
A. Bunov and N. Shunko

Scientific Support for the Design of the Marine Terminal: “Nakhodka …

109

Table 1 Comparative table of normative and calculated stability coefficients
No.
1

Calculated case

Standard stability
coefficient* (minimum)

Calculated stability
coefficient

In construction period

1.14

2.29

Natural state during the operational
period

1.33

2.75

Seismic impact of the PZ level during the 1.27
operational period

2.1

Seismic impact of the MRZ level during
the operational period

1.9

1.20

* Note The standard stability coefficient during the construction period is presented for slopes;
during the operation period—for the retaining wall

Table 2 Table of results of calculation of retaining walls
Section No.

Calculated
combinations of loads
and impacts

Element

Calculated section

Section using factor

1–1

Basic combination
(normal operation
period)

Wall

1–1

0.205

Wall

2–2

0.219

Wall

3–3

0.358

Plate

4–4

0.417

Plate

5–5

0.077

Wall

1–1

0.367

Wall

2–2

0.219

Wall

3–3

0.358

Plate

4–4

0.525

Plate

5–5

0.201

Special combination
(seismic impact)

110

A. Bunov and N. Shunko

Fig. 12 Calculated sections
along the retaining wall

8 Conclusions
Based on the results of the experimental and numerical studies, the following
conclusions can be made:
1. The experimental studies of the impact of the most wave-hazardous storm of
the western direction h5% = 3.3 m, Taverage = 12.5 s (in-kind data) on the
construction of the technological platform of the berth of the NZMU marine
terminal showed:
• the overall efficiency of the structure of the technological platform of the
berth is acceptable, the structure is stable. In accordance with this, the design
structure of the cargo berth is recommended for inclusion in the composition
of the hydraulic structures of the marine terminal project
• additional testing of the operation of all structures of the cargo berth is required
on a three-dimensional model in a hydrowave basin.
2. The performed geotechnical calculations of the stress–strain state of the foundation of the designed structure and the strength calculations of the NZMU retaining
wall showed:
• the results of numerical calculations of the assessment of the stability of coastal
slopes under static and seismic impacts [19] showed that in accordance with
paragraph 5.2.3 of SP 116.13330.2012 [20], the minimum design stability
factors do not exceed the permissible (normative) values of the stability
factors.

Scientific Support for the Design of the Marine Terminal: “Nakhodka …

111

• the bearing capacity of the retaining wall under the main and special combinations of loads and impacts is ensured taking into account the joint operation
of all coastal protection structures.
• it is recommended to provide for constant geotechnical monitoring during
the construction of the structure and for a period of at least 1 year after the
completion of construction according to a separately developed program. If
movements exceeding the design values occur, the Customer and operating
organizations should be immediately informed.

References
1. Shunko NV, Shunko AA (2025). Study of the berth structures of the “Multifunctional Cargo
Area facility”. Collection of abstracts of the scientific and practical seminar, VIII All-Russian
scientific and practical seminar “Modern problems of hydraulics and hydraulic engineering”,
Moscow, 2025
2. Shunko NV, Shunko AA (2025). Study of deep-water berth structures of the sea terminal
“Western transport and logistics hub”. Proceedings of the International Scientific Conference,
FORM 2025, Brest
3. Analysis of the fertilizer market in Russia (2025). TEBIZ GROUP. chrome-extension://
efaidnbmnnnibpcajpcglclefindmkaj/https://tebiz.ru/assets/pdf/mi/rynok-udobrenij-v-rossii.
pdf. Accessed 19.06.2025
4. Solov’ev S (2025). From Methane to Methanol: Industrial Production and Possibilities of Use.
In: GazPro Blog: Natural Gas Production and Use. Available via DIALOG. https://rosstip.ru/
news. Accessed 20.06.2025
5. Vjatkin JuL, Lishhiner II, Sinicyn SA, Kuz’min AM (2020). Promising directions of chemical
processing of hydrocarbon raw materials. In: Neftegaz.RU, 4. Available via DIALOG. https://
magazine.neftegaz.ru/articles/pererabotka/. Accessed 19.06.2025
6. Carbon footprint (2020). https://neftegaz.ru/tech-library/ekologiya-pozharnaya-bezopasnosttekhnika-bezopasnosti. Accessed 19.06.2025
7. Lemm EA, Petrov IV, Sharkova AV (2021) Possibilities of implementing the principles of a
circular economy in the petrochemical and energy industries of the Far East and the Arctic. In:
Neftegaz.RU, 10. Available via DIALOG. https://magazine.neftegaz.ru/articles/pererabotka/.
Accessed 19.06.2025
8. Cherepovicyn AE, Lebedev A (2022) Possibilities of using closed-loop technologies in the oil
and gas complex. Russian Journal of Innovation Economics 12:1185–1198. https://doi.org/10.
18334/vinec.12.2.114923
9. Cherepovitsyna A, Kuznetsova E (2022) CC(U)S initiatives: Prospects and economic efficiency
in a circular economy. Energy Rep 8:1295–1301. https://doi.org/10.1016/j.egyr.2021.11.243
10. SP 38.13330.2018 (2018) Loads and impacts on hydraulic structures (wave, ice and from ships).
Standardinform, Moscow
11. GOST R 70023–2022 (2022) Physical modeling of wave impacts on port hydraulic structures.
Requirements for model construction, experiments and processing of results, RST, Moscow
12. Tljavlina GV, Tljavlin RM, Vjalyj EA (2022) Port hydraulic structures: requirements for
physical modeling of wave effects. Transport construction 3:24–26
13. Vyaly EA (2024) Physical modeling of island structures. Power Technology and Engineering
58:26–31. https://doi.org/10.1007/s10749-024-01772-4
14. Shahin VM, Radionov AE, Shelushinin JuA, Kravchinskij AV, Baklanov AA (2024) Protection
of sea berths from storm waves. Hydrotechnics 3:10–13

112

A. Bunov and N. Shunko

15. SP 350.1326000.2018 (2018) Standards for technological design of seaports. Standardinform,
Moscow
16. Resolution No. 986 (2013) On the classification of hydraulic structures, the Government of the
Russian Federation. Moscow
17. Helps for Midas Civil and MIDAS GTS NX (2020) MIDAS IT Co., Ltd. https://midasoft.ru.
Accessed 20.06.2025
18. Dem’janceva DA (2024) Numerical modeling of settlement of pile foundations in MIDAS GTS
NX. Comparison with the normative method (SP 24.13330.2021 “Pile foundations”). Bulletin
of Science 12(81)
19. SP 14.13330.2018 (2018) Construction in seismic areas. Standardinform, Moscow
20. SP 116.13330.2012 (2012) Engineering protection of territories, buildings and structures from
hazardous geological processes. Basic provisions, Analitik, Moscow

Improvement of Thermal Protection
and Durability of Timber Houses
with Walls with Wooden Siding and Air
Gap
N. P. Umnyakova

Abstract Wooden houses made of logs have been built in Rus’ for centuries. Beginning from the seventeenth century, wooden cladding began to be installed on the
outside of log walls, creating an air gap between the boards and logs of the frame,
which was ventilated through the gaps between the siding boards. Such structures
became the prototypes of modern ventilated facade systems, in which wooden siding
protected the logs from the negative effects of the atmosphere and contributed to the
increased durability of the log house. The development of stone house building
pushed the research of wooden structures into the background, however, at present,
due to the revival of wooden house construction, the study of the properties of wooden
structures has been resumed, but very little research has been devoted to thermal engineering studies of wooden house elements. In this regard, the article presents a study
of the thermal insulation qualities of wooden log houses with wooden siding and air
gap. The work shows that the board siding allows the increase of the temperature
on the inner surface of the log house, including in the groove area, by 3.5–4.5 °C.
This eliminates the formation of condensation on the inner surface of the wooden
structure in winter and ensures high durability of wooden walls. Also, siding protects
the log house from negative wind impacts, and helps to reduce the infiltration impact
on the structure by 1.5 times.
Keywords Heat protection · Wooden siding · Log house · Air gap · Infiltration

N. P. Umnyakova (B)
Moscow State University of Civil Engineering (MGSU), Moscow, Russia
e-mail: n.umniakova@mail.ru
NIISF RAABC, Moscow, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_10

113

114

N. P. Umnyakova

1 Introduction
Wooden log houses were traditional buildings in ancient Russia. However, over time,
from the eighteenth century to the beginning of the twenty-first century, stone buildings began to displace wooden ones. Moreover, in the twentieth century, much attention began to be paid to research of stone and brick structures, large-panel buildings,
etc., and scientific work on the study of the properties of wooden buildings and their
elements faded into the background, and research on the thermal insulation qualities of wooden structures practically ceased. However, in the last decade, wooden
housing construction has begun to revive in Russia and research on wooden structures is becoming actual again. Moreover, wood has been the main building material
in Rus’ for centuries. Russian carpenters were famous for their skill in cutting houses
with an axe, without using a saw, which allowed them to protect the wood from rotting
and ensure the durability of the log house. During operation, the logs of the house
were exposed to various atmospheric influences—alternating temperatures, solar
radiation, wind and rain, which caused the aging of the log house wood. To protect
wooden walls from atmospheric influences in the sixteenth–seventeenth centuries in
Rus’, they began to use wooden board siding on the outside of the walls. However, in
those days, the process of manufacturing boards from logs was quite labor-intensive:
it was necessary to use an axe to “split” the log into boards (separate the log into
parts in fiber direction). Then these boards were set up on the external surface of the
log walls. However, over time, the technology for producing boards was simplified
and as a result of sawing logs, boards began to be produced that were significantly
cheaper and protected the logs from the negative effects of the atmosphere.
In the regulatory documents of the early twentieth century [1, 2], in the chapter
“Wooden parts of the building”, it is recommended that when constructing a log
house, wooden board siding should be set up on wooden vertical bars from the
outside to protect the log walls from bad weather, (Fig. 1). The siding was made
of horizontally located edged boards, which were connected to each other in butt
joint, rabbet joint, in tongue-and groove joint (Fig. 2). The boards were planed with
a beveled edge, which were set up to vertical bars or beams—fur. Due to the interstices
in the joints between the boards, the air permeability of the siding was quite high.
As a result, a ventilated air space was formed between the board siding and the
logs of the wall. Thus, the structure of the external wall with wooding cladding and
ventilated air space is a ventilated facade [3, 4].

2 Problem Formulation
The installation of a board siding with an air gap on the outside of the wooden
logs help to improve thermal protection of the external walls and increase the durability of the log walls, which the board siding protects from adverse atmospheric
effects. However, the analysis of works devoted to wooden structures has shown

Improvement of Thermal Protection and Durability of Timber Houses …

115

Fig. 1 External wall
cladding of the log house
with boards on bars with the
formation of an air space
between the logs and the
wooden siding with normal
grooving of 6-inch logs [1]

Fig. 2 Joining by flat surfaces а straight joint (or butt joint); b rabbet joint; c tongue-and groove
joint range

116

N. P. Umnyakova

that the influence of board siding with an air gap on the thermal insulation qualities of log walls has not been studied to the proper extent. A significant part of the
works on thermal engineering studies of wooden structures is devoted to the study
of the thermal conductivity of single wood samples and to the studies of thermal
conductivity of different types of wood. [5–13]. Much research has been aimed at
studying the heat-protective qualities of building envelope, made of various materials [14–16]. Heat protection properties of unventilated air gaps into brick walls
were also investigated by many scientists, including [17]. But none of those works
[14–17] account for the infiltration through the ventilated air cavity and radiation
heat exchange inside them. Much researches connected with linear thermal nonuniformity, which resulted in regulatory documents—Codes of Practice in Russia, DIN
in Germany, etc. A number of scientists were engaged in research and calculation of
linear thermal nonuniformity in light weight walls with a wooden frame and insulation filling [18, 19]. Considerable attention has been paid to studies of thermal
protection of log walls [20]. However, studies of thermal protection of wooden log
houses with wooden cladding, which have become widespread in Russia, have not
been carried out to the required extent, except for works [21–23].

3 Modeling of Thermal Protection of the Structure of Log
External Walls with Wooden Siding and Air Gap
Let consider the thermal insulation properties of an outside wooden wall structure
consisting of a 0.26 m thick wooden log, an air space and 0.02 m thick wooden
siding, and establish the temperature distribution in it. Air layers and spaces 5–6 cm
thick have become widespread in the construction of external walls made of logs
and beams. When calculating temperature fields, we will assume that the thermal
conductivity of spruce or pine for conditions B is λb = 0.18 W/(m °C); tow with
a density of γ = 150 kg/m3 and thermal conductivity λ = 0.069 W/(m °C); the
thermal conductivity of moss λ = 0.065 W/(m °C) [1]. It can be seen, the thermal
conductivity coefficient of tow and plant moss does not differ from each other.
We will calculate the temperature fields for a wall structure made of 0.26 m thick
logs without siding and with wooden siding with boards on a 0.02 m thick with offset
[24]. The thickness of the air space is taken equal 0.06 m.
First, a calculation was made for a wooden wall made of logs without siding with
a log groove of 15.5 cm (Fig. 3a). Then the temperature fields of a wooden wall made
of 0.26 m thick log with a log groove of 15.5 cm s with siding board of 0.02 m thick
board and air gap were calculated (Fig. 3b).
The calculations showed that in the absence of board siding with a groove equal to
15.5 cm, the temperature on the inner surface at outside temperature text = −20 °C
drops to 11.46 °C; at text = −30 °C to 9.77 °C; at text = −40 °C to 8.52 °C. At an
internal air temperature of tint = 18 °C, condensation on the inner surface of the wall

Improvement of Thermal Protection and Durability of Timber Houses …

117

Fig. 3 Temperature distribution on the inner surface of a 26 cm thick log wall with 15.5 cm log
grooving and a tow caulking without siding and b with wooden siding at: I—tint = +18 °C,
text = −40 °С; II—tint = +18 °C, text = −30 °С; III—tint = +18 °C, text = −20 °С

in the joint area will form, respectively, at an internal air humidity above 65, 58 and
53%.
The installation of wooden siding with an air space thickness of 0.06 m on the
outside of the log house allows increasing the temperature on the internal surface of
the log wall with a groove of 15.5 cm at text = −20 °C to 14.89 °C; at text = −30 °C
to 14.21 °C; at text = −40 °C to 13.48 °C. At an internal air temperature of tint = 18
°C, condensation will form in the groove zone in the sealing area when the indoor
air humidity is higher than 82, 78 and 75%.
Thus, calculations of temperature fields showed that the presence of an air gap
between the logs and wooding siding allows to rise temperature on the inner surface
of the logs, especially in the area of their joints by 3.5–4.5 °C. At the same time,
the relative humidity of the internal air, at which condensation can form, increases
significantly, which not only improves comfortable thermal conditions, but also helps
to avoid the formation of condensation in the log joint area, avoid wood rotting, and
increase the durability of the log structure.

118

N. P. Umnyakova

4 Calculation of Air Infiltration Processes Through Board
Siding with Air Gap for Log Walls
When outside covering the walls, horizontally placed wooden boards were joined to
each other in butt joint, rabbet joint, in tongue-and-groove joint (Fig. 2) Due to the
leakiness in the connection of the boards, the wooden siding is air permeable and
when there is wind, air infiltration occurs into the air gap.
Let us analyze the effect of air infiltration through wooden board sheathing on the
temperature regime of air gaps based on the solution of the heat balance equation.
The value of the heat flow considering infiltration through wooden board sheathing
will be:
inf

inf

Qsd = Ksd (t − text ),

(1)

inf

where Ksd —the heat transfer coefficient through the board siding considering infiltration, W/(m2 ºC); text —the outside air temperature, °C. To determine the heat
transfer coefficient considering infiltration, we will use the formula proposed in
[18]:
inf

Ksd = Ksd +

K = Ksd +

cW (Ksd + cW )
2Ksd + cW

(2)

where Ksd —the heat transfer coefficient through wooden siding without considering
infiltration, W/ (m2 °C); cW —the filtration heat exchange coefficient, W/(m2 °C).
In the work [23], the air permeability value of wooden sidings with a thickness
of 20 mm is:
• edged boards with straight jointing i = 12.4 kg/ m2 h Pa ;
• edged boards with rabbet joint i = 8.2 kg/ m2 h Pa ;
• joint boards with tongue-and-groove joint i = 0.7 kg/ m2 h Pa .
Let us analyze the influence of wind flow speed on the change in air temperature
in the air space during infiltration. The difference in air pressure p on the outer
and inner surfaces of wooden board siding caused by the action of wind pressure is
determined by the following expression [25]
p = 0.55H (γext −γair.gap ) + 0.03γext v2 ,

(3)

where H —the vertical height of the building, m; γext , γair.gap —the density of the
outside air and the air in the airspace, kg/m3 ; v—the estimated wind speed, m/s.
The amount of infiltered air, kg/ m2 h , passing through the wooden board
sheathing will be
W =J p

(4)

Improvement of Thermal Protection and Durability of Timber Houses …

119

Let us carry out a thermal engineering calculation of the outer wall of a two-story
building with a floor height of 3 m for an internal air temperature of plus 18 °C and
an external air temperature of minus 26 °C. The outer wall is made of 0.26 m thick
logs with wooden cladding, made of 0.02 m thick boards and an air gap of 0.06 m.
The estimated wind speed is 4.9 m/s.
When carrying out engineering thermal calculations, we replace the logs of the log
house with a diameter of 0.26 m with a beam of equivalent cross-section measuring
0.22 × 0.22 m. We calculate that the average air temperature in the air space between
the wooden wall and the board cladding is minus 19.86 °C.
Using formula (3), we determine Δp for the external wooden cladding from the
boards of the first floor.
p = 0.556(1.43−1.38) + 0.03 · 1.43 · 24.01 = 1.19 Pa
The amount of air passing through the wooden siding will be:
• with edged board and straight joint W = 12.4 · 1.19 = 14.766 kg/ m2 h ;
• with edged board and rabbet joint W = 8.2 · 1.19 = 9.760 kg/ m2 h ;
• with edged board and tongue-and-groove joint W = 0.7·1.19 = 0.833 kg/ m2 h .
Graphs of changes in the amount of air penetrating into the air layer, depending on
the type of bonding of the cladding boards and the wind speed are shown on Fig. 4.
Let us calculate the numerical values of the filtration heat transfer coefficient for
various variants of board connections and with different amounts of infiltrating air:
• for edged boards with straight joint cW = 0.278·14.766 = 4.102 W/(m2 °C);
• for edged boards with rabbet joint cW = 0.278·9.760 = 4.713 W/(m2 °C);

Fig. 4 Graphs of the dependence of the amount of air, passing through the board siding, on the
wind speed at p = 1.19 Pa

120

N. P. Umnyakova

• for edged board with tongue and groove joints cW = 0.278·0.833 = 0.232 W/
(m2 °C).
The heat transfer resistance of wooden cladding made of boards with an air gap
will be
Rinf .sd = Rext +

δ
0.02
+ Rair.g = 0.043 +
+ 0.075 = 0.229 (m2 ·◦ C)/W
λ
0.18
Ksd = 4.366 ≈ 4.37 W/(m2 ·◦ C)
inf

The heat transfer coefficient of wooden cladding considering infiltration Ksd =
+cW )
Ksd + cW2K(Ksdsd+cW
will be:
inf
• for edged boards with straight joint Ksd
=
4.366 +
4.102(4.366 + 4.102)/(2 · 4.366 + 4.102) = 7.071 = 7.07 W/(m2 °C);
inf
• for edged boards with rabbet joint Ksd
=
4.366 +
2.713(4.366 + 2.713)/(2 · 4.366 + 2.713) = 6.043 = 6.04 W/(m2 °C);
• for edged board with tongue and groove joints
inf
• Ksd
= 4.366 + 0.232(4.366 + 0.232)/(2 · 4.366 + 0.232) = 4.483 = 4.48 W/
(m2 °C).

Let study the influence of the process of infiltration and exfiltration on the heat
protection properties of wooden cladding made of boards 0.02 m thick, located
at the offset of a log wall 0.26 m thick. To do this, we will use the well-known
relationship—the difference between the heat transfer coefficients during infiltration
and exfiltration. This difference can be represented in the following form
inf

exf

Ksd − Ksd = cW

(5)

From the considered dependence (5) it is possible to obtain the value of the heat
transfer coefficient during exfiltration, calculating the ratio of air passing through the
wooden sheathing to 1 m2 of its surface
exf

inf

Ksd = Ksd − cW

(6)

or
exf

Ksd = Ksd +

cW (Ksd + cW )
− cW
2Ksd + cW

(7)

Based on the results of calculations using formulas (2) and (7), we will analyze
the thermal protection of wooden cladding made of boards and air gap. During the
operation the cladding can be located on the windward side (infiltration occurs) or
on the leeward side (exfiltration occurs) of the building.

Improvement of Thermal Protection and Durability of Timber Houses …

121

The obtained values of the heat transfer coefficients of the wall cladding of lowrise buildings, considering infiltration and exfiltration at different amounts of air
passing through the cladding of the house, are shown in Fig. 5. As can be seen
inf
from the graph (Fig. 5), the values of heat transfer coefficients for infiltration Ksd
exf
and exfiltration Ksd depend on the filtration heat transfer coefficient cW , which is
determined by the type of connection if siding boards. Thus, during infiltration, the
inf
heat transfer coefficient Ksd increases with increasing cW , and during exfiltration,
exf
the heat transfer coefficient Ksd decreases with increasing cW .
The data presented show that when wooden cladding made of boards is located
on the windward side of the building, under the influence of the infiltration process,
the heat transfer resistance of the cladding is reduced to 0.223 (m2 °C)/W, and when
the walls siding is made of the boards with straight joints, its value drops to 0.141
(m2 °C)/W. As can be seen, the heat transfer resistance of the skin during infiltration
decreases by 1.56 times.
The obtained numerical values of heat transfer resistance during air filtration
through board siding are understandable. The convective heat transfer coefficient for
the cladding on the windward side decreases and increases on the leeward side. Thus,
depending on the direction of the wind, the heat-insulating properties of wooden
cladding made of boards will either decrease or increase.

inf

Fig. 5 Dependence of the air heat transfer coefficient during infiltration Ksd (curve 1) and
exf

exfiltration Ksd (curve 2) of outside air through the board siding of a log wall.

122

N. P. Umnyakova

Currently, residential buildings with plastic siding have become widespread in
low-rise housing construction. Considering that the plastic siding boards have special
holes for ventilation of the air space between the wall with insulation and the siding
boards with air gap, the developed method for calculating the temperature regime of
external walls with siding at different air permeability of the skin is applicable for
calculating the temperature regime of the external walls of modern low-rise buildings,
trimmed with boards from various types of siding (wooden, metallic, plastic, etc.).

5 Conclusions
The conducted studies of the heat-insulating qualities of wooden external walls with
wooden cladding and an air gap allowed us to draw the following conclusions:
1. An analysis of the construction solution of wooden log walls with board
cladding (siding) and a ventilated air gap between them showed that these design
conceptions are prototypes of ventilated cladding facade systems.
2. As a result of mathematical modeling using the finite element method of the
structures of a log wall with an air space and wooden board cladding on the
side, a picture of the temperature distribution along the inner surface of the log
walls was obtained, which made it possible to establish that the presence of
cladding made of boards with an air space in the structure of a log house allows
to improve the thermal protection of walls and increase the temperature on their
internal surfaces.
3. Based on the theoretically obtained expression for calculating the heat transfer
coefficients of the cladding, the heat-shielding qualities of wooden cladding are
determined for its different air permeability during infiltration and exfiltration of
outside air.
4. The developed method for calculating the temperature regime of external log
walls of low-rise buildings made it possible to establish that the presence of air
space and plank cladding eliminates the possibility of condensation forming on
the inner surface of the walls, with their significantly smaller thickness compared
to unclad walls.
5. The proposed method for calculating the air temperature in the air space of a log
house wall with plank cladding can also be used to calculate external walls with
cladding made from various types of siding.

References
1. Roshefort NI (1906) Illustrated lesson position. A guide for drawing up and checking estimates,
designing and performing work. Moscow, p 730
2. Roshefort NI (1928) Illustrated schedule for civil works. Part I and II. Under general ed. S. M.
Geralsky, Part I—Moscow, Leningrad, p 320; Part II—p 356

Improvement of Thermal Protection and Durability of Timber Houses …

123

3. Podyapolsky SS, Bessonov GB, Belyaev LA, Postnikov TM (1988) Restoration of architectural
monuments: textbook for universities. Stroyizdat, Moscow, p 264
4. Umnyakova NP (2012) Prototypes of ventilated facade structures in buildings of Ancient Rus’.
Hous Constr 6:25–28
5. Umnyakova NP (2018) Features of design solutions for external walls that ensure the safety of
wooden monuments of Russian architecture. BLS 6:15–19
6. Yapıcı F, Özçifçi A (2011) The effect of grain angle and species on thermal conductivity of
some selected wood species. BioResources 6(3):2757–2762
7. Swedish Wood (n.d.) Properties of softwood. https://www.swedishwood.com/wood-facts/
about-wood/from-log-to-plank/properties-of-softwood/swedishwood.com
8. Niemz P, Sonderegger W, Hering S (2010) Thermal conductivity of Norway spruce and
European beech in the anatomical directions. Ann Wars Univ Life Sci For Wood Technol
72:66–72
9. Zhao J, Feng S, Kou Z, Meissner F, Ruisinger U, Grunewald J (2023) Characterization of
hygrothermal properties of two wood species—the impact of anisotropy on their thermal and
moisture behaviors. Preprint posted on SSRN, April 2023. https://www.papers.ssrn.compap
ers.ssrn.com
10. Maeda K, Tsunetsugu Y, Miyamoto K, Shibusawa T (2021) Thermal properties of wood
measured by the hot-disk method: comparison with thermal properties measured by the
steady-state method. J Wood Sci 67(20):1–11. https://doi.org/10.1186/s10086-021-01951-1
11. Yu Z-T, Xu X, Fan L, Hu Y (2011) Experimental measurements of thermal conductivity of wood
species in China: effects of density, temperature, and moisture content. For Prod J 61(2):130–
135. https://doi.org/10.13073/0015-7473-61.2.130
12. Bučar B, Straže A (2007) Determination of the thermal conductivity of wood by the hot plate
method: the influence of morphological properties of fir wood (Abies alba Mill.) to the contact
thermal resistance. Holzforschung 62(3):362–367. https://doi.org/10.1515/hf.2008.021
13. Vay O, Busquets-Ferrer M, Emsenhuber G, Huber C, Gindl-Altmutter W, Hansmann C (2021)
Thermal conductivity of untreated and chemically treated poplar bark and wood. Holzforschung
75(12):1125–1135. https://doi.org/10.1515/hf-2020-0268
14. Building envelope thermal bridging guide (2014) Part1. Building Envelope Thermal Analysis.
Morrison Hershfeild, Vancouver, p 25
15. Hendriani AS, Hermawan H, Retyanto B (2017) Comparison analysis of wooden house thermal
comfort in tropical coast and mountainous by using wall surface temperature difference. AIP
Conf Proc 1887:020007
16. Palme M, Guerra J, Alfaro S (2014) Thermal performance of traditional and new concept houses
in the ancient village of San Pedro De Atacama and surroundings. Sustainability 6:3321–3337
17. Svoboda Z, Kubr M (2011) Numerical simulation of heat transfer through hollow bricks in the
vertical direction. J Build Phys 34:325–350
18. Prata J, Simões N, Tadeu A (2018) Heat transfer measurements of a linear thermal bridge in
a wooden building corner. Energy Build 158:194–208. https://doi.org/10.1016/j.enbuild.2017.
09.073
19. Zhang S, Huang Z, Wu Y, Zhu Y (2023) Effect of thermal bridge in light-frame wood wall.
BioResources 18(1):367–381
20. The Energy Performance of Log Homes (2021) Documented energy-efficiency and thermal
mass benefits. In: Prepared by the construction codes & standards committee, log & timber
homes council, building systems councils, National Association of Home Builders, p 40
21. Briling RE (1948) Air permeability of enclosing structures and materials. Publishing House of
Construction Literature, Moscow, p 100
22. Vlasov OE (1938) Fundamentals of construction heating engineering. VIA RKKA, Moscow,
p 93
23. Fokin KF (2006) Construction heat engineering of enclosing parts of buildings. AVOC-PRESS,
Moscow, p 256

124

N. P. Umnyakova

24. Umnyakova N (2018) Numerical modeling of heat transfer through the interlayer, considering
the surface radiation. APCSCE IOP Conf Series Mater Sci Eng 456. https://doi.org/10.1088/
1757-899X/456/1/012096
25. SP 50.13330.2020 “SNiP 23-02-99 (2020) Thermal protection of buildings. Moscow, p 87

Research of the Stress–Strain State
of the Thread Using the Generalized
Unknown Method
A. V. Ignatiev, S. A. Kalinovsky, M. I. Bochkov, and I. S. Zavyalov

Abstract The object of study in this article is a thread subjected to a nodal load, as
an element of suspended structures, such as suspension bridges. The relevance of the
research lies in the necessity to enhance accuracy in selecting the geometric parameters of the thread. The methods employed in the research include the finite element
method in its classical mixed form and the method of generalized unknowns. As a
result of the calculations performed on internal forces in sections of the thread and the
thrust, dependencies of internal forces on geometric and physical parameters have
been obtained, and the most effective relationships between the geometric parameters of the thread have been identified. In particular, based on the provided graphs,
it can be noted that the allowance for the thread—elongation relative to the span
between supports is most appropriately chosen within the range of 10% to 20% of
the span length, as a reduction in allowance leads to a sharp increase in forces within
the thread and thrust. Conversely, increasing the allowance beyond 20% results in
a decrease in forces and thrust that cannot compensate for the increase in load due
to self-weight, nor justify an increase in the height of supporting structures. Previously, in engineering practice, the relationship between geometric parameters (the
length of the thread and the sag) was often accepted empirically; however, this study
provides precise explanations for these relationships, and the results obtained may
be beneficial for practical design applications.
Keywords Cable · Sagging · Initial length · Support · Tensile forces

A. V. Ignatiev · M. I. Bochkov · I. S. Zavyalov
Volgograd State Technical University, Volgograd, Russia
S. A. Kalinovsky (B)
Moscow State University of Civil Engineering (National Research University), Moscow, Russia
e-mail: KalinovskiiSA@mgsu.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_11

125

126

A. V. Ignatiev et al.

1 Introduction
The calculation of extensible cables is of immense significance across various fields
of practical engineering and construction science. Cables are employed in numerous
structures, ranging from simple ropes and wires to complex cables and steel ropes [1–
3], which are utilized in bridges, cable cars, and other constructions. Understanding
the behavior of extensible cables under different loads is essential for ensuring safety
and reliability in cable-stayed structures, power lines, and other engineering facilities
that incorporate such structural elements [4–6]. Cable-stayed structures are used in
the construction of facilities of varying classes [7–10], and their calculation methods
are also applied in other areas of design [11].
The development of nonlinear methods in structural mechanics [12] represents a
pressing challenge currently facing this field of knowledge. Accounting for nonlinearity allows for solving structural mechanics problems in a more general sensedescribing the stress–strain state of a structure at different stages of its life cycle.
This capability will enable the design of more complex engineering structures on
one hand and optimize more traditional structures commonly used in design practice on the other. A significant number of publications are dedicated to the non-linear
analysis of construction structures based on various methods and approaches [13–18].
The necessity and importance of accounting for the extensibility of structures
are directly linked to the development of new materials from which construction
structures are designed. Flexible cables made from modern composite materials
play a crucial role in contemporary engineering and construction, offering a wide
range of possibilities for developing innovative designs and architectural solutions.
These materials, including fiberglass, carbon fiber, and reinforced polymers, possess
high strength, elasticity, and flexibility, making them ideal for various engineering
challenges.
Due to their high flexibility, cables made from modern materials allow for the
creation of complex shapes and structures, opening vast opportunities for innovative
architectural design [19, 20]. Furthermore, they exhibit high resistance to various
aggressive environmental factors such as moisture, chemical agents, and extreme
temperatures, rendering them reliable and durable materials for use in construction.
Thus, flexible strands made from modern materials represent an important engineering component of contemporary construction, contributing to the development
of sustainable, innovative, and functional structures and facilities. The calculation of
such structures is a relevant task in structural mechanics [21], and the methods developed during these studies can also be applied to the analysis of specific engineering
constructions, such as overhead power lines (OPL) [22].
Modern methods for solving problems related to the stretching of strands include
numerical modeling using the finite element method (FEM). This method allows
for the consideration of complex nonlinear effects in material behavior and provides
accurate results for various types of loads and geometries of strands. Analytical
methods are also employed, such as the method of decomposing loads into a trigonometric series, which accounts for nonlinearities in material behavior and yields an

Research of the Stress–Strain State of the Thread Using the Generalized …

127

analytical solution for the problem of strand stretching. In our work, a modified finite
element method in the form of a classical mixed method [23, 24] will be applied to
solve such problems. According to studies conducted within our research school,
FEM in the form of a classical mixed method has shown high efficiency in solving
nonlinear problems in structural mechanics [25], and it has also been applied to
the analysis of flexible strands [26]. Therefore, its application to the calculation of
nonlinear problems involving flexible strands is justified.
A distinctive feature of the finite element method in the form of a classical mixed
method is the presence of two groups of equations among the governing equations:
equations of equilibrium at nodes and equations of continuity of deformations. Consequently, both displacements and forces arising at the nodes are included as unknowns
in the established equations. The fact that no additional computations are required to
determine the forces occurring in sections defines an advantage of the method we are
considering for problems involving nonlinear behavior. The parameters that define
the nature of the material’s nonlinear response do not need to be computed separately, which provides several advantages when solving problems using algorithms
outlined in articles [25, 26] and other works dedicated to this method.

2 Methods
The object of study in this article is a strand with fixed supports positioned at the
same level, loaded by concentrated forces. The strand under consideration is depicted
in Fig. 1.
In the figure, the following notations are used: l—length of the span, l —length of
the strand with allowance but without considering elongation, тогда l —length of
the stretched strand, d horizontal distances between the points of force application
(inter-nodal distances).
Let us represent the applied nodal load on the strand as a trigonometric series:

Fig. 1 Calculation scheme of the extensible strand

128

A. V. Ignatiev et al.
n−1

Fi =

Fk sin
i=1

kπ i
n

(1)

The coefficients of the expansion Fk are also determined by the expansion into a
discrete trigonometric series in sines:
Fk =

2
n

n−1

Fi sin
i=1

kπ i
n

(2)

The nodal displacements fi , acquired by the string in the absence of tension and the
displacements of the stretched thread fi can also be represented as a discrete trigonometric series expansion in terms of sines. The relationship between the coefficients of
the load function expansion and the nodal displacement function is established based
on the dependence between the bending moment in a fictitious beam of similar span
and the thrust. The sag of an unstretched thread at any point is determined according
to the expression:
fi =

Mib
H

(3)

The sag of a stretched thread at any point is then determined according to the
expression:
fi =

Mib
H

(4)

where Mib —is the so-called “beam moment” H is the thrust, which, in this case, due
to the symmetric loading of the thread only with vertical loads, remains constant,
and fi and H —is the sag of the stretched thread and thrust after stretching. The
string takes the shape of a broken line since the beam moment depends linearly on
the magnitudes of concentrated forces.
The value of the bending moment can also be expressed as a discrete trigonometric
series:
n−1

Mi =

Fk
k=0

d
4 sin2 kπ
2n

sin

kπ i
n

(5)

Thus, the sag of the inextensible and extensible strings can be represented
accordingly:
fi =

1
H

n−1

Fk
k=0

d
4 sin2 k2nπ

sin

kπ i
n

(6)

Research of the Stress–Strain State of the Thread Using the Generalized …

129

and
fi =

n−1

1
H

sin

4 sin2 k2nπ

k=0

kπ i
n

(7)

Let us denote li;i−1 as the difference in lengths between the stretched and
inextensible threads in each segment:
li;i−1 = li;i−1 − li;i−1

(8)

where li;i−1 is the length of the segment of the string when it is stretched. At the same
time,
li;i−1 =

Ni;i−1 li;i−1

(9)

In expression (9), N i;i−1 represents the magnitude of the longitudinal tensile force
in this segment of the thread. Е is the modulus of elasticity of the string material,
and А—is the cross-sectional area of the thread.
The allowance for the stretched thread in each segment in this case is:
li;i−1 =

li;i−1 +

li;i−1

(10)

or substituting expression (9) into expression (10):
li;i−1 =

li;i−1 +

Ni;i−1 li;i−1

(11)

The length of the segment of the inextensible thread is:
li;i−1 =

(fi − fi−1 )2 + d 2

(12)

Then, according to (11) and (5):

l =

n−1
i=1

Ni;i−1 (fi − fi−1 )2 + d 2
EA

n−1
i=1

(Mi −Mi−1 ) 2
H2

Ni;i−1

+ d2

or:
n−1

l =

l+d
i=1

Ni;i−1
EA

n−1
k=1

Fk2 sin

kπi
n

− sin

16H 2 sin4

kπ(i−1)
n

kπ
2n

Let us determine the magnitude of the thrust in the stretched state.

(13)

130

A. V. Ignatiev et al.

The length of the segment of the stretched string can be expressed as follows:
li;i−1 =

fi − fi−1

+ d 2,

(14)

Substituting expressions (9), (12), and (14) into expression (8), we can express the
thrust of the stretched string in terms of internal forces and thrust in the inextensible
thread.
Ni;i−1 (fi − fi−1 )2 + d 2
EA
fi − fi−1
fi − fi−1

+ d2 =

fi − fi−1

(fi − fi−1 )2 + d 2

+ d2 −

(fi − fi−1 )2 + d 2 1 +
1+

= (fi − fi−1 )2 + d 2

Ni;i−1 li;i−1
EA

Ni;i−1 li;i−1

(15)

(16)

− d2

(17)

According to (3)–(7):
(Mi − Mi−1 )2
=
H2

(Mi − Mi−1 )2
+ d2
H2
n−1
k=1

H =
i=1

n−1
k=1

Fk2

sin

kπ(i−1)
kπi
n −sin
n
4 kπ
2
16H sin 2n

Fk2 sin

Ni;i−1
EA

kπ(i−1)
kπi
n −sin
n
4 kπ
16 sin 2n
2

− d2

(18)

(19)
Ni;i−1
EA

−1

It is important to note that with the application of load to the thread and its
stretching, the cross-sectional area changes. Moreover, this change is not uniform.
Due to the constancy of the material volume, which can be defined as the product
of the current length of the segment of the string and its cross-sectional area, the
cross-sectional area in each segment of the thread will be:
Ai;i−1 =

Ai;i−1 (d + li;i−1 )
d + li;i−1 + li;i−1

(20)

In turn, it should be noted that the nodal load F i itself, in order to increase the
accuracy of the calculation, should be represented at each node as the sum of the
directly applied payload and the equivalent concentrated force, defined as the resultant of the net weight of each section of the thread. Initially, the points of application
of forces divide the span into n equal sections. Taking into account the fact that
threads always has a longer length than the overlapped span, due to the allowance,
its own weight is assumed in accordance with the expression:

Research of the Stress–Strain State of the Thread Using the Generalized …

q0 (l +
l

131

(21)

where q0 is the net weight of one linear meter of thread.
Then its own weight is redistributed into nodes according to the expression:
Qi = q · d ,

(22)

where Qi is the equivalent concentrated force for a section of thread of length d,
which is added to the conventionally accepted payload Pi .
Fi = Qi + Pi

(23)

The Qi forces thus increase in modulus with increasing allowance. Thus, the
total forces of Fi also increase with a change in the allowance, despite the constant
payloads of Pi . Accounting for the difference in the lengths of the interstitial sections
of the thread can be carried out by introducing an intermediate calculation iteration.
The specified value of the concentrated load applied to each discrete node of the
system is determined by the formula:
Qi = q

(fi−1 − fi )2 + d 2 +
2

(fi − fi+1 )2 + d 2

(24)

Thus, the geometric nonlinearity of the thread is taken into account with a high
degree of accuracy.

3 Results and Discussion
The results of calculations for a specific structure with the following elastic and
geometric parameters are presented below: the span covered is 100 m; the thread is
made of steel cable with a diameter of 76 mm, and the weight per linear meter is
0.198 kN. The thread is divided by nodes into n = 10 equal sections, each d = 10 m
long. Table 1 presents the results of the calculation of the tension in the thread for
a preload value of Δl = 15 m, without accounting for the difference in lengths of
the inter-nodal sections. Similar calculations for this thread were also performed for
preload values of Δl = 1; 3; 5; 10; 20; 25; 30; 35; 40 m. Other threads were also
considered.
We will compare the nonlinear calculation with the previously performed linear
one:
Thus, as a result of the nonlinear calculation, Table 2 was formed a table of
relationships between the geometric characteristics of the loaded thread and the
resulting forces for different values of thread preload. The obtained results were

132

A. V. Ignatiev et al.

Table 1 Extensions of thread sections, deflections at its nodes, and tensile forces at a preload value
of Δl = 15 m
i

F i , кN

102.544

2.835

9.018

684.763

102.319

2.339

16.054

621.754

102.143

1.545

21.091

569.39

102.029

0.691

24.118

531.311

101.99

0.09

25.128

511.105

102.029

0.09

24.118

511.105

102.143

0.691

21.091

531.311

102.319

1.545

16.054

569.39

102.544

2.339

9.018

621.754

2.835

684.763

fI , m

N I , кN

processed in the form of graphs depicted in Figs. 2, 3, 4, where the calculated values
were approximated with sufficient accuracy.
In this case, we observe a slight difference compared to our previously obtained
calculation results, which were conducted under the assumption that the thread is
inextensible [26]. However, if we reduce the modulus of deformation, the differences
become quite significant. Below, we present calculations for a thread with similar
other parameters under the condition that the modulus of elasticity is 100 MPa, which
is characteristic of rubber. Tables 3 and 4 present the results of calculations for a
thread with the same geometric parameters made from a material with an elastic
modulus E = 100 MPa. Figures 5, 6, and 7 similarly present graphs showing the
relationships between tension and preload, sag and preload, and maximum tensile
forces and preload.
Table 2 Values of maximum
sag fmax , tension H, and
maximum tensile forces N max
for various preload values Δl

H , кN

N max , кN

6.185

2062.469

2112.977

10.791

1182.447

1268.092

14.027

909.9

1018.736

20.182

632.774

781.346

25.128

508.515

684.763

29.478

433.747

631.401

33.461

382.345

597.444

37.194

344.181

573.964

40.745

314.385

556.809

44.155

290.283

543.772

Δl, m

fmax , m

Research of the Stress–Strain State of the Thread Using the Generalized …
Fig. 2 Graph of tension as a
function of preload for steel
cable

Fig. 3 Graph of sag as a function of preload for steel cable

133

134

A. V. Ignatiev et al.

Fig. 4 Graph of tensile forces as a function of preload for steel cable

Table 3 Extensions of thread sections, deflections at its nodes, and tensile forces at a preload value
of Δl = 15 m
i

F i , кН

102.556

2.897

9.206

680.25

102.327

2.391

16.388

616.777

102.147

1.58

21.53

563.947

102.031

0.707

24.621

525.469

101.99

0.092

25.652

505.028

102.031

0.093

24.621

505.028

102.147

0.707

21.53

525.469

102.327

1.58

16.388

563.947

102.556

2.391

9.206

616.777

2.897

680.25

Similarly to the previous case, as a result of the nonlinear calculation, Table 4 was
formed—a table of relationships between the geometric characteristics of the loaded
thread and the resulting forces for different values of thread preload. The obtained

Research of the Stress–Strain State of the Thread Using the Generalized …
Table 4 Values of maximum
sag f max , tension H, and
maximum tensile forces N max
for various preload values Δl

135

H , кN

N max , кN

9.266

1376.804

1604.798

12.352

1033.114

1174.089

15.106

844.951

981.193

20.847

612.605

771.367

25.652

498.158

680.25

29.934

427.153

628.835

33.879

377.64

595.786

37.591

340.565

572.802

41.128

311.466

555.948

44.531

287.842

543.107

Δl, m

fmax , m

Fig. 5 Graph of tension as a function of preload for polymer thread

results were processed in the form of graphs depicted in Figs. 5, 6, 7, where these
values were also approximated with sufficient accuracy.
Additionally, it can be noted that in a number of works by various authors, calculations are performed based on a given value of the sagging boom, but in order to
ensure a particular sagging, it is necessary to select a particular lengthening of the
thread—allowance. Our calculations show the dependence of the sagging boom on
the allowance. For a thread loaded with a uniformly distributed load, its full length can

136

Fig. 6 Graph of sag as a function of preload for polymer thread
Fig. 7 Graph of tensile
forces as a function of
preload for polymer thread

A. V. Ignatiev et al.

Research of the Stress–Strain State of the Thread Using the Generalized …

137

be determined with sufficient accuracy using, for example, the expressions proposed
in [27]. Our approach allows us to correlate these geometric parameters for a thread
loaded with concentrated forces as well.
As the thread length values approach the length of the overlapped thread span,
the spacer increases significantly, tending to infinity in the absence of an allowance.
When the allowance is increased from 1 to 3% of the length for a steel rope, the
gap value is reduced by 74%. The maximum tensile force N in the thread is reduced
by 66.6%. With an increase in the allowance from 3 to 5% of the length, the spacer
decreases by 30%, and the maximum tensile force by 24.5%. When the allowance
increases from 5 to 10 percent of the length, these values decrease by 43.7% and
30.3%, respectively. This is very significant for any thread parameters and may mean
that an allowance of less than 10% of the length should not be provided. At the same
time, with an increase in the allowance from 10 to 15%, the decrease in the values of
H’ and N is 24.4% and 14%, and with an increase in the allowance from 15 to 20%,
the decrease in the values of H’ and N is 17.2% and 8.4%, respectively. Increasing the
tolerance from 15 to 20% reduces the values of H’ and N by 13.4% and 5.6%. Further
increase of the allowance: 1. it will cause a decrease in internal forces by a smaller
percentage than the elongation of the thread, which will be ineffective. 2. And even a
5% reduction in thrust and effort is not relevant because it is not significant, including
taking into account the likely errors in calculations and measurements. And it will
be even more ineffective when increasing the proportion of its own weight from
additional loads. With a decrease in the modulus of elasticity, we obtain a decrease
in the amount of expansion to a slightly lesser extent, for example, by 37.9% and by
27.2% for internal tensile forces with an increase in the allowance from 5 to 10%
of the span length. However, the general trend continues. Thus, an allowance in the
range of 15% to 25% of the span length is advantageous.

4 Conclusions
Based on the above, we can draw the following conclusions:
1. An algorithm has been developed for calculating flexible cable systems under
nodal loads, based on the postulates of the finite element method in the form of
a classical mixed method. The algorithm combines considerations of geometric
and physical nonlinearity in processes occurring in cable systems.
2. The impracticality of accounting for stretching in calculating threads made from
materials with high stiffness has been confirmed; the increase in stress for steel
threads in both linear and nonlinear formulations does not exceed 1%.
3. Based on the above, it can be noted that it is rational to extend the thread in
relation to the span in the range from 15 to 25%. With a decrease in the allowance,
the struts and tensile forces increase significantly, which leads to an increase in
the material consumption of the thread, since it therefore becomes necessary to
increase its cross-section. In addition, significant horizontal loads on the supports

138

A. V. Ignatiev et al.

also lead to an increase in their material consumption. With an increase in the
allowance above the indicated limits, changes in the magnitude of forces and
struts do not significantly affect the selection of the thread section, but its material
consumption increases due to the length, in addition, lengthening the thread will
be ineffective from the point of view of the structure layout, since significant
sagging requires an increase in the height of the supports.
4. Relationships have been established that describe the correlations between the
magnitude of resulting tension, maximum tensile forces, and sag for various
preload values. The obtained relationships can be utilized in practical design of
flexible threads.

References
1. Krivoshapko SN (2016) Cable-stayed structures. J Construction mechanics of engineering
structures and structures 1:9–22. https://journals.rudn.ru/structural-mechanics/issue/view/683
2. Chen WF, Duan L (2014) Bridge engineering handbook, second edition: fundamentals. Taylor,
London, p 591. https://doi.org/10.1201/b15616
3. Perel’muter AV (1969) Fundamentals of calculation of cable-rod systems. Strojizdat, Moscow,
p 190
4. Kara H, Bosia D (2016) Design engineering refocused AD smart. Wiley, USA, p 82
5. Orton A (2013) The way we build now. Taylor, London, pp 94–95. https://doi.org/10.4324/978
1315024684
6. Kuzhahmetova ER (2019) Calculation methods of cable-stayed structures. Bull BSTU Named
After VG Shukhov 2:39–48
7. Cai J, Feng J, Jiang C (2014) Development and analysis of a long-span retractable roof structure.
J Constr Steel Res 92:175–182
8. Tarasov DA, Semyonov DY (2017) Mathematical modeling of the stress-strain state of flexible
filaments taking into account physical nonlinearity. Model, Syst, Netw Econ, Technol, Nat,
Soc 3(23):175–185
9. Panteleeva VS (2020) Features of construction and construction of Akashi-Kaike. J Young
scientist 22(312):173–174. https://moluch.ru/archive/312/70790/
10. Sitnikov IR, Golikov AV (2018) Regulation of efforts in large-span structures during the development of a rational structural form of the dolphinarium building in Volgograd. Constr Mech
Eng Struct Struct 14(4):278–292. https://doi.org/10.22363/1815-5235-2018-14-4-278-292
11. Kornev VA (2019) Analytical calculation of pressure hoses by flexible thread method. Probl
Mod Sci Educ 30(72):22–26
12. Ladevèze P (2012) Nonlinear computational structural mechanics. Springer Science & Business
Media, p 230
13. Nikolaev, A., Vakhnina, O., Sobolevskaya, T., Klochkov, M., Klochkov, Y (2023) Stress-strain
state of elastic shell based on mixed finite element. Mag Civ Eng 4(120):34–47. https://doi.
org/10.34910/MCE.120.3
14. Nikolaev, A., Vakhnina, O., Sobolevskaya, T., Klochkov, M., Klochkov, Y (2022) Physically nonlinear shell deformation based on threedimensional finite elements. Mag Civ Eng
5(113):159–17. https://doi.org/10.34910/MCE.113.14
15. Lukashevich AA (2022) Finite element models based on the approximation of discontinuous
stress fields. Mag Civ Eng 110(2):11004. https://doi.org/10.34910/MCE.110.4
16. Kushch VA, Yashchenko VP (2021) Taking into account physical nonlinearity when calculating a flat reinforced concrete frame using the SCAD computer system. News Univ Invest
Construction Estate 11:38–47

Research of the Stress–Strain State of the Thread Using the Generalized …

139

17. Krasnorutskiy DA (2016) The method for analyzing mechanics of thin elastic rod systems
using the differential approach. PNRPU Mech Bull 2:69–88. https://doi.org/10.15593/perm.
mech/2016.2.06
18. Taranukha NA, Zherebko KV, Petrov MR (2003) Mathematical model of a hinged rod system
with large node movements. News High Educ Inst Constr 3:12–18
19. Eremeev PG (2021) Suspension large span roofs structures in Russia. Int J Comput Civ Struct
Eng 17(2):34–42. https://doi.org/10.22337/2587-9618-2021-17-2-34-41
20. Buzalo NA (2022) Deformation calculation of cable-stayed structures covering sports facilities.
Housing construction 10:46–49. https://doi.org/10.31659/0044-4472-2022-10-46-49
21. Guzeev RN (2020) Free nonlinear oscillations of a shroud with an external damper. Bulletin
of Civil Engineers 4(81):100–105. https://doi.org/10.23968/1999-5571-2020-17-4-100-105
22. Valiullin AA, Danilin AN, Feldshteyn VA (2022) Normal vibrations of sagging conductors of
overhead power lines. Int J Comput Civ Struct Eng 18(3):147–158. https://doi.org/10.22337/
2587-9618-2022-18-3-147-158
23. Ignatyev AV, Ignatyev VA (2014) Specific features and advantages of the finite element method
in the form of classical mixed method as an alternative for the traditional finite element method.
Int J Comput Civ Struct Eng 10(4):121–124
24. Ignatyev VA, Ignatyev AV (2022) Finite element method in the form of a classical mixed
method of structural mechanics (theory, mathematical models and algorithms). ASV, Moscow,
p 306
25. Bochkov MI, Ignatyev VA (2023) Development of single-node finite elements for the calculation of systems with unilateral constraints by FEM in the form of the classical mixed method. In:
Proceedings of the 7th international conference on construction, architecture and technosphere
safety ICCATS 2023, Sochi, Springer Cham, pp 222–231
26. Ignatiev VA, Ignatiev AV, Kalinovsky SA (2024) Calculation of internal forces and geometric
parameters of a thread loaded in equidistant nodes along the span length. News High Educ Inst
Constr 4(784):23–33. https://doi.org/10.32683/0536-1052-2024-784-4-23-33
27. Moskalev NS (1980) Designs of hanging coverings. Stroiizdat, Moscow, p 331

Application of Ray Expansions
for Studying Nonstationary Motion
of a Nonlinear Plate on an Elastic
Half-Space
M. V. Shitikova and A. S. Bespalova

Abstract The ray method is an effective method for solving problems dealing with
the propagation of wave surfaces of strong and weak discontinuities, including
problems of dynamic contact interaction. Unsteady vibrations could be initiated
by instantaneous loads applied on the plate, resulting in plane waves propagating
within an elastic half-space. The solution behind the wave fronts up to the contact
boundary is constructed using ray expansions. Unknown functions entering in the
ray series coefficients and in the equation of plate motion could be found from the
boundary conditions of the contact interaction between the plate and the half-space.
“Manual” procedure (without using any mathematical packages) for calculating the
ray series coefficients is rather cumbersome, therefore an algorithm to solve this
problem using the Maplesoft has been suggested by the authors for different types of
contact conditions first for linear problems. In the present research, the ray expansion
method and the developed algorithm are applied to analyze the unsteady response
of an infinitely long elastic nonlinear classical von Karman plate lying on an elastic
isotropic half-space.
Keywords Dynamic contact · Ray method · Nonlinear plate · Elastic half-space

1 Introduction
Despite the fact that problems related to the analysis of impact interaction of bodies
have long attracted the attention of scientists, they remain relevant today, since they
have a wide practical use [1–3]. Physical phenomena involved in impact action
include dynamic reactions of contacting bodies, effects of contact conditions, and
wave propagation. Since these problems relate to problems of dynamic contact interaction, their solution is associated with significant mathematical and computational
difficulties, which are caused not only by complex equations describing the dynamic
M. V. Shitikova (B) · A. S. Bespalova
National Research Moscow State University of Civil Engineering, Moscow, Russia
e-mail: ShitikovaMV@mgsu.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_12

141

142

M. V. Shitikova and A. S. Bespalova

behavior of a continuous medium, but also by the variety of boundary conditions
arising on the contacting surfaces of solids.
Dynamic contact problems could be categorized into two groups. The first
group involves problems associated with the excitation of harmonic oscillations and
harmonic wave propagation, in the cases when bodies are either in constant contact
with each other or enter into long-term contact. The second type includes problems
dealing with the generation of surfaces of strong or weak discontinuities [4–6] or
leading to non-stationary oscillatory motions, in the cases when bodies enter into
short-term contact with each other, i.e. impact interaction [7–9].
Different mathematical methods are used for solving problems of the first and
second types. One of the most effective approaches for studying problems from
the second group, related to propagation and attenuation of non-stationary waves
carrying a jump in field parameters on the front, are ray methods [4–6] based on the
theory of geometric optics and its generalizations [10].
The most significant drawback of classical ray methods is the asymptotic nature of
the solutions, which is expressed in the fact that in stationary wave problems the solutions obtained with their help are applicable only when the wavelength is less than
the characteristic dimensions of the problem (short-wave or high-frequency asymptotics), and in the non-stationary case—in the vicinity of the wave front (near-front
asymptotics). However, this drawback is compensated by their clarity and universality, since ray series can be successfully used in solving both groups of problems
[4–6].
The expansion of the application area of ray methods occurs both by limiting the
asymptotic nature of the solutions obtained (local expansion) and by including new
problems in the application area of ray methods (global expansion). Local expansion
is primarily implemented by considering the higher-order terms of the series into
[11], as well as by using the specially developed method of uniformly valid “forwardarea regularization” [12], enabling one to improve the truncated ray series, which
approximate the solution in a given wave region, without involving additional terms
in the ray expansion.
The global expansion in recent years is illustrated by the solution of numerous
dynamic problems. Thus, in 2020, Springer Publishing House published the Encyclopedia of Continuum Mechanics [13], which involves not only a state-of-the-art article
covering in detail the theory of ray expansions [14], but also a series of entries dealing
with various aspects of wave propagation and solutions of boundary value dynamic
problems using ray methods, including the propagation of shock waves, waves in
inhomogeneous media, discontinuity surfaces in elastic-viscoplastic media, rays in
stochastically inhomogeneous media and media with a deterministic structure, the
use of ray expansions in dynamic problems of contact and impact interaction.
The combination of ray theory with the discontinuity theory proposed by Thomas
[15] made it possible to investigate successfully the propagation of wave surfaces of
strong and weak discontinuities in various media: linear homogeneous viscoelastic
media [12, 16], inhomogeneous elastic [17] and viscoelastic media [18], microstructural Cosserat [19] and Mindlin [20] media, micropolar elastic [21] and thermoelastic

Application of Ray Expansions for Studying Nonstationary Motion …

143

[22] media, as well as in pre-stressed thin-walled open-section rods arbitrary curved
in space [23].
Local expansion of the ray method has recently become possible due to the use of
modern mathematical packages. Thus, in [11] a description of the algorithm developed by the authors on the basis of the Maple software package is given for solving
the contact dynamic problem of transient oscillations of a linear isotropic plate lying
on an elastic half-space. This problem was solved earlier in [8] by the ray method,
which helped to find the dynamic deflection in the form of a three-term ray series.
The constructed algorithm made it possible to obtain a solution in [11] considering
30 terms of the ray expansion, which was impossible in manual calculations.
In this paper, the ray method is used to analyze non-stationary oscillations of an
infinitely long nonlinear classical von Karman plate lying on an elastic isotropic halfspace. Oscillations are excited by instantaneous application of a load to the plate’s
free boundary, resulting in plane non-stationary waves in the thick substrate, behind
the fronts of which the solution is constructed using ray expansions. To conduct
numerical studies, the algorithm proposed in [11] for a linear problem is generalized
for the analysis of non-linear vibrations.

2 Governing Equations for the Formulated Problem
Let us study transient vibrations of an infinitely long elastic nonlinear plate with the
thickness h being in smooth contact with an elastic isotropic half-space. The motion
of such a plate in the rectangular Cartesian coordinate system (x1 , x2 ) is described
by the following set of equations [24]:
D

w−

∂2
∂ 2w
∂ 2w ∂ 2
∂ 2w
∂ 2w ∂ 2
+2
−
+ ρ1 h 2 = q,
2
2
2
2
∂ x1 ∂x2 ∂ x1 ∂x2
∂t
∂ x1 ∂ x2
∂ x2 ∂ x1
(1)
1
Eh

∂ 2w ∂ 2w
+ 2
−
∂x1 ∂x22

∂ 2w
∂ x1 ∂x2

= 0,

(2)

where w = w(x1 , x2 , t) is the plate deflection, D = Eh3 /12(1 − ν 2 ) is the cylindrical
rigidity, ρ1 is the material density, q(x1 , x2 , t ) is the intensity of the transverse load,
E is the elastic modulus, ν is the Poisson’s ratio, is the stress function, t is the
time, and is the Laplace operator.
The equations of the dynamic behavior of an isotropic half-space have the form
∂uj
∂σij
∂ui
∂ 2 ui
∂uk
,
= ρ 2 , σij = λ
δij + μ
+
∂xj
∂t
∂xk
∂xj
∂xi

(3)

144

M. V. Shitikova and A. S. Bespalova

where σij and ui are the stress tensor and displacement vector components, respectively, ρ is the density of the half-space material, λ and μ are Lame’s elastic constants,
δij is the Kronecker symbol, and Latin indices take on the values 1, 2, and 3.
Suppose that the plate is in a smooth contact with the half-space at x3 = h/2, i.e.
it is subjected to the following boundary conditions:
σ33 (x1 , x2 , h/2, t) = q(x1, x2 , t),
στ 3 (x1 , x2 , h/2, t) = 0 (τ = 1, 2),

(4)

u3 (x1 , x2 , h/2, t) = w(x1, x2 , t).
Transient vibrations of the plate are excited by snap-action loads such that the
plate particles at the initial point in time are brought to the speeds
∂w
∂t

= V0 (x1 , x2 ),

(5)

t=0

where V0 (x1 , x2 ) is a given function.

3 Solution for a half-space
Two surfaces of strong discontinuity (volume waves of compression and shear)
appear in the half-space, caused by the action of the initial speeds (5) of the plate.
Behind the wave fronts the solution for a certain function to be found is constructed
in the form of a series in terms of powers y(α) = t − (x3 − h/2)G (α) ≥ 0, i.e. the ray
series [14, 16].
2

∞

Y (x1 , x2 , t) =
α=1 k=0

1 (α)
Y ,(k)
k!

y(α) H y(α) ,

(6)

y(α) =0

where Y (α) ,(k) = (∂ k Y (α) /∂t k )+ − (∂ k Y (α) /∂t k )− are the jumps in the kth time
derivatives of the function on the fronts of the shock waves, the signs «+» and «−»
denote that the given function is calculated immediately ahead of and behind the
wave front, respectively, α signifies the ordinal number of the wave: α = 1 for the
quasi-longitudinal wave and α = 2 for the quasi-transverse wave, respectively, G (α)
are the wave velocities, and H y(α) is the unit Heaviside function.
To determine the coefficients of the ray series (5) for the desired functions, let us
differentiate the first and the second equations of (3) k and k + 1 times with respect
to time, respectively, take their difference on the different sides of each of the wave
surfaces, and apply the compatibility condition [15] for discontinuities of the (k + 1)
st derivatives of the function Y (x1 , x2 , t)

Application of Ray Expansions for Studying Nonstationary Motion …

δ Y ,(k)
∂ Y ,(k) ∂xi
∂Y ,(k)
= − Y ,(k+1) νi +
,
νi + G
∂xi
δt
∂xα ∂xα

145

(7)

where νi are components of a vector normal to the wave surface, and δ/δt is the
Thomas δ-derivative [15]. Hereafter the upper index in brackets indicating the ordinal
number of the wave is omitted for ease of presentation.
As a result of straightforward calculations, we obtain the recurrent relationships
in terms of the discontinuities in the partial time derivatives of the displacement
velocities
ρG 2 − (λ + 2μ) ω(k+1) = −2(λ + 2μ)
ρG 2 − μ Wτ (k+1) = −2μ

δω(k)
− (λ + μ)GWα(k),α − F(k−1) , (8)
δt

δWτ (k)
− (λ + μ)Gω(k),τ − Fτ (k−1) ,
δt

(9)

where ω(k) = vi,(k) νi , Wτ (k) = vτ,(k) , vi = ui,(1) are the velocity vector components, an index without brackets after a comma labels differentiation with respect to
the corresponding coordinate,
F(k−1) = −(λ + 2μ)
Fτ (k−1) = −μ

δ 2 ω(k−1)
δWα(k−1),α
,
− μG 2 ω(k−1),αα − G(λ + μ)
δt
δt 2

δ 2 Wτ (k−1)
δω(k−1),τ
− μG 2 Wτ (k−1),αα − (λ + μ)G 2 Wα(k−1),ατ − G(λ + μ)
.
δt
δt 2

(10)

The velocities of two
√ types of waves could be√determined from (8) and (9) at
k=−1, namely: G (1) = (λ + 2μ)/ρ and G (2) = μ/ρ, as well as the values ω((α)
k)
and Wτ(α)
on
the
first
wave
at
α
=
1
within
the
accuracy
of
t
he
arbitrary
functions
(k)
f(k) (x1 , x2 ) and on the second wave at α = 2 with the accuracy of the arbitrary
functions gτ (k) (x1 , x2 ) at k = 0, 1, 2, 3....
(α)
Knowing the values ω((α)
k) and Wτ (k) , we substitute them into the ray series (6) and
hence obtain the expressions for the desired functions u3 and σj3 ( j=1,2,3) behind
the surfaces of strong discontinuity up to the boundary of the plate contact with the
half-space in terms of the truncated ray series.

4 Solution for a Nonlinear Elastic Plate
To construct the solution for the plate, the ray series for the values u3 , σ33 and στ 3
need to be written at the contact interface at x3 = h/2, resulting in
1
1
f
+ gα(0),α G (2) t 2 +
f
+ gα(1),α G (2) t 3
u3 x =h/2 = f(0) t +
3
2 (1)
6 (2)
1
1
1
1
+
+ gα(2),α G (2) + gα(0),ββα G (2)3 t 4 +
+ gα(3),α G (2) + gα(1),ββα G (2)3 t 5 + · · · ,
f
f
24 (3)
2
120 (4)
2

(11)

146

M. V. Shitikova and A. S. Bespalova
2
σ33 x =h/2 =
3

α=1

1
(α)
(α)
(α)
(α)
−(λ + 2μ)G (α)−1 ω
t + −(λ + 2μ)G (α)−1 ω
+ −(λ + 2μ)G (α)−1 ω
+ λW
(0)
(1)
τ (0),τ
(2)
2

+ (λ + 2μ)G (α)−1
⎛
+
2
στ 3 x =h/2 =
3

α=1

(α)
δω
(1)
(α)
t2
+λW
τ (1),τ
δt

⎤
⎞
(α)
δω
1⎜
(α)−1 ω(α) + (λ + 2μ)G (α)−1 (2) + λW (α) ⎟t 3 + ...⎥,
⎝−(λ + 2μ)G
⎦
⎠
(3)
τ (2),τ
6
δt

(12)

(α)
(α)
(α)
−μG (α)−1 W
t
+ μ −G (α)−1 W
+ω
τ (0)
τ (1)
(0),τ

⎤
⎞
⎛
(α)
δW
1
1 ⎜
τ (2)
⎥
(α)
(α) ⎟ 3
(α)
(α)
+ μ −G (α)−1 W
t + · · ·⎦.
+ G (α)−1
+ω
t 2 + μ⎝−G (α)−1 W
+ω
⎠
τ (3)
(2),τ
τ (2)
(1),τ
2
6
δt

(13)

Let us seek the stress and deflection functions entering in (1) and (2) in the form
of the following power series:
∞

x1 , x2 , t) =
k=2
∞

w (x1 , x2 , t) =
k=1

1
ϕ(k) (x1 , x2 )t k ,
k!
(14)
1
w(k) (x1 , x2 )t k .
k!

Substituting relationships (11)–(14) into equations of plate motion (1) and (2)
and equating the coefficients at the same powers of t with due account for initial
conditions (5) yield arbitrary functions f(k) (x1 , x2 ) and gτ (k) (x1 , x2 ) to be determined
at each step (k = 0, 1, 2, 3...), as well as the required values w(k) and (k) . Then
considering the found values with due account for (14), one could construct the ray
series to define the plate’s displacement.

5 Numerical investigations
For further investigation, let us assume that function V0 (x1 , x2 ) is given in the
following form:
V0 (x1 , x2 ) = a sin

nx2
mx1
sin
,
h
h

(15)

where a, m and n are given constant numbers.
Considering (15), the ray series (14) for the plate deflection w is reduced to the
following form:
w

⎧
⎤
⎡
⎡
2
3
⎨
2 t3
ρG (1)
ρG (1)
ρG (1) t 2
D
ρ
1
m2 + n2 ⎦
=a t−
−
+
4G (2)2 G (1) − G (1)3 − 4G (2)3
+⎣
−⎣
⎩
ρ1 h 2
ρ1 h
ρ1 h
6
ρ1 h
ρ1 h
2

Application of Ray Expansions for Studying Nonstationary Motion …
⎡
2
(1) 4
D ρG (1)
2
t4
3 Ea2
⎢ ρG
m4 cos 2nx2 + n4 cos 2mx1 −
m2 + n2
+
+⎣
3
24
ρ1 h
2 ρ1
ρ1 h
⎫
⎤
2
⎬
4
mx1
nx
t5
ρG (1)
D2
−
+ ... sin
sin 2 .
m2 + n2 +
4G (2)2 − G (1)2 m2 + n2 ⎦
⎭
ρ1 h
120
h
h
ρ1 h 2

147

× m2 + n2

(16)

The main attention in the study of nonstationary oscillations of a plate is its
dynamic deflection, since this value is of practical importance. With this aim in mind,
we will analyze the dimensionless deflection as a function of the dimensionless time
by introducing the following dimensionless quantities (which are designated by *):
tG (1)
ρ1
μ1
w
, t∗ =
, ρ ∗ = , μ∗ =
,
h
h
ρ
μ
a
G (2)
xi
xi∗ = , (i = 1, 2), a∗ = (1) , G ∗ = (1) .
h
G
G

w∗ =

(17)

To conduct a numerical study of the dynamic response of a nonlinear plate lying
on an elastic half-space, we will use the algorithm [11], developed by the authors
on the basis of the Maple software package, to solve the contact dynamic problem
of transient oscillations of a linear isotropic plate resting on a thick elastic substrate.
For this purpose, we will generalize it with due account for the nonlinear nature of
the problem under consideration.
First, it is necessary to use a subroutine for determining jumps based on the
equations of motion of the medium. In this subroutine, parameters and properties of
the medium should be specified. In our case, the following properties of the medium
are introduced: homogeneity, isotropy. Then a cycle is written to determine N values
of the functions ω(k) and Wτ (k) on the first wave, and similar actions are performed
for the second wave. At the output of the program, we obtain the desired functions
for the substrate and the plate in the form of ray expansions (6).
At the second stage, the algorithm shown in Fig. 1 is used for the analysis of the
plate’s dynamic response.
As an example, we consider a variant of a two-layer medium (represented by
a nonlinear relatively light and pliable plate and an elastic half-space) with the
following parameter values: ρ ∗ = 0.75, μ∗ = 0.1, m = 1, n = 1, sin mx1∗ = sin nx2∗ =
1, a∗ = 0.1, and ν = ν1 = 0.25.
The calculated results via the developed algorithm based on Maple are shown in
Fig. 2 for different number of terms in the ray decomposition, namely: for N = 4, 6,
and 7.
To estimate the amplitude and period of oscillations during dynamic contact interaction, the following characteristic moments of time were determined: the values t ∗
at which the dimensionless deflection w∗ reaches its maximum and minimum values,
i.e. the extremes of the function w∗ , and the values t ∗ of the half-periods, i.e. when
w∗ = 0 (the data are given in Table 1).
From the analysis of Fig. 2 it follows that the oscillation period is approximately
equal to t ∗ ≈ 4.6. So, if we are interested in the oscillation period, then it is necessary

148

M. V. Shitikova and A. S. Bespalova

Fig. 1 Schematic representation of the algorithm for determining the dynamic deflection of a plate
during nonstationary vibrations

to take 7 terms of the ray series into account. And if the task is to determine the
maximum deflection or estimate the maximal stresses to check the local strength,
then in principle it is sufficient to limit ourselves by 4 terms of the ray series or take
6 members into account to obtain a more accurate value.
From (16) it is seen that the deflection of the nonlinear plate represents the sum
of linear and nonlinear terms, in so doing nonlinearity begins to manifest itself only
in the terms involving the time t in the third power and above.

Application of Ray Expansions for Studying Nonstationary Motion …

149

Fig. 2 The dimensionless
time t ∗ dependence of the
dimensionless deflection w∗
for different numbers of
elements of the ray
decomposition N for a
classical nonlinear plate:
N=4—dashed-dotted line,
N=6—dotted line,
N=7—solid line

Table 1 The obtained values within the first half-wave.
Number of terms of
the series

The value of t ∗ = T ∗ /2
for w∗ = 0

The value of
t ∗ = T ∗ /2 for
∗
w∗ = wextr

N =4

3.918

2.029

∗
The value w∗ = wextr

0.094

N =6

2.844

1.734

0.088

N =7

3.478

1.856

0.090

Figure 3 shows a comparison of solutions for the case of dynamic contact interaction of a classical nonlinear (solid line) and linear (dashed line) plates with an
elastic half-space for N=4 (Fig. 3a) and N=6 (Fig. 3b). The maximal values of
∗
the dimensionless deflection for this case are the following: wlinear
extr = 1.026,
∗
∗
∗
wnonlinear
=
0.94
for
N=4
and
w
=
1.123,
w
extr
linear extr
nonlinear extr = 0.88 for N=6
(at a∗ = 1 for a nonlinear plate).
In [11], it has been established that to determine the period of nonstationary
vibrations of a classical light and compliant plate, it is necessary to take a fairly large
number of terms of the series into account, in contrast to a nonlinear plate with the
same properties, as shown in this study. Thus, from Fig. 2 it follows that the period
of vibrations of a nonlinear plate begins to manifest itself starting from the 7-term
truncated ray series, while for a linear plate it takes place at N = 15 [11].
In principle, four terms are sufficient to determine the maximum amplitude for
a nonlinear plate. However, if the problem is to analyze the behavior of a system

150

M. V. Shitikova and A. S. Bespalova

Fig. 3 Dependence of dimensionless deflection w∗ on dimensionless time t ∗ for the number of
terms of the ray expansion a N=4 and b N=6: for a nonlinear plate—a solid line, for a linear
plate—a dotted line

considering more long time, it is necessary to take a large number of terms in the ray
expansions into account, what leads to a sharp increase in the volume of calculations.

6 Conclusion
In this paper, the ray method is used to analyze transient vibrations of an infinitely
long nonlinear classical von Karman plate lying on a thick elastic substrate. An
algorithm developed on the basis of the Maple software package is described for
solving contact dynamic problems associated with the generation and propagation
of wave surfaces of strong and weak discontinuity.
Numerical studies have shown that the Maple software package allows one to solve
quite complex mathematical and engineering problems. In the considered example,
it has been possible to obtain a solution for a significant number of terms of the
ray series, which was previously impossible with «manual» calculations, as well
as to construct the time-dependence of the deflection and to analyze the values of
the amplitude and period for a two-layer medium. It has been established that to
determine the period of nonstationary vibrations, it is necessary to consider a fairly
large number of members of the series (seven or more). Meanwhile four members are
sufficient to determine the maximum amplitude and to estimate the local strength,
but if the task is to analyze the behavior of the system considering more long time,
then it is necessary to determine a larger number of terms, what leads to a sharp
increase in the volume of calculations.
Thus, the developed algorithm based on the Maple software package allows us
to advance in time during the wave process. It could be applied for other types of
boundary and initial conditions and for the analysis of dynamic contact interaction

Application of Ray Expansions for Studying Nonstationary Motion …

151

for more complex dynamic systems. In other words, the problem considered and the
algorithm proposed for its solution provide a good example of the local and global
expansion of the ray method.

References
1. Porutchikov VB (1986) Methods of dynamic theory of elasticity. Nauka, Moscow (in Russian)
2. Rakhmatulin HA, Demyanov YA (2020) Strength of materials under intensive short-term loads.
Universitetskaya kniga, Moscow (in Russian)
3. Shitikova MV (2019) Wave theory of impact and Professor Yury Rossikhin contribution in the
field (A memorial survey). J Mat Eng Performance 28:3161–3173. https://doi.org/10.1007/s11
665-018-3824-6
4. Rossikhin YA, Shitikova MV (1995) Ray method for solving dynamic problems connected
with propagation of wave surfaces of strong and weak discontinuities. Appl Mech Rev 48:1–39.
https://doi.org/10.1115/1.3005096
5. Podil’chuk YN, Rubtsov YK (1996) Use of ray methods in problems of wave propagation and
scattering (review). Int Appl Mech 32:907–930. https://doi.org/10.1007/BF02086475
6. Achenbach JD (1973) Wave propagation in elastic solids. Elsevier, North-Holland
7. Rossikhin YA (1978) On nonstationary vibrations of plates on an elastic foundation. J Appl
Math Mech 42:347–353. https://doi.org/10.1016/0021-8928(78)90153-3
8. Rossikhin YA, Shitikova MV (1995) Non-stationary vibrations of a plate on an elastic halfspace. J Sound Vibr 181:417–429. https://doi.org/10.1006/jsvi.1995.0149
9. Rossikhin YA, Shitikova MV (1995) Thermal shock upon the surface of a plate resting on
a thermoelastic isotropic half-space. J Thermal Stresses 18:291–311. https://doi.org/10.1080/
01495739508946304
10. Achenbach JD, Gautesen AK, McMaken H (1982) Ray methods for waves in elastic solids.
Pitman, Boston
11. Shitikova MV, Bespalova AS (2024) Numerical analysis of unsteady vibrations of a plate
resting on an elastic isotropic half-space. WSEAS Trans Appl Theor Mech 19:12–20. https://
doi.org/10.37394/232011.2024.19.2
12. Rossikhin YA, Shitikova MV (1994) To the construction of uniformly valid forward-area
asymptotics in terms of ray method in dynamic problems of linear viscoelasticity. Trans ASME
J Appl Mech 61:744–746. https://doi.org/10.1115/1.290153
13. Altenbach H, Öchsner А (eds) (2020) Encyclopedia of continuum mechanics. Springer, BerlinHeidelberg. https://doi.org/10.1007/978-3-662-53605-6
14. Rossikhin YA, Shitikova MV (2020) Ray expansion theory. In: Altenbach H., Öchsner A (eds)
Encyclopedia of continuum mechanics, vol 3, pp 2126–2141. Springer, Berlin-Heidelberg.
https://doi.org/10.1007/978-3-662-53605-6_97-1
15. Thomas TY (1961) Plastic flow and fracture in solids. Academic Press, New York
16. Achenbach JD, Reddy DP (1967) Note on wave propagation in linearly viscoelastic media.
ZAMP 18:141–144. https://doi.org/10.1007/bf01593905
17. Morfey CL, Cotaras FD (2024) Propagation in inhomogeneous media (Ray theory). In:
Hamilton MF, Blackstock DT (eds) Nonlinear acoustics, pp 337–370. Springer, Cham. https://
doi.org/10.1007/978-3-031-58963-8_12
18. Amiri SN, Esmaeily A (2013) Transient wave propagation in non-homogeneous viscoelastic
media. Int Rev Mech Eng 7:847–856
19. Rossikhin YA, Shitikova MV (2020) Transient waves in Cosserat beams, Ray expansion
approach. In: Altenbach H., Öchsner A (eds) Encyclopedia of continuum mechanics, vol 3, pp
2563–2572. https://doi.org/10.1007/978-3-662-53605-6_103-1

152

M. V. Shitikova and A. S. Bespalova

20. Rossikhin YA, Shitikova MV (2020) Transient waves propagation in the Mindlin microelastic
medium. Mech Adv Mat Struct 27:1653–1657. https://doi.org/10.1080/15376494.2018.152
4033
21. Murashkin EV, Radayev YN (2021) On a pseudotensor generalization of the HugoniotHadamard linking boundary conditions. Vestnik Chuvashskogo Gosudarsvennogo Pedagogicheskogo Universiteta im. I.Ya. Yakovleva. Seriya: Mekhanika Predel’nogo Sostoyaniya
2:104–114. (in Russian)
22. Murashkin EV, Radayev YN (2015) On a classification of weak discontinuities in micropolar
thermoelasticity. Mat Phys Mech 23:10–13
23. Rossikhin YA, Shitikova MV (2011) Dynamic response of pre-stresses spatially curved thinwalled beams of open profile. In: Series: springer briefs in applied science and technology.
Springer, Berlin-Heidelberg. https://doi.org/10.1007/978-3-642-20969-7
24. Birger IA, YaG Panovko (eds) (1968) Strength, stability, vibrations, vol 3. Mashinostroenije,
Moscow (in Russian)

The Effect of Nanomodifying Additives
on the Properties of Dispersed
Reinforced Concrete
V. A. Perfilov, D. A. Lyashenko, I. A. Tomareva, M. E. Nicolaev,
and V. I. Klimenko

Abstract The article provides literature data on the use of steel fiber reinforced
concrete. The results of the development of fiber-reinforced concrete compositions
modified with a nano-additive are presented. The dependence of the strength characteristics of fine-grained concrete on the amount of carbon nanotubes introduced has
been determined. Studies of the stability of a suspension of mixing water with the
inclusion of carbon nanotubes obtained using ultrasonic dispersion technology with
the UZG13-01/22 device have been carried out. The optimal time for using activated
sealing water has been set, which is 100 min from the moment of preparation. As a
result of the conducted research, the composition of concrete was selected with the
integrated use of Mixarm steel fiber with a diameter of 1 mm and a length of up to
54 mm and Taunit-M carbon nanotubes. According to the data obtained, the combined
use of these additives with the Polyplast SP-3 superplasticizer makes it possible to
increase compressive and flexural strength by 30%. In addition, an improvement
in the intensity of concrete strength gain in the early stages of hardening has been
determined.
Keywords Fiber-reinforced concrete · Steel fiber · Carbon nanotubes ·
Dispersion · Superplasticizer

1 Introduction
Modern building materials science is aimed at obtaining new or improving existing
materials technologies related to improving basic operational properties, which will
significantly improve the quality and durability of structures [1, 2]. This will reduce
the cost of their costs by reducing the number of construction and installation works
and reducing the material consumption of building structures. One of the promising
V. A. Perfilov · D. A. Lyashenko (B) · I. A. Tomareva · M. E. Nicolaev · V. I. Klimenko
Volgograd State Technical University Institute of Architecture and Construction, Volgograd,
Russia
e-mail: dmitiry.lyashenko@yandex.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_13

153

154

V. A. Perfilov et al.

directions for solving problems in this field is the use of nanomodifying additives for
concrete, including fiber-reinforced concrete with the addition of carbon nanoscale
tubes [3, 4]. In recent years, the construction industry has been focused on reducing
the thickness of building structures. This is due to the large range of products, the
creation of high-strength concrete and the increasing complexity of engineering
tasks in the construction of buildings and structures. Fibrocrete has technological
advantages, namely: a significant reduction in density, which reduces labor costs for
reinforcing work, as well as reducing the load on vertical formwork [5–7]. Despite
this, there is practically no experience in the use of fiber-reinforced concrete in the
industry. This is primarily due to the high cost of steel fiber. A promising area of
technology for high-functional and high-strength fiber-reinforced concrete is the use
of various modifications of nano-additives.

2 The theoretical part
Concretes have low flexural tensile strength compared to compressive strength. When
such loads are perceived, concrete is prone to cracking. Various types of fibers can
be used for concrete reinforcement, as well as carbon nanotubes as nanoarming crystallization centers. The introduction of nanomodifiers reduces crack propagation at
the nanoscale. Many studies indicate an increase in the strength of nanomodified
concretes by 15–20% [8, 9]. Nanotechnology is being actively introduced into the
construction industry to improve the properties of concrete. Nanomodifying additives such as carbon nanotubes (CNTs), nanoscale SiO2 and feo3 , as well as microand nanosilicon are actively used in modern construction. These additives significantly improve the mechanical properties of concrete, including the adhesion of the
cement binder, impact strength and durability of the composite [10, 11]. Nanomodification makes it possible to reduce crack opening by strengthening the structure at the
nanoscale, which reduces the number of nanocracks, which subsequently form large
cracks [12]. CNTs have unique properties such as high strength, modulus of elasticity and chemical resistance, which makes them a promising material for concrete
reinforcement. The introduction of such additives into the concrete mixture regulates
crystallization processes, making the cement stone a composite material. According
to the literature data, the optimal amount of CNT is 0.001-0.01% of the binder weight
[13–15].
Steel fiber reinforced concrete
Steel fiber is mainly used to increase the load-bearing capacity of the structure. In
this regard, it is recommended to use steel fiber in floor slabs and walls experiencing bending loads. During the reconstruction of buildings, this additive is used
to strengthen load-bearing structures. Thus, for damaged vertical structures, a fiberreinforced concrete layer can be used as a reinforcing element, which significantly
increases the bending strength of the structure [16, 17]. Steel fiber concrete is a
type of reinforced concrete that includes steel fibers in a concrete matrix, thereby

The Effect of Nanomodifying Additives on the Properties of Dispersed …

155

reducing the need for concrete reinforcement and achieving savings by eliminating
reinforcement frames and reducing labor costs for their manufacture. The process
of manufacturing steel fiber concrete consists in preparing a concrete mixture using
mixers, by adding an estimated amount of dispersed steel fiber and mixing the components until a homogeneous mixture. After that, the mixture is laid and subjected to
vibration compaction. Rational compositions were selected for steel fiber concrete:
the ratio of cement and sand for them is 1:1.9 to 2.0, the water-cement ratio is from
0.4 to 0.5%, plasticizing additives in the amount of 0.6 to 1% by weight of the binder
are also used. The reinforcement parameters of a steel-fiber concrete mix are characterized by the following values: the volume content of fiber is up to 2%, the ratio
of fiber length to diameter is from 30 to 45, and the diameter is up to 1.5 mm. Steel
fiber has a disadvantage when it is introduced into a concrete mix, namely, it is prone
to fiber sticking together and forming “hedgehogs” when mixed. In this regard, the
fiber has length limitations [18]. The strength of steel fiber concrete is proportional
to the distance between the fibers, the optimal value of which is 6-10 mm, which
can lead to material hardening up to 2.5 times [19, 20]. However, structures using
steel fiber may fail due to insufficient fiber bonding. An increase in fiber concentration by more than 3% is prone to an increased increase in fiber adhesion, and,
consequently, compaction becomes more difficult and the strength of the material
decreases. Thus, one of the relevant studies is the issues of determining the optimal
technological process capable of providing maximum strength characteristics of steel
fiber concrete.

3 The experimental part
The following materials were used in the study: Eurocement M500 Portland cement,
sand with a grain size of 1.8–2.0, crushed stone fractions of 5–10 mm and 5–20 mm,
Taunit-M carbon nanotubes with an inner diameter of 8 and an outer diameter of
15 nm, nanotube length of no more than 2 microns, Mixarm steel fiber with a diameter of up to 1 mm and up to 54 mm long, the main advantage of such fiber is a
high coefficient of retention in concrete (95%), which is achieved by cone-shaped
anchors, superplasticizer SP-3 in powder form. Application of a nanomodifying
additive To assess the effect of nanomodifiers on concrete strength, cement, quartz
sand, superplasticizer SP-3 and CNT Taunit-M were used. Control formulations and
mixtures with the addition of plasticizer and CNT in various concentrations were
prepared. The nanomodifier was introduced using an ultrasonic dispersant UZG13
0.1/22 (fig. 1) with an ultrasound frequency of 22 kHz. In this study, fine-grained
concrete modified with nanobucks was produced. The samples were kept for 28 days
and tested for durability.
For all compositions, the compressive strength was determined using a nondestructive method at the ages of 7.14 and 28 days. The cooking technology was
as follows: The calculated amount of CNTs, as well as a superplasticizer, were introduced into the sealing water. Next, the working body was immersed in a container

156

V. A. Perfilov et al.

Fig. 1 Ultrasonic dispersant
UZG13-01/22.

with water, where it was activated by ultrasound for 5 min. During the operation
of the device, due to the high frequency of ultrasound and cavitation forces, highly
dispersed carbon agglomerates are broken up and evenly distributed throughout the
entire volume of the mixing water. In parallel, the dry components were stirred to
further mix the concrete mixture and form the sample beams. The results of the
obtained series of studies are presented in Table 1.
According to the data obtained, it can be concluded that CNT formulations in the
amount of 0.005–0.01 have higher strength indicators compared to control samples.
It should be noted that the increase in strength is already observed on the 7th day.
So for composition 11, it was 15.5%. Increasing the strength characteristics in the
early stages of concrete hardening has a positive effect on production processes.
Thus, the optimal amount of the added additive is 0.005% by weight of cement.
Table 1 Dependence of the strength of fine-grained concrete on the amount of nano-additive
introduced
Compound CNT, % by weight Rcom 7 days, MPa Rcom 14 days, MPa Rcom 28 days, MPa
of cement
1

–

36.4

40.8

0.001

39.2

40.9

45.6

0.002

40.9

43.7

0.003

39.8

42.6

47.1

0.004

41.2

42.8

45.9

0.005

41.9

43.7

47.7

0.006

41.5

44.6

46.8

0.007

41.8

47.7

0.008

41.1

43.5

47.3

0.009

40.9

43.5

47.2

The Effect of Nanomodifying Additives on the Properties of Dispersed …

157

Suspension stability To assess the stability of CNT injection into the mixing water,
a photocolorimetry study was performed on a FC-3 device. The method is based
on the property of colored solutions to absorb light of a certain wavelength passing
through it. The more intensely colored the solution is, the greater the decrease in
light intensity as it passes through the solution. When CNT solid particles settle,
the coloration of the mixing water decreases. During the study, the intensity of the
light passing through the solution was evaluated. The readings were taken when the
obtained samples were settled from the moment of preparation to 120 minutes. The
results of the data obtained are shown in Table 2 and Figs. 2 and 3.
It can be seen from the graphs that the optimal time for the application of activated sealing water after the introduction of CNT using ultrasonic dispersion with
a frequency of 20 kHz is 80 min, with the use of plasticizer, the time increases to
100 min. Subsequent settling leads to an increase in the intensity of light transmission by more than 50% in both cases (Figs. 2 and 3). Steel fiber reinforced concrete
modified with nano additives The final stage of this work was the selection of the
composition of fiber-reinforced concrete modified with nanoscale additives. Formulations with a C content were selected for laboratory studies.:N: W = 1:2:3.85, with
Table 2 Stability of the suspension of water mixing with CNT
Sample

0 min 20 min 40 min 60 min 80 min 100 min 120 min

The intensity of the transmitted 53.5
light T, % Through: Water +
CNT

77.5

The intensity of the transmitted 10
light T, % Through:
Water+CNT+SP-3

10.2

10.5

11.3

Fig. 2 Water + CNT resistance

158

V. A. Perfilov et al.

Fig. 3 Water + CNT+SP-3 resistance

a water-cement ratio of W /C = 0.5. According to the data obtained earlier, the introduction of carbon nanotubes was carried out in an amount of 0.005 and 0.01% by
weight of cement. Steel fiber was introduced in the range of up to 2% by weight of the
binder. The concentration of superplasticizer SP-3 was 0.5% by weight of cement.
Compressive strength was determined at the ages of 3,7,14 and 28 days. At the end of
the curing period, the samples were tested on presses to determine bending strength.
The characteristics of fiber-reinforced concrete using CNT in the amount of 0.005
and 0.01% by weight of cement are shown in Tables 3 and 4, respectively.
Table 3 Characteristics of fiber-reinforced concrete using CNT in the amount of 0.005 % by weight
of cement
No. Fiber
Unt, % by m.c. Bending strength Compressive strength, MPa
(28 days), MPa
“Mixarm” % by
3 days 7 days 14 days 28 days
m.c.
1

–

6.2

26.4

42.2

46.5

48.5

–

0.005

7.6

26.1

49.5

52.5

54.3

0.25

0.005

8.5

28.3

49.9

52.1

55.9

0.5

0.005

9.6

29.2

51.5

56.5

58.2

0.75

0.005

10.2

30.7

52.5

56.9

58.7

1.0

0.005

10.9

31.5

54.1

59.8

60.8

1.5

0.005

12.6

31.0

58.1

61.8

63.0

2.0

0.005

13.0

32.0

58.6

62.5

63.8

The Effect of Nanomodifying Additives on the Properties of Dispersed …

159

Table 4 Characteristics of fibrocrete using CNT in an amount of 0.01 % by weight of cement
No. Fiber “Mixarm” Unt, % by m.c. Bending strength Compressive strength, MPa
% by m.c.
(28 days), MPa
3 days 7 days 14 days 28 days
1

–

5.7

25.2

41.0

46.5

47.8

–

0.01

7.9

26.9

50.2

55.5

56.8

0.25

0.01

8.1

29.4

51.5

55.1

57.6

0.5

0.01

10.3

29.7

52.4

56.5

58.2

0.75

0.01

10.8

30.1

53.7

57.9

59.9

1.0

0.01

11.7

32.1

55.2

60.8

62.5

1.5

0.01

11.1

31.8

56.0

60.8

61.1

2.0

0.01

13.6

32.9

58.9

63.5

64.3

Analysis of laboratory data indicates the positive effect of steel fiber reinforcement
on nanomodified concrete. There is an increase in both compressive and flexural
strength. Compositions 8 with a content of 0.005 and 0.01 had maximum strength
characteristics. An increase in the amount of fiber over 2% by weight of the binder is
economically impractical. It should be noted that an increase in strength is observed
with the introduction of a nanomodifier, so in formulations 2 for both concentrations
of CNT, there is an increase in bending and compressive strength by 15%.
Figure 4 shows a graph showing the effect of steel fiber on concrete bending
strength. There is an increase in strength with an increase in fiber content. Compositions of 8 with a content of 2% steel fiber by weight of cement had the maximum
strength. The increase in strength was more than 30%. An increase in strength of up
to 30% compared to samples without the use of steel fiber can be explained by the
combined effect of CNT and steel fiber additives. This is how nanotubes provide a
reinforcing effect at the macro level, while steel fiber reinforces concrete at the micro
level.
Figure 5 shows a graph of the rate of compressive strength gain of the studied
compounds. It can be seen that the control formulations without the use of CNTs
had a lower intensity of strength gain in a short period of hardening (from 3 to
7 days). The strength characteristics are improved due to the formation of a denser
fiber-reinforced concrete structure. Analysis of laboratory data indicates the positive
effect of steel fiber reinforcement on nanomodified concrete.
There is an increase in both compressive and flexural strength. Composition 8
had maximum strength characteristics. An increase in the amount of fiber over 2%
by weight of the binder is economically impractical. Thus, it is established that the
optimal amount of fiber is in the range from 1 to 2% by weight of cement.

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Fig. 4 Effect of fiber content on bending strength

Fig. 5 Graph of concrete strength gain intensity

4 Conclusions
Conclusions In the course of the study, the effect of steel fiber and nanomodifiers on
the characteristics of steel fiber concrete was considered, and the optimal composition
was selected with the combined use of these additives and superplasticizer. Studies
have shown that the complex additive SP-3 in combination with carbon nanotubes

The Effect of Nanomodifying Additives on the Properties of Dispersed …

161

“Taunit-M” provide a significant increase in concrete strength compared to control
samples. At the same time, each of these additives, applied separately, also demonstrates positive results, but their combined use gives the greatest effect. A technology
for introducing nano-additives into the concrete mix using ultrasonic dispersion was
selected. The stability of the suspension of activated sealing water was also studied.
Thus, the optimal time for using the mixing water obtained by dispersion together
with CNT and plasticizer is 100 min. The optimal volume content of Mixarm steel
fiber ranges from 1% to 2.0%. At the same time, the best strength results are achieved
at 2.0%, and an increase in this indicator negatively affects the economic feasibility
of using this additive. At the same time, steel fibers provide increased strength both
in bending and, to a lesser extent, in compression. The introduction of a complex
additive containing Mixarm steel fiber and a complex nanomodifying additive into
the fiber-concrete mixture significantly increases the strength of concrete, including
in the early stages of hardening. This is achieved by optimizing the structure formation and improving the physical and mechanical properties of the material, as well
as by improving the structure of the material at the nanoscale.

References
1. Palamarchuk AA, Shishakina OA, Kochurov DV, Arakelyan AG (2018) Polymer concretes—
promising building materials. Int Stud Sci Bull 6:105
2. Endzhievskaya IG, Demina AV, Endzhievsky AS, Dubrovskaya SD (2022) Assessment of the
interaction of additives in concrete. Bull Tomsk State Univ Arch Civ Eng 24(3):128–137.
https://doi.org/10.31675/1607-1859-2022-24-3-128-137
3. Moiseeva VI, YaV P, Tyumentsev ME, Pankov PA (2019) Nanotechnologies in the field of
production of construction materials. Innov Invest 11:293–297
4. Pimenov AI, Ibragimov RA, Izotov VS (2014) The influence of carbon nanotubes and the
method of their introduction on the properties of cement compositions. News High Educ Inst
Constr 6(666):26–30
5. Seydibeyoglu, MO, Mohanty, AK, Misra M (2017) Fiber technology for fiber-reinforced
composites. In: A volume in Woodhead Publishing series in composites science and
engineering. Woodhead Publishing. Cambridge, p 336
6. Shcherban EM, Stelmakh SA, Nazhuev MP, Nasevich AS, Geraskina VE, Peshev AU (2018)
The influence of various types of fiber on the physico-mechanical properties of centrifuged
concrete. Bull Eurasian Sci 6:10
7. Sedykh SA (2023) Fibroconcrete prospects of modern construction. Colloquium-Journal
14(173):16–21
8. Lyashenko DA, Perfilov VA (2024) Nanomodified cement composition. Bull MGSU
19(7):1116–1124. https://doi.org/10.22227/1997-0935.2024.7.1116-1124
9. Sadovskaya EA, Leonovich SN (2021) Optimization of composition of nanofiber concrete in
terms of fracture toughness by matrix modifiсation. Sci Tech 21(6):499–503. https://doi.org/
10.21122/2227-1031-2022-21-6-499-503
10. Zhdanok SA, Polonina EN, Leonovich SN, Khroustalev BM, Koleda EA (2019) Physicomechanical characteristics of concrete modified by a nanostructured carbon-based plasticizing
admixture. J Eng Phys Thermophys 92(1):12–18. https://doi.org/10.1007/s10891-019-01902
11. Zhdanok SA, Leonovich SN, Polonina EN (2022) Synergetic effect of SiO2 nanoparticles and
carbon nanotubes on concrete properties. Dokl Natl Acad Sci Belarus 66(1):109–112. https://
doi.org/10.29235/1561-8323-2022-66-1-109-112

162

V. A. Perfilov et al.

12. Bazhenov VK, Chervontseva MA (2018) Application of modified basalt microfiber in concrete.
Bull Mosc Inf Technol University—Moscow Inst Arch Civ Eng 3:21–26
13. Lyashenko DA, Perfilov VA, Vesova LM (2022) Fine-grained nanomodified concrete. Inzhenernyy vestnik Dona 10(94):369–378
14. Lyashenko DA, Perfilov VA, Lukyanitsa SV, Lupinogin VV (2022) Development of the
composition of nanomodified cement. Inzhenernyy vestnik Dona 5(89):393–402
15. Monina TA, Antonov II (2021) Modern materials and technologies in prototyping. Nanotechnologies and nanomaterials. Decorative art and the subject-spatial environment. Bull MGHPA
2(2):20–28
16. Singh SK, Kirthika S, Maruthupandian S (2018) Durability studies on basalt fibre reinforced
concrete. Indian Concr J 92(4):45–55
17. Dung DTM, Khai LTQ (2021) Design parameters of steel fiber concrete beams. Mag Civ Eng
2(102):14
18. Ushakov VV (2016) Report on the research work “Study of frost resistance of road fiber
cements.” Progress center llc, Moscow, p 10
19. Abed F, Alhafiz AR (2019) Effect of basalt fibers on the flexural behavior of concrete beams
reinforced with BFRP bars. Compos Struct 215:23–34. https://doi.org/10.1016/j.compstruct.
2019.02.050
20. Khan LU, Gul A, Khan K, Akbar S, Irfanullah (2022) Mechanical properties of steel-fiberreinforced concrete. ICEC 22(1):6. https://doi.org/10.3390/engproc2022022006

Computer Simulation of a Spatial Rod
Arch
N. Tsaritova, A. Kurbanova, A. N. Korchagin, N. Raschenko, and A. Fedorov

Abstract The development of an information model of spatial rod coverage based
on a regular core structure using modern digital programs is an urgent task. The
article analyzes the types of spatial coverings distinguished by geometric features
and selects one of them for further research. The main options of transformable
coatings available on the market are considered. The authors present the result of the
development of an information digital model of an arched transformable coating in
the COMPAS-3D software package, with a new type of hinge joint. The introduction
of modern technologies in the construction industry makes it possible to obtain new
types of structural systems, process and receive the necessary information in a short
time.
Keywords Computer simulation · Spatial structures · The information model · 3D
printing

1 Introduction
Currently, various information modeling technologies are being introduced in the
construction industry to obtain and generate data about the construction site and track
all stages of the life cycle of a building or structure [1–6]. Therefore, it is necessary
to create new approaches and principles of shaping using digital technologies. The
use of spatial rod coatings has become widespread in the world, as such coatings
have a number of advantages.
Spatial rod structures of coatings have “high production efficiency and low material consumption, provide the possibility of wide unification of structural elements,
N. Tsaritova (B) · A. Kurbanova · A. N. Korchagin · N. Raschenko
Platov South-Russian State Polytechnic University (NPI), Novocherkassk, Russia
e-mail: ncaritova@yandex.ru
A. Fedorov
JSC Control Systems and Instruments, St. Petersburg, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_14

163

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Fig. 1 Rogers stadium sliding cover, Toronto

taking into account industry and intersectoral requirements; they allow for the organization of in-line production of a limited range of similar elements, allowing to
obtain a wide variety of coatings with high architectural characteristics and aesthetic
properties that it can create” [7–9]. Spatial coatings are used in areas such as civil
and industrial construction, energy and engineering structures, and unique buildings
and structures. One of the most striking examples is the spatial rod arch Fig. 1.
Spatial rod arch are widely used in the construction of sports facilities, as they
allow significant spans to be blocked without the use of intermediate supports, which
creates comfortable conditions for both spectators and athletes.
The purpose of this study is to develop an information model Spatial Rod Frame
based on a regular core structure using modern digital programs that are widely
available on the market. This study uses the Russian software COMPAS-3 D.

2 Methods and Materials
Load-bearing spatial systems can be classified according to the geometry of the
surface; according to the design scheme; according to the material from which the
system elements are made; according to the shape in the plan; according to the method
of manufacture and installation [10–16]. The following types of spatial coverings are
known, distinguished by geometric features: plane grid framework (Fig. 2); shell of
positive (negative, zero) gaussian curvature and similar ones prismatic shell (Fig. 3);
positive gaussian curvature shell and similar ones convex polyedral shells (Fig. 4),
coatings of double—negative gaussian curvature (Fig. 5).
The authors were particularly interested in coatings of single–zero gaussian curvature, with the possibility of transformation. There are few examples of such types of
structures, let’s look at a few presented on the modern market.
1. A deployable rod structure, which consists of: “rod elements made of two parts
connected by a hinge and mutually spring-loaded. The hinge assembly of the
structure contains a housing with forks for fastening the forming rod elements.

Computer Simulation of a Spatial Rod Arch

165

Fig. 2 a With uniaxial arrangement of elements (crease); b with biaxial arrangement of elements
(plates)

Fig. 3 a Cylindrical shell (vaults); b closed cylindrical shell; с cylindrical hanging shell

Fig. 4 a Elliptical sail shell; b pyramidal (tent) shell; с spherical dome; d polyhedral (geodesic)
dome; e closed elliptical shell; f elliptical hanging shell (cup-shaped)

Fig. 5 a Hyperbolic (saddle-shaped) shells; b hanging type shells (saddle-shaped); с hanging type
shells (tent type)

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The housings provide rotation on the axes. The core elements of the structure are
hollow, the flexible rod is made in the form of a metal cable” [17] (Fig. 6).
2. Combined spatial structural coating: “refers to the field of construction and is
applicable for the construction of coatings for buildings of various spans. The
structure is a spatial core structure equipped with reinforcing elements in the
middle part of the frame in the longitudinal direction” [18] (Fig. 7).
The authors of the article are developing a coating consisting of rod arches with
a unique nodal connection, which allows for the transformation of the structure and
facilitates the installation of this structure. The main advantages of rod arches:

Fig. 6 Diagram of the unfolding frame: 1—forming rod element of the reflecting surface, 2—
forming rod element of the rear surface, 3—diagonal rod element, 4—hinge of the rod element,
5—hinge assembly

Fig. 7 The scheme of the combined spatial structure: 1—spatial frame; 2—nodes of the BGTU
system; 3—rods of belts; 4—rods of braces; 5—supports; 6—lower span reinforcing elements;
7—lower contour reinforcing elements

Computer Simulation of a Spatial Rod Arch

167

• Cost–effective—reducing the weight of the structure reduces the load on the foundation and reduces construction costs. The use of innovative materials such as
carbon fiber and heavy-duty alloys increases economic efficiency.
• Flexibility of forms—the ability to create complex architectural solutions,
including curved and adaptive structures that resemble natural shapes. The
geometry of the arches may vary depending on the functional purpose of the
building.
• Strength and stability—arches can withstand significant loads due to the uniform
stress distribution. This is especially true for structures exposed to high dynamic
loads, such as stadiums and train stations.
• Adaptability to external conditions—core arches are used in areas with high
seismic activity and extreme climatic conditions. Modern technologies allow us
to create structures that are resistant to temperature fluctuations, humidity and
strong gusts of wind.
• Bionic principles—imitation of natural forms, such as leaf ribs, mammalian bones
or insect honeycombs, allows you to optimize load distribution and use a minimum
amount of materials. This increases the durability of structures and reduces the
total amount of raw materials used.
The main task is to maximize the automation of the design process, the speed
of manufacturing components and rod coating, ease of installation and the ability
to assemble/disassemble the structure, convenience of storage and delivery to the
construction site. With the help of modern additive technologies, this problem has a
solution.

3 Results
For designers, arched systems are attractive for their variety of crystal structures,
which they are formed by. Thanks to this, specialists have the opportunity to vary
the exterior surfaces of buildings, as well as the shape of the surfaces in the plan,
creating architecturally expressive buildings and structures. The basic principle of
spatial structures is multi-connectivity. Due to this, the structures have a number
of advantages over other structural solutions, the elements of which are rafter and
sub-rafter trusses, girders.
It is also important to note that in such systems there is a uniform distribution
of the material. When mobile unevenly applied loads act on the system, they are
perceived by a large number of rods. This makes it possible to create lightweight
load-bearing structures for coatings. Spatial core structures have a variety of crystal
structures, which allows designers and architects to vary the shapes of surfaces in
plan and in sections of buildings. The multiple connectivity and spatial operation of
structures make them more rigid than flat ones.
The structures of the system are regular and repeatable, which makes it possible
to unify the structural elements as much as possible: rods and nodes. This makes it

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possible to organize highly mechanized in-line production and reduce specific labor
costs for manufacturing.
The biggest disadvantage of such systems is the large number of nodes and rods,
which creates difficulties when trying to find a rational solution. More than eight
rods can converge in one node of the system. In spatially-rod systems of regular
structure, thin-walled profiles are used, for example, round or rectangular pipes. The
complexity of assembling structures on the assembly site depends primarily on the
design of the components.
According to the type of mounting joints, the nodal joints are divided into: welded;
bolted (bolt-on, shift-bolted); keyways; contact, contact-friction; combined.
In the conditions of site assembly, mounting welded joints are performed. In a
bolted connection, the main elements are the bolts themselves. They can perceive
longitudinal forces, being axial-bolted, or transverse forces, being already shearbolted. A keyed joint is formed when the bolts in the shift-bolt joint are replaced
with overhead or keyed ones. Not all bolts are replaced, leaving those that will
prevent the connected elements from opening in a direction perpendicular to the
acting force. The meaning of the contact node coupling is that the transfer of forces
occurs due to the pressure of adjacent elements. Most often, the tips of the rods are
fixed between the stops that prevent axial movement of the rods, the nodal element.
Contact-friction coupling works by transferring forces through contact, and partly
due to friction forces.
The authors of the article have developed a hinge assembly, which consists of separate parts: upper and lower clamping discs, rods with spherical tips, central clamping
bolt, clamping bolts. It is possible to mount up to twelve rods in this node. The main
advantage of such a connection is the possibility of compact delivery, maximum
unification of all node elements, quick assembly and the ability to disassemble the
structure.
The article presents the result of the development of a digital model of an arched
coating with maximally unified elements and new nodal connections that allow accelerated assembly and disassembly of the structure. The model is made in COMPASS3D, this software package was created: “for solid-state modeling and includes all
the necessary tools, such as using a previously developed model and editing it by
redefining variables, the ability to make changes to the object’s binding to monitor
its behavior in the component system” [19–21].
Screenshots of the visualization screen for solid-state modeling of the elements
of the arched structure in question are shown in Figs. 8, 9, 10 and 11.
Fig. 8 a 3D model of the
rod in COMPAS-3D; b 3D
model of the clamping disc
in COMPAS-3D

Computer Simulation of a Spatial Rod Arch

169

Fig. 9 The hinge knot in COMPAS-3D
Fig. 10 The section in
COMPAS-3D

The assembly consists of pressure plates and hinged tips for attaching rods in
them, twelve rods can be connected at once in the assembly, which gives a great
variability in the geometric shapes of spatial rod structures. All the elements of the

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Fig. 11 a The arch in COMPAS-3D before the transformation; b The arch in COMPAS-3D after
the transformation

assembly are maximally unified, which makes it possible to speed up the installation
of the coating structure. The node is shown in Fig. 9.
The developed arch consists of rods of the same length, all elements can be
assembled in sections (Fig. 10), the length of the arrow in the section is 2.4 m. The
lower belt of the arch can be transformed due to actuators, they allow to reduce
the length of the arrow and, as a result, change the shape and take the necessary
parameters on the construction site.
The COMPAS-3D software package allows you to make drawings for assigning
tasks to related parties, in our case, to prepare the model for 3D printing and
processing in a slicer, which is used in 3D printing, since the end of our work will
be an experiment with an arch model, both numerical and full-scale.
Then the arch frame was assembled before the structure was transformed (Fig. 11).
As a result, a digital model spatial rod arch in COMPAS-3D was obtained (Fig. 12).
A huge advantage of this complex is the ability to create working drawings for further
use by designers.
A technology for manufacturing a hinge joint of rods using modern additive
technologies has been developed and presented. PETG—polyethylene terephthalate
+ glycol was used as the printing material, unlike PLA and HIPS, the material has
a smooth glossy surface. The 3D printer “QIDI Tech Q1-Pro” was used in the work,
printing was performed as follows:
• development of nodal connection parts in COMPAS-3D (presented above);
• in the Cura Slicer, a computer program that converts a virtual 3D model of an
object into machine code (G-code) to control printing on a 3D printer, a COMPAS3D model was prepared (basic printing parameters are set: layer thickness, type
of filling, etc.)—Fig. 13a;
• transfer information to the printer;
• plastic supply;
• print speed selection;
• printing (Fig. 13b);
• obtaining the model (Fig. 13с).

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Fig. 12 a Working drawings in COMPAS-3D

As a result of the developed technology, prototypes of the hinge joint elements
were obtained, with the possibility of further study and improvement of the design.
The advantage of this technology is the complete automation of the process, the speed
of manufacturing elements, and the ability to make adjustments at the design stage.
An undoubted advantage is the saving of material, since additive manufacturing
makes it possible to use as much material as is necessary to manufacture the product,
with an accuracy of fractions of a gram, and it also minimizes waste, since there
are practically no trimmings. It should be noted that parts with a high degree of
complexity were made, such as a pressure disc, which are more laborious and take a
lot of time to create in the traditional way. The authors also managed to minimize the
cost of setting up equipment and creating tooling. In traditional manufacturing, it is

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Fig. 13 a The model in the “Cura” slicer; b the printing; с the resulting models

often necessary to develop and manufacture special molds, molds, etc. to manufacture
new parts.
The ability to obtain design documentation and transfer drawings to production
based on the created 3D model significantly reduces the number of various errors
associated with the lack of a unified information base. Exporting a model to any
calculation software is a relatively simple task. The authors transferred the computational model to the ANSYS complex for further numerical experiments and selection
of cross sections, depending on the size of the arch span. This type of arch can be
made from both steel elements and some types of 3D plastic to facilitate temporary arch-based structures. Such structures can be produced in different areas, as the
production process does not require large capacities and areas.

Computer Simulation of a Spatial Rod Arch

173

In further work, the authors will develop an arch model using modern additive
technologies for experimental studies of the nodal junction and the arch as a whole.
Since with the current level of automation of design processes, it is possible to
obtain prototypes of an invention for conducting experiments, and thanks to the
unification of all elements of the resulting arch, it is possible to increase the speed
of manufacturing elements and ease of assembly of the structure.

4 Conclusion
1. The introduction of new types of spatial architectural and structural systems into
the practice of construction, capable of solving the problems of socio-functional,
technological and aesthetic formation of the architectural environment on the
basis of industrial methods, is the historical objectivity of the interaction of
architecture and scientific and technological progress.
2. Based on the COMPASS-3D software package, digital modeling of the nodal
connection and the spatial arch itself was performed, obtaining design documentation and transferring drawings to production based on the created 3D was
tested. All this speeds up the design and documentation development process,
fully automating the process.
3. The authors tested the developed 3D printing technology to obtain a nodal connection, checked all the steps and obtained a competitive node model as a result.
The advantage of this technology is the speed and full automation of the process.
The advantage of this technology is automation and speed.
4. This type of transformable spatial framework with a hinged angular connection
will allow the construction of cultural or special-purpose structures in hard-toreach parts of the Russian Federation.

References
1. Lukmanova IG, Ukhalkin EV (2023) Activation of implementation of information modelling
technologies in the Russian construction industry. Vestnik MGSU 18(12):2004–2014. https://
doi.org/10.22227/1997-0935.2023.12.2004-2014
2. Azhar S, Nadeem A, Mok JYN, Leung BHY (2008) Building Information Modeling (BIM):
a new paradigm for visual interactive modeling and simulation for construction projects. In:
Proceedings of first international conference on construction in developing countries, рp 435–
446
3. Cao D, Li H, Wang G (2017) Impacts of building information modeling (BIM) implementation
on design and construction performance: a resource dependence theory perspective. Front Eng
Manag 4(1):20–34. 10.15302/ J-FEM-2017010
4. Volkov AA (2012) Modern and promising information technologies in construction. Ind Civ
Eng 9:5–6

174

N. Tsaritova et al.

5. Lieyun D, Ying Z, Burcu A (2014) Building Information Modeling (BIM) application framework: the processof expanding from 3D to computable. Autom Constr 46:82–93. https://doi.
org/10.1016/j.autcon.2014.04.009
6. Sacks R, Koskela L, Dave BA, Owen R (2010) Interaction of lean and building information
modeling in construction. J Constr Eng Manag 136(9). https://doi.org/10.1061/(ASCE)CO.
1943-7862.0000203
7. Fu F, Parke GAR (2018) Assessment of the progressive collapse resistance of double-layer grid
space structures using implicit and explicit methods. Int J Steel Struct 18:831–842. https://doi.
org/10.1007/s13296-018-0030-1
8. Gasbarria P, Montia R, Sabatinib M (2014) Very large space structures: non-linear control and
robustness to structural uncertainties. Acta Astronaut 9:252–265
9. Mushchanov VF, Orzhekhovskiy AN, Mushchanov AV, Tseplyaev MN (2024) Reliability of
spatial rod metal structures of high level of responsibility. Vestnik MGSU 19(5):763–777.
https://doi.org/10.22227/1997-0935.2024.5.763-777
10. Russo M (2022) Geometric analysis of a space grid structure by an integrated 3D survey
approach. Int Arch Photogramm, Remote Sens Spat Inf Sci. XLVI-2/W1-2022:465–472. https://
doi.org/10.5194/isprs-archives-XLVI-2-W1-2022-465-2022
11. Buzalo N, Versilov S, Platonova I, Tsaritova N (2019) Energy efficient building structures
based on gridshell. IOP Conf Ser: Mater Sci Eng 698:022010. https://doi.org/10.1088/1757899X/698/2/022010
12. Chilton J (2000) Space grid structures. Architectural Press, New York
13. Klyuev SV (2007) Optimal design of a core spatial structure. Proc Kazan State Univ Arch Civ
Eng 1(7):17–22
14. Travush VI, Antoshkin VD, Erofeev VT, Gudozhnikov SS (2012) Mode constrctive and
technological solutions of spherical shells. Constr Reconstr 6(44):45–55
15. Buzalo NA, Alekseev SA, Tsaritova NG (2014) Automation of design of spatial core structures.
News High Educ Inst North Cauc Reg Ser: Tech Sci 6(181):83–87
16. Gaydzhurov P, Tsaritova N, Kurbanov A, Kurbanova A, Iskhakova E (2022) Numerical simulation of the process of directed transformation of a regular hinge-rod system. Int J Comput
Civ Struct Eng 18(3):14–24. https://doi.org/10.22337/2587-9618-2022-18-3-14-24
17. Blinov AF, Bondarev AV, Himmelman VG et al (2013) Unfolding reflector frame: No.
2011132996/11. Patent No. 2480386 C2 Russian Federation, Federal State Unitary Enterprise
“Arsenal Design Bureau named after M.V. Frunze”
18. Dragan VI, Mukhin AV, Zinkevich IV et al (2009) Combined spatial structural coating. Utility
Model Patent No. 80471 U1 Russian Federation, No. 2008116753/22, Educational Institution
Brest State Technical University
19. Lyakina PV, Gorbatenko AI (2019) The use of information technologies in the field of construction. In: The collection: profession engineer. Collection of materials of the Youth scientific and
practical conference, pp 230–234
20. Serdyuk AV (2022) СOMPAS 3D—a domestic computer modeling program in construction.
In: Profession of an engineer: a collection of articles of the X All-Russian Youth scientific
and practical conference “Profession of an engineer” dedicated to the 40th anniversary of the
Faculty of Agricultural Engineering and Energy Supply, pp 371–376
21. Kudryavtsev EM (2010) COMPAS-3D. Design in architecture and construction. In: DMK
press, Moscow, p 544

Analysis of Reinforced Concrete Beams
in Road Bridge Superstructures
According to Limit State Method
N. V. Pham, T. H. Tran, T. T. V. Tran, T. B. Q. Vu, and T. Q. T. Nguyen

Abstract The article discusses the findings of a study focused on evaluating the
load-bearing capacity of road bridge superstructures that are designed based on standard models widely adopted in the Russian Federation and Vietnam. The research
reveals that the shift from the traditional allowable stress design method to the more
modern limit state design method now implemented in current engineering standards
plays a key role in explaining why the actual load-bearing capacity of these bridge
superstructures is substantially greater than the loads anticipated during the original
design phase. This transition in design methodology accounts for a more realistic
and conservative assessment of structural performance, ultimately resulting in safer
and more resilient bridge constructions.
Keywords Reinforced concrete beam · Road bridge · Superstructure · Limit state
method · Design model

1 Introduction
Reinforced concrete highway bridge girder systems constructed in accordance with
the standard design model known as “Issue 56,” together with the load specifications codified by the Russian Federation during the 1960s and 1970s, were widely
utilized in bridge construction projects throughout both Russia and Vietnam. These
standardized designs formed the backbone of national bridge-building programs and
were extensively implemented over a period of approximately 15 years, extending
N. V. Pham
Vietnam Maritime University, Hai Phong, Vietnam
T. H. Tran · T. T. V. Tran (B) · T. B. Q. Vu
Hanoi Architectural University, Hanoi, Vietnam
e-mail: vanttt@hau.edu.vn
T. Q. T. Nguyen
University of Transport and Communications, Hanoi, Vietnam
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_15

175

176

N. V. Pham et al.

into the late 1970s. As a result, they continue to constitute a substantial portion of
the current bridge infrastructure. Notably, within the Russian Federation, such girder
systems still account for more than 10% of all active bridge span structures currently
in service [1], underscoring their lasting presence and engineering legacy.
One of the key advantages that contributed to the widespread adoption of these
girder systems was their compatibility with industrialized construction techniques,
which enabled the rapid and large-scale production of standardized components.
This high level of construction efficiency proved particularly beneficial in addressing
the urgent post-war demand for transportation infrastructure in both countries. The
standardized design facilitated streamlined manufacturing, reduced on-site labor
requirements, and minimized construction timelines—all of which were crucial in the
context of post-war reconstruction and national development efforts. These factors
combined to make the “Issue 56” model a practical and effective solution for bridge
construction during that era.
However, the operational conditions of these bridges have changed considerably
since their initial construction. Today, they are exposed to vehicular loads that significantly exceed the original design parameters. According to [1], temporary live loads
have increased markedly over the past five decades. Notably, vehicle weights have
risen by approximately 30–50%, and the equivalent load from wheeled traffic has
grown by about 25–30% compared to that from tracked traffic, which was commonly
considered during the original design phase. This substantial increase in loading
necessitates a thorough evaluation of the residual or reserve load-carrying capacity
of these girder span systems to ensure continued structural safety and serviceability.
The “Issue 56” bridge design model was developed in two distinct structural variants, each corresponding to different traffic load classifications in accordance with the
regulatory framework of the time. Specifically, these variants are identified as N13 in
combination with NG-60, and N18 paired with NK-80. The fundamental differences
between the two configurations lie in the concrete strength class utilized and the
cross-sectional area of the primary longitudinal reinforcement, both of which were
tailored to meet the respective load-bearing requirements of each traffic category.
During the period in which these bridges were originally designed, structural
calculations were conducted based on the allowable stress design method a traditional approach widely used before the introduction of modern limit state design
philosophies. This method involved ensuring that the stresses induced in structural
components under applied loads did not exceed predefined permissible limits. The
traffic loading conditions applied in these calculations were derived from the N13
and N18 load models, which were officially recognized and enforced under the
design standards of that era. These historical load models reflected the vehicle types,
axle configurations, and traffic intensities typical of mid-20th-century transportation
systems, forming the basis for engineering design decisions during that time.
The primary aim of this paper is to reassess and quantify the load-carrying capacity
of these existing bridge span structures by means of computational analysis that
adheres to current limit state design principles. The study utilizes modern advances in
information technology and employs the finite element method (FEM) for simulation
and modeling. Updated traffic load models A11 and A14 are applied within the FEM

Analysis of Reinforced Concrete Beams in Road Bridge Superstructures …

177

framework to reflect present-day loading conditions more accurately. It is important
to note that this study focuses solely on structural capacity in idealized conditions
and does not account for material deterioration. According to recent survey data,
the majority of girder elements in these bridge spans remain in satisfactory technical
condition, owing to ongoing maintenance efforts and regular structural rehabilitation.

2 Reinforced Concrete Beams and Road Bridge
Superstructures
According to the findings reported in [1], temporary live loads on highway bridges
have experienced a substantial increase over the past 50 years, driven primarily by
the evolution of transportation systems and the rising demands of modern logistics.
Specifically, the average weight of vehicles using the highway network has increased
by approximately 30–50%, a trend that reflects the widespread use of heavier trucks
and higher axle loads. Moreover, the equivalent live load exerted by wheeled traffic
lanes has risen by an estimated 25–30% in comparison to that of tracked traffic lanes,
which were more common in earlier traffic scenarios.
This escalation in traffic loads presents critical challenges to the structural integrity
and serviceability of existing bridges, particularly those designed according to earlier
standards that did not account for such increases. For instance, the reinforced concrete
bridge girders constructed under the standard design model referred to as “Issue
56” were developed in two primary variants tailored to specific load classes. The
first variant was designed for load classes N13 and NG-60, while the second was
intended for N18 and NK-80. These designations correspond to differing assumptions
about traffic intensity and vehicle types. Importantly, these variants also exhibit key
differences in their material specifications most notably in the strength class of the
concrete and the cross-sectional area of the primary reinforcement bars.
Such design distinctions were originally calibrated to meet the traffic conditions
and regulatory expectations of their time. However, in light of the significant increase
in live loads over the decades, there is a growing need to reevaluate the adequacy
of these older design approaches. This is particularly important when assessing the
residual load-bearing capacity of in-service bridges and determining their safety
margins under current operational demands. The data underscores the importance
of updating analytical models and applying modern design philosophies such as the
limit state method to more accurately reflect contemporary loading scenarios and
ensure the continued safety and functionality of aging bridge infrastructure.
Table 1 presents the key technical parameters of the bridge girders, including
the cross-sectional height and the cross-sectional area of the main reinforcement at
mid-span and at the quarter-span locations. The girder materials consist of concrete
grade M300 (B22.5) for span structures designed for load classes N18 and NK-80,
and concrete grade M250 (B19) for span structures designed for reference live load
classes N13 and NG-60.

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N. V. Pham et al.

Table 1 Technical specifications of 14.06-m-long girders designed according to standard model
“Version No. 56”ю
Calculated span
L, m

Beam height h,
cm

Effective height,
h0
at mid span
at quarter span

11.1

70.3
72.3

Reinforcement area As
at mid span
at quarter span

Reference Live
load
N13, NG-60

Reference Live
load
N18, NK-80

44.2
36.2

52.3
48.2

Figures 1 and 2 illustrate the cross-sectional geometry and reinforcement arrangement of a standard 11.36 m reinforced concrete girder from the “Issue 56” design
with a total length of 11.36 m, which forms part of a highway bridge span structure. These examples are provided to emphasize the progression and refinement of
structural detailing practices, as well as the changes in design standards that have
occurred over the decades.
Figure 1 shows the original cross section as adopted in the 1957 Soyuzdorproject
standard, with an effective roadway clearance of G7 + 2 × 0.75 m. The section
consists of: (1) a T-shaped reinforced concrete beam with conventional reinforcement, (2) diaphragms, (3) reinforced concrete curbs with metal railings, (4) metal
safety barriers, and (5) multilayer pavement. This configuration reflects the structural
and detailing practices of its time, designed for the N13/NG-60 or N18/NK-80 live
load classes.
Figure 2 presents the reinforcement scheme for the same beam length in the
N18/NK-80 variant, including (a) the longitudinal reinforcement layout and (b) the
corresponding cross section with reinforcement placement. The main tensile reinforcement consists of 2Ø32 mm bars (1) and 2Ø16 mm bars (2) in the studied spans.
Compared to the original 1957 version, this layout reflects modifications introduced
800

4
55

190
Q/2

110

190
5

q/2

140=840

Fig.1 Cross section of a span structure with a length of 11.36 m and a G8 + 2 × 0.75, with beams
according to “Issue 56” of Soyuzdorproject (1957): 1—T-beam with conventional reinforcement,
2—diaphragms, 3—reinforced concrete curbs with metal railings, 4—metal barrier guards, 5—
multilayer pavement

Analysis of Reinforced Concrete Beams in Road Bridge Superstructures …

179

Fig. 2 Reinforcement layout for an 11.36 m beam (N18/NK-80): a—Longitudinal reinforcement,
b—Cross-section and reinforcement layout; 1—2Ø32, 2—2Ø16 in the studied spans

in later reconstructions to improve bending resistance, ductility, and compliance with
modern load requirements, while maintaining the original geometric envelope.
In contrast, Fig. 2 illustrates the updated design implemented during the reconstruction and modernization phase of the bridge girder, which was undertaken to
align the structure with current structural codes, performance criteria, and increased
loading requirements. In this revised version, the effective span width was extended to
G8 + 2 × 0.75 m, indicating a deliberate increase in the clear span length to accommodate broader roadway lanes, enhanced vehicle capacity, or improved structural efficiency under higher live load demands. This evolution in design is marked by notable
adjustments in the reinforcement scheme, especially in the arrangement, number, and
distribution of the longitudinal tensile reinforcement bars. These changes reflect the
application of modern engineering principles aimed at improving the girder’s loadbearing performance, structural ductility, and durability over time. The comparison
between Figs. 1 and 2 highlights the strategic and technical adaptations employed in
the rehabilitation and upgrading of legacy bridge infrastructure, demonstrating how
older structures are being modified to meet contemporary traffic volumes, safety
standards, and serviceability expectations.

3 Analysis Methods for Reinforced Concrete Beam
Calculation in Road Bridge Superstructures
The stirrup reinforcement in the girders belongs to the A-II class. As noted in [1], in
calculations based on the allowable stress design method, the dynamic load factors
for the studied span lengths were chosen close to those currently applied. However,

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N. V. Pham et al.

unlike the limit state design method, the allowable stress method does not consider
reliability factors for loads. Instead of directly calculating the load-bearing capacity
of concrete and reinforcement, the allowable stress method uses significantly reduced
“permissible stresses.“ Consequently, structures designed by this method inherently
possess a relatively large reserve in load-carrying capacity.
The structural analysis of the studied girders indicates that the critical factor
influencing the design approach and load-bearing capacity assessment is the strength
check based on the bending moment values. In calculations using the allowable
stress design method, this check is also decisive in determining the girder crosssectional dimensions and the cross-sectional area of the main reinforcement. The
design and placement of reinforcement in the girders, according to the standard
design, are developed such that when the full load-bearing capacity for the design
bending moment is utilized, the reserve strength remains preserved for other checks
in accordance with the first and second limit states specified in SNiP 2.05.03-84*
(under the same vertical design load).
Figure 3 shows the interaction diagrams of the “ultimate” and “allowable” bending
moments (material envelope curves) obtained using the limit state method and the
allowable stress method for the 11.36 m long girder, based on the reinforcement distribution according to the standard design. Additionally, Table 2 presents a comparison
of the “ultimate” and “allowable” bending moments at mid-span and quarter-span
locations of the girder for the two reinforcement variants corresponding to the two
load classes mentioned earlier. The data from Fig. 3 and Table 2 indicate that the
maximum bending moment determined by the limit state method is more than 1.6
times greater than the allowable bending moment calculated using the allowable
stress method.
When determining the bending moments in girders subjected to temporary loads,
spatial analyses were carried out using two methods: the method proposed by
Donchenko [2] and the finite element method (FEM), employing the calculation
schemes 3 and 4 from references [3–6]. The spatial calculation results of the bridge
span structure, along with the diagrams in Fig. 3, demonstrate that to verify the
load-bearing capacity of the girder, it is not necessary to compare the calculated and
ultimate (allowable) moments along the entire girder length; it suffices to compare
the corresponding bending moments at mid-span. Therefore, the subsequent computational analysis was performed for the mid-span sections of the span structures and
for individual girders subjected to the highest loads (located at coordinate x = l/2).
Figure 4 illustrates an example of the distribution diagram of the ratio (moment
distribution coefficient) of bending moments Md acting on the girders (from girder
1 to girder 7) relative to the total calculated bending moment Mcal at the mid-span
of an 11.36 m long span structure with overall dimensions of G8 + 2 × 0.75 m.
This is under the application of two temporary vertical load strip AK approaching
the left-side barrier (“second case” load according to clause 2.12 of SNiP 2.05.03 *).
The calculations performed indicate that the values of the ratio kpu = Mb /Mcal
obtained by the two methods [2, 3] for a span length of 11.36 m are nearly identical.
For overall span widths of G7, G8, and G10, the bending moment ratios calculated
from two temporary traffic lanes on the most heavily loaded girder fall within the

Analysis of Reinforced Concrete Beams in Road Bridge Superstructures …

181

Fig. 3 Moment envelopes (ultimate vs. allowable) for 11.36 m beams using limit state and allowable
stress methods

Table 2 Ultimate and allowable bending moments at mid-span and quarter-span of the beams for
two reinforcement variants
Reference Live load

Unit

kNm

Calculated parameters
At the mid span

At the quarter span

11.36 m

736

609

N13, NG-60

Mult
Mallow

kNm

461

382

N18, NK-80

Mult

kNm

847

801

Mallow

kNm

529

507

range of kpu,max = 0.20−0.22 for load type A11. Correspondingly, the maximum
bending moment in the 11.36 m long beam is Mb,max = 448−493 kNm.
The data presented in Table 3 reveal that, when utilizing the limit state design
method rather than the allowable stress method that was commonly employed in
design practices of the 1960s along with the application of more advanced and precise
computational techniques, it is possible to uncover the latent reserve in the loadbearing capacity of existing span structures. These structures, despite having been
in continuous service for several decades, still demonstrate the ability to sustain
current traffic loads effectively. The shift to the limit state approach, which accounts
more accurately for both material strengths and load combinations, shows that the
calculated load-bearing capacity of the concrete and reinforcing steel components is

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N. V. Pham et al.

Fig. 4 Bending moment coefficient kpu = Mb /Mcal at midspan of 11.36 m beam (G8 + 2 ×
0.75 m): 1—Donchenko’s method; 2—FEM

Table 3 Calculated bending moments in beams according to different methods
Calculated parameters

Unit

Calculated parameters of
11.36 m beam

Reinforcement area, As

cm2

44.23

52.26

Ultimate bending moments according to Limit
state method, Mult

kNm

736

847

Allowable bending moments according to
Allowable stress method, Mallow

kNm

461

527

11.36

significantly higher by approximately 30–32% than what was determined under the
original design method. This increase in capacity under live load conditions confirms
that span structures originally designed to support load classes N18 (or N13) continue
to meet safety requirements for modern traffic loads equivalent to types A14 (or A11),
without compromising structural integrity.

4 Conclusions
The results of the structural calculations unequivocally demonstrate that the adoption
of the limit state design method has led to a marked and measurable improvement in
the load-bearing capacity of reinforced concrete girders utilized in highway bridge

Analysis of Reinforced Concrete Beams in Road Bridge Superstructures …

183

spans that were originally designed in accordance with outdated or earlier generation design standards. This significant enhancement in structural performance underscores the existence of a considerable latent reserve in load-carrying potential within
many of these legacy bridge systems. Importantly, a substantial number of these
structures are currently operating under traffic volumes and vehicular loads that far
exceed the parameters and assumptions established during their initial design period.
This reality is particularly noteworthy, as it provides a scientifically grounded rationale for the re-evaluation of the structural adequacy of such bridges under current
loading conditions.
Furthermore, the insights gained from these findings offer valuable guidance for
structural engineers, bridge managers, and transportation authorities in formulating
evidence-based recommendations related to permissible load limits, structural safety
margins, and long-term serviceability. The outcomes not only affirm the inherent
robustness and durability of these older reinforced concrete bridge girders but also
support the feasibility of extending their functional lifespan through comprehensive
reassessments, targeted strengthening, and proactive maintenance strategies. In this
regard, the study contributes to a broader understanding of how existing infrastructure
can be sustainably adapted to meet evolving transportation demands and modern
safety expectations.
Acknowledgements The authors acknowledge the financial support from Vietnam Maritime
University for the research, authorship, and publication of this article.

References
1. (2003) Temporary guidelines for determining the load-bearing capacity of bridge structures on
roads (ODN 218.0.032-2003). Rosavtodor, Moscow
2. Donchenko VG (1953) Spatial analysis of beam span systems in highway bridges. Avtotransizdat, Moscow, p 324
3. Shapiro DM, Agarkov AV (2005) Finite element method analysis of ribbed beam span structures.
In: Proceedings of the Voronezh State University of Architecture and Civil Engineering. Series:
“Modern Methods for Static and Dynamic Analysis of Buildings and Structures”. Voronezh, pp
51–60
4. Hieu TT, Van TTT (2014) Stress-strain state of reinforced concrete road bridge beams in
nonlinear deformation analysis. J Transp Commun 8:24–27
5. Shapiro DM, Agarko AV, Van TTT (2008) Spatial non-linear deformational analysis of road
bridge multy-beam superstructures. Scientific herald of Voronezh State University of architecture
and civil engineering. Ser Constr Arch 2:29–37
6. Shapiro DM, Van TTT (2007) Analysis of road bridge multi-beam superstructures of the standard
design in 1957. Sci Her Voronezh State Univ Arch Civ Eng 3:63–70

Investigation of the Strength
of Monolithic Reinforced Concrete Slabs
with Non-removable
Truncated-Pyramidal Hollow Formers
B. K. Dzhamuev and O. S. Matukhova

Abstract The evaluation of the effectiveness of the use of non-removable void
formers in monolithic reinforced concrete slabs is based on the analysis of the results
of numerical modeling of four series of samples with different dimensions in plan and
the main working reinforcement. A comparative analysis of the values of compressive
stresses in concrete and reinforcement, as well as tensile stresses in reinforcement
for reference samples (full-bodied) and samples with non-removable void generators
of the Sibform system was performed. According to the results of the study, it was
revealed that the use of non-removable void formers in a monolithic reinforced
concrete slab does not affect its strength, but it allows to reduce the consumption of
concrete and, as a result, the weight of the structure by an average of 20%.
Keywords Floor slab · Reinforced concrete · Non-removable voids · Strength ·
Bearing capacity · Finite element model · Numerical modeling

1 Introduction
From year to year, the volume of construction around the world is increasing. A
significant share of these volumes is occupied by monolithic housing construction
using reinforced concrete as a durable, reliable and durable material. In addition,
reinforced concrete is also used in the reconstruction of dilapidated and dilapidated
buildings, for example, in cases where a wooden floor that has served for more
than 100 years needs to be replaced with a modern durable and rigid reinforced
concrete one. However, the load-bearing capacity of vertical elements (existing or
projected walls, columns, foundations) does not always allow this to be done, due to
the noticeable difference in the weight of the materials being replaced. Thus, the main
significant disadvantage of reinforced concrete slabs is their high intrinsic weight,
B. K. Dzhamuev (B) · O. S. Matukhova
National Research Moscow State University of Civil Engineering (MGSU), Moscow, Russia
e-mail: dbk-07@mail.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_16

185

186

B. K. Dzhamuev and O. S. Matukhova

Fig. 1 General view of a prefabricated reinforced concrete slab with longitudinal voids (a) and a
coffered monolithic floor (b)

which may limit their use or require additional work, for example, strengthening
vertical structures (walls, columns, foundations) in the case of reconstruction of
existing buildings or designing initially more durable and rigid vertical elements in
the case of a new building.
One of the main ways to reduce concrete consumption during the construction
of buildings and reduce their total weight is the use of precast reinforced concrete
multi-hollow slabs (see Fig. 1a) as an element of floor-to-floor overlap and coating.
The development of this area led to the development and adoption in the Russian
Federation of a new standard in 1991—GOST 9561-91 [1], thanks to which precast
reinforced concrete slabs with longitudinal voids became widespread and widely
used in housing construction.
In the field of monolithic construction, research has also been conducted to reduce
the weight of floor structures. For example, one of the widespread methods is the
use of various lightweight materials (mainly low-density: expanded polystyrene,
gas silicate, mineral wool, etc.) as liners in the body of a reinforced concrete slab.
A method of reducing the weight of the floor by using cross beams (see Fig. 1b),
combined with a single plate (coffered floor), has also become widespread. At the
same time, non-removable hollow formers are often used to create a coffered ceiling
to reduce labor costs.
The use of hollow formers in monolithic floors began relatively recently in 1992,
the inventor is considered to be the Danish civil engineer Jorgen Brenning. In the
last decade, this method has become the most popular, as it corresponds to the global
trend of reducing carbon dioxide emissions into the atmosphere. Since the early
2000s. several models and methods of using void formers have been patented: a
liquid container made of rubber or a plastic bag with water [2], tubes made of paper
or plastic [3], polyethylene terephthalic bottles [4], a container in the form of a hollow
plastic or sealed rotating body [5] a rectangular container made of plastic or moistureresistant cardboard [6], cardboard and polyethylene pipes [7]. Currently, there are
many technologies in the world based on the use of non-removable voids, the most
common of which in Russia are U-Boot, Cobiax, Bubble Deck, Simkar and Sibform
(see Fig. 2). For the possibility of using certain types of hollow formers in monolithic

Investigation of the Strength of Monolithic Reinforced Concrete Slabs …

187

Fig. 2 General view of the void generator

reinforced concrete slabs, standards of organization STO 38311046-001-2019 [8] and
STO 35546020.001-2016 [9] were developed.
Most of the analyzed studies on the effect of non-removable voids on the strength
of reinforced concrete slabs, carried out by both foreign authors [10–17] and Russian
[18–20], indicate that the presence of plastic voids in the body of a reinforced concrete
slab reduces its weight and, as a result, reduces concrete consumption. At the same
time, the authors did not note a significant decrease in load-bearing capacity due to
the absence of the calculated section of concrete in these studies. Some authors even
note the positive effect of the presence of a void in the body of a reinforced concrete
slab: the maximum stresses in concrete are reduced to 40%.

2 Models and Methods
Due to the fact that previous studies conducted by various authors demonstrate a
significant variation in the strength of the same type of slabs with and without
voids (full-bodied), as well as contradictory conclusions in individual studies, a
test program has been developed to investigate the effectiveness of the use of nonremovable voids in terms of their effect on the bearing capacity of monolithic
reinforced concrete slabs. A partially similar issue was considered in [19].
The object of the study is a square monolithic reinforced concrete slab with nonremovable hollow formers. Since a fragment of a slab of a beam floor is to be studied,
during modeling, the beams located along the contour are replaced by a rigid seal.
The load used in the study is evenly distributed over the entire surface of the structure.
To evaluate the effectiveness of the use of non-removable voids in terms of their
effect on the bearing capacity of a monolithic reinforced concrete slab, 4 series of
models with lengths of 3.0 m, 4.0 m, 5.0 m and 6.0 m have been developed. Each
series consists of two finite element models: one-piece monolithic without artificial
voids (symbol “1”) and hollow with truncated-pyramidal voids. forms (symbol “2”).
As void formers, elements similar in size to the elements of the Sibform system

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B. K. Dzhamuev and O. S. Matukhova

with characteristics in accordance with STO 35546020.001-2016 [9] were modeled:
height—100 mm, plan size 500 × 500 mm.
Thus, the following series of samples were used in the study:
1. The “30” series is a monolithic reinforced concrete slab 200 mm thick, measuring
3.0 × 3.0 m in plan, made of concrete of compressive strength class B25, reinforced with individual Ø8 A500C rods laid in 200 mm increments along the
upper and lower faces in the longitudinal and transverse directions. Fixed hollow
formers in the amount of 16 pieces are installed in the body of the plate, as shown
in Fig. 3a.

Fig. 3 The layout of the void formers in the series samples “30”, “40”, “50”, “60”

Investigation of the Strength of Monolithic Reinforced Concrete Slabs …

189

2. The “40” series is a monolithic reinforced concrete slab with a thickness of
200 mm, measuring 4.0 × 4.0 m in plan, made of concrete of compressive strength
class B25, reinforced with individual rods Ø10 A500C, laid in 200 mm increments along the upper and lower faces in the longitudinal and transverse directions. Non-removable hollow formers in the amount of 36 pieces are installed in
the body of the plate, as shown in Fig. 3b.
3. The “50” series is a monolithic reinforced concrete slab with a thickness of
200 mm, measuring 5.0 × 5.0 m in plan, made of concrete of compressive strength
class B25, reinforced with individual rods Ø12 A500C, laid in 200 mm increments along the upper and lower faces in the longitudinal and transverse directions. Non-removable hollow formers in the amount of 49 pieces are installed in
the body of the plate, as shown in Fig. 3c.
4. The “60” series is a monolithic reinforced concrete slab with a thickness of
200 mm, measuring 6.0 × 6.0 m in plan, made of concrete of compressive
strength class B25, reinforced with individual Ø14 A500C rods laid in 200 mm
increments along the upper and lower faces in the longitudinal and transverse
directions. Non-removable void formers in the amount of 81 pieces are installed
in the body of the plate, as shown in Fig. 3d.
The number and locations of the voids were determined in such a way that
the number was the maximum allowable and met the requirements of STO
35546020.001-2016 [9], in terms of the maximum allowable height of the voids
(100 mm) for a plate 200 mm thick and the thickness of the rib formed between the
voids, not less than 100 mm. The distance from the face of the section to the center of
gravity in stretched and compressed fittings is assumed to be the same in all models
and is 30 mm.
When constructing the model, the requirement for a minimum distance from the
voids to the contour beams was also taken into account, as can be seen from Fig. 3—it
is more than one and a half times the working height of the section. The reference
model in each series is identical to the studied model with hollow formers in terms
of geometric and physical parameters and is necessary for a comparative analysis of
stresses occurring in concrete and reinforcement.
The study was performed on finite element models made of bulk and core elements
using the LIRA-CAD computing system (see Fig. 4). In length and height, the model
is divided into final elements measuring 50 mm and 20 mm, respectively. In the area
of the protective layer, the end elements have a height of 15 mm. The height of the
core elements corresponds to the accepted diameter of the reinforcing rod.
Physically nonlinear universal spatial elements of the KE236 type were used in the
models to simulate concrete components. To describe the deformation of concrete,
an exponential dependence (No. 35) was used, taking into account the adhesion of
the material to the reinforcing. To construct the σ-ε diagram, a software package was
used that automatically took into account the class and type of concrete. Plate reinforcement was modeled using physically nonlinear universal spatial core elements
of the KE210 type. To describe the deformation of the reinforcement, a piecewise
linear relationship (No. 14) was used, based on the data of SP 63.13330.2018 [21]. In

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B. K. Dzhamuev and O. S. Matukhova

Fig. 4 Investigated a and reference b finite element models of the floor slab

Table 1 Maximum calculated evenly distributed load
The
h0 (mm) Rs (MPa) Rb (MPa) As (mm2 ) l (m) x (mm) Mult (kNm) qmax (kPa)
symbol
of the
sample
30/1

170

435

14.5

252

3.0

7.56

18.22

34.2

40/1

170

435

14.5

393

4.0

11.79

28.05

28.9

50/1

170

435

14.5

566

5.0

16.98

39.77

25.7

60/1

170

435

14.5

770

6.0

23.1

53.07

23.4

models 30/2, 40/2, 50/2, and 60/2, voids were modeled by removing the volumetric
elements of CE236 in the void zones according to Fig. 3. Connections were placed
around the perimeter of each model, prohibiting movement and rotation in all planes
(rigid sealing). The following loads were used in the calculations:
• own weight—set automatically by the program;
• evenly distributed long-term load.
The maximum calculated value of the evenly distributed load applied to the models
is preliminarily determined analytically, taking into account the requirements of SP
63.13330.2018 [21]. The values of this load are shown in Table 1.
Thus, the numerical models involved in the study and used in the software package
fully corresponded to their real counterparts. The calculation was performed using
a step-by-step method, which made it possible to load the structure step by step and
solve a linearized system of equations for each step.

3 Research Results and Their Analysis
The analysis of the results of the conducted research allows us to note the following:

Investigation of the Strength of Monolithic Reinforced Concrete Slabs …

191

Table 2 Characteristics of the samples
The symbol of
the sample

Plate size in plan
(m)

The volume of
concrete (m3 )

Reinforcement

30/1

3.0 × 3.0

1.80

Ø8A500 step
200 mm

–

30/2

3.0 × 3.0

1.47

Ø8A500 step
200 mm

18.3

40/1

4.0 × 4.0

3.20

Ø10A500 step
200 mm

–

40/2

4.0 × 4.0

2.46

Ø10A500 step
200 mm

23.1

50/1

5.0 × 5.0

5.0

Ø12A500 step
200 mm

–

50/2

5.0 × 5.0

4.0

Ø12A500 step
200 mm

20.0

60/1

6.0 × 6.0

7.2

Ø14A500 step
200 mm

–

60\2

6.0 × 6.0

5.35

Ø14A500 step
200 mm

22.9

Reducing the
volume of
concrete relative
to the reference
sample (%)

1. The use of Sibform system hollow formers in the body of a monolithic reinforced concrete slab with characteristics in accordance with STO 35546020.0012016 [9], when installed according to Fig. 3, will lead to a reduction in concrete
consumption by (Table 2):
(a)
(b)
(c)
(d)

18.3% for a 3.0 m long slab (“30” series);
23.1% for a 4.0 m long plate (“40” series);
20.0% for a 5.0 m long plate (“50” series);
22.9% for a 6.0 m long plate (“60” series).

2. Compressive stresses in both the concrete of the structure (see Fig. 5) and in the
reinforcement (see Fig. 6) did not exceed the maximum permissible values for the
specified classes: B25 and A500. At the same time, in each batch, a uniformly
distributed load was applied to the samples, corresponding to the maximum
permissible load, determined analytically (Table 1). The available load-bearing
capacity indicates a redistribution of stresses, which is not taken into account in
manual calculations.
3. From the graphs in Fig. 5, it can be seen that at the maximum allowable load on
the slab:
(a) the maximum compressive stresses in concrete of the “30/1” model were
2.78 MPa, and in the “30/2” model with hollow formers were 2.74 MPa,
which is 1.4 less %;

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B. K. Dzhamuev and O. S. Matukhova

Fig. 5 Graphs of the dependence “load—compressive stresses in concrete”

Fig. 6 Graphs of the dependence “load—tensile stresses in fittings”

Investigation of the Strength of Monolithic Reinforced Concrete Slabs …

193

(b) the maximum compressive stresses in the concrete of the “40/1” model were
4.8 MPa, and in the “40/2” model with hollow formers they were 4.68 MPa,
which is 2.5 less %;
(c) the maximum compressive stresses in the concrete of the “50/1” model were
7.29 MPa, and in the “50/2” model with hollow formers they were 7.03 MPa,
which is 3.6 less %;
(d) the maximum compressive stresses in the concrete of the “60/1” model were
9.77 MPa, and in the “60/2” model with hollow formers were 9.38 MPa,
which is 4.0% less.
4. From the graphs in Fig. 6, it can be seen that at the maximum allowable load on
the plate:
(a) the maximum tensile stresses in the fittings of the “30/1” model were
21.47 MPa, and in the “30/2” model with hollow formers were 21.07 MPa,
which is less by 1.9%;
(b) the maximum tensile stresses in the fittings of the “40/1” model were
47.9 MPa, and in the “40/2” model with hollow formers were 47.13 MPa,
which is 1.6 less %;
(c) the maximum tensile stresses in the fittings of the “50/1” model were
72.33 MPa, and in the “50/2” model with hollow formers were 73.03 MPa,
which is 1.0 more %;
(d) the maximum tensile stresses in the fittings of the “60/1” model were
129.09 MPa, and in the “60/2” model with hollow formers were 131.74 MPa,
which is an increase of 2.1%.
5. As can be seen from Fig. 7, peak compressive stresses in concrete at maximum
load occurred in the lower part of the base zone of the slab, and tensile stresses
in the upper part, which corresponds to generally accepted ideas about the nature
of the work of slab structures under load.
6. A comparative analysis of the stresses occurring in concrete and reinforcement
of solid slabs and slabs with void generators at the maximum load level shows
the following:

Fig. 7 Areas with peak compressive stresses in concrete slabs (highlighted in red): full-bodied
(a) and with voids (b)

194

B. K. Dzhamuev and O. S. Matukhova

(a) in slabs with voids, compressive stresses in concrete are lower by 1.4-4.0%
than in full-bodied plates;
(b) in plates with void generators, the compressive stresses in the reinforcement
are lower by 2.4–9.6% than in full-bodied plates;
(c) the difference in compressive stresses in rebar and concrete in slabs with
void formers and full-bodied slabs increases with increasing length of the
structure;
(d) tensile stresses in the reinforcement of plates with void generators 3.0 m
and 4.0 m long are 1.6–1.9% lower than in full-bodied plates;
(e) tensile stresses in the reinforcement of plates with void generators 5.0 m
and 6.0 m long are 1.0–2.1% higher than in full-bodied plates.
The results of the study allow us to state the following:
1. The use of non-removable void generators in a monolithic reinforced concrete
slab does not significantly affect its strength, so this fact can be ignored in
calculations for the 1st group of limit states.
2. At the maximum permissible evenly distributed load, in the plate, due to the use of
voids, stresses in compressed concrete are reduced by 1.4–4.0%, in compressed
reinforcement by 2.4–9.6%, in stretched reinforcement by 1.6–1.9% (only for
slabs with a span of 3.0 and 4.0 m). At the same time, for plates with a span
of 5.0 and 6.0 m, a slight increase (by 1.0–2.1%) in the stress in the stretched
reinforcement of samples with void generators was noted. This feature must be
taken into account when designing monolithic reinforced concrete slabs with
non-removable voids.
3. The use of non-removable voids reduces the consumption of concrete by an
average of 20%, which gives a significant advantage over a traditional solid slab
in terms of economic efficiency.

References
1. GOST 9561-91 (1991) Reinforced concrete multi-cavity floor slabs for buildings and structures
technical specifications. Principles and guidelines. Standardinform, Moscow
2. Prilutsky OG (2005) Method of manufacturing a monolithic building element. Russian Patent
No.RU2243889C2. 10.01.2005
3. RegionStroj K (2005) OOO Multi-cavity reinforced concrete floor slab. Patent No.RU49853U1.
12.10.2005
4. Kotenkov IA (2011) Multi-hollow reinforced concrete floor slab. Patent of Belarus
No.BY7667U. 30.10.2011
5. UO “BGTU” (2012) Void-forming girderless floor slab. Patent of Belarus No. BY8418U.
30.08.2012
6. Martynov AA (2013) Method of manufacturing buildings and structures with a layout
transformed during operation. Patent of Russia No. RU2488667C2. 27.07.2013
7. Pushkarev BA (2017) Method of manufacturing monolithic reinforced concrete floor slabs
with round voids, using non-removable cardboard-polyethylene void formers. Russian Patent
No.RU2634156C2. 24.10.2017

Investigation of the Strength of Monolithic Reinforced Concrete Slabs …

195

8. STO 38311046-001-2019 (2019) Monolithic reinforced concrete lightweight slabs with Simkar
void formers. Rules of design and construction
9. STO 35546020.001-2016 (2016) Fixed formwork (voids and couplings) Sibforma ®. General
information about the technology, product range. Recommendations for the calculation and
design of monolithic girderless floor slabs with non-removable formwork Sibform ® in
accordance with SP 63.13330.2012
10. Tiwari N, Zafar S (2016) Structural behavior of bubble deck slabs and its application: main
paper. IJSRD Int J Sci Res Dev 4:433–437
11. Ibrahim AM, Ali NK, Salman WD (2013) Flexural capacities of reinforced concrete two-way
bubbledeck slabs of plastic spherical voids. J Print Iraq 06(02):9–20
12. Valivonis J, Skuturna T, Daugeviius M, Šneideris A (2017) Punching shear strength of
reinforced concrete slabs with plastic void formers. Constr Build Mater 145:518–527
13. Saifulla M, Azeem MA (2017) Comparative seismic performance of a conventional slab and
flat slab over a bubble deck slab. Int J Emerg Technol Adv Eng 7:137–143
14. Teja PP, Kumar PV, Mounika CR, Saha P (2012) Structural Behavior of Bubble Deck Slab
1:383–388
15. Lakshmikanth L, Poluraju P (2019) Performance of structural behaviour of bubble deck slab.
Int J Recent Technol Eng (IJRTE) 7(6C2)
16. Varghese JP, George M (2018) Parametric investigation on the seismic response of voided and
solid flat slab systems. IJISET—Int J Innov Sci, Eng Technol 5:256–258
17. Mahalakshmi SS, Nanthini S, Saha AP (2017) Experimental Studies on Comparison of
Conventional Slab and Bubble Deck Slab Based on Strength 5:580–588
18. Orlova MD, Mnushkin MA, Evtushenko IS, Vinogradova KI, Egarmin KA (2017) Analysis of
the use of hollow formers from recycled polypropylene in the creation of lightweight monolithic
floors. In: Research of various directions of modern science: collection of materials of the XXI
International Scientific and practical Conference. Part 1. Moscow, pp 562–567
19. Filimonova ES (2022) Analysis of the stress-strain state of a monolithic floor slab with void
generators according to the Cobiax system based on various computational models. J Young
Scientist 20:107–109
20. Malahova AN (2016) Hollow coffered floor slabs of monolithic multi-storey buildings. J Vestnik
MGSU 6:15–24
21. SP 63.13330.2018 (2018) Concrete and reinforced concrete structures. The main provisions.
Updated edition of SNiP 52-01-2003. Code of Practice. Gosstroy of Russia, Moscow

Selection of a Waterproofing Solution
for the Underground Part of a Building
Under the Module-Based Methodology
E. G. Davletshin, Z. R. Mukhametzyanov, A. A. Yudin, T. F. Suleymanov,
and I. I. Kuznetsova

Abstract Stable and long-term operation of buried foundations, tunnels, and
underground structures requires maximum protection against groundwater exposure. Current waterproofing methods are quite effective for protecting subterranean
spaces from flooding and concrete structure degradation. However, 95% of newly
constructed facilities experience issues related to waterproofing system failures. The
development and implementation of new waterproofing technologies, digital monitoring systems, and early warning systems for waterproofing integrity breaches represent a critical task for the construction and manufacturing sectors thereby demanding
advancement and refinement of relevant research methodologies. The research objective of this paper is to develop a methodology for selecting optimal waterproofing
solutions for underground part of a building. The key research outcome is the development of an algorithm for finding optimal waterproofing module-based solutions
for underground part of buildings. This methodology enables evidence-based selection of the most effective waterproofing installation or repair technology for current
underground structures, accounting for diverse design stage conditions. The developed methodology comprises three modules for selecting design solutions: economic
impact assessment comparing initial waterproofing system installation costs with
future repair expenditures; classification of site geological conditions and operational environment factors; evaluation of installation timelines and projected repair
intervals during the building’s service life. The proposed methodology may be treated
as a conceptual framework for advancing quality assessment criteria—specifically,
by augmenting the decision-making toolkit with optimized parameters for selecting
future planned waterproofing installation and repair system.
Keywords Foundation waterproofing · Waterproofing technology · Modular
approach · Traditional method · Innovative method

E. G. Davletshin · Z. R. Mukhametzyanov · A. A. Yudin (B) · T. F. Suleymanov · I. I. Kuznetsova
Ufa State Petroleum Technological University, Ufa, Russia
e-mail: salov@list.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_17

197

198

E. G. Davletshin et al.

1 Introduction
Current political situation, including sanctions imposed by several states against
our country should be noted to have prompted domestic manufacturers to develop
proprietary waterproofing materials, make and implement new waterproofing technologies, implement digital monitoring systems, and establish early warning systems
for waterproofing integrity breaches [1–12]. Given the above factors, identifying the
most effective technological solutions for waterproofing underground structures of
operational buildings in dense urban environments, along with methods for real-time
visual/digital monitoring and urgent repair, is critically essential.
Studying the properties of materials is the basis for the formation and improvement
of the technology for waterproofing underground parts of buildings. Such traditional
technologies as adhesive, liquid-applied coatings, and similar systems no longer fully
meet the technical requirements of underground parts of building.
Deformations, cracks, bends of load-bearing structures should be monitored,
since in case of their destruction and appearance of defects therein, the traditional
waterproofing is also damaged. Therefore, protective materials should preferably be
selected among elastic or self-healing compositions, as well as with the possibility
of repair without excavating.
Current research in developing new and improved waterproofing technologies
for underground parts of buildings primarily focuses on material enhancements,
with significantly less attention given to installation methodologies that incorporate
innovative or upgraded solutions at the design stage [9, 13].
The issues of improving technological processes both in construction, reconstruction, and capital repair were dealt with by scientists, with scientific papers
thereof becoming the basis for the theoretical and methodological basis of this study:
Afanasiev, et al. etc. [14–16].
The development of the methodological approaches listed above by the scientists
was the basis for increasing the efficiency of the technology for installing waterproofing systems for the underground parts of buildings in dense urban areas during
construction and repair and construction work, depending on various conditions. But
at the same time, the issues of developing an algorithm for determining the optimal
option for waterproofing the underground part of the building were practically not
considered.

2 Research Methods
Many research institutes in Russia focus on the issue of improving the technology
of arrangement and service resistance of waterproofing materials. Consequently,
when designing waterproofing systems in the practice of the present-day construction
there is an increasing tendency to provide for current waterproofing materials and

Selection of a Waterproofing Solution for the Underground Part …

199

technologies of application thereof, but still little attention is paid to the possibility
of repairing the waterproofing.
According to various studies, up to 90% of underground and buried structures
have unsatisfactory waterproofing protection system associated with wrong engineering solutions, incorrect selection of insulation materials, poor quality of work
and operation, etc. It results in waterlogging of underground structures, increased
wear and tear of bearing structures, etc.
A whole range of protective measures, including primary and secondary protection
of concrete, should be carried out to protect building structures against water and
moisture and to ensure normal thermohydraulic conditions for building operation,
as well as to increase the durability of structures.
The primary protection is realized at the stage of engineering and manufacturing
of structures and is ensured by proper selection of concrete composition, technology
of concrete mix placement, and required concrete curing.
Secondary protection provides for the arrangement of waterproofing systems, with
the main elements thereof being waterproofing coatings, heat and vapor barriers,
drains, ventilation and air conditioning systems. Therefore, waterproofing systems
are a set of elements intended:
• to ensure watertightness of structures (antifiltration waterproofing);
• to increase the durability of building structures under physical or chemical
aggressiveness of groundwater (anti-corrosion waterproofing);
• to prevent water from entering the environment (examples of such structures are
water towers, reservoirs, canals, swimming pools, sewage treatment plants, etc.).
Secondary protection measures include providing a reliable waterproofing coating
on the surface of the structure.
Currently, such technologies as adhesive and mechanically fastened ones are
widely used as secondary protection of structures. These technologies are used
to protect new and repair old buildings providing the uniform coatings efficiently
operating together with the protected structure.
Mechanically fastened waterproofing involves the laying of roll materials
(bitumen or bitumen-polymer coating, polymer membranes, bentonite mats) to be
mechanically fixed to the base using special fasteners. Mounted waterproofing is
made of separate structural elements (e.g. metal and plastic sheets), specially formed
for this construction. These elements are attached to the main structure by mounting
fasteners or by adhesive bonding.
According to the type of basic waterproofing material there are:
• bitumen-based: bitumen and bitumen-polymer roll and mastic materials; asphalt
plaster mortars and mastics;
• polymer-based: membrane, sheet, and coating materials;
• cement-based: coating and penetrating compositions; plaster mortars;
• bentonite clay-based roll materials;
• metal materials: steel sheets for waterproofing to be installed.

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E. G. Davletshin et al.

Focusing on the experience of past years, engineering designers try to take into
account the technological basis for the application of a certain type of waterproofing
and methods of reliable assessment of its operational resource, to ensure that the
average service life of materials used in repair and construction work is 40–50 years,
as well as providing an opportunity for cost-effective repair.
The inappropriate or no waterproofing system in the underground part of operating buildings is to be noted to reduce the service life of the buildings themselves,
while unforeseen deformations of underground structures have a negative impact on
the waterproofing made, destroying it and causing further difficulties in repair and
restoration of the building.
Early failures of waterproofing of the underground part of buildings can be
explained by insufficient attention to improvement of technologies of waterproofing
and repair of the underground part of buildings in operation depending on various
conditions, as well as by low quality of repair and construction work, economy of
funds allocated therefor, market availability of a significant number of untested and
low-quality materials or solutions that do not meet the conditions of construction.
Early deterioration of structures is also caused by the opening of foundation joints,
whereby the tightness of the waterproofing is broken and water penetrates into the
underground part of the buildings.
Therefore, to ensure efficient operation of the underground part of buildings,
construction specialists must account for critical factors including: the adverse
impacts of precipitation, surface runoff from nearby areas, groundwater infiltration,
as well as anthropogenic factors such as leakage from reservoirs, treatment facilities,
settling ponds, water mains and sewer lines. These factors cause persistent basement
dampness, structural degradation of underground elements, and rebar corrosion.
Proceeding from the above, it is imperative to strictly adhere to approved design
specifications, execute timely repairs of both load-bearing structures and waterproofing systems, prioritize reliability and maintainability when selecting waterproofing types, specifically, the long-term preservation of performance parameters
within defined limits, ensuring: sustained water-resistance properties under design
service conditions, cost-effectiveness in both: initial system selection, and future
repair feasibility.
These measures will enable to reduce the costs of repair and maintenance for
waterproofing of the underground part of buildings in confined environments.
However, during design, repair, and operational stages it is often impossible to
predict all adverse effects on underground structures.
The application technology of sheet waterproofing materials—even durable and
costly ones—presents several limitations. During repair works to restore underground waterproofing in confined urban areas, required earthworks are often unfeasible. For vertical waterproofing applications on building underground parts, reliable integration with existing horizontal waterproofing cannot be guaranteed. Horizontal waterproofing systems are virtually irreparable; any restoration attempts prove
exceptionally labor-intensive and cost-prohibitive.
Industry experience has demonstrated that under challenging economic conditions, consumers increasingly opt for higher-quality, maintainable waterproofing

Selection of a Waterproofing Solution for the Underground Part …

201

systems, despite higher material costs and perceived installation complexities.
Currently, repairable waterproofing solutions represent only a small fraction of the
market, thereby highlighting the critical need to advance repair methodologies that
enable effective maintenance and monitoring without costly earthworks after project
completion and commissioning.
Russia has seen significant import substitution in recent years, with domestic
production displacing foreign supplies. 2021 figures show an 80% reduction in
imported rolled bitumen and a 90% drop in bitumen-polymers.
The study aims to systematize the selection process for waterproofing solutions
in underground parts of buildings. The research methodology included:
• Consolidation and structuring of core concepts for protecting underground parts
of buildings influencing solution selection;
• Development of quality criteria aligned with system modules;
• Establishment of interrelationships between cost, quality, and reliability modules;
• Proposal of an algorithmic framework for foundation waterproofing system
selection.
The research outcomes delineate three core modules for the waterproofing system
selection:
• Economic impact analysis comparing initial installation costs versus lifecycle
repair expenditures;
• Geotechnical condition classification and operational environment assessment;
• Installation timeline optimization and repair interval forecasting during the
building’s service life

3 Economic Efficiency Module
During building design to assess the economic efficiency of proposed solutions, the
following analyses are conducted:
Cost analysis of installing the selected waterproofing system compared to alternative methods and systems under identical geological conditions, where the selection criteria will include high groundwater level, operation of underground building
spaces, as well as, foundation construction method—either open excavation or
“diaphragm wall” method.
• Cost analysis of future waterproofing system repairs in comparison with other
methods at two stages: the stage of installation of the structure, where the likelihood of damage to the waterproofing coating is very high, under equal geological
conditions, and the stage of further operation under changing conditions.
• Time-efficiency analysis of comparable waterproofing systems installation and
repair processes followed by further criteria formation.
• Compliance with base preparation requirements for the waterproofing system
installation.

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E. G. Davletshin et al.

• Constraints in flameless method installation or in cold-weather operation.
Unlike waterproofing systems made of bitumen-polymer roll materials, polymer
membranes do not require full adhesion to the base. These membranes are manufactured with thicknesses ranging from 1.5 to 3.0 mm and are typically installed in a
single layer (occasionally in two layers). The roll dimensions (20 × 2 m) minimize the
number of weld seams in the membrane and significantly increase installation speed.
Another key feature of polymer membranes is their flameless installation method,
while seams are welded using hot air, with the weld strength therewith exceeding
the base material’s strength. Additionally, polymer membranes offer the following
advantages: no need for careful base leveling; near-zero water absorption, high resistance to aging, rotting, and root penetration. Unreinforced membranes based on
plasticized polyvinyl chloride (PVC) in rolls are the most widely used in underground waterproofing. PVC membranes contain specialized stabilizers that provide:
high biological resistance, durability against salt solutions present in the ground and
resistance to weak inorganic acids and alkalis.

4 Construction Geotechnical Indicators Module
Classification of the geotechnical conditions of a construction site and consideration
of the operating conditions are required when selecting an insulation system [17–25].
Proposed categorization of geotechnical factors:
Group 1. No problematic soils at the construction site; predominance of sandy soils.
Groundwater either absent or a single persistent aquifer located significantly below
foundation slab level, with waters thereof being chemically homogeneous with low
aggressiveness.
Group 2. Localized problematic soils; predominance of clayey/loamy soils. Seasonal
perched water table from melt/rainwater accumulation. One or more distinct aquifers
at or above foundation level. Chemically heterogeneous water with contaminants.
Group 3. Widespread problematic soils; clayey/loamy soils dominant. Seasonal
perched water table from melt/rainwater accumulation. One or more artesian aquifers
of variable thickness above foundation level. Chemically heterogeneous water with
various contaminants.
The following criteria are considered for waterproofing operating conditions:
•
•
•
•
•

Construction in dense urban environments; Open-cut foundation excavation;
High groundwater table (GWT) conditions;
Low groundwater table conditions;
Summer construction conditions;
Winter construction conditions;
The system selection algorithm incorporating these criteria is presented in Fig. 1.

Selection of a Waterproofing Solution for the Underground Part …

203

Fig. 1 Waterproofing system selection algorithm

This algorithm establishes a decision-making framework to streamline the selection process and reduce variability in composite waterproofing system components.

5 Module of Labor-Cost Indicators for New Construction
and Further Operation (Repair)
This module assesses: for new construction: reduction in installation time; for
operation/repair: reduction in water-protection functional recovery time [18].
Reduction in installation time
The following criteria are evaluated for comparative analysis of installation speed
(Table 1).

Table 1 Installation speed
impact criteria

Criterion

Traditional method Innovative method

Installation method

Manual

Auto

Adhesion to the base Continuous

Localized

Installation safety

Flame

Flameless

Damp base

Unacceptable

Acceptable

Winter installation

Above + 5 °C

Above – 20 °С

Quality control

Visual

Parametric

204
Table 2 Repair time
optimization criteria

E. G. Davletshin et al.

Type of work

Traditional method

Excavation

Required

Not required

Base cleaning

Required

Not required

Leak detection

Low accuracy

High accuracy

Innovative method

Method of installation: automatic equipment is used for membrane welding with the
possibility of adjusting the PVC welding temperature and speed of movement in the
seam depending on the ambient temperature and wind conditions. This automated
process minimizes human error during waterproofing layer installation.
Adhesion type determines cavity utilization for future repairs via control/injection
ports.
Installation safety: if waterproofing is installed in explosion- and fire-hazardous facilities, the flameless method is clearly preferred in preparing the waterproofing layers
and provides safety in the event of violations of fire hazard regulations.
A damp base primer-based installation and full torch-on application of traditional
systems unlike polymer membranes system, where welding is made at overlaps only
and to pre-installed PVC waterstops.
Quality control of the traditional systems is visual inspection only.
Welded seam quality control is made via compressed air injection into the seam
cavity, thereby minimizing risks and ensuring seam repairs prior to backfilling.
Repair Time Reduction
A comparative analysis of material compositions and application methods for
waterproofing system repairs aimed at minimizing functional recovery time for water
protection is presented in Table 2.

6 Conclusions
Proposed algorithm for optimal waterproofing selection for the underground part of
a building on the developed modular decision-making framework enables systematic
identification and justification of the most effective waterproofing technology for the
underground part of buildings considering various conditions at the design stage.
This approach represents an evolution in quality evaluation approaches by
augmenting the decision-making toolkit with rational selection parameters for future
waterproofing system design/repair.
The rationality and algorithmic modular approach will enhance the maintainability
and service life of underground building structures while reducing labor intensity
during repair and protection works.

Selection of a Waterproofing Solution for the Underground Part …

205

References
1. Krutov VI (1988) Foundations and footings on bulk soils. Stroyizdat, Moscow, p 224
2. Krutov VI (1982) Foundations and footings on collapsible soils. Budivelnyk, Kyiv, p 256
3. MGSN 2.07-01 (2004) Foundations, footings, and underground structures. Inspection and
monitoring during construction and reconstruction of buildings and underground structures:
Manual to MGSN 2.07-01: Adopted and enacted by Order of the Moscow Committee for
Architecture No. 180 dated 01.12.2004. Moscow Committee for Architecture, Moscow
4. Design and construction guidelines for foundation bases in high-density urban areas of
Moscow. Approved and enacted by Moscow Committee for Architecture (Moskomarkhitektura), Directive No. 2, 13 January 1999, Moscow Government, Moskomarkhitectura, Moscow,
p 155
5. Design and construction guidelines of foundations, base structures and underground facilities
during reconstruction of civil buildings and historic developments: Approved and enacted by
Moscow Committee for Architecture (Moskomarkhitektura), Directive No. 21, dated 3 July
1998, Government of Moscow, Moskomarchitectura, Moscow, p 147
6. Zamyatina OM (2009) Modeling systems: textbook. Publishing House of TPU, Tomsk, p 204
7. Makarenko SI (2019) Reference book of scientific terms and notation. Science-intensive
technologies, St. Petersburg, p 254
8. Shilin AA, Zaitsev MV, Zolotarev IA, Lyapidevskaya OB (2003) Waterproofing of underground
and buried structures during construction and repair. Rus. trademark, Tver, p 396
9. Recommendations for the design of waterproofing of underground parts of buildings and
structures. Structural details of waterproofing. OJSC “TsNIIPromzdaniy”, Moscow, 2009, p
118
10. RD 11-02-2006 (2006) Requirements for the content and maintenance of as-built documentation during construction, reconstruction, and major renovation of capital construction
projects including technical inspection reports for work, structures, and utility network sections:
approved: December 26, 2006, B.I., Moscow, p 24
11. RD 11-05-2007 (2009) Master work log. Regulations for maintaining general and/or special
work logs during construction, reconstruction, and major renovation of capital construction
projects: effective since April 13, 2007, DEAN, St.-Petersburg, p 64
12. Ryabinin IA (2000) Reliability and safety of structurally complex systems. Polytechnic, St.Petersburg, p 247
13. STO 72746455-4.2.2-2020 (2020) TECHNONICOL Insulation systems, foundation insulation systems—technical specification. Design, material, product, and structural requirements.
TechnoNICOL—Construction Systems LLC, p 49
14. Oleinik PP, Brodsky VI (2012) Methods for determining the duration of construction of
facilities. Ind Civ Constr 12:30–32
15. Mukhametzyanov Z, Oleinik P (2021) Formation of organizational and technological solutions
for the construction of industrial complexes. In: E3S web of conferences. Series “ural environmental science forum “sustainable development of industrial region UESF 2021”, Russia,
Chelyabinsk
16. Mukhametzyanov ZR, Mogucheva TA (2022) Conditions for achieving sustainability of
organizational and process solutions in the facilities construction. AIP Conf Proc 2559:22–27
17. SNiP 1.04.03-85 (1990) Norms for construction duration and work-in-progress in the construction of enterprises, buildings, and structures. USSR State Construction Committee, Moscow,
p 291
18. Mezentsev SD, Smirnova NV, Smirnov AV (2017) Application of reliability theory to ensure
the operational properties of waterproofing systems for underground parts of buildings and
structures. Sci Rev 20:45–48
19. Mukhametzyanov ZR, Gusev EV (2018) Numerical modeling of technological volume between
adjacent construction processes. In: IOP conference series: materials science and engineering,
international conference on construction, architecture and technosphere safety 2018, ICCATS
2018, South Ural State University Chelyabinsk, Russia, vol 451

206

E. G. Davletshin et al.

20. Vinnichenko V, Gabitov A, Salov A, Gaisin A, Kuznetsov D (2018) The heat loss calculating methods of external walls in the buildings reconstruction. In: MATEC web of conferences 7. “7th International scientific conference “reliability and durability of railway transport
engineering structures and buildings” (Transbud 2018), vol 230, Article number 02038, pp 1–6
21. Bedov AI, Gabitov AI, Gaisin AM, Salov AS, Chernova AR (2018) CAD technologies under
thermal properties analysis of wall cladding of framed buildings. In: IOP conference series:
materials science and engineering, vol. 465, VII international symposium actual problems of
computational simulation in civil engineering, Novosibirsk, Russia, p 1–8
22. Gabitov AI, Ryazanova VA, Gaisin AM, Salov AS, Timofeev AA (2020) Manufacture of
construction materials by energy-saving technology through the example of the Bashkir region.
In: IOP Conference series: materials science and engineering. Series “innovative technology
in architecture and design, ITAD 2020”, р 012049
23. Yudin AA, Biktasheva AR, Gabitov AI, Salov AS (2022) Peculiarities research of buildings
and structures energy efficiency. In: IOP Conference series: earth and environmental science.
International science and technology conference “earth science”, ISTC earth science 2022,
Chapter 4”, p 052039
24. Bedov AI, Gabitov AI, Terekhov IG, Salov AS (2022) Forecast durability for protective
penetrating waterproof coating. Lect Notes Civ Eng 197:181–185
25. Vinichenko V, Ryazanova VA, Gabitov AI, Udalova YA, Salov AS (2019) Efflorescence
processes in exterior wall surface of buildings. Mater Sci Forum 968 MSF, pp 115–121

Calculations of Standard Cells
of Structures Made of Film and Fabric
Orthotropic Membranes
R. F. Vagapov, S. A. Gabitov, A. S. Salov, A. R. Biktasheva,
and R. K. Koksharov

Abstract A unified approach in solving equilibrium problems of standard cells of
membrane structures made of various absolutely flexible film and fabric materials
is presented in this paper. The objects of study are rectangular membranes. The
problems were considered in a geometrically nonlinear formulation, with the deformations and the squares of the rotation angles thereunder being considered to be
comparable with each other, but small compared to unity. A resolving system of
differential equations in partial derivatives expressed in a mixed form is obtained
therewith. These equations combining with the presented boundary conditions are
numerical models of a number of fragments of real membrane structures. The closed
nonlinear system of equations was integrated using the continuation method. Therewith, the known solution for a square isotropic membrane was used to select the
initial values of stresses and displacements. The problem of equilibrium of a square
isotropic membranes rigidly fixed under a uniformly distributed load is presented
as an example. The resulting graphs and tables show the distribution of forces and
displacements. They may be used for calculating the membrane structures. The developed technique may be applied to those values of the initial parameters under which
the calculations have not yet been made.
Keywords Membranes · Membrane structures · Compliant contour · Free
boundary · Peculiar points · Continuation method · Folded zone

1 Introduction
The study of the deformation process of shell structures is essential for various fields
of industry.

R. F. Vagapov · S. A. Gabitov · A. S. Salov (B) · A. R. Biktasheva · R. K. Koksharov
Ufa State Petroleum Technological University, Ufa, Russia
e-mail: salov@list.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_18

207

208

R. F. Vagapov et al.

In construction, such structures are often used, including for covering large-span
structures. For example, such a need arises in the construction of public buildings: stadiums, concert halls, markets; in the construction of industrial buildings:
warehouses, hangars for machinery and equipment, and factory buildings.
The main requirement for building structure shells is to ensure safe and long-term
structural performance under specified load conditions. Equally important is reducing
material consumption while maintaining structural integrity. Covering shells are
made of reinforced concrete, steel or composite materials, which have high stiffness but are considerably lighter. However, the limited use of composite materials
for the structures of large-span building structures is due to the high cost of the material and insufficient research into their performance. Some of these materials can be
considered as orthotropic materials.
Depending on their construction and purpose, orthotropic membranes are divided
into two main types: film-based and fabric-based. Both types possess unique characteristics, but share a common feature—anisotropy, i.e. difference in strength and
stiffness along the longitudinal and transverse axes.

2 Types of Membranes
Film-based membranes are made from polymer materials such as polyethylene,
polypropylene, PVC, Teflon (PTFE), polyimides and others. These membranes are
produced through extrusion or casting processes, with the material being oriented
in one or two directions during manufacturing to achieve the desired anisotropy.
For example, during biaxial orientation, the polymer film is first stretched in the
longitudinal direction and then in the transverse direction, significantly enhancing
its strength and dimensional stability.
Key properties of film-based membranes:
•
•
•
•
•

Low thickness and weight;
High tensile strength in specified directions;
Gas- and moisture-impermeability;
Chemical resistance and durability;
Easy integration into composite structures.

Fabric-based membranes are materials based on textile structures, typically made
from synthetic fibers (polyester, aramids, glass fibers) and coated with special
polymer compositions such as silicones, PTFE or PVC. Due to their woven structure,
fabric membranes exhibit pronounced orthotropy, determined by the orientation of
warp and weft threads.
Key properties of fabric orthotropic membranes:
• High mechanical strength and resistance to tearing;
• Flexibility and ability to mold complex geometric surfaces;
• Durability with UV and weather resistance

Calculations of Standard Cells of Structures Made of Film and Fabric …

209

• Custom functionality through impregnation/lamination (waterproofing, fire resistance, etc.).
Conducting comprehensive studies of shell deformation using the most accurate mathematical models will enable evidence-based engineering decisions, thereby
promoting their safe operation, as well as reducing the material consumption and
lowering the production cost thereof.
Thin-walled shell structures can fail not only due to irreversible material degradation (loss of strength), but also through stability loss, where a minor load variation
triggers rapid, significant displacement growth (deflections). Unfortunately, most
existing studies focus exclusively on either strength or stability analysis, but not both
simultaneously.
Stiffening thin-walled shells with various reinforcing elements significantly
enhances their operational performance. Rib-stiffened shells can withstand loads
several times higher than unstiffened ones. These shells find wide applications
across industries, including shipbuilding, aerospace engineering, rocket design, civil
construction, etc. Strategic reinforcement configuration enables stress redistribution
at critical zones and optimal structural efficiency.
The stability analysis of shells under static loading was initially based on Euler’s
method, which involved solving eigenvalue problems. This approach reduced the
task to solving linear equations. However, investigating specific and general forms
of shell stability and their post-critical behavior requires solving nonlinear equations.
This challenge was significantly simplified after V. V. Petrov published the successive
loading method in 1959. Later, the arc-length continuation method was developed,
where the solution is parameterized by the arc length of the equilibrium path curve.
Detailed descriptions of this method can be found in papers by V. I. Shalashilin and
E. B. Kuznetsov.
During the first three decades of active research in the theory of thin plates and
shells, scholars focused primarily on static problems. However, the 1970s marked a
turning point, with rapidly growing interest in dynamic analysis, largely driven by
the demands of aerospace engineering. Nevertheless, studying dynamic structural
behavior is equally critical for shipbuilding and civil engineering.
The dynamic behavior of shell structures has been most extensively studied for
single-layer isotropic shells. In recent decades, however, composite material shells
(fiberglass, graphite-epoxy, boron composites, etc.) have been of significant interest.
Yet the mechanical behavior of such shells, particularly when stiffened with ribs,
remains insufficiently studied, both in static loading scenarios and dynamic loading
conditions.
The key research areas for shell structures under dynamic loading focus on their
stability, strength, and vibration characteristics. A review of existing studies on shell
dynamics reveals that the majority of research has been devoted to vibration analysis
(both free and forced vibrations), while significantly fewer studies address stability
issues.

210

R. F. Vagapov et al.

Problems of elastic equilibrium of rectangular orthotropic membranes bearing
a uniformly and non-uniformly distributed transverse load under various fixing
conditions are considered.
A material is considered isotropic if its mechanical and thermal properties are identical along all directions. A material is considered orthotropic if its mechanical and
thermal properties are unique and independent along three mutually perpendicular
directions.
Isotropic materials may have homogeneous or non-homogeneous microstructure. For example, steel has isotropic properties despite its non-homogeneous
microstructure.
A material is considered orthotropic when the mechanical and thermal properties are unique and independent along three mutually perpendicular directions.
Orthotropic materials are wood, most minerals and rolled metal.
For example, the mechanical properties of wood at a given point are characterized
along the longitudinal, radial, and tangential directions.
Orthotropic membranes exhibit direction-dependent mechanical properties (e.g.,
elasticity, strength) along mutually perpendicular axes. That is, if a force is applied
to an orthotropic membrane, it will deform differently depending on the direction in
which the force is applied.
The membrane deflections are assumed to be large in comparison with the thickness, while the deformations and squares of the rotation angles are comparable with
each other, but small in comparison with the unity. The problems of equilibrium of
isotropic membranes in this formulation have been repeatedly solved [1–6]. However,
there are no such solutions for rectangular membranes made of a nonisotropic material. The stress–strain state (SSS) of a rectangular orthotropic membrane was studied
by one of the authors of this article in [7], therewith resolving equations being used
in the displacements.
Thin shells, in addition to their use in construction, are widely employed as structural elements in shipbuilding, aerospace and missile engineering, nuclear power,
and the chemical industry. Recently, alongside metals, materials such as fiberglass,
fabrics, rubber, and various polymer composites have been extensively used in the
fabrication of shells. The application of new polymer materials enables to solve a
number of technical challenges that were practically unsolvable using traditional
materials.
The problem of determining the stress state, shape, and load-bearing capacity has
its own specific features in this case. This is due to the fact that displacements of
the load-bearing surface can be the of the initial dimensions order, while relative
deformations may turn out to be significantly greater.

Calculations of Standard Cells of Structures Made of Film and Fabric …

211

3 Calculations of Orthotropic Membranes
In most published studies, the primary focus has been on shells of rotation, the
determination of critical loads and deformations, and the construction of “loadmaximum deformation” diagrams. However, very little attention has been paid to
investigating the relationship between different local phenomena and studying the
subcritical behavior of shells. Additionally, the theory of superimposing small deformations on large ones has not been sufficiently developed in the analysis of shell
stress states.
The theoretical solution of specific problems encounters a practically insoluble
obstacle i.e. the construction of an analytical solution due to the nonlinearity of the
solving equations. Therefore, various numerical methods are typically employed to
solve them. However, these methods often fail to distinguish between the general
and specific features inherent in the physical versus the geometric characteristics
of the structure. The numerical algorithms used for solving nonlinear equations
generally have a limited range of applicability. For moment-free (membrane) shells,
difficulties in constructing numerical solutions may arise both in the domain of small
deformations (due to the ill-conditioned nature of the governing equations) and in
the domain of large deformations. In the latter case, stress states may emerge with
localized deformations of the middle surface, such as local “buckling” phenomena.
In the literature, the problem stretching of a rectangular membrane is typically
solved only for the case of small deformations. For large deformations, studies either
consider a homogeneous stress state (uniform deformation) or rely on numerical
methods to construct solutions.
The complex formulation of the general theory of isotropic shells was first introduced by V. V. Novozhilov. Expressing the equations in complex form reduced the
number of unknowns by half and lowered the order of the system of differential
equations. An attempt to construct a similar complex formulation for the similar
differential equations of orthotropic shells encountered a fundamental difficulty: the
emergence of complex-conjugate unknown functions. This prevented any reduction
in the number or order of the original differential equation system. Nevertheless, this
formulation enables a more compact formulation of the equations. In some cases,
it enables to calculate the complex-conjugate function explicitly. For axisymmetric
deformations, this function goes to zero, while in other cases the influence of the
complex-conjugate function may be neglected.
A method covering rectangular area of the procedure for calculating elliptical
membranes proposed in [8] is applied herein. The known solution for a square
isotropic membrane [9] was taken here as the initial approximation. The step method
by geometrical and physical parameters was applied further. Applying the finite
difference method (FDM) a transition from nonlinear differential equations in partial
derivatives to algebraic ones was made, in the solution thereof the multidimensional
method of chords was used at each step by values. Therewith, the basic functions
found through the use of known solutions remained [8, 9].

212

R. F. Vagapov et al.

For an in-plane stretched membrane, the emergence of compressive principal
forces may result in a loss of stability of the flat equilibrium configuration.
Consequently, only cases involving tensile forces are considered hereafter.
For a flat membrane under homogeneous stress state, a condition for the existence
of asymmetric solutions under symmetric loading is derived. This condition is shown
to be contained, on the one hand, in the material stability postulate and, on the other
hand, is not related to the existence of the ultimate load. Given the presence of a
maximum point in the “load-strain” dependence, the solution of the problem may
also be nonunique. In this case, beyond the critical point in the “framework” of the
shell equations used, the solution may not exist.
The resolving system of equations expressed in a mixed form and used in the
elliptical membrane calculation in [8] is used herein to study rectangular orthotropic
membranes rigidly fixed along the contour. Therewith, the traditional unknowns
remain: the stress /F/ and deflections /W / functions. According to [9–16], the
resolving system of equations may be written in the following dimensional form:
∂2W
∂2W
∂F 2 ∂ 2 W
∂F 2
·
+ Q = 0;
+
·
−2·
∂X · ∂Y ∂X · ∂Y
∂Y 2
∂Y 2 ∂X 2
⎡
ν
ν
∂4F
∂4F
1
∂2W
1
·
− YX − XY
·
+
=⎣
GXY · H
EX · H
EY · H
EY · H ∂X 4
∂X · ∂Y
∂X 2 ∂Y 2
∂F 2

∂X 2

1
∂4F
·
+
EX · H ∂Y 4

2
−

⎤
∂2W ∂2W ⎦
.
·
∂X 2 ∂Y 2

(1)

These relations are analyzed using the above method of undetermined coefficients
under which all the functions may be written as:
W = kw · w,
F = kf · f ,
X = kx · x,
Y = ky · y.

(2)

Additionally, we introduce:
E = Ex · Ey
ν̃ = νxy · νyx
GXY
.
g̃ =
E

1
2

,
1
2

,
(3)

Since relations (1) do not establish unique expressions for the reduction factors,
the following connections will be taken for them:
kf = kw · E · H ,
kx = a,
ky = b.

(4)

Calculations of Standard Cells of Structures Made of Film and Fabric …

213

Then from the first Eq. (1) we may determine:
kw =

Q̃ · a2 · b2
E·H

1
3

kf = Q̃2 · a4 · b4 · E · H

1
3

(5)

Here, Q̃ is a parameter characterizing the load. For a uniformly distributed load it is
the value of intensity thereof, while for a non-uniform load it is the average intensity.
Taking into account all the above, let us rewrite the solving system (1) as:
∂ 2w
∂ 2f ∂ 2w ∂ 2f ∂ 2w
∂ 2f
·
= −1 − q̃,
·
+
·
−
2
·
∂x2 ∂y2
∂y2 ∂x2
∂x · ∂y ∂x · ∂y
1 ∂ 4f
·
+
γ ∂y4

∂ 4f
1
∂ 4f
− 2 · ν̃ · 2
+
γ
·
=
g̃
∂x · ∂y2
∂x4

∂ 2w
∂x · ∂y

−

∂ 2w ∂ 2w
·
.
∂x2 ∂y2
(6)

here we use:
a2
· λ,
b2
Q
q̃ = − 1.
Q̃

γ2 =

(7)

where, q̃ is a parameter characterizing the deviation from the uniform load.
Hence, a system of two equations was obtained for established values f and w
[8], that for the isotropic membrane case coincides with the system of resolving
equations obtained by Föppl [11].
The expressions for the displacements excluded from the resolving Eqs. (6) may
be given proceeding from the geometric and physical relations [12, 13]:
x

u=
0

1 ∂ 2f
∂ 2f
1 ∂w
· 2 − ν̃ · 2 −
γ ∂y
∂x
2 ∂x

−ν̃ ·
0

∂ 2f
1 ∂w
∂ 2f
+γ · 2 −
2
∂y
∂x
2 ∂x

dx,
2

dy.

(8)

Due to symmetry, the solution is made for one quadrant (Fig. 1). Boundary conditions correspond to no displacements on two edges, shearing stresses, one of the
horizontal and one of the angular displacements along each of the coordinate axes:
x = 1 : u = v = w = 0,

214

R. F. Vagapov et al.

Fig. 1 Boundary conditions

∂ 2f
∂f
=u=
= 0,
∂x · ∂y
∂x
∂f
∂ 2f
=v=
= 0,
y=0:
∂x · ∂y
∂y
y = k : u = v = w = 0.
x=0:

(9)

No displacement components on the edges enable to conclude that there are no
appropriate deformations thereon:
x = 1 : εy = 0,
y = k : εx = 0.

(10)

Recall that k is the ratio of the sides of the rectangular membrane.
The system of Eqs. (6) under boundary conditions (9) and (11) is reduced to a
system of nonlinear algebraic equations by FDM. Therewith, the central differences
with an error of the remainder term of the second series of the step are also applied
on the rectangular grid.
Composing Eqs. (6) for all grid nodes located inside and on the inner boundaries of
the first quadrant (Fig. 1), we obtain 2·k ·n2 equations containing unknown values of f
and w at all grid points; the number of desired functions is 2·(n + 1)·(k · n + 1). Here
and below, n = ah is the number by which half of the side of the membrane parallel to
x axis is divided, when making a grid for the transition to difference equations (here
h is the grid step). In the absence of equations we refer to the boundary conditions of
the problem. We may write (k · n + n + 1) equations for w as per (9). Conditions (11)
give us more (n + k · n) equations. The stress function is described by a parabola,
defined to the linear part. Therefore, the last missing equation may be obtained by
arbitrary choosing the “initial level” of this function, by zeroing the value thereof at
some point, as in [1, 13].

Calculations of Standard Cells of Structures Made of Film and Fabric …

215

Therefore, the difference analogues of Eqs. (6) with conditions (9) and (11) form
a closed algebraic nonlinear system, with solving thereof at a given step, we may
find f and w at all grid points. Therewith, the known solution for a square isotropic
membrane [11] is taken here as the initial approximation, from which we move
stepwise in geometric (k) and physical (ν, λ) (k) (ν, λ) parameters to the desired
solutions. Then the functions characterizing the stress state are determined. Further,
after numerical integration of relations (8), the corresponding values of displacements
u and v may be obtained. From these functions, we may proceed to the dimensional
quantities required for the analysis of the stress–strain state:
U =

Q̃2 · a · b4
E2 · H 2

V =

Q̃2 · a4 · b
E2 · H 2

W =

Q̃ · a2 · b2
E·H

1
3

· u,
· v,
· w,

Q̃2 · a4
·H
Nx = E ·
b2
Ny =

Q̃2 · b4
·H ·E
a2

Nxy = Q̃2 · a · b · E · H

1
3

· βx ,
· βy ,
· βxy .

(11)

here we use:
∂ 2f
,
∂y2
∂ 2f
βy = 2 ,
∂x
∂ 2f
.
βxy = −
∂x · ∂y
βx =

(12)

Note that the calculation results found according to this and the above [7] methods
for isotropic membranes coincide, while for orthotropic membranes they differ
exactly as much as the uncertain coefficients of these algorithms do.
Specific problems of elastic equilibrium of orthotropic membranes in a geometrically nonlinear formulation are considered here. The mechanical characteristics of
materials where the membranes may be implemented in are taken from [14]. They
are given in Table 1.
To demonstrate the influence of anisotropy in all figures together with the diagrams
of characteristic functions for membranes made of orthotropic materials (solid lines),

216

R. F. Vagapov et al.

Table 1 The mechanical characteristics of materials
Nos.

Material

Ex , kg/m

νxy

νyx

Polyethylene film
(GOST 10354-82
Polyethylene film.
Specifications)

1.349

1205

893

379

0.313

0.422

Polyethylene film
(TU 38.1051901-89
Rubberized balcony
fabrics.
Specifications)

1.282

513

400

155

0.384

0.492

Polyethylene
terephthalate film

0.769

4762

6250

1923

0.438

0.333

Balloon fabric No.500 3.152
(TU MHP 1205-54)

3030

962

463

0.375

1.182

Rubber fabric No.60 4.2
(TU 38 105893-85
Rubberized
non-vulcanized fabric
591. Specifications)

4000

952

472

0.381

1.600

Ey , kg/m

Gxy , kg/m

the corresponding curves for an isotropic membrane [12, 16] are presented (dashed
lines).
The values of the required functions given in Table 2 (increased by 1000 times)
at characteristic points enable to observe some common factors of stress–strain state
changes in membranes made of materials with fixed characteristics E, ν̃, g̃. Here
and further on the following parameters are used: w0 —deflection in the membrane
y
center, βi —maximum force intensity, β0x and β0 —forces in the membrane center in
y
the direction of the corresponding coordinate axes, βbx and βb —forces in the middle
y
x
of one of the edges, βa and βa —forces in the middle of the other edge.
The calculation results for polyethylene film (VTU MHP M709-56) and rubber
fabric No.60 (VTU 4.2 IRP 38-8-82-65) are given in Figs. 2 and 3.
Here are some qualitative conclusions:
Table 2 The values of the required functions at characteristic points
y

βi

β0x

β0

βbx

βb

βax

βa

1.0

698

603

448

186

511

186

1.2

697

627

479

417

192

482

542

180

1.349

695

644

499

397

195

464

562

176

1.4

694

649

505

391

197

458

568

174

1.5

693

658

517

380

199

447

580

172

1.6

683

698

567

336

208

404

629

162

Calculations of Standard Cells of Structures Made of Film and Fabric …

217

Fig. 2 The calculation results for polyethylene film a membrane deflection; b forces in the
membrane in the x-axis direction; с forces in the membrane in the x-axis direction

Fig. 3 The calculation results for rubber fabric No.60 a membrane deflection; b forces in the
membrane in the x-axis direction; с forces in the membrane in the x-axis direction

1. Relatively stiffer orthotropic materials are characterized not only by larger values
of λ, but also by a higher level of E.
2. Shear forces in orthotropic membranes, as well as in isotropic ones, are one order
of magnitude lower than in chain membranes.
3. For fixed values of E and ν̃ as λ is increased, the maximum intensity of the forces
is increased while the deflections are decreased.
4. Considerations on the optimum orientation of the stiffer fibers of an orthotropic
membrane along the short side.
These conclusions may be used in actual engineering.
Under the operation of membrane structures, situations of non-uniform loading are
possible, e.g. when calculating building structures, considering the temporary (snow)
load, with the nature thereof being ultimately determined by the deformed geometry of the bearing element. That is why the temporary load was approximated by
a combination in the first approximation—linear functions, in the second—trigonometric ones. Three situations of temporary load with the same values of average intensity were compared. As expected, the uneven distribution of the load significantly
changes the stress–strain state. So, when the ratio of the average temporary intensity

218

R. F. Vagapov et al.

(weight of the snow cover for the area of Ufa) to the permanent intensity (own weight
of the membrane) of the load equal to 14, non-uniform loading (for a second approximation) increases the maximum deflection of a rectangular a b = 1.3 orthotropic
(film VTU MHP 709-56) membrane by 1.3, while the efforts by 1.4 times.

4 Conclusion
In conclusion, the obtained diagrams and tables are noted to show the nature of
the distribution of forces and displacements in membranes for a quite wide range
of changes in the main parameters of the structures thereof. They may be used
in calculations of membrane systems. For those values of the parameters, for the
calculations therewith were not being carried out, the developed procedure and the
program may be applied.

References
1. Vagapov RF, Grigoriev AS, Konovalov MB, Trushina VM (1987) Problems of equilibrium of
membranes and membrane structures. In: Proceedings of the 14th all-union conference on the
theory of plates and shells, Tbilisi, pp 255–260
2. Bedov A, Vagapov R, Gabitov A, Salov A (2022) Calculations of 3D anisotropic membrane
structures under various conditions of fixing. Int J Comput Civ Struct Eng 18(1):92–98
3. Vagapov RF (1986) Problems of equilibrium of isotropic and anisotropic membranes under
different conditions of fixing. Ph.D. thesis in Engineering Science. MSEI named after V.V.
Kuibyshev, Moscow, p 217
4. Trofimov VI, Eremeeva PG (eds) (1990) Membrane structures of buildings and structures:
handbook. Central Research Institute of Building Structures named after V.A. Kucherenko,
Stroyizdat, Moscow, p 446
5. Shadrin VA (1982) Problems of equilibrium of isotropic and anisotropic elastic membranes.
Ph.D. thesis in Engineering Science. MSEI named after V.V. Kuibyshev, Moscow, p 183
6. Hencky H (1921) Die Berechnung dünner rechteckiger Platten mit verschwindender Biegungsteifigkeit. ZAMM 1:81–89
7. Vagapov RF (1990) Equilibrium of rectangular orthotropic membranes with a free edge. Struct
Mech Anal 1:62–65
8. Konovalov MB (1986) Equilibrium problems for flexible membrane and membrane structures.
Ph.D. thesis in Engineering Science. MSEI named after V.V. Kuibyshev, Moscow, p 245
9. Grigoriev AS, Trushina VM, Shadrin VA (1982) Equilibrium of rectangular and round
orthotropic membranes at large deflections. Current problems in Mechanics and Aviation,
Moscow, pp 106–113
10. Ermolov VV et al (1983) Pneumatic building structures Stroyizdat, Moscow, p 439
11. Föppl A (1907) Vorlesungen über technische Mechanik, Leipzig, no 3, р 298
12. Perelmuter AV, Slivker VI (2007) Calculation models of structures and analysis thereof. DMK
Press, Moscow, p 600
13. Alekseev SA, Kononenko PI (1974) Measurement of elastic constants of some thin films and
fabrics. Izv SSSR: Mech Rigid Bodies 4:166–170
14. Yudin AA, Biktasheva AR, Gabitov AI, Salov AS (2022) Peculiarities research of buildings
and structures energy efficiency. In: IOP Conference series: earth and environmental science.
International science and technology conference “earth science”, vol 4, pp 052039

Calculations of Standard Cells of Structures Made of Film and Fabric …

219

15. Bedov AI, Gabitov AI, Terekhov IG, Salov AS (2022) Forecast durability for protective
penetrating waterproof coating. Lect Notes Civ Eng 197:181–185
16. Gabitov AI, Ryazanova VA, Rolnik LZ, Salov AS, Timofeev VA (2020) Utilization of chemical
waste and by-products as one of technological progress directions. In: IOP Conference series:
materials science and engineering. Innovative technology in architecture and design, vol 907,
pp 012046. https://doi.org/10.1088/1757-899X/907/1/012046

Static-Dynamic Deformation and Force
Resistance of a Monolithic Reinforced
Concrete Frame During Brittle
and Plastic Fracture
P. A. Korenkov, N. V. Fedorova, and S. R. Meliksetyan

Abstract This article investigates the problem of enhancing the robustness of multistory reinforced concrete building frames under progressive collapse initiated by the
local failure of load-bearing elements. Modern approaches to analyzing structural
resistance, including experimental and numerical methods, are reviewed. Particular
attention is paid to the influence of reinforcement type, loading conditions, and the
flexibility of nodal connections on the system’s behavior under emergency conditions. Numerical calculations of the dynamic force redistribution in a reinforced
concrete frame following the sudden removal of a column were conducted. The
simulation was performed considering material nonlinearities and geometric nonlinearity. Various levels of service load, ranging from 30 to 90%, and two reinforcement
schemes, characterized by different failure modes (ductile and brittle), were investigated. The results showed that joint flexibility significantly affects the structure’s
ultimate limit state, particularly in sections where failure occurs due to concrete
crushing (the influence varies from 45 to 65%). The stiffness of the nodal connections, to a lesser extent, alters the absolute values of the internal forces but dictates
the dynamics of their redistribution. Under high loads (0.9 qs ), an avalanche-like
(catastrophic) collapse is observed in the case of brittle failure, whereas with ductile
reinforcement, the system maintains stability. The importance of accounting for joint
flexibility when designing buildings with enhanced resistance to progressive collapse
has been established. The obtained data can be used to optimize structural designs
and develop methods for strengthening reinforced concrete frames.
Keywords Reinforced concrete · Progressive collapse · Force resistance · Node
compliance · Dynamic analysis · Nonlinear modeling

P. A. Korenkov (B) · N. V. Fedorova · S. R. Meliksetyan
Moscow State University of Civil Engineering, Moscow, Russia
e-mail: kpa_gbk@mail.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_19

221

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1 Introduction
Currently, research on the protection of structural systems in reinforced concrete
buildings and structures against progressive collapse has advanced significantly [1].
Numerous issues related to predicting the behavior of load-bearing systems during
reconstruction following the loss of certain structural elements, as well as their
components, have been addressed. Studies [2–6] reviewed a substantial number of
publications and regulatory documents, summarizing and systematizing the factors
that significantly affect the survivability of structural systems.
A key objective in refining approaches to enhance the survivability of load-bearing
systems lies in experimental research, conducted both on model and full-scale specimens. It is important to note that the influence of various types of reinforcement in
reinforced concrete structures on resistance to progressive collapse has been established through increased plastic deformation capacity [7–11]. The nature of the load
applied to the test specimens also plays a significant role [12]. Investigations into the
behavior of monolithic reinforced concrete beam-column joints [13] have enabled the
development of alternative loading mechanisms that simulate progressive collapse
under quasi-static conditions.
The primary principle for enhancing the survivability of a load-bearing system,
achieved by engaging nodal interfaces during emergency impact, is energy dissipation through the development of significant inelastic deformations within the structural elements [14]. Although this phenomenon has not yet been sufficiently studied,
numerous techniques for strengthening nodal joints have already been developed.
These include the use of concrete-steel shells [15], reinforcement with polymer fibers
[16], epoxy resin injections [17, 18], among others.
Currently, there are limitations to the correct application of simplified models
used for analyzing the resistance of reinforced concrete structures [14]. These
models, implemented in software packages, may lead to significant inaccuracies due
to specific structural characteristics. Therefore, more detailed studies of modeling
approaches are required, grounded in comprehensive experimental research of physical processes at both the level of individual elements and the entire load-bearing
system. For instance, the authors observed different failure modes in load-bearing
systems with identical topology and design, depending on the number of operational longitudinal reinforcements [15–20] and other design features [21–24]. The
failure of sections caused by concrete crushing in the compressed zone of the most
heavily loaded elements, as well as the formation of plastic hinges in adjacent span
and support sections of beams and columns, leads to significant alterations in the
structural model following local impact, such as the removal of edge supports. Additionally, the live load level substantially influences the dynamic characteristics of
the load-bearing system, yet studies on this effect remain relatively scarce. Consequently, issues related to accounting for structural and loading factors in framed
structural systems are gaining increasing relevance, especially given the annual rise
in mechanical safety requirements for emergency scenarios [25].

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223

The comprehensive investigation of progressive collapse phenomena in structural engineering presents considerable methodological challenges, primarily due
to the extensive temporal and financial resources required for large-scale experimental testing. In response to these constraints, the scientific community has increasingly turned to the development and refinement of numerical simulation techniques
and analytical modeling approaches as computationally efficient alternatives for
assessing structural vulnerability [19–22]. These methodologies enable researchers
to simulate complex failure scenarios and evaluate system-level responses under
various loading conditions that would be prohibitively expensive or physically
impractical to recreate in laboratory settings.
However, it is crucial to acknowledge the inherent limitations of such computational approaches. Numerical analyses aimed at determining the precise stress–
strain state of complex structural systems frequently produce results that deviate
substantially from empirical observations. These discrepancies primarily stem from
simplifying assumptions in material constitutive models, imperfect representation
of boundary conditions, and inadequate characterization of the intricate interaction
between different structural components during failure propagation. The accuracy
of computational predictions is particularly compromised when modeling structures
with complex load-redistribution mechanisms and non-linear material behavior.
Consequently, the imperative for experimental validation remains paramount in
this field of research. Physical testing provides indispensable empirical data for verifying numerical predictions and refining computational models. This is especially
critical when investigating the behavior of nodal connections—the critical interfaces between structural elements whose performance fundamentally determines
overall system resilience. Particular attention must be devoted to quantifying the
influence of joint compliance (the rotational and translational flexibility of connections) on global structural behavior, as this parameter significantly affects force redistribution pathways and energy dissipation mechanisms during collapse progression
[8, 9, 23, 26, 27].
The present study aims to address these research gaps through a comprehensive
examination of two fundamental factors influencing progressive collapse resistance:
the ductility characteristics of nodal joints and the configuration of reinforcement
schemes in reinforced concrete moment frames. The research methodology incorporates sophisticated numerical modeling of dynamic response following the sudden
removal of critical load-bearing elements, complemented by analytical assessment
of structural survivability. Specific objectives include: (1) quantitative evaluation
of stress–strain distribution patterns during collapse propagation; (2) assessment of
structural integrity and redundancy under extreme loading conditions; (3) identification of relationships between operational load levels (ranging from service conditions
to ultimate capacity) and dynamic response characteristics; and (4) development of
practical recommendations for enhancing structural robustness through improved
connection detailing and reinforcement design.

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2 Models and Methods
Several framed reinforced concrete frames are considered as the object of research,
the reinforcement scheme and geometric dimensions of which are shown in Fig. 1.
The frame has 3 levels and 2 spans, which properly allows analyzing the behavior
of load-bearing elements during progressive collapse. Analyzed 4 models: S1_H—
frame with a rigid hub pair of elements, the destruction of plastic (ξ < ξR ), S1_
P—frame with supple nodal pair of elements, the destruction of plastic (ξ < ξR ),
S2_H—frame with a rigid hub pair of elements, destruction of fragile (ξ > ξR ), S2_
P—frame with supple nodal pair of elements, destruction of fragile (ξ > ξR ).
The frame models are made of B30 grade concrete. The location of the reinforcement in the concrete body is shown in Fig. 1b. The size of the cross-section of the
columns and crossbars is 100 × 100 mm. Two reinforcement options are considered. The transverse reinforcement in all variants is made in the form of clamps
with a pitch of 50 mm in the support zones and 100 mm in the span, reinforcement
Ø4A500C. The column section in all variants has a symmetrically arranged armature
Ø8A500C. The cross-section of the bolt in the first variant also has symmetrically
arranged reinforcement Ø8A500C, and in the second variant, 2 more rods Ø8A500C
are additionally installed in the stretched zone of the supporting sections of the bolt
(1/4 span), thereby increasing the bearing capacity of the section and changing the
fracture pattern to brittle, since the relative height of the compressed section zone
(ξ) is greater than the boundary (ξR ). For a qualitative assessment of the structural
behavior, the strength and deformation characteristics of the materials were set in a
non-linear interpretation.
The load parameters in the form of concentrated forces located at a distance of 1/3
of the span were selected by an iterative method based on the maximum values of the

Fig. 1 a Overall dimensions and load application scheme; b reinforcement of frame elements

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225

bearing capacity of the section, taking into account the safety factor in accordance
with GOST 8829-2018 and the load reliability coefficient (SP 20.13330.2018).
The flexibility of the nodal connections was modeled using single-node finite
elements characterized by nonlinear moment-rotation and shear force–deformation relationships. These constitutive diagrams were developed in compliance with
the standard methodology prescribed by the current Russian building code SP
20.13330.2018 for the design of reinforced concrete structures. The transition from
material stress–strain curves for concrete and reinforcement to these generalized
force–deformation relationships for the sections was achieved through a numerical stress integration procedure across the normal cross-section. Distinct flexibility
parameters for the moment-rotation response were defined for each of the two
reinforcement configurations under investigation.
To analyze the dynamic force redistribution mechanisms within the alternative
load path (or secondary structural system) of the reinforced concrete frame following
a column loss scenario, a nonlinear dynamic analysis was performed simulating the
sudden removal of a critical column. The duration of the dynamic response phase,
characterized by the time to reach maximum displacements, was found to average
approximately 0.12 s. The strength and deformation properties of the constituent
materials were scaled to account for the effects of high strain rates associated
with this rapid dynamic event. Energy dissipation within the structural system was
incorporated into the computational model through Rayleigh damping coefficients.
Furthermore, to inform the experimental phase of the research–specifically, to
optimize the placement and selection of sensors on physical scale models of the
connections and to validate the overall testing protocol–a high-fidelity computational simulation of the frame’s dynamic survivability was conducted. This analysis
explicitly accounted for both the physical nonlinearity of the materials (concrete
and steel) and the geometric nonlinearity associated with large displacements and
rotations of the structural members.

3 Research Results and Their Analysis
The computational analysis was carried out at the loading level, which corresponds
to the range from 0.3 qexp to 0.9 qexp for frame models considered under the condition
of failure of the middle column of the first floor. In the course of the calculation, the
nature of the change in displacement over time, as well as the internal forces for the
elements of the structural system, which received the greatest increase in dynamic
forces, was revealed. This is especially true for cross-sections of crossbars located
in close proximity to both undisturbed and destroyed columns. To understand the
behavior of the system, an analysis of the stress state is carried out, which is expressed
in values relative to their limit values, which allows you to see how close the internal
forces of the structural elements are to critical values.
Analyzing the dynamic characteristics of the frame under the condition of failure
of the middle column of the first floor, several interesting aspects can be noted

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Fig. 2 The nature of changes in time of displacement in the node located above the column to be
removed

(see Fig. 2). For example, for a relatively low payload level, which is 0.3 qexp , the
aКmplitude deflection values for the frame of the second series are twice as high
as for the frame of the first series. This indicates that the design solutions in the
second series are less resistant to stress. At the same time, the total displacement
value, measured from the maximum to the minimum point, shows a more significant
variation, differing by almost three times. This fact indicates the need for a detailed
study of the behavior of various design solutions in order to guarantee the reliability
and safety of frame systems under real operational loads.
The computational analysis was conducted across a spectrum of loading conditions, corresponding to applied loads ranging from 0.3 qexp to 0.9 qexp . This investigation focused on the scenario involving the sudden failure of the first-floor middle
column for all considered frame models.
The calculations elucidated the time-history of displacements and the dynamic
amplification of internal forces within the structural elements most affected by the
sudden load redistribution. This was particularly evident in the cross-sections of the
beams (crossbars) adjacent to both the remaining intact columns and the location of
the removed column.
To quantitatively assess the structural response, an analysis of the stress state
was performed. The internal forces (moments, axial forces, shear) were normalized
against their respective ultimate capacities. This approach provides a clear, dimensionless metric for evaluating the proximity of the structural elements to their critical
failure limits under the dynamic event.
Analysis of the frame’s dynamic characteristics following the loss of the firstfloor middle column revealed several critical insights (see Fig. 2). For instance, at a
relatively low operational load level of 0.3 qexp , the peak deflection amplitudes for
the frame model of the second series (e.g., S2_H or S2_P) were observed to be twice
as high as those for the first series (e.g., S1_H or S1_P). This indicates a significantly
reduced stiffness and resilience in the second series’ design solutions under dynamic
impact.
Furthermore, the total oscillation range, measured from the maximum to the
minimum displacement point, exhibited an even more pronounced discrepancy,
differing by almost a factor of three between the series. This substantial variation
in dynamic response underscores the critical influence of specific design parameters

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Fig. 3 The nature of changes in time of velocity in the node located above the column to be removed

(such as joint flexibility and reinforcement type) on the global structural behavior.
Consequently, these findings highlight the imperative for a detailed and systematic
investigation into the performance of various design configurations. Such research
is essential to ensure the structural reliability and safety of frame systems when
subjected to exceptional loading events and real-world operational conditions.
A progressive increase in the magnitude of the operational load induces substantial alterations in the dynamic characteristics of the structural system’s oscillatory
response. Experimental observations demonstrate a pronounced divergence in the
dynamic behavior between the two frame series under investigation. This divergence
is quantitatively evidenced by a 35% elongation of the oscillation period in one
series relative to the other, alongside distinct differences in the amplitude-frequency
characteristics of their respective dynamic responses.
A particularly significant finding is the markedly more rapid attenuation of vibrations exhibited by the first series of structures. This observed damping behavior
indicates a superior capacity for energy dissipation within these structural systems,
a critical factor for resilience under dynamic loading scenarios. The comparative
vibration decay is illustrated graphically in Fig. 3.
Conversely, as the applied load approaches the ultimate limit state, corresponding to 0.9 qexp , fundamentally divergent structural behaviors are observed. The
second series frames undergo an almost instantaneous, catastrophic (avalanche-like)
collapse. This failure mode is precipitated by the brittle fracture of concrete elements,
which lack the ductility to facilitate progressive force redistribution. In stark contrast,
the first series structures demonstrate stable inelastic deformation, maintaining
structural integrity with maximum deflections remaining within permissible limits
prescribed for special limit states under exceptional loading conditions.
A detailed analysis of the system’s kinematic response reveals critical insights
from the velocity time-history of the node located directly above the removed column.
Numerical simulations established that the peak nodal velocities are attained at load
levels of 0.3 qexp and 0.6 qexp , with maximum values occurring approximately 0.05 s
after the initiation of the column loss event. The computed peak velocities for these
load levels range from 90 mm/s to 150 mm/s, which aligns with expected parameters
for such rapid dynamic processes.
The relationship between peak nodal velocity and the magnitude of the applied
load exhibits significant nonlinearity. This nonlinear dependence is particularly

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Fig. 4 The nature of changes in time of acceleration in the node located above the column to be
removed

pronounced at intermediate load levels. Notably, at a load level approaching the
maximum operational value (0.9 qexp ), the amplitude of the nodal velocity increases
substantially, reaching values up to 250 mm/s. This marked amplification underscores the heightened dynamic effects and increased kinetic energy present in the
system under severe loading conditions, prior to the onset of collapse in non-ductile
systems.
Analysis of the acceleration time-history (Fig. 4) as a function of the operational
load magnitude reveals several critical behavioral patterns of the structural system.
At a relatively low load level (0.3 qexp ), the system’s dynamic response is characterized by pronounced oscillations in acceleration sign, primarily attributable to
elastic deformations of the structural members. This effect is most evident during the
initial phase of the dynamic event (0–0.2 s), where the load-bearing system exhibits
predominantly elastic oscillatory behavior. Subsequently, at approximately t = 0.35 s,
a significant attenuation of oscillations is observed, indicating the system’s transition
to a quasi-static equilibrium state with minimal residual vibrations.
As the load intensity increases to higher levels (0.6 qexp and 0.9 qexp ), the
dynamic response undergoes substantial transformation. This is evidenced by a 25–
40% increase in the fundamental period of oscillation compared to the 0.3 qexp
case, reflecting a reduction in system stiffness due to inelastic material behavior.
Concurrently, peak acceleration amplitudes increase by approximately 50% relative
to the baseline level, indicating the development of significant inertial forces within
structural elements.
The most profound change is observed in the morphology of the oscillatory
response. Under elevated load levels, the system exhibits a complex, highly nonlinear
dynamic response pattern characterized by non-harmonic oscillations and stiffness
degradation effects, markedly differing from the simpler elastic response observed
at lower loads.
A detailed examination of the oscillatory process dynamics reveals three distinct
phases of the dynamic response: (1) an initial phase of rapid acceleration increase
(0–0.1 s), (2) a stabilization phase characterized by peak parameter values (0.1–
0.3 s), and (3) a subsequent phase of oscillation attenuation (beyond 0.3 s). As
the load increases from 0.6 qexp to 0.9 qexp , a consistent 15–20% amplification in
acceleration amplitudes is observed across all phases, accompanied by a prolongation

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229

Fig. 5 Change of bending moment depending on the level of loading in the crossbar adjacent to
the undestroyed columns

of transient durations and the emergence of additional high-frequency components
in the oscillation spectrum.
The analysis of the structural system’s stress state was conducted using normalized values, expressed as ratios relative to their respective ultimate capacities. This
methodology provides universal criteria for assessing structural performance, independent of specific absolute load magnitudes or element geometries. Particularly
noteworthy are the findings regarding the distribution of bending moments in two
critical sections, which demonstrate fundamentally different behavioral mechanisms
under dynamic excitation.
For the section adjacent to the intact column, upon reaching a load level of 0.6 qexp ,
a stabilized stress state is rapidly achieved within 0.05 s following the initial impact.
This indicates highly efficient force redistribution in this region, the activation of a
plastic moment redistribution mechanism, and consequently, the effectiveness of the
reinforcement detailing in the nodal joint area (Fig. 5).
At a lower level of the design load (0.3 qexp ), the stress stabilization process
proceeds much more slowly. For frames of the first series, the duration of the stabilization phase of the oscillatory process increases by 4 times, for frames of the second
series—by 6 times compared to the 0.3 qexp mode, there is a significant change in
the values of the acting internal forces. These circumstances in the behavior of the
series are explained by the peculiarities of reinforcement (the first series has a more
plastic reinforcement), and as a result, the different malleability of the nodal joints,
which led to a different mechanism of cracking, and as a result of the destruction of
sections.
A comparative analysis of the stress stabilization process reveals significant differences in structural behavior at lower design load levels. At an applied load of 0.3 qexp ,
the process of stress redistribution and stabilization occurs considerably more slowly
across all frame configurations. Quantitative analysis demonstrates that for frames
of the first series (designed with ductile reinforcement details), the duration of the
oscillatory stabilization phase increases by approximately four times compared to
their response under higher load conditions. Meanwhile, frames of the second series
(characterized by more brittle reinforcement configurations) exhibit an even more
pronounced extension of this stabilization period, with phase duration increasing
by up to six times relative to their performance under the 0.3 qexp loading regime.

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This prolonged stabilization phase is accompanied by substantial fluctuations in the
magnitude and distribution of internal forces throughout the structural system.
These observed behavioral differences between the two structural series are
fundamentally attributed to their distinct reinforcement characteristics. The first
series incorporates reinforcement designs that promote enhanced plastic deformation capacity, while the second series utilizes reinforcement configurations that result
in more brittle failure modes. This fundamental difference in material behavior
directly influences the flexibility and energy dissipation capacity of the nodal joints,
ultimately leading to divergent crack propagation patterns and failure mechanisms
throughout the structural elements.
Examination of the cross-sectional behavior in the beam region adjacent to the
removed column reveals several important structural mechanisms (Fig. 6). In the vast
majority of analyzed cases (exceeding 83%), the calculated bending moments remain
below their ultimate capacity limits even under the maximum investigated load condition of 0.9 qexp . This phenomenon is explained by three primary structural behaviors:
(1) effective redistribution of forces to adjacent structural elements through alternative load paths; (2) the formation of compensatory force transmission mechanisms
within the structural system; and (3) the beneficial effect of increased static indeterminacy, which enables the mobilization of redundant load-carrying capacities within
the structural system. This collective behavior demonstrates the system’s inherent
capacity to develop alternative load paths following the loss of a primary structural
element.
The empirically established correlation between the applied load level and the
corresponding stress stabilization time represents a finding of particular significance. This relationship provides a quantifiable metric that can substantially refine the
evaluation criteria for assessing special limit states in reinforced concrete structures.
Traditionally, the definition of a special limiting condition—particularly
concerning robustness and progressive collapse resistance—has relied on static force
thresholds or ultimate displacement criteria. The incorporation of temporal parameters, specifically the duration required for a system to reach a new force equilibrium after damage initiation, introduces a more sophisticated, dynamic dimension to
structural assessment.

Fig. 6 Change of bending moment depending on the level of loading in the crossbar adjacent to
the destroyed columns

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This time-dependent behavior serves as a direct indicator of the system’s redundancy, ductility, and overall energy dissipation capacity. A prolonged stabilization
phase under a given load may signal the activation of multiple alternative load paths
and the development of significant inelastic deformations, both hallmarks of a robust
design. Conversely, an abrupt or unstable response might indicate a brittle failure
mechanism and insufficient structural resilience.
Consequently, the integration of stress stabilization time into existing analytical
frameworks offers the potential to develop more precise and physically meaningful
criteria for verifying structural integrity under exceptional loading scenarios, ultimately leading to more reliable and economically efficient design methodologies for
enhanced structural safety.

4 Conclusions
Investigation into the dynamic response of reinforced concrete frame systems
subjected to an emergency scenario–specifically, the sudden removal of a first-story
middle column–has yielded several significant scientific and practical findings. The
computational analysis, conducted across a broad spectrum of loading conditions
from 0.3 qexp to 0.9 qexp , revealed substantial differences in the structural response
between the various frame series when subjected to extreme dynamic loading. These
differences are of fundamental importance for advancing structural safety standards
in monolithic reinforced concrete construction.
The research results demonstrate that accounting for joint flexibility (compliance)
significantly influences the assessment of a structure’s ultimate limit state. This effect
is particularly pronounced in sections where failure is governed by concrete crushing,
with the magnitude of influence varying between 45 and 65% depending on the
applied load level. Conversely, the stiffness characteristics of the nodal connections
exhibit a more limited effect on the absolute values of internal forces within the
stress state. However, they substantially influence the temporal characteristics of
force redistribution, thereby affecting the dynamic response and energy dissipation
mechanisms of the structural system.
The obtained results carry considerable practical implications for advancing
structural engineering practice. Specifically, they contribute to:
1. The refinement of computational methodologies for structures subjected to
exceptional loads;
2. The optimization of structural detailing and design solutions for beam-column
connections;
3. The enhancement of established criteria for evaluating special limit states through
incorporation of temporal parameters (such as oscillation stabilization time) and
relative operational load levels.
Findings substantiate the critical necessity of considering both the ductility characteristics of nodal joints and the specific nature of reinforcement detailing when

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designing reinforced concrete frame systems. Such considerations are paramount
for ensuring adequate resistance against progressive collapse triggered by various
emergency scenarios, including both natural hazards and anthropogenic events.
Acknowledgements This work was supported by the Russian Science Foundation grant No. 2449-10010, https://rscf.ru//project/24-49-10010/.

References
1. Fedorova N, Savin S (2021) Progressive collapse resistance of facilities experienced to localized
structural damage—an analytical review. Build Reconstr 3:76–108
2. Kolchunov V, Tur V (2023) Directions of designing structural systems in special calculation
situations. Ind Civ Eng 7:5–15
3. Kolchunov V, Ilyushchenko T, Fedorova N et al (2024) Survivability of structural systems of
buildings and structures: an analytical review of research. Constr Reconstr 3:31–71
4. Karpenko N, Belostotsky A, Pavlov A et al (2020) Review of methods for calculating reinforced concrete structures under complex stress states taking into account physical nonlinearity, anisotropy and structural heterogeneity. In: Part 1: developments of domestic scientists.
Fundamental, exploratory and applied research of the Russian Academy of Architecture and
Construction Sciences on scientific support for the development of architecture, urban planning and the construction industry of the Russian Federation in 2019: Collection of scientific
papers of RAACS/Russian Academy of Architecture and Construction Sciences, vol 2. ASV
Publishing House, Moscow
5. Karpenko N, Belostotsky A, Pavlov A et al (2020) Review of strength criteria for reinforced
concrete structures. In: Part 2. Developments of foreign scientists. Fundamental, exploratory
and applied research of the Russian Academy of Architecture and Construction Sciences on
scientific support for the development of architecture, urban planning and the construction
industry of the Russian Federation in 2019: Collection of scientific papers of RAACS/Russian
Academy of Architecture and Construction Sciences, vol 2. ASV Publishing House, Moscow
6. Azim I, Yang J, Bhatta S et al (2019) Factors influencing the progressive collapse resistance
of RC frame structures. J Build Eng 27. https://doi.org/10.1016/j.jobe.2019.100986
7. Ali B, Mete Güneyisi E, Bigonah M (2022) Assessment of different retrofitting methods on
structural performance of RC buildings against progressive collapse. Appl Sci 12. https://doi.
org/10.3390/app12031045
8. Fei-Fan F, Hyeon-Jong H, Yun Z, Jing-Ming S, Hu-Zhi Z, Jun-Ho R, Su-Min K, Wei-Jian
Y (2024) Effect of three-dimensional space on progressive collapse resistance of reinforced
concrete frames under various column removal scenarios. J Build Eng 90. https://doi.org/10.
1016/j.jobe.2024.109405
9. Korenkov P, Meliksetyan S (2024) Influence of compliance of the connection of reinforced
concrete structures in the analysis of progressive collapse hazard. In: E3S web conference, vol
533, pp 02004. https://doi.org/10.1051/e3sconf/202453302004
10. Qiang H, Yang J, Feng P, Qin W (2020) Kinked rebar configurations for improving the progressive collapse behaviours of RC frames under middle column removal scenarios. Eng Struct
s211. https://doi.org/10.1016/j.engstruct.2020.110425
11. Alogla K, Weekes L, Augusthus-Nelson L (2016) A new mitigation scheme to resist progressive
collapse of RC structures. Constr Build Mater 125:533–545
12. Cheng Y, Sun L, Liu J et al (2024) Dynamic performance of a remaining RC frame with a
central-column failure subjected to impact loads. Arab J Sci Eng 47:12479–12496. https://doi.
org/10.1007/s13369-021-06525-3

Static-Dynamic Deformation and Force Resistance of a Monolithic …

233

13. Ahmadi R, Rashidian O, Abbasnia R, Mohajeri Nav F, Usefi N (2016) Experimental and numerical evaluation of progressive collapse behavior in scaled RC beam-column subassemblage.
Shock, pp 1–17
14. Patel P, Desai A, Bid S, Desai P (2024) An experimental study for effectiveness of steel fibre
reinforced exterior beam-column joints under cyclic resistance. Constr Build Mater 411. https://
doi.org/10.1016/j.conbuildmat.2023.134511
15. Noyan M (2014) Experimental study on the behavior of RC beam-column joint retrofitted
with ferrocement jacket under cyclic loading. Thesis Submitted to Bangladesh University of
Engineering and Technology, vol 79
16. Karayannis C, Chalioris C, Sideris K (1998) Effectiveness of RC beam–column connection
repair using epoxy resin injections. J Earthquake Eng 2(2):217–240. https://doi.org/10.1080/
13632469809350320
17. Obaidat Y, Abu-Farsakh G, Ashteyat A (2019) Retrofitting of partially damaged reinforced
concrete beam–column joints using various plate-configurations of CFRP under cyclic loading.
Constr Build Mater 198:313–322. https://doi.org/10.1016/j.conbuildmat.2018.11.267
18. Ma C, Wang D, Wang Z (2017) Seismic retrofitting of full-scale RC interior beam–column-slab
subassemblies with CFRP wraps. ComposStruct 159:397–409. https://doi.org/10.1016/j.com
pstruct.2016.09.094
19. El-Ariss B, Elkholy S, Shehada A (2022) Benchmark numerical model for progressive collapse
analysis of RC beam-column sub-assemblages. Buildings 12:122
20. Li Z-X, Liu H, Shi Y, Ding Y, Cui J (2022) Analytical model on progressive collapse resistance
of prestressed precast concrete frame under middle column removal scenario. Adv Struct Eng
25:1583–1608. https://doi.org/10.1177/13694332221085314
21. Fedorova N, Ngoc T (2020) Deformation and failure of monolithic reinforced concrete frames
under special actions. In: Journal of physics: conference series: international scientific conference on modelling and methods of structural analysis, Institute of Physics Publishing, Moscow,
1425:012033
22. IrreñoPalomo I, Frappa G, Carlos de Almeida L, Mouta Trautwein L, Pauletta M (2024)
Analytical and numerical models to determine the strength of RC exterior beam–column joints
retrofitted with UHPFRC. Engineering Structures, vol 312. https://doi.org/10.1016/j.engstruct.
2024.118244
23. Korenkov P, Meliksetyan S (2023) Numerical modeling of nodal connections of reinforced
concrete structures under emergency impacts. In: Construction—formation of the living environment: collection of materials from the seminar of young scientists of the XXVI International
Scientific Conference, Tashkent, 2023, National Research Moscow State University of Civil
Engineering, Moscow, pp 132–138
24. Tong Z, Xu L, Wei C, Chi Y, Huang L (2024) Upgrading seismic performance of beam-column
joints using steel-polypropylene hybrid fiber: experiment and numerical simulation. J Build
Eng 86:108681. https://doi.org/10.1016/j.jobe.2024.108681
25. Korenkov P, Fedorova N, Meliksetyan S (2025) Stress-strain state of nodal joints of reinforced
concrete structures during static-dynamic deformation. Academia. Arch Constr 2:190–199.
doi.https://doi.org/10.22337/2077-9038-2025-2-190-19925
26. Hou S, Shi D, Fan J, Wu T, Sun W, Wu G, Fan X (2024) Comparative study on failure mechanism of full-scale precast and cast-in-place beam-column joints based on acoustic emission
technology. Structures 65(6):106629. https://doi.org/10.1016/j.istruc.2024.106629
27. Bao Y, Tan KH (2022) Performance of precast concrete beam-column joint with a hidden corbel
under progressive collapse scenarios. Eng Struct 267:114679. https://doi.org/10.1016/j.engstr
uct.2022.114679

Numerical Simulation of Surface
Degradation Process in Cement
Granular Composite
N. V. Makarova, M. V. Polonik, and A. A. Mantzubora

Abstract This article focuses on the degradation process of the concrete surface
layer as a two-phase composite. The cause of wear is considered to be a change
in the deformation characteristics of the cement-sand matrix due to microcracking,
corrosion, etc. A simple mesoscale model of surface wear as a process of aggregate
grains falling out of the matrix is proposed. Simulation experiments were conducted
to study the process of formation of destruction centers leading to grain rotation inside
the matrix. The ANSYS software package was used for numerical calculations. The
proposed numerical model can be useful for predicting the behavior of heterogeneous
materials during wear depending on the degree of change in the mechanical properties
of their structural elements throughout the life cycle. Finally, an engineer can propose
methods of protecting the concrete surface and ways of its repair by using this model.
Keywords Wear · Concrete surface · Composite materials · Degradation ·
Numerical modeling

1 Introduction
Concrete surface wear is a process of concrete degradation, leading to its destruction
in the near-surface layers. The causes of this process can be physical, chemical and
mechanical, and depend on the operating conditions. Physical causes of degradation are freeze–thaw cycles, exposure to high temperatures, shrinkage and cracking.
Chemical causes of degradation are as follows: aggressive substances impact, carbonation, corrosion of rebar and others. Mechanical causes of degradation are abrasion,
shock, vibration, erosion and cavitation. Manifestations of concrete degradation are
surface, thorough and shrinkage cracks; peeling and crumbling; loss of adhesion
between cement matrix and aggregates, as well as between layers of concrete. In
such cases, material damage, degradation of the cement matrix, increase in porosity
N. V. Makarova (B) · M. V. Polonik · A. A. Mantzubora
Institute of Automation and Control Processes of Far Eastern Branch of RAS, Vladivostok, Russia
e-mail: maknat@bk.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_20

235

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N. V. Makarova et al.

and decrease in strength, as well as the creation of favorable conditions for sulfate
corrosion of concrete, chloride corrosion of reinforcement and reduced resistance
to freeze–thaw cycles are observed [1–6]. As a result, concrete degradation from
the surface layers can extend to a depth of several centimeters or more, which can
ultimately lead to the destruction of the structure.
Applying protective coatings by using different materials or resurfacing techniques can shield the concrete surface from wear and degradation [7, 8]. However,
these methods are insufficient in large structures, such as bridge supports, railway
sleepers, road surfaces, oil platform foundations, etc., which operate in particularly
difficult conditions.
Thus, designing a concrete mix composition with high wear resistance to is an
important problem. Numerous factors, including compressive strength, water-cement
ratio, surface characteristics and quality of aggregate, curing conditions, etc., affect
the ability of concrete to wear resistance [9, 10].
Currently, micro- and nano- silica, fly ash and fiber reinforcement are successfully
used for this purpose [11, 12]. To design new compositions, it is necessary to make
laboratory experiments to determine the optimal mix of cement materials. However,
it is a challenging problem due to the need for many multifactorial experiments.
Moreover, unlike concrete compression testing, abrasion, erosion, and corrosion tests
are labor-intensive, time-consuming, and require additional equipment [2–4, 11–16].
Recently, machine learning-based models (ML) have been successfully used to
design new efficient concrete compositions. However, these models are also based on
experimental data. Thus, the use of ML only reduces the number of labor-intensive
experiments [17–21]. As previously noted, degradation processes begin with the
surface layers and end with cracking of the matrix, disruption of adhesion and loss
of aggregates, regardless of the type of external influence.
Therefore, there is a need for methods of modeling such composites that allow
prediction of the wear process considering the heterogeneous structure based on solid
mechanics. Models of concrete surface wear with consideration of its heterogeneous
structure are presented in [22–26]. However, the strength and deformation properties
of the structural elements remain constant throughout the process.
The mechanical behaviors of this composite, including elastic and plastic behaviors, damage initiation and crack propagation, emerges from the behaviors of its
constituents and their arrangement in the meso-and macroscale. Over a long period
of time, the properties of the aggregates remain unchanged, while the properties of
the cement matrix change from brittle and elastic to elastic–plastic.
In our work, a simple model of the process of concrete surface degradation at the
macro level is proposed as a process of reducing the deformation modulus of the
cement matrix.

Numerical Simulation of Surface Degradation Process in Cement …

237

2 Modeling
2.1 Statement of the Problem
The wear process according to [23, 24, 27–30] is divided into the following possible
stages:
• crushing of the solvation shells and exposing of the grains of aggregate;
• the wear process of the grains of aggregate and cement-sand matrix;
• destruction of the concrete surface because of the fall out of aggregate granules
from the matrix.
In paper [24], the surface degradation criterion is adopted as the height of the
granule exposure. Moreover, in this work, based on the solution of the FEM problem,
it was established that the maximum height of grain exposure is 0.4h.
The paper [27] considers two possible causes of grain fallout: fatigue matrix failure
(extensive microcracking) between grains; propagation of a fatigue macrocrack at the
boundary between grains and the matrix (Fig. 1). After the exposure of the surface of
the aggregate granules, a surface is formed by a set of areas with different mechanical
characteristics. The experimental studies have shown that the type of destruction is
affected by the ratio of the stiffness parameters of the matrix and aggregate, as well
as the distance between the grains.
Summarizing all the above, modeling the process of surface degradation of a
cement composite as a gradual fatigue crashing of the matrix and failure of adhesion is
a rather complex problem. We have developed a simple model where the degradation
process of the surface layer of a granular composite occurs in stages due to a decrease
in the stiffness of the matrix. This approach was adopted based on recommendations
SP 430.1325800.2018 to consider the nonlinearity of the material. In this work, three
computational experiments were performed with the Young’s modulus of the matrix
equal to Eb , 0.6Eb and 0.2Eb . At the same time, the stiffness of the granules remains
constant.

Fig. 1 Failure mechanism associated with exposed aggregates

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N. V. Makarova et al.

Fig. 2 a a—the grain size, l—is the distance between the grains, h—is the exposed height;
b graphical realization of the near-surface layer with the grains in ANSYS

2.2 FE Models
The technique of numerical image processing and parameterization methods are the
most popular approaches in three-dimensional (3D) modeling of various phases of
materials. However, concrete is a heterogeneous material and due to the complexity
of three-dimensional modeling of the mesostructure and high computational costs,
it is more expedient to study the stress–strain state in two-dimensional (2D) models.
In this work we modeled concrete as a heterogeneous material composed of coarse
aggregate granules, cement-sand matrix, and interfacial transitional zones (ITZs).
In the study of concrete degradation process, the most interesting is the nearsurface layer. Therefore, we have modeled this layer as an elastic layer with granular
inclusions. In two-dimensional (2D) mesoscopic modeling, the near-surface level is
represented as an elastic layer with round inclusions, the distance between grains l,
the grain size a and the height of the exposed h Fig. 2a.
In order to study concrete wear at the degradation stage as an interaction between
the material components (matrix and grains), we assumed that the real dynamic wear
process under load can be reduced to the application of a static load to the grains.
Thus, we fix the bottom of the layer and apply a uniformly distributed load P at
an angle β(ctgβ = 0.6) to half of the open part of the grains Fig. 2b. The finite
element method (FEM) is the most suitable for solving such problems. All calculations were conducted using the ANSYS software. For two-dimensional modeling of
solid structures, the ANSYS element—PLANE182 is used.
In this paper, numerical studies were performed to analyze the stress–strain state
and determine the location of the expected destruction zones of the near-surface
material within ITZ. Three numerical experiments were conducted with different
elastic characteristics of the matrix. By reducing the elastic modulus of the matrix in
the numerical experiments, we model the process of its degradation. The parameters
for the experiments are given in Table 1, where E1 is the Young’s modulus of the
cement-sand matrix, E2 is the Young’s modulus of the grains, v1 is the Poisson

Numerical Simulation of Surface Degradation Process in Cement …

239

constant of the matrix, v2 is the Poisson constant of the grains. The data in Table 1
are based on the solution to the problem of grain falling out of the matrix [24].
The calculations were performed in the ANSYS system in the Cartesian coordinate
system. For clarity, the calculation results are given in Local Coordinate Systems,
corresponding to the cylindrical local coordinate system (LCS). In this case, the
strains with components drr will correspond to radial strains, and the strains with
components drϕ will correspond to tangential strains acting at the ITZ. The results
of numerical calculations of strains are shown in Figs. 3, 4 and 5.
Table 1 Basic geometric and physical parameters of experiments
Parameters
Experiment
no.

h,
mm

E1 , 109 Pa

E2 , 109 Pa

a,
mm

l, mm

P, 106 Pa

0.2

0.25

100

0.2

0.25

100

0.2

0.25

100

Fig. 3 a radial strains (drr ); b tangential strains drϕ for experiment 1

Fig. 4 a radial strains (drr ); b tangential strains drϕ for experiment 2

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N. V. Makarova et al.

Fig. 5 a Radial strains (drr ); b tangential strains drϕ for experiment 3

According to the calculations obtained in Figs. 3, 4 and 5, with a decrease in the
elastic modulus of the matrix, the strains in the matrix increase, while the strains of
the grain remain virtually unchanged. An increase in strains at the ITZ from the side
of the applied load is also recorded.
According to the calculation results in Figs. 3, 4 and 5, it can be concluded that
the maximum and minimum strains are concentrated at ITZ.

3 Results and Discussion
The simulation results of strain state in surface layer elements within one grain for
different values of the elastic modulus are shown in Figs. 3, 4 and 5. Let us consider
the process of material degradation by reducing E1 of the matrix.
At a fixed value of the load P and the same geometric dimensions, the greatest
radial tensile strains are observed at the maximum value of E1 = 20 MPa on the
matrix surface in the red elements (Fig. 3a).
A decrease in the deformation modulus to E1 = 12 MPa leads to a simultaneous
increase in tensile strains in this zone both in the matrix and in the grain already at
the ITZ.
At a value of E1 = 4 MPa, tensile strains decrease, this may indicate that with a
decrease in the deformation modulus in this zone, a crack has already opened at the
ITZ boundary (Fig. 5a).
This is confirmed by the simultaneous increase in tangential tensile strains on the
ITZ in the matrix on the opposite side on the lower side of the grain (Fig. 5b). Also
in the lower ITZ zone, a local region of increasing compressive strain (blue color) is
formed in the matrix.
Thus, it can be assumed that when certain values of both compressive and tensile
strain are reached, the grain will fall out of the matrix, which confirms the solution
[24]. For numerical analysis we plotted graphs of the value of drr and drϕ at the ITZ

Numerical Simulation of Surface Degradation Process in Cement …

241

for experiments 1–3 depending on the angle ϕ measured at the grain center from the
horizontal axis (Figs. 6 and 7).
On these graphs one can identify the peak points of the drr and drϕ values at
different E1 (Table 1).
Let us consider the graphs of the drr and drϕ values on the ITZ in grain (Fig. 6).
Several peak points can be identified on the graphs. At an angle ϕ = 168◦ , the radial
values of drr reach maximum compressive values, while the tangential values of
drϕ , on the contrary, reach maximum tensile values. But when moving away some
distance from the surface, already at ϕ = 171◦ , the radial compressive strains change
the plus sign to minus and reach maximum tensile strains (Fig. 6a).
Tangential strains (Fig. 6b) when moving away from the surface reach maximum
compressive strains at ϕ = 118◦ , and then when approaching the surface reach
maximum tensile strains at ϕ = −32◦ .

Fig. 6 Material of grain. The value of drr (a) and drϕ (b) at the ITZ for experiments 1–3 depending
on the angle ϕ measured at the grain center from the horizontal axis

Fig. 7 Material of matrix. The value of drr (a) and drϕ (b) at the ITZ for experiments 1–3 depending
on the angle ϕ measured at the grain center from the horizontal axis

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Table 2 Strains drr at the ITZ for experiments 1–3 depending on the angle ϕ measured at the grain
center from the horizontal axis
Experiment no.

ϕ,°

drr × 10−4
matrix

| drr | × 10−4
aggregate

168

0.212

− 0.268

0.48

− 62

− 0.315

− 0.183

0.132

− 0.114

− 0.064

0.05

168

0.189

− 0.286

0.475

− 62

− 0.539

− 0.188

0.351

− 0.208

168
− 62
12

− 0.060

0.148

− 0.294

0.385

− 1.66

− 0.194

1.467

− 0.683

− 0.055

0.628

0.0912

It is important to note that the change in matrix rigidity had virtually no effect on
grain strains. The strains value does not depend on the change in E1 and is much less
than the limit values for rocks used as coarse aggregate for concrete.
Let us consider the graphs of the drr and drϕ values on the ITZ in the matrix
(Fig. 7). Several peak points can be identified on the graphs. At an angle ϕ = 168◦ ,
the radial values of the drr reach maximum compressive values, while the tangential
values of the drϕ , on the contrary, reach maximum tensile values.
Radial deformations throughout the entire ITZ are compressive, with a maximum
value at ϕ = 62◦ (Fig. 7a).
Tangential strains (Fig. 7b) when moving away from the surface reach maximum
compressive strains at ϕ = 105◦ , and then when approaching the surface reach
maximum tensile strains at ϕ = −15◦ .
Let us analyze the numerical values of strains at peak points (Tables 2 and 3). If
the destruction along the boundary of the ITZ will occur from reaching the limiting
values of strains, we will determine the difference in deformations in the filler and
matrix. The maximum difference in radial deformations in experiment 3 reaches
its maximum value at ϕ = −62◦ (Table 2). The maximum difference in tangential
strains in experiment 3 reaches its maximum value at ϕ = −105◦ (Table 3). Having
accepted the limiting values of strains, we can conclude that in experiment 3, the
ITZ boundary will be violated not only at the surface of the material, but along the
entire contour of the aggregate grain.

4 Conclusions
A simple model of concrete surface degradation as a process of grain loss from the
matrix is proposed.

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243

Table 3 Strains drϕ at the ITZ for experiments 1–3 depending on the angle ϕ measured at the grain
center from the horizontal axis
Experiment no.

ϕ,°

drϕ × 10−4
Matrix

168
− 105

0.0396
− 0.423

drϕ × 10−4
Aggregate
0.675

0.635

− 0.280

0.143

− 14

0.297

0.163

0.134

168

− 0.105

0.752

0.857

− 105

− 0.694

− 0.297

0.397

− 14

0.480

0.143

0.337

168

− 0.578

0.856

1.434

− 105

− 2.060

− 0.319

1.741

− 14

1.340

0.119

1.221

Destructive changes in the matrix are considered here as a process of reducing
the deformation modules. This made it possible to avoid the need to introduce
inelastic and other special finite elements during FEM modeling, which significantly
complicates the calculation.
The computational experiments performed confirmed the possibility of applying
the proposed approach when compared with the results of other theoretical and
experimental studies.
In engineering practice, the developed simple model can be applied both in the
design of compositions of durable materials with a granular structure and in the
assessment of the residual resource during operation.
Acknowledgements The research was carried out within the state assignment of IACP FEB RAS
(Theme FWFW-2021-0005).

References
1. Xia X, Guo J, Xu H, Zhang P (2025) Synergistic degradation effects of environmental factors
on dam concrete: experimental insights and constitutive model. Eng Fail Anal 171:109399.
https://doi.org/10.1016/j.engfailanal.2025.109399
2. Liu D, Wang C, Gonzalez-Libreros J, Guo T, Cao J, Tu Y, Sas G (2023) A review of concrete
properties under the combined effect of fatigue and corrosion from a material perspective.
Constr Build Mater 369:130489. https://doi.org/10.1016/j.conbuildmat.2023.130489
3. Ismaeil RH, Hilo AN, Al-Gasham TS (2021) Review of abrasion mechanisms and influential variables on the disintegration resistance of concrete. IOP Conf Ser: Mater Sci Eng
1058:012056. https://doi.org/10.1088/1757-899x/1058/1/012056
4. Subedi A, Kim H, Lee SJ, Lee MS (2025) Assessing abrasion resistance in concrete pavements:
a review. J Appl Sci 15(4):2101. https://doi.org/10.3390/app15042101

244

N. V. Makarova et al.

5. Liu P, Chen Y, Wang W, Yu Z (2020) Effect of physical and chemical sulfate attack on performance degradation of concrete under different conditions. Chem Phys Lett 745(4):137254.
https://doi.org/10.1016/j.cplett.2020.137254
6. Szweda Z, Skórkowski A, Konečný P (2024) The influence of corrosion processes on the
degradation of concrete cover. Materials 17:1398. https://doi.org/10.3390/ma17061398
7. Pan X, Shi Z, Shi C, Ling TC, Li N (2017) A review on concrete surface treatment part
I: types and mechanisms. Constr Build Mater 132:578–590. https://doi.org/10.1016/j.conbui
ldmat.2016.12.025
8. Elias L, Geethanjali CV, Bijimol BI, Anil A, Shafna MA, Shibli SMA (2025) Influence of finerecycled concrete aggregate derived SiO2 composite on corrosion protection and anti-wear
characteristics of zinc and zinc phosphate coatings. J Ind Eng Chem. https://doi.org/10.1016/
j.jiec.2025.05.009
9. Jacobsen S, Scherer GW, Schulson EM (2015) Concrete–ice abrasion mechanics. Cem Concr
Res 73:79–95. https://doi.org/10.1016/j.cemconres.2015.01.001
10. Bayazıt Y, Karakurt C, Bakış R (2023) Investigation of erosive wear effect on concrete water
structures: the case of Porsuk Dam. Turkey Mag Concr Res 75:529–540. https://doi.org/10.
1680/jmacr.22.00240
11. Silva CA, Gonçalves MR, Rosenkranz A, Hammes G, Costa HL (2025) Effects of MXenes
(Ti3 C2 Tx ) deposition by drop casting on the fretting wear of structural concrete. Wear
570:206056. https://doi.org/10.1016/j.wear.2025.206056
12. Su J, Yang H, Wang S, Tian J, Cai X, Shui F, Fan Z (2025) Effects of dual incorporation
of Nano-SiO2 and Nano-CaCO3 on the abrasion resistance and microstructure of concrete. J
Wuhan Univ Technol-Mater Sci Ed 40:509–518. https://doi.org/10.1007/s11595-025-3086-8
13. Li YJ, Gong YL, Yin J (2011) Strength and durability of high performance road concrete
containing ultra-fine fly ash. J Appl Mech Mater 99:1264. https://doi.org/10.4028/www.scient
ific.net/amm.99-100.1264
14. Yuan S, Zhang F, Du S, Li K, Luo J, Liu Y, Lin J (2024) Research on the wear resistance and
impact resistance of modified rubberized concrete. Phys Chem Earth, Parts A/B/C 135:103680
15. Zhang K, Ni H, Tian J, Yang B, Guo A, Dai Q (2024) Study of erosion wear to concrete
by different gravel particle sizes: laboratory test and numerical simulation. Case Stud Constr
Mater 20(03):e02893. https://doi.org/10.1016/j.cscm.2024.e02893
16. Wang X, Feng R, Li J, Liu S, Yan C (2022) Wear characteristics and degradation mechanism
of natural pumice concrete under ice friction during ice flood season. Constr Build Mater
341:127742. https://doi.org/10.1016/j.conbuildmat.2022.127742
17. Ren J, Zhao H, Zhang L, Zhao Z, Xu Y, Cheng Y, Wang J (2022) Design optimization of
cement grouting material based on adaptive boosting algorithm and simplicial homology
global optimization. J of Building Engineering 49:104049. https://doi.org/10.1016/j.jobe.2022.
104049
18. Amin MN, Arifee SU, Qadir MT, Alsharari F, Faraz MI (2025) AI-powered interpretable
models for the abrasion resistance of steel fiber-reinforced concrete in hydraulic conditions.
Case Studies in Construction Materials 22(11):e04755. https://doi.org/10.1016/j.cscm.2025.
e04755
19. Cui X, Gong L, Zhang R, Zhang L, Xu X, Li R (2025) Prediction of concrete wear resistance
under wind erosion based on the LSTM deep learning model. Constr Build Mater 481:141616.
https://doi.org/10.3390/su17104624
20. Malazdrewicz S, Sadowski Ł (2021) Neural modelling of the depth of wear determined using
the rotating-cutter method for concrete with a high volume of high-calcium fly ash. Wear
477:203791. https://doi.org/10.1016/j.wear.2021.203791
21. Khan A, Khan M, Ali M, Khan M, Khan AU, Shakeel M, Gamil Y (2024) Predictive modeling
for depth of wear of concrete modified with fly ash: a comparative analysis of genetic
programming-based algorithms. Case Studies in Construction Materials 20:e02744. https://
doi.org/10.1016/j.cscm.2023.e02744
22. Dandapat R, Deb A (2016) A probability-based model for the erosive wear of concrete by
sediment bearing water. Wear 350:166–181. https://doi.org/10.1016/j.wear.2016.01.012

Numerical Simulation of Surface Degradation Process in Cement …

245

23. Liu Q, Wu M (2023) Experimental and numerical investigations on concrete abrasion of
hydraulic structures. In: International RILEM conference on synergizing expertise towards
sustainability and robustness of CBMs and concrete structures. Springer Nature Switzerland,
Cham, pp 191–202. https://doi.org/10.1007/978-3-031-33211-1_18
24. Itoh Y, Yoshida A, Tsuchiya M, Katoh K, Sasaki K, Saeki H (1988) An experimental study
on abrasion of concrete due to sea ice. In: Offshore technology conference, Houston, Texas
OTC-5687-MS. https://doi.org/10.4043/5687-MS
25. Chen F, Zou C, Zhou Y, Hu S, Mao J (2025) Correlation analysis of abrasion resistance of rubber
concrete with microstructure and pore structure. Constr Build Mater 475:141211. https://doi.
org/10.1016/j.conbuildmat.2025.141211
26. Barbhuiya S, Jivkov A, Das BB (2023) A review of multi-scale modeling of concrete deterioration: fundamentals, techniques and perspectives. Constr Build Mater 406:133472. https://
doi.org/10.1016/j.conbuildmat.2023.133472
27. Makarova NV (2013) Relations between concrete structural parameters and abrasion resistance.
J Appl Mech Mater 357:1259–1262. https://doi.org/10.4028/www.scientific.net/amm.357-360.
1259
28. Makarova NV, Polonik MV (2013) Abrasion wear of heterogeneous materials. J Appl Mech
Mater 248:355–360. https://doi.org/10.4028/www.scientific.net/amm.248.355
29. Makarova N, Polonik M (2018) Optimization of structural parameters of cement composites
with high wear resistance. IOP Conf Ser: Mater Sci Eng 365:032068. https://doi.org/10.1088/
1757-899x/365/3/032068
30. Makarova NV, Polonik MV, Mantsybora AA (2018) Abrasive wear of cemented granular
composites: experiments and numerical simulations. IOP Conf Ser: Mater Sci Eng 463:032002.
https://doi.org/10.1088/1757-899x/463/3/032002

Wind Loads: Analysis of Deformations
in Building Structures
E. N. Egereva, A. O. Kresik, and S. A. Martyusheva

Abstract The paper presents a detailed analysis of wind-induced deformations in a
16-story residential structure located in Kaliningrad, Russia (Wind Region II). Using
advanced numerical modeling techniques in Lira SAPR 2016 R5, the study examines
both static and dynamic wind load effects on the building’s structural integrity. Key
aspects include the evaluation of stress distribution, deformation patterns, and resonance risks through modal and direct dynamic analysis. The results indicate significant deviations under wind loads, with maximum displacements reaching 61.4 mm
along the longitudinal axis and 1.03 mm transversely. These findings emphasize the
critical role of dynamic wind components in structural design, particularly for highrise buildings, and highlight the importance of integrated modeling approaches to
enhance safety and performance.
Keywords Structural deformations · Wind load effects · Dynamic response
analysis · Tall building design · Computational modeling

1 Introduction
Deformations in building structures under wind loads refer to cases where excessive
or uneven wind impact on any part of a building leads to significant deformations
and overstresses in other elements, which can cause damage or collapse. Since it
is impossible to completely eliminate the probability of extreme wind effects, it
is necessary to ensure the stability of the building and the safety of people and
equipment inside by reducing the risk of deformations under local wind loads. Any
building, especially a high-rise one, is a complex dynamic system where wind load
on one structural element inevitably affects others. Thus, changes in the stress–
strain state in one part of the building due to wind influence the entire structure as
a whole. Therefore, it is essential to understand how the building will behave under
E. N. Egereva (B) · A. O. Kresik · S. A. Martyusheva
Moscow State University of Civil Engineering, Moscow, Russia
e-mail: akresik2003@gmail.com
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_21

247

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E. N. Egereva et al.

various wind load scenarios, including their unevenness and pulsation. This can be
verified by analyzing deformations under wind loads using numerical simulation
methods. Modern building codes and regulations require a thorough approach to the
design of complex and high-risk structures. For tall buildings, methods that take into
account wind loads are particularly important because it is often wind that causes
serious accidents and structural failures. Various engineering approaches are used in
calculating stress–strain state, including probabilistic analysis techniques that allow
assessing risks of catastrophic events development. The most crucial research tool
is computer simulation, which helps analyze deformation changes in all structure
elements under different loading conditions. Additionally, climatic conditions of the
construction region, altitude above sea level, presence of obstacles, and proximity
to water surfaces enhancing air mass speed are taken into account. These factors
increase complexity of studies and raise requirements for accuracy of calculations
performed. Using comprehensive models and verifying results through field testing
minimizes risks and increases reliability of constructed objects.
As part of the study, a simulation of a sixteen-story residential building was
performed, with a frame based on series 1.020–1/87 and a spatial system type: braced
(Fig. 1). The building dimensions along the extreme axes “1–9” and “A-G” are 37.2
× 15.0 m. The basement height is 2.8 m, the first-floor height is 3.3 m, and the height
from the second to the fifteenth floor is 3 m. The height from ground level to the
top of the building is h = 45.84 m. The construction area for snow and wind load
collection was chosen as Kaliningrad, Kaliningrad Oblast (Fig. 2), according to the
regulatory document SP 20.13330.2016, wind region (II), with a normative wind
pressure value of w0 = 0.30kPa, terrain type [1]. The general view of the building
frame is shown (Fig. 3).

Fig. 1 Floor plan

Wind Loads: Analysis of Deformations in Building Structures

249

Fig. 2 Wind region for
Kaliningrad, Kaliningrad
Oblast

Fig. 3 General view of the
building frame

2 Materials and Methods
The calculation in Lira SAPR 2016 R5 [2–4] software was carried out for basic
and special load combinations, including wind loads applied according to regulatory requirements. The calculation involves determining deformations for each
created loading case, including various directions and pulsation components of wind
loads. Based on the obtained deformations, an analysis of the stress–strain state of
building structure elements is conducted, identifying the most heavily loaded areas
and checking the carrying capacity of the elements.

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In addition, the program allows taking into account additional features of reallife operation by introducing safety factor coefficients reflecting adverse external
conditions, deviations from material standard values, and other random factors. After
completing the analysis, the results are displayed as tables and diagrams, facilitating
visualization of the nature of deformation and concentration of stresses in critical
zones of the structure. Thanks to flexible settings, a wide range of actual operational
situations can be modeled, including vibrational processes, thermal expansion, and
compressive efforts typical for unique projects such as high-rise buildings and bridge
crossings.
Dynamic load analysis in Lira SAPR 2016 R5 [5] can be performed using several
methods, including direct dynamic analysis (Newmark method, Wilson’s method)
and modal analysis. Each of these methods has its own specifics and application area.
• Direct Dynamic Analysis. This method tracks changes in the stress–strain state
of the structure over time when subjected to specified dynamic loads. Among the
algorithms of direct dynamic analysis, Newmark’s method and Wilson’s θ-method
stand out. They are widely used to study the response of the structure to sudden
short-term impulses, such as impact or ground shaking during earthquakes.
• Modal Analysis. Modal analysis aims at identifying natural frequencies and vibration modes of the structure. Determining these characteristics is essential when
studying the stability of the structure against external dynamic influences since
it allows detecting potential resonance phenomena capable of causing significant
amplitude growth and premature damage to the structure.
Based on the analysis results, deformations corresponding to hazardous load combinations are processed by postprocessors in Lira SAPR. This information serves as
the basis for mandatory checks of bearing capacities of steel and reinforced concrete
structural elements, ensuring their strength, reliability, and durability. Additional
configuration options for boundary conditions, analysis capabilities, and convenient
tools for data visualization make this software indispensable for engineers, enabling
them to quickly obtain accurate data and reduce project errors.
The building was calculated using a spatial shell-rod finite-element model
consisting of 572 nodes and 1763 elements, which accounts for the complex
geometric shapes of the building and the distribution of wind loads on its surface.
The obtained results allow evaluating wind-induced deformations in the structure
and optimizing design solutions to enhance its stability and safety.

3 Calculation
In the LIRA SAPR 2016 R5 [6] calculation, the self-weight of frame elements such
as columns, beams, braces, ties, and reinforced concrete slabs was automatically
accounted for through their stiffness parameters. Permanent loads from floors and

Wind Loads: Analysis of Deformations in Building Structures

251

roofs, including self-weight, were applied as area-distributed loads on the corresponding slabs. The calculation of permanent loads on the floor and roof is presented
in Tables 1 and 2, respectively.
The collection of temporary short-term live loads is presented in Table 3.
The calculation of snow load on the roof of buildings and structures is performed
according to Section 10 of SP 20.13330.2016, Amendment 4, considering Scheme
B.1 of Appendix B.
The normative value of temporary short-term snow load is determined by the
formula:
S0 = Ce · Ct · μ · Sg = 1.0 · 1.0 · 1.0 · 1.0 = 1.0kPa

(1)

Table 1 Load collection for the floor
γf

Design value qp , kPa

Floor covering with linoleum, 0.036
2 mm thick, ρ = 1800 kg/m3

1.2

0.043

CSP, 60 mm thick, ρ =
1800 kg/m3

1.08

1.3

1.41

Soundproofing mineral wool
boards, 50 mm thick, ρ =
350 kg/m3

0.175

1.2

0.21

Total

1.291

Type of load

Normative value qn , kPa

1.663

Table 2 Load collection for the roof
No

Type of load

Normative value qn , kPa

γf

Design value qp , kPa

Polymer membrane, 6 mm
thick, ρ = 2000 kg/m3

0.12

1.2

0.144

CSP, 60 mm thick, ρ =
2100 kg/m3

1.26

1.3

1.64

Thermal insulation mineral
wool boards, 100 mm thick, ρ
= 100 kg/m3

0.175

1.2

0.21

Total

1.55

1.99

Table 3 Collection of temporary short-term loads for the floor
No

Type of load

Normative value qn , kPa

γf

Design value qp , kPa

Residential building
apartments

1.5

1.3

1.95

Total

1.5

1. 95

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E. N. Egereva et al.

where Ce = 1.0; Ct = 1.0; for Kaliningrad (II snow region); μ-coefficient of transition from the weight of snow cover on the ground to the weight on the roof, determined
according to Appendix B. The roof slope angle α < 15, according to paragraph B.5,
only option 1 is considered, with uniform snow distribution on the roof and coefficient
μ = 1.0.
The design value of snow load:
S = S0 · γf = 1.0 · 1.2 = 1.2 kPa

(2)

The temporary short-term snow load was applied over the area of the plates
modeling the roof slabs at the elevation of + 45.000 m.

4 Calculation of Normative Wind Load
In all cases, the normative value of the main wind load should be determined as the
sum of the average and pulsating components [7]:
w = wm + wg

(3)

where:wm –average component of wind load, determined depending on the equivalent
height:
wm = w0 · k(ze ) · c · γf

(4)

where w0 —normative wind pressure for wind region II, equal to 0.30 kPa; k(ze )—
coefficient accounting for changes in wind pressure for height ze ; ze —equivalent
height; c—aerodynamic coefficient; wg —pulsating component of wind load.

5 Design Value of the Average Wind Load Component
(External Pressure on External Walls)
For the calculation, Kaliningrad, Kaliningrad Oblast, was chosen according to regulatory document SP 20.13330.2016, corresponding to Wind Region II, with a normative
wind pressure of w0 = 0.30kPa and Terrain Type B (urban areas). The load reliability factor was set to γf = 1.4.Aerodynamic coefficients for external pressures
were defined separately for different sides of the structure:
• Windward side facing the direction of the wind: c = +0.8
• Leeward side located in the shadow: c = −0.5

Wind Loads: Analysis of Deformations in Building Structures

253

This distribution reflects the regularities of force exertion by wind on the facade
elements of the building. The adopted values correspond to standardized recommendations for urban territories. These coefficients help more accurately calculate the
actual loads acting on the structure, improving the quality of design and increasing
the service life of constructions [5].
Consideration of these values made it possible to develop a realistic model for
calculating wind loads applicable to a wide range of high-rise buildings situated in
urban environments, taking into account the climate-specific features of Kaliningrad
Oblast.
Next, consider the wind action along the X-axis (Figs. 4, 5) shows the load along
the X-axis.
The building height h = 47.795 m, transverse dimension d = 15.840 m (actual
building length from wall to wall).
Thus, h > 2d (47.795 m > 30.000 m)—the building is divided into 3 sections.

Fig. 4 Wind action on the
side of the building along the
X-axis

Fig. 5 Load on the side of
the building along the X-axis

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E. N. Egereva et al.

Section 1:
z ∈ [0m; 15.840m]; ze = d = 15.840m;
k(ze = 15.840m) = 0.65(15.840/10)2·0.2 = 0.781;
W (+) = 0.03t/m2 · 0.781 · 0.8 · 1.4 = 0.0262t/m2 ;
W −) = 0.03t/m2 · 0.781 · 0.5 · 1.4 = 0.0164t/m2 ;
Section 2:
z ∈ [15.840m; 31.955m]; ze = d = 15.840m;
k(ze = 15.840m) = 0.65(15.840/10)2·0.2 = 0.781;
W (+) = 0.03t/m2 · 0.781 · 0.8 · 1.4 = 0.0262t/m2 ;
W (−) = 0.03t/m2 · 0.781 · 0.5 · 1.4 = 0.0164t/m2 ;
k(ze = 24.840m) = 0.65(24.840/10)2·0.2 = 0.935;
W (+) = 0.03t/m2 · 0.935 · 0.8 · 1.4 = 0.0314t/m2 ;
W (−) = 0.03t/m2 · 0.935 · 0.5 · 1.4 = 0.0196t/m2 ;
k(ze = 31.955m) = 0.65(31.955/10)2·0.2 = 1.034;
W (+) = 0.03t/m2 · 1.034 · 0.8 · 1.4 = 0.0347t/m2 ;
W (−) = 0.03t/m2 · 1.034 · 0.5 · 1.4 = 0.0217t/m2 ;
Section 3:
z ∈ [31.955m; 47.795m]; ze = h = 47.795m;
k(ze = 47.795m) = 0.65(47.795/10)2·0,2 = 1.215;
W (+) = 0.03t/m2 · 1.215 · 0.8 · 1.4 = 0.0408t/m2 ;
W (−) = 0.03t/m2 · 1.215 · 0.5 · 1.4 = 0.0255t/m2 .
Also consider the action of the Y-axis wind (Fig. 6).
The building height h = 47.795 m, transverse dimension d = 38.040 m (actual
building length from wall to wall).
Thus, d < h < 2d(38.040 m < 47.795 m < 76.080 m)—the building is divided into
2 sections.
Section 1:
z ∈ [0 m; 9.755 m]; ze = d = 38.040 m;
k(ze = 38.040 m) = 0.65(38.040/10)2·0.2 = 1.109;

Wind Loads: Analysis of Deformations in Building Structures

255

Fig. 6 Wind action on the
front of the building along
the Y-axis

W (+) = 0.03 t/m2 · 1.109 · 0.8 · 1.4 = 0 · 0373t/m2 ;
W (−) = 0.03 t/m2 · 1.109 · 0.5 · 1.4 = 0.0233t/m2 ;
Section 2:
z ∈ [9.755 m; 47.795 m]; ze = d = 47.795 m;
k(ze = 47.795 m) = 0.65(47.795/10)2·0.2 = 1.215;
W (+) = 0.03t/m2 · 1.215 · 0.8 · 1.4 = 0.0408t/m2 ;
W (−) = 0.03t/m2 · 1.215 · 0.5 · 1.4 = 0.0255t/m2 ;
Shows the load on the side of the building along the Y-axis (Fig. 7).
Wind loads have been applied to the computational model in Lira SAPR 2016 R5
at floor levels in the form of uniformly distributed loads simulating realistic wind
pressure effects on the structure. Load distribution ensures precise representation
of aerodynamic forces acting upon the facade surface. Based on calculated average
values of wind load and masses of individual floors, a dynamic analysis of the building
has been carried out aimed at investigating the structure’s reaction to variable dynamic
factors.
Special attention is given to accounting for the pulsating component of wind load
(wg), determined based on mean load value (wm) with consideration of the dynamic
properties of the structure itself. The magnitude of the pulsating component is calculated using specialized formulas dependent on parameters like building height, air
density, environmental roughness, etc. It also takes into account wave propagation velocity along the façade, aerodynamic coefficient, and additional amplification
effects due to turbulent airflow.
These calculations provide an accurate assessment of how wind pulsations
affect overall stability and rigidity of the structure, minimizing the risk of resonant phenomena and reducing the likelihood of significant deformations and crack
formation. Such an approach enhances the reliability and safety of designed facilities,
especially relevant for high-rise buildings and large industrial complexes [8].

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E. N. Egereva et al.

Fig. 7 Load on the side of
the building along the Y-axis

Oscillations of the structure under wind gusts cause inertial forces that affect the
stress–strain state. When the natural frequencies of the structure coincide with the
wind pulsation frequency, resonance-like conditions may occur, leading to increased
forces, stresses, and displacements (Fig. 8).
The modal analysis conducted in Lira SAPR 2016 R5 allowed us to determine
key characteristics of the structure’s natural oscillations. According to Table 4,
the first N forms of natural oscillations exhibit frequencies below the limiting

Fig. 8 Pulsation X. Vibration modes 15, 18

Wind Loads: Analysis of Deformations in Building Structures

257

frequency f1, beyond which resonance may occur. This indicates that the primary
mode of vibration lies outside the potentially dangerous frequency range, thus
guaranteeing minimal oscillations under standard wind loads.
A critical step in subsequent analysis involved automatic computation of gustinduced loading, performed automatically by Lira SAPR 2016 R5 for every predefined static wind load. This automated process accounts for specific properties of
the particular structure and geographical site conditions, ensuring precision and
completeness in evaluating the full spectrum of dynamic behavior.
By jointly considering both static and gust components, we gain the capability to
accurately assess the building’s resistance to possible negative consequences arising
from resonant processes induced by interactions between the structure and external
environmental factors [9, 10].
The dropdown list will show the results of the pulsating wind load component for
each mode, the total dynamic load, and the combined effect of the average component
and its corresponding pulsating component. Show the vibration modes (Figs. 8 and
9).

Table 4 Vibration analysis results
Mode number

Eigenvalue

Frequency
(rad/s)

0.451519

2.214744

Period
(Hz)

(s)

0.352666

2.835542

0.316843

3.156137

0.50257

1.989774

0.274823

3.638704

0.579411

1.725889

0.084522

11.831177

1.883945

0.530801

0.05745

17.406355

2.771713

0.360788

0.050833

19.672436

3.132553

0.319228

0.044431

22.506915

3.583904

0.279025

0.04443

22.507388

3.583979

0.279019

0.042479

23.541299

3.748614

0.266765

0.041367

24.173998

3.849363

0.259783

0.041366

24.174292

3.84941

0.25978

0.041365

24.175064

3.849533

0.259772

0.039891

25.068465

3.991794

0.250514

0.038164

26.202748

4.172412

0.23967

0.035606

28.084793

4.472101

0.223609

0.024475

40.857413

6.505957

0.153705

0.023143

43.209036

6.88042

0.14534

0.021725

46.029614

7.329556

0.136434

0.021206

47.156771

7.50904

0.133173

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E. N. Egereva et al.

Fig. 9 Pulsation Y. Vibration modes 5, 6

6 Conclusion
The performed calculations provided a comprehensive understanding of the behavior
of the studied object under the combined effect of both static and pulsating
components of wind load. Key findings include:
1. Maximum Deviations Caused by Individual Components:
• Static load resulted in maximum deviations of 10.85 mm along the X-axis and
31.8 mm along the Y-axis.
• Pulsating component caused similar deviations: approximately 10.85 mm
along the X-axis and around 31.8 mm along the Y-axis respectively.
2. Combined Effect of Loads: Simultaneous influence of both components led to
the following maximum total deflections:
• Maximum deviation along the X-axis reached 61.4 mm.
• Along the Y-axis, the maximum deviation amounted to 1.03 mm.
3. Interpretation of Results: These figures indicate the substantial role played
by the pulsating component of wind load in shaping the overall picture of
deformations. Despite relatively small individual displacements, simultaneous
exposure to two types of load significantly increases node displacement values,
emphasizing the necessity of incorporating dynamic effects comprehensively
into structural analyses.
Thus, the conducted calculations confirmed the importance of simultaneously
considering both static and dynamic aspects of wind load to achieve a high degree of
accuracy and adequacy in designing buildings and structures. The results demonstrate
sufficient stiffness of the structure and its ability to sustain anticipated wind impacts

Wind Loads: Analysis of Deformations in Building Structures

259

without exceeding permissible limits of movement. However, further refinement and
detailed investigation within specialized assessments are recommended to ensure
safe long-term use of the facility.

References
1. SP 20.13330.2016 (2017) Loads and actions: code of practice approved by Order No. 891/pr
dated December 3, 2016 of the ministry of construction and housing-communal services of the
Russian federation (Minstroy Russia). FGUB “RST”, Moscow
2. LiraSoft LLC (2023) User manual for lira-SAPR software v.2023. St. Petersburg, Russia,
Electronic manual
3. Demidov DA, Shklyarov EP (2016) Using Lira-SAPR software for structural analysis and
design optimization of steel frames subject to dynamic wind loads. Proc Eng 143:121–126
4. Nikitina IN, Soloviev OB (2018) Application of FEM-based software systems (Lira-SAPR)
for calculation of wind-induced vibrations in super-tall residential buildings. Int J Adv Struct
Eng 10(1):1–13
5. Guvernyuk SV, Gagarin VG (2006) Computer simulation of aerodynamic effects on facades
of high-rise buildings. AVOK 8:18–24
6. Kolesnikov AI (2020) Methodology for calculating high-rise buildings subjected to wind load
using modern computational engineering tools. Molodoy Uchenyy 6(296):65–74. https://mol
uch.ru/archive/296/67214/. Accessed 25 Feb 2023
7. Mikhailova MK, Dalinchuk VS, Bushmanova AV, Dobrogorskaya LV (2016) Design, construction and operation of high-rise buildings taking into account aerodynamic aspects. Construct
Unique Build 10(49):59–74
8. Kolesnikov AI (2020) Methodology for calculating high-rise buildings subjected to wind load
using modern computational engineering tools. Molodoy Ucheny 6(296):65–74. https://mol
uch.ru/archive/296/67214. Accessed 25 Feb 2023
9. Liu H, Chouw N, Liang Z (2016) Aerodynamic loads on tall buildings in typhoon-prone regions.
J Struct Eng 142(10):04016088. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001592
10. Balendra T, Yap JYL, Cheong HF (2007) Vibration control of tall buildings under wind loading.
Earthquake Eng Struct Dynam 36(1):1–16. https://doi.org/10.1002/eqe.611

Development of Approaches to Assessing
the Energy Efficiency of Capital
Construction Facilities in the Context
of Climate Change
T. V. Dolgushev and E. A. Korol

Abstract The article is devoted to the development of approaches to assessing the
energy efficiency of capital construction facilities in the context of climate change.
The traditional approach is limited to estimating the internal energy consumption of
buildings, without taking into account the nature and origin of the energy resources
used. The authors propose to introduce the concept of energy-carbon efficiency,
which allows us to develop a standard approach to energy efficiency and combines
an assessment of the energy consumption of a capital construction facility, taking into
account the carbon footprint created during energy generation. The study analyzes
current Russian regulatory documents, and reveals a lack of an integrated approach
to energy efficiency assessment, which does not take into account regional differentiation in energy generation sources. Since Russia is divided into eight zones with
different types of electricity generation, the authors emphasize that the same type of
facilities located in different zones may demonstrate a similar level of energy efficiency, but significantly differ in the level of carbon footprint. The proposed concept
of energy and carbon efficiency will allow for a comprehensive analysis of the impact
of a capital construction facility on the environment, taking into account the regional
factor. It is concluded that it is necessary to develop new rules and regulations that
encourage the implementation of low-carbon practices in the construction and operation of facilities. The study offers a solution to an urgent task—achieving comprehensive consideration of energy efficiency and environmental safety requirements in
the context of combating climate change.
Keywords Life cycle · Energy efficiency · Capital construction facility · Climate
change · Sustainable development

T. V. Dolgushev (B) · E. A. Korol
National Research Moscow State University of Civil Engineering, Moscow, Russia
e-mail: dolgushew@yandex.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_22

261

262

T. V. Dolgushev and E. A. Korol

1 Introduction
Currently, the problem of ensuring the energy efficiency of capital construction facilities (ACS) is one of the key ones, especially in the context of global climate change
[1, 2]. As the world’s population grows and the proportion of urbanized territories
increases, the need for the construction of ACS increases significantly. An increase
in the number of ACS leads to an increase in the amount of energy consumed by
these facilities to ensure the fulfillment of their function. An increase in energy
consumption, in turn, leads to an increase in the emission of climatically active gases
(greenhouse gases) [3]. In this regard, the problem of increasing the energy efficiency
of ACS in order to build sustainable ACS is becoming increasingly acute [4].
The existing methods for assessing the energy efficiency of designed, constructed
and operated ACS are to assess the consumption of energy resources and the energy
characteristics of the building: the thermal protection of the building, the specific
characteristics of the consumption of heat energy for heating and ventilation during
the heating period and the characteristics of the thermal power of heating and ventilation systems. These indicators are important and allow us to assess the efficiency
of using energy resources in the ACS. However, such an assessment is not comprehensive, since it ignores a significant aspect that characterizes the effectiveness of
the building in the context of ensuring low–carbon development of the country—the
origin of the energy used and its role in shaping the total greenhouse gas emissions
produced by the ACS.
The energy used in the ACS can be produced by various methods and using
different types of energy resources, each of which has its own greenhouse gas emissions. In this regard, it is necessary to develop existing ideas about the efficiency of the
building’s life cycle, moving from linear thinking and estimating watts consumed to
a systematic approach that provides a comprehensive assessment taking into account
the need to achieve sustainable development [5].
The modern global agenda is devoted to the search for solutions to ensure the
energy efficiency of ACS in the context of the rapidly developing climate change
crisis [6]. Potential threats related to the depletion of natural resources and an increase
in the concentration of greenhouse gases in the atmosphere necessitate a reassessment
of traditional approaches to the construction and operation of buildings [7]. The
effectiveness of facilities should not be limited solely to their technical performance,
but must take into account their impact on the environment [8]. In this regard, during
the implementation of this study, the task was set to develop existing approaches
to energy efficiency assessment in such a way as to take into account both the total
amount of energy consumed and the source of its origin. Solving this problem will
improve the efficiency of ACS lifecycle management and take into account not only
energy consumption, but also the specifics of energy supply in the location region,
including the predominance of certain methods of energy generation, which should
be a step towards reducing the carbon footprint of ACS and ensuring the achievement
of sustainable development of the industry and the country.

Development of Approaches to Assessing the Energy Efficiency …

263

2 Relevance and Scientific Significance with a Brief
Literature Review
The strategy for the development of the construction industry and housing and
communal services in many countries, including Russia, implies the need to ensure
the implementation of measures to prevent negative environmental impacts and
climate change. Energy efficiency of buildings is one of the key factors that are
determined to minimize negative impacts. In this regard, many countries, realizing the
potential environmental risks caused by climate change, have begun to pay increased
attention to the development of green technologies and improving energy efficiency
standards.
In the USA, for example, the LEED (Leadership in Energy & Environmental
Design) certification system has been established, which is a recognized leader in
assessing the environmental and energy characteristics of buildings. LEED certification covers a wide range of issues, from energy efficiency and environmental
friendliness of building materials to water reuse and minimizing the environmental
footprint. The BREEAM (Building Research Establishment Environmental Assessment Method) system, created in the 1990s, is widely used in the UK. It evaluates the
environmental characteristics of buildings in many categories, including energy efficiency, environmental friendliness, water consumption, waste volume and impact on
the surrounding landscape. This system has formed the basis of many international
standards.
The German DGNB system (Deutsche Gesellschaft fur Nachhaltiges Bauen)
has also earned recognition by offering a comprehensive approach to assessing
the sustainability of buildings, covering aspects such as environmental friendliness, social responsibility and economic impact. France has introduced its own
HQE (Haute Qualitative Environmentale) system, which focuses on environmental
efficiency and the comfort of building residents.
Each of these systems combines traditional energy efficiency criteria with environmental responsibility, trying to create harmony between ensuring a high quality
of life and environmental sustainability. Russia is still lagging behind in this movement, as the strategy for the development of the construction industry until 2030 [9]
defines two main tasks:
• adaptation to the adverse effects of climate change on industrial, civil, and
engineering infrastructure facilities;
• improving the energy efficiency of buildings and structures, reducing internal
losses of energy resources, including electricity.
Indeed, in the climate change review contest, the main directions are to limit negative impacts in order to prevent the development of socio-economic development
scenarios associated with significant greenhouse gas emissions, as well as adaptation to observed and forecast climate changes. The Russian strategy explicitly defines
the need for adaptation and measures to reduce emissions by increasing energy efficiency. However, the approach based on a simple reduction in energy consumption is

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not comprehensive and requires development to ensure the ultimate goal of achieving
sustainable development of a low-carbon economy.
That is why it is necessary to develop the existing approach into a new one that
combines energy efficiency and environmental responsibility, which we will call
energy-carbon efficiency. It requires not only the development of a new approach,
but also a regulatory and technical framework provided by relevant legislation, as
well as tools for its integration into the practice of the construction and housing
and communal services industry [10]. The implementation of such an integrated
approach will make it possible to make informed decisions about the design and
operation of buildings in the context of achieving the strategic goals of the state in
the implementation of the climate doctrine, the strategy for the development of the
construction industry and ensuring the environmental, energy and economic security
of the country.

3 Problem Statement
The current regulatory document in the field of energy efficiency of buildings GOST
R 56295-2014 [11] makes it possible to assess the economic feasibility of investing
in increasing the level of heat protection indicators of enclosing structures and developing energy-saving measures for engineering systems at the stage of a pre-project
or project. The approach to assigning the characteristics of enclosing structures
that determine energy consumption using a feasibility study is undoubtedly important, however, its use in regions with low cost of energy resources will lead to the
paradoxical conclusion that a low level of thermal protection indicators is sufficient.
The described disadvantage makes it possible to offset the normalization of the
minimum level of the specific characteristic of heat consumption for heating and
ventilation and the establishment of standards for the energy efficiency class of
a building, which for modern buildings implies meeting the minimum level with
additional reserve. However, this approach focuses on the internal characteristics of
the ACS and does not take into account the carbon footprint generated during the
production of the energy used.
Another current regulatory document, GOST R 70934-2023 [12], is used to ensure
a consistent and comprehensive assessment of greenhouse gas emissions, but not for
all ACS, but only for an industrial enterprise or commercial organization. Despite all
the advantages of this document, it allows you to classify the existing carbon footprint
and prioritize risk management. This approach allows existing enterprises to assess
their existing carbon footprint and develop measures to reduce it and adapt to risks.
However, to implement an integrated approach, it is necessary to take into account
a wide range of ACS and take measures at the pre-operational stages to implement
investment and construction projects that ensure sustainable development.
A significant disadvantage of the current modern approach to assessing energy
efficiency of ACS is the lack of correlation between the level of energy consumption
and the quality of energy resources and the specifics of regional energy supplies.

Development of Approaches to Assessing the Energy Efficiency …

265

Consideration of ACS implemented according to a typical project of the same series,
having the same level of energy consumption, but located in different regions, will
lead to the same level of energy efficiency, however, their actual carbon footprint may
vary greatly due to different sources of energy resources provided by local energy
systems. Thus, the research objective of this work can be formulated as identifying the
shortcomings of the current approach to assessing the energy efficiency of ACS and
proposing a new analysis method in terms of environmental impact and greenhouse
gas emissions.

4 Theoretical Framework
The energy efficiency of the ACS is traditionally determined through a quantitative
assessment of the energy consumed and the operating costs related to the resources
needed to maintain comfortable conditions inside the facility. Today, the generally
accepted practice is based on calculating the energy characteristics of ACS, such as
the thermal protection of a building, the specific characteristic of the consumption
of thermal energy for heating and ventilation during the heating period, and the
characteristic of the thermal capacity of heating and ventilation systems, which makes
it possible to evaluate ACS from the perspective of energy efficiency. These indicators
provide useful information about the technical condition of the building, but they
remain limited in their coverage, as they focus on only one aspect—reducing energy
and heat costs.
However, current trends require an expansion of the traditional assessment of
energy efficiency. Global climate change forces us to think about the impact of the
human factor on the state of the planet’s ecosphere. According to the data presented
in the strategy for the development of the Russian construction industry until 2030,
buildings use about 40% of all primary energy consumed, and also produce 35% of
all carbon dioxide emissions. Therefore, there is an urgent need to supplement the
concept of energy efficiency with a new dimension—the impact of a building on the
environment through its carbon footprint.
The concept of energy and carbon efficiency is aimed at combining classical
energy efficiency indicators with criteria of environmental impact, expressed by
the volume of greenhouse gas emissions. The main purpose of introducing this
concept is to create a single metric that allows comparing different types of buildings,
regardless of their location and local energy supply characteristics. This concept can
make a significant contribution to the formation of rational approaches to architectural design and spatial planning, providing architects and engineers with tools for
optimal selection of energy-efficient solutions with minimal impact on the Earth’s
atmosphere.
Let’s take a closer look at the components that form a new approach to energy
efficiency assessment. The first component is a traditional energy efficiency indicator,
calculated by determining the ratio of energy consumption for heating, cooling,
lighting, etc. to the total area of the room. The second component is accounting for

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the carbon footprint, determined by the type of fuel used to produce energy supplied
to the facility. It is important to emphasize that the electricity supplied to different
parts of the country differs in its composition, and mapping at the regional level
will allow for the heterogeneity of generation sources [13]. For example, in a region
dominated by nuclear power, greenhouse gas emissions will be negligible, while
the area supplied with energy produced by coal-fired power plants has a significant
carbon footprint. At the same time, it is important to assess the projected structure
of energy production and the impact of climate change on existing power generation
facilities [14, 15].
The third element of the model is a comparison of the efficiency of similar buildings located in different regions. Thanks to the new approach, ACS with the same
technical characteristics will be able to receive different energy and carbon efficiency
ratings depending on the location. Thus, an OKS built in an area with high rates of
renewable energy use will receive a higher rating than a similar facility located next
to a large coal-fired thermal power plant.
Thus, the proposed concept is a multidimensional space of criteria, including the
following elements:
• Energy consumption of the object (watt-hours);
• Sources (types of power plants: TPP (Thermal Power plant), HPP (hydroelectric
power plant), NPP (Nuclear power plant), WPP (Wind power plant), SPP (Solar
power plant), etc.);
• The amount of greenhouse gas emissions corresponding to each type of energy.
The regional differentiation of energy sources in Russia has been sufficiently demonstrated and confirms the need for a detailed study of energy efficiency criteria, taking
into account the regional factor, see Fig. 1 [prepared using data from 16].
By integrating these components, the new concept will make it possible to develop
standardized procedures for measuring energy efficiency and the carbon footprint of
buildings using the energy-carbon efficiency criterion, ensuring a balanced approach
to sustainable development, resource conservation and environmental protection.

Fig. 1 a The structure of the installed capacity of power plants of the Russian energy system (as of
01.01.2025); b The structure of electricity generation by power plants of the Russian energy system
(as of 01.01.2025)

Development of Approaches to Assessing the Energy Efficiency …

267

Following the principles of the new concept, cities and settlements will be able to
switch to using sustainable energy consumption models, improving the quality of
life of the population and reducing the negative anthropogenic impact on the global
climate system.

5 Practical Implications
The proposed concept of energy and carbon efficiency will require further development and refinement to ensure practical implementation on a federal or national scale.
Practical implementation will require comprehensive cooperation between government authorities, construction companies, housing and communal services companies, and the scientific community. It is necessary to give a comprehensive assessment
of the available foreign and international documents in the field of ensuring sustainable development in the field of construction and housing and communal services,
in order to assess existing practices, identify advantages and disadvantages, develop
and successfully implement methodologies, techniques and algorithms for achieving
sustainable development in Russia.
Figure 2 illustrates the rate of increase in greenhouse gas emissions and the longterm trend of anthropogenic emissions sources from 1850 to 2019, and Fig. 3 shows
the contribution to the total greenhouse gas emissions for 2023 of the six largestemitting countries (including Russia) and the rest of the world. Russia stands out for
its significant contribution to total global emissions, ranking fifth after China, the
United States of America, India and the 27 member States of the European Union.
These illustrations clearly demonstrate the importance of reforming approaches to
energy efficiency assessment and the transition to energy-carbon efficiency in the
domestic construction and housing and communal services sectors to ensure a change
in the trajectory of climate change.
Let’s look at the key actions required for the further development of the energycarbon efficiency concept. First, it is necessary to prepare specialized standards and
regulations governing the calculation of energy and carbon efficiency of buildings.
National building codes and regulations play a special role here, which should contain
specific recommendations for taking into account the specifics of energy supply and
the climatic conditions of individual regions. Such standards will make it possible to
implement ACS that are initially adapted to local conditions and take into account the
requirements of environmental conservation and sustainable development, which, in
the face of projected climate change, will lead to a revision of approaches to ACS
design not only from the point of view of improving energy efficiency [20], but also
from the point of view of changing prevailing energy consumers throughout the life
cycle of ACS [21].
Secondly, government subsidies and tax incentives for enterprises and organizations implementing sustainable construction technologies are becoming the most
important tool to support the practical implementation of conceptual ideas. By
supporting financial incentives, the government will be able to attract significant

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Fig. 2 a Change in anthropogenic greenhouse gas emissions from 1850 to 2019 [17]; b Long-term
trend of anthropogenic CO2 emissions sources from 1850 to 2019 [18]

Fig. 3 Greenhouse gas emissions and the contribution of the six countries with the largest emissions
and the rest of the world in 2023 (in Gt CO2 -eq. and as a percentage of the global total) [19]

investments in upgrading existing buildings and creating new zero-carbon areas.
The market for carbon units in Russia is still underdeveloped, and the development
of tools for integrating this practice into the construction industry seems to be a
promising area of research.
Another important area is conducting scientific research and developing innovative technologies that can reduce the carbon footprint of ACS by category, since
different types of ACS have significant differences, both in terms of ways to ensure
sustainable development and in terms of adaptation to observed and projected climate
changes. Widespread use of local renewable energy sources [22] will be required,
such as photovoltaic panels, wind turbines, solar collectors, etc., capable of producing
energy directly at the place of consumption, thereby eliminating the need to transport
large amounts of energy over long distances.
In addition, information support for the concept of energy and carbon efficiency is
needed not only among the general public by increasing environmental literacy and

Development of Approaches to Assessing the Energy Efficiency …

269

awareness of the population in preventing further development of climate change
along the current trajectory, but also integrating relevant courses into the training
program for engineers, architects and all related specialties in the field of construction
and housing and communal services.
Finally, the successful implementation of this concept is impossible without the
close cooperation of the scientific community, since the task is interdisciplinary and
requires the involvement of specialists from many industries. Many countries face
similar challenges, and the exchange of experience in the field of energy efficiency
and environmental protection can accelerate the process of transition to sustainable
forms of management, both at the micro, meso, and macro levels. Joint projects
and partnership agreements will help overcome technological barriers and ensure an
effective exchange of knowledge and technology between countries.
The adoption and implementation of practical conclusions arising from the
concept of energy and carbon efficiency pave the way to solving global environmental
problems, enhance the competitiveness of domestic manufacturers of construction
products, create conditions for attracting foreign investment and enhance Russia’s
international prestige as a leader in the global movement in the field of sustainable
development and low-carbon economy.

6 Conclusions
The energy-carbon efficiency concept considered in this paper is intended to lay the
foundation for the development of a comprehensive methodology and appropriate
techniques and algorithms that will allow for the beginning of transformations in
the Russian construction and housing and communal services sector. The transition
from a simple assessment of energy efficiency to a comprehensive consideration
of environmental and economic impacts is inevitable in the light of the accelerating
process of changes in the global climate system. An in-depth study of the mechanisms
of the carbon footprint of buildings makes it possible to identify real opportunities
for optimizing energy consumption and reducing the negative impact on nature.
Taking into account the zoning of Russia according to the structure of electricity
generation by power plants of the energy system will allow us to develop existing
approaches and will be the first step towards the formation of an energy-carbon
efficiency methodology.
An important result of the conducted research was the justification of the need to
revise the current building codes and regulations for the transition from the concept
of energy efficiency of ACS to a comprehensive assessment of energy and carbon
efficiency of ACS. An analysis of the current regulatory practice has shown that
traditional regulation is far from perfect and requires development. The development
of the existing theoretical and methodological framework should become the basis
for the development of regulatory and technical approaches and practical methods
for implementing the ACS, ensuring the sustainable development of the construction

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complex and the implementation of the strategy for the socio-economic development
of Russia with low greenhouse gas emissions until 2050 [23].
At the same time, scientific research aimed at developing highly efficient materials
and technologies capable of providing a low level of energy loss combined with a
reduced carbon capacity is of great importance, thereby achieving the conditions
required to ensure that the ACS performs its function while reducing the carbon
footprint.
Summarizing the results obtained, it can be argued that the introduction of the
energy-carbon efficiency concept will not only improve the quality of life of the
population by reducing utility costs, but additional jobs will be created in high-tech
industries engaged in the production of equipment and materials with a low carbon
footprint. Russia has all the necessary resources and intellectual potential to develop
the concept of energy and carbon efficiency, which is already needed and will ensure
a strong international position in achieving sustainable development.

References
1. Sheina SG, Chernyavskiy IA (2025) Management of capital construction facilities’ lifecycle
under climate change conditions. Young Don Investigator 10(1):72–75
2. Sheina S, Chernyavsky I (2024) Approaches to mitigation of climate change at all stages of
the life cycle of a construction facility. BIO Web of Conferences 141:04061. https://doi.org/
10.1051/bioconf/202414104061
3. Wang F et al (2021) Technologies and perspectives for achieving carbon neutrality. The Innov
2(4):100180. https://doi.org/10.1016/j.xinn.2021.100180
4. Chen L et al (2022) Strategies to achieve a carbon neutral society: a review. Environ Chem Lett
20(4):2277–2310. https://doi.org/10.1007/s10311-022-01435-8
5. Dolgushev TV, Larionov AN (2024) Impact of forecasted climate changes on economic
effectiveness of housing projects. Econ Construct 12:460–463
6. Rey-Hernández JM et al (2018) Modelling the long-term effect of climate change on a zero
energy and carbon dioxide building through energy efficiency and renewables. Energy Build
174:85–96. https://doi.org/10.1016/j.enbuild.2018.06.006
7. Carter JG et al (2015) Climate change and the city: Building capacity for urban adaptation.
Progr Plan 95:1–66. https://doi.org/10.1016/j.progress.2013.08.001
8. Shushunova N, Korol E, Luzay E, Shafieva D (2023) Impact of innovative green wall modular
systems on urban air. Sustainability 15(12):9732. https://doi.org/10.3390/su15129732
9. Government Resolution Russian Federation (2022) Strategy for development of construction industry and housing-communal services of Russia until 2030 with forecast up to 2035
(amended on October 21, 2024). Collection of Legislation of the Russian Federation 45:7815
10. Miezis M et al (2016) Climate change and buildings energy efficiency—the key role of residents.
Env Clim Technol 17(1):30–43
11. GOST R 56295-2014 (2019) Energy efficiency of buildings. Economic evaluation methodology
for energy systems in buildings. Standartinform, Moscow
12. GOST R 70934-2023 (2023) Environmental management. Guidance on greenhouse gas
emission assessment and control. FGUP “RST”, Moscow
13. Lorenzo-Sáez E et al (2020) Energy efficiency and GHG emissions mapping of buildings for
decision-making processes against climate change at the local level. Sustainability 12(7):2982.
https://doi.org/10.3390/su12072982

Development of Approaches to Assessing the Energy Efficiency …

271

14. Panteli M, Mancarella P (2015) Influence of extreme weather and climate change on the
resilience of power systems: impacts and possible mitigation strategies. Electr Power Syst
Res 127:259–270. https://doi.org/10.1016/j.epsr.2015.06.012
15. Osman AI et al (2023) Cost, environmental impact, and resilience of renewable energy under
a changing climate: a review. Environ Chem Lett 21(2):741–764. https://doi.org/10.1007/s10
311-022-01532-8
16. Russian Electric Power Systems (2025) Russian power system operator. https://www.so-ups.
ru/functioning/ups/ups2025. Accessed 30 Jun 2025
17. IPCC (2023) Climate change 2023: synthesis report. In: Contribution of working groups I, II
and III to the sixth assessment report of the intergovernmental panel on climate change. In:
Lee H, Romero J (eds) Core writing team. IPCC, Geneva, Switzerland, pp 184. https://doi.org/
10.59327/IPCC/AR6-9789291691647
18. Pathak M et al (2022) Technical summary. In: Shukla PR, Skea J, Slade R et al (eds.). Climate
change 2022: mitigation of climate change. In: Contribution of working group III to the sixth
assessment report of the intergovernmental panel on climate change. Cambridge University
Press, Cambridge, UK and New York, NY, USA. https://doi.org/10.1017/9781009157926.002
19. European Commission, Joint Research Centre (2024) GHG emissions of all world countries.
Publ Off Eur Union, Luxembourg.https://doi.org/10.2760/4002897
20. Tho VD, Lam TV, Korol EA et al (2020) Thermal insulation properties of effective lightweight
concretes for three-layer enclosing coatings of buildings. Ind Civ Eng 5:36–44
21. Karimpour M et al (2015) Impact of climate change on the design of energy-efficient residential
building envelopes. Energy Build 87:142–154. https://doi.org/10.1016/j.enbuild.2014.10.064
22. Chen Y et al (2023) Impacts of climate change and building energy efficiency improvement
on city-scale building energy consumption. J Build Eng 78:107646. https://doi.org/10.1016/j.
jobe.2023.107646
23. Government Resolution Russian Federation (2021) Strategy for socio-economic development
of Russia with low greenhouse gas emissions by 2050. Collection of Legislation of the Russian
Federation 45:7556

Ensuring Operational Resistance of Paint
and Varnish Coatings Due
to the Comprehensive Effect
of Nano-Additives on Metal Surfaces
A. V. Pchelnikov, A. P. Pichugin, M. H. Iskandarov, and A. K. Tuliaganov

Abstract One of the main reasons for the reduction in the service life of metals is the
low adhesion of protective coatings to metal surfaces, which does not allow forming
the required level of performance indicators for reliable protection of metals. As a
result of a detailed theoretical analysis, it was found that the solution to this issue
is possible due to the improvement of the technology of preparing metal surfaces
for painting using nanomaterials. One of the greatest attention in the development
of this solution was paid to such a nanomaterial as carbon nanotubes. The use of
a suspension based on mixed solvents and carbon nanotubes in the technology of
preparation for painting allows obtaining coatings, in comparison with traditional
ones, with up to three times greater adhesive strength, one and a half or more times
better abrasion resistance and resistance to deformation effects, up to two times
more antistatic, and also with greater thermal resistance and thermal stability (the
temperature transition point to the destructive state on the thermomechanical curves
is 100–150 ˚C higher). The improvement of the coating properties occurs due to the
formation of a uniform dense intermediate layer between the metal and the coating,
providing increased adhesion and other quality characteristics of the coating, due
to the process of chemisorption with the metal surface due to the excess amount of
electrons on the surface of carbon nanotubes, as characterized by the results of the
electron microscopy study.
Keywords Paints and varnishes · Nanomaterials · Adhesion strength · Carbon
nanotubes · Preparation for painting

A. V. Pchelnikov (B) · A. P. Pichugin · M. H. Iskandarov
Novosibirsk State Agrarian University, Novosibirsk, Russia
e-mail: pchelaleksandr@mail.ru
A. K. Tuliaganov
Novosibirsk State University of Architecture and Civil Engineering, Novosibirsk, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_23

273

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A. V. Pchelnikov et al.

1 Introduction
The current state of metal elements of buildings of various industrial enterprises
indicates insufficient consideration of factors affecting the surfaces of steel metal
structures and their protective coatings, which reduces the service life of metals by
2–3 or more times. One of the main reasons for the reduction in the service life of
building metal structures is low adhesion of protective coatings to metal and weak
cohesive interaction in coatings, which does not allow forming the required level of
performance indicators for reliable protection of metal structures [1, 2].
To improve the quality of metal protection from various operational impacts,
special attention, in the process of creating coatings, must be paid to technological
operations related to the preparation of surfaces before painting. It is advisable to
directly link the quality of preparation of metal surfaces with the degree of adhesion
of the protective coatings applied to them, while it is important to take into account
both the amount of adhesion and the uniformity of this parameter over the entire
protected surface [2–4].
Thus, surface preparation before painting can include up to 6–7 different operations. The number and composition of operations are determined by a number of
factors, including the type of metal, service conditions, and adhesion requirements.
Mechanical treatments, such as abrasive blasting, are effective in removing rust and
scale, providing a rough surface for better adhesion (ASTM D4417). For example,
chemical treatments, including phosphating or chromating, create a conversion layer
that improves corrosion resistance and adhesion (ISO 9227:2017). The choice of a
specific method should be based on an analysis of costs, effectiveness, and environmental considerations, taking into account regulatory requirements (e.g. VOC
directives). A combination of methods can provide optimal surface preparation for
specific service conditions (GOST 9.402-2004).
Known traditional methods of preparing metal surfaces for painting (GOST 9.402
“Paint and varnish coatings. Preparation of metal surfaces for painting”) include
mechanical preparation of the surface, degreasing and, if necessary, chemical preparation by various methods (phosphating, chromating, etc.). However, carrying out
the entire range of operations is labor-intensive and requires special technical equipment, which makes it applicable only in stationary conditions, and also cannot always
ensure high and uniform adhesion of the coating over the entire metal surface. Other
modern methods of preparing metal surfaces, as a rule, are also characterized by high
labor intensity of their implementation and the need for special equipment.
A method and device for applying metal nanoparticles to a metal surface under
normal conditions are known (RU Patent 2733530), the implementation of which
consists in applying metal oxide nanoparticles to a metal surface using a special
device, which allows obtaining abrasion-resistant coatings. The disadvantages of
this method include the fact that it is used in the field of mass spectrometry in
the preparation of biological samples and is not suitable for use in the technological
process of preparing metal surfaces for painting in order to protect them under various
operating conditions.

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275

A method for treating the surface of metal products before applying coatings is
known (RU Patent No. 2453637), which consists of pre-treating metals in a sealed
electric furnace at a temperature of 250–550 ˚C while exposing the surface to water
vapor, which improves the adhesion of coatings to the surface of products by forming
a sublayer on their surface in the form of an oxide film of optimal thickness and
porosity. The disadvantage of this method is that this method is stationary and requires
special equipment, and does not provide the necessary adhesion of coatings for
long-term operation in corrosive environments over a wide temperature range.
The closest to the proposed solution is the method of gas-thermal spraying of
polymer coatings on metal products and structures (RU Patent No. 2545301), which
includes preliminary mechanical treatment and degreasing of surfaces, as well as
subsequent application of an aqueous composition consisting of a 30% silica sol
solution and 2–4% three-percent dispersion of CNTs. The disadvantages of this
method include the fact that this composition is suitable only for inorganic polymeric
materials applied by flame spraying, and that it requires special equipment.
Today, the development of promising protective materials and methods for
creating coatings is directly related to the use of various nanomaterials [5–13]. Thus,
when preparing metal surfaces before painting using a chemical method and using
functional nanomaterials that help change the physicochemical properties of the
metal, chemical processes may occur that help increase the interaction between the
metal and the protective coating [1, 4, 14].
Based on this, the purpose of this study was to increase the operational durability of
paint and varnish coatings on metal surfaces by surface treatment with nanomaterials
in preparation for painting.

2 Materials and Methods
Paints and varnishes based on acrylic copolymers, as well as various nanomaterials were selected for the research: bismuth, cerium, zinc oxides, aluminum and
magnesium hydroxides, silicon dioxide, carbon nanotubes (CNT).
The technology for creating a paint and varnish coating was as follows: in the
process of preparation for painting, the metal surface is subjected to mechanical treatment and degreasing, after which, using the pneumatic spraying method, a composition is applied to it, which is a solution based on mixed solvents containing an
adapted concentrate of nanomaterials in an amount of 0.01–2%. After drying, an
organo-dilutable paint and varnish material is applied to this surface using the pneumatic spraying method. The following standard methods were selected to evaluate the
properties of paint and varnish coatings: Determination of adhesion by the pull-off
method (ISO 4624:2002, MOD), Shore hardness (ISO 868:2003), coating flexural
strength (ISO 1519:2011), coating abrasion resistance (GOST 20811-2025).
The dielectric characteristics of paint and varnish coatings were determined using
an E 4-11 quality factor meter (calculation of dielectric characteristics in accordance
with GOST R 8.623-2015).

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Electron microscopic examination of samples was carried out using a Tescan Mira
3 XMU scanning electron microscope, in high vacuum, at an accelerating electron
beam voltage of 5 kV and an intensity of 8.5 (beam size 7.4 nm).
Thermomechanical studies were carried out using the method of measuring the
deformation of uniaxial compression under the influence of a continuously acting
load under conditions of heating the sample at a constant rate in the temperature
range from room temperature to 350 ºС.

3 Results and Discussion Conclusions
Table 1 presents the results of the study of the influence of nanomaterials on the
performance characteristics of protective coatings of metal surfaces.
The greatest positive effect on the properties of paint coatings is provided by such
nanomaterials as bismuth oxide and carbon nanotubes.
Thus, when using carbon nanotubes, when preparing a metal surface for painting,
the adhesive strength increases from 1.3 to 3.8 MPa, with a change in the nature of
the separation towards cohesive (A10-K90). The best result is achieved when using
a solution with 0.05% CNT (Fig. 1).
In view of the results obtained at the first stage, further attention was focused on
the studies of coatings obtained using CNTs.
When assessing the resistance of paint and varnish coatings to deformation effects
(Table 2), it was found that when preparing a metal surface with a suspension based
on CNTs 0.05%, the number and size of microcracks is reduced to a minimum, while
the diameter of the rod at which the coating begins to deteriorate is 3 mm.
Based on the results of the studies of the dielectric characteristics of paint and
varnish coatings, it was found that the use of CNTs in the surface treatment of
metal allows obtaining coatings with a lower value of the dielectric loss tangent (tgα
decreases from 0.017 at 0% CNTs to 0.008 at 0.2% CNTs), which indicates the
production of an antistatic coating (Fig. 2).
The results of thermomechanical studies (Fig. 3) characterize that with preliminary treatment of the metal surface with a composition with CNTs, the temperature
of the onset of destruction of the paint coating increases, which indicates its high
thermal stability and heat resistance, as well as strengthening of the coating due to
the formation of a more mesh structure, due to the fact that CNTs in the polymer
act as both structure-forming centers and provoke surface orientation of the polar
groups of polymer molecules. The best results are achieved by coating with surface
treatment of metal with a suspension containing CNTs in an amount of 0.05%—the
temperature of the onset of destruction increases by 100–150 ˚С.
The results of a scanning electron microscope study of the end surfaces of coating
samples created on metal substrates (Fig. 4) showed that when the substrate is treated
with a suspension containing CNTs, a uniform dense intermediate layer is formed at
the metal-coating interface (Fig. 4b), which ensures increased adhesion of the paint

Ensuring Operational Resistance of Paint and Varnish Coatings Due …

277

Table 1 Results of the study of the physical and mechanical characteristics of coatings with
preliminary preparation of metal surfaces with various nanomaterials
Concentration of
nanomaterials in the
composition for surface
treatment, %

Shore
hardness

Abrasion, g

Adhesive
strength, MPa

Peel-off behavior
(adhesive/cohesive
(A/C)),%

56…59

0.031…0.034

1.2…1.4

А-С 100–0

63…66

0.034…0.037

2.8…3.0

А-С 90–10

No additives
0
Bismuth oxide
0.25
0.5

62…67

0.030…0.033

3.0…3.3

А-С 90–10

81…88

0.028…0.032

3.3…3.5

А-С 10–90

76…82

0.028…0.033

3.2…3.4

А-С 10–90

Magnesium hydroxide. aluminum hydroxide
0.25

61…64

0.035…0.037

2.0…2.2

А-С 100–0

0.5

62…66

0.035…0.039

2.1…2.4

А-С 100–0

65…70

0.036…0.040

2.3…2.7

А-С 95–5

64…68

0.035…0.038

2.4…2.9

А-С 90–10

Silicon dioxide
0.25

63…66

0.033…0.036

2.3…2.6

А-С 90–10

0.5

63…69

0.034…0.038

2.5…2.9

А-С 80–20

65…71

0.030…0.033

2.8…3.2

А-С 60–40

64…72

0.031…0.035

2.7…3.1

А-С 60–40

62…65

0.036…0.038

2.2…2.5

А-С 90–10

Cerium oxide. zinc oxide
0.25
0.5

61…64

0.035…0.038

2.3…2.5

А-С 90–10

61…63

0.037…0.040

2.4…2.8

А-С 90–10

63…67

0.036…0.039

2.6…2.9

А-С 80–20

Carbon nanotubes
0.01

63…65

0.032…0.036

2.4…2.9

А-С 95–5

0.05

66…68

0.023…0.026

3.7…3.8

А-С 10–90

0.1

70…73

0.025…0.029

2.7…3.0

А-С 50–50

0.2

71…74

0.028…0.032

2.3…2.5

А-С 50–50

coating due to the process of chemisorption with the metal surface due to the excess
amount of electrons on the surface of the carbon nanotubes.
As a theoretical justification for the above research results, a number of provisions
of the theory of physical chemistry of polymers and the electrical theory of adhesion
are consistent [1, 14, 15]. Based on this, it can be said that when preparing metal
surfaces before painting using a chemical method and using nanomaterials that help

278

A. V. Pchelnikov et al.

Fig. 1 Change in the adhesive strength of paint coatings from the concentration of nanoadditives

change the physical and chemical properties of the metal, chemical processes may
occur that help increase the interaction between the metal and the protective coating.
One of these processes is donor–acceptor interaction. This type of interaction
is based on the exchange of electrical charges between donors and acceptors—
molecules that are capable of giving up or accepting electrons, respectively. This
interaction has a significant effect on the adhesion of coatings to metals and,
consequently, on the corrosion resistance and durability of protective layers (Fig. 5).
Metal surfaces, as a rule, have high electronegativity, which makes them attractive
acceptors for donors, which can be functional groups on polymer molecules or other
components of protective coatings. Such interactions facilitate the formation of a
strong bond, which is critical for the durability of the coating.
The use of nanomaterials becomes an important factor in this context, as they
can not only improve adhesion, but also have an affinity for metal surfaces, which is
ensured by their high surface area to volume ratio and high chemical activity. Nanomaterials, due to their size and shape, can be embedded in the surface microrelief,
forming additional donor–acceptor bonds that improve the adhesion of coatings and
corrosion resistance.
In addition to the above, chemisorption, defined as the process of chemical adsorption of molecules on the surface of solids, plays a vital role in the formation of durable
protective coatings on metal structures. This process involves the formation of strong
covalent or ionic bonds between adsorbates (coating molecules) and surface atoms
of the material (metal) (Fig. 5). It contrasts with physical adsorption, which is characterized by weaker Van der Waals forces and, accordingly, lower bond strength.
The chemisorption process begins with the diffusion of coating molecules to the
metal surface, where they react with atoms at the interface. During this interaction,

Ensuring Operational Resistance of Paint and Varnish Coatings Due …

279

Table 2 Results of tests of deformation resistance of paint and varnish coatings
Concentration Appearance of the coating after testing (photo size 10 × 10 mm; Description
of CNTs by
magnification × 500)
of the result
weight, %
(rod
diameter at
which the
bending
strength of
the coating
was tested
– 3 mm)
0

The surface
contains
large cracks
in the
coating,
chips and
areas of
delamination
of the
coating from
the metal
substrate

0.01

There is
damage in
the form of
transverse
cracks on the
surface of
the coating

0.05

The
protective
coating has
no visible
damage

(continued)

280

A. V. Pchelnikov et al.

Table 2 (continued)
Concentration Appearance of the coating after testing (photo size 10 × 10 mm; Description
of CNTs by
magnification × 500)
of the result
weight, %
(rod
diameter at
which the
bending
strength of
the coating
was tested
– 3 mm)
0.1

There is
damage in
the form of
transverse
cracks on the
surface of
the coating

0.2

There are
large cracks
in the
coating, and
there are
visible areas
of peeling of
the coating
from the
metal
substrate

new chemical bonds can be formed, which significantly reduces the likelihood of
adhesion failure under the influence of external factors.
One of the key aspects of chemisorption is its dependence on the nature of both the
adsorbate and the adsorbent. Metals differ in their electronegativity, which affects the
nature of the interaction with the coating molecules. For example, more electronegative metals, such as zinc or aluminum, are able to form stronger bonds with certain
polymeric materials than less electronegative ones, such as iron. It is also important
to consider that the presence of different functional groups on the coating molecules
can lead to a change in the nature and strength of chemisorption. Due to the high
surface-to-volume ratio, nanomaterials have large active zones for interaction with
coating molecules, which contributes to the formation of stronger adhesive bonds
at the atomic level. This becomes especially relevant when it comes to composite
coatings containing a combination of traditional polymer and nanostructured components. Nanoparticles can improve the distribution of adsorbates over the metal surface
and, as a result, improve the mechanical properties of the resulting coating, which

Ensuring Operational Resistance of Paint and Varnish Coatings Due …

281

Fig. 2 Dependence of the change in the tangent of the dielectric loss angle on the concentration of
CNTs

Fig. 3 Thermomechanical curves of the modified coating: 1—without treatment; 2—CNT 0.01%;
3—CNT 0.05%; 4—CNT 0.1%

opens the way to the creation of more reliable and durable protective layers capable
of effectively protecting metal structures from corrosion and destruction.
Based on the above and the studies conducted, the increase in the adhesion of the
paint coating during preliminary treatment of the metal surface with a suspension
with CNTs occurs both due to an increase in the donor–acceptor interaction between

282

A. V. Pchelnikov et al.

Fig. 4 Microphotographs of paint coating samples: a without preliminary treatment; b with
preliminary treatment with a composition containing 0.05% CNT

Fig. 5 Scheme of formation of donor–acceptor interaction between coating and metal during
surface treatment of metal surface with nanomaterials

the metal and the coating, and as a result of the chemisorption process with the metal
surface due to the excess amount of electrons on the surface of the carbon nanotubes.
The obtained results were tested using the example of metal structures of bridge
structures (bridge 99 km of the R-254 “Irtysh” highway, Siberia, Russia). The coating
testing period was 12 months. For the studies, paint and varnish coatings were applied
with preliminary preparation of metal surfaces with CNTs. During the testing period,
it was established that there were no areas of peeling, cracking or other damage on the
coating applied with preliminary preparation of surfaces with nanomaterials, as well
as no areas of corrosion. While the coating obtained by the traditional method after

Ensuring Operational Resistance of Paint and Varnish Coatings Due …

283

Fig. 6 Testing the technology of surface preparation of metal structures of bridge structures using
nano-additives (bridge, Russia, Novosibirsk region, highway R-254 “Irtysh”, 99 km)

12 months of operation in the Siberian climate almost completely lost its protective
qualities (Fig. 6).

4 Сonclusion
Optimization of preparation processes for painting due to the use of modern nanomaterials contributes to both increasing the service life of metal surfaces of various
building metal structures, and, as a result, reducing the costs of their maintenance
and service. The use of technologies for preparing metal surfaces with nanomaterials
provides a comprehensive improvement in the properties of the resulting coatings.
This is especially important for objects located in aggressive atmospheric conditions, such as the sea coast or industrial zones with increased chemical activity.
Thus, the introduction of new technologies for the preparation of metal structures is
a strategically correct decision, both from an economic and environmental point of
view.
This is confirmed by successful examples of the implementation of new technologies in various projects, where, due to the optimization of preparation methods, not
only financial efficiency but also the general ecology of the objects under construction has significantly improved, which meets modern requirements for sustainable
development.

References
1. Pichugin AP, Pchelnikov AV, Smirnova OE, Tkachenko SN (2023) Influence of surface tension
forces of modifiers on some properties of composite materials. In: Proceedings of the 6th

284

4.
5.

7.
8.

9.
10.

11.
12.
13.

14.
15.

A. V. Pchelnikov et al.
international conference on construction, architecture and techno sphere safety 308:268–276.
https://doi.org/10.1007/978-3-031-21120-1_26
Pchel’nikov AV, Pichugin AP (2025) Chemically resistant nanostructured protective coatings
for metal surfaces. J Adv Mater Technol 10(2):117–128. https://doi.org/10.17277/jamt-202510-02-117-128
Romashev DV, Pchelnikov AV, Ilyasov AP, Tuliaganov AK (2024) Efficient protection of
agricultural machinery and equipment from ionizing effects. Steel in Translat 54(11):1052–
1057. https://doi.org/10.3103/S0967091224701912
Zimon AD (1977) Adhesion of slicks and coatings. Chemistry, Moscow, p 52
Yang H, Ye L, Gong J, Li M, Jiang Z, Wen X, Chen H, Tian N, Tang T (2017) Simultaneously improving the mechanical properties and flame retardancy of polypropylene using
functionalized carbon nanotubes by covalently wrapping flame retardants followed by linking
polypropylene. Front 1:716–726
Polyanskikh IS, Yakovlev GI, Pervushin GN (2019) Structure formation of construction materials modified with natural and man-made nanoadditives. In: Selected papers of the 13th international conference “Modern Building Materials, Structures and Techniques”. Vilnius Gediminas
Technical University, pp 125–132
Wen X, Tian NN, Gong J, Chen Q, Qi YL, Liu Z, Liu J, Jiang ZW, Chen XC, Tang T (2013)
Polymer advanced technologies. CrossRef CAS, pp 971–977
Nizina TA, Balykov AS, Korovkin DI, Volodin VV (2019) Physical and mechanical properties
of modified fine-grained fibre-reinforced concretes containing carbon nanostructures. Int J
Nanotechnol 16(6–10):496–509
Song PA, Liu LN, Fu SY, Yu YM, Jin CD, Wu Q, Zhang Y, Li Q (2013) Nanotechnology.
CrossRef PubMed 24:125704
Vance ME, Kuiken T, Vejerano EP, McGinnis SP, Hochella MF, Rejeski DH, Matthew S
(2015) Nanotechnology in the real world: redeveloping the nanomaterial consum-er products
inventory. Beilstein J Nanotechnol 6(1):1769–1780
Cao H, Zheng Н, Yin J (2010) Mg(OH)2 complex nanostructures with superhydrophobicity
and flame re-tardant effects. J Phys Chem 114:17362–17368
Reggente M, Rossi M, Angeloni L (2015) Atomic force microscopy techniques for nanomechanical characterization: a polymeric case study. JOM 67:849–857
Ma PC, Siddiqul NA, Marom G, Kim JK (2010) Dispersion and functionalizaition of carbon
nanotubes for polymer-based nanocomposites: a review. Compos Part A: Appl Sci Manufact
41(10):1345–1367
Kargin VA, Slonimskiy GL (1967) Brief essays on the physical chemistry of polymers. Moscow,
pp 232
Tager AA (1968) Physicochemistry of polymers. Moscow, pp 320

Transformation of Discrete Force
Equations into a Unified Formula
A. A. Sobakin, D. A. Nikolaeva, and D. V. Aleksandrov

Abstract Various equations are used in structural analysis to determine internal
forces. Typically, different formulas are applied to different sections of a structure
to calculate forces or construct shear and moment diagrams. For the convenience of
subsequent stress–strain analysis, it is preferable to use a single expression in which
all internal forces are represented by one unified equation. Despite the availability
of modern structural analysis methods utilizing specialized computational software,
the analytical form of force representation offers undeniable advantages over purely
numerical methods. Using the example of a simple beam under various loading conditions, this work outlines general rules for formulating equations that express internal
forces as a unified expression. The availability of a single equation that allows force
determination at any cross-section of a structure enables a clear assessment of the
overall stress–strain distribution, the identification of critical areas, the determination
of the most vulnerable sections, the selection of an optimal arrangement for supports
and hinges, efficient force redistribution management, and ultimately the choice of
the most rational structural solution. Efforts expressed as analytical formulas can
be computed using off-the-shelf calculation software, without requiring specialized
computational complexes.
Keywords Unified expression · Beam analysis · Force equation · Analysis
control · Position function

A. A. Sobakin (B) · D. V. Aleksandrov
North-Eastern Federal University, Yakutsk, Russia
e-mail: influenta@mail.ru
D. A. Nikolaeva
Chuvash State University, Cheboksary, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_24

285

286

A. A. Sobakin et al.

1 Relevance
Modern structures form intricate technical systems composed of interrelated
elements. Loads applied to the load-bearing framework are transferred not only
to adjacent members but also engage other parts of the structure. Consequently,
multiple connected structural elements act together, redistributing internal forces.
During the design phase, it is essential to assess the stress–strain state of structures
under any combination of load cases that may occur during service. This becomes
particularly critical when selecting the most efficient structural scheme in parametric
design, where a large number of loading and calculation schemes must be evaluated. Maximum internal forces—often the critical ones—are significantly easier to
identify when the governing equations can be expressed in a finite set of analytic
expressions. In solving many practical problems related to structural analysis, the
governing equations are usually valid only within limited sections of a structure.
In other regions, the expressions used to determine internal force components are
generally defined by different equations. This significantly complicates the computational process and hinders the application of automated structural analysis methods.
Furthermore, stress–strain analysis using common mathematical operations becomes
considerably more complex when the equations are represented in discrete form. In
practice, only a few specific load cases exist in which internal forces can be described
by a single equation.
Such cases include a simply supported beam or column subjected to a uniformly
distributed load across the entire span, or a concentrated moment applied at the
support. Similarly, if a cantilever beam is subjected to a concentrated force or moment
at the free end, or a uniformly distributed load along its full length, each internal force
can be described using a single equation. These cases allow the structures to be treated
as continuous systems, making it possible to employ the full range of mathematical
tools for assessing their stress–strain state. In real-world conditions, structures typically form complex systems in which resulting forces cannot be described by a single
analytical expression. This paper continues a broader series of theoretical studies
aimed at solving problems initially defined in discrete form by transforming them
into a unified analytical expression better suited for mathematical analysis [1, 2].
The availability of a single, continuous equation enables a more accurate formulation of many structural theory problems compared to numerical methods. As highlighted in works [3–11], structural analyses involving dynamic loads or the stability
of compressed members can be solved more simply if the problem is formulated as
a continuous function.

Transformation of Discrete Force Equations into a Unified Formula

287

2 Theoretical Background
The analysis begins by dividing the structural element into characteristic sections,
within each of which the internal forces are governed by a single expression.
To construct a unified equation, all individual expressions are combined into one
formula. To manage the computational process, an additional position function must
be introduced to track the location of the section under consideration. This position
function is used to select the appropriate equation for determining the internal forces
in a specific segment based on the sectional coordinate. A sign function [12], in a
slightly modified and more convenient form, can be used as the position function. If
a specific equation does not apply to the segment under consideration, the position
function must be designed to return zero. In the segment where the internal forces are
governed by a particular equation, the position function should return one, thereby
activating the corresponding expression.
For the sake of simplicity in presenting the method, we consider simple beams
as the structural elements. Internal forces in common beam loading scenarios can be
determined using a limited set of position function expressions, presented in Table 1.
Depending on the structural model, load character, and interaction with adjacent
constructions, the table of formulas may be supplemented with position-dependent
expressions tailored to the specific scenario.
To clarify the approach described above, let us consider a statically determinate
beam subjected to a concentrated force P applied at the free end of a cantilever
(Fig. 1). As is well known, the internal forces are described by different equations
depending on the segment of the beam being analyzed and the current coordinate
x. To transform the force equations presented in discrete form into a single unified
expression, we apply a special method previously proposed for simple beams [1, 2].
In the first segment a, internal forces arise only from the applied force P, while in
segment b, additional forces are induced due to the support reaction Ra . To unify
Table 1 Position functions
No Condition

x<a x>a x=0 x=a а<x<a+в x>a+в x=а
+в

sign(a − x)

sign(x − a)

−1

–

1−sign(a−x)
2
1−sign(x−a)
2
1+sign(a+b−x)
2

–

1 + sign(a − x)(x − a) 0

–

1+sign[(x−a)(a+b−x)]
2

–

1−sign[(x−a)sign(x−a−b)]
2

–

−1

–

[1+sign(a−x)]sign(x−a)
2

−1

–

288

A. A. Sobakin et al.

Fig. 1 Loading diagram with a concentrated force

these equations, we use a function that defines the position of the current coordinate
x and activates the equation corresponding to the relevant segment of the beam.
The unified equations for the bending moment and shear force are given as follows
Mx = −Px +

P(a + b)
(x − a) 1 − sign(a − x) ,
2b

(1)

P(a + b)
1 − sign(a − x) .
2b

(2)

Qx = −P +

In segment a, when the coordinate x lies within the range 0 ≤ x ≤ a, internal
forces arise solely due to the concentrated force P. The second terms in Eqs. (1)
and (2) must be excluded using an auxiliary expression defined by the sign function No. 3 in Table 1, which becomes zero when the condition x ≤ a is satisfied. In
the second segment b, when x > a, internal forces result from the combined action
of force P and the support reaction RA . In this case, under the condition x > a,
the second terms of the equations are activated due to the fact that the expression
0.5 1 − sign(a − x) 1 − sign(a − x) evaluates to one. Thus, instead of two independent piecewise equations describing internal forces on separate spans, we derive
a single continuous equation for both bending moment and shear force over the full
beam length.
In the general case, the variation of internal forces across individual segments of
a structure usually differs from the expressions describing force variation in other
spans. Therefore, direct application of equations similar to (1) and (2) is not always
feasible. In such situations, it is necessary to limit the domain of applicability for each
internal force expression to the segment over which it is valid. To illustrate, consider
the previous example: the bending moment and shear force caused by a concentrated
force Р are given by the same expressions on spans а, and b namely –Рх and –Р.
Often structural models yield different internal-force formulas in different spans. In
such cases, the domain of each equation must be limited appropriately, and each span
uses its own analytic expression.
As an example, let us consider a beam subjected to a distributed load applied to
the cantilever part of the span (Fig. 2).
As is well known, the law of internal force variation differs across the various
segments of the beam. In the first segment, only the uniformly distributed load is

Transformation of Discrete Force Equations into a Unified Formula

289

Fig. 2 Loading diagram with a uniformly distributed load applied to the cantilever section

active. In the second span, additional internal forces arise due to the support reaction
RA . Internal forces induced by a uniformly distributed load within one span are
described by different formulas, since bending moment and shear arise from the load
distributed along the entire span а. To construct a unified expression across both
segments, we first formulate the force equations for each segment and then introduce
auxiliary expressions—Function No. 4 (Table 1) for the first segment and Function
No. 3 (Table 1) for the second—which serve to control the computational process. In
the second span the forces are determined by the entire distributed load. The resulting
equations for bending moments and shear forces take the following form
qx2
1 − sign(x − a)
4
qa b +
a
−
− qa x −
2
b

Mx = −

a
2

Qx = −qxsign 1 − sign(x − a) − qa −

1 − sign(a − x)
,
2

(x − a)
qa b +
b

a
2

(3)

sign 1 − sign(a − x) .
(4)

When the beam consists of three or more segments, each governed by different
internal force equations, it becomes necessary to clearly delimit the applicability
of each expression. This is achieved by introducing appropriate control functions
that positionally track the location of the analyzed segment based on the current
coordinate x. This is especially relevant for loads whose effects differ across spans
and require different equations. As an example, consider a beam subjected to a
concentrated bending moment M and a point force P (Fig. 3). Loads acting on
different spans result in forces that vary in form.
If the calculation is performed sequentially from the left end of the beam, the
moment M affects the entire length of the beam, the support reaction RA acts within
the span b–c, and the force P contributes only in the segment c. If the problem is
solved in reverse order, from support B moving left to right, the internal forces due to
the support reaction RB will act throughout the second span, while the force PPP will
produce effects only within segment b. A concentrated moment will induce internal
forces only in the first span. Therefore, a more compact equation can be obtained

290

A. A. Sobakin et al.

Fig. 3 Loading diagram with a bending moment and a concentrated force

by using the first solution approach, where the origin of coordinates is placed on
the left side. Based on this order of evaluation, the bending moment and shear force
equations can be written as follows
Pc − M
1 − sign(a − x)
(x − a)
b+c
2
1 − sign(a + b − x)
,
− P(x − a − b)
2

Mx = M +

Qx =

1 − sign(a + b − x)
Pc − M 1 − sign(a − x)
−P
.
b+c
2
2

(5)
(6)

Depending on the specific conditions of the problem, appropriate control expressions can be selected to manage the calculation of internal forces for various structural configurations and loading scenarios Let us now consider a beam subjected to
a concentrated force and a uniformly distributed load applied to a part of the span
(Fig. 4).
This type of loading is among the most convenient for analysis, as it allows a
single internal force equation to be formulated for each load. The equations used to
determine internal forces along the entire length of the beam can be written in the
following form
Mx = −Px + RA (x − a)

1 − sign(a + b − x)
1 − sign(a − x)
− q(x − a − b)2
,
2
4
(7)

Fig. 4 Loading diagram with a concentrated force and a uniformly distributed load

Transformation of Discrete Force Equations into a Unified Formula

Qx = −P + RA

1 − sign(a + b − x)
1 − sign(a − x)
− q(x − a − b)
,
2
2

291

(8)

.
where the support reaction RA = 2Pl+qc
2l
In some cases, a uniformly distributed load is applied only to a specific span of
the structural element, resulting in different internal force distributions across the
various segments of the span. When a load acts on a limited span segment that is
not adjacent to the supports, it is necessary to eliminate the influence of this load
outside its region of application by introducing a position function that activates
the corresponding equation only within the loaded segment. In such cases, it is
recommended to use a function that tracks the location of the current coordinate x
and becomes active when x lies within the loaded interval. For example, one may
employ a position function defined as follows
1 + sign[(x − a)(a + b − x)]
,
2

(9)

or in the form of an equivalent expression
1 − sign (x − a)sign(x − a − b)
,
2

(10)

whose values are given in Table 1.
In both cases, when the current coordinate x lies outside segment b (x ≤ a or
x > a + b), both functions evaluate to zero. In such cases, the internal forces are
determined by both the resultant of the uniformly distributed load and the influence
of other applied loads. If the section under consideration falls within segment b (a <
x ≤ b), both functions equal one and the equations intended to determine the internal
forces on that segment become active. As an example, consider a beam subjected
to a concentrated moment and a uniformly distributed load q on the intermediate
segment b, as shown in Fig. 5.
The internal force equations for a uniformly distributed load in the second span
will differ between segments b and с. On segment b, the equations will include only
the portion of the distributed load that depends on the current coordinate x, while on
segment с, they will include the resultant of the entire distributed load q. Under this

Fig. 5 Loading diagram with a bending moment and a uniformly distributed load

292

A. A. Sobakin et al.

loading scheme, and using the above position function (9), the internal forces at an
arbitrary section of the beam can be determined by the following expressions
1 + sign(x − a) q(x − a)2 1 + sign[(x − a)(a + b − x)]
+
2
2
2
b 1 + sign(a + b − x)
− qb x −
(11)
,
2
2

Mx = −M + Ra (x − a)

1 + sign[(x − a)(a + b − x)]
1 + sign(x − a)
+ q(x − a)
2
2
b 1 + sign(a + b − x)
− qb x −
.
2
2

Qx = Ra

(12)

If the position function (10) is used instead, the corresponding equations take the
form
RA (x − a) 1 + sign(x − a)
q(x − a)2 1 − sign (x − a)sign(x − a − b)
+
2
2
2
b 1 + sign(a + b − x)
− qb x −
,
2
2

Mx = −M +

1 − sign (x − a)sign(x − a − b)
1 + sign(x − a)
+ q(x − a)
2
2
b 1 + sign(a + b − x)
,
− qb x −
2
2

(13)

Qx = RA

(14)

2P(a+b)+q(b2 −c2 )
where RA =
.
2b
For beams with multiple loads (Fig. 6), the number of terms in the internal-force
equations will correspondingly increase. To achieve a more concise equation form,
it is recommended to avoid redundant inclusion of certain load contributions across
different segments by selecting appropriate position functions. Let us consider a
beam subjected to loads applied at different sections (see Fig. 6). As is well known,
internal forces are determined based on the location of load application relative to
the support structures.

Fig. 6 Loading diagram with concentrated forces

Transformation of Discrete Force Equations into a Unified Formula

293

For example, the internal forces in a beam with two span loads on the same segment
(Fig. 6) can be determined as described above, based on the following expressions
in which each load appears in the equation only once
RA (x − a)
1 − sign(a + b − x)
1 − sign(a − x) − P1 x − P2 (x − a − b)
2
2
1 − sign(l − d − x)
,
− P3 (l − d − x)
(15)
2

Mx =

1 − sign(a + b − x)
RA
1 − sign(a − x) − P1 − P2
2
2
1 − sign(l − d − x)
,
− P3
2

Qx =

(16)

)+P3 d
.
where RA = P1 l+P2 (c+d
l
For a two-cantilever beam with an additional segment, it becomes necessary to
account for the reaction of the second support. In this case, it is recommended to fix
the coordinate of the sections being analyzed to one free end and evaluate the forces
from both sides. When calculating internal forces in the opposite cantilevered part of
the beam, the origin of the coordinate system should be shifted to the opposite end,
and measurements should be taken in the reverse direction. However, to preserve
consistency and avoid changes in the analytical expressions, the current coordinate x
should still be referenced from the originally defined origin. By limiting the action of
the span loads to include only a single support reaction, the internal-force equations
can be presented in a more compact form. This will be demonstrated using the
example of the beam shown in Fig. 7.
In this case we obtain the following internal-force equations, restricting the action
of the concentrated force P to segment d by means of the corresponding position
function, thereby excluding its influence on the other parts of the beam.

1 + sign[(x − a)(a + b + c − x)]
−M
2
1 − sign[(x − a − b)(l − d − x)]
− q(x − a − b)2
4

Mx = RA (x − a)

Fig. 7 Loading diagram with a bending moment, a uniformly distributed load, and a concentrated
force

294

A. A. Sobakin et al.

Fig. 8 Loading diagram with a uniformly distributed load, inclined force, and horizontal force

−

P(l − x) 1 − sign(l − d − x)
,
2

(17)

1 + sign[(x − a)(a + b + c − x)]
2
1 − sign(l − d − x)
1 − sign[(x − a − b)(l − d − x)]
+P
,
− q(x − a − b)
2
2
(18)

Qx = Ra

−c )
where RA = 2P(a+b)+q(b
.
2b
For this loading scheme one may also use the position function of the current coordinate in the form of expression (10). The combined action of individual elements
within a load-bearing structure can result in internal forces acting in arbitrary
directions.
When horizontal or inclined forces are applied to different segments of the beam,
it is necessary to account for the longitudinal components of such loads. The axial
forces may take different values in each segment depending on the load’s position
relative to the pinned support (Fig. 8).
The vertical component of an inclined force P1 will generate shear forces and
bending moments, while its horizontal component will produce axial forces. The
equations for all internal forces at the sections of such a beam can be written in the
following form, where the axial force in segments a and b depends respectively on
loads P1 and P2
2

qx2
1 − sign(a − x)
+ RA (x − a)
,
2
2

(19)

1 − sign(a − x)
1 + sign(a − x)
+ P2
,
2
2

(20)

Mx = −P1 sinϕx −
Nx = −P1 cosϕ

where RA = ql2b + P1 l bsin ϕ .
On roofs with a slight slope, snow accumulation during the winter can be modeled
as a uniformly distributed load across the entire span. The resulting internal forces
can then be calculated using the previously derived equations. Quite often, so-called
“snowdrifts” form on the roofs of buildings and structures with annexes (Fig. 9). In
2

Transformation of Discrete Force Equations into a Unified Formula

295

Fig. 9 Loading diagram with uniformly and non-uniformly distributed loads on roofs of buildings
with annexes

some areas of the roof, the snow layer may have a constant thickness. In such cases,
the ordinate of a linearly increasing, non-uniformly distributed load at section x can
be calculated by the formula
qx = q1 +

q2 − q1
(x − a).
b

(21)

Taking into account the effects of the shown loads, the internal forces in the beam
can be determined by the following expressions
Mx = RA x −

qx (x − a)2 1 − sign(a − x)
q1 x2
,
−
12
2

(22)

Qx = RA −

qx (x − a) 1 − sign(a − x)
q1 x2
−
,
2
4

(23)

where RA = q21 l + (q2 −q6 1 )b .
On the roofs of buildings and structures located between elevated annexes, a nonuniformly distributed load arises due to snowdrifts forming on both sides (Fig. 10).
Moreover, the thickness of the snow and the length of the loaded segment may
vary depending on the height of adjacent structures and the prevailing wind direction.
In such cases, it is more rational to compute the internal forces on segment a on the
left side of the beam and on segment b on the right side. The final expressions
for determining the internal forces along the entire length of the beam, after the
transformations, take the following form
2

Mx = RA x −

a
q1 (x − a)3 1 − sign(x − a)
q1 a
x−
+
2
3
6a
2

+ RB (l − x) −

b
q2 b
l−x−
2
3

q2 (a − x)3 1 + sign(x − a)
,
6b
2

(24)

296

A. A. Sobakin et al.

Fig. 10 Loading diagram with non-uniformly distributed loads on roofs between elevated annexes

Qx = RA −

q1 a q1 (x − a)2 1 − sign(x − a)
+
2
2
2

+ RB −
2

q2 b q2 (a − x)2 1 + sign(x − a)
+
.
2
2
2

(25)

where RA = q2l1 a l − a3 + q16lb ,RB = q16la + q22 b l − b3 .
On the roofs of buildings and structures with parapets, snow accumulates on
limited-length segments adjacent to the supports (Fig. 11).
The current ordinates of the distributed load on segments a and c are expressed
by the following relationships
q1 − q2
(x − a),
a

(26)

q3 − q2
(x − a − b).
c

(27)

on segment a qxa = q2 +
on segment c qxc = q2 +

Fig. 11 Loading diagram with uniformly and non-uniformly distributed loads on roofs with
parapets

Transformation of Discrete Force Equations into a Unified Formula

297

Under this loading scheme, the internal forces can be determined using the
following equations
Mx = RA x − x2 qxa +

2(q1− qxa ) 1 − sign(x − a)
3
2

q2 (x − a)2
sign{1 + sign[(x − a)(a + b − x)]}
2
1 − sign(a + b − x)
q2
qxc − q2
−
,
(x − a − b)2 +
(x − a − b)2
2
3
2

−

(28)

q1− qxa 1 − sign(x − a)
2
2
− q2 (x − a)sign{1 + sign[(x − a)(a + b − x)]}

Qx = RA − x qxa +

− q2 (x − a − b) +

1 − sign(a + b − x)
qxc − q2
,
(x − a − b)
2
2

(29)

where RA = q22 l + q1−2lq2 a l − a3 + (q3−6lq2 )c .
In buildings and structures with a flat horizontal roof, snow is blown off the nearsupport zones of the load-bearing elements. The resulting snow load distribution on
such roofs approximates a triangular shape (Fig. 12).
For a triangular distributed load, the internal forces in the supporting elements
can be calculated by the following expressions:
2

qx3 1 − sign(x − a)
6a
2
q(x − l + b)(x − a)2 1 − sign(a − x)
q(l − x)(x − a)2
+
,
−
2b
6b
2

Mx = RA x −

Qx = RA −

q(l − x)(x − a)
qx 1 − sign(x − a)
q(x − l + b)(x − a) 1 − sign(a − x)
−
+
,
2
2
b
2b
2

Fig. 12 Loading diagram with a triangular non-uniformly distributed load

(30)
(31)

298

A. A. Sobakin et al.
2

where RA = qa
l − 2a
+ qb3l .
2l
3
Using the proposed approach, it is possible to derive expressions for calculating internal forces under other structural configurations and loading scenarios.
For specific problem conditions, the position functions (Table 1) can be extended or
modified in accordance with the loading requirements, following the methodology
described above.

3 Conclusions
1. A unified form of the internal-force equation extends the rational scope of
analytical structural-analysis methods.
2. The approach proposed in the article allows us to present the problem of
calculating structures in the form of a continuous model.
3. By using a single equation to determine internal forces at any point along the
beam, it becomes possible to assess the stress–strain state of structures with
established mathematical-analysis techniques.
4. When implementing a calculation program, the algorithm for computing internal
forces in complex problems—such as buckling stability of compressed members
and structural dynamics—is greatly simplified by introducing only one equation
that accounts for all loading conditions and features of the analysis scheme.
5. Structural systems can be analyzed using the proposed methodology without
relying on specialized computational suites, employing only general-purpose
software.
6. The given method of conversion of the design model can be used to solve a wide
range of problems.

References
1. Sobakin AA, Nikolaeva DA, Androsov VA (2020) General formula of displacements in bending
elements. IOP Conference Ser: Mater Sci Eng (MSE) 1079(2021):032014
2. Sobakin AA, Fedorov VK (2022) General formula of beams strengthening. In: Proceedings of
the 6th international conference on construction, architecture and technosphere safety. ICCATS
2022. Lecture notes in civil engineering, vol 308. Springer, Cham, pp 308:118–127. https://
doi.org/10.1007/978-3-031-21120-1_12
3. Smirnov MS (2006) Building dynamics. Determination of frequencies and modes of natural
oscillations of the structure. St. Petersburg
4. Kazemahvary S, Radford D, Deshpande VS, Fleck NA (2007) Dynamic failure of clamped
circular plates subjected to an underwater shock. J Mechan Mater Struct 2:2007–2023
5. Qiu X, Deshpande VS, Fleck NA (2004) Dynamic response of a clamped circular sandwich
plate subject to shock loading. J Appl Mechan 71:637–645
6. Allachverdov BM, Ribina II (2017) Modern problems of the dynamics of structures. St.
Petersburg
7. Maslennikov AM (2016) Dynamics and stability of structures. Moscow

Transformation of Discrete Force Equations into a Unified Formula

299

8. Onundi LO, Matawal DS, Elinwa AU (2010) The influence of Euler critical load on the
method of unicial parameters for the dynamic analysis of multi-story buildings subjected to
aerodynamic forces. Continental J Eng Sci 5:1–13
9. Bosokov SV (2021) The mixed method of construction mechanics in the problems of plate
dynamics. Struct Mechan Anal Construct 3:66–70
10. Solovyova AA, Solovyov SA (2021) Structural reliability analysis of steel truss elements on
buckling using p-box approach. Struct Mechan Anal Construct 1:45–53
11. Pattel VI (2013) Nonlinear inelastic analysis of concrete-filled steel tubular slender beamcolumns. Dissertation doctor of philosophy. Melbourne
12. Bronstein IN, Semendyaev KA (1981) Reference book in mathematics for engineers and
students of universities. Moscow

Organomineral Mixtures for Road
Foundations Based on Industrial Waste
A. I. Leskin, S. V. Aleksikov, D. I. Gofman, L. M. Leskina, and I. I. Glazunov

Abstract This study presents experimental research on the feasibility of using
waste products from various industrial sectors for the development of organomineral
mixtures intended for constructing road bases for motor roads. The materials considered include milled asphalt concrete, oil sludge, technical hydrolysis lignin, and limecontaining waste (fine-milled sludge waste). The physical and mechanical properties of these materials were examined, and optimal ratios of each component within
the mixture were determined. Each component contributes to forming a durable
framework, increasing density, water resistance, adhesion, and cohesion properties,
thereby enhancing strength and resistance to crack formation. A comparative analysis of the produced samples confirmed their compliance with established strength
standards. Tests for rutting resistance demonstrated that the developed organomineral mixtures meet regulatory requirements. The results provide a scientific basis
for further development of waste utilization technologies and improvements in road
construction methods, which is particularly relevant given resource shortages and
increasing environmental considerations in road construction materials.
Keywords Organomineral mixtures · Recycled asphalt concrete (RAP) ·
Industrial waste · Motor roads · Road bases · Road construction materials

1 Introduction
Recently, at the national level, there has been a sharp increase in the issue of improving
the effectiveness of the current environmental safety system in the Russian Federation
and the preservation of natural resources. Since 2012, the State Program has been
approved [1], aimed at reducing the environmental burden through the enhancement
of ecological efficiency in the economy. This goal should be achieved by restoring
and reclamating land affected by negative impacts, by efficient waste management
A. I. Leskin (B) · S. V. Aleksikov · D. I. Gofman · L. M. Leskina · I. I. Glazunov
Volgograd State Technical University (VolgSTU), Volgograd, Russia
e-mail: leskien@inbox.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_25

301

302

A. I. Leskin et al.

for production and consumption, and by creating a sustainable system for handling
solid municipal waste (sorting, reducing waste volumes sent to landfills).
The main regulatory legal acts defining state policy in the use of raw materials
and resources, waste prevention and reduction, hazard classification, processing,
recycling, and disposal are the Federal Law “On Waste of Production and Consumption” [2] and the Federal Law “On Environmental Protection” [3]. A specific role in
implementing the above programs is played by industrial production waste [4], which
can be reused either directly or after additional processing. Many modern industrial
processes generate waste with various characteristics that are comparable to natural
raw materials, making them valuable resources in secondary material production. The
utilization of waste from various industries is a promising direction that contributes
to solving environmental problems and creating sustainable economic development,
aligning with global trends toward a circular economy (“closed-loop economy”).

2 Relevance of the Research Topic and Problem Statement
Annual construction, repair, and reconstruction of roads in the Russian Federation
require a comprehensive approach to the application of innovative technologies that
lead to reduced economic costs through the development and further implementation of new road construction materials, enabling the use of industrial waste as raw
materials. Since the primary types of road surfaces and bases are organic-mineral
mixtures, including asphalt concrete, one of the actual tasks in road construction is to
explore the possibility of applying and recycling asphalt concrete granulate obtained
through cold milling of such surfaces. It is also crucial to study the properties of the
removed material, including determining the uniformity of its grain composition, the
need for adjustments, as well as the quantity and properties of the binder contained
within it [5–8].
To effectively use processed asphalt concrete (RAP) as a mineral filler in organicmineral mixes, additional research is needed to select mixture compositions considering the physical and mechanical properties of this material. Moreover, it is important to account for the fact that heterogeneity in RAP’s composition and properties can significantly impact the quality of the resulting mixes; therefore, developing standardized quality control methods is essential for the widespread adoption
of this technology. It is also worth noting that during the long-term operation of
asphalt concrete pavements, complex chemical transformations occur in the upper,
thin surface layer under the influence of air oxygen, ultraviolet radiation, water, and
temperature, leading to aging of the organic binder, which causes significant changes
in its composition and structural type. An effective way to restore the dispersed structure of bitumen in asphalt granulate is the use of secondary products from the chemical
and oil refining industries. Regenerating additives may include synthetic fatty acids,
used lubricants, heavy vacuum gas oils, bituminous production solvents, technical
hydrolysis lignin, gossypol resin, resins from coal gasification, styrene rectification
bottoms, and others [9–13].

Organomineral Mixtures for Road Foundations Based on Industrial Waste

303

A particular interest is the use of technical hydrolysis lignin as a stabilizing additive. It is a product of chemical processing of wood through acid hydrolysis of
polysaccharides in the cell walls of wood fibers. This type of lignin is widely used in
the production of composites, building materials, sorbents, and biodegradable polymers. Physicochemical characteristics of hydrolysis lignin show that it is a polydisperse system with a fibrous thread structure, with particle sizes ranging from several
millimeters to microns or less, and it possesses high adhesion properties, capability
to improve mixture structures, and increase strength and crack resistance of finished
pavements [14].
Another promising direction for creating organic-mineral compositions based on
asphalt granulate is incorporating oil sludge as a filler. Oil sludge forms during oil
extraction and is a mixture of water, sand, heavy hydrocarbon fractions, and solid
particles. In the reservoirs of the Volgograd region, a significant amount of this waste
from oil refining has accumulated over the decades, which currently has no further
application. These reservoirs, large open earthen tanks, occupy extensive areas and
prevent the rational use of land, as well as pose serious environmental threats because
they can become sources of pollution [15, 16].
Many countries successfully use calcium oxide hydrate additives Ca(OH)2 to
improve the characteristics of organic-mineral mixes. An analogous material is a
by-product of calcium carbide production at Volgograd’s OJSC “Khimprom.” This
product is a fine-disperse, light-gray powder containing at least 80% by mass of
Ca(OH)2 . The use of slaked and unslaked lime in cold asphalt mixes and wet organicmineral compositions offers significant advantages and prerequisites for applying
relatively inexpensive waste in rapid road repair technologies [17].
A comprehensive analysis of hot and cold organic-mineral mixes used in road
construction, especially on low-traffic roads, is provided in the review by candidate
of technical sciences L.A. Gorelysheva. The work discusses principles of mixture
design, main characteristics, methods of production, and features of material use
[18].
Research on utilizing local materials and industrial waste in organic-mineral mixes
conducted by foreign specialists is of great interest. An example is a study on the
properties of fillers for such mixes, published in Salt Lake City, USA [19].
The effective application of organic-mineral mixes based on recycled asphalt
concrete (RAP) and industrial waste in road bases is impossible without experimental
and theoretical studies of the process of forming a durable structure of the new
material. To achieve this, the following tasks were addressed:
1. Investigated the physical and mechanical properties of organic-mineral mixes
with justified calculations of their strength and deformation indicators, considering the normative requirements for road bases.
2. Analyzed the physicochemical properties of asphalt granulate, oil sludge, technical hydrolysis lignin, and lime-containing waste. Optimal dosages for each
component were established to ensure the best operational characteristics of the
finished mix.

304

A. I. Leskin et al.

3. Developed compositions of organic-mineral mixes with high content of recycled
materials and local mineral fillers, characterized by improved physic-mechanical
properties and temperature resistance.

3 Experimental Part
For testing, samples of asphalt granulate obtained by milling asphalt concrete surfaces
from three different milling machines were collected, along with oil sludge taken
from a storage pond, technical hydrolysis lignin, and sludge waste from the industrial
production of OJSC “Khimprom.”
The grain compositions of the mineral part of the collected asphalt granulate
samples, determined in accordance with national standard [20] for organic-mineral
mixes prior to the addition of binders, are presented in Table 1.
The grain composition of sample No. 2 meets the requirements for the grain
compositions of organomineral mixes OMM 16 with a nominal maximum aggregate
size of 16.0 mm. Studies [15, 21] have shown that components of oil sludge influence the bituminous films of asphalt granulate, gradually softening and restoring
them. After the compaction process and moisture evaporation, they contribute to the
formation of a uniform and durable layer with high water resistance and low water
absorption. Oil sludges contain a large amount of resins and asphaltenes, which
makes them suitable for use in the preparation of organomineral mixes [22, 23].
Analysis of the group composition of the oil sludge used in the research
revealed that it contains 25.3% emulsified water, 30.2% mechanical impurities, and
44.5% organic matter, including: 8.2% asphaltenes, 28.3% resins, 19.3% paraffinic
hydrocarbons, 14.8% naphthenic hydrocarbons, and 29.4% aromatic hydrocarbons.
Table 1 Grain composition of the mineral part of RAP
Cutter/sample Name of Complete passes, %, through a sieve with a mesh size, mm
no
the mix 45 31.5
22.4
16
11.2
4
2
Requirements OMM
of GOST
32
ОМM
16
Wirtgen
W2000/
Sample № 1
Caterpillar
PM 620/
Sample №2
XCMG
XM1205F/
Sample №3

ОМM
16

100 From 90 From 60 –
to 100
to 90
–

–

From 20 From 15
to 50
to 40

100

From 90 From 70 From 35 From 20
to 100
to 90
to 60
tо 50

100 100

98.7

96.1

92.4

69.6

56.8

–

100

97.4

86.4

51.3

37.8

–

100

92.4

78.4

46.6

34.3

Organomineral Mixtures for Road Foundations Based on Industrial Waste

305

Granulometric analysis of lignin samples showed the following characteristics:
the fraction with particle sizes exceeding 250 μm accounted for 50–80%; the fraction
smaller than 250 μm varied from 20 to 45%; the content of the fraction with particle
sizes less than 1 μm ranged from 0.2–4.3% [24].
The sludge waste from the industrial production of OJSC “Khimprom” is a finedispersed light gray powder with a specific mass of 3.90 g/cm3 . The main chemical
composition of this waste is as follows:
•
•
•
•
•
•
•
•
•

Iron(II) sulfate: Fe2 SO4 — 4.52%,
Iron(II) oxide: FeO — 14.03%,
Aluminum oxide: Al2 O3 — 0.932%,
Phosphorus(V) oxide: P2 O5 — 0.09%,
Calcium oxide: CaO — 52.0%,
Titanium dioxide: TiO2 — 0.098%,
Silicon dioxide: SiO2 — 4.79%,
Manganese(II) oxide: MnO — 5.77%,
Magnesium oxide: MgO — 17.77%.

Considering the high calcium oxide (CaO) content, this waste potentially can be
used as an active component in the production of concrete, construction mortars,
or other building materials, providing an improvement in their physico-chemical
properties.
The content of fine-milled sludge waste with particle sizes of 0.315…0.071 mm
in the composition with hydrolyzed lignin can vary from 3 to 5% of the total mixture
weight.
Based on regulatory documents [25] and methodological recommendations for
restoring asphalt concrete pavements and bases of roads by cold regeneration [26],
seven compositions of organomineral mixes with the use of oil sludge as a binder—
containing from 0.5% to 3% of RAP mass—and hydrolyzed lignin as a stabilizing
additive—from 0 to 0.9% of RAP mass—were designed based on sample No. 2.
Below is Table 2, showing the accepted compositions and the measured density of
each tested experimental batch.
The mass fraction of oil sludge has a significant impact on the density of the
mixture. Acting as an additional binding component alongside RAP, oil sludge
strengthens the internal structure of the mixture by filling voids between mineral particles and forming additional contacts among them. The high dispersity and viscosity
of the sludge ensure better distribution of mineral elements and enhance overall adhesion quality. The fine-grained sludge waste, serving as an extra source of solid particles, further promotes the formation of a dense structure. The high-dispersity particles
of the waste are evenly distributed throughout the mixture volume, increasing the
degree of pore filling and creating an additional foundation for dense structure formation. As a result, the mixture gains greater stability and density. Hydrolyzed technical
lignin acts as an additional stabilizer of the structure. Its molecules form a fine film
around mineral particles, strengthening mutual adhesion, improving cohesion within
the material thanks to its film-forming properties, preventing mixture delamination,
and reducing micro-pore volume. This mechanism functions like glue, reinforcing

306

A. I. Leskin et al.

Table 2 Compositions of organomineral mixtures and their density
Sample №

Mass fraction
of oil sludge,
%

Mass fraction
of fine grind
sludge waste,
%

Mass fraction
of hydrolysis
lignin, %

Mass fraction
of RAP, %

Mixture
density, g/cm3

0.5

99.5

2.36

0.5

0.3

98.2

2.38

1.5

1.0

0.6

96.9

2.40

1.5

0.9

95.6

2.41

2.5

2.0

0.45

95.05

2.43

2.0

0.15

94.85

2.42

0.8

1.0

0.75

97.45

2.39

the structure and preventing the development of internal defects. The highest density
(2.43 g/cm3 ) was observed in mixture No. 5, which contains the largest amount
of fine-grained sludge waste (2.0%). This combination of substances allowed for
the most uniform distribution of minerals and a high compaction ratio. Conversely,
the lowest density (2.36 g/cm3 ) was recorded in mixture No. 1, which lacked sludge
waste and contained the minimal amount of oil sludge (0.5%). Increasing the content
of oil sludge and sludge waste leads to a gradual increase in mixture density up to a
certain point (mixture No. 5). Further increasing one of the components (mixture No.
6) may cause a slight decrease in density, likely due to an imbalance of components
and the excess of organic impurities, which disrupt the integrity of the microstructure
of the mixture.
During the conducted research, the prepared samples of the developed compositions underwent tests for physico-mechanical properties, as specified by relevant
standards and technical requirements [25, 26]. The results of these tests are presented
in Table 3.
By combining the data from Tables 2 and 3, it is evident that there is a clear relationship between the physico-mechanical properties of the organomineral mixtures
and the composition and mass fractions of their main components. For example, the
maximum density (2.43 g/cm3 ) in sample No. 5, which contains 2.5% oil sludge,
2.0% fine-grained sludge waste, and 0.45% hydrolyzed lignin, positively influences
the compressive strength (2.89 MPa) and high water resistance (0.96). The water
absorption indicator is directly related to the content of oil sludge and fine-grained
sludge waste in the mixture. Compositions No. 4, No. 5, and No. 6, which have high
mass fractions of both components, exhibit the lowest water absorption. Samples No.
4–No. 6 are characterized by excellent water resistance (> 0.8), indicating a positive
effect of combining oil sludge, fine-grained sludge waste, and hydrolyzed lignin.
Conversely, sample No. 7 shows relatively low water resistance (0.58), possibly due
to an imbalance of components.
Sample No. 1 demonstrated high compressive strength at 20 ºC (3.05 MPa), but
its low water resistance raises questions about its practical applicability. The best

Organomineral Mixtures for Road Foundations Based on Industrial Waste

307

Table 3 Indicators of the physico-mechanical properties of organomineral mixtures at 7 days of
age
Name of the
indicator

GOST R
ODM
Values for the composition
70197.1-2022 218.6.1.005-2021 1
2
3
4
5

Density, g/
сm3

Not normal

2.36 2.38 2.40 2.41 2.43 2.42 2.39

Not normal
Water
saturation, %

Not normal

11.8 9.8

Water
resistance,
not less than

0.5

0.56 0.61 0.84 0.88 0.96 0.96 0.58

Not normal

3.05 2.73 2.85 2.56 2.89 2.38 2.82

0.7

Compressive Not normal
strength
limit, MPa, at
temperature,
°С, not less
than: 20

8.24 7.96 7.78 7.0

10.2

Not normal

0.95 0.85 0.87 0.76 0.82 0.57 0.90

Indirect
tensile
strength
limit, kPa, at
temperature,
°С, not less
than: 22

300

409

366

374

344

380

312

387

200

298

276

295

225

290

205

291

1200

890

806

825

798

951

845

756

Tensile
1000
strength limit
under
indirect
tension at a
temperature
of 22 °C, at
28 days of
age, in kPa,
not exceeding

tensile strength at 22 ºC (409 kPa) was observed in sample No. 3, which contains
1.5% oil sludge, 1.0% fine-grained sludge waste, and 0.6% hydrolyzed lignin, while
the lowest strength (312 kPa) was found in sample No. 6.
To assess the fatigue properties of the organomineral mixes, tests were conducted
on samples with compositions No. 3–No. 5 for rutting resistance using the wheel
loading method [27]. The tests were performed at 60 ºC on laboratory-prepared
samples aged 7 days. The results obtained were compared with the requirements of
GOST R 58406.2-2020 [28] concerning hot mixes for bases, as this indicator is not
standardized for organomineral mixtures. The shear resistance indicator is presented
in Table 4.

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A. I. Leskin et al.

Table 4 Indicators of shear strength stability of organomineral mixes at 7 days of age
Indicator

Requirements of Mix composition Mix composition Mix composition
GOST [25] for
№3
№4
№5
foundations

Average rut depth, 9.0
mm, at a
temperature of 60
ºC after 20,000
wheel passes, not
exceeding

7.61

8.32

6.25

Slope angle of the 0.4
rut formation
curve, mm per
1000 cycles, not
exceeding

0.31

0.36

0.22

The rutting resistance tests showed that all the considered organomineral mixture
compositions (Nos. 3, 4, and 5) meet GOST requirements, as the average rut
depth after 20,000 wheel passes at a temperature of 60 ºC does not exceed the
minimum specified value of 9.0 mm. Composition No. 5 demonstrated the best
results, exhibiting the smallest rut depth (6.25 mm), making it the most favorable
material for areas with heavy traffic flow and adverse climatic conditions.

4 Conclusion
In this study, an analysis and experimental investigation were conducted on the
possibility of producing compositions of organomineral mixes based on industrial
waste for their subsequent use in road base layers. Based on the obtained data, the
following main conclusions were made:
1. The use of waste from various industries is one of the priority tasks that contribute
to solving environmental problems and transitioning to a circular economy.
2. The increase in milling volumes of worn-out asphalt concrete pavements and the
growing need for materials for the construction and repair of roads promote the
development of methods for applying RAP. Incorporating various waste-based
compositions into its structure can significantly save natural resources and reduce
environmental impact.
3. The physico-chemical properties of asphalt granulate, oil sludge, technical
hydrolyzed lignin, and lime-containing waste were analyzed. Optimal dosages
for each component were established, which play a crucial role in forming
the necessary indicators of the developed organomineral mixture compositions.
RAP serves as the main filler, increasing the density and strength of the final
product, while the organic binder it contains acts as an additional adhesive.
Oil sludge reinforces the internal framework of the mixture, enhances density,

Organomineral Mixtures for Road Foundations Based on Industrial Waste

309

and promotes better distribution of mineral elements. Fine-grained sludge waste
improves strength, increases water resistance, fills voids, and raises density.
Hydrolyzed technical lignin forms a protective layer around mineral particles,
prevents mixture separation, and improves cohesion, thereby increasing strength
and resistance to cracking.
4. The conducted tests allowed for selecting an optimal mixture composition characterized by high density, good compressive strength (2.89 MPa), and water resistance (0.96). These physico-mechanical properties confirm the mixture’s ability
to withstand intensive loads and maintain performance under various climatic
conditions.
5. Wheel tracking tests for rutting resistance showed that three compositions of
organomineral mixes (Nos. 3, 4, and 5) meet GOST requirements concerning
the permissible rut depth after 20,000 wheel passes (≤ 9.0 mm). Among them,
mixture No. 5 demonstrated the best results, maintaining a rut depth of 6.25 mm,
which ensures high operational reliability and durability of the base.
The developed compositions of organomineral mixes with high content of recycled
materials and industrial waste, featuring improved physico-mechanical properties
and temperature stability, represent an effective solution for the major repair and
construction of road bases.
Acknowledgements The research was supported by a grant in the form of subsidies from the
Committee of Economic Policy and Development of the Volgograd Region, No. 3, dated December
12, 2024, on the topic “Development of technology for the production of asphalt-granular concrete
mixtures for road surfaces in the Volgograd region.”

References
1. Passport of the State Program of the Russian Federation “Environmental Protection”. Approved
by the resolution of the Government of the Russian Federation dated April 15, 2014, No. 326
(with amendments and additions)
2. Federal Law No. 89-FZ of June 24, 1998, On Production and Consumption Waste
3. Federal Law No. 7-FZ of January 10, 2002, On Environmental Protection
4. GOST R 54098-2010 (2010) Resource conservation. Secondary material resources. Terms and
definitions. FSUE “VNI CSMV”, FSUE “NITC PURO”. Approved by order of the federal
agency for technical regulation and metrology dated November 30, 2010, No. 761-st
5. Zhuravlev DV (2017) Requirements for designing compositions of asphalt granulate concrete.
In: International scientific and technical conference of young scientists of BSTU named after
V.G. Shukhov, Belgorod, pp 2082–2087
6. Yeryomin AV, Kurdjukov RP (2019) Determination of the recipe for preparing asphalt granulate concrete mix. High technologies in the construction complex. Voronezh State Technical
University, Voronezh, pp 37–41
7. Emery JJ (1993) Asphalt concrete recycling in Canada. Pavement surface courses, stone
mastic asphalt pavements, and asphalt concrete recycling. National Research Council (USA).
Transport Res Board 1427:38–46
8. Miliutenko S, Björklund A, Carlsson A (2013) Opportunities for environmentally improved
asphalt recycling: the example of Sweden. J Clean Prod 43:156–165

310

A. I. Leskin et al.

9. Asad T, Yunusov MY, Umarov SS, Sairakhmonov RK (2020) Theoretical aspects, experimental
studies of the effectiveness of using a complex additive of various functional purposes in the
composition of road binders. Polytechnic Bullet Ser: Eng Res 1(49):123–128
10. Romasjuk EA, Abaza MA (2016) Experience in applying plasticizing additives to restore
properties of bitumen in milled asphalt concrete. Modern Trends in Developm Prospects for
Implement Innov Technol Mechan Eng Educ Econ 2(1):120–125
11. Leskin AI, Gofman DI, Aleksikov SV, Al-Karaguli MM (2019) Organic composition for
restoring binder properties in asphalt granulate. Bulletin of volgograd state architectural and
construction University. Series: Construct Architect 1(74):33–39
12. Leskin AI, Aleksikov SV, Gofman DI (2020) Organic composite binder improving the physical
and mechanical properties of low-strength stone materials. IOP Conference Series: Materials
Science and Engineering, Sochi, pp 022002. https://doi.org/10.1088/1757-899X/962/2/022002
13. Leskin AI, Gofman DI, Katasonov MV, Vovko VV, Skorobogatchenko DA (2018) Use of
Local waste from chemical industry in binders. Bulletin of volgograd state architectural and
construction university. Series: Construct Architect 53(72):83–91
14. Dat LCM, Balabanov VB, Protsenko MY (2019) Use of hydrolytic lignin as a stabilizing
additive for crushed stone-mastic asphalt concrete. Proc Universit Investm Construct 2:334–
341. https://doi.org/10.21285/2227-2917-2019-2-334-341
15. Gramatikov IV (1999) Utilization of oil sludge and aniline resin in road construction (Environmental Protection Method). Dissertation. Candidate of Technical Sciences. Volgograd, pp
208
16. Brehman AI, Ilyina ON, Trifonov AA (2010) Organic-mineral mixtures based on oil sludge.
Proc Kazan State Architect Construct Univer 1(13):264–267
17. Gofman DI, Leskin AI, Aleksikov SV, Keyta F Mohamed Lamin (2018) Emulsion-mineral
mixtures on lime-containing waste. Bull Volgograd State Archit Constr Univ Ser Constr Archit
54(73):69–75
18. Gorelysheva LA (2000) Overview information. Automobile roads. Organic-mineral mixtures
in road construction. Overview information. Road Traffic Information Center, 3
19. Kavussi A, Hicks RG (1997) Properties of bituminous mixtures containing different fillers.
Association of asphalt paving technologists (AAPT). Salt Lake City, Utah, USA
20. GOST R 70197.1-2022 (2022) National standard of the Russian Federation. Roads of General
Use. Cold Organic-Mineral Mixtures Using Recycled Asphalt Concrete. General Technical
Conditions. Approved and Implemented by Order of Rostandard dated August 2, 2022, No.
718-st., Russian Institute of Standardization, Moscow, p 11
21. Kayumov AK, Zinevich SI, YaN K (2022) Foundations of road pavements from recycled materials. Sci Technol 21(6):504–510. https://doi.org/10.21122/2227-1031-2022-21-6504-510
22. Lofler M, Shelegov VG, Slobodchikova NA (2018) Directions for using oil sludges in road
construction. Bulletin of Universities. Investments. Construction. Real Estate 8(4):98–104.
https://doi.org/10.21285/2227-2917-2018-4-98-104
23. Trifonov AA (2005) Organic-mineral road construction materials using oil sludge. Dissertation.
Candidate of Technical Sciences, pp 194
24. Chudakov MI (1983) Industrial use of lignin. Lesnaya Promyshlennost, Moscow, p 94
25. GOST R 70197.2–2022 (2022) National standard of the Russian federation. Roads of
general use. Cold organic-mineral mixtures using recycled asphalt concrete. Testing methods.
Approved and Implemented by Order of Rostandard dated August 2, 2022, No. 719-st., Russian
Institute of Standardization, Moscow, pp 12
26. ODM 218.6.1.005-2021 (2021) Methodological recommendations for restoring asphalt
concrete pavements and bases of roadways by cold Rejuvenation (with Amendment). Issued
based on the order of the Federal Road Agency dated February 17, 2021, No. 570-r, with
amendments adopted by the order of the Federal Road Agency dated January 18, 2022, No.
18-r., Moscow, pp 50
27. GOST R 58406.3-2020 (2020) National standard of the Russian federation. Roads of general
use. Asphalt concrete mixtures for road and asphalt concretes. Method for determining rut
resistance by rolling loaded wheel, Standartinform, Moscow, pp 12

Organomineral Mixtures for Road Foundations Based on Industrial Waste

311

28. GOST R 58406.2–2020 (2020) National standard of the Russian federation. Roads of
General Use. Hot Asphalt Concrete Mixtures and Asphalt Concretes. Technical Conditions,
Standartinform, Moscow, pp 29

Study of the Properties of Slag-Based
Cold Asphalt Concrete Produced
with a High Content of RAP Aggregates
A. I. Leskin, S. V. Aleksikov, D. I. Gofman, I. I. Glazunov, and L. M. Leskina

Abstract Recently, technologies involving the reuse of demolition materials from
transportation structures and local industrial waste have gained increasing importance in road construction. These methods help reduce manufacturing and transportation costs while also protecting the environment. Such technologies are especially significant in regions where natural stone aggregates are scarce, particularly in
the production of asphalt concrete mixes. This study investigates the possibility of
producing cold asphalt concrete using metallurgical slag and recycled asphalt pavement (RAP) with foam bitumen. A comprehensive analysis was conducted of the
physical and mechanical properties of slag fillers and asphalt granulate, confirming
their suitability for use in road pavements. Optimal asphalt concrete formulations
were developed, incorporating up to 65% RAP and 35% slag gravel, which demonstrated high compressive and tensile strength despite moderate water resistance indicators. Regression analysis was used to determine the relationships between strength
characteristics and water resistance indicators and the content of components. To
enhance the operational properties, a modifier based on lignosulfonates—a byproduct
of hydrolysis production—was proposed. It was established that adding 5% of this
modifier relative to the mineral part significantly reduces water saturation, increases
the water resistance coefficient, and improves the mixture’s homogeneity. The results
presented demonstrate the effectiveness of a comprehensive approach to utilizing
industrial and construction waste in the production of cold asphalt concrete, ensuring
ecological sustainability and economic feasibility of the proposed technology.
Keywords Asphalt granulate concrete · Recycled asphalt pavement (RAP) ·
Metallurgical slag · Aggregate · Lignosulfonate · Density · Water resistance ·
Compressive strength · Modification

A. I. Leskin (B) · S. V. Aleksikov · D. I. Gofman · I. I. Glazunov · L. M. Leskina
Volgograd State Technical University (VolgSTU), Volgograd, Russia
e-mail: leskien@inbox.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_26

313

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A. I. Leskin et al.

1 Introduction
Currently, in the Russian Federation, there is an annual increase in the length of
the network of paved roads, a significant part of which consists of unbound road
pavements made of asphalt concretes (over 600 thousand km). At the same time, the
following trends in the development of the road construction industry are observed:
• Increasing volumes of current and capital repairs of roads;
• Use of local construction materials, which significantly reduce transportation
costs;
• Application of monolithic water-resistant materials and compositions in the bases
and lower layers of pavements that can withstand elastic deformations;
• Development of recycling of waste obtained during the dismantling of transport
structures.
Timely provision of road construction production with resources such as construction
materials, semi-finished products, structures, and energy carriers at minimal costs,
combined with the constant rise in construction costs and changes in traditional
material suppliers, requires the widespread adoption of local construction materials,
including industrial waste. Closely related to this direction are technologies for the
use of milling waste from structural layers of road pavements.
Even after the designed service life, asphalt concrete retains the ability to recover
up to 80–90% of its useful mass [1–4]. The reuse of old asphalt in the form of granulate is regulated by its types, main parameters, technical requirements, and control
methods [3]. Asphalt granulate is an optimal product for repairing road surfaces, as
it contains crushed stone and 3 to 8% of old asphalt binder. As numerous studies
show, when processing asphalt scrap and reusing it, the mineral components that
retain a film of asphalt binder on their surface exhibit properties characteristic of
activated materials. For example, processing 1000 tons of old asphalt saves up to
900 tons of mineral materials (crushed stone, sand, mineral powder) and about 70
tons of bitumen, leading to significant economic benefits [5–7].
In the USA, it is believed that, considering all circumstances, up to 70% RAP can
be used in asphalt mixtures [8–10]. In our country, industrial experience shows that
when using domestic materials and bitumen to produce acceptable-quality mixtures,
no more than 20% RAP should be used. If its content increases to 30%, special regenerators for aged binders are required. The properties of asphalt mixes change during
operation due to aging of the bitumen in their composition. Oxidation and polymerization deteriorate the deformation properties of bituminous films that bind mineral
materials [5, 7]. The regenerator added to the updated mixtures eliminates excessive
stiffness of the aged binder film surrounding RAP granules, shields mineral grains
exposed during milling, ensures adhesion between filler grains added to increase
gravel content or adjust the granulometric composition, partially fills intergranular
voids, reduces water saturation of asphalt granulate, decreases intergranular friction
to improve packing during compaction, and helps “heal” microdefects that occur
during operation [4, 11].

Study of the Properties of Slag-Based Cold Asphalt Concrete Produced …

315

Methods of cold recycling of bases and pavements containing organic binders
are promising, allowing effective use of asphalt granulate as a filler for new
mixtures. Industry guidelines for selecting optimal regeneration technology have
been approved and implemented, establishing requirements for cold asphalt granulate concrete mixes [12]. Technological solutions have been tested and adopted
that enable increasing the share of milling waste from asphalt concrete up to 90%
in lower layer materials and up to 40% in upper layers, while maintaining physical
and mechanical properties that meet the requirements for new structures [1]. The
possibility of implementing cold recycling technologies on-site (cold recycling, use
of mobile mixing complexes, etc.) as well as at stationary asphalt plants is a relevant
trend in road construction.
The growing demand for high-quality crushed stone, sand, mineral powder, and
asphalt concrete mixes based on them can be fully satisfied by using slags from ferrous
and non-ferrous metallurgy. In terms of chemical and mineralogical composition,
strength, and frost resistance, slags are valuable raw materials for producing nonaggregate materials used in asphalt mixes for road pavements [13]. Replacing crushed
stone from rocks with slag is relevant in regions lacking significant deposits of
durable stone rocks, such as the Volgograd and Lipetsk regions, and the Kalmykia
and Tatarstan republics.
According to sources [14–16], slag asphalt concretes meet the requirements of
regulatory documents, and the pavements and bases constructed from them satisfy
transport operation indicators during road use. However, their widespread adoption requires consideration of technological limitations, such as heterogeneity of
strength properties, possible high-porosity pumice-like grains, metallic scale content,
slag structure stability against lime, silicate, ferric, and manganese decay, increased
porosity of slag crushed stone, which increases bitumen consumption and negatively
impacts water resistance. Therefore, the application of hydrophobic methods in the
development of slag asphalt concrete compositions is relevant.
Analysis of scientific, technical, and normative literature has allowed formulating the research goal: to theoretically and experimentally substantiate the technology for producing asphalt granulate concrete based on slag fillers with maximum
involvement of recycled asphalt pavement in the mix.
To achieve this goal, the following tasks were solved:
• Developed compositions of asphalt granulate concrete with optimal structure
using slag fillers and RAP.
• Experimentally established the influence of slag filler content on the physical and
mechanical properties of asphalt granulate concretes.
• Investigated the effect of a modifier based on secondary products of hydrolysis
production on the strength and water resistance indicators of the obtained asphalt
granulate concretes.

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2 Research of the Properties of Initial Components
and Development of Asphalt Granulate Concrete
Compositions Using Slag Fillers and RAP
For the development of asphalt granulate concrete compositions, a selection of steelmaking slag fractions was carried out: 0(d) – 4(D) mm and 8(d) – 22.4(D) mm after
preliminary sorting at the production site of the road construction organization in
Volgograd. The results of granulometric composition and the physical–mechanical
properties of the samples are presented in Table 1.
Table 1 Physical and mechanical properties of metallurgical slag samples
Parameter being measured

Test results
Sample
№1

Sample
№2

GOST 32826–2014
[17] Requirements

Grain size distribution, full pass in
(%) through control sieve, (mm):

90/10

100.00

1,4D

100.00

96.8

100.00

From 90.00 to
100.00

1.58

1.75

From 0 to 10.00

d/2

1.13

From 0 to 2.00

Average density, (g/cm3 )

3.60

3.61

–

Bulk density, (g/сm3 )

1755

1750

–

(g/cm3 )

3.05

3.1

–

Crushing resistance (mass loss after
test, (%))

10.3

11.1

Not more than 9–12
inclusive

Resistance to crushing and wear

13.2

True density,

Grade/class

1200

14.8

Up to 15 inclusive

Frost resistance (mass loss after test, 4.0/150
(%)/number of cycles)

4.2/150

No more than 5%
after 150 cycles

F150

Content of flaky (plate-like) and
needle-shaped grains

3.1

Up to 10 inclusive

Content of dust-like and clay
particles, (%)

0.1

0.3

No more than 1% for
asphalt concrete

Slag activity, MPa

0.87

Up to 1.0 MPa
inclusive

Non-active

Structural stability of grains against
disintegration (mass loss after test,
(%))

2.5

2.7

Up to 3 inclusive

Stable(1)

Hazard class (GOST 12.1.007), fire
safety assessment (GOST 30244)

4th class (low-hazard substances); Non-combustible
material

Study of the Properties of Slag-Based Cold Asphalt Concrete Produced …

317

The metallurgical slag of the studied samples exhibits high strength properties,
corresponding to grade 1200 and class 1 for resistance to crushing and wear. Frost
resistance is F150, indicating low mass loss after multiple freeze–thaw cycles. The
average content of dust-like and clay particles is minimal, ensuring good adhesion
of components in asphalt granulate concrete mixes. The slag is characterized by
structural stability against disintegration and low activity, maintaining stable physical properties over time. All these characteristics allow classifying this material
as environmentally safe and suitable for construction of motor roads and other
structures.
The asphalt granulate was sampled during the milling of the top pavement layer
on a main street in the city of Volgograd. The residual content of road bitumen in the
asphalt granulate was determined by ignition of the binder method and amounted to
4.97% at the binder dosage included in 100% of the asphalt concrete mix. The binder
was washed out to obtain an aggregate, which was then tested for grade according to
crushing 600 (average mass loss of 17.4%). The granulometric composition of the
sampled asphalt granulate complies with the requirements of regulatory documents.
The conditional designation according to GOST R 55052-2012 [3] is 25 AG 0/20,
and according to GOST R 59118.1-2020 [18], it is RAP 0.063-22.4 B. In terms of
foreign impurities, the granulate belongs to category 1.
The selection of the grain size composition for the asphalt granulate concrete mix
was carried out based on the limits of full passes regulated by ODM 218.6.1.0052021 [12] for AGBS 16. Using a calculation method, the possible limits for varying
component contents in the mix were established to ensure optimal granulometric
composition. The required amount of new bitumen was determined according to the
following basic mixture recipe:
•
•
•
•

Asphalt granulate – 65%
Slag crushed stone 8–22.4 mm – 25%
Slag crushed stone 0–4 mm fraction – 10%
Bitumen BND 70/100 – 2.5%; 3.0%; 3.5% of the mineral part’s weight.

For the preparation of mixtures, a cold technology was adopted, involving the
addition of bitumen heated to a temperature of 160 °C into a pre-mixed, moistened
mineral material with 5% water introduced to ensure uniform dispersion of the binder.
The total mixing time of the material in the laboratory mixer did not exceed 3 min.
The physico-mechanical properties (Table 2) of the prepared mixture demonstrated
the validity of the adopted component ratios, with the possibility of meeting the
requirements of ODM 218.6.1.005-2021 [12].
The physico-mechanical properties of the prepared asphalt granular concrete
mixture are characterized by increased water absorption of 6.2%, exceeding the
established requirement of 6.0%, and low water resistance of 0.61, which is below
the necessary level of 0.65. This is likely due to an insufficient amount of organic
binder in the mixture and its porosity. Nevertheless, the compressive strength significantly exceeds regulatory requirements at temperatures of 50 °C (0.96 MPa) and

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A. I. Leskin et al.

Table 2 The physico-mechanical properties of the asphalt granular concrete mixture with a newly
added bitumen content of 3.0% by weight of the mineral part
Indicator name

ODM 218.6.1.005-2021 requirements [12] for
asphalt granular concrete AGBS-16-V-P

Actual
value

Water saturation of samples
molded from AGBS, (%)

No more than 6.0

6.2

Water resistance

No less than 0.65

0.61

Compressive strength at 50 °C,
(MPa)

No less than 0.9

0.96

Compressive strength at 20 °C,
(MPa)

No less than 1.3

2.47

Indirect tensile strength at 20 °C,
(MPa)

No less than 0.15

0.37

Indirect tensile strength at 40 °C,
(MPa)

No less than 0.03

0.05

Average density p, (g/cm3 )

Not regulated

2.46

Sample swelling, (%) by volume

Not regulated

0.00

Compressive strength at 20 °C in
water-saturated state (MPa)

Not regulated

1.5

Long-term water saturation
strength, (MPa)

Not regulated

0.83

20 °C (2.47 MPa). The indirect tensile strength also meets the established requirements at 20 °C and amounts to 0.37 MPa. To determine the optimal content of all
components in the mixture, a series of experiments was conducted.

3 The Study Investigates the Influence of Slag Fillers
and RAP Content on the Physico-Mechanical Properties
of Asphalt Granular Concretes
To assess the influence of slag fillers and RAP content on the physico-mechanical
properties of asphalt granular concrete, a mathematical design of a three-factor experiment was carried out, involving the construction of an orthogonal central composite
plan. The following factors were varied (Table 3), and the planning matrix was
established (Table 4):
A regression analysis of the factorial experiment results was conducted, with the
calculation of regression equations for the following indicators: water absorption
(W ), compressive strength at 20 °C (R20), and compressive strength at 50 °C (R50)
W = 5.97 − 0.95X3 − 0.582X1 + 0.5X2 − 0.369X32
+ 0.207X12 − 0.436X22 + 0.025X3 X1 − 0.025X3 X2

(1)

Study of the Properties of Slag-Based Cold Asphalt Concrete Produced …

319

Table 3 Variation of mixture component content
№

Name of the
variable factor

Factor
designation

Factor value at Variability
the zero level interval X
X

Range of factor
variation
−1

Content of asphalt
granulate, (%)

Content of
X2
metallurgical slag
fraction 8–22.4 mm,
(%)

Bitumen content,
(%) over 100%

3.0

0.5

2.50

3.50

Table 4 Experimental planning matrix
No. of
experiment

Coded factors and their values
X1

Actual (natural) factor values, mass (%)
Asphalt
granulate
content, (%)

Content of
metallurgical slag
fraction 8–22.4 mm,
(%)

Bitumen
content, (%)
over 100%

−1

2.50

−1

2.50

−1

2.50

−1

-1

3.50

−1

2.50

−1

3.50

−1

3.50

3.00

−
1.215

58.93

3.00

−
1.215

18.93

3.00

−
1.215

2.40

+
1.215

71.08

3.00

+
1.215

31.08

3.00

+
1.215

3.60

320

A. I. Leskin et al.

R20 = 2.488 + 0.058X3 + 0.1123X1 + 0.2676X2
− 0, 2299X32 − 0, 0572X12 − 0.1453X22
+ 0.0338X3 X1 − 0.0262X3 X2 − 0.0313X1 X2

(2)

R50 = 0.9588 − 0.086X3 − 0.069X1 + 0.12X2 − 0.0937X32 − 0, 0192X12
− 0.0497X22 + 0.0338X3 X1 + 0.0312X3 X2 − 0.0313X1 X2

(3)

The graphical representations of the response functions (response surfaces) were
obtained for the following indicators: water absorption (W )—Fig. 1, compressive
strength at 20 °C (R20)—Fig. 2, and compressive strength at 50 °C (R50)—Fig. 3.

Fig. 1 The response surface for the water absorption indicator (W, %)

Study of the Properties of Slag-Based Cold Asphalt Concrete Produced …

Fig. 2 The response surface for the compressive strength limit at 20 °C (R20, MPa)

Fig. 3 The response surface for the compressive strength limit at 50 °C (R50, MPa)

321

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A. I. Leskin et al.

4 The Influence of the Modifier Based on a Secondary
Product from Hydrolysis Production on the Strength
and Water Resistance Indicators of the Obtained
Asphalt–granular Concretes
To enhance the strength characteristics and water resistance of the developed asphalt–
granular concrete mixture, it is proposed to use a composition based on a secondary
product from hydrolysis production that exhibits properties of anionic surfactants—
specifically, a molecule with difility, which is associated with the presence of polar
(hydrophilic) and non-polar (hydrophobic) parts within the molecule. This structure
enables the molecules to penetrate microcracks in the porous material and, upon
sorption on its surface, to engage in a wedge-breaking mechanism. The developed
composition includes various organic acids, alcohols, and polymers, which have the
potential to improve the adhesion of bitumen to mineral materials, thereby increasing
the overall durability of the asphalt–granular concrete [19, 20]. The introduction of
such a modifier can potentially improve the following key characteristics:
• Increased compressive and tensile strength. Organic additives can enhance intermolecular bonds within the bitumen matrix, improving load distribution and
reducing the risk of cracking.
• Improved water repellency. Thanks to the hydrophobization of mineral particle
surfaces, the coating becomes less susceptible to moisture penetration, which
decreases the likelihood of cracks and erosion.
• Greater resistance to aging. The addition of active molecules slows down
degradation processes in the bitumen, extending the service life of the pavement.
The preparation of the modifier based on a secondary product of hydrolysis production was carried out as follows: powdered technical lignosulfonate was introduced
into water heated to 50 °C, followed by stirring until the solution stabilized, and
then cooled to 20 °C. The modifier was added to a pre-mixed mixture with an
unchanged composition: asphalt crumb – 65%, metallurgical slag crushed stone
8–22.4 mm – 25%, metallurgical slag crushed stone 0–4 mm – 10%, bitumen BNd
70/100 – 3.0% by weight of the mineral part, and the modifier (M) – 5% of the
mineral part’s weight. The physico-mechanical properties of asphalt crumb concrete
at lignosulfonate concentrations in the solution of 10%, 20%, and 50% are presented
in Table 5.
Based on the obtained results and previous studies, the following hypothesis can
be proposed regarding the mechanism of influence of a composition based on a
secondary product of hydrolysis production on asphalt crumb concrete mixes: the
modifier creates a hydrophobic film on the surface of the mineral filler, penetrates
into pores, capillaries, and microcracks of both metallurgical slag and exposed areas
of the mineral filler surface in the asphalt crumb, and exerts a coagulating effect on
small filler particles.
Additionally, an increase in the foamability of the introduced bitumen has been
observed during dispersion. Thus, at low concentrations of the composition solution,

Study of the Properties of Slag-Based Cold Asphalt Concrete Produced …

323

Table 5 Physical and mechanical properties of asphalt granulate concrete with different ratios of
modifying composition
ABGS

ABGS +
10% М

ABGS +
20% М

ABGS +
50% М

2.46

2.48

2.50

2.56

5.8

4.3

4.1

2.4

0.05

2.47

2.72

2.48

1.69

Flexural
strength in
water-saturated
state, MPa

1.5

1.76

1.58

1.66

Flexural
strength after
long-term water
saturation, MPa

0.83

0.92

0.65

0.51

Indicator

Requirements of ODM
218.6.1.005–2021
Base layers

Cover layers

Average density
Water saturation No more than
8.0

No more than
6.0

Swelling
Flexural
strength at
20 °C, MPa

No less than
1.0

No less than
1.3

Flexural
strength at
50 °C, MPa

No less than
0.6

No less than
0.9

0.96

0.91

0.81

0.87

Water
permeability
coefficient

No less than
0.60

No less than
0.65

0.61

0.65

0.64

0.98

Indirect tensile
strength at
20 °C, MPa

No less than
0.15

0.37

0.41

0.38

0.27

Indirect tensile
strength at
40 °C, MPa

No less than
0.03

0.05

0.04

TSR (Water
resistance
coefficient)

No less than
0.50

No less than
0.65

0.57

0.67

0.64

0.77

No more than
0.25

0.09

0.06

0.07

0.09

Homogeneity of No more than
mixture Cv
0.30

the diffusion of bitumen’s oil fractions into the pores of the filler is reduced, enhancing
the surface treatment efficiency of the grains. However, at higher concentrations of
lignosulfonate in the solution, the adhesion between bitumen and filler decreases,
which is reflected in a reduction of the compressive strength limit at 20 °C.

324

A. I. Leskin et al.

5 Conclusion
An analysis of the current state of technology for the application of metallurgical slags
as fillers in asphalt crumb concrete mixes has been conducted. Methods, features,
and limitations of using slag crushed stone in cold asphalt regeneration have been
identified.
Compositions of asphalt crumb concrete with slag fillers containing increased
amounts of RAP (reclaimed asphalt pavement) have been developed. Based on experimental research, a mathematical model has been created to determine the influence
of slag filler content, asphalt granulate, and dispersed binder on the physical and
mechanical properties of asphalt crumb concrete.
For the first time, the use of a modifier based on a secondary product of hydrolysis
production has been proposed to improve the strength, water absorption, and water
resistance indicators of slag asphalt crumb concrete.
The proposed technology enables the reuse of resources (asphalt granulate and
industrial waste), reducing their volume and the need for new raw materials. By
optimizing the composition and production method, costs for manufacturing and
transportation are decreased, which is beneficial from both economic and ecological
perspectives.
Acknowledgements The research was supported by a grant in the form of subsidies from the
Committee of Economic Policy and Development of the Volgograd Region, No. 3, dated December
12, 2024, on the topic “Development of technology for the production of asphalt-granular concrete
mixtures for road surfaces in the Volgograd region.”

References
1. Lupanov AP, Silkin VV (2019) Reuse of asphalt concrete at the asphalt concrete mixing plant:
monograph. Ekonom-Inform, Moscow, p 191
2. Lupanov AP, Gladyshev NV, Silkin AV, Silkin VV, Rudakova VV (2018) Reuse of old asphalt
concrete granulate. Roads of Russia, No. 1(103)
3. GOST 55052–2012 (2013) Old asphalt concrete granulate. Technical specifications. Standartinform, Moscow, pp 61
4. Bakhrah GS (1998) Restoration of coatings and non-rigid pavements. Sci Technol Road Indus
3:18–21
5. Gladyshev NV (2015) Improvement of technology for preparing and laying asphalt concrete
mixes with the addition of old asphalt concrete granulate: abstract of candidate thesis in
engineering science. Moscow, pp 22
6. Shtabinsky VV, Skvortsov EA, Grakovich DP (2008) Studies of aggregate and grain size
composition of asphalt granulate. Automot Roads Bridges 2:68–72
7. Chernykh DS, Stroeva DA, Zadorozhny DV (2013) Assessment of the influence of the amount
of asphalt granulate and its delivery technology on the properties of prepared asphalt concrete
mixes. IVD 4(27). https://cyberleninka.ru/article/n/otsenka-vliyaniya-kolichestva-asfaltogr
anulyata-i-tehnologii-ego-podachi-na-svoystva-prigotavlivaemyh-asfaltobetonnyh-smesey.
Accessed 07 July 2025

Study of the Properties of Slag-Based Cold Asphalt Concrete Produced …

325

8. Epps JA, Terrel RL, Little DN, Holmgreen RJ (1980) Guidelines for recycling asphalt
pavements. J Assoc Asphalt Paving Technol 49:144–176
9. Symposium Recycling of Asphalt Pavement (1997) J Assoc Asphalt Paving Technol 49:685–
802
10. Kanhal PS, Mallick RB (2002) Development of rational and practical mix design system for
full depth reclaimed (FDR) mixes. University of New Hampshire. Final Report, pp 1–103
11. Sunyi GK, Usmanov KH, Feinberg ES (1984) Reclaimed road asphalt concrete. Transport,
Moscow, p 118
12. ODM 218.6.1.005-2021 (2021) Methodological recommendations for restoring asphalt
concrete Pavements and Bases of Roadways by Cold Rejuvenation (with Amendment). Issued
based on the order of the Federal Road Agency dated February 17, 2021, No. 570-r, with
amendments adopted by the order of the Federal Road Agency dated January 18, 2022, No.
18-r., Moscow, pp 50
13. Pimenov AT, Pribylov VS (2018) Modification of metallurgical slag mixtures to enhance their
hydraulic activity. Modern Mater Equipm Technol 6(21):106–112
14. Tulaev AYa, Korelev MV, Isayev VS, Yumashev VM (1986) Road pavements using slags.
Transport, Moscow, pp 221
15. Goncharova MA, Bondarev BA, Shtefan GE (2005) Asphalt concrete on slag aggregates:
Monograph. LGTU, Lipetsk, pp 181
16. Prozorova LA (2011) Development of compositions and prediction of durability of crushed
stone mastic asphalt concrete on slag aggregates: Ph.D. dissertation in technical sciences
(specialty 05.23.05 “Construction Materials and Products”). Lipetsk, pp 140
17. GOST 32826–2014 (2019) Roads of general use. Crushed stone and slag sand. Technical
requirements. Standartinform, Moscow, pp 15
18. GOST R 59118.1—2020 (2020) Recycled asphalt concrete for roads of general use.
Specifications. Standartinform, Moscow, pp 10
19. Leskin AI, Aleksikov SV, Gofman DI (2020) Organic composite binder improving the physical
and mechanical properties of low-strength stone materials. In: IOP conference series: materials
science and engineering, Sochi, pp 022002. https://doi.org/10.1088/1757-899X/962/2/022002
20. Gofman DI (2021) Low-strength carbonate rocks processed with a modified composition
based on the hydrolysis adduct: Ph.D. dissertation in technical sciences (specialty 05.23.05
“Construction Materials and Products”). Volgograd, pp 147

Study of the Reduction of the Bearing
Capacity of a Steel-Reinforced Concrete
Floor Under the Influence of Various
Factors
Yu. A. Shaposhnikova

Abstract The objective of this work was to study the influence of such factors as
the overweight of the slab with concrete mix at the concreting stage and complete
loss of adhesion of the corrugated sheeting to concrete on the strength of composite
slabs at the operational stage. The object of the study was single-span orthotropic
composite slabs made on permanent formwork in the form of corrugated sheeting of
grades H75, H144, H153 and TRP200. The coefficients of utilization of composite
slabs at the operational stage were determined, obtained by increasing the weight
of concrete mix with the development of the ultimate deflection greater than the
standard at the concreting stage of composite slabs. The factors influencing the
decrease in maximum bending moments in composite slabs at the operational stage
with complete loss of adhesion of the corrugated sheeting to concrete were analyzed.
The obtained data indicate the need to increase the working reinforcement of the slabs
when corrugated sheet deflections occur at the concreting stage for different grades
of corrugated sheet at different load levels and slab spans. Based on the results of
the study, a conclusion was made about the need to carry out clarifying strength
calculations when corrugated sheet deflections occur at the concreting stage, as well
as under the influence of such loads and impacts that increase the risks of loss of
adhesion during the operation stage.
Keywords Combined structure · Deflection · Corrugated sheet · Permanent
formwork · Profiled sheeting · Reinforced concrete slab · Steel-reinforced concrete
structures · Strength

Yu. A. Shaposhnikova (B)
Moscow State University of Civil Engineering, Moscow, Russia
e-mail: yuliatalyzova@yandex.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_27

327

328

Yu. A. Shaposhnikova

1 Introduction
Steel-reinforced concrete structures are a promising and rapidly developing area of
monolithic construction. Combined structures are used in the design of warm and
cold parking buildings, shopping and office centers and other civil buildings [1, 2].
Steel profiled sheeting is used in steel-reinforced concrete floors as permanent
formwork, as well as external reinforcement. The function of the profiled sheeting
as external reinforcement increases the bending rigidity and strength of the slab
structure. And the function of the sheet as permanent formwork protects concrete
from aggressive external environmental influences, thereby increasing its durability
[3–5].
Many Russian and foreign scientists have studied various issues of the operation of
composite floors supported by metal beams. Zamaliev et al. studied the stress–strain
state of a combined floor as a whole, taking into account the pre-operational state
of its elements [6, 7]. The works of Bedov and Shaposhnikova present an analysis
of the influence of various factors, such as the type of corrugated sheeting, span and
thickness of the slab, etc., as well as defects in the slab structure at the concreting
stage, on the deflections and strength of the composite floor [8–10].
The features of calculating combined floors are presented in the works of
Urgalkina et al. [11–13]. Albarram et al. studied the influence of rib geometry and
type of profiled sheet on the characteristics of composite beams and the features
of their operation [14]. Chaparanganda and Lazovsky were engaged in the creation
of a methodology for designing monolithic floor slabs with external profiled reinforcement made of steel sheets based on the use of material stress–strain diagrams
[15]. The work of Vasdravellis et al. presents an experimental and numerical study of
the ultimate strength of steel–concrete composite beams subjected to the combined
effects of bending and axial compression [16].
In the work of Almazov and Arutyunyan, a comparison of the design of steelreinforced concrete floor slabs according to Eurocode 4 and Russian standards is
presented [17].
The topic of numerical modeling of various combined structures is widely
presented in a large number of different studies, for example, in the works of: Tamayo
et al. [18, 19]. Reginato et al. considered numerical models of a steel-reinforced
concrete floor, as well as the influence of various factors on the result of a numerical
experiment [20].
In addition to the advantages described, combined structures also have a number of
disadvantages and are quite complex to design and construct [1, 5, 8]. As mentioned
above, corrugated sheets serve as formwork during concreting at the construction
stage and are also load-bearing reinforcement during operation. Therefore, one of
the most important factors is to ensure reliable joint operation of the corrugated
sheets and floor concrete. This issue has been studied by many researchers. Tonkikh
and Chesnokov were engaged in the calculation and assessment of the strength and
deformability of corner anchor stops in monolithic steel-reinforced concrete floors

Study of the Reduction of the Bearing Capacity of a Steel-Reinforced …

329

[21]. Sougata and Hellmark studied the operation of various anchor connectors operating in shear and shear [22, 23]. Suvaid et al. [24] were also engaged in the study
of the joint operation of various components of the floor.
Also, the joint work of corrugated sheets with concrete can be greatly affected
by the impact of aggressive environments and subsequent corrosion, as well as fire
exposure. For example, in the work of Davidenko and Artemenko, an assessment
of fire resistance is given based on the criterion of loss of bearing capacity of steelreinforced concrete floor slabs [25]. In the scientific literature, many studies are
devoted to the loss of adhesion of corrugated sheets with concrete due to various
factors [19, 21]. A large number of works are devoted to corrosion processes in bridge
structures, however, the issues of corrosion processes specifically in steel-reinforced
concrete floors are practically not covered [26, 27].
The specific features of the operation of steel-reinforced concrete floors, as well
as poorly studied areas and non-standard operating conditions of such structures,
motivate research engineers to study in detail their stress–strain state at all stages of
the life cycle. The purpose of this work was to study the influence of such factors
as the overweight of the slab with concrete mix at the concreting stage and the
complete loss of adhesion of the profiled sheeting to the concrete, on the strength of
steel-reinforced concrete slabs at the operational stage.

2 Materials and Methods
The object of the study is a composite floor slab laid on permanent formwork made of
profiled sheeting with the smallest manufactured thickness of the corrugated sheet.
We used corrugated sheets with compressed wide shelves with ribs on the walls of
the corrugated sheets of the following grades: H75 with a thickness of t = 0.7 mm
with a total slab thickness of h = 150 mm; H144, t = 0.8 mm, h = 200 mm; H153,t =
0.8 mm, h = 250 mm according to GOST 24045–2016; TRP200 according to GOST
R 52246, t = 0.9 mm, h = 300 mm. The yield strength of the corrugated sheet steel
is Ry = 250 N/mm2 . The slab is single-span on corrugated sheeting, the spans varied
from 3 to 6 m with a step of 0.5 m. The slab concrete is heavy, class B20. The slab is
reinforced with non-stressed reinforcement: a mesh of Ø10 A500C is laid over the
entire area of the slab in the upper zone with a step of 200 mm in both directions with
az = 30 mm; in each rib, the reinforcement is class A500C (according to strength
calculation), az = 30 mm. The load from the floor structure is taken to be 1 kPa, the
useful load was taken to be 1.5, 3, 4 and 5 kPa.
According to SP 266.13330, the profiles that perform the functions of the working
reinforcement of the slab must be able to transmit horizontal shear forces along the
contact surface with concrete. Joint operation of the decking with concrete during the
slab’s operation in transverse bending must be ensured by the presence of stampings
in the form of local dents or bulges (riffles) with a depth of 3 to 5 mm on the walls
of the corrugations. The thickness of the steel profiles is recommended by standards

330

Yu. A. Shaposhnikova

Fig. 1 Geometric dimensions of the section of the steel-reinforced concrete floor slab

from 0.7 to 1.5 mm. The geometric dimensions of the steel-reinforced concrete floor
slab are shown in Fig. 1.
According to SP 20.13330, the deflection from standard loads f n should not exceed
1/150 of the span l for floors hidden from view by suspended ceilings. According to
SP 266.1325800, if the deflection of the flooring is more than 1/10 of the slab section
height, an additional load from the dead weight of freshly laid concrete Δqb should
be taken into account, which is equal to qb = 0.7 · γ · fn , where γ is the safety factor
taken depending on the method of laying the mixture (with a concrete pump or from
a bucket). However, at the construction site, the initial deflections of the corrugated
sheet are not always clearly monitored during the concreting of structures. If it does
occur, its manifestation is considered a minor defect [8]. Recalculation with the
increased weight of the reinforced concrete slab is usually not performed, since this
information often does not reach the designer.
The relationship between the maximum deflections of corrugated sheets according
to the standards f = l/150 and the maximum deflections in parts from the total height
of the slab at hpl = 300, 250, 200, 150 mm is presented in Table 1. The cells for which
the maximum deflection of corrugated sheets in parts from the span l is greater than
the deflection hpl /10 in parts from the height of the slab section, when exceeding
which it is necessary to calculate the additional load from the weight of freshly laid
concrete, are marked in red.
Thus, from Table 1 it is clear that for most spans and floor thicknesses it is
necessary to take into account the additional mass of freshly laid concrete mix.
For further calculations of the slab strength at the operational stage, the full
primary deflection of the corrugated sheet at the concreting stage f max was taken
taking into account the parabolic part of the load from the concrete mix (Fig. 2), but
not more than the limit, equal to 1/150 of the slab span l. This is due to the fact that
the corrugated sheet does not pass the strength test at the concreting stage of the slab
with the limit standard deflection greater than l/150.
The maximum bending moment M p,max from a parabolic load for a single-span
beam is calculated in accordance with (1) according to [28], and the bending moment
M d from a uniformly distributed part of the load according to the well-known formula

Study of the Reduction of the Bearing Capacity of a Steel-Reinforced …

331

Table 1 The relationship between the maximum deflections of corrugated sheets and the maximum
deflections in parts of the total height of the slab
h/10 ratio for profiles

Spansl, m
3

3.5

4.5 5

5.5

TRP200, 300 mm

30 30

Н153, 250 mm

25 25

Н114, 200 mm

20 20

Н75, 150 mm

15 15

Maximum deflection of corrugated sheets according to 20 23.3 26.7 30
standards,l/150

33.3 36.7 40

Fig. 2 Load on the slab from the dead weight of concrete during operation, taking into account the
overweight: a—uniformly distributed part of the load; b—parabolic part of the load; f n —maximum
deflection from uniformly distributed part of the load; f max —maximum deflection from full load
(uniformly distributed and parabolic parts of the load); l—calculated span

(2).
Mp,max = 5qp · l 2 /48

(1)

Md = ql 2 /8

(2)

where l—the calculated span of the deck; q—the calculated uniformly distributed
load; qp —the maximum calculated parabolic load.
Thus, the total bending moment from all design loads can be determined according
to (3)
M = Md + Mp,max = ql 2 /8 + 5/48 · qp · l 4

(3)

It is worth paying attention to the fact that due to the increase in the load on the slab
from the dead weight of the concrete, the external moment will increase. But due to
the inevitable increase in the concrete cross-section in the span zone of the composite
slab, the internal moment of the section will also increase due to the overestimated

332

Yu. A. Shaposhnikova

working height of the section h0. However, it is worth noting that the working height
of the section can be considered overestimated only if the lower longitudinal working
reinforcement installed in the ribs of the corrugated sheet does not maintain its design
position, but bends together with the corrugated sheet, which works as permanent
formwork. For the object of study, the longitudinal reinforcement in the ribs of the
corrugated sheet is adopted as rod, class A500C, according to strength calculation,
with diameters from Ø10 to Ø18. The use of reinforcement diameters over 10 mm
virtually eliminates the possibility of its bending due to sufficient rigidity of the rods,
therefore, in the presented work, the possibility of overestimating the working height
of the section in the calculations was not taken into account.
According to SP 266.1325800 “Steel-reinforced concrete structures. Design
rules” at the operational stage, a steel-reinforced concrete slab is calculated as a reinforced concrete structure with external working reinforcement made of steel profiled
sheeting and with flexible rod reinforcement. A continuous reinforced concrete slab,
reinforced with profiled sheeting, in the absence of the calculated flexible reinforcement above the supports, is calculated as a single-span structure. When installing
the calculated rod reinforcement above the slab supports, the forces in the slab are
determined as in a continuous reinforced concrete structure. In the presented work,
a single-span steel-reinforced concrete slab was considered.
The height of the compressed zone of concrete x must satisfy the condition х ≤
ξR · h0 , where h0 is the working height of the section, and ξR = 0.493 is the relative
height of the compressed zone of the section when using longitudinal reinforcement
of class A500C. If the condition is not met, then the thickness of the slab should be
increased, the class of concrete for compressive strength should be increased. It is
also necessary to place additional rod reinforcement in the compressed zone so that
the height of the compressed zone does not exceed the boundary.
According to SP 266.1325800, when the neutral axis is located within the thickness of the slab flange, the height of the compressed zone of the slab section is determined from condition (4). And when calculating the strength of the slab, condition
(5) is checked.
Rb · bf · x = γc · Ry · An + Rs · As − Rsc · As ;

(4)

M ≤ Rb · bf · x(h0 −0, 5x) + Rsc · As · (h0 −a ),

(5)

where An —the cross-sectional area of one corrugation of the deck; As —the crosssectional area of the tensile reinforcement bar; A’s —the cross-sectional area of the
compressed reinforcement bar; Rb —the design compressive strength of concrete;
Ry —the design tensile strength of the steel deck; Rs —the design tensile strength of the
tensile reinforcement bar; Rsc —the design compressive strength of the compressed
reinforcement bar; М—the bending moment in the section of the slab under consideration from full loads; bf —the width of the upper part of the design section; х—the
height of the compressed zone of concrete; а’—the protective layer of the compressed

Study of the Reduction of the Bearing Capacity of a Steel-Reinforced …

333

reinforcement bar; h0 —the height of the working section of the slab; γс —coefficient
of working conditions.

3 Results and Discussion
Table 1 presents the results of the utilization factor of the composite slab at the
operational stage, obtained with an increase in the weight of the concrete mix during
the development of the ultimate deflection l/150 at the concreting stage of composite
slabs. The results were obtained for different spans (3–6 m) and useful load values
(1.5–5.0 kPa) for the grades of corrugated sheets H75, H144, H153 according to
GOST 24045–2016 and TRP200 according to GOST R 52246 and for the most typical
slab thickness for each grade of corrugated sheet (h = 300, 250, 200, 150 mm).
Based on the calculation results from Table 2, it is clear that with the lowest useful
load (1.5 kPa) and the largest span (6 m), the addition of a parabolic load leads to
the greatest excess of the utilization factor of the steel-reinforced concrete slab—by
14–15%.
Table 2 The utilization factor of a steel-reinforced concrete slab obtained by increasing the weight
of the concrete mix during the development of the ultimate deflectionl/150, depending on the span
and the value of the useful load
Brand of
corrugated sheet,
plate thickness
hpl , m

Payload qu ,
kPa

3.5

4.5

5.5

TRP200, 300 mm

1.5

1.02

1.03

1.06

1.10

1.11

1.12

1.14

Н153, 250 mm

Н114, 200 mm

Н75, 150 mm

Utilization factor for span l, m

1.01

1.03

1.05

1.08

1.09

1.10

1.11

1.01

1.02

1.04

1.07

1.08

1.09

1.01

1.02

1,04

1.06

1.07

1.08

1.5

1.02

1.03

1.06

1.10

1.11

1.12

1.13

1.01

1.03

1.05

1.08

1.09

1.10

1.01

1.02

1.04

1.07

1.08

1.09

1.01

1.02

1.04

1.06

1.07

1.08

1.5

1.02

1.04

1.08

1.10

1.11

1.12

1.13

1.02

1.04

1.06

1.08

1.09

1.10

1.11

1.02

1.03

1.05

1.07

1.08

1.09

1.01

1.03

1.05

1.06

1.07

1.08

1.5

1.07

1.09

1.08

1.11

1.13

1.14

1.15

1.05

1.07

1.08

1.09

1.10

1.11

1.12

1.05

1.06

1.07

1.08

1.09

1.10

1.04

1.05

1.06

1.07

1.08

1.09

334

Yu. A. Shaposhnikova

However, it is worth noting that the utilization factor of the composite slab will
be exceeded in the case when the longitudinal working reinforcement is initially
selected without overspending. That is, the excess of the utilization factor specified
in Table 2 is the moment from the parabolic load (due to the manifestation of the
deflection of the decking at the concreting stage) as a percentage in relation to the
moment from the standard loads in the standard calculation. Therefore, the percentage
of excess of the utilization factor will not in all cases affect the need to install an
additional percentage of working reinforcement. Often, during the design process,
reinforcement is adopted with a reserve (from 1–3% to the maximum recommended
15%). The need to install an additional percentage of reinforcement will depend
primarily on the adopted diameter of the longitudinal working reinforcement, as
well as on the load, span and section parameters of the composite slab.
It is worth noting that often when the deflection of the corrugated sheeting develops
to l/150 or more at the concreting stage, the corrugated sheeting often no longer passes
the strength calculation from the weight of the freshly laid concrete mix. Therefore,
considering the effect of additional parabolic load from the weight of the concrete
mix with deflections greater than l/150 is not advisable.
When analyzing the performance of composite slabs with corrugated sheeting, the
following factors should be taken into account in addition to the presented calculations of strength under bending moment. Reinforced concrete slabs must be designed
for the action of transverse forces, and it is also necessary to check the adhesion of
the corrugated sheet to the concrete and calculate the rib on the supports. Particular
attention should be paid to the calculations of the thinnest slabs (h = 150 mm, grade
H75) and thin corrugated sheets (t < 1 mm).
As can be seen from formula 4, the neutral axis position taken into account in the
calculation is greatly influenced by the grade of the corrugated sheet, i.e. its crosssection and the calculated tensile strength of the steel. The loss of adhesion of the
corrugated sheet to concrete can occur due to various factors: due to insufficient size
of the corrugated sheet ribs, due to insufficient resistance of the anchor stops to shear,
as well as due to corrosion damage to the corrugated sheet and concrete. In case of
complete loss of adhesion of the corrugated sheet to concrete, the neutral axis will be
significantly displaced—above the level of the upper flange of the corrugated sheet.
The strength calculation should be made as for a reinforced concrete section of a
T-shaped profile with the neutral axis located in the web. Consequently, the strength
of such a floor will be significantly reduced.

4 Conclusions
Based on the results of this study, general conclusions and recommendations can be
made.

Study of the Reduction of the Bearing Capacity of a Steel-Reinforced …

335

1. The calculation of the total deflections of the corrugated sheet at the concreting
stage of the steel-reinforced concrete slab must be carried out taking into account
the overload of the slab with concrete mixture.
2. For slab spans over 4 m (l ≥ 4 m), thin corrugated sheets (t ≤ 1 mm) do not
pass the strength test at the concreting stage. For corrugated sheets of grades
H75, H144, H153 according to GOST 24,045–2016 for spans over 4 m, it is
recommended to use additional supports with a step of 1–2 m in the span zone
of the corrugated sheet.
3. For TRP200 grade corrugated sheets according to GOST R 52,246 with spans
over 4 m, it is recommended to use corrugated sheets only with compressed
narrow flanges or to use additional supports with a step of 1–2 m.
4. For spans of 3.5 m and above (l ≥ 3.5 m), with useful loads over 3.0 kPa,
deflection at the concreting stage due to the action of a parabolic load from
the increased weight of the concrete mixture may lead to the need to install
reinforcement in the ribs of the slab with an area exceeding the requirements of
the standard calculation.
5. For spans over 3.5 m, it is recommended to check the initial deflections of the
corrugated sheets, even with preliminary installation of additional supports.
6. If a deflection of the composite slab at the concreting stage exceeds l/200, a
mandatory verification calculation of the composite slab strength at the operational stage should be performed, taking into account the additional weight
of concrete from the excessive deflection of the corrugated sheet. Taking into
account the initial deflections of the corrugated sheet allows for a more accurate
assessment of the actual strength of the composite slab for a more complete use
of its bearing capacity at the operational stage.
7. If there are probable risks of loss of adhesion of the corrugated sheet to the
concrete due to various impacts at the operational stage, it is necessary to perform
additional clarifying strength calculations for the operational stage.
8. When concreting composite slabs, it is necessary to supply concrete uniformly,
using a concrete pump, especially when using thin corrugated sheets (t ≤ 1 mm).
Concrete mix supply from a bucket is unacceptable, since excessive local load
in the span zone can lead to abnormal deflections of the corrugated sheet at the
concreting stage and subsequent overload of the slab, and in the worst case, to
the collapse of sections of the corrugated sheet used as permanent formwork.
The obtained data can be used in the design of steel-reinforced concrete floor slabs
and in the inspection of the technical condition of erected steel-reinforced concrete
slab structures.
A further direction of research may be the study of the influence of aggressive
environments on the strength of the steel-reinforced concrete floor.

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References
1. Babalich VS, Androsov EN (2017) Steel-reinforced concrete structures and the prospect of their
application in the construction practice of Russia. The Successes of Modern Sci 4:205–208
2. Nikulina OV, Cymdjankina NJu (2019) Analysis of structural solutions for steel-reinforced
concrete floors. Orenburg horizons: past, present, future. Collection of materials of the AllRussian scientific and practical conference dedicated to the 275th anniversary of the Orenburg
province and the 85th anniversary of the Orenburg region. OOO “Frontier”, Orenburg region,
pp 157–161
3. Budoshkina KA, Kuznetsov VS, Murlysheva YA et al (2018) Analysis of the operation of
combined beams in a wide range of loads. Eng J Don 2. http://www.ivdon.ru/ru/magazine/arc
hive/N2y2018/4925
4. Lu L, Ding Y, Ya G et al (2022) Flexural performance and design method of the prefabricated
RAC composite slab. Structures 38:572–584. https://doi.org/10.1016/j.istruc.2022.02.022
5. Yao G, Chen Y, Yang Y et al (2023) Investigation on buckling performance of prefabricated
light steel frame materials under the action of random defects during construction. Materials
16(16):5666. https://doi.org/10.3390/ma16165666
6. Tamrazyan AG, Arutyunyan SN (2017) Investigation of initial stresses and deflections of
profiled deck arising during the construction of composite floor slabs. The Safety of the
construction Fund of Russia. Problems and solutions 1:139–146
7. Zamaliev FS, Tamrazyan AG (2021) To calculation of steel-reinforced concrete ribbed plates
for refurbished floors. Build Reconstruct 5(97):3–15. https://construction.elpub.ru/jour/article/
view/401/377?locale=ru_RU. https://doi.org/10.33979/2073-7416-2021-97-5-3-15
8. Bedov AI, Shaposhnikova YuA (2024) Bearing capacity of steel-reinforced concrete floor
elements before the operation period. Magazine of Civil Eng 17(1). https://doi.org/10.34910/
MCE.125.1
9. Shaposhnikova YuA (2024) Analysis of the influence of various factors on the deflections of
profiled flooring during slab concreting. Eng J Don 5(113):551–568. http://www.ivdon.ru/upl
oads/article/pdf/IVD_71N5y24_Shaposhnikova.pdf_c46918c268.pdf
10. Shaposhnikova YuA (2024) The influence of various factors on the deflections and strength
of profiled sheeting at the stage of concreting a steel-reinforced concrete slab. Reinforced
Concrete Struct 7(3):44–53. https://doi.org/10.22227/2949-1622.2024.3.44-53
11. Urgalkina DA (2019) Application of deformation model to calculation of reinforced concrete
lines on steel profile sheet. World Sci 6(27):527–531
12. Zulpuev AM, Abdullaev UD, Iranova NA et al (2025) Calculation of strength and movement
of slabs steel profiled deckings under local loads. In the World of Sci Educ 1:150–159. https://
doi.org/10.24412/3007-8946-2025-152-150-159
13. Kuznetsov V, Shaposhnikova Yu (2018) Features of calculation and design of complex concrete
monolithic slabs. In: MATEC web of conferences, pp 251.https://doi.org/10.1051/matecconf/
201825102027
14. Albarram A, Qureshi J, Abbas A (2020) Effect of rib geometry in steel-concrete composite
beams with deep profiled sheeting. Int J Steel Struct 20(3):931–953. https://doi.org/10.1007/
s13296-020-00333-5
15. Chaparanganda E, Lazouski D (2024) Design method for cast in-situ floor slab with external
profiled steel deck as reinforcement. In: Architectural and construction complex: problems,
prospects, innovations, pp 73–83
16. Vasdravellis G, Uy B, Tan EL et al (2015) Behaviour and design of composite beams subjected
to sagging bending and axial compression original research. J Constr Steel Res 110:29–39.
https://doi.org/10.1016/j.jcsr.2015.03.010
17. Almazov VO, Arutjunjan SN (2015) Design of composite reinforced concrete slabs according
to Eurocode 4 and Russian recommendations. Proc Moscow State Univers Civil Eng 8:51–65
18. Tamayo JLP, Franco MI, Morsch IB et al (2019) Some aspects of numerical modeling of steelconcrete composite beams with prestressed tendons. Latin Amer J Solids Struct 16(7). https://
doi.org/10.1590/1679-78255599

Study of the Reduction of the Bearing Capacity of a Steel-Reinforced …

337

19. Trofimov DS (2022) Research of monolithic floor performance on metal beams with broken
adhesion using numerical model. Young Scientist 21(416):73–78
20. Reginato LH, Tamayo JLP, Morsch IB (2018) Finite element study of effective width in steelconcrete composite beams under long-term service loads. Latin Amer J Solids Struct 15(8).
https://doi.org/10.1590/1679-78254599
21. Tonkih GP, Chesnokov DA (2024) Strength and ductility evaluation of L-shape shear connectors
in composite floors. Reinforced Concrete Struct 5(1):27–44. https://doi.org/10.22227/29491622.2024.1.27-44
22. Sougata C, Umamaheswari N (2022) Numerical investigation of steel-concrete composite
beams using flexible shear connectors. AIMS Mater Sci 9(5):668–683
23. Hällmark R, Collin P, Hicks SJ (2019) Post-installed shear connectors: push-out tests of coiled
spring pins versus headed studs. J Constr Steel Res 161:1–16. https://doi.org/10.1016/j.jcsr.
2019.06.009
24. Suwaed ASH, Karavasilis TL (2020) Demountable steel-concrete composite beam with fullinteraction and low degree of shear connection. J Constr Steel Res 171:106–152. https://doi.
org/10.1016/j.jcsr.2020.106152
25. Davidenko AI, Artemenko AA, Borisov SD (2024) Assessment of fire resistance by the criterion
of loss of bearing capacity of reinforced concrete floors with external reinforcement. Lugansk
State University Named After Vladimir Dahl 3(81):21–26
26. Ovchinnikova T, Marinin A, Ovchinnikov I (2014) Corrosion and corrosion protection of
reinforced concrete bridge structures. Internet magazine Naukovedenie 5(24):11
27. Nikonorov AN, Zaitsev AA (2020) Protection of bridge structures from atmospheric corrosion.
Problems Sci 1(49):12–15
28. Umansky AA (1972) Directory of the designer of industrial, residential and public buildings
and structures. In: Calculated-theoretical. 2nd edn. Stroyizdat, Moscow

Analysis of the Efficiency of Pavement
Structures at Automatic Weighing
Stations
R. A. Tonkikh, A. O. Glazachev, R. M. Akhmetshin, D. T. Murtazin,
and V. V. Sokolova

Abstract The urgency of deploying automated weighting and dimension control
stations on highways is explained due to the significant growth of freight traffic
using road transport. The study substantiates the critical issue of pavement wheel
tracking within weighing and dimension control stations. Addressing this problem is
essential because road surface conditions at measurement points significantly influence the accuracy of controlled parameters. To minimize errors in dynamic vehicle
weighing, maintaining specified pavement smoothness standards must be prioritized.
The article analyzes the operating control stations in the Republic of Bashkortostan
and Krasnodor Territory. The adopted structure of road pavements in various sections,
both with rigid and non-rigid pavements, is described herein. The results of computational analysis of wheel tracking depending on the ambient temperature effect for
different types of pavements are given. Findings indicate that elevated temperatures
cause softening of the organic binder leading to reduced strength characteristics
in asphalt concrete layers, thereby consequently accelerating plastic deformations
contributing to rapid wheel tracking formation. These deficiencies are absent in
cement concrete pavements. The study also examines the influence of base stiffness
in both rigid and non-rigid pavement structures. The results demonstrate that a low
elastic modulus of the base layer significantly increases residual vertical deformations, particularly within wheel load zones, thereby requiring for base reinforcement during engineering, especially under heavy traffic conditions and frequent
heavy vehicles. This effect is observed across all pavement types, though concrete
pavements exhibit reduced susceptibility due to their superior load-distribution
capacity.
Keywords Weighing stations · Wheel tracking · Plastic deformations · Pavement
stiffness

R. A. Tonkikh · A. O. Glazachev · R. M. Akhmetshin (B) · D. T. Murtazin · V. V. Sokolova
Ufa State Petroleum Technological University, Ufa, Russia
e-mail: ranisahmetshin@mail.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_28

339

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R. A. Tonkikh et al.

1 Introduction
Global trends in transportation infrastructure have significantly influenced Russia’s
road industry. The sector has already automated its core processes and is now
focused on implementing end-to-end digital solutions and developing advanced
digital services.
Currently, Russia is implementing the socially oriented “Safe Quality Roads”
national project across 84 regions. This initiative is transforming the country’s
transport infrastructure through: the construction of modern highways, bridges, and
overpasses; and implementation of advanced technologies and materials [1].
Road freight remains the most sought-after mode of cargo transportation globally.
By 2027, its share of the worldwide logistics market is projected to reach 39% of
total market volume, surpassing all other transport modes by 6–10% or more.
The road utilization intensity in Russia significantly exceeds that of neighboring
and adjacent states, which is due to geopolitical and economic factors of transport
infrastructure development, including high-volume freight flows between Europe
and Asia, with road network development, primarily following West-East highway
corridors and to a lesser extent from South to North. While in the central part of
Russia the road network is more developed from South to North, in the East of the
Volga region the main transportation network is developed from West to East.
The formation of wheel tracking on roadways significantly compromises traffic
safety through multiple mechanisms. Consequently, enhancing pavement resistance
thereto and deformation is a matter of urgency.
The implementation of Intelligent Transport Systems (ITS), integrated with such
subsystems as automated traffic monitoring cameras and weigh-in-motion (WIM)
and dimension control stations is aimed at improving the level of safety and security
in highways.
Weight and dimension control serves as a proven method for preventing pavement
destruction. This requires the construction of specialized Automated Weight and
Dimension Control Stations (hereinafter referred to as AWDCS).
The primary condition for proper functioning of weigh-in-motion equipment is
maintaining strict longitudinal and transverse evenness of the pavement at AWDCS
measurement zones. The accuracy of weight measurements is significantly influenced by the road surface condition in these designated areas. To minimize weighing
errors during vehicle movement, the pavement must meet enhanced smoothness
requirements, which are substantially stricter than those for regular road sections.
The key monitored parameter includes: longitudinal and transverse evenness. While
such an important indicator as the tire-to-surface friction coefficient does not affect
the accuracy of vehicle weight measurements.
According to some foreign data [2, 3], the required range for wheel tracking is
from 3 to 10 mm, and under the International Roughness Index (IRI)—from 1.3 to
4.0 m/km..

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According to 5.2 of GOST 50597–2017 [4] “National Standard of the Russian
Federation. Automobile roads and streets. The requirements to the level of maintenance satisfied the traffic safety. Methods of testing”, the permissible wheel tracking
depth for Category III roads is up to 30 mm, while the International Roughness Index
(IRI) requirements are as follows: at commissioning stage (GOST 59120–2021 [5]):
2.4–2.6 m/km, and during operation (GOST 50597–2017 [4]): 5.0–5.5 m/km.
One of the first regulatory documents governing the requirements for the
access ways to Automated Weight and Dimension Control Stations (AWDCS) is
GOST 33242–2015 [6] (“Interstate Standard. Automatic instruments for weighing
road vehicles in motion and measuring axle loads. Metrological and technical
requirements. Tests”).
Key Provisions of GOST 33242–2015 [6].
1. Development and Approval: The standard was developed by the Belarusian
State Institute of Metrology (BelGIM) and submitted by the State Committee
for Standardization of the Republic of Belarus.
2. Scope: The standard applies to automatic weighing instruments installed at
designated weighing sites for dynamic weighing of road vehicles in motion.
3. Factors Affecting Measurement Accuracy: Clause 4.7 specifies the key operational conditions including the permissible temperature range and power supply
requirements to ensure correct operation of the equipment.
4. Access ways requirements (Annex B, Clause B.4)
“Each of the sections of the access ways in front of and behind the loading device
shall be at least 16 meters long. Prior to testing (and implementation of the standard),
each State may set a different minimum length for the access sections, either longer
or shorter. Longitudinal slopes are not permitted in these sections to prevent load
redistribution between the vehicle axles.
Comment on applicability in the Russian Federation: Paragraph B.4 contradicts
the requirements of the Russian legislation, in particular the provisions of PNST 663–
2022 “Public Roads. Automatic weight and gauge control points. Design requirements” [7] and Order of the Ministry of Transport of the Russian Federation No. 348
of 31.08.2020, which regulates other design parameters of access sites.
5. Pavement Evenness: Annex B describes the limits of pavement roughness
applicable in the Republic of Belarus.
6. Control Methods: The same annex contains methods for detecting elevation deviation developed mainly for concrete pavements, thereby limiting their direct
application to asphalt-concrete structures.
This leads to the conclusion that GOST 33242–2015 [6] should not be referenced as
a legislative standard. It may only be cited as an example for specifying access zone
requirements, but nothing more.
Current regulatory framework for AWDCS implementation in Russia are set out
in the Order of the Ministry of Transport No. 348 of 31.08.2020, the accuracy of
measurements is set out in the Government Decree No. 1847 of 16.11.2020, and the

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requirements for road structures in the zone and on the access ways to the zone of
AWDCS are defined in PNST 663–2022 [7].
AWDCS should be installed on crossings of Category 1–4 highways with the
pavement types of capital-grade or lightweight designs with the intensity of traffic
of cargo vehicles more than 100 vehicles per day with an axle load of 115 kN
and 100 kN, respectively. Longitudinal/transverse evenness must be maintained for
pavement stability. Therefore, a change in transverse evenness by 1 mm requires
calibration of the weighing equipment.
Key study by Sinyansky M.V. (JSC “VIK”Tenso-M”) [8] shows that substandard
longitudinal evenness induces vehicle oscillations, increasing measurement errors.
In the Russian Federation, the requirements for longitudinal evenness have different
values, that differ at the stage of putting a highway into operation and in the process
of operation.
According to [9], the maximum permissible IRI evenness for I-II category roads is
not more than 2.2–4.1 m/km; III-IV categories 2.6–4.6 m/km and V category—more
than 4.6 m/km depending on the pavement material. At the operational stage, the
requirements for longitudinal evenness by IRI measured by profilometer, according
to [4], are from 4 to 8 m/km depending also on the road category, and pavement
material. The given indicators at each stage exceed foreign requirements by times
[9].
The actual IRI of up to 1.3 m/km (in accordance with foreign requirements and the
requirements of some manufacturers of AWDCS) is unachievable. Even for newly
constructed highways of categories IA and IB at their acceptance into operation the
IRI value exceeds no 2.2 m/km. Currently manufactured asphalt-laying machines
and new types of asphalt-concrete mixtures do not provide pavement flatness of up
to 1.3 m/km. This is due to the requirement to ensure the roughness of the road
surface and the required value for tire-to-surface friction coefficient. Smooth surface
of road asphalt concrete pavement with a coefficient of less than 0.3 does not meet
the requirements [4].
Russian manufacturers currently produce [4, 7] AWDCS with two primary sensor
technologies: tendometric or piezoelectric weighing sensors. These systems are
designed to operate optimally under the following pavement conditions: wheel
tracking depth: ≤10–12 mm, and IRI index: ≥2.2 m/km, that at the moment is the
most optimal, in contrast to manufacturers producing AWDCS with wheel tracking
requirements of 3–6 mm, and on the IRI index of 1.3 m/km.
The formation of progressive longitudinal/transverse unevenness typically results
from inadequate pavement structures. Most AWDCS on regional/inter-municipal
roads are retrofitted onto existing highways, predominantly Category III (occasionally Category IV) roads with weak road base pavements.

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2 Research
A comprehensive evaluation was conducted across 24 AWDCS stations, with
20 located in the Republic of Bashkortostan, covering key transport corridors
in the following districts: Blagoveshchensky, Khaibulinsky, Baymaksky, Ufimsky,
Nurimanovsky, Ishimbaysky, Tatyshlinsky, Chishminsky, Karaidelsky, Blagovarsky,
Zianchurinsky, Uchalinsky, Arkhangelsky, Sterlitamaksky, Mechetlinsky and Dyurtiulinsky. These stations are deployed on Regional highways and Approaches to
federal routes. All AWDCS stations exhibit: high traffic volumes, dominance of
overloaded trucks, with the increased load on the pavement structure, requiring
the optimization of engineering solutions taking into account specific operating
conditions.
During the study at each of the stations, the pavement structural details, the actual
condition, deformations and failures in the period over a 3-year monitoring period
were recorded.
An additional 4 AWDСS are operational in Krasnodar Territory, covering
Tikhoretsk—Belaya Glina settlement, Kalininskaya—Novonikolaevskaya stanitsa,
Timashevsk—Poltavskaya stanitsa, and.
Zhuravskaya stanitsa—Tikhoretsk. The location of the AWDСS in Krasnodar
Territory covers both regional and federal highways, thereby enabling to obtain
a representative sample for analyzing pavement performance operating in various
climatic, geotechnical and transportation conditions. The stations provided an opportunity to clearly analyze the factors influencing the formation of wheel tracking,
pavement deformation and pavement failure.
To assess the efficiency of pavement designs at AWDCS, a classification was
conducted based on structural characteristics. Four primary pavement types were
identified, differing in materials, rigidity, and load-bearing capacity. Below are their
specifications, performance metrics, and application guidelines.
As a result of the analysis, the 24 AWDCS were classified by pavement type:
Option 1—three-layer asphalt concrete pavement with two-layer crushed stone
base;
Option 2—two-layer asphalt concrete pavement on cement-stabilized crushed
stone and soil-cement base;
Option 3—one-layer cement concrete pavement on one-layer crushed stone base;
Option 4—one-layer cement concrete pavement on two-layer crushed stone base.
The Republic of Bashkortostan and Krasnodar Territory exhibit divergent climatic
conditions, necessitating distinct approaches to roadway design and maintenance for
AWDCS.
The Republic of Bashkortostan is situated in a temperate continental climate zone,
characterized by distinct seasonal variations: cold winters and warm summers.. The
average annual temperature is about +2... + 4 °C. In winter the temperature may drop
to −20 °C and below, and in summer - rise to +30 °C. Annual precipitation varies
from 500 to 800 mm, with the majority thereof falling in the warm season. The winter
period is accompanied by a stable snow cover and alternating cycles of freezing and

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thawing, requiring the consideration of frost heave of soils. According to climatic
conditions, the Republic of Bashkortostan is referred to the III road-climatic zone
[10], characterized by moderately severe winters and the requirement to ensure frost
resistance and stability of structural layers of pavement to seasonal deformations.
The Krasnodar Territory despite its milder climate is classified under RoadClimatic Zone IV. The region exhibits significant climatic diversity from moderately continental in the north to humid subtropical on the Black Sea coast. The
average annual temperature ranges from +10 to +14 °C. Winters are generally mild
and snowy, while summers are hot. Rainfall varies from 400 mm in the plains to
1200 mm in the mountains and on the coast. The main climatic impacts are related to
high humidity, excessive pavement base wetting and intense solar radiation. Despite
more favorable winter conditions, the IV road-climatic zone requires the application of solutions ensuring water drainage, thermally stable materials and high-load
resistance due to freight traffic dominance.
The first option of the pavement design used on the sections with AWDCS is a
three-layer asphalt-concrete pavement laid on a two-layer crushed stone base with
an extra sandy layer. This design is widely implemented on high-traffic highways,
particularly in areas with significant heavy truck loads. Its effectiveness is largely
determined by climatic conditions, temperature extremes and traffic load intensity.
It is especially relevant for the regions belonging to the III road-climatic zone.
This pavement structure has been deployed on highway sections with Automated Weight and Dimension Control Stations (AWDCS) across multiple districts of
Bashkortostan. Given the traffic intensity ranging from 2000 to over 12,000 vehicles
per day, the design prioritizes durability and load-bearing capacity. Characteristics
of the pavement layers, their type and thickness are given in Table 1.
To analyze the effect of temperature fluctuations on the reliability and durability
of the pavement structure, the temperature effect was calculated so as to consider
possible deformations and stresses.
This pavement structure is most susceptible to deformation during summer,
when surface layer temperatures (especially in asphalt concrete) reach peak values.
Under elevated temperatures, the following degradation mechanisms occur i.e. binder
softening, strength reduction thereby resulting in plastic deformations promoting
accelerated wheel tracking formation.
Simply increasing the number of asphalt layers or their thickness does not significantly improve wheel tracking resistance. In fact, such measures may increase
stress concentration in lower layers and accelerate structural failure if the base has
insufficient bearing capacity.
Under conditions of high traffic loads and intense temperature exposure, the use of
option 1 without adjusting the design may lead to intensive accumulation of residual
deformations, premature rutting and, in the long term, to a complete loss of the
operational suitability of the pavement.
To obtain more precise data and evaluate how the base layer influences pavement resistance to wheel tracking formation, the calculation using different base
types with varying elastic moduli was made. The simulations were performed by

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the INDORCAD software, enabling detailed engineering analysis of base stiffness
effects on deformation distribution in pavement layers.
The study systematically replaced base materials with varying elastic moduli
while maintaining identical environmental conditions. The results of calculations
confirmed that low modulus of elasticity of the base significantly increases the magnitude of residual vertical deformations, especially in the wheel track area. Accordingly,
to ensure the stability of the structure in summer period, the attention should be paid
not only to the top layers, but also to the base parameters, especially when designing
sections with heavy traffic and heavy trucks.
The second option of pavement construction used on the sections with automatic
weight and dimensional control points (AWDCP) is a two-layer asphalt concrete
pavement laid on a multilayer base of stabilized crushed stone and soil cement.
This structure has increased load-bearing capacity due to the stabilized layers and
reinforcing elements, enabling more efficient redistribution of the load from vehicle
wheels and reducing the risk of residual deformations, including wheel tracking
formation.
The design is actively used on a number of road sections equipped with
AWDCS, thereby confirming its compliance with current requirements to the
strength and durability of road pavements. These sections are arranged in different
districts of the Republic of Bashkortostan, including Dyurtulinsky, Mechetlinsky,
Blagoveshchensky and Sterlitamaksky districts. In each of these districts the operating conditions have their own peculiarities—various composition and traffic intensity, relief and climate peculiarities, degree of moisture and seasonal temperature fluctuations. All this significantly affects the performance characteristics of the pavement.
This pavement design demonstrates exceptional load-bearing capacity, successfully
operating under traffic volumes ranging from 1800 to over 11,000 vehicles per day,
including heavy trucks, specialized vehicles, and buses.
The detailed structure of layers, their composition, the type of materials used, as
well as the calculated depth of each layer are presented in Table 2 enabling a clear
assessment of the design solutions and the feasibility of their application in the road
conditions of the Republic of Bashkortostan.
Similar to the first design option, this type of pavement is also subject to temperature analysis. Temperature analysis is required to assess the resistance of stabilized
pavements and asphalt concrete pavements to seasonal temperature fluctuations, and
to identify possible risks of deformation, cracking and other damage occurring in
summer and winter operating conditions.
The design with a two-layer asphalt concrete pavement, the safety factor of this
design does not meet the requirements [7] for the use of an additional coefficient for
the permissible elastic deflection when calculating the road surface in the APVGK
zone, but this design will meet the requirements [11–13] imposed on sections of
the III category highway, taking into account the temperature regime of the asphalt
concrete layers.
Building on the evaluation of Design Option 1, parallel simulations were
conducted in INDORCAD software to assess how base layer stiffness influences

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Table 1 Three-layer asphalt concrete pavement with two-layer crushed stone base (option 1)
Pavement structure layers and materials

Thickness,
cm

Top layer of pavement—Crushed stone-mastic asphalt concrete according to
6
GOST R 58406.1–2020 SMA-16 using polymer-bitumen binder PBV 60 according
to GOST 52056–2003 (or on modifier “DorArm” STO 27856743–001-2018)
Middle pavement layer—Asphalt concrete (GOST R58406.2–2020) A16Nt for the 6
lower pavement layer on bitumen binder of grade BND 70/100 according to GOST
33133–2014 (or on modifier “DorArm” STO 27856743–001-2018), with a
maximum grain size of 16 mm
Lower pavement layer—Asphalt concrete (GOST R58406.2–2020) A16Nt for the 6
lower pavement layer on bitumen binder of grade BND 70/100 according to GOST
33133–2014 (or on modifier “DorArm” STO 27856743–001-2018), with a
maximum grain size of 16 mm
Top base layer—Asphalt concrete (GOST R58406.2–2020) A16Nt for the bottom 6
layer of the pavement on bitumen binder of grade BND 70/100 according to GOST
33133–2014 (or on modifier “DorArm” STO 27856743–001-2018), with a
maximum grain size of 16 mm
Bottom layer of the base—fractionated crushed stone not less than M800, fraction 40
31.5–63 mm (GOST 32703–2014), 2 layers of 16 cm with choking of the top layer
with fractionated fine crushed stone, fraction 8–16 mm and additionally fraction
4–8 mm
— Geomax 450 needle-punched nonwoven fabric for separation of base layers,
drainage
Additional base layer—Medium coarse sand with 3% dusty-clay fraction, GOST
32824–2014

— Geomax 200 needle-punched nonwoven fabric for separation of base layers,
drainage
Subgrade soil—Clayey loam

–

stress distribution across pavement layers and residual deformation under repeated
loading.
Simulation results confirmed that at low modulus of elasticity of the base,
the residual vertical deformations increase significantly, especially in the area of
wheel load. These findings underscore the necessity of strengthening the base layer
during design, particularly for high-traffic corridors, heavy truck routes, and summer
operational stability.
The third pavement design option for AWDCS zones is a cement concrete pavement system characterized by high rigidity, durability, and minimal susceptibility
to temperature and climatic effects. This design is particularly effective in areas
with heavy traffic, as well as in areas subject to seasonal temperature variations and
moisture saturated soils.

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Table 2 Two-layer asphalt concrete pavement on a base of stabilized crushed stone and soil cement
Pavement structure layers and materials

Thickness,
cm

Top layer of pavement—Crushed stone-mastic asphalt concrete according to
6
GOST R 58406.1–2020 SMA-16 with the use of polymer-bitumen binder PBV 60
according to GOST 52056–2003 (or on modifier “DorArm” STO
27856743–001-2018)
Lower pavement layer—Asphalt concrete (GOST R58406.2–2020) A16Nt for the 6
lower pavement layer on bitumen binder of grade BND 70/100 according to GOST
33133–2014 (or on modifier “DorArm” STO 27856743–001-2018), with a
maximum grain size of 16 mm
— Polyester Geomax 120/120–40 geogrid
Top base layer—crushed stone stabilized by impregnation with sand-cement
mixture with sand-cement consumption of 25% of crushed stone weight

Lower base layer—soil cement of grade 40 made of silt sandy loam and loam
(mixed in the unit) for artificial bases of rigid pavements

Subgrade soil—Clayey loam

–

Table 3 Cement concrete pavement design
Pavement structure layers and materials

Thickness, cm

Surface layer — HW concrete of grade B tb 3.6

Non-woven geotextile Geomax 200
Base—crushed stone-sand mixtures, with maximum grain size 0–31.5 mm
according to GOST 70458–2020

Polyester Geomax 120/120–40 geogrid
Supplementary base layer—medium coarse sand with dusty-clay fraction of
3%, GOST 32824–2014

Geomax 450 needle-punched nonwoven fabric for separation of base layers,
drainage
Subgrade soil — Clayey loam

–

Table 4 Design of a pavement made of heavy monolithic concrete
Pavement structure layers and materials

Thickness, cm

Surface layer of HW concrete of grade Btb 4.4 according to GOST 26633–2015 30
— Separating interlayer made of polyethylene airfield film according to
technical specifications 32,245–001–37,232,863-2012
Upper base layer made of crushed stone-gravel-sand mixture stabilized with
Portland cement, conforming to grade M40, GOST 23558–94

Lower base layer made of crushed stone-sand mixture C4 (crushability grade
not less than M600) according to GOST 25607–2009

Subgrade soil—dark brown hard clay

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R. A. Tonkikh et al.

Cement concrete pavement ensures stable operation of weighing and measuring
systems due to high strength and resistance to deformations, eliminating the formation of wheel tracking and reducing the accuracy of measurements. Such structures are used in the Republic of Bashkortostan on sections with high operational load, where traffic intensity reaches 15,000 vehicles per day. This applies
to the directions connecting major cities and industrial centers, such as the routes
Ufa–Inzer–Beloretsk, Ufa–Iglino–Pavlovka, Sibai–Akyar and others.
The application of cement concrete pavements on such sections is stipulated by
the requirement to ensure durability of the pavement, resistance to heavy loads and
stable geometry of the roadbed during a long service life. The main characteristics
and composition of structural layers are given in Table 3.
Cement concrete pavement is laid on a crushed stone-sand mixture stabilized
with geogrid, with an additional underlying layer of sand and separating geotextile. This multilayer system provides high stiffness and uniform load distribution,
reducing stresses in the underlying layers. Calculation of elastic deflection at various
temperature conditions was performed to analyze the strength characteristics of this
design.
Cement concrete pavement is laid on a crushed stone-sand mixture stabilized
with geogrid, with an additional underlying layer of sand and separating geotextile. This multilayer system provides high stiffness and uniform load distribution,
reducing stresses in the underlying layers. The design demonstrates resistance to
temperature fluctuations minimizing deformations and wheel tracking, as possessing
a significant safety. The durability of the pavement is confirmed by over 3-year monitoring where wheel tracking has not exceeded 1–2.5 mm per year thereby complying
with regulatory requirements and ensuring stable operation of weighing and loading
systems.
The key advantages of the design include high load-bearing capacity, resistance to
moisture and temperature effects, long service life and reduced maintenance costs.
However, the implementation of such a design requires precise adherence to the
design solutions, including temperature joints and drainage system, as well as the
application of quality materials in making cement concrete mix positively affecting
the abrasion resistance of pavements.
Furthermore, a calculation was performed using various types of bases with
different moduli of elasticity. The purpose of the simulation was to evaluate the
influence of the stiffness of the base on the behavior of the entire design under
operational loads.
The study revealed that variations in base layer elastic modulus do not significantly
impact the structural performance of this rigid pavement design. The high stiffness of
the cement concrete layer provides for reliable load transfer and distribution thereby
making the structure insensitive to variations in the base parameters and confirming
of no need to select or replace the underlying layers under design.
The cement concrete pavement design therefore remains efficient and stable
regardless of changes in the stiffness of the base course.
The fourth option applied in the automatic weight and dimension control stations
(AWDCS) zones is a design with monolithic cement concrete pavement made of

Analysis of the Efficiency of Pavement Structures at Automatic …

349

high-strength HW concrete. This design is characterized by increased rigidity and
ability to efficiently absorb both static and dynamic loads arising from heavy vehicles.
As a result, it demonstrates some of the best performance characteristics of all the
design solutions considered, including resistance to deformation, high compressive
strength and temperature resistance.
Such a design is widely used in Krasnodar Territory where AWDCS are deployed
on road sections with heavy traffic. In a number of directions, the intensity exceeds
18,000 vehicles per day, especially on strategically important highways connecting
regional centers, major population centers and exits to federal highways. Monolithic
cement concrete pavement on such sections ensures reliable operation of the road
pavement and high accuracy of weight measurement during the entire service life
thereof.
The detailed composition of the design with monolithic cement concrete pavement
is presented in Table 4.
To assess the strength and stability of the rigid pavement structure under
varying temperature conditions, computational analyses were performed to determine temperature effects on structural behavior. Primary focus was given to evaluating elastic deflection values, as this parameter indicates the pavement’s ability to
withstand traffic loads without developing permanent deformations.
The modeling accounted for seasonal temperature fluctuations typical of the
region and demonstrated high structural stability under varying thermal conditions.
The obtained results confirm the reliability of the selected pavement design for use
in high-traffic areas.
The pavement structure with a single-layer cement concrete surface course placed
on a two-layer crushed stone base demonstrates high stability under various temperature conditions. Due to the significant stiffness and strength of the cement concrete
layer, temperature fluctuations have minimal effect on structural performance. Unlike
multi-layer asphalt concrete systems where temperature significantly influences
the development of residual deformations, thermal effects in this case cause no
measurable changes in the stress-strain state of the structure.
Similar to Design Option 3, in this case changing the base type or modifying its
modulus of elasticity does not significantly affect the pavement’s strength characteristics. The rigid top layer effectively redistributes loads, minimizing stress transfer to
underlying layers, thereby maintaining structural stability regardless of base properties. This enables simplified design solutions and reduces the need for base variations
while preserving high pavement reliability and durability.
The least deformation-resistant configuration proved to be the three-layer asphalt
concrete pavement on a two-layer crushed stone base. Under elevated temperatures
and heavy traffic loads, this structure is prone to significant wheel tracking formation. Computational analysis revealed that reduced base layer modulus of elasticity
substantially degrades performance characteristics. The alternative design with twolayer asphalt concrete over stabilized base demonstrated better resistance, though
fails to meet several regulatory requirements for AWDCS areas without additional
reinforcement measures.

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The best performance was demonstrated by cement concrete pavements, both on
single-layer and two-layer crushed stone bases. They exhibit high rigidity, remain
unaffected by temperature fluctuations, and maintain stable characteristics regardless
of variations in the base layer’s modulus of elasticity. This significantly simplifies
design solutions and ensures long-term durability under heavy traffic conditions. The
analysis results therefore confirm the requirement of selecting rigid-surface structures
with stabilized bases or cement concrete pavements for reliable and durable operation
of road sections with AWDCS.

3 Conclusion
The review results indicate that currently there are no regulatory legal acts establishing technical requirements for AWDCS regarding permissible wheel tracking
depth values on access roads.
The fundamental approach for AWDCS growth is to ensure effective pavement
performance by providing sufficient stiffness and strength of the pavement structure.
The primary cause for wheel tracking formation in non-rigid pavements is plastic
deformation in summer and deterioration of base characteristics during periods of
excessive moisture.
The primary cause for wheel tracking formation For rigid pavements formation
in rigid pavements are abrasion processes during spring-winter periods, as well as
reduced base performance during water saturation periods.
The research results determined that the most effective and economical solution
is the implementation of rigid pavement structures.

References
1. National project Safe quality roads. Access mode: https://bkdrf.ru/,free
2. SP 13–102-2003 (2003) Rules for inspection of load-bearing structures of buildings and
facilities. Gosstroy of Russia, Moscow, p 56
3. Vasiliev AP (2016) Section 5.5 in road engineer’s reference Encyclopedia, volume II. Applicability analysis of present-day repair technologies and wheel tracking prevention methods for
roads. Current issues in humanities and natural sciences 10-1:102–106
4. GOST R gy-2017 (2017) Automobile roads and streets. The requirements to the level of
maintenance satisfied the traffic safety. Methods of testing. Standartinform, Moscow, p 26
5. Standard catalog of flexible pavement structures for various road-climatic zones. Federal
Highway Agency (Rosavtodor) (2020) Rosavtodor, Moscow, p 248
6. GOST 33242–2015 (2015) Automatic instruments for weighing road vehicles in motion and
measuring axle loads. Metrological and technical requirements Tests. State Standard of the
Republic of Belarus, Minsk, p 40
7. PNST 663–2022 (2022) Public roads. Automated weight and dimension control stations.
General Technical Requirements. Rosstandart, Moscow
8. Senyansky MV (2021) Actual issues in metrology of weight control of freight vehicles. JSC
“VIK”Tenso-M". https://www.tenso-m.ru/publications/405/

Analysis of the Efficiency of Pavement Structures at Automatic …

351

9. SP 78.13330.2012 (2012) Highways. Updated version of SNiP 2.05.02–85. Minregion of
Russia, Moscow, p 112
10. SP 131.13330.2020 (2020) Building climatology. Updated version of SNiP 23–01-99*.
Minstroi of Russia, Moscow, p 95
11. PNST 542–2021 (2021) Public roads. Non-rigid road pavements. Design rules. Since
01.06.2021. Standardinform, Moscow, p 144
12. Glazachev AO, Ivanova OV, Pavlov SY, Salov AS, Akhmetshin RM (2024) Synergetic improvement of technological characteristics of highway road surfaces by bitumen microdispersed
emulsions. Nanotechnologies Constr 16(5):463–472
13. Ostroukh AV, Nedoseko IV, Surkova NE, Fattakhov MM, Nuruev YM, Salov AS (2015)
Automated information-analytical system for dispatching control of transportation concrete
products. Int J Appl Eng Res 10(19):40063–40067

The Effect of Reinforced Methods
for Beams with Openings
Viet-Phuong Nguyen, Van-Nam Nguyen, Cong-Vinh Pham,
and Trong-Tuan Tran

Abstract The appearance of openings in beams is considered inevitable for structures that require aesthetic considerations, where the clear height of the floor is
limited, and the arrangement of suspended ceilings as well as complex spatial layouts
is necessary. Openings will cause many inconveniences for the behavior of typical
beam systems such as deformation, load-bearing capacity, and stability. In the context
of Vietnam, with the trend of renovating building spaces, openings often appear
after the design has been completed, so understanding how the behavior of beams
changes when openings appear is very necessary. This paper analyzes the behavioral
changes of beams when openings appear, as well as the impact of various reinforcement methods around the openings by the simulation of ABAQUS. The research
results show that openings located within the shear span of the beam significantly
reduce the load-bearing capacity and deformation of the beam. The most effective
reinforcement option when there is an opening is the option that includes diagonal
reinforcement bars around the opening. Vertical stirrups around the opening provide
little improvement in the behavior of beams with openings.
Keywords Opening beam · ABAQUS software

1 Introduction
Building MEP systems are typically installed below the structural beams. This causes
issues related to the aesthetics of the architecture, affects usable space, and ensures
the clear height of the floors. Especially for apartment-type buildings, the use of
hanging ceiling systems will add height to the structures. For high-rise apartments,
increasing the building’s height is calculated by adding the cumulative height of
beams, the clear height of the floor, and the space below the beams for pipes and
false ceilings. This will lead to an increase in load and dangerous internal forces in the
V.-P. Nguyen (B) · V.-N. Nguyen · C.-V. Pham · T.-T. Tran
Hanoi Architectural University, Hanoi, Vietnam
e-mail: phuongnv@hau.edu.vn
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_29

353

354

V.-P. Nguyen et al.

building due to lateral loads. To overcome this issue, pipes can be passed through the
reinforced concrete beams, which helps save floor height—especially effective for
large projects, offering benefits such as increasing the number of floors when height
is limited and potentially reducing load. Especially with the situation of buildings
in Vietnam having low floor heights, the demand for hanging ceilings increases,
complex room layouts, and the appearance of openings in reinforced concrete beams
often becomes inevitable.
The design of openings in reinforced concrete beams significantly affects the
stability and load-bearing capacity of the structure. The holes are usually round,
square, or rectangular because they are easy to construct, while complex shapes like
ellipses or triangles are more difficult to construct and require careful consideration
of stress and strain. The shape, position (mid-span or near supports, inside or outside
the shear span), size, and number of openings all affect the stress distribution and
stiffness of the beam. If the design is not reasonable, the opening can cause stress
concentration, cracking, increased deflection, and reduce the lifespan of the structure.
Mansur et al. (1991) [1] study showed that large rectangular openings significantly
affect the load-carrying capacity and deformation of reinforced concrete beams. The
opening is placed in the region of high bending moment, which reduces the failure
load and increases the beam’s deformation. As the size of the opening increases,
both the cracking and failure loads decrease, reducing the load-bearing capacity.
Subsequent experimental studies by Mansur and Tan [2], Ashour and Rishi [3], HeeChang-Eun [4], Ahmed, Fayyadh [5], Aykac et al. [6], Farouk et al. [7], Hamoda
et al. [8], … have also indicated that certain parameters of the opening affect the
behavior of RC beams.
Studying the influence of parameters on the behavior of beams with openings
provides an overview for developing appropriate structural measures, adjustments,
and additional solutions to address the effects leading to beam degradation. Since
experiments and theoretical analysis are difficult and costly, using the ABAQUS
simulation software is an effective solution, helping to accurately simulate structural
behavior at a significantly lower cost and time compared to real-world experiments.

2 Investigated and Validated Model in ABAQUS
Based on previous studies, several survey models were developed to assess the influence of parameters such as the shape, size, number, and location of openings on the
behavior of ordinary beams. When the influencing parameters change in the models,
the remaining parameters of the beam will remain constant. The beam model with a
length of L = 6.3 m was selected according to the empirical formula corresponding
to a regular beam, where h = (1/2 – 1/2)L, and the beam width was selected according
to the formula b = (0.3 ÷ 0.5)h. From this, the size of the surveyed beam is chosen:
b × h = 300 × 600 (mm).
The materials used include B25 grade concrete, longitudinal reinforcing steel
using CB400-V steel group; and stirrup steel using CB240-T steel group. All beam

The Effect of Reinforced Methods for Beams with Openings

355

samples are arranged with 2ϕ16 for the top longitudinal steel and 5ϕ16 for the bottom
longitudinal steel. The diameter of the stirrups throughout the beam is chosen to be
ϕ8. The analyzed and compared cases in this paper (see Fig. 1) include:
• Behavior investigation of the position of web openings compared to solid beam
(named NOW): web openings in the middle of the beam (OSM300), web openings
under the point of force application—at one-third of beam length (OST300),
and web openings located within the shear span—at one-fourth of beam length
(OSQ300).
• Investigate the influence of reinforced reinforcement around the openings: for mid-span opening (OSMP300V—only vertical reinforced stirrups,
OSMP300HV—additional longitudinal reinforcement and OSMHQ300—additional diagonal reinforcement), for openings under the point of load application (OST300, OSTP300V, OSTP300HV and OSTHQ300), for openings located
within the shear span (OSQ300, OSQP300V, OSQP300HV and OSQHQ300).
All models were simulated in ABAQUS software with materials that fully considered
their corresponding properties related to nonlinear behavior. The two compressive
(dc) and tensile (dt) damage parameters of concrete are defined and declared in
the “Concrete Compression Damage” and “Concrete Tension Damage” sections of
ABAQUS. The ductility of the steel reinforcement is also considered through a twosegment stress-strain curve simulation, as specified in Vietnamese standard TCVN
5574–2018 [9].
The elements of the beam are divided into: (1) the concrete part of the beam; (2)
the reinforcement cage. The concrete part is modeled using C3D8R elements, and the
reinforced concrete frame system uses T3D2 elements. The entire reinforcement cage
is embedded within the concrete using an “Embedded constraint” in the software.
At the same time, the boundary conditions for the support joints at both ends of the
beam are modeled by constraints on displacements in the X and Y directions and
rotation about the Z direction. The load is simulated using a displacement control
method. The size of the meshed elements used is 25 mm.
The experiment of a solid beam and a beam with a web opening in the paper by
authors Ata El-kareim Shoeibl and Ahmed El-sayed Sedawy [10] were simulated in
a similar way. The test results, as shown in Figs. 2 and 3, demonstrate the reliability
of the simulation method using ABAQUS and can be applied to conduct numerical
research for survey models.

356

Fig. 1 Investigated model

V.-P. Nguyen et al.

The Effect of Reinforced Methods for Beams with Openings

357

Fig. 2 Validated displacement-force curves

3 Simulated Result and Discussion
3.1 The Influence of the Position of Web Opening in Normal
Beam
The results of the graph in Fig. 4 show that the working process of the beam samples
is divided into two main stages. In the initial stage, corresponding to a load from 0
to 50 kN (with a corresponding displacement of 2.1 mm), the beam samples (both
with and without web openings) all operate in the elastic stage, and the behavior
of the beam samples is the same. When the load increases, the load-displacement
curve begins to transition to a nonlinear state, reflecting the change in the load-bearing
mechanism of the component. The load-bearing capacity of the beams with openings
significantly decreases compared to the corresponding load-bearing capacity of the
solid beams. At the end of the survey (corresponding to a beam deflection of 45 mm),
the load achieved by the solid beam was 201.19 kN, while the load on the beam with
an opening in the middle was only 191.87 kN (a reduction of 4.63%), on the beam
with an opening under the load position was 192.32 kN (a reduction of 4.41%), and

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Fig. 3 Concrete behavior of validated solid beam and beam with opening

on the beam with an opening in the shear span was 185.37 kN (a reduction of 7.86%).
This demonstrates that the presence of web openings in the shear span of the beam
will significantly reduce the load-bearing capacity of the beam.
In addition, several special points on the displacement-load curve are used to
correspond to the point of first appearance of the yield of the stirrups (SiY), the first
yield of the longitudinal reinforcement (LRiY), and the moment when the concrete
reaches its compressive strength limit (CrC). The reinforcement at the position below
the load application point reaches the first yield limit in all beam samples with
openings at similar times, and the difference compared to beams without openings
is negligible (less than 5%). At the same time, the concrete at the position just below
the load application point also reaches a similar compressive strain limit among
the samples. This can be explained by the phenomenon of local compression at
the load application position. The yield point of the longitudinal reinforcement in
the beam, which is characteristic of the beam’s bending capacity, decreases when
openings appear. Particularly, the closer the opening is to the shear span, the greater
this reduction becomes. The yield point of the longitudinal reinforcement in a beam

The Effect of Reinforced Methods for Beams with Openings

359

Fig. 4
Displacement—applied load
curve in case of changing
opening position

without openings is 170.68 kN, with an opening in the middle of the beam it is
167.2 kN, with an opening under the point of load application it is 157.58 kN (a
reduction of more than 7%), and with an opening in the shear span it is 140.58 kN
(a reduction of more than 17%).
The survey of the deflection of the beam along its length shows that the deflection
of the beam when the opening is located within the shear span will be greater by 2–
10% compared to cases where the opening is outside the shear span, depending on the
position of the points on the beam measured from the edge of the opening located
within the shear span. For openings located outside the shear span, the deflection
changes insignificantly. In particular, the deformation of the beam with the presence
of an opening in the shear span is also different from other positions of openings on
the beam.
When an opening occurs in the shear span, a diagonal crack will form connecting
the corner of the opening with the location of the applied load as shown in Fig. 5.
This indicates the necessity for reinforcement of the rebar in this area.

360

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Fig. 5 Concrete behavior in case of changing opening position

3.2 The Influence of the Reinforced Reinforcement around
the Web Openings
In Fig. 6, it is observed that at the corresponding displacement points of beam with the
mid-span web opening, the load between the unreinforced beam (OSM300) and the
beam reinforced only with vertical stirrups (OSMP300T) shows negligible differences (from 0.00 to 0.64%). Compared to the beams reinforced with both horizontal and vertical reinforcement (OSMP300HT) and those with additional diagonal
one (OSMHQ300), the differences become more pronounced (from 3.41 to 6.46%).
However, there is almost no difference between the two beam models OSMP300HT
and OSMHQ300. Thus, it can be seen that the load-bearing capacity of the beam
with web opening, when reinforced with both vertical and horizontal reinforcement,
is significantly increased, but there is no clear difference when additional diagonal
reinforcement is added in the case where the opening is located outside the shear
span. Reinforcing only the vertical stirrups does not effectively improve the loadbearing capacity of the beam when openings appear. Observing Fig. 6, when the beam
is reinforced with longitudinal and diagonal reinforcement, the load-displacement
curve is significantly improved. The load-bearing capacity of the reinforced beam
with openings will be equivalent to or even greater than that of the beam without
openings, depending on the amount of reinforcing steel.
Similarly, for beams with openings in the shear span, at the end of the survey,
the load of the unreinforced beam reached 185.37 kN. Meanwhile, the load corresponding to the case of only vertical reinforcement reached 187.31 kN (an increase
of 1.04%), the case of vertical reinforcement and longitudinal reinforcement reached
194.22 kN (an increase of 4.77%), and the case of additional diagonal reinforcement

The Effect of Reinforced Methods for Beams with Openings

361

Fig. 6 Displacement—applied load curve in case of changing the reinforced method

reached 196.29 kN (an increase of 5.89%). The load achieved on the solid beam
is 201.19 kN, which is just over 2.43% compared to the beam with opening that
has been reinforced with diagonal reinforcement. This once again demonstrates the
effectiveness of reinforcing with diagonal bars to improve the behavior of beams that
typically have openings.
For special moments on beams with openings that are reinforced with diagonal
bars, such as the moment when the first stirrup yields, the moment when the first
longitudinal bar yields, or when the concrete reaches the compressive strain limit,
these values are similar to those obtained on beams without openings.
• For the beam with mid-span opening, the moment the first stirrup yields: (1) beam
without holes is 112.25 kN; (2) beam with reinforced diagonal holes is 112.86 kN.
The moment the first vertical reinforcement yields: (1) 167.02 kN; (2) 164.15 kN.
The moment the concrete reaches the compressive strain limit: (1) 140.76 kN; (2)
137.94 kN.
• For the beam with opening inside the shear span, the moment the first stirrup yields:
(1) beam without holes is 112.25 kN; (2) beam with reinforced diagonal holes is
112.14 kN. The moment the first vertical reinforcement yields: (1) 167.02 kN;
(2) 166.19 kN. The moment the concrete reaches the compressive strain limit: (1)
140.76 kN; (2) 136.52 kN.
At the similar applied load of 160 kN, the displacement of solid beam at mid-span
can be observed that it is 17.69 mm. Meanwhile, this value of beam with opening
inside the shear span is 19.32 mm and 18.21 corresponding to the beam with midspan opening. When the beam with opening is reinforced, the displacement values
are improved to varying degrees depending on the position of the openings in the
beam. Specifically as follows:

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Fig. 7 Concrete tensile behavior in case of changing the reinforced method

• For beams with an opening in the middle: The corresponding displacement values
are 17.88 mm (only vertical stirrups), 16.67 mm (vertical stirrups and longitudinal
reinforcement), 16.35 mm (when there is diagonal reinforcement)
• For beams with openings in the span subjected to shear: The corresponding deflection values are 18.57 mm (only vertical stirrups), 18.12 mm (vertical stirrups and
longitudinal reinforcement), 18.00 mm (when there is diagonal reinforcement)
For the behavior of concrete in Fig. 7, reinforcing the diagonal steel around the
opening has improved the failure of the concrete region beneath the opening as
well as the cracks that form between the edge of the opening and the point of load
application. The cracks are pushed further away from the edge of the opening and
are particularly more effective for beams with openings located in the shear span.

4 Conclusion
In the scope of the research of the article on beams with openings, some comments
can be made as follows:
• The beam with an opening in the shear span reduces the load-bearing capacity by
approximately 3.69%, and the displacement increases by 2–10%. The stress and
plastic deformation of the stirrups and longitudinal reinforcement increase rapidly,
leading to the stirrups yielding earlier compared to openings in other positions.
The opening in the shear span causes the formation of a diagonal failure mode
from the edge of the opening to the point of load application.
• The beam with only vertical stirrups reinforcement does not cause any significant impact compared to the unreinforced beam (the difference is always below
1%). Meanwhile, beams reinforced with additional longitudinal and diagonal bars
will significantly improve the behavior of the beam. The deflection of the beam

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363

decreases by 7.11–9.4% when additional longitudinal bars are reinforced and
by 8.34–10.89% when additional diagonal bars are reinforced. Reinforcing the
vertical and diagonal bars around the opening also reduces the damage to the
concrete area just below the opening. The stress and plastic deformation for the
stirrups and vertical steel also decrease and approach the behavior of a solid beam.

References
1. Mansur MA, Lee YF, Tan KH, Lee SL (1991) Tests on RC continuous beams with openings.
J Struct Eng ASCE 117:1593–1606
2. Mansur MA, Tan KH (1999) Concrete beams with openings: analysis and design. CRC Press
LLC, Boca Raton, Florida, p 220
3. Ashour AF, Rishi G (2000) Tests of reinforced concrete continuous deep beams with web
openings. ACI Struct J 97(3):418–426. https://doi.org/10.14359/4636
4. Eun H-C (2006) On the shear strength of reinforced concrete deep beam with web opening.
The structural design of tall and special buildings. Struct Design Tall Spec Build 15:445–466.
https://doi.org/10.1002/tal.306
5. Ahmed A, Fayyadh MM, Naganathan S, Nasharuddin K (2012) Reinforced concrete beams
with web openings: a state of the art review. Mater Des 40:90–102. https://doi.org/10.1016/j.
matdes.2012.03.001
6. Aykac B, Kalkan I, Aykac S, Egriboz YE (2013) Flexural behavior of RC beams with regular
square or circular web opening. Eng Struct 56:2165–2174. https://doi.org/10.1016/j.engstruct.
2013.08.043
7. Farouk MA, Moubarak AMR, Ibrahim A, Elwardany H (2023) New alternative techniques for
strengthening deep beams with circular and rectangular openings. Case Stud Constr Mater 19.
https://doi.org/10.1016/j.cscm.2023.e02288
8. Hamoda A, Yehia SA, Ahmed M, Abadel AA, Baktheer A, Shahin RI (2024) Experimental
and numerical analysis of deep beams with openings strengthened with galvanized corrugated
and flat steel sheets. Case Stud Constr Mater 21. https://doi.org/10.1016/j.cscm.2024.e03522
9. TCVN 5574-2018 concrete and reinforced concrete structure - design standard. Vietnamese
standard
10. Shoeib A E-k, Sedawy A E-s (2017) Shear strength reduction due to introduced opening in
loaded rc beams. J Build Eng S2352–7102(16):30295–30299. https://doi.org/10.1016/j.jobe.
2017.04.004

Kinetic Characterization of Densified
Wood under an Assumed Real Fire Curve
Using Thermogravimetric Analysis
T. T. Tran, T. B. Q. Vu, and Viet-Phuong Nguyen

Abstract This study investigates the thermal degradation behavior of densified
wood through thermogravimetric analysis (TGA) under an assumed real fire curve.
The mass loss and mass loss rate of virgin and densified spruce powders were
compared to assess the effect of densification on pyrolysis behavior. Experimental
results show negligible differences between the two materials, attributed to the use of
fine powders minimizing heat conduction effects. A kinetic model based on the threestep decomposition mechanism proposed by Broström (2012) was applied, focusing
on hemicellulose, cellulose, and lignin as pseudo-components. Kinetic parameters
were estimated using an inverse modeling approach with least squares optimization,
and validated by comparing simulation results with experimental data. The model
demonstrates good agreement, with activation energy values closely matching those
reported in the literature. The findings confirm the suitability of the simplified threestep model and the effectiveness of the applied methodology for simulating thermal
degradation of lignocellulosic biomass under realistic heating conditions.
Keywords Thermogravimetric analysis (TGA) · Densified wood · Real fire
curve · Inverse method

1 Introduction
Thermo-mechanically densified wood has emerged as a promising material in
sustainable construction due to its enhanced mechanical performance and potential
for adhesive-free dowel-based connections. This development supports large-scale,
all-wood structural systems while promoting the efficient use of renewable forest
resources. In addition to its structural advantages, densified wood aligns with modern
environmental goals by offering a low-carbon alternative to fossil-based construction
materials and contributing to energy-efficient building design.
T. T. Tran (B) · T. B. Q. Vu · V.-P. Nguyen
Hanoi Architectural University, Hanoi, Viet Nam
e-mail: tuantt@hau.edu.vn
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_30

365

366

T. T. Tran et al.

Understanding the thermal degradation behavior of lignocellulosic materials such
as wood is essential, particularly in the context of fire performance and pyrolysis
modeling. Thermogravimetric analysis (TGA) has been widely used to investigate
the mass loss behavior and reaction kinetics of wood and wood-based composites
[1–5]. However, most existing models are developed based on uncompressed or
homogeneous wood and assume fixed heating rates, which limits their accuracy when
applied to thermally modified or densified materials. In densified wood, reduced
porosity and altered cell structures significantly influence heat and mass transfer
mechanisms, requiring refined modeling approaches.
This study aims to investigate the pyrolysis behavior of densified spruce wood
powder under an assumed real fire curve using thermogravimetric analysis. A threestep kinetic model, accounting for the thermal decomposition of hemicellulose, cellulose, and lignin, is applied and calibrated through inverse modeling techniques. The
estimated kinetic parameters are validated against experimental data and compared
with literature values. By addressing the limitations of traditional models and incorporating realistic heating conditions, the proposed approach enhances the accuracy
of thermal degradation modeling for densified wood products.

2 Thermogravimetric Tests
Thermogravimetric analysis (TGA) measures the mass change of a small sample
over time as it is subjected to increasing temperatures. This technique quantifies
mass loss and identifies the thermal degradation temperatures of materials. TGA also
enables the determination of kinetic parameters—such as activation energy and preexponential factor—via inverse analysis, which are essential for applying Arrheniusbased models in simulating the pyrolysis behavior of wood components.

2.1 Test Pieces and Materials
To assess the effect of the densification process on thermal degradation, thermogravimetric analysis was conducted on virgin and densified wood powders. The samples
were prepared by crushing local spruce wood and sieving the resulting particles to
a maximum thickness of approximately 4 mm, in line with recommendations in the
literature to minimize thermal gradients during testing [4]. All samples were ovendried at 105 °C to reduce moisture content below 4%. The powdered form allows
for better temperature uniformity across the sample and ensures reliable mass loss
measurements. The test specimens used for the mass loss experiments are shown in
Fig. 1.

Kinetic Characterization of Densified Wood under an Assumed Real …

367

Fig. 1 Thermogravimetric test apparatus

2.2 Experimental Setup
Thermogravimetric test was performed using a thermobalance apparatus (Fig. 1),
which records mass loss and temperature evolution. The system comprises a data
controller linked to Setsys software, a graphite-resistance furnace with water cooling
and PDI-regulated heating rates (1–50 K/min), and a high-precision microbalance
(±0.1 K). To ensure thermal uniformity and avoid intra-particle gradients, the sample
is continuously balanced in a fixed position. An inert atmosphere is maintained by
purging the chamber with argon (7.2 L/h at 273 K, 1 atm) for 20 min prior to heating.

2.3 Heating Condition
Several authors have shown that the kinetic parameters Ai [1/s] and Ei [J/mol] depend
solely on the material and its thermal degradation mechanism, and are assumed to
remain constant regardless of test boundary conditions [2, 6–9]. However, previous
studies have primarily relied on constant heating rates, while the effect of assumed
real fire curves on kinetic parameter estimation has not yet been investigated. This
study addresses that gap by applying an assumed real fire curve in thermogravimetric
testing to evaluate its influence on mass loss behavior (Fig. 2).

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Fig. 2 Heating condition

2.4 Experimental Results
Figure 3 presents a comparison of the m/m0 ratio and the mass loss rate (dm/dt)
for virgin and densified wood powders subjected to an assumed real fire curve,
highlighting the influence of densification on thermal degradation behavior.
The evolution of the normalized mass ratio m/m0 with increasing temperature
shows that virgin and densified spruce powders exhibit nearly identical thermal degradation behavior. Both materials begin to lose mass significantly around 300 °C, with
the majority of decomposition completed by approximately 450 °C. This suggests
that the densification process does not substantially alter the overall degradation
pattern when the wood is tested in powdered form.
Similarly, the mass loss rate (dm/dt) profiles of the two samples display sharp,
overlapping peaks near 370 °C, indicating that the main pyrolysis stage occurs at
the same temperature for both materials. The close agreement in both mass loss
1,2

0,007

1,0

0,006
0,005

MLR [g/s]

0,8

Mass [%]

Virgin spruce (TGA)
Densified spruce (TGA)

0,6
0,4

0,004
0,003
0,002

0,2

0,001
0,000

0,0
0

100

200

300

400

Temperature [°C]

500

600

100

200

300

400

500

600

700

800

Temperature [°C]

Fig. 3 Comparison of mass loss and its time derivative between virgin and densified wood powders

Kinetic Characterization of Densified Wood under an Assumed Real …

369

and derivative curves highlights that the densification effect is negligible under these
conditions. This outcome can be explained by the use of fine powder samples in TGA
testing, which minimizes heat conduction effects and ensures uniform temperature
distribution within the specimens.

3 Thermogravimetric Analysis
A schematic representation of the thermogravimetric analysis process is provided in
Fig. 4.

3.1 Kinetic Modeling of Pyrolysis
Broström et al. [4] proposed a kinetic model to characterize the thermal decomposition and oxidation behavior of lignocellulosic materials, comprising five parallel
reactions governed by mass fractions 1 through 5 . The model includes three primary
decomposition reactions (k1 , k2 , k3 ), representing the degradation of hemicellulose,
cellulose, and lignin, respectively, along with two oxidation reactions (k4 and k5 )
that describe the transition from solid-phase pyrolysis to gas-phase combustion.
This framework enables a detailed description of the coupled pyrolysis–oxidation
processes, as schematically illustrated in Fig. 5.

Fig. 4 Thermogravimetric analysis diagram

370

T. T. Tran et al.

Fig. 5 Thermal degradation mechanism of wood proposed by Broström et al. [9]

In the present study, the model is adapted to simulate only the thermal
decomposition of pseudo-components—hemicellulose, cellulose, and lignin-without
accounting for the oxidation stage. The mass conservation equations governing the
model are formulated as follows:
d ρ1
= −k1 .ρ1
dt

(1)

d ρ2
= −k2 .ρ2
dt

(2)

d ρ3
= −k3 .ρ3
dt

(3)

The mass variation of the sample during thermal decomposition is governed by a set
of six key parameters: the mass fractions α1 , α2 , α3 and the corresponding reaction
rate constants k 1 , k 2 , k 3 . These parameters influence the degradation behavior at a
given temperature and under defined environmental conditions. The reaction kinetics,
as described in Eqs. (1) to (3), dictate the evolution of the decomposition process.
Furthermore, Eq. (4) expresses the temperature dependence of the reaction rates
ki through the Arrhenius equation, which relates the rate constant to the activation
energy and the pre-exponential factor.
ki = Ai . exp

Ei
RT

(4)

In Eq. (4), R (J/(mol·K)) denotes the universal gas constant, with a value of 8.314 J/
(mol·K), while i (s−1 ) and i (J/mol) represent the pre-exponential factor and activation energy, respectively. These kinetic parameters will be identified through thermogravimetric analysis by applying an inverse modeling approach in conjunction
with experimental data.

Kinetic Characterization of Densified Wood under an Assumed Real …

371

3.2 Kinetic Parameter Estimation Approach
The initial stage of the analysis process involves a graphical inspection of the experimental data to identify observable trends. In this study, parameter estimation is
performed using the standard least squares regression method. This approach minimizes the discrepancy between the experimental data and the model predictions by
reducing the sum of squared residuals. Squaring the errors ensures all terms are positive and facilitates the application of differential calculus for optimization, thereby
avoiding complications associated with absolute values. The total least squares error
functions for mass loss and mass loss rate (MLR) are defined as follows, respectively:

δim =

δidm =

tfinal

t
− t0

mnum (t) − mexp (t)

(5)

t0
tfinal

dmnum (t) dmexp (t)
−
dt
dt

(6)

3.3 Characterization of the Kinetic Parameters
The finite difference method was employed to solve the governing equations, with
a time step of Δt = 0.1 min selected to ensure numerical accuracy. However,
this approach presents certain limitations. Specifically, the optimization process—
conducted using the Solver tool in Excel is highly sensitive to the initial guesses of the
kinetic parameters. If these initial values deviate significantly from the actual solution, numerical convergence may not be achieved. Moreover, the optimized parameter values, while minimizing the error between simulated and experimental data, do
not always correspond to physically meaningful representations of the underlying
thermo-chemical reactions. Instead, they serve as effective parameters for achieving
the best curve-fitting performance within the model framework. Table 1 presents the
errors associated with the parameter optimization process.
The results of thermogravimetric analysis and corresponding simulations based on
the model, applied to densified wood under an assumed real fire curve, are presented
in Fig. 6. Three successive peaks are observed in the mass loss rate curve, each
corresponding to the decomposition of a distinct pseudo-component of wood. A
Table 1 Errors on m and dm/
dt

Heating conditions

δim

δidm

Assumed real fire curve

3,3 × 10−4

3,8 × 10−6

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T. T. Tran et al.

Fig. 6 Mass evolution and mass loss rate of densified wood powder under asumed real fire curve
condition

Table 2 Estimated kinematic
constants

Reactions

Ei [kJ/mol]

Ai [1/s]

(1)

102

1.15 × 107

(2)

220.9

1.16 × 1016

(3)

5.85 × 10−1

comparison between the peak temperatures identified in this study and those reported
in the literature is provided to assess the model’s accuracy.
The first peak, associated with hemicellulose degradation, appears at approximately 320 °C, which aligns well with the reported decomposition range of 210–
320 °C [10]. The second peak, representing cellulose decomposition, occurs near
375 °C, consistent with the literature range of 300–375 °C [10]. Finally, the third
peak at around 420 °C falls within the typical range of 350–450 °C for lignin degradation [11]. These results demonstrate good agreement with established data and
confirm the reliability of the kinetic model for describing the thermal behavior of
densified wood. The optimized kinetic parameters employed in the simulations are
summarized in Table 2.

3.4 Validation Model
Table 3 presents a comparison between the results obtained using the three-step
kinetic model proposed by Di Blasi (2012) and those reported in the current literature
on biomass devolatilization under inert conditions. The literature data are typically
based on differential measurements and, in some cases, involve the use of multiple
experimental curves for kinetic parameter estimation [12].
The three-step kinetic mechanism demonstrates good predictive capability for
the devolatilization process, yielding parameter estimates (Table 3) that are consistent with values reported in the literature. The activation energies for the first and

Kinetic Characterization of Densified Wood under an Assumed Real …

373

Table 3 Estimated kinematic constants
Reactions

Limit of E i [kJ/mol]

Estimated value E i [kJ/mol]

(1)

100 to 122

102

(2)

195 to 240

220,9

(3)

35 to 65

second reaction steps—102 and 221 kJ/mol, respectively—fall within the typical
ranges for hemicellulose (100–122 kJ/mol) and cellulose (195–240 kJ/mol) decomposition [12]. The third-step activation energy, estimated at 30 kJ/mol, is slightly
below the commonly reported range for lignin decomposition (35–65 kJ/mol) [12].
This discrepancy may be attributed to the broader range of heating rates used in this
study, as well as variations in the biomass source, including geographic origin, age,
and anatomical location within the tree [13]. Overall, the kinetic parameters obtained
in this work can be considered accurate and physically meaningful.

4 Conclusion
This study examined the thermal degradation behavior of densified wood under
an assumed real fire curve using thermogravimetric analysis. Experimental results
demonstrated that the densification process has negligible influence on mass loss
behavior when wood is tested in powdered form. A three-step kinetic model, based on
the decomposition of hemicellulose, cellulose, and lignin, was applied and calibrated
using inverse modeling and least squares optimization.
The estimated kinetic parameters showed good agreement with values reported in
the literature, confirming the validity of the model. Although the activation energy
for lignin decomposition was slightly lower than typical values, this deviation is
likely due to the wide range of heating conditions and differences in material origin.
Overall, the proposed methodology proves effective for simulating biomass pyrolysis
under realistic heating scenarios and offers a reliable approach for kinetic parameter
estimation in fire-related applications.

References
1. Branca C, Di Blasi C (2004) Global interinsic kinetics of wood oxidation. Fuel 83:81–87
2. Grioui N, Halouani K, Zoulalian A, Halouani F (2006) Thermogravimetric analysis and kinetics
modeling of isothermal carbonization of olive wood in inert atmosphere. Thermochim Acta
440:23–30
3. Di Blasi C (2008) Modeling chemical and physical processes of wood and biomass pyrolysis.
J Energ Combust Sci 34:47–90
4. Broström M, Nordina A, Pommer L, Branca C, Di Blasi C (2012) Influence of torrefaction on
the devolatilization and oxidation kinetics of wood. J Anal Appl Pyrolysis 96:100–109

374

T. T. Tran et al.

5. Cueff G, Mindeguia J, Dréan V, Breysse D, Auguin G (2018) Experimental and numerical
study of the thermomechanical behaviour of wood-based panels exposed to fire. Constr Build
Mater 160:668–678
6. Shen DK, Fang MX, Luo ZY, Cen KF (2006) Thermogravimetric analysis and kinetics modeling
of isothermal carbonization of olive wood in inert atmosphere. Fire Saf J 42:210–217
7. Di Blasi C (1993) Analysis of convection and secondary reaction effects within porous solid
fuels undergoing pyrolysis. Combust Sci Technol 90:315–340
8. Park WC, Antrya A, Baum HR (2010) Experimental and theoretical investigation of heat and
mass transfer processes during wood pyrolysis. Combust Flame J 157:481–494
9. Thi VD, Khelifa M, Khennane A, El Ganaoui M, Rogaume Y (2016) Finite element modeling
of the pyrolysis of wet wood subjected to fire. Fire Saf J 81:85–96
10. Zhao C, Zhang X, Liu L, Yu Y, Zheng W, Song P (2019) Probing chemical changes in
Holocellulose and lignin of timbers in ancient buildings. Journal List, Polymers, Basel
11. Nassar M, Mackay M (1984) Mechanism of thermal decomposition of lignin. Wood Fiber Sci
16:441–453
12. Várhegyi G, Antal M.J, Jakab E, Szabo P (1997) Kinetic modeling of biomass pyrolysis. J Anal
Appl Pyrolysis 42:73–87
13. Várhegyi G, Gronli MG, Di Blasi C (2004) Effects of sample origin, extraction and hot water
washing on the devolatilization kinetics of chestnut wood. J Ind Eng Chem Res 43:2356–2367

Special and Unique Structures
Construction

Aerodynamics of Ultra-Flexible
Structures
E. F. Khrapunov, S. A. Mozhayskiy, A. N. Novikov, V. V. Sokolov,
and S. Y. Solovev

Abstract Wind load is a key factor determining the design of most ultra-flexible
structures such as masts, towers, and flagpoles. Flagpoles with a height exceeding
100 m are probably the most complex objects. Traditionally, the wind load on a
flagpole is divided into two components: the load on the metal structure of the flagpole
and the load on the flag. The higher the flagpole, the larger the cloth attached to it.
As a rule, the cloth does not have any “supporting” rigid elements and can freely
change shape under the influence of wind, the speed of which at heights above 100 m
can reach 30–40 m/s. The paper presents an approach to conducting aerodynamic
studies of a flagpole model with a full-scale height exceeding 170 meters. The main
principles of creating a dynamically similar flagpole model are described, including
taking into account the probable form of icing of the structure. The principles of
conducting experimental studies of a flag whose natural dimensions exceed 30 m
in each direction are discussed separately. The main results of the studies are both
the characteristics of the dynamic response of the flagpole structure and additional
resistance coefficients induced by the flag.
Keywords Physical experiment · High-rise buildings · Unique structures · Wind
loads · Dynamic response · Wind tunnel · Vortex shedding · Icing · Aeroelastic
stability

1 Introduction
Of the ultra-flexible structures (such as masts and towers), the flagpole is the most
challenging in terms of wind load. This is partly due to the design characteristics of the
flagpole itself (hereafter: the metal base to which the flag is attached), which is usually
a long tube with a relatively small diameter, and partly due to the need to consider
the wind effect on the flexible flag fabric [1, 2]. It is a mistake to believe that the
E. F. Khrapunov (B) · S. A. Mozhayskiy · A. N. Novikov · V. V. Sokolov · S. Y. Solovev
Krylov State Research Centre, Petersburg, Russia
e-mail: hrapunov.evgenii@yandex.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_31

377

378

E. F. Khrapunov et al.

assignment of wind loads to a flagpole does not present any great difficulties. The need
to consider the loss of stability of the vortex excitation type in the initial configuration
of the object [3–6] as well as other types of loss of stability for configurations that
consider icing [7] can cause significant difficulties.
From the point of view of aerodynamic effect, however, the flag cloth is the
most complex element. The cloth is a flexible three-dimensional element with an
insignificant thickness (compared to the dimensions in the plan), which makes it
difficult to construct an analytical solution or perform numerical modeling. The only
method to study the cloth is a physical experiment in wind tunnels. However, the scale
effect must be taken into account in experimental studies [8–11]. Data on studies of
full-scale flags can be found in the literature, but these data are limited and were
obtained in an environment that does not quite match the real conditions for securing
modern flags. At the same time, the data obtained in wind tunnels describe models
whose dimensions in the plan rarely exceed 2 m in any direction.
The interaction of the flag material with air flow is determined by two aerodynamic
processes: the process of friction on the surface of the material (boundary layer
growth) and the process of air vortex movement due to surface deformation [1].
Numerous studies investigating the interaction of flexible fabric and airflow have
allowed us to identify several key properties that influence the flow:
•
•
•
•

The aspect ratio of the fabric,
The specific weight of the fabric material,
The strength properties of the fabric material,
The thickness of the fabric.

When conducting experimental studies in a wind tunnel, the similarity criterion can
be a series of values that are described in the papers [1–4].
U·

M3
ρair 2 D

1/2

(1)

This dimensionless complex is the only criterion for similarity for flags where no
additional longitudinal tension occurs during attachment.
This article describes a complete cycle of aerodynamic studies carried out in a
wind tunnel for a flagpole model with a full-scale height of over 170 meters. The
main principles for creating a dynamically similar flagpole model are described,
including consideration of the likely shape of the structure’s icing. The principles
of conducting experimental studies on a full-scale flagpole with dimensions greater
than 30 m in each direction are discussed separately. The main results of the studies
are both the characteristics of the dynamic response of the flagpole structure and
additional drag coefficients induced by the flag.

Aerodynamics of Ultra-Flexible Structures

379

2 Models Description and Test Rig
All the studies described in this article were carried out in the Large Wind Tunnel of
the Krylov State Research Centre. This tunnel is a closed-type wind tunnel with an
open test section with an elliptical cross-section. The dimensions of the test section
are: major axis of the ellipse—4.00 m, minor axis—2.30 m, cross-sectional area of
the test section—7.32 m2, length of the test section—5.00 m. The degree of nonuniformity and turbulence of the flow in the test section of the tunnel did not exceed
1.0% and 0.5% respectively. Fig. 1 shows a diagram of the Large Wind Tunnel.
From the point of view of the effect of wind on the metal structure of a flagpole,
both the integral values of the forces and tilting moments and the characteristics
of the dynamic reaction are of interest. Since most flagpoles are structures with a
circular cross-section, the time-averaged values of the aerodynamic force can be
determined using reference data on the drag coefficients of cylindrical bodies. The
general formula for calculating the aerodynamic drag force is
Fx = 0, 5 · ρ · u2 · D · cx

(2)

where ρ—air density, kg/m3 ; u—air velocity at the height of the object, m/s; D—the
diameter of the object, m.
It is known that the value of the drag coefficient for cylindrical surfaces is strongly
dependent on the Reynolds number. Diagrams on the dependence of the drag coefficient on the Reynolds number are also presented in the technical literature [4, 5].
The determination of the static forces acting on the flagpole (without icing and the
influence of the flag cloth) can therefore be carried out based on of reference data
and does not require any experimental investigations.
From the point of view of the aerodynamics of flagpoles, the most interesting
properties are the dynamic response. The most advanced method to determine the
dynamic response of a structure to wind action is to carry out experimental studies
with aeroelastic models. Aeroelastic models (fully dynamically similar) require not

Fig. 1 Scheme of the large wind tunnel of the Krylov State Research Center

380

E. F. Khrapunov et al.

only geometric similarity but also a similarity in mass, stiffness, and damping properties. The addition of new parameters to the modeled system requires the consideration
of new similarity criteria, which are listed in Table 1.
The analysis of the similarity criteria presented in Table 1 leads us to the following
conclusion. The total mass of the object is scaled as a cube of linear scale, maintaining
the density of the environment in which the full-scale structure and its model are
located. The dimensions of a full-scale flagpole (in the context of this work—over
170 meters). A model reduced even by a factor of 170 (linear scale 1:170) requires a
reduction in mass of almost 5 × 106 times. Considering that the mass of a full-scale
structure is less than 3 × 105 kg, it is impossible to produce a complete, dynamically
similar model. For this reason, a two-part dynamic model is produced for highly
flexible structures. The first part is responsible for the stiffness of the structure. The
second part for the geometric similarity. During the experimental studies, the first
section is outside the airflow, as its flow does not correspond to the full-size structure.
This division allows the linear scale of the problem to be increased, as the geometric
similarity is ensured by having only one fragment of the model in the airflow. Thus,
in the present studies, the linear scale of the problem was 1:20 and the scale of the
total mass was 1:8 × 103 .
The lower element of the model used is a metal rod with a diameter of 50 mm
and a length of 1200 mm. The properties of the steel, the diameter of the rod, and
its length are chosen so as to ensure similarity with the natural object in terms of
stiffness properties (the Cauchy criterion from Table 1). The upper element of the
model is a wooden cylinder with a diameter of 90 mm. The diameter of the cylinder
ensures geometric similarity with the natural structure at a scale of 1:20. The length
of the cylinder is 1750 mm. During the experimental tests, the entire wooden cylinder
is in the airflow. The connection between the metal rod and the cylinder is located in
the test section of the wind tunnel at the level of the lower boundary of the airflow.
In order to eliminate the influence of this model unit on the properties obtained, it is
covered with a paneling that has no rigid connection with the model.
During the experimental studies with optical distance measurement sensors, the
displacements of the top of the model were recorded in two orthogonal directions:
along and across the flow. The resulting temporal records of the displacements made
it possible to calculate the following characteristics: average displacements of the
top of the flagpole under the action of the airflow; the amplitude of the oscillations
of the top of the flagpole under the action of the airflow.
Taking into account the characteristics of the icing of cylindrical surfaces and
the possible development of aeroelastic instabilities caused by this icing [5], the
Table 1 Similarity criteria for aeroelastic models
Criterion

Formulae

General description
·

L 4 )−1

Cauchy

Ca = (E · J) · (ρ ·

Newton

Nw = M · (ρ · L 3 )−1

Mass similarity M

Scruton

Sc = M · δ · (ρ · L 3 )−1

Damping similarity δ

Stiffness similarity E J

Aerodynamics of Ultra-Flexible Structures

381

Fig. 2 Flagpole icing form
adopted in accordance with
[7]

characteristics of the dynamic response to changes in the shape of the model surface
were investigated in experimental studies. The calculation of the changed shape of
the object, taking into account ice deposits, was carried out on the basis of the data
presented in [7]. The simulated shape of the icing is shown in Fig. 2. In addition to
the shape of the icing, the additional mass created by the ice frozen on the surface of
the object was also simulated. When calculating the mass, it was taken into account
that it is ice deposits that are being formed.
Since the analyzed object is axially symmetrical, the freezing area of the ice can
form on any of the surfaces. For this reason, studies were carried out in the present
work at different flow angles in the presence of icing.
Before conducting the main series of experimental studies, the logarithmic decrement of the model oscillations was measured. It was found that the value of the
decrement for the model produced was 0.025. Note that modeling the decrement for
flexible flagpoles is a difficult task as, by the requirements of the technical documents [12], it is recommended to assume a logarithmic decrement value of 0.0125
for steel pipes. For this reason, one of the objectives of the studies was to determine
the dependence of the vibration amplitudes on the decrement value to subsequently
construct an approximating and extrapolating dependence.
To solve the problem, a system of flexible struts was used, which were rigidly
attached to the top of the model and to the fixed parts of the wind tunnel. The outer
diameter of the struts was no more than 2 mm. The struts were arranged symmetrically
to the symmetry axis of the model. The use of thin, symmetrically arranged struts
made it possible to minimize their influence on the structure of the flow around the
model of the investigated object.
The main series of experimental investigations of the flagpole was carried out
according to the following algorithm. After installing the model in the test section of
the wind tunnel, an airflow was generated, the speed of which was set by the operator.
For a certain period (usually several minutes), the deviations of the upper point of

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E. F. Khrapunov et al.

the model under the action of a uniform flow at a certain speed were recorded. If no
oscillations occur, the flow speed is increased to the next selected value.
Since the studies were carried out at a higher decrement value, at velocity values
close to the critical limit, the model was additionally excited, whereupon the measurement system recorded the development of these disturbances. This technique allowed
us to determine the characteristics of the stability of the system to perturbations that
could not occur in the main series of experimental studies.
Since the purpose of the conducted research was to obtain information on the
aerodynamic properties of the flagpole structure considering the flag, a separate
series of studies were carried out to determine the additional drag generated by the
flag cloth. It is known that in the dynamics of a flexible cloth, the most important
determining parameters are the aspect ratio and the density of the material [8–11].
At the same time, the question of the scale effect when transferring the results of
experimental studies to a true-to-scale object has not yet been fully clarified. For this
reason, samples of the same materials were used for the experimental studies from
which the cloths of the full-scale object were used to be produced.
The canvas of the natural flag is a rectangle with side dimensions 50 m × 30 m.
Two fabric samples were analyzed: with a density of approximately 114 g/m2 and
128 g/m2 . The flag models were analyzed in scales 1:20, 1:25, 1:30, and 1:40.
A special stand was used for the experimental studies, consisting of two vertical
walls with streamlined edges and a metal rod to which the models to be analyzed were
attached. In each of the vertical walls, there are multi-component dynamometers to
whose measuring platforms the ends of the rod are rigidly attached. The use of the
described system allows us to obtain the values of the components of aerodynamic
force and torque relative to the axis of the rod. The axes of the XOY coordinate
system were orientated as follows: OX—along the flow, OY—vertically upwards.
Prior to the main test series, the rod resistance was measured at various airflow
velocities without taking the plume models into account. The values obtained were
considered as the initial resistance at the corresponding speed in the main series of
experimental studies. The system for attaching the models to the rod corresponds to
the natural system.

3 Results of the Experimental Studies
As a result of the aerodynamic studies of the initial configuration of the model,
the following dependencies of the natural variables on the natural wind speed were
determined:
• Average displacement of the upper point of the structure relative to the initial
position XH and YH along the axes of the associated coordinate system;
• Maximum amplitudes of the oscillations of the upper point of the structure AXH ,
max and AYH , max along the axes of the associated coordinate system relative to
the average displacements.

Aerodynamics of Ultra-Flexible Structures

383

Fig. 3 Dependencies of average displacements of the top of the structure in the initial configuration

The values of the average displacements of the top of the structure XH and YH
for the range of full-scale velocities are shown in Fig. 3.
The values of the displacements XH relative to the initial position in the initial
configuration grow proportionally to the velocity pressure. Theoretically, the flow of
a uniform airflow around a symmetrical body should not lead to the formation of a
lateral force. However, real objects do not have ideal symmetry and always exhibit
a certain deviation from the symmetrical shape. The effects of asymmetry become
more active when the intensity of the impact increases, i.e., when the flow velocity
increases. For this reason, the values of the displacements YH were recorded during
the experimental investigations of the model, which turned out to be dependent on
the flow velocity of the air. It is noteworthy that the displacement across the flow
increases at high velocities.
The maximum values of the amplitudes of the top of the structure AXHmax and
AYHmax for the range of natural velocities are shown in Fig. 4.
The values of the maximum amplitudes of the longitudinal oscillations AXHmax
of the model top increase monotonically with increasing speed. This is due to the
presence of a non-zero dynamic response of the system to the airflow. The characteristics of the dynamic response (not the loss of stability), which are determined

Fig. 4 Dependencies of the maximum amplitudes of oscillations of the top of the structure in the
initial configuration

384

E. F. Khrapunov et al.

in a low-turbulence flow, are generally underestimated and must be corrected when
transferred to a full-scale structure. The values of the maximum amplitudes AYHmax
allow the conclusion that there is a vortex resonance at a velocity of about 2 m/s
in full-scale. The Strouhal number is calculated on the basis of the diameter of the
upper part of the model and the critical velocity is 0.27, which corresponds to the
supercritical flow regime and is in good agreement with the known data for circular
cylinders.
It is well-known that the flow properties around cylindrical bodies depend on a
variety of factors. However, the Strouhal number determined from experimental data
suggests that the supercritical flow regime characteristic of a full-scale object was
realized during the experimental studies. Therefore, the data on the loss of aerodynamic stability obtained during experimental studies in the wind tunnel can be used
for a full-scale object (considering the linear scale) without additional adjustments.
The maximum amplitudes of the oscillations of the upper surface of the model
during vortex resonance do not exceed 70 mm. With increasing velocity, the amplitudes of the oscillations along and across the flow increase, which is explained by
the development of non-stationary processes in the flow around cylindrical bodies.
The maximum values of the oscillation amplitudes of the top of the structure
during vortex resonance at different decrement values are shown in Fig. 5.
The dependence of the maximum amplitude of the top of the structure on the
decrement value, which we obtained through experimental investigations, allows us
to estimate the maximum vibration amplitudes at lower damping values. For this
purpose, the experimentally determined amplitude values were approximated by a
power function. The type of the function and the values of its coefficients are shown
in Fig. 6.
The values of the average displacements of the top of the structure ΔX H ice and
ΔY H ice for the range of natural velocities are shown in Fig. 6. The presence of icing
at an angle of 5° leads to an increase in the average deviations in the direction across
the flow, while the presence of icing at angles of 0, 15, 45° does not cause an average

Fig. 5 Dependence of the amplitude of oscillations of the top of the structure during vortex
resonance on the value of the decrement

Aerodynamics of Ultra-Flexible Structures

385

Fig. 6 a Displacements of the top of the structure in X direction; b displacements of the top of the
structure in Y direction

displacement in the specified direction. In the presence of icing, a general tendency
towards an increase in the average deviation of the model tip along the flow can
be observed. At the same time, at an angle of 5° there is a strong increase in the
deviation, which is comparable in its values to the deviation at an angle of 45°.
The maximum values of the amplitudes of the top of the structure AXHmax ice and
AYHmax ice for the range of natural speeds are shown in Fig. 7.
As in the initial model configuration, the maximum values of the oscillation amplitudes along the flow increase with the increase of the natural velocity in the presence
of icing. In this case, the amplitude values depend only weakly on the angle.
As with the initial configuration of the model, in the presence of icing, the model
is characterized by the phenomenon of vortex resonance, which is observed in the
velocity range of 2 to 3 m/s. As the flow angle increases, the maximum values of the
amplitudes increase.
Photo of bunting models in the test section of the wind tunnel during the research
is shown at the Fig. 8. It can be seen that regardless of the scale of the model, the
part of the cloth that is closer to the pole remains in a stable position, the effect of the
air flow leads to small local curvatures of the plume surface. The trailing edge of the
model is most susceptible to vibrations, the shape of the curvature of which changes
significantly over time during the investigation. In addition to the curvature of the
trailing edge, the cloth is capable of “collapsing”: under the effect of an unevenly
distributed pressure, a fold is formed that is not stable. The further effect of the

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E. F. Khrapunov et al.

Fig. 7 a Maximum amplitudes of vibrations of the top of the structure in X direction; b maximum
amplitudes of vibrations of the top of the structure in X direction

flow smoothest the crease considerably, creating an additional contribution to the
resistance.
The dimensionless aerodynamic drag coefficient of the flag models was determined using the following relationship

Fig. 8 Flag models in the test section of the wind tunnel

Aerodynamics of Ultra-Flexible Structures

387

Fig. 9 Dependence of the aerodynamic drag coefficient of flag models on the flow speed

cx,fl = 0, 5 · ρ · u2 · Sfl

−1

· Fx,fl

(3)

where F x,fl —aerodynamic drag force, N; S fl —the area of the flag, m2 .
During the experimental studies, the air flow velocity was varied from 5 to 35 m/
s. The results of the experimental studies of the flag models are presented in Fig. 9.
The dependencies from Sect. 7.12 [4], calculated for flag models of the corresponding densities are also shown in Fig. 9. Good agreement was obtained between
the experimental data and the data from [4].
Experimental studies of flag models have shown that after a certain flow velocity,
the value of the aerodynamic drag coefficient Cxfl remains virtually unchanged.
Starting from speeds of 15 m/s, the values of the Cxfl coefficients for all flag models
are in the range of 0.045 with a spread of ±0.007.

4 Conclusion
The paper presents the results of modeling a flagpole over 170 m high and a flag cloth.
It shows how to use a dynamically similar model to conduct a study of the stability
of the flagpole, as well as to assess the effect of the icing shape of the structure
on aerodynamic stability. Small values of the attenuation decrement, typical for a
natural object, were taken into account.
The studies of the flag were conducted taking into account the difficulty of
translating the research results to full scale.

388

E. F. Khrapunov et al.

References
1. Morris-Thomas MT, Steen S (2009) Experiments on the stability and drag of a flexible sheet
under in-plane tension in uniform flow. J Fluids Struct 25(5):815–830. https://doi.org/10.1016/
j.jfluidstructs.2009.02.003
2. Fairthorne RA (1930) Drag of flags. Reports and Memoranda, The Aeronautical Research
Council, UK 1345:887–891
3. SP 20.133330.2016 (2016) Loads and actions. Standartinform, Moscow
4. EN 1991-1-4:2005+A1 (2010) Eurocode 1: actions on structures 1–4: general actions—wind
actions. CEN, Brussels
5. Simiu E, DongHun Y (2019) Wind effects on structures. Modern Structural Design for Wind,
Wiley Blackwell, London
6. Scruton C, Flint AR (1964) Wind-excited oscillations of structures. Proc Inst Civ Eng 27:673–
702. https://doi.org/10.1680/iicep.1964.10179
7. ISO 12494 (2017) Atmospheric icing of structures. International Standard confirmed, p 58
8. Carruthers AC, Filippone A (2005) Aerodynamic drag of streamers and flags. J of Aircraft
42(4):976–982. https://doi.org/10.2514/1.9754
9. Taneda S (1967) Waving motions of flags. J Phys Soc Jpn 24(2):392–401. https://doi.org/10.
1143/JPSJ.24.392
10. Tand L, Païdoussis MP (2008) The influence of the wake on the stability of cantilevered flexible
plates in axial flow. J Sound Vib 310(3):512–526
11. Yamaguchi N, Ito K, Ogata M (2003) Flutter limits and behaviors of flexible webs having a
simplified basic configuration in high-speed flow. ASME J Fluids Eng 125(2):345–353. https://
doi.org/10.1115/1.1537254
12. The CICIND chimney book industrial chimneys of concrete and steel. https://cicind.org/pub
lications/steel-chimneys.html

Main Characteristics of Equal-Strength
Six-Span Beam
M. V. Alexandrovsky, S. A. Martyusheva, S. V. Merkulova,
and E. S. Lazutina

Abstract The paper examines a six-span, equal-strength beam used in modern
construction to create stable and efficient structures. The main characteristics and
advantages of equal-strength six-span beams are noted: a multi-span, equal-strength
beam differs from other types of beams by having the same strength along the entire
length of the beam and ensures uniform load and stress distribution. Six spans separated by supports make it possible to distribute the load on the building structure more
efficiently, while reducing bending and deformation of the building structure. In an
equally strong multi-span beam, all sections have the same shape and dimensions,
which simplifies calculation and design. With the reduced weight of the multi-span
beam, in comparison with traditional beams, its strength and rigidity remain. A
numerical calculation has been performed in the Python programming language for
the maximum calculated tangential stress depending on the cross-section height of
a six-span beam at different values of its span lengths. The loads that a multi-span
beam can withstand are determined, as well as ensure its reliability, strength and
safety during the operation of the erected building structure. Based on the results
of the calculations performed, graphs of the dependences of normal and tangential
stresses on the height of the section in a six-span beam are constructed. The dependence of stresses in the cross section of an equal-strength six-span beam on the length
of its span has been established.
Keywords Multi-span beam · Evenly distributed load · Optimization method ·
Normal stress · Tangential stress · Design stress · Load · Beam span · Stress

M. V. Alexandrovsky · S. A. Martyusheva · S. V. Merkulova · E. S. Lazutina (B)
Moscow State University of Civil Engineering, Moscow, Russia
e-mail: lazutinaekaterina909@gmail.com
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_32

389

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M. V. Alexandrovsky et al.

1 Introduction
The span beam is one of the important elements in construction that ensure the reliability and strength of the floors. These structures play a key role in load distribution
and maintaining the integrity of structures. A multi-span equal-strength beam differs
from other types of beams in several key parameters: the same strength along the
entire length of the beam, ensuring uniform distribution of load and stress; multi-span:
Structural form—multi-span beams consist of several spans that are connected
to each other, which allows uniform distribution of loads along the entire length of
the structure and makes them more resistant to deformation, increasing their overall
strength; single-span beams have only one span and are easier to calculate, but are
not effective for large spans due to the concentration of forces in the center;
Load distribution—in multi-span beams, loads are distributed over several spans,
which reduces the maximum moments and forces acting on the structure, and
allows the use of smaller section sizes compared to single-span beams where loads
are concentrated on a single support, resulting in larger maximum moments and,
consequently, the need for more massive sections;
Stability and stiffness—multi-span equal-strength beams have greater stiffness
and resistance to bending deformations due to the distribution of the load among
several spans. This makes them preferable for large spans and complex structures
such as bridges and industrial buildings; single span girders may be less stable at
larger spans, requiring additional structural solutions such as the use of additional
supports or reinforcement of sections [1, 2].
In general, multi-span equal-strength beams offer a number of advantages in terms
of stability and load distribution. Optimized geometry leads to minimizing the use of
material and, consequently, to minimizing costs, achieving sustainable development
goals, reducing its own weight, as well as to many architectural advantages [3], which
makes the beams in question an important element in modern construction. Their
use is particularly relevant in applications where high load-bearing capacity must be
combined with aesthetics and environmental friendliness. For example, in projects
with stringent carbon footprint requirements or in the creation of unique architectural
forms where traditional solutions are too bulky. Thanks to their adaptability, such
beams continue to find new applications, pushing the boundaries of engineering.
In a statically defined beam, the transverse force and bending moment are independent of the stiffness distribution along its length. In contrast, in statically indeterminate beams, a change in stiffness in a particular section leads to a redistribution of
loads, which complicates the task of optimizing the geometry of the section. Traditional calculation methods based on analytical solutions often turn out to be too
complex or inaccurate for complex geometric shapes and uneven loads. Nowadays,
the optimization method is increasingly used to solve the problems of calculating
multi-span beams, making it possible to find optimal design parameters that ensure
maximum efficiency and reliability [4].

Main Characteristics of Equal-Strength Six-Span Beam

391

2 Methods and Materials
Let’s consider a method for optimizing continuous beams using the example of a
beam loaded with a uniformly distributed load q (Fig. 1).
Let’s define efforts using the forces method:
⎧
⎪
δ x + δ12 x2 + δ13 x3 + δ14 x4 + δ15 x5 + Δ1p
⎪
⎪ 11 1
⎪
⎪
⎨ δ21 x1 + δ22 x2 + δ23 x3 + δ24 x4 + δ25 x5 + Δ2p
δ31 x1 + δ32 x2 + δ33 x3 + δ34 x4 + δ35 x5 + Δ3p
⎪
⎪
⎪
δ
41 x1 + δ42 x2 + δ43 x3 + δ44 x4 + δ45 x5 + Δ4p
⎪
⎪
⎩δ x + δ x + δ x + δ x + δ x + Δ
51 1
52 2
53 3
54 4
55 5
5p

=0
=0
=0
=0
=0

Consider a six-span equal-strength beam with a load q acting on it. Let’s show on
this beam a cargo and a single plot of the force method (Fig. 2).
We use Mohr’s formulas to determine the unit and load coefficients, where we
calculate the integrals using the trapezoid method:
δij =

Mi Mj
dx
EJ (x)

(1)

Δip =

Mi Mp
dx
EJ (x)

(2)

Fig. 1 An uncut beam loaded with a distributed load q. Diagrams of transverse forces Qy and
bending moments M x

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Fig. 2 The main system, cargo and unit diagrams of the force method

As a cross–section of the beam, we will take the type of welded I-beam made of steel
[5] of class C235, where b is the variable width of the shelf, and the other dimensions
are constant (Fig. 3).
Defining geometric characteristics:
J =

bt 3
h+t
dh3
+2
+ bt
12
12
2

(3)

A = 2bt + dh

S(y) =

⎧
⎨ bt
⎩b
2

Fig. 3 Steel I-beam—the
cross section of a welded
beam

2
h+t
+ d2 h4 − y2 , 0
2
2
h
+ t − y2 , 2h ≤ y
2

(4)
≤y≤
≤

h
2

(5)

Main Characteristics of Equal-Strength Six-Span Beam

393

To find the calculated voltage, normal and tangential stresses are required:
σ (y) =
τ (y) =

QS(y)
,0
dJ
QS(y) h
,2
bJ

M
y
J
≤y≤
≤y≤

(6)
h
2
h
2

(7)

According to the IV theory of strength, the design stress can be calculated using the
formula (8) [5], substituting (6) and (7):
σrach =

σ 2 + 3τ 3

(8)

It is known that normal stresses in a beam vary in cross-section height according to
a linear law, reaching the highest values at the points furthest from the neutral axis.
Tangential stresses vary along a parabola, reaching their maximum value at points
lying on the neutral X-axis [6].
It is also known that the bending moment reaches its maximum value in those
sections of the beam where the transverse force is zero (Q = 0).
The beam will be equally strong if the maximum design stresses in each section
are the same.
The optimization method will be as follows:
1. First, we take the width of shelf b as a constant and calculate the maximum design
stresses in each section.
2. Next, we change the size of the width of shelf b in proportion to the stresses that
have arisen
b∗ (x) = b(x)

σrach (x)
max
σrach

(9)

max
is the maximum design stress along the entire length of the beam, σ rach
where σrach
is the maximum stress in a given section.
In order for the mass of the beam to remain the same when approaching, it is
necessary to multiply the value b in each section by the coefficient

V0
,
V

(10)

where V 0 = AL is the volume of the beam of constant cross-section,
L

V =

A(x)d (x)

is the volume of the beam of variable cross-section.

(11)

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Fig. 4 Change of design stresses at l = 8 m, l = 13 m, l = 17 m
max
The process will continue until σrach
the maximum calculated stresses in the
previous and subsequent approximations cease to differ from each other by more
than 1% [7].
The graph shown (Fig. 4) shows how the calculated height stress in the section
changes for different span lengths l = 8 m, l = 13 m, l = 17 m.
The main elements of the graph are the variable y, the height in section, measured
in meters (m), and the design voltage, measured in (kN/m2 ).
Graph lines: blue line (l = 8 m). This line shows the smallest percentage ratio,
which follows a low growth as the value (y) increases. The results remain almost
constant, but with minor fluctuations. Orange line (l = 13 m): This line shows a
more pronounced increase in the percentage ratio, which varies significantly from (y
= 0.3) to (y = 0.5). Green line (l = 17 m): The highest percentage, marked by the
sharpest increase on the graph. The line shows steady growth, reaching a maximum
and then sharply decreasing at higher values (y).
Figure 5 shows the dependences of the normal voltage (kN/m2 ) on the coordinate
of the cross-section height y (m) for l = 8 m, l = 13 m, l = 17 m.
The main elements of the graph are: on the X-axis, the section height (m); on the
Y-axis, the normal voltage (kN/m2 ). The basic percentage growth shown by the blue
line on the graph at l = 8 m shows that the growth rate is the lowest among those
presented. The orange line (l = 13 m) shows a more pronounced increase compared
to the blue one, which means that the percentage continues to grow, but its slope is
noticeably steeper than that of the previous line, indicating a faster increase in the y
range.

Main Characteristics of Equal-Strength Six-Span Beam

395

Fig. 5 Change of normal stresses at l = 8 m, l = 13 m, l = 17 m

The green line (l = 17 m) shows the highest percentage increase. This line shows
the steepest slope among the three graphs, which indicates a significant increase in
the percentage ratio as y increases.
Figure 6 shows the dependence of the tangential stress on the height in the section
at various values l = 8 m, l = 13 m, l = 17 m. It can be seen from the graph that the
greatest tangential stress is observed in the center of the sample and decreases as it
approaches the value of y = 0.55. In this case, the tangential stress for the case l =
17 m is less than for the case l = 13 m, and the stress for the case l = 13 m is less
than for the case l = 8 m. There is a sharp decrease in the tangential stress at the edge
of the sample. Tangential stresses are maximal in the central part of the section (y =
0) and decrease towards the edges. This is due to the fact that the upper and lower
parts of the section experience lower transverse forces.

3 Results and Discussion
The use of beams of variable cross-section is rational as load-bearing structures of
coatings, structures of various kinds of technological platforms, beams of railway
wagons, load-bearing structures of bridges and overpasses [8].
Bridges: in welded split beams, the cross-section can change several times
depending on design decisions and structural requirements. Usually, cross-section
changes occur in places where it is necessary to take into account loads, transitions
between different materials, or joint features. The method of changing the section,

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M. V. Alexandrovsky et al.

Fig. 6 Change of tangential stresses at l = 8 m, l = 13 m, l = 17 m

including changing the height of the wall, allows you to optimize the strength, reduce
the weight of the bridge, increase rigidity and adapt to specific conditions.
Industrial buildings: cross-section changes can occur from one to several times
along the beam, depending on design decisions and requirements. They usually occur
in cases of load changes, transitions between different materials, or simplification of
the structure. Optimization of cross sections allows you to redistribute loads, save
materials, improve thermal performance and adapt to technological requirements.
Sports facilities: on average, cross-section changes can occur from 2 to 5 times,
but this number may vary depending on the specific project and its features. In
such structures, cross-sectional changes may be related to functional zones, transitions between levels, and architectural forms. Changing the cross-section, including
changing the height of the wall, is actively used in the construction of sports facilities, taking into account acoustic characteristics, aesthetics, functionality, technical
systems and safety.
Residential complexes: on average, cross-section changes in residential
complexes occur from 2 to 4 times, but the exact number depends on the specific
project and its features. Usually, cross-section changes occur at the junctions with
other elements, when changing the functional purpose of the premises and depending
on the architectural design. Changing the height of the wall as a method of changing
the cross-section is widely used in the construction of residential complexes, although
it is most often used not along the entire wall, but along its individual parts.
Advantages include functionality, aesthetics, and cost-effectiveness.
Shopping malls: in shopping malls, cross-section changes can occur from 3 to
6 times, but this number can vary significantly depending on the specific project
and its features. Usually, cross-section changes occur during transitions between

Main Characteristics of Equal-Strength Six-Span Beam

397

floors, in areas with high loads, and at junctions with other structural elements.
Changing the wall height as a method of changing the cross-section is actively used
in the construction of shopping malls, including storefronts, atriums, zoning and
architectural elements.
A few less obvious but important examples of applications:
• Aerospace structures: beams of variable cross-section have found wide application
in the construction of hangar structures for aircraft. Their use makes it possible
to create unsupported slabs of significant spans, effectively absorbing loads from
roof structures and suspended process equipment. This structural element is of
particular relevance in the construction of rocket launch complexes, where it is
required to ensure the stability of service towers and protective structures under
unevenly distributed loads.
• Shipbuilding and port infrastructure: an integral component of crane trestles. Their
cantilever design optimally distributes the load, reaching maximum values at the
base and gradually decreasing towards the end of the boom. The same principle
applies to ship docks and slips, where the load-bearing elements are subjected to
considerable alternating loads during the launching and lifting of ships.
• Energy and industrial plants: the effective use of such beams in the construction
of transmission towers and transmission masts. The progressive reduction of the
cross-sectional area in height allows optimal counteraction to wind loads, the
intensity of which decreases as the height of the structure increases. In wind power
engineering, this approach is implemented in the design of tower structures and
supporting elements of blade systems, which contributes to reducing the total
weight of the structure and minimizing aerodynamic resistance.
• Agricultural structures: when erecting arched greenhouse complexes and
granaries. The use of multi-span beams provides uniform distribution of snow
and wind loads, which is especially important in regions with extreme climatic
conditions. In livestock complexes (cowsheds and poultry houses) the use of such
beams allows to create large-span ceilings with a minimum number of supports,
which significantly increases the ease of operation of the premises.
• Transport infrastructure: beams of variable cross-section have found application
in the construction of noise barriers along highways. Their design features make it
possible to effectively absorb dynamic loads caused by wind and vibrations from
passing traffic. In depots for electric trains and subways, these elements provide
reliable overlapping of spans under significant uneven loads from overhead
utilities.
• Cult and historical buildings: when restoring churches and cathedrals, beams are
invisibly integrated into old structures for reinforcement without changing the
visual appearance. And in the construction of modern temples with domed ceilings, they can be used to create lightweight but strong frameworks with complex
shapes.
• Temporary and mobile structures: collapsible emergency hangars equipped with
such structural elements have increased resistance to extreme weather conditions
(snow loads, hurricane winds). In the sphere of organizing mass events, trusses

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M. V. Alexandrovsky et al.

with variable cross-section are successfully used to create stage structures capable
of withstanding significant loads from suspended sound and lighting equipment.
The advantages in these examples are:
• Material savings—thickening only in areas of maximum stress.
• Weight reduction—critical for high-rise and mobile structures.
• Design flexibility—adaptation to non-standard shapes (arches, consoles).
It is also possible to use six-span beams in large-span column-free underground
spatial structures, which is described in the articles [9].

4 Conclusion
A method for optimizing the calculation of continuous beams is considered using
the example of a six-span beam loaded with a uniformly distributed load. The loads
that a multi-span beam can withstand, as well as ensuring its reliability, strength and
safety during the operation of the erected building structure, have been determined.
All dynamic calculations for a multi-span beam are performed in the Python
programming language. However, to optimize the design of reinforced concrete
beams, including detailing, you can use the Python PyRCD object–oriented package
[10–13]. Based on the results of the calculations performed, graphs of the dependences of normal and tangential stresses on the height of the section in the beam
are constructed. The dependence of stresses in the cross section of an equal-strength
six-span beam on the length of its span has also been established. The values of
normal and tangential stresses for different span lengths of a six-span beam were
compared.
It is shown that with a span length of l = 8 m, an I-beam wall height of h = 1 m,
an I-beam shelf thickness of t = 8 cm, an I-beam wall thickness of d = 6 cm, an
I-beam shelf width of b = 52 cm, and a load of q = 50 kg/m, the maximum rated
voltage will be 11.8 MPa.

References
1. Span beams: the key to the reliability and strength of your floors, investsteel.ru. https://
investsteel.ru/blog/novosti/proletnyie-balki-gorizontalnyie-metallicheskie-konstrukczii,podderzhivayushhie-perekryitiya?ysclid=m32yyhm9ir444700019. Accessed 25 Nov
2024
2. Calculation of statically indeterminate beams, soprotmat.ru. https://soprotmat.ru/sila4.htm.
Accessed 12 Jan 2025
3. Deligia M, Congiu E, Marano GC, Briseghella B, Fenu L (2021) Structural optimization of
composite steel trussed-concrete beams. Procedia Struct Integr 33(2011):613–622. https://doi.
org/10.1016/j.prostr.2021.10.068

Main Characteristics of Equal-Strength Six-Span Beam

399

4. Lingyu Z, Liping W, Liqiang J (2022) Materials of steel structures. Des Steel Struct:19–67.
https://doi.org/10.1016/B978-0-323-91682-0.00016-9
5. Calculation of statically indeterminate beams, soprotmat.ru. https://soprotmat.ru/sila4.htm.
Accessed 20 Jan 2025
6. Chepurnenko AS, Andreev VI, Jazyev BM (2014) Model of equal-stressed cylinder based on
the Mohr failure criterion. Adv Mater Res 887-888:869–872. https://doi.org/10.4028/www.sci
entific.net/AMR.887-888.869
7. Case J (2014) Stresses in flat plates due to bending. Strength Mater:489–501. https://doi.org/
10.1016/B978-1-4831-9652-7.50079-7
8. Andreev VI (2012) The method of optimization of thick-walled shells based on solving inverse
problems of the theory of elasticity of inhomogeneous bodies. Computer aided optimum Design
in Engineering XII, vol 13. WITpress, pp 189–201. https://doi.org/10.2495/OP120171
9. De Biagi V, Chiaia B, Marano GC, Fiore A (2020) Series solution of beams with variable
cross-section. Procedia Manuf 44:489–496. https://doi.org/10.1016/j.promfg.2020.02.265
10. Liang S, Hou W, Gao Y, Guo W (2024) Local multiscale method for beam-column joint
and its application in large-span column-free underground spatial structures. Structure 61(9–
10):106031. https://doi.org/10.1016/j.istruc.2024.106031
11. Izhar T, Ahmad SA, PyRCD NM (2024) Object-oriented python package for detailed multiobjective design optimization of reinforced concrete beams. Dep Civ Eng 21(4):100691. https://
doi.org/10.1016/j.simpa.2024.100691
12. Egereva EN, Zubov AO, Egerev AY (2018) Transverse oscillatory motion in viscous fluid in
contact with porous medium. Mordovia Univ Bull 28(2):164–174. https://doi.org/10.15507/
0236-2910.028.201802.164-174
13. Egereva EN, Barmenkov AS (2019) Overload in the roof trusses of the media Center building
in Saransk. In: E3S web of conferences, vol 110, p 01079. https://doi.org/10.1051/e3sconf/201
911001079

Application of the Theory of Elasticity
to the Study of Cracks in Bridge
Structures
M. V. Alexandrovskyi, R. R. Khakimzyanov, V. A. Vyatkin,
and M. A. Denisenko

Abstract The causes of bridge structure failures are examined, with a focus on
technologies aimed at increasing bridge reliability and extending service life. The
analysis considers dynamic loading and the physical and mechanical properties of
materials. Structural modeling is conducted under the assumption of linear elasticity. The methods employed include the theory of elasticity and the finite difference
method, allowing for the consideration of various physical properties of individual
bridge components. Relationships are established between crack width and reinforcement diameter, as well as between stiffness tensor components and crack orientation angle. The study investigates the development of both normal and inclined
cracks under operational loads, and assesses the influence of reinforcement geometry, crack orientation, and material stiffness on structural behavior. Special attention is given to fatigue cracks caused by repeated traffic loading, which are critical
for bridge durability. Analytical models are developed using the non-interaction
approximation of cracks, enabling the evaluation of effective material properties
in damaged zones. Graphical dependencies illustrate how crack geometry affects
stiffness tensor components, offering deeper insight into the mechanical state of
bridge elements. The methodology includes numerical tools in Python for simulating crack propagation and assessing the mechanical response of the structure.
The results highlight the importance of comprehensive monitoring and control of
cracking in bridge design, particularly in areas exposed to resonance, cyclic loading,
and external factors. Recommendations are proposed to enhance durability through
optimized reinforcement and structural solutions.
Keywords Theory of elasticity · Cracks · Operational defects · Allowable load ·
Bridge structure · Stiffness tensor components

M. V. Alexandrovskyi · V. A. Vyatkin · M. A. Denisenko (B)
Moscow State University of Civil Engineering, Moscow, Russia
e-mail: denisenko.mishaden@yandex.ru
R. R. Khakimzyanov
Russian University of Transport (RUT MIIT), Moscow, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_33

401

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M. V. Alexandrovskyi et al.

1 Introduction
Crack formation is a common phenomenon in constructed reinforced concrete
bridges and is considered dangerous for structures, despite the fact that reinforced
concrete theory treats cracks as a normal occurrence. They are highly likely to appear
on the concrete surface and are usually detected there during processing or before
the application of protective coatings. Cracks occur in monolithic structures, mainly
in slabs and lintels, as well as in support columns within a limited range. Crack
openings can reach up to 2 mm.
In recent decades, steel–concrete composite bridge decks (CBDs) have received
significant attention due to their efficiency and the reduction of local stress amplitudes
in the steel deck [1, 2], opening new possibilities for bridge design. Extensive studies
on the flexural behavior of composite girder (steel-concrete) structures [3] have
shown that transverse connections play a critical role in CBDs by preventing interface
slippage. This phenomenon ensures favorable stress distribution during structural
deflection, with the upper concrete layer under compression and the lower steel
plate under tension. However, under dynamic or cyclic loading, the upper concrete
layer in CBDs-especially in tensile zones such as wet joints-inevitably experiences
tensile stress. Ordinary concrete, with its low tensile strength, easily cracks in these
areas, reducing the durability of CBDs. Moreover, the upper concrete layer in CBDs
often exceeds 120 mm in thickness to meet design requirements, which increases
self-weight and reduces economic efficiency.
Steel bridges in operation are subjected to a large number of variable loads under
long-term traffic stress and are therefore prone to the development of fatigue cracks,
which disrupt normal functionality and pose a threat to structural safety. Timely and
accurate detection of fatigue cracks is crucial for the maintenance and repair of steel
bridges. Among various maintenance methods, visual inspection performed by experienced engineers and inspectors remains the most common approach. Subsequently,
several non-destructive testing (NDT) methods are employed for visual verification
[4], including acoustic emission testing, ultrasonic inspection, and infrared thermography. Recently, a combination of unmanned aerial vehicles and image recognition
technologies has been introduced to enhance efficiency and overcome the limitations
of subjective judgment. These emerging technologies make the initial visual inspection more effective and objective, yet also more specific, as they require specialized
tools and complex procedures. Damage detection methods based on dynamic information are more appealing due to their non-destructive nature and independence
from additional equipment. Dynamic detection techniques have been developed for
both linear and nonlinear problems and have been applied in various domains, such
as small mechanical rotors and large hydraulic dams.
Researchers have conducted a series of studies on the behavior of steel bridge
structures under fatigue failure, with particular attention to single-crack testing and
simulation analysis. Several studies [5–7] systematically investigated the variation in
crack propagation rate depending on numerous variables, such as material properties,

Application of the Theory of Elasticity to the Study of Cracks in Bridge …

403

loading conditions, and specimen configuration, analyzing the entire crack propagation process. Additionally, the propagation of mixed-mode cracks has been examined [8], where the behavior of fatigue cracks in steel bridges was more accurately
predicted using Bayesian networks. Although many studies have provided extensive
data, multiple cracks frequently appear in active components of steel bridges, often
occurring in close proximity to one another [9]. As cracks propagate, they may merge,
forming new cracks that continue to grow until structural failure occurs. Cracks may
also inhibit each other, delaying the failure process. Compared to single cracks, the
propagation and effects of multiple cracks are more complex and therefore require
closer investigation.
Bridge design is one of the most demanding tasks in construction, requiring
a deep understanding of material and structural behavior under load. As critical
elements of the transportation network, transport structures must meet high safety
standards. The reliability of bridges depends on the strength and durability of their
components. Since bridge structures cannot indefinitely resist environmental influences, including long-term material degradation, their components have a limited
service life. To prevent premature failure, proper operation and maintenance must be
ensured. The expected service life is approximately 70 years, and up to 100 years for
supports. However, some bridges fail in less than 20 years due to poor maintenance
and operational practices [10].
The theory of elasticity provides tools for analyzing and designing bridge structures by accounting for the distribution of stresses arising under external loads. The
fundamental concept is that materials exhibit linear deformation within a certain
stress range, meaning that under small loads, the material behaves like an elastic
spring and returns to its original shape once the load is removed.
An important component of the theory of elasticity is Hooke’s law, which describes
the relationship between stress and strain within the elastic range [11]. It enables
calculations and the prediction of material behavior under various loading conditions.
The application of elasticity theory is also essential for determining the safe limit
states of structures. For this, the ultimate states of the material must be considered. To
verify structural strength, the following condition is used: σ max ≤ σ a , where: σ max —
maximum stress in the structure, and σ a —allowable stress. To verify deformation
limit states, the following is used: εmax ≤ εa , where εmax maximum strain, and εa —
allowable strain.
Strength calculations are considered to ensure the structure can withstand
maximum loads without deformations leading to damage or failure. It is also important to emphasize that the theory of elasticity applies not only to static loads but
also to the study of dynamic processes, including oscillations and vibrations. This is
crucial in construction, where engineers must account for dynamic loads—such as
in the design of bridges or buildings - to prevent structural failure [12].
The theory of elasticity is based on the laws of mechanics describing the behavior
of bodies under external forces. Key aspects include deformation (the change in
shape and size of a body under load), stress (force per unit area caused by an applied
load), and the modulus of elasticity (a measure of a material’s ability to return to its
original shape after load removal).

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In bridge design, it is important to consider the following stages: load determination (identifying all possible loads on the bridge, including self-weight, traffic
loads, wind loads, and dynamic effects); structural modeling (creating a mathematical model of the bridge and using numerical methods to solve elasticity theory
equations, enabling the determination of stress and strain distribution throughout
the structure); stability analysis (assessing the bridge’s stability under various loads,
including lateral displacement, deflections, and deformations); and structural optimization (using the obtained data to select optimal material properties and structural
form, ensuring maximum strength with minimal cost).
The load-bearing capacity of the entire span structure depends on the configuration and condition of the joints connecting theEquation Section (Next) slabs to
the main beams. The most heavily loaded elements, subjected to both permanent
and temporary loads, are the reinforced concrete roadway slabs. Studies show that
roadway slabs most often determine the properties governing the material response
to various physical processes and loads [13].
Fracture mechanics is a branch of mechanics that studies structural materials and
their ability to resist failure under external forces in the presence of fatigue cracks
and various technological and operational defects [14]. The main research focuses
on developing methods to prevent material failure during service. A comprehensive approach to fracture problems is employed, combining continuum mechanics
methods with experimental and theoretical physics, metallurgical chemistry, mathematical elasticity theory, and structural mechanics. This approach directly considers
the combined effects of stress states and defect parameters.
The causes of bridge failure can be conditionally divided into two types: some
accidents result from operational damage, while others stem from errors made during
construction and design [15]. The main causes include resonance, exceeding allowable loads, natural disasters, operational defects, design and operational errors, and
excessive wear. One of the most well-known causes of bridge failure is resonance,
which is the phenomenon of a sharp increase in the amplitude of system vibrations
under periodic external excitation [16].

2 Methods and Materials
In Russia, concretes used for bridge construction comply with GOST standards,
taking into account the type of structure, operational loads, climatic conditions,
and service life. The primary regulatory document is GOST 26633–2015 “Heavy
and fine-grained concretes. Technical specifications,” which specifies that heavy
concretes of strength classes from B10 to B60 are used for bridges. In practice,
concrete of at least class B30 is most commonly employed for load-bearing bridge
elements, possessing compressive strength of: Rs = 39, 2MPa. For highly stressed
sections, such as span structures and supports, B35 concrete is used Rs = 45, 8MPa,
B40 - Rs = 52, 0MPa, B45 - Rs = 58, 5MPa, B50 - Rs = 65, 0MPa. Less critical
structural components may be made of B25 concrete, with a compressive strength

Application of the Theory of Elasticity to the Study of Cracks in Bridge …

405

Fig. 1 Bridge elements

of: Rs = 32, 7MPa. GOST 31384–2017 “Concrete. Guidelines for Mix Design”
is also used, describing methods for producing concrete with specified properties.
According to SP 35.13330.2011 (updated edition of SNiP 2.05.03–84 “Bridges and
Culverts”), heavy concrete of at least class B30 must be used for concrete and reinforced concrete bridges, with water resistance not less than W6 and frost resistance
not less than F200. Depending on the climatic zone and durability requirements, these
properties may be increased—frost resistance up to F300–F400 and water resistance
up to W8–W10. Workability and abrasion resistance of the concrete mix are also
important, especially for elements exposed to abrasive loads.
Figure 1 shows the bridge elements: 1—approach embankment; 2—embankment
cone; 3—abutment; 4—superstructure with top roadway; 5—superstructure with
bottom roadway; 6—intermediate pier (bull pier); 7—foundation of the support;
LWL—low water level; HWL—high water level; L—bridge length; H—bridge
height; H 0 —clearance under the bridge; h—structural depth.
Bridges and other artificial structures are designed using the limit state method.
Limit states are conditions under which a structure ceases to meet operational requirements due to applied forces [17]. According to GOST 27751–2014 “Reliability of
Building Structures and Foundations. Basic Provisions,” limit states are divided into
two groups: the first group is characterized by the inability to use the structure
or loss of overall load-bearing capacity; the second group involves difficulties in
normal use and reduced design service life. First-group limit states include loss of
bearing capacity of foundation soils, loss of strength, loss of shape stability, loss of
positional stability, and fatigue failure. Second-group limit states include complications in normal operation, excessive deformations, crack formation, cracks reaching
maximum allowable widths, and unacceptable vibrations under temporary loads.
Bridge design calculations are performed for both limit state groups. Normal operation is considered to occur without restrictions or extraordinary repairs. A first-group
limit state is not reached if the maximum possible force N max does not exceed the
minimum bearing capacity value:
Nmax

min

(1)

The left side of the inequality depends on the load applied to the structure, the
structural scheme, and the dimensions of the structure, while the right side depends on

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the material strength, shape, and cross-sectional dimensions of the structural element.
The loads acting on the structure, material strength, and element dimensions are not
precisely defined values; they exhibit statistical variability.
Let us determine the crack width in reinforced concrete elements (both normal
and longitudinal to the longitudinal axis), designed according to crack resistance
categories. According to SP 63.13330.2018: for the first category, cracks are not
allowed: w = 0 mm; this applies to highly critical structures. For the second category,
fine cracks are permitted w ≤ 0, 15 mm; this is used in external wall elements, floor
slabs, and beams. For the third category, crack openings that do notEquation Section
(Next) impair strength and operational reliability are allowed w ≤ 0, 30 mm; this
applies to structures without special requirements for appearance and watertightness.
The following formula is used for this purpose:
w=

1
· εsm · kt · d
ρef

(2)

where: ρef = AAefs —effective reinforcement ratio; As —area of tensile reinforcement, mm2 ; Aef —effective concrete cross-sectional area in the tensile zone, mm2 ;
εsm —average strain of tensile reinforcement between cracks, considering creep
and shrinkage; k t —coefficient accounting for reinforcement profile type: 0.6 for
deformed bars, 0.8 for smooth bars; d—diameter of tensile reinforcement, mm.
For mixed reinforcement (i.e., combined use of prestressed and non-prestressed
reinforcement), determining crack width requires accounting for the behavior of each
reinforcement type. The calculated crack width w in such elements can be determined
using the Equation Section (Next)modified formula:
w = β · εsm · l0

(3)

where: εsm —average relative strain in the tensile reinforcement zone between cracks;
l0 —crack spacing; β—coefficient accounting for the inclination of the crack relative
to the longitudinal axis of the element (typically taken as 1, but may exceed 1 for
inclined cracks).
The average relative strain is calculated Equation Section (Next) using the
formula:
εsm =

σs − αp · Δσp
Es

(4)

where: σ s —stress in non-prestressed reinforcement at the service stage, MPa; Δσ p —
stress increment in prestressed reinforcement after loss of initial concrete compression, MPa; αp —coefficient accounting for the influence of prestressed reinforcement
on section behavior (typically from 0.5 to 1.0 depending on reinforcement position
and structural configuration); E S —modulus of elasticity of reinforcement, MPa.
The stress in non-prestressed reinforcement at the service stage is determined
based on equilibrium conditions and the combined action of reinforcement and

Application of the Theory of Elasticity to the Study of Cracks in Bridge …

407

concrete. Once the concrete in the tensile zone has cracked, the reinforcement
primarily resists the tensile forces. It is calculated using the formula: Equation Section
(Next)
σs =

M · as
· Es
Ief

(5)

where: M—bending moment in the section due to service loads, MPa; as —distance
from tensile reinforcement to the neutral axis, mm; I ef —moment of inertia of the
cracked section transformed with reinforcement, mm4 ; E S —modulus of elasticity of
reinforcement, MPa.
For calculating the crack spacing, the following formula is used:Equation Section
(Next)
l0 = k1 · k2 ·

d
ρef

(6)

where: d—reinforcement diameter, mm; ρef —effective reinforcement ratio; k 1 —
coefficient accounting for bond quality (0.8 for deformed bars, 1.6 for smooth bars)
(Table 1); k 2 —coefficient accounting for cracking conditions.
The dependence of crack width w on reinforcement diameter d is linear: with
an increase in diameter, all other factors being equal, the crack width increases.
This occurs because larger reinforcement has a smaller specific bonding surface
Table 1 Relationship between reinforcement type and the coefficient accounting for the degree of
bond between reinforcement elements and concrete
No

Type of
reinforcement

Nature of bond
between
reinforcement and
concrete

Type of
reinforcement
profile

Bond coefficient k 1

Reinforcement with a Good
deformed (ribbed)
profile

Hot-rolled, A500,
A400, and others

0.8

Smooth
reinforcement (plain
bars)

Round (steel B-1)

1.6

Composite
Moderate
reinforcement
(fiberglass and others)

Sand-coated/spiral
surface

1.2

Prestressed wire or
strands

With high adhesion 0.6–0.8
properties

Reinforcement with
Reduced
anti-corrosion coating
(epoxy-coated)

Weak

Enhanced (due to
anchorage)

Regardless of
profile

1.2–1.5

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M. V. Alexandrovskyi et al.

with concrete, which increases the spacing between cracks and reduces resistance to
crack opening. According to SP 63.13330.2018, formula (3) reflects this relationship.
To plot the graph in Fig. 2 showing the dependence of crack width on reinforcement diameter, we expand formula (3) by substituting formulas (4–6), resulting in
the following expression: Equation Section (Next)
w=

αp · Δσp
M · as
−
Ief
Es

k1 · k2 · d
ρef

(7)

where: M bending moment, MPa · mm; as —distance from tensile reinforcement to
neutral axis, mm; I ef —moment of inertia of the cracked section transformed with
reinforcement, mm4 ; E s —modulus of elasticity of reinforcement, MPa; Δσ p —stress
increment in prestressed reinforcement after loss of initial concrete compression,
MPa; αp —coefficient accounting for the influence of prestressed reinforcement on
section behavior (typically ranging from 0.5 to 1.0 depending on reinforcement position and structural configuration); d—reinforcement diameter, mm; ρef —effective
reinforcement ratio; k 1 —coefficient accounting for bond quality (0.8 for deformed
bars, 1.6 for smooth bars); k 2 —coefficient accounting for cracking conditions.
Calculations were performed using the following values selected according to
SP 63.13330.2018: M = 150 · 106 H · mm; as = 50mm; I ef = 2 · 108 mm4 ; E s =
200000MPa; ρef = 0, 03; k 1 = 0.7 − 1.6; k 2 = 0.9. Diameters of various types
of reinforcement are as follows: for deformed bars: d = 6 − 40mm; for smooth
bars: d = 6 − 40mm; for composite reinforcement: d = 4 − 32mm; for prestressed
reinforcement: d = 5 − 15mm; for coated reinforcement: d = 10 − 25mm.

Fig. 2 Dependence of crack width on reinforcement diameter

Application of the Theory of Elasticity to the Study of Cracks in Bridge …

409

Thus, the graph shows that all types of reinforcement exhibit an increase in
crack width with increasing diameter; smooth reinforcement produces the largest
crack widths; prestressed reinforcement provides better crack width control, as it
is typically designed for crack self-closure; deformed reinforcement also shows
limited crack opening due to good bonding; some curves exceed the allowable limits
according to SP, indicating that larger diameters lead to wider cracks.
According to SP 63.13330.2018, the load-bearing capacity of reinforcement
is determined by the required cross-sectional area of reinforcement that must be
provided by the set of bars. The following formula is used for this purpose: Equation
Section (Next)
req

req

As
4 · As
=
A1
π · d2

(8)
req

where: n—required number of reinforcement bars (rounded up); As —required total
2
—cross-sectional area of a
cross-sectional area of reinforcement, mm2 ; A1 = π ·d
4
2
single bar with diameter d, mm .
Using formula (8), we determine the dependence of the number of bars on the
reinforcement diameter by plotting the graph in Fig. 3.
Calculations were performed using the following values selected according to
req
SP 63.13330.2018, GOST 5781–82, GOST 7348–81, and GOST 13840–68: As =
2
1131mm ; Diameters of various types of reinforcement are as follows: for deformed
bars: d = 6 − 40mm; for smooth bars: d = 6 − 40mm; for composite reinforcement: d
= 4 − 32mm; for prestressed reinforcement: d = 5 − 15mm; for coated reinforcement:
d = 10 − 25mm.

Fig. 3 Dependence of the number of bars on reinforcement diameter

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M. V. Alexandrovskyi et al.

Thus, the graph shows that all types of reinforcement require the same number
of bars for a given diameter; the larger the bar diameter, the fewer bars are needed;
differences between types are reflected in the allowable diameter ranges.
An example of structural failure is the collapse of the Silver Bridge. This renowned
aluminum suspension bridge suddenly collapsed, causing 32 vehicles to fall into the
icy Ohio River [18]. Analysis of the debris revealed that a 0.1-inch defect in one of
the bridge’s metal eyebars led to its failure. Traffic congestion during peak hours and
poor maintenance throughout the bridge’s service life also contributed to its lack of
durability. The cause of the collapse was directly related to construction technology.
When two rods were connected via a pin, the eyelets inside the connection were
hidden from view, and there was no way to inspect the integrity of this component
without dismantling the entire structure. The collapse was triggered by a crack in the
lower part of the eyelet on the rod. This crack developed over the entire service life due
to metal corrosion and constant multidirectional loading. Because the properties of
the steel grade used were not sufficiently studied during construction, it was unknown
that its interaction with exhaust gas compounds would make the steel more brittle
and prone to cracking. The crack width in the metal grew over many years until one
reached 2.5 mm.
Let us consider the physics of crack formation: a crack occurs in a material when
the local stress exceeds the tensile strength limit: σ max ≥ Rt or the Griffith energy
criterion is satisfied: G ≥ Gc or K 1 ≥ K 1c , where: G—energy released during crack
propagation; Gc —critical fracture energy; K 1 , K 1c —stress intensity factors. Once
sufficient energy accumulates in the material, a defect forms—an initial microcrack.
With further loading, the crack lengthens in the direction of the principal tensile
stresses, distributes into a system forming a family of parallel cracks, and affects
the macroscopic properties of the body, especially stiffness and anisotropy. The
appearance of cracks reduces the effective stiffness of the material, as part of the
volume no longer behaves as a continuous elastic medium. In the case of a family
of parallel cracks, the body becomes anisotropic, and its behavior is described by an
eff
effective stiffness tensor Cijkl . We consider a macroscopic body containing numerous
thin, flat cracks oriented in parallel, all of equal length and evenly spaced. In this
approximation, we aim to determine how the material’s stiffness depends on the
crack length, the spacing between cracks, and the crack orientation angle.
Assume the material is an isotropic elastic matrix with Young’s modulus E and
Poisson’s ratio ν; the matrix contains a sparse family of parallel flat cracks oriented
along a single axis; the cracks do not interact with each other. To calculate the change
in stiffness, an approach analogous to the theory of dilute inclusions is applied. In
this approximation, the stiffness tensor changes by a small amount depending on the
geometry and orientation of the defects.
For a two-dimensional plane stress model with parallel cracks oriented perpendicular to the loading direction, the effective Young’s modulus E eff along the loading
direction is expressed as: Equation Section (Next)
Eeff
≈ 1 − π Na2
E

(9)

Application of the Theory of Elasticity to the Study of Cracks in Bridge …

411

where: E—Young’s modulus of the undamaged material; N—number of cracks per
unit area or volume; a—half-length of the crack.
eff
eff
Then the corresponding stiffness tensor component C1111 or C22 (in the plane
model) decreases as follows: Equation Section (Next)
eff

Cijkl = Cijkl · 1 − π Na2

(10)

eff

where: Cijkl —effective stiffness tensor; N—number of cracks per unit area or volume;
eff

a—half-length of the crack; Cijkl ≈ E—modulus of elasticity.
According to formula (10) and SP 63.13330.2018, we determine the dependence
of the stiffness tensor component on crack length in the approximation of noninteracting parallel crack families as follows:
The following parameters, selected according to regulatory documents, were used
to construct the graph in Fig. 4: C ijkl ≈ E = 30000MPa; N = 100crack/m2 ; a = 1 −
30mm.
The graph analysis shows that crack elongation weakens the material; since
the weakening is proportional to a2 , stiffness reduction accelerates; even short but
numerous cracks significantly reduce load-bearing capacity.
If cracks are spaced at equal intervals, then the crack density per unit length is:
Equation Section (Next)
N=

1
L

(11)

Fig. 4 Dependence of the stiffness tensor component in the non-interaction approximation with a
family of parallel cracks on crack length

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M. V. Alexandrovskyi et al.

Fig. 5 Dependence of the stiffness tensor component in the non-interaction approximation with a
family of parallel cracks on crack spacing

Therefore, formula (10) takes the form: Equation Section (Next)
eff

Cijkl (L) = Cijkl · 1 −

π a2
L

(12)

According to formula (12) and SP 63.13330.2018, we determine the dependence of
the stiffness tensor component on the spacing between cracks in the approximation
of non-interacting parallel crack families as follows:
The following parameters, selected according to regulatory documents, were used
to construct the graph in Fig. 5: C ijkl ≈ E = 30000MPa; L = 20 − 500mm; a = 10mm.
The graph analysis shows that as the spacing between cracks decreases, the effective stiffness of the material reduces; conversely, as L increases, cracks become less
frequent and their impact on stiffness diminishes.
Let there be a family of identical parallel cracks in an isotropic elastic medium,
oriented at an angle θ to the principal loading axis. In this case, the material becomes
anisotropic, and the crack orientation angle affects which components of the stiffness
tensor are weakened.
For the two-dimensional plane stress case, it is common to represent the reduction
of the C 1111 component as a function of the angle θ as follows: Equation Section
(Next)
eff

C1111 (θ ) = C1111 · 1 − π Na2 cos4 (θ )
Similarly: Equation Section (Next)

(13)

Application of the Theory of Elasticity to the Study of Cracks in Bridge …

413

Fig. 6 Dependence of the stiffness tensor component in the non-interaction approximation with a
family of parallel cracks on crack orientation angle
eff

C2222 (θ ) = C2222 · 1 − π Na2 sin4 (θ )

(14)

C1122 (θ ) = C1122 · 1 − π Na2 cos2 (θ )sin2 (θ )

(15)

eff

According to formulas (13–15) and SP 63.13330.2018, we determine the dependence
of the stiffness tensor component on the crack orientation angle in the approximation
of non-interacting parallel crack families as follows:
The following parameters, selected according to regulatory documents, were used
to construct the graph in Fig. 6: C 1111 , C 2222 ≈ E = 30000MPa; C 1122 ≈ E =
10000MPa; N = 1000crack/m2 ; a = 10mm.
eff
The graph analysis shows that C1111 (θ ) decreases most at θ = 0◦ , when cracks are
perpendicular to the load, directly weakening longitudinal stiffness; it increases at θ
= 90◦ , when cracks are parallel to the load and have minimal effect. The behavior
eff
eff
of C2222 (θ ) is the mirror opposite of C1111 (θ ): maximum at θ = 0◦ , minimum at θ =
eff
◦
90 ; The shear stiffness C1122 (θ ) reaches maxima at θ = 0◦ and 90◦ , and a minimum
at θ = 45◦ , where cracks most strongly reduce the material’s resistance to shear.

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3 Conclusion
This study investigates the mechanical behavior of bridge structures with cracks based
on elasticity theory combined with numerical modeling. Calculations were performed
under the assumption of linear elasticity using physical parameters regulated by
Russian standards (SP 63.13330.2018, GOST 26633–2015, etc.).
Analytical relationships were obtained for crack width as a function of reinforcement diameter, as well as for stiffness tensor components depending on the
geometric characteristics and orientation of families of parallel cracks. Graphical
analysis showed that increasing reinforcement diameter and poor bond with concrete
lead to larger crack openings, whereas prestressed and ribbed reinforcement help limit
crack width within permissible limits.
The analysis of stiffness reduction utilized the approximation of non-interacting
parallel cracks. It was established that the effective stiffness of the material
with cracks decreases nonlinearly with increasing crack length and decreasing
spacing between them. Additionally, crack orientation significantly affects material
anisotropy: the greatest weakening occurs when cracks are oriented perpendicular
to the loading direction, and the least when oriented parallel.
The proposed theoretical and numerical approach demonstrates the importance
of considering crack geometry and structural reinforcement in the design of bridge
elements. The obtained results can serve as a basis for improving calculation methods,
as well as for developing diagnostic and monitoring tools to assess the strength and
operational reliability of structures.

References
1. Hayek R, Fladr J et al (2019) Experimental evaluation of the blast resistance of heterogeneous
concrete-based composite bridge decks. Eng Struct 179:204–216. https://doi.org/10.1016/j.eng
struct.2018.11.017
2. Jiang X, Han X et al (2017) Experimental study and numerical analysis on the mechanical
behavior of T-shaped stiffened orthotropic steel-concrete composite bridge decks. Int J Steel
Struct 17(4):1051–1062. https://doi.org/10.1007/s13296-017-9004-y
3. Xiang Z, Zhu ZW (2018) Fatigue behavior of orthotropic composite bridge decks without
cutouts at rib-to-floorbeam intersections. J Constr Steel Res 146:63–75. https://doi.org/10.
1016/j.jcsr.2018.02.008
4. Ma X, Wang Y, Wang X et al (2023) Investigation of fatigue crack propagation behavior in
U71Mn and U75V rails using peridynamics. Eng Fract Mech 281:109097. https://doi.org/10.
1016/j.engfracmech.2023.109097
5. Peng A, Ma Y et al (2024) A digital twin-driven platform for fatigue life prediction of welded
structures considering residual stresses. Int J Fatigue 168:107377. doi:https://doi.org/10.1016/
j.ijfatigue.2024.107377
6. Ma YF et al (2023) Prediction of corrosion fatigue crack growth in bridge suspender cables
using Bayesian Gaussian processes. Int J Fatigue 168:107377. https://doi.org/10.1016/j.ijfati
gue.2023.107377

Application of the Theory of Elasticity to the Study of Cracks in Bridge …

415

7. Miao XL et al (2024) Study on the durability and propagation of multiple cracks with uniform
and non-uniform fusion in an approximate plane. Theor Appl Fract Mech 132:103010. https://
doi.org/10.1016/j.tafmec.2024.103010
8. Zhang R et al (2023) Automatic modeling of initiation and propagation of interface and matrix
cracks using the Variational crystal finite element method (VCFEM). Theor Appl Fract Mech
132:103010. https://doi.org/10.1016/j.tafmec.2023.103010
9. Internet Journal "Transport Structures". https://t-s.today/. Accessed 29 May 2025
10. Struzhanov VV, Burmasheva NV (2019) Theory of elasticity: basic principles. Ural Federal
University, Yekaterinburg
11. What is strength calculation. https://telegra.ph/V-chem-zaklyuchaetsya-raschet-na-prochnostRazbiraemsya-v-osnovah-nadezhnosti-konstrukcij-11-06. Accessed 29 May 2025
12. Building materials. Basic concepts. https://www.tpribor.ru/stroymat.html. Accessed 29 May
2025
13. Calculation of fracture mechanics parameters in ANSYS Mechanical 15.0. https://sapr.ru/art
icle/24556. Accessed 29 May 2025
14. Maistrenko IY, Ovchinnikov II, Ovchinnikov IG, Kokodeev AV (2017) Accidents and failures
of bridge structures: analysis of causes. Internet J Transp Struct 4(4)
15. Why bridges fail. https://www.vokrugsveta.ru/article/299041/. Accessed 29 May 2025
16. Methodology for calculation of metal structures according to limit states. https://studizba.
com/lectures/stroitelstvo/lekcii-po-metallokonstrukcijam/46220-metodika-rascheta-metallich
eskih-konstrukcij-po-predelnym-sostojanijam.html. Accessed 29 May 2025
17. About the Silver Bridge and eye-shaped rods. https://rudzin.livejournal.com/55097.html.
Accessed 29 May 2025

Influence of Beam and Column
Cross-Section on Deflection of Monolithic
Floor Slab
D. I. Romensky, R. R. Khakimzyanov, V. A. Vyatkin, and D. R. Buev

Abstract The construction of modern buildings and structures requires careful analysis of load-bearing structures, especially monolithic slabs, which play a key role
in the stability and durability of buildings, and key role in ensuring the stability
and durability of buildings. Correctly specified parameters of beams and columns
directly affect the deflection of slabs, which, in turn, determines the reliability of
the entire structure. In the conditions of increasing number of floors and increasing
loads on buildings, the relevance of research in this area becomes especially important. In this paper, the influence of beam and column cross-sections on the deflection
of monolithic slabs in four-storey buildings is considered. The study was carried out
using LIRA CAD software package, which allowed to obtain accurate data on the
behavior of structures under different loads. The results of the work will help design
engineers to optimize the parameters of load-bearing elements, providing a balance
between strength and economy.
Keywords Slab deflection · Floor loading · Beam section · Column section ·
Dynamic analysis · LIRA CAD · RC structures

1 Materials and Methods
Two four-story buildings of 13.20 m height each are considered. The first building
has beam sections of 40 × 40 cm and columns of 40 × 50 cm, the second building has
beam sections of 50 × 70 cm and columns of 50 × 50 cm. Both buildings are designed
with monolithic slabs, which can be either ribbed with beam slabs or girderless. It
should be noted that monolithic slabs can be considered of two types: ribbed with
beam slabs and beamless. The bearing system of a monolithic frame building is
D. I. Romensky · V. A. Vyatkin · D. R. Buev (B)
Moscow State University of Civil Engineering, Moscow, Russia
e-mail: buevdaniil@gmail.com
R. R. Khakimzyanov
Russian University of Transport (RUT MIIT), Moscow, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_34

417

418

D. I. Romensky et al.

formed mainly by slabs, columns and foundations. The floors together with the
columns are a kind of frame structures capable of taking vertical and horizontal
loads. The exterior walls in this case are self-supporting for one storey.
In this building structure with incomplete frame, the exterior walls are loadbearing. At the same time, it should be noted that often the bearing system of the
building includes elements of fencing staircase and elevator units, which are included
in the work of the bearing system under the action of vertical and horizontal loads.
It should be noted that with large dimensions of the building in the plan in the
elements of the frame can occur large temperature stresses. Therefore, in necessary
cases, the building must necessarily be divided into separate blocks by transverse
and longitudinal temperature joints. Each temperature block works independently
without redistribution of external and internal influences on neighboring blocks. The
design standards establish the limit dimensions of the temperature blocks at which
the influence of climatic temperature effects can be disregarded in the design. The
following types of loads were considered for the analysis:
•
•
•
•
•
•
•

Own weight of the structure.
Weight of the pavement (0.291 kN/m2 ).
Weight of the floor (0.12 kN/m2 ).
Weight of the internal walls (0.21 kN/m2 ).
Snow load (0.18 kN/m2 ).
Useful load (0.195 kN/m2 ).
Weight of staircase structures (0.8 kN/m2 ).

Numerical calculation was performed in LIRA CAD, which allowed dynamic
analysis of structures. To verify the results we used data from the works of Malakhova
[1], Perunov [2], as well as international studies [3–8]. Through numerical dynamic
analyses, we investigate how beam and column sections affect the deflection of monolithic floor slabs. Additionally, a numerical calculation was conducted considering
previously selected concrete and reinforcement parameters. The obtained results
were compared with allowable values [4]. To verify these theoretical hypotheses
numerically, the Lira SAPR software package was also employed. Calculated combinations of internal forces (RCF) were determined for all components of the computational model, which subsequently informed the reinforcement of reinforced concrete
members and verification of assigned cross sectional dimensions of the structures.
Based on the calculated efforts, the stability of the building’s structural elements was
assessed depending on their predefined properties [5–8].
Modelling features:
• Temperature deformations that can occur in large-sized buildings are taken
into account. For this purpose, temperature joints separating the building into
independent blocks are provided.
• A stability check has been carried out, taking into account reinforcement of
reinforced concrete elements.

Influence of Beam and Column Cross-Section on Deflection …

419

The first construction design being analyzed represents a building with predetermined beam cross-sections measuring 40 × 40 cm and column cross-sections sized
at 40 × 50 cm, as depicted in Fig. 1.
From Figs. 2 and 3, it follows that the maximum deflection of the monolithic floor
slab of the construction under consideration, subject only to its own weight, amounts
to − 3.07 mm.
It follows from Figs. 4 and 5 that the maximum deflection of the monolithic floor
slab due to the weight of the roof structure is − 0.737 mm.
It follows from Figs. 6 and 7 that the maximum deflection of the monolithic floor
slab due to the weight of the floor structure is − 0.345 mm.
It follows from Figs. 8 and 9 that the maximum deflection of the monolithic floor
slab due to the weight of interior walls is − 0.604.
It follows from Figs. 10 and 11 that the maximum deflection of the monolithic
floor slab due to snow load is − 0.456 mm.
It follows from Figs. 12 and 13 that the maximum deflection of the monolithic
floor slab due to live load is − 0.773 mm.

Fig. 1 Floor plan of the first building

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Fig. 2 Deformation of the monolithic floor slab due to self-weight loads

Fig. 3 Deformation of the monolithic floor slab caused by self-weight loads (only floor slabs are
shown)

Fig. 4 Deformation of the monolithic floor slab due to the weight of the roof structure

Influence of Beam and Column Cross-Section on Deflection …

421

Fig. 5 Deformation of the monolithic floor slab caused by the weight of the roof structure (only
floor slabs are displayed)

Fig. 6 Deformation of the monolithic floor slab due to the weight of the floor structure

Fig. 7 Deformation of the monolithic floor slab caused by the weight of the floor structure (only
floor slabs are displayed)

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Fig. 8 Deformation of the monolithic floor slab due to the weight of interior walls

Fig. 9 Deformation of the monolithic floor slab caused by the weight of interior walls (only floor
slabs are displayed)

Fig. 10 Deformation of the monolithic floor slab due to snow load

Influence of Beam and Column Cross-Section on Deflection …

423

Fig. 11 Deformation of the monolithic floor slab caused by snow load (only floor slabs are
displayed)

Fig. 12 Deformation of monolithic floor slabs due to live load

Fig. 13 Deformation of monolithic floor slabs caused by live load (only floor slabs are displayed)

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D. I. Romensky et al.

It follows from Figs. 14 and 15 that the maximum deflection of the monolithic
floor slab due to the weight of stair constructions is − 0.229 mm.
Based on the conducted analysis of Building No. 1, it can be concluded that the
deflections of monolithic floor slabs vary significantly depending on different types
of loads. These calculations predict potential deflections of the floor slabs under
specific loading scenarios. Therefore, it is crucial to consider the intended purpose of
the building during the design phase [9–13]. An engineering designer sets necessary
parameters for the future building to ensure long-term serviceability without major
repairs or failures of supporting structures [14–17].
As another example, a second building was analyzed where the column crosssection measures 50 × 50 cm and the beam cross-section is 50 × 70 cm.
It follows from Figs. 16, 17 and 18 that the maximum deflection of the monolithic floor slab of Building No. 2 under self-weight loads is − 1.94 mm, which is
approximately 1.58 times less than that of Building No. 1 (− 3.07 mm).

Fig. 14 Maximum deformation of monolithic floor slabs due to the weight of stair constructions

Fig. 15 Maximum deformation of monolithic floor slabs caused by the weight of stair constructions
(only floor slabs are displayed)

Influence of Beam and Column Cross-Section on Deflection …

Fig. 16 Typical floor plan of Building No. 2

Fig. 17 Maximum deflection of monolithic floor slabs due to self-weight loads

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D. I. Romensky et al.

Fig. 18 Maximum deflection of monolithic floor slabs caused by self-weight loads (only floor slabs
are displayed)

It follows from Figs. 19 and 20 that the maximum deflection of the monolithic
floor slab of Building No. 2 due to the weight of the roof structure is − 0.463 mm,
which is about 1.59 times smaller than that of Building No. 1 (− 0.737 mm).
It follows from Figs. 21 and 22 that the maximum deflection of the monolithic
floor slab of Building No. 2 due to the weight of the floor structure is − 0.223 mm,
which is approximately 1.55 times smaller than that of Building No.1 (− 0.345 mm).
It follows from Figs. 23 and 24 that the maximum deflection of the monolithic
floor slab of Building No. 2 due to the weight of interior walls is − 0.39 mm, which
is approximately 1.55 times smaller than that of Building No. 1 (− 0.604 mm).
It follows from Figs. 25 and 26 that the maximum deflection of the monolithic
floor slab due to snow load is − 0.287 mm, which is approximately 1.59 times smaller
than that of Building No. 1 (− 0.456 mm).

Fig. 19 Maximum deflection of floor slabs due to the weight of roof structures

Influence of Beam and Column Cross-Section on Deflection …

427

Fig. 20 Maximum deflection of floor slabs caused by the weight of roof structures (only floor slabs
are displayed)

Fig. 21 Maximum deflection of monolithic floor slabs due to the weight of floor structures

Fig. 22 Maximum deflection of monolithic floor slabs caused by the weight of floor structures
(only floor slabs are displayed)

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Fig. 23 Maximum deflection of monolithic floor slabs due to the weight of interior walls

Fig. 24 Maximum deflection of monolithic floor slabs caused by the weight of interior walls (only
floor slabs are displayed)

Fig. 25 Maximum deflection of monolithic floor slabs due to snow load

Influence of Beam and Column Cross-Section on Deflection …

429

Fig. 26 Maximum deflection of monolithic floor slabs caused by snow load (only floor slabs are
displayed)

It follows from Figs. 27 and 28 that the maximum deflection of the monolithic
floor slab due to live load is − 0.499 mm, which is approximately 1.56 times smaller
than that of Building No. 1 (− 0.773 mm).
It follows from Figs. 29 and 30 that the maximum deflection of the monolithic floor
slab due to the weight of staircase structures is − 0.128 mm, which is approximately
1.79 times smaller than that of Building No. 1 (− 0.229 mm).
Based on the analysis of Building No. 2, it becomes evident that the deflections of
the monolithic floor slabs have decreased significantly compared to those observed in
the previous building studied earlier. This clearly demonstrates the substantial influence of design parameters and engineering calculations on the performance characteristics of the structure [18–20]. Consequently, engineers must carefully evaluate
the advantages and disadvantages associated with their decisions. On one hand, cost
savings could be achieved through reduced usage of materials like concrete and
rebar, leading to lower performance levels. However, avoiding such compromises

Fig. 27 Maximum deflection of monolithic floor slabs due to live load

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Fig. 28 Maximum deflection of monolithic floor slabs caused by live load (only floor slabs are
displayed)

Fig. 29 Maximum deflection of monolithic floor slabs due to the weight of staircase structures

Fig. 30 Maximum deflection of monolithic floor slabs caused by the weight of staircase structures
(only floor slabs are displayed)

Influence of Beam and Column Cross-Section on Deflection …

431

ensures improved outcomes. Future architects and designers must strike a balance
between reliability and economy so that constructed objects remain functional over
extended periods while maintaining their structural integrity [21, 22]. The data and
characteristics of the two investigated buildings and structures have been compiled
into Tables 1 and 2 to provide a clearer representation of the research findings.
Table 1 Deflection of monolithic floor slab under given loads
Units of measurement
Column cross-section

cm (centimeters)

Beam cross-section

Characteristics of
building No. 1

Characteristics of
building No. 2

40 * 40

50 * 50

40 * 50

50 * 70

Maximum deflection of monolithic floor slab under applied loads
− 3.07

− 1.94

Weight of roof
structure

− 0.737

− 0.463

Weight of floor
structure

− 0.345

− 0.223

Weight of interior
walls

− 0.604

− 0.39

Self-weight of
structure

mm (millimeters)

Snow load

− 0.456

− 0.287

Live load

− 0.773

− 0.499

Weight of staircase
structures

− 0.229

− 0.128

Table 2 Specified loads on monolithic floor slab of construction structure

Column section

Unit of measurement

Characteristics
building No. 1

Characteristics
building No. 2

cm (centimeter)

40 * 40

50 * 50

40 * 50

50 * 70

Beam section
Loads on monolithic floor slab
Weight of roof
structure

kN/m2

0.291

Weight of floor
structure

0.12

Weight of interior
walls

0.21

Snow load

0.18

Live load

0.195

Weight of stair
constructions

0.8

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D. I. Romensky et al.

The highest deflection in the first building was observed under its own load (−
3.07 mm), in the second building this index decreased to − 1.94 mm (1.58 times
less). A similar trend was observed for all load types:
• Pavement weight: − 0.737 mm (1st building) versus − 0.463 mm (2nd building).
• Useful load: − 0.773 mm versus − 0.499 mm.
Increasing the cross-section of beams and columns in the second building resulted
in a significant reduction in deflections. For example, the deflection from snow load
decreased from − 0.456 to −0.287 mm, which confirms the effectiveness of using
more massive load-bearing elements.

2 Influence of Concrete and Reinforcement Parameters
Additionally, the effect of concrete grade and reinforcement class on deflection was
analysed. The use of B30 grade concrete and A500C reinforcement reduced the
deformation by 15–20% compared to less strong materials.

3 Discussion
The study demonstrates that increasing the cross-section of beams and columns not
only reduces deflection, but also increases the safety margin of the structure. This is
especially important for buildings operating under variable loads (e.g. in seismically
active regions).
The study also identified additional aspects affecting the behaviour of monolithic
floor slabs. One of the key factors is the consideration of temperature deformations, especially for buildings with large plan dimensions. Calculations have shown
that dividing the building into temperature blocks allows the stresses arising from
temperature variations to be minimised, which has a positive effect on the durability
of the structure. This aspect is especially important for regions with sharp seasonal
fluctuations in climatic conditions.
In addition, the study emphasises the importance of dynamic analysis of structures.
The use of the LIRA CAD software package allowed not only to estimate static
loads, but also to take into account the influence of dynamic factors such as wind
and vibration loads. This is especially relevant for high-rise buildings and structures
located in seismically active zones. The results showed that increasing the crosssection of columns and beams not only reduces deflections, but also increases the
stability of the structure against dynamic effects.
An important conclusion is also the need to optimise materials. The use of B30
class concrete and A500C reinforcement reduced the deformations by 15–20%,
which confirms the importance of selecting high quality materials at the design

Influence of Beam and Column Cross-Section on Deflection …

433

stage. This opens up prospects for further research, e.g. investigating the influence of
modern composite materials or fibre concrete on the behaviour of monolithic slabs.
Thus, an integrated approach, including consideration of temperature effects,
dynamic loads and material optimisation, allows for the design of more reliable and
cost-effective structures. This is especially important in the context of increasing
demands for safety and durability of buildings.

4 Practical Recommendations
1. For buildings with high loads (shopping centres, industrial buildings), it is recommended to use column sections of at least 50 × 50 cm and beam sections of 50
× 70 cm.
2. Not only static but also dynamic loads (wind, vibrations) should be taken into
account in the design.
3. The optimum combination of concrete and reinforcement parameters allows to
achieve a balance between cost and reliability.

5 Conclusion
Numerical calculations confirmed that increasing the cross-section of beams and
columns significantly reduces the deflection of monolithic slabs. For example, in the
second building the deflections decreased on average by 1.5–1.8 times compared
to the first building. This demonstrates the importance of careful selection of the
parameters of load-bearing elements at the design stage.
Thus, numerical studies have shown that the peculiarities of the monolithic beam
slab under load can be related to the stiffness parameters of the slab contour beams.
Thanks to numerical calculations performed in the LIRA CAD software package,
the behavior of the monolithic slab of a building structure under given loads and
characteristics is shown.
Prospects for further research:
• Analysing the effects of combined loads (e.g. wind + snow).
• Study of the behaviour of structures using modern materials (e.g. fibre concrete).
Acknowledgements The authors would like to thank colleagues at Moscow State University of
Civil Engineering and Russian University of Transport (RUT (MIT)) for assistance with calculations
and data analysis.

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References
1. Malakhova AN (2013) Features of operation of monolithic beam floors under load.
Cyberleninka 1–8. https://cyberleninka.ru/article/n/osobennosti-raboty-monolitnogo-baloch
nogo-perekrytiya-pod-nagruzkoy/viewer. Accessed 21 July 2025
2. Perunov VA, Doroshin IN (2020) Method for measuring deformations in monolithic floors
with limited visibility of structures. Cyberleninka 1–13. https://cyberleninka.ru/article/n/spo
sob-izmereniya-progibov-monolitnyh-perekrytiy-pri-ogranichennoy-vidimosti-konstruktsiy/
viewer. Accessed 21 July 2025
3. Li QN, Li LJ, Jiang WS (2012) Structure and deflection analysis of a new assembled floor. Scientific. Net, AMR 446–449, p 2998. https://www.scientific.net/AMR.446-449.2998. Accessed 21
July 2025
4. Kuznetsov V, Shaposhnikova U (2016) Definition of deflections in monolithic slabs with mixed
reinforcement during limit equilibrium stage. In: Matec conferences. https://www.matec-con
ferences.org/articles/matecconf/pdf/2016/36/matecconf_tpacee2016_04015.pdf. Accessed 21
July 2025
5. Kuznetsov VS, Maksyashkina EA, Shaposhnikova YA (2020) Deflections of monolithic flat
overlaps with post-tensioning at different side ratio of slab cells. IVDON, no. 2. http://www.
ivdon.ru/en/magazine/archive/N2y2020/6338. Accessed 21 July 2025
6. Perunov AS, Doroshin IN (2020) Method for measuring deflections of monolithic floors with
limited structural visibility. ESJ, no. 6. https://esj.today/PDF/42SAVN620.pdf. Accessed 21
July 2025
7. Kuznetsov V, Shaposhnikova Y (2018) deflections of monolithic flat ceiling slabs with
high-strength reinforcement without adhesion to concrete. ResearchGate. https://www.resear
chgate.net/publication/325716294_Deflections_of_slabs_of_monolithic_flat_ceilings_with_
high-strength_reinforcement_without_adhesion_to_concrete. Accessed 21 July 2025
8. Gaidzhurov PP, Volodin VA (2022) Strength calculation of joint between floor slab and monolithic reinforced concrete frame column using FEM. Vestnik DSTU, no. 1939. https://www.
vestnik-donstu.ru/jour/article/view/1939. Accessed 21 July 2025
9. Portayev DV (2011) Calculation and design of monolithic prestressed structures for civil
buildings. ASV, Moscow
10. Afanasyev AA (1990) Construction and assembly of monolithic reinforced concrete buildings.
Stroyizdat, Moscow, p 380
11. Polikutin AE et al (2018) Reinforced concrete and masonry structures for multistory buildings.
Voronezh State Technical University, Voronezh, p 50
12. Egereva EN et al (2019) Development and implementation of urban planning policy case study
on saransk. E3S Web Conf 164(11024):6–28. https://doi.org/10.1051/e3sconf/202016411024
13. Egereva EN, Barmenkova AS (2019) Roof truss overloading in media center building in
Saransk. E3S Web Conf 110(01079):10–21. https://doi.org/10.1051/e3sconf/201911001079
14. Rusakov AI (2010) Experimental-theoretical evaluation technique for deflections of monolithic
armored floors. Ind Civ Eng 3 (in Russian)
15. Bondarenko VM et al (2002) Rebar-reinforced concrete and masonry construction. Higher
School Publ., Moscow, p 876 (in Russian)
16. Paillé GM (2013) Calculation of reinforced concrete structures. AFNOR, Paris
17. Sitnikov SL (2011) Method for manufacturing prestressed reinforced concrete structures. Patent
RU 2427686, Moscow
18. Kravchenko GM et al (2019) Modeling nonlinear behavior of monolithic concrete slab using
finite elements. NaukaRU. https://naukaru.ru/ru/nauka/article/33867/view. Accessed 21 July
2025
19. Kanakov ID et al (2022) Analysis of monolithic reinforced concrete structures in civil construction: advantages, current issues, and solutions. Cyberleninka. https://cyberleninka.ru/article/n/
analiz-monolitnyh-zhelezobetonnyh-konstruktsiy-v-grazhdanskom-stroitelstve. Accessed 21
July 2025

Influence of Beam and Column Cross-Section on Deflection …

435

20. Najia Sh (2018) Design analysis of reinforced concrete building structures. Moluch, no. 208.
https://moluch.ru/archive/208/51123. Accessed 21 July 2025
21. Rusakov AI (2010) Experiential-theoretical approach to assessing deflections in monolithic
slabs. http://rusakov.donpac.ru/Durability/Estimation%20of%20Deflections.pdf. Accessed 21
July 2025
22. Taleskiy VV (2020) Design of reinforced concrete structures for multi-storey buildings.
http://elib.bsut.by/bitstream/handle/123456789/4190/%D0%9C%D0%B5%D1%82%D0%
BE%D0%B4%D0%B8%D1%87%D0%BA%D0%B0%20%D0%96%D0%91%D0%9A_%
D0%A2%D0%B0%D0%BB%D0%B5%D1%86%D0%BA%D0%B8%D0%B9_2020.pdf?
sequence=1&isAllowed=y. Accessed 21 July 2025

Progressive Limit States of a Flat Model
of Portal Frame
L. Yu. Stupishin, K. E. Nikitin, and M. L. Moshkevich

Abstract The variational criterion of critical strain energy levels used by the authors
determines changes in a state of self-stress of the structure due to the shutdown of
internal links in it. The technique of progressive limit state, based on this criterion,
provides an opportunity to trace the process of disabling links within the structure,
until the load-bearing capacity is completely exhausted, when the system becomes
unstable. In addition to this, the use of the rod approximation method allows to represent a structure of almost any shape as a system of rod elements. In this case, the
technique of progressive limit state becomes more visual. The paper investigates a
structure in the form of a portal frame. To determine the extreme self-stress forces
in the rod structure, a mathematical model of the problem in the form of an eigenvalue problem is used. The schemes of sequential disconnection of the links, which
were obtained during the analysis of self-stresses in the structure, are presented. The
diagrams of unstable structures that appear when their bearing capacity is exhausted
are also given.
Keywords Rod approximation method · Limit states · Loss of bearing capacity ·
Critical energy levels · Weak link

1 Introduction
Currently, the most common and effective approach to solving problems of structural
mechanics is an approach based on the use of the variational principle of minimizing
the total strain energy of the structure (Lagrange’s approach) [1–11]. Despite its
indisputable effectiveness, the theories and techniques based on it, in some cases,
L. Yu. Stupishin · K. E. Nikitin (B)
Moscow State University of Civil Engineering, Moscow, Russia
e-mail: niksbox@ya.ru
M. L. Moshkevich
Kursk Branch of ANO PO IMCCT “Academy of TOP”, Kursk, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_35

437

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L. Yu. Stupishin et al.

lead to difficulties in calculations, and discrepancies between the obtained results
and experimental data.
The authors develop an alternative approach to solving complex problems of
structural analysis, which involves the use of a variational criterion of critical strain
energy levels. This approach makes it possible to determine the extreme values of the
parameters of a deformable system based on the solution of the eigenvalue problem.
It becomes available to determine the residual value of the load-bearing capacity of
the structure, and to identify the ‘weak’ element in which the limit state will arise
first.
Sequentially removing the ‘weak’ element from the design scheme, and repeating
the analysis, we obtain a sequence of progressive limit states. By analyzing up to the
splitting of the structure into parts, or obtaining an unstable structure, it is possible
to trace the process of exhausting the bearing capacity of the structure. This is the
essence of the progressive limit state technique used by the authors in this study.
At present, much attention is paid to methods of calculating structures for progressive destruction [12–16]. This topic is close to that considered in this paper, but
the problem statement and solution methods usually used in such problems differ
significantly from those proposed by the authors.

2 Methods and Materials
Various concepts are used to construct design schemes of the structure: in the form
of a set of rods, flat elements (as the plane elastic problem), or solid bodies (as the
three-dimensional elasticity problem).
The flat portal frame under study is considered as an inverted U-shaped strip
of constant thickness (Fig. 1a) in the framework of the plane elastic problem. It
is assumed that the frame is deformed only in its plane and there is a plane stress
condition.
For the convenience of solving the problem and the visualization of tracking
the process of the progressive limit state, the selected flat model is represented by a

Fig. 1 a The flat frame model; b A rod approximation of the continuum by rod cells

Progressive Limit States of a Flat Model of Portal Frame

439

hinge-rod structure. The method of rod approximation [17] transforms the continuum
model into a rod model, including many cells from a uniform set of rod finite elements
and nodes. In the nodes, the degrees of freedom of the continuum at a given point
are selected. One of the regions of the rod structure, the properties and the degrees
of freedom at the nodes are shown in Fig. 1b. The rods of this structure model and
clearly show the functioning of the internal links of the material of the structure—
longitudinal and shear.
The stiffness of the longitudinal and inclined rods of this regular structure was
calculated as follows:
EA1 =

1
3
b · t · E; EA2 = √ EA1
4
2

(1)

here b is the step of the lattice of rods; t is the thickness of the structure (the size in
the direction perpendicular to the plane under consideration).
Currently, the most common method of structural analysis is the finite element
method, which allows you to create a structural model in the form of a set of finite
elements of any dimension (1D, 2D or 3D). The approach proposed by the authors,
based on the variational criterion of critical strain energy levels, uses the algorithm
of the finite element method to construct stiffness matrix or flexibility matrix (in the
case of the method of forces) of a system of elements. However, the further algorithm
for solving the problem using the obtained matrix differs from the algorithm of the
finite element method. The traditional approach is to solve a system of equations
where a fixed external load is taken into account in the right-hand side. The nodal
displacements (or forces, in the case of the method of forces) are calculated, and
according to them the internal forces for one loading variant.
In the proposed approach, the properties of the continuum strain field (transformed
into the parameters of the rod approximation) are investigated. These properties are
determined by the geometry of the structure, its geometric and mechanical characteristics and boundary conditions. They do not depend on a specific load, since they
reflect the general patterns of self-stress of the structure. Here it is necessary to clarify
that external forces (for example generated, by the gravitational field), and the strain
field of the structure and the state of self-stress are different fields with their own laws
of existence. The self-stressed state of the structure allows us to reveal in what ratios
the elements of the load-bearing system take on external influences. This ratio for
the rods will not change until the self-stressed state changes. Therefore, the search
for the most stressed rods of the structure is carried out without taking into account
external loads. In order to find the most stressed rods, the problem is formulated as
an eigenvalue problem for the obtained stiffness matrix (or flexibility matrix) of the
system of elements.
The problem of determining the extreme values of the parameters of a deformable
structure can be solved within the framework of any of the structural mechanics
formulations: the method of forces, the deformation method, or a mixed method.
However, each case has its own specifics. This paper, the method of forces is used to

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solve this problem. Extreme values of nodal reactive forces are found based on the
flexibility matrix constructed for the system of elements.
The condition of the critical state of strain energy of the structure, according to
the variational criterion of critical strain energy levels [18–20], is formulated as:
δU (χ ) = 0;

Uj (χ ) = 1;

(χ ) = 0

(2)

here U is the potential strain energy of the structure; χ is the extremals of generalized
displacements and forces (problem variables).
The formulation of the eigenvalue problem, which expresses the condition of the
critical state of the structure based on the structure’s flexibility matrix [19], has the
form:
[L]{

} = λL {

}

(3)

where: [L] is the matrix of structural compliance formed using the finite element
method; { } is the vector of variation of the amplitude values of the generalized
reactive forces in all directions of the degrees of freedom of the structure for the selfstress states of the structure; λL is an eigenvalue matrix, which has the meaning of
unit nodal displacements of the structure.
Based on the results of solving the eigenvalue problem (3), the vector of maximum
nodal displacements of the structure is calculated as:
{Zmax } = λLmax {

max }

(4)

Next, strains in the elements and internal forces in the rods can be found based
on the values of the vector (4) of maximum displacements:
{ε} = −[A]T {Zmax }

(5)

{N } = [C]{εmax }

(6)

here: [C] is the matrix of internal rigidity; [A]T is the transposed static matrix of
structure.
According to the values of the forces found, the element (or elements) with the
greatest value of force (or strain) is searched for. We consider that the limit state
will occur in this element(s) in the first place. By sequentially removing such ‘weak’
elements from the computational scheme, and by reanalyzing the updated computational scheme, we obtain a chain of limit states, up to obtaining a unstable system.
At the moment of obtaining such a system, it is considered that the structure finally
loses its load-bearing capacity. This completes the calculation.

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This algorithm was implemented as a computer program for analyzing structures
using the method of critical strain energy levels called “CLE”, developed by the
authors [19, 20]. The results presented below are obtained in this program.

3 Results and Discussion
The results of applying the approach under consideration to obtaining a sequence of
limit states in the rod approximation model, up to the formation of a geometrically
variable system, are given below. The study was carried out for models of the frame
(Fig. 1a) with dimensions: T = D = 0.4 m, B = 4 m, and with different heights: H
= 1, 4, 6, 8 m.
The frame supports were taken in two forms (see Fig. 2). The first, shown in
Fig. 2a, restricts the displacements in all directions of only two points-nodes on the
lower boundary of the frame contour. These points are located exactly in the middle
of the legs, on their axes (shown in Fig. 2a by a dotted line). Such fixation forms the
simply supported end of the frame leg. The second attachment, shown in Fig. 2b,
restricts all displacements of all nodes located along the lower boundary of the frame
contour. This fixation scheme implements a model of fixed end of the frame leg.
The following values of the mechanical properties of the frame material were
taken: the modulus of elasticity is E = 30 × 103 MPa; the Poisson’s ratio is ν = 0, 2.
Formed on the basis of the initial model (Fig. 1a), the rod approximation model
(Fig. 1b) is obtained as a set of finite elements of the flat truss type. This model
has two degrees of freedom in each free node (Fig. 1b). The stiffness of the rods
in this model was calculated in accordance with (1), and the following values were
assumed: EA1 = 900 MN, EA2 = 636 MN.
The progressive limit state method is applied to frames of the accepted dimensions
and with the specified types of boundary conditions, based on the variation criterion
of critical strain energy levels. As a result, a chain of limit states of the frame is
formed, which ultimately leads to obtaining a geometrically variable system, that is

Fig. 2 Boundary constraints specified along the bottom edge of the frame contour: a of the first
type; b of the second type

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considered a point at which the load-bearing capacity of the structure is completely
exhausted. The key states of the structure are given and their analysis is performed.

3.1 Frames with Simply Supported Ends (Fig. 2a)
For frames with short legs (H = 1 m), weak links appear primarily in the beams. The
first to be switched off were the links in the bottom zone of the beam near the ends of
its span (Fig. 3). This led to a decrease in the rigidity of the structure in these places,
and a redistribution of forces in the calculation scheme of the bearing structure. Then
the weakening of the beam stops, and new weak connections are revealed already in
the legs, near the places of their connection with the beam (Fig. 4a). The progressive
limit state in the beam of the structure finishes with the disappearance of all links
that prevent the beam from turning relative to the legs, which is equivalent to the
appearance of hinges at these places. As a result, the rod approximation model of
the frame is an unstable system (see Fig. 4b).
In case of a large height of frame legs (H > 4 m), the sequence of occurrence of
limit states in the rod approximation model is slightly different (Fig. 5). In this case,
the first weak links also appear in the beam, but their number is noticeably smaller.
After some weakening of the beam rigidity, limit states begin to occur in the legs.
Furthermore, they cover a fairly large area—not only the zone near the connection
joints of the legs with the beam, but also spread along the length of the legs, up to its
middle. Weak links also appear directly inside the connection joints. Most of such

Fig. 3 First stages of progressive limit states of the frame with short legs

Fig. 4 a Final stage of progressive limit states of the frame (an unstable system); b A rod
representation of the unstable frame

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Fig. 5 Final stage of progressive limit states of the high frame. An unstable system

links, after their appearance and elimination, only reduce the rigidity of the structure,
but do not lead to the loss of its bearing capacity. But the concentration of weak links
in the legs, near the connection joints with the beam, is crucial. Subsequently, the
links preventing the beam from turning relative to the legs disappear, and a kind of
hinge joint appears, leading to the formation of an unstable system (Fig. 4b). This
moment can be considered the moment of exhaustion of the bearing capacity of such
a structure.

3.2 Frames with Fixed Ends (Fig. 2b)
In the case of a small height of the frame legs (H = 1 m), the process of development
of limit states occurs in several stages. At the first stage (Fig. 6), the removal of weak
links helps to form a connection in the frame, which does not prevent the left half of
the frame from turning relative to the right half. A kind of hinge is formed, located
below the central axis of the beam.
At the same time, the links in the beam begin to disappear near the junction with
the legs. The second stage of the development of limit states begins, during which
the internal links of the structure near these junctions disappear. This stage ends with
the formation of a connection near these joints that does not prevent the rotation of

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Fig. 6 The first hinge connection appearance in the frame

the legs relative to the beam (Fig. 7). A kind of hinge is formed, located slightly
above the central axis of the beam.
Despite the process of formation of three hinges, the appearance of an unstable
system does not occur immediately. This is due to the fact that the centers of the
zones in which the formation of hinges occurs are not located on the same line. The
parts of the beam, separated by the zones of formation of hinges, form a kind of
suspended system.
The final stage of the process of development of limit states in the internal links
of the frame occurs near the supports (Fig. 8a). At this stage, the internal connections
that restrain the posts from turning relative to supports gradually disappear. The next
hinges are formed, which eventually lead to the formation of an unstable system and
the final loss of the bearing capacity of the frame (Fig. 8b).
In the case of high frames (H > 4 m), the character of the development of the
progressive limit state process changes somewhat. With such frame sizes, it does not
depend significantly on the H parameter of the frame, and at its various values it is

Fig. 7 The next hinge connections appearance in the frame

Fig. 8 a Final hinge connections appearance in the frame (an unstable system); b A rod
representation of the unstable frame/

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Fig. 9 First stages of progressive limit states of the frame

approximately the same. At first, when the limit states in the rods of the structure
occurs, the links near the frame supports disappear until something similar to a hinged
support is formed (Fig. 9).
At the second stage, the links in the posts near the beam-legs connection node
gradually disappear (Fig. 10). As a result, only those links remain that do not prevent
the rotation of the legs relative to the beam. Connections similar to hinged ones are
formed (Fig. 4b). As a result, the frame becomes an unstable system, and finally
loses its load-bearing capacity.

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Fig. 10 Final stage of progressive limit states of the frame. An unstable system

4 Conclusion
As a result of the calculations carried out using the method of progressive limit states
for portal frames with different sizes, sequences of destruction of internal links were
obtained up to the complete exhaustion of the bearing capacity of the structure. They
demonstrated that when limit states occur in a frame structure, such combinations
of internal connections are formed that behave like plastic hinges considered in the
plastic limit analysis of rod structures. However, in the plastic limit analysis theory,
the number and locations of plastic hinges are usually established on the basis of
experimental studies, based on the experience of observing the destruction of similar
structures. But as the results of the studies conducted by the authors show, these data
can also be obtained by calculation, using the proposed technique of progressive
limit states.
It should be noted that the solutions obtained on the basis of the variational criterion of critical strain energy levels do not require specifying the values and locations
of the loads. The order of occurrence of the limit states and the process of their
development depends only on the geometric structure and shape of the structure, the
mechanical properties of the structural material and boundary conditions, but not on
the magnitude, direction or location of the load.
The proposed technique makes it possible to study the process of the occurrence
of the limit state in the frame structure sequentially and step-by-step, through the

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failure of the structural connections. The calculation methods known to us do not
allow us to trace the process of destruction of a structure in the case of uncertainty
in the action of loads.
The obtained results confirm the correctness of the plastic limit analysis theory
of structures under rigid plastic deformations of the material.

References
1. Pejatović M, Caspeele R, Belis J (2024) Numerical study of the in-plane bending behaviour of
a novel steel-reinforced glass frame prototype. In: Louter C, Bos F, Belis J (eds) International
conference on the architectural and structural application of glass challenging glass conference,
9–19 & 20 June 2024, vol 9. https://doi.org/10.47982/cgc.9.542
2. Yi W, Yao Z, Luo L, Ashour A, Ge W, Sushant S, Qiu L (2025) Bending performance of
reactive powder concrete frame beams reinforced with steel-FRP composite Bars. Case Stud
Constr Mater 22:e04219. https://doi.org/10.1016/j.cscm.2025.e04219
3. Monserrat-López A, Faria DMV, Brantschen F, Ruiz MF (2025) Performance of nodal regions
of reinforced concrete frame corners subjected to opening bending moments. Eng Struct
322A:119041. https://doi.org/10.1016/j.engstruct.2024.119041
4. Huang Z, Wang K, Liu Y, Zhang W, Cao C (2024) Full-scale testing of the bending behavior
of UHPC gravity–grouted sleeve–prestressed anchor joints in assembled frame tunnels. Constr
Build Mater 457:139403. https://doi.org/10.1016/j.conbuildmat.2024.139403
5. Zhao JZ, Liu TS, Tao MX (2025) Design formulae for ultimate bending capacity of composite
frame beam under vertical load. Structures 71:107939. https://doi.org/10.1016/j.istruc.2024.
107939
6. Turk K, Katlav M, Bitkin RE (2025) The use of high-volume hybrid steel fiber instead of
compression rebar to improve the structural performance of high-strength SCC beams under
bending. Constr Build Mater 470:140521. https://doi.org/10.1016/j.conbuildmat.2025.140521
7. Shi G, Wang D, Wang F (2025) Experimental investigation of the critical collapse behavior
of stiffened box girders under impact bending load. Structures 79:109440. https://doi.org/10.
1016/j.istruc.2025.109440
8. Shi GJ, Ji YH, Xu JB, Wang DY, Xu ZT (2024) Experimental study of structural failure and
ultimate strength of GFRP girder with hat stiffeners and foams under bending load. Mar Struct
96:103607. https://doi.org/10.1016/j.marstruc.2024.103607
9. Jaaranen J, Fink G (2024) A finite element simulation approach for glued-laminated
timber beams using continuum-damage model and sequentially linear analysis. Eng Struct
304:117679. https://doi.org/10.1016/j.engstruct.2024.117679
10. Shen J, Arruda MRT, Pagani A, Carrera E (2024) A regularized higherorder beam elements for
damage analysis of reinforced concrete beams. Mech Adv Mater Struct 31(1):79–91. https://
doi.org/10.1080/15376494.2023.2245825
11. Aursand M, Frøseth GT, Haagensen PJ, Skallerud BH (2024) Crack growth in high strength
mooring line steel under variable amplitude loading. Mar Struct 93:103534. https://doi.org/10.
1016/j.marstruc.2023.103534
12. Shen B, Liu HJ, Lv S, Li Z, Cheng W (2022) Progressive failure analysis of laminated CFRP
composites under three-point bending load. Adv Mater Sci Eng 1:3047319. https://doi.org/10.
1155/2022/3047319
13. Wang C, Zhao J, Zheng W (2023) Progressive failure analysis of soil slope with strain softening
behavior based on peridynamics. Adv Civ Eng 1:6816673. https://doi.org/10.1155/2023/681
6673
14. Zhong D, Chen J, Zhou H, Chen X, Jiang Y (2022) Study on progressive failure of hard rock
tunnel after excavation under high stress. Adv Civ Eng 1:4755417. https://doi.org/10.1155/
2022/4755417

448

L. Yu. Stupishin et al.

15. Zhong D, Chen J, Zhou H, Chen X, Jiang Y (2023) Progressive failure of surrounding rock
in underground engineering and size effect of numerical simulation. Adv Civ Eng 1:9454079.
https://doi.org/10.1155/2023/9454079
16. Yang KB, Zhu YP, Wu LP, Duan XG, Shi DB, Du XT (2022) Analysis on deformation failure
and structural mechanical characteristics of multistage loess slope supported by frame structure
with anchors. Adv Civ Eng 1:4158265. https://doi.org/10.1155/2022/4158265
17. Rzhanicyn AR (1982) Stroitel’naja mehanika (Structural mechanics). Vysshaja shkola publ,
Moscow
18. Stupishin LY, Mondrus VL (2023) Implementation of the weak link problem for trusses.
Buildings 13(5):1230. https://doi.org/10.3390/buildings13051230
19. Stupishin LY, Nikitin KE, Moshkevich ML (2024) The process of progressive limiting state
and determination of the residual strain energy of a structure based on the force method. In:
Radionov AA, Ulrikh DV, Timofeeva SS, Alekhin VN, Gasiyarov VR (eds) Proceedings of the
7th International conference on construction, architecture and technosphere safety, ICCATS
2023. Lecture notes in civil engineering, vol 400. Springer, Cham, pp 280–289. https://doi.org/
10.1007/978-3-031-47810-9_26
20. Stupishin, LY, Nikitin KE, Moshkevich ML (2024) Self-stressing state and progressive limit
method study of a flat strip. In: Radionov AA, Ulrikh DV, Gasiyarov VR (eds) Proceedings of
the 8th International conference on construction, architecture and technosphere safety, ICCATS
2024. Lecture notes in civil engineering, vol 565. Springer, Cham, pp 349–357. https://doi.org/
10.1007/978-3-031-80482-3

Information Modeling Technologies
for Russian Wooden Architecture
Objects as a Basis for Modern Design
G. Zakharova and A. Romanov

Abstract The example of a small tourist cluster on the territory of the MuseumReserve of Wooden Architecture in the Nizhnyaya Sinyachikha village, Sverdlovsk
Region, shows a modern approach to the integrated design of a site using BIM
technologies for historical wooden buildings. As a result of the analysis of historical
analogues, characteristic features of residential wooden architecture were identified.
The created complex fits harmoniously into the village, the architecture of the peasant
estates of the museum echoes the architecture of the tourist cluster. The development
of the project is based on the BIM technology of wooden buildings, which performs
element-by-element modeling of the nail-free log system, typical for Russian wooden
architecture. The features and complexity of displaying various types and design
features of traditional carpentry joints in log buildings in the program are noted. BIM
will help to visualize these joints and transfer them further to 3D printing to create a
three-dimensional constructor of a wooden log house in order to clearly demonstrate
the principles of operation of structures. The project began with the creation of
a concept using manual sketching, then the layouts of buildings and territory was
transferred to the CAD system, where the general plan, plans for engineering systems,
improvement and landscaping were developed. An important result of the work is
the general technological scheme of information flows indicating all the software
involved. Effective visualization of the project allows you to evaluate the project as
a whole. In conclusion, the main capabilities and advantages of HBIM technology
are formulated, prospects for further development are outlined.
Keywords Wooden architecture · Tourist cluster · Historical heritage ·
Information modeling · BIM · HBIM

G. Zakharova (B) · A. Romanov
Ural State University of Architecture and Art named for N.S. Alferov, Ekaterinburg, Russia
e-mail: zakharova@usaaa.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_36

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1 Introduction
Nowadays, the use of traditional forms of folk architecture is becoming popular in
wooden house-building. Many city dwellers, tired of the urban environment, want
to build a house outside the city. Architects and builders offer many solutions for
low-rise residential buildings, differing in appearance and structural systems. The
use of wood as the main building material imposes certain aesthetic requirements.
Along with functionality, the building should look presentable and emphasize the
character of the owner. The best means of expression in this case is the use of
national styles—German half-timbered houses, Austrian chalets, Norwegian hutte
[1], Russian wooden architecture. It is the latter that is attracting increasing interest,
in particular, due to some exoticism in the eyes of modern people.
One of the most unusual objects in the Russian style is the estate in the village of
Astashovo in the Kostroma region, known as the “Forest Terem” [2]. The two-story
house with a rich carved pattern was built in the late nineteenth century and arranged
as an estate with outbuildings, a carved gazebo, a garden, and dug ponds. During the
Soviet period, the house stood empty and deteriorated for many years, overgrown
with forest, until complex restoration work began in 2011. The work was carried out
using historical technologies and materials. In 2016, “Astashovo—Forest Terem”
opened as the first hotel-museum in Russia, where, in addition to accommodation,
tourists can take advantage of a variety of active recreation programs [3].
A similar task of developing a small tourist cluster on the territory of an open-air
museum was set in our project, based on the results of which this article was written.
The I.D. Samoilov Museum-Reserve of Wooden Architecture and Folk Art, opened
in 1978, is located in the ancient Nizhnyaya Sinyachikha village in the Sverdlovsk
Region along the banks of the Sinyachikha River on an area of 52 hectares. It presents
various types of residential and utility buildings from the eighteenth to twentieth
centuries, brought from different places of the Urals, as well as a collection of Ural
house painting, wood carving and other applied art products. The museum complex
includes more than 20 different buildings and structures.
On a free plot of about 4000 m2 it was necessary to design a tourist complex
containing a group of three wooden houses: a five-wall house in the style of wooden
architecture of the early twentieth century with a traditional interior of that time,
where there will be a common space for meeting guests, and two guest houses in the
style of the seventeenth–eighteenth centuries for tourists to stay—several families of
up to 20 people in total. It was necessary to develop the appropriate infrastructure,
which should contain a bathhouse, gazebos, a playground, a vegetable garden, a mini
zoo and other components.
An effective and de facto standard approach in modern construction is the BIM
modeling approach [4]. We will show below how this technology was used in the
project and what advantages it provides.

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2 Stages of Project Development
One of the important principles of project development was the appeal to historical
materials, careful work with sources on Russian wooden architecture.
The most interesting approach in the context of our research is BIM—building
information modeling; the term HBIM—Historic BIM [5] is used for historical
objects. In this section, we will show how you can combine the areas of research,
design and construction through HBIM. BIM modeling allows you to flexibly make
changes during the project development process, automatically receive all types
of documentation, generate information on materials and cost calculations in a
single environment, facilitate effective control during construction, and track changes
during further operation.

2.1 Research and Application of Historical Analogs
in the Project
All houses in the project are designed based on historical analogs. As a result of
the analysis, characteristic features of wooden housing architecture inherent in the
Sverdlovsk Region were identified [6]. The main buildings chosen as analogs were
architectural heritage monuments in the open-air museum in Nizhnyaya Sinyachikha,
as well as objects of traditional wooden architecture of the Sverdlovsk Region.
The overall composition of the guest houses and the canopy was chosen as threepart, or “under three horses”. The analog of this solution was a triple house in the
Vorob’i village, Pervouralsky region (Fig. 1a) [7]. This composition of a hut, a barn
and a yard was common in the territory of the Middle Urals. In our project, two
two-story guest houses are connected by a gable canopy, which is a smaller version
of the roofs of the main houses (Fig. 1b).
The guest houses were analogous to a two-story six-wall house from the
Luchinkino village, Tugulymsky Region, built in 1806–1807 (before being transported to the Nizhnyaya Sinyachikha village) [6]. This building was restored on

Fig. 1 a historical analogue for the guest houses project; b general composition of the guest houses
with the gable canopy obtained from BIM-model

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the territory of the museum in Nizhnyaya Sinyachikha based on photographs and
measurements. Two-story six-wall houses became widespread in the late nineteenth–
early twentieth centuries. The guest houses have a “male-skid” roof system, which
allows for a more expressive roof overhang over the pediment, as well as the use of
carved gables. The door frames do not have shutters, they are made monolithically,
without fractional carving in order to emphasize the historical five-wall house. The
two guest houses differ in the design of their facades: different types of attic balconies
and door frames are used. The first floor is a public space with a living room and a
small kitchen area, the second floor is occupied by bedrooms.
The hut from the village of Karagaevo in the Garinsky region from 1935–1940
was taken as an analogue of the five-wall house [7]. Huts of this type spread in the
Urals by the end of the nineteenth century. The five-wall house is the dominant one in
the composition of the complex; it greets visitors with its façade, and the façade also
stands out for its decorative design. The architecture of the hut here more accurately
corresponds to the historical analogue: the fifth capital wall asymmetrically divides
the volume into two parts: the upper room and the main hut. The roof of the fivewall house is a hipped rafter with a large projection of the hemmed profiled cornice,
which is decorated with carvings together with the platbands. Traditional Middle Ural
painting is used in the design of the platbands. The five-wall house in the structure of
the complex is a non-residential space; it is planned to place a small area for meeting
guests, as well as a kitchen and a dining room; for this purpose, a significant area in
the house is occupied by a Russian stove.
According to the chosen concept, the guest houses and the canopy are equipped
with protective skates, which, according to folk mythology, represent the spirits of
the earth, forest and water and, accordingly, have the shape of a horse’s head, a bird’s
head and a wave shape [8, 9].

2.2 Information Modeling of Wooden Buildings
One of the first articles on BIM modeling of historical wooden buildings is the work
of Novosibirsk scientists [10], which describes the methodology for constructing
the most realistic model of an architectural heritage of the seventeenth–eighteenth
centuries, the Church in Zashiversky Fortress, transported from the Polar Region to
the Novosibirsk Open-Air Museum of Wooden Architecture. For the purposes of
museumification, the BIM model was created “log by log”, the task was to develop a
structurally reliable electronic “duplicate” of the architectural monument. The model
contains not only comprehensive research information on the architectural and artistic
features of the object, but also quantitative characteristics describing the condition
of the building and allowing for the possibility of their further filling and adjustment
as a result of the surveys. Article [11] develops the theme of modeling wooden
architecture towards the parameterization of elements, introduces the concept of an
“intelligent” log and contains several unique BIM models of buildings of varying
complexity, confirming the possibility and necessity of information modeling.

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It is in the article [11] that the information model of the complex wooden object
“Astashovo—Lesnoy Terema” was built. The authors note the experimental nature of
the work. Since all architectural monuments are unique in their own way, no library of
elements will be exhaustive for their modeling; it will always be necessary to create
new parts and units. Therefore, in the information modeling of architectural heritage,
the most important thing is not the library of elements itself, but the methodology for
its creation. The work has shown that today there are no restrictions on the modeling
of wooden structures either in complexity or in the volume of work performed.
We set the task of using such models in modern house-building in the traditions
of Russian wooden architecture. BIM models of wooden buildings were studied in
the article [12, 13], where the abbreviation HWBIM—Historic Wooden BIM was
introduced for them, and the modeling features that must be taken into account for
log structures were noted.
In our previous studies, the problem of parameterization of the basic unit of
wooden construction—a log—turned out to be unsolved. Many factors were not
taken into account—grain size, resin content and density of wood, its age, internal
structure, defects, curvature and taper of the trunk. The location of the log in the
log system, as well as the nature of its processing, depend on these parameters. In
addition, many ways of connecting wooden structures to each other were not taken
into account. Among them are carpenter’s notches (along the length, along the height,
in the corners) and joinery joints (frame). These identified problems still need to be
solved in future projects.

2.3 Basic Principles of Modeling Wooden Elements
In the context of studies of old wooden architecture, a theoretical researcher, as a rule,
has certain difficulties in understanding what a carpenter-restorer knows, namely, the
types and design features of traditional carpentry joints [6, 14]. The most accessible
method for demonstrating the spatial logic of a carpenter is the visualization of these
joints using BIM modeling tools [15, 16], and in the future, using 3D printing tools.
The creation of a three-dimensional constructor of a wooden log house, made using
a nail-free system at a scale of 1:20, would make it possible to clearly demonstrate
the principles of operation of structures.
In this work, an element-by-element modeling of a nail-free log system, typical
for Russian wooden architecture, was performed. At the first stage, log walls were
assembled in the Renga system using the “profile beam” tool. Window and door
openings, internal walls were marked, then the rafter and samtsov-sleg systems were
assembled. The platbands were made using the “assembly” tool, and the cornice
carving was done using the “profile beam” tool. Figure 2 shows the roof structure of
a five-wall house: hipped rafters with a large overhang of a profiled cornice, which
is decorated with carvings along with the platbands.

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Fig. 2 The structure of the roof of a five-wall house (from Renga project) and traditional Russian
names of its elements

3 Software Used in the Project
The created information model of buildings on the site are close to the spatial logic
of traditional construction.
The project uses mainly Russian software. Work with site plans was done in the
NanoCAD program, and the design of wooden houses was done in the Renga BIM
program. The stove in the five-wall house, the ridges and gables were in the SketchUp
program and then imported into the Renga program via the “element” tool in the c3d
format.

3.1 Technological Scheme for Designing a Site
with Buildings
First of all, the project concept was created using manual sketching technique. The
resulting layout of buildings and planning was transferred to the NanoCAD software
environment, taking into account the scale and size of the cadastral land plot allocated for the design (Fig. 3a, b). The drawing allowed the buildings to be located
with clarification of their dimensions and to create a system of improvement and
landscaping (Fig. 3c).
A general site plan, utility plan, landscaping plan, and dendroplan were developed.
To the left of the main gate, there is a parking lot for four cars. A children’s playground
is provided in the area furthest from the wind. A barbecue area is located nearby.
On the eastern side of the site there is a driveway for a fire truck with a turning
area. The greenhouse and vegetable garden area is located near the barn, behind
the hotel complex. Engineering communications include such sections as electricity,
water supply, sewerage, and heat supply. For heating, the most rational solution
was to install electric boilers in guest houses. Considering the predominance of the

Fig. 3 a photo of the site; b cadastral land plot; c the resulting layout of buildings and planning in NanoCAD software

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westerly wind direction along the western border of the site, a strip of greenery for
wind protection is provided, consisting of a row of bushes and a row of trees.
The advantage of drawing graphics is the speed of creating a schematic basis for
further modeling, which at the same time is mathematically accurate (corresponds
to real dimensions in the metric system). From the NanoCAD system, finished plans
were exported in dwg format for subsequent work.
The landscaping elements and the playground were modeled in ArchiCAD taking
into account the existing terrain. The buildings of the tourist complex were modeled
in the Renga program, where the accompanying documentation was automatically
generated based on the model. Elements of traditional decor (amulet skates, different
for each guest house, in the form of a horse’s head, a bird’s head and a wave) were
obtained in the SketchUp program and imported into the building model in the Renga
program using the c3d format.
When working with the interiors of the houses, descriptions of the structure of
Ural huts of the nineteenth–early twentieth centuries were studied: the interior of a
traditional peasant dwelling in the Middle Urals was a certain system in which each
element carried a deep symbolic meaning. Interiors with elements of folk Ural decor
were developed in the 3ds Max program, then the model was loaded into the Lumion
system for visualization, or you can use Vray for final renderings.
The site model with landscaping elements and building models were transferred
to the Lumion system for visualization based on the export of dae and IFC formats.
Setting the orientation of the site and the surrounding terrain in this program allows
simulating various weather conditions and determining the strengths and weaknesses
of the project. In addition, Lumion tools make it possible to record animation for a
more effective demonstration of the project. The general technological scheme of
project development with all information flows is shown in Fig. 4.

3.2 Consolidated Project of the Tourist Complex
After the 3D model was completed, all drawings were automatically obtained from
it: plans, sections, facades and exploded diagrams. This is one of the most obvious
advantages of BIM technology. Figure 5 shows the plans and sections of the designed
guest houses.
Visualization of the project—different types of buildings and improvement
elements, obtained from a consolidated model assembled in the Lumion program,
where an animated video with a walk-through and fly-through of the territory was
also created. Figure 6 shows one of the views of the tourist complex, where you can
see how from the main gate we get to the territory, which provides optimal movement scenarios. From a one-story hut with a Russian stove, in which items of ancient
painting and home decoration are displayed, where the hostess greets guests, we
move to the guest house for settlement. The canopy between the houses will protect
from the rain, and also provide a beautiful view of the river. And then you can walk

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Fig. 4 The general technological scheme of project development

through all the recreation areas, the children’s playground, and the mini zoo. In the
corner part near the fence there is a Russian bathhouse.

Fig. 5 Documentation: drawings from the Renga program. Author: USUAA student Alexandra Permyakova

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Fig. 6 Visualization: general view of the site. Authors: USUAA students Alina Shmakova, Alena
Shagarova

4 Conclusion
One of the important principles of developing the project for a small tourist complex
on the territory of the museum in the Nizhnyaya Sinyachikha village was the use of
historical materials and careful work with sources on Russian wooden architecture.
As a related result, we collected the electronic library containing about 50 books for
the period from 1890 to 1950 in order to study the features of wooden architecture of
the Middle Urals. As a result, the entire complex fits harmoniously into the architecture of the Nizhnyaya Sinyachikha village, the architecture of the peasant estates of
the open-air museum echoes in some elements and techniques with the architecture
of the tourist cluster.
The proposed project meets the requirements of the technical specifications and
contains all the necessary zones and buildings: a five-wall house from the early
twentieth century, two guest houses in the style of the seventeenth and eighteenth
centuries, a bathhouse, gazebos for relaxation, a barbecue area, a children’s playground with a mid-twentieth century carousel, a zoo with cages for rabbits, chickens
and geese; a vegetable garden with a bed for growing vegetables and berries, paths
made of natural stone. A solution for utility lines has been proposed. Parking for four
cars is provided.
The use of BIM technology in the design allowed us to obtain the following
advantages:
• joint work on the project,

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• high design accuracy: BIM allows you to create precise three-dimensional models
of objects, which significantly reduces the likelihood of errors at the construction
stage,
• the relationship of the 3D model with drawings and calculations: any change in
the model is displayed on the documentation sheets, which saves development
time,
• fast and error-free preparation of working documentation.
Further work with the developed BIM project involves optimization of construction costs and deadlines: due to the accurate analysis of the volumes of materials,
structures and resources, it is possible to estimate the cost of work and the project
implementation deadlines in advance, and calculate the corresponding schedule.
The BIM model sets the predictability of processes: the ability to simulate various
scenarios of operation and behavior of structures will help minimize the risks of
defects during operation.
The BIM model can become the basis for developing a digital twin of the selected
building for research purposes: studying and evaluating the behavior of the corresponding materials over time. The technology can be extended to historical buildings
in Nizhnyaya Sinyachikha.
Finally, the research will be continued in the direction of forming a comprehensive
LIM project [17], which will allow all calculations for the project to be performed,
including the landscape with elements of utility lines and landscaping.

References
1. Nikel D (2022) Norway’s cabin culture: all hail the hytte. https://www.lifeinnorway.net/nor
way-cabin-culture. Accessed 29 Jun 2025
2. Vajs E (2021) Terem XXI veka: kak moskovskie predprinimateli vosstanovili zabroshennuyu
usadbu v kostromskom sele (A 21st-century mansion: how Moscow entrepreneurs restored an
abandoned estate in a Kostroma village). https://snob.ru/entry/239228/. Accessed 25 June 2025
3. Terem Astashovo (2025). https://astashovo.com/. Accessed 25 June 2025
4. BIM for Wood Buildings (2025). https://www.naturallywood.com/resources/bim-for-woodbuildings/?utm_medium=website&utm_source=archdaily.com. Accessed 29 June 2025
5. Zaharova GB (2022) HBIM-informacionnoe modelirovanie istoricheskih zdanij: osobennosti, primery, opyt razrabotki modelej (HBIM-information modeling of historical buildings:
features, examples, experience of developing models). In: 2nd International scientific and
practical conference: dialogues on the protection of cultural values, Ekaterinburg, Ural State
University of Architecture and Art, pp 20–23
6. Dolgov AV (2012) Derevyannoe zodchestvo Urala (Wooden architecture of the Urals). Socrates,
Yekaterinburg, p 232
7. Bubnov EN (1988) Russkoe derevyannoe zodchestvo Urala (Russian wooden architecture of
the Urals). Stroyizdat, Moscow, p 183
8. Chagin GN (1991) Kultura i byt russkih krestyan Srednego Urala (Culture and life of Russian
peasants of the Middle Urals). Tomsk University Publishing House, Perm Branch, p 112
9. Predaniya i legendy Urala (Traditions and Legends of the Urals) (1991) Middle Ural Book
Publishing House, p 290

Information Modeling Technologies for Russian Wooden Architecture …

461

10. Talapov VV, Kozlova TI (2011) BIM v Rossii: Zashiverskaya cerkov (BIM in Russia: Zashiverskaia Church). http://isicad.ru/ru/articles.php?article_num=14459&compage=3. Accessed 25
June 2025
11. Talapov VV (2021) BIM-tehnologiya i arhitekturnye pamyatniki derevyannogo zodchestva
(BIM-technology for the restoration of architectural monuments of wooden architecture).
https://integral-russia.ru/2021/12/07/bim-tehnologiya-i-arhitekturnye-pamyatniki-derevyann
ogo-zodchestva/. Accessed 25 June 2025
12. Romanov AS (2023) Osobennosti informacionnogo modelirovaniya derevyannyh
sooruzhenij—pamyatnikov arhitektury (Features of information modeling of wooden
structures—architectural monuments). New information technologies in architecture and
construction. In: Proceedings of the VI International scientific and practical conference.
Ekaterinburg, p 64
13. Kovalchuk AL (2019) Delat beshitrostno, kak mera i krasota skazhut (Mystery of carpentry).
Kizhi Museum-Reserve, Petrozavodsk
14. Romanov AS, Matrosov RD (2024) BIM-modelirovanie uzlov plotnickih soedinenij v
kontekste issledovanij pamyatnikov russkogo derevyannogo zodchestva. (BIM modeling of
carpentry joints in the context of research of Russian wooden architecture monuments). In:
Proceedings of the 15th International conference: new information technologies in the study
of complex structures, Tomsk, pp 31–32
15. Krauze SM, Zaharova GB, Romanov AS (2024) Informacionnoe modelirovanie derevyannogo
istoricheskogo zdaniya—kottedzha M.V. Rejshera (Information modeling of a wooden historical building—M.V. Reisher’s cottage). In: Proceedings of the 7th International scientific
and practical conference: new information technologies in architecture and construction,
Ekaterinburg, p 57
16. Romanov AS, Chumanov AA, Koshkarov AA (2024) Modelirovanie uzlov plotnickih
soedinenij russkogo derevyannogo zodchestva s ispolzovaniem tehnologii informacionnogo
modelirovaniya (Modeling of carpentry joints of Russian wooden architecture using information modeling technology). In: Proceedings of the 7th International scientific and practical
conference: new information technologies in architecture and construction, Ekaterinburg, p 84
17. Zaharova GB (2022) LIM—Informacionnoe modelirovanie landshafta cherez vzaimodejstvie s
GIS i BIM (LIM—Landscape Information Modeling through interaction throuth GIS and BIM).
Architecton: News Univ 79(3):77–90. https://doi.org/10.47055/1990-4126-2022-3(79)-13

Architectural Aesthetics and Additive
Construction in the Field of Rapid
Construction
M. Saleh

Abstract Additive manufacturing (AM) methods are poised to become a cornerstone in the development of rapidly deployable architecture. This article explores
the influence of AM technologies on the aesthetic qualities of fast-erected buildings. It examines the transformation of architectural concepts of form, materiality,
and texture under the influence of 3D printing and robotic construction. Drawing on
theoretical research and realized projects, the article proposes a conceptual framework for a new architectural language in modular construction shaped by AM.
Special attention is given to architectural movements fundamentally impacted by
3D printing, including parametricism, morphogenesis, and object-oriented ontology.
Additionally, the study investigates the potential alignment of AM technologies
with phenomenological approaches in architecture and art. Unlike research that
focuses purely on technological dimensions, this paper examines how AM can
be integrated with phenomenological design principles, offering new strategies for
sensory-centered design.
Keywords Additive manufacturing · Rapid construction · Construction 5.0 ·
Sculpture

1 Introduction
Additive manufacturing (AM), commonly known as 3D printing in construction, is
rapidly shaping contemporary architectural practice. In contrast to other modular
construction methods, 3D-printed buildings offer expressive and sustainable solutions due to their design flexibility and material efficiency, minimizing waste while
adapting to local environmental conditions. This technology facilitates the integration of organic forms and bespoke solutions, surpassing the limitations of traditional
prefabricated systems.
M. Saleh (B)
Moscow Architectural Institute, Moscow, Russia
e-mail: m.saleh@markhi.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_37

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When coupled with generative design algorithms and artificial intelligence (AI),
AM fosters new aesthetic paradigms within architectural movements like parametricism and morphogenesis. These methods enable the creation of intricate, optimized
structures and biomimetic forms with high precision and automation. The evolution of 3D printing transforms digital and theoretical design into viable physical
architecture.
Moreover, 3D printing is central to the transition towards Construction 5.0,
promoting customization and personalization in building processes. Human-centered
innovation is critical for the future of architecture and construction, addressing
the needs of both users and practitioners. As Chen et al. [1] argue, “Construction
5.0 represents a shift from the automation-centric focus of Construction 4.0 to an
emphasis on human-centered innovation”.
At the same time, the architectural community expresses concerns about the integration of AI. While AI can enhance design efficiency and sustainability, it must
be guided by human architects to preserve cultural significance, social context, and
emotional resonance. AI should serve as a collaborative tool, not a substitute for
human creativity and empathy.
In this context, one may ask: does a human-centered technological shift promise
a more creative approach to rapid construction?
Traditional architectural education emphasizes tactile engagement with materials
and physical modeling as fundamental to spatial reasoning and intuitive design.
Phenomenological architecture, as discussed by Pallasmaa [2] and Holl [3], stresses
sensory perception and emotional connection to built environments. This approach
aligns with neurobiological studies in art and architecture, such as Gallese and
Gattara’s concept of “embodied simulation.” Preserving human bodily experience and kinesthetic design is crucial when integrating the efficiencies of additive
construction.
Nonetheless, the potential of merging AM with phenomenological principles
remains underexplored. There exists a tension between the precision-driven nature
of digital fabrication and the subjective, embodied experience emphasized in
phenomenology.

2 Materials and Methods
This study analyzes practices of architects, design studios, and sculptors who use
manual sketching and physical modeling as initial steps, followed by digital integration and AM-based realization of architectural or artistic objects. The research investigates the relationship between 3D printing and creative workflows in the design of
unique structures and artworks. The study also includes a literature review on additive
construction and 3D printing technologies.

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Objective
The main objective is to identify the aesthetic characteristics and cultural significance
of rapidly constructed architecture within the evolving field of additive manufacturing. The article also explores the integration of manual prototyping with advanced
tools such as 3D scanning and robotic fabrication.

3 Results
In sculpture, AM expands artistic possibilities, although it remains vital to preserve
traditional art forms and cultural heritage. Responsible innovation demands inclusive
discourse that humanizes progress.
In architecture, technologies such as 3D/4D printing, autonomous systems, and
advanced communication networks enable highly personalized and customizable
construction processes. These developments are especially impactful in architectural
styles like parametricism and morphogenesis.
Additive methods have profoundly influenced parametric and morphogenetic
architecture by enabling complex, algorithmically generated geometries and
biomimetic forms previously unattainable through conventional means.

3.1 Parametricism in Architecture and Additive
Manufacturing
In parametricism, AM allows for the optimization of structural and functional
elements through the creation of cellular structures and gradient materials. Generative
design, combined with 3D printing, facilitates architecture that visibly demonstrates
structural forces and material logic. Patrick Schumacher’s concept of tectonism
exemplifies this [4]: here, structure and form coalesce into an expressive architectural
language that reflects both constructional truth and digital fabrication logic.
An exemplary project is Tor Alva (ETH Zurich, 2025), whose geometry results
from algorithmic modeling based on material properties, structural load paths,
and AM processes. The tower, composed of prefabricated 3D-printed components,
visually articulates the distribution of forces and embodies tectonic expressiveness.
It is worth highlighting developments in the field of 3D-printed horizontal loadbearing elements: their manufacturing complexity is associated both with the necessity of reinforcement and the fundamental principle of additive construction—layerby-layer printing. Examples include experimental projects by CREATE Lab (University of Southern Denmark) (Fig. 1a) and Vertico in collaboration with PSL (University
of Pennsylvania), University of Gent, and the Technion Israel Institute of Technology

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Fig. 1 a 3DLightBeam+, CREATE lab (2023), b Topology optimised bridge, Vertico + the University of Gent and the Technion Israel Institure of Technology (2020), c Diamanti bridge, Vertico +
Polyhedral structures laboratory (PSL) at the University of Pennsylvania (2025 Venice Biennale)

(Fig. 1b, c) [5–7]. The researchers aimed to develop rational structures utilizing innovative geometry and additive manufacturing technologies to minimize material usage
and maximize the operational performance of the constructions.
Overall, AM technologies enable the creation of structures with specified strength
and elasticity characteristics, optimize their weight, and also integrate functional
elements directly into the body of the structure.

3.2 Morphogenesis in Architecture and Additive
Manufacturing
Morphogenetic architecture draws inspiration from natural processes to develop
organic forms. AM enables the precise fabrication of complex, non-Euclidean geometries mimicking biological structures, enhancing performance through improved load
distribution, ventilation, and lighting.

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The 2021 Tecla project by Mario Cucinella Architects and WASP is emblematic of
this approach. Tecla’s monolithic, optimized form embodies the frozen result of algorithmic design. Looking ahead, morphogenetic architecture envisions co-constructed
environments that evolve over time, driven by interactions between natural agents
and human intervention.
Innovative firms such as OXMAN, Exploration Architecture, and ecoLogicStudio
push the boundaries of adaptive, sustainable architecture. One notable example is
Aguahoja I, a five-meter pavilion by OXMAN. This project demonstrates the potential of morphogenetic thinking, using 3D printing to fabricate a layered biocomposite
structure made from abundant biopolymers. The pavilion is designed as a hierarchical
network optimized for both strength and flexibility, capable of responding to changes
in temperature and humidity and ultimately, fully biodegradable, returning its components to the ecosystem [8]. Morphogenetic research also fuels the development of 4D
printing, in which materials alter shape or behavior over time in response to external
stimuli [9].
At the 2025 Venice Biennale, several morphogenetic projects addressed the theme
“Intelligens: Natural. Artificial. Collective”:
• Biotopia: Propagative Structures (MVRDV) features a growing scaffold inspired
by mangrove roots, highlighting architecture’s role in ecological systems. The
project positions architecture as an active participant in the planet’s metabolic
flows— a partner within the ecosystem (Fig. 2a).

Fig. 2 a Biotopia: propagative Structures, MVRDV (2025). Photography by Celestia studio.
b Picoplanktonics (2025) Living room collective. Photograph by HERO, c FundamentAI (2025)
ecoLogicstudio, synthetic landscape lab at Innsbruck University and the urban morphogenesis lab
at the Bartlett, UCL

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• Picoplanktonics (Living Room Collective) explores CO2 -absorbing microstructures, based on picoplankton carbon-absorbing cyanobacteria. This work highlights the importance of biomorphic design and raises critical questions about the
necessity of collaboration between humans, living systems, and technologies in
addressing the climate crisis (Fig. 2b).
• FundamentAI (ecoLogicStudio) integrates sensors and AI within 3D-printed,
biodegradable columns, responding to local environmental data. The structure
responds to ecological parameters of the Venetian lagoon, modeling scenarios for
bio-adaptive architecture. Here, 3D printing serves as a vital mediator between
data, material, and environmental context, underscoring the urgency of preserving
Venice (Fig. 2c).
These projects demonstrate the evolution of 3D printing from a utilitarian tool
into a medium for creating responsive, ecologically sensitive architectural systems.
All three projects exemplify a shift in how additive manufacturing is understood—
not merely as a utilitarian tool, but as a foundational medium for the development
of architecture as a living, bio-adaptive organism. These works demonstrate the
potential of additive techniques not only to generate complex geometries, but to
support morphogenetic constructs capable of addressing urgent global challenges.
In the field of rapidly deployable biomimetic architecture with practical significance, the projects developed by the University of Stuttgart stand out. The experimental architecture of pavilions such as the BUGA Fibre Pavilion becomes possible
through the integration of architectural design, structural engineering, and robotic
fabrication in a continuous computational feedback loop [10].
Architectural objects created via additive construction, regardless of stylistic
direction or paradigm (e.g., parametricism, morphogenesis), share a common technological foundation characterized by digital design, automated production, and the
ability to realize complex geometries with high material efficiency. Biomimetic environments in this context are shaped by biological agents with varying degrees of
autonomy and intelligence or through the simulation of their behavior.
Industry 5.0 focuses on leveraging the creative and artisanal capacities of humans
along with the speed, consistency, and productivity of robots, to promote effective
collaboration by integrating their complementary strengths [11].
Despite this, there is a notable lack of literature examining the influence of
human factors and ARAS (Augmented Reality Assistance Systems) beyond traditional ergonomic considerations, such as skill levels, trust, values, psychological
capital, emotions, and feelings.
Therefore, future research in human-centered digitalization and intelligent manufacturing should draw upon perspectives, methodologies, and tools from multiple
disciplines beyond engineering and production—including psychology, behavioral
sciences, movement (e.g., dance), management, law, and computer science. Based
on this, the following future research directions are proposed:
Interdisciplinary approaches to human-centered production research;
Human-centered algorithms for cyber-physical systems and manufacturing,
including the development of Human-Centered Algorithm Design (HCAD);

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Human-centered key performance indicators (expanded productivity metrics);
Human Digital Twins (HDTs) and ARAS for enhanced monitoring, performance
optimization, and operator well-being [12].
Adaptive automation (AA), in the context of human-oriented technologies,
assumes that the level of automation should dynamically adjust in response to
the human operator’s condition and needs. The goal is to avoid assigning workers
repetitive tasks and to support their cognitive well-being.
Unlike nature-imitating projects, those that draw from traditional construction
and craft techniques are less common. Examples include TerraPerforma, as well as
Gaia and TECLA by WASP, which aim to create sustainable and scalable housing
solutions. These projects demonstrate the viability of combining ancient building
practices and materials (such as earth) with modern 3D printing technology, resulting
in geometries optimized to reduce solar heat gain and improve ventilation.

3.3 Embodied Modeling
A complex aesthetic emerges in architecture that mimics natural forms: biomimetic
and synthetic, associated with natural beauty. As a result, such architectural realizations often exhibit a detachment from embodied modeling (Gallese and Gattara),
manifesting in the lack of visible and tangible connection between the human creator
and the architectural object perceived by the observer.
However, in the fields of art and sculpture, a broader exploration of embodied
creation is evident.
Three-dimensional scanning and printing represent the first widely adopted innovative technique for sculpture-making since lost-wax casting. Common 3D scanning technologies include photogrammetry, structured light scanning, laser scanning,
and computed tomography. Among these, photogrammetry is the most widespread
and accessible. However, for the precise transfer of detail to a digital environment,
more advanced and expensive equipment is often required. Structured light scanners
project a light pattern onto the scanned object or environment and are well-suited for
smaller objects. Laser scanners, on the other hand, are designed for scanning largescale objects and spaces. With the development of more advanced sensors and algorithms, 3D scanning is expected to become increasingly affordable and accessible,
facilitating its broader adoption [13].
These technologies allow artists to transfer hand-made prototypes crafted from
pliable materials into larger scales and more durable materials, as well as to replicate
multiple versions. This significantly alters sculptors’ cognitive processes, problemsolving schemes, and decision-making cycles, due to the rapid prototyping and
iterative reproduction of design variations enabled by 3D printing.
For example, Urs Fischer creates monumental aluminum sculptures from the
Big Clay series that mimic the appearance of freshly modeled clay objects. The
technological process involves 3D scanning a small clay model shaped by the
artist’s fingers, digitally processing the data, casting the elements in aluminum, and

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assembling and painting them to recreate the texture and visible traces of manual
clay modeling. Fischer’s method thus combines digital modeling with industrial
techniques to generate the illusion of direct manual creation.
The distinctive aesthetic and conceptual significance of this contemporary
approach to sculpture lies in its ability to reflect cultural and technological achievements of a given historical period particularly in the context of public space even
when the artistic value may be contested. However, it is worth noting that the method
of 3D scanning and printing has not yet overcome the challenge of preserving the
material poetics of the original [14].

4 Discussion
In object-oriented ontology, additive manufacturing (AM) has contributed to the
emergence of autonomous, context-dependent architectural elements with unique
properties capable of interacting with their surroundings. This has significantly
expanded the boundaries of architectural form-making and functional programming.
For instance, Mark Foster Gage Architects demonstrate the potential of additive fabrication by combining the development of original parametric systems with the integration of pre-existing 3D models and presets to create unique architectural elements
[15]. This approach striking a balance between customization and efficiency enables
the extension of expressive and scalable capacities of digital form-generation in
architecture.
Many scholars agree that the Industrial Revolution disrupted the traditional
connection between craftsperson, material, and product. The architect became
separated from the machine that produced their design [16].
However, emerging 3D printing technologies, according to researchers, offer
the potential to restore this lost connection and encourage architects to create
individualized objects and projects at the intersection of art and construction.
Returning to the creative method of Mark Foster Gage Architects, the ability
to rapidly reproduce design iterations plays a crucial role in the iterative analysis
process. One example is the design of vases for a gallery, developed in the firm’s
signature aesthetic. By physically materializing digital variants, experimenting with
scale, forms, and materials, and engaging in manual refinement, architects arrive at
optimal designs for final production. The convenience of transferring a digital model
into the physical realm for evaluation by all project participants has contributed to
the widespread adoption of 3D printers as essential tools in architectural studios.
Thus, when speaking of the embodied experience in architecture, we can observe
a shift—from the direct articulation of architectural works through human hands
and bodies to the exploration and evaluation of new perceptual experiences through
interaction with large-scale models and spatial environments.
Although the embodied experience of generations of craftsmen and builders is
limited within the paradigm of additive manufacturing, certain projects that integrate
contemporary and traditional techniques are of particular interest. The Traditional

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House of the Future project exemplifies an innovative approach to rural housing
renovation in China by integrating robotic 3D printing with authentic woodworking
techniques. 3D-printed walls of various configurations are combined with accessible
timber construction. The aim is to develop a sustainable architectural model that
reflects cultural specificity, modern individualized housing needs, and the potential
of local production. The methodology includes 3D scanning of existing buildings,
adaptive design using 3D printing, community engagement, and repurposing traditional materials to ensure both ecological and social sustainability [17]. Such applications are of interest not only for their potential in rapidly deployable housing but
also for their architectural and aesthetic value.

5 Conclusion
This paper presents a comprehensive overview of contemporary architectural trends
that have experienced a surge in development and become physically realizable
through additive manufacturing (AM), including parametricism, morphogenesis, and
object-oriented ontology. It examines the applications of 3D printing that allow these
approaches to reach their full potential, drawing upon experimental projects (Table 1).
Additive manufacturing methods exert a significant influence on the aesthetics
of rapidly deployable architecture, reshaping notions of form, material, and texture.
AM offers new opportunities for the creation of unique, functionally optimized,
Table 1 Influence of additive manufacturing on contemporary architectural paradigms
Architectural paradigm

Key characteristics

Role of additive manufacturing
(AM)

Parametricism

Algorithmic design;
continuous surfaces;
functional integration

Enables complex geometries,
structural optimization, and
tectonic expression [4, 7]

Morphogenesis

Biomimetic forms;
evolutionary geometry;
environmental adaptation

Supports non-Euclidean
geometries, material efficiency,
and bio-responsive structures [8,
9]

Object-oriented ontology

Autonomy of elements;
uniqueness; interaction
with context

Facilitates mass customization
and the design of context-aware,
responsive components [15]

Phenomenological design

Sensory experience;
embodied perception;
material authenticity

Limited integration; potential
exists through hybrid
manual-digital prototyping [1, 2,
14]

Traditional techniques + AM

Integration of craft and
vernacular methods; local
adaptation

Revives craft heritage via digital
tools; promotes sustainable,
culturally relevant solutions [17]

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and environmentally sustainable structures that meet the demands of contemporary
society.
The architectural language emerging through AM is characterized by functionality, sustainability, innovation, and accessibility. Further research and development
in the field of AM will expand the range of applicable materials, improve the strength
and durability of 3D-printed components, and contribute to the establishment of
clear construction norms and standards, facilitating the widespread adoption of the
technology in practice.
The identified directions parametricism and morphogenesis enabled by AM,
address both local and global challenges. The case studies discussed in this article
demonstrate how additive manufacturing serves as a key enabler in the advancement of sustainable and rapidly deployable architecture. Progress in these areas has
been made possible through the efforts of specialized firms and interdisciplinary
collaboration.
At the same time, the accessibility of rapid prototyping and deployable architecture to individual users allows for the resolution of creative and personalized
challenges, enabling customization according to the needs of individual users.
The aesthetics of additive manufacturing and rapidly deployable architecture
emerge from the process and objectives of design. They are shaped by agents
operating within digital and material environments.
In the context of the transition toward Industry 5.0 or Construction 5.0, the study
of human-centric approaches in the work environment remains highly relevant—
not only in terms of the operator’s psychophysiological comfort, but also in recognizing the value of embodied, tactile experience as it is transferred into architectural
expression.
Acknowledgements The study was supported by a grant from the Russian Science Foundation
No. 24–28-00960.

References
1. Chen X, Liu F, Ghaffarianhoseini A, GhaffarianHoseini A, Guo B (2025) From Construction
4.0 to Construction 5.0: principles and enabling technologies. In: GhaffarianHoseini A, Ghaffarianhoseini A, Rahimian F, Babu Purushothaman M (eds) Proceedings of the international
conference on smart and sustainable built environment (SASBE 2024), SASBE 2024. Lecture
notes in civil engineering, vol 591, Springer, Singapore. https://doi.org/10.1007/978-981-964051-5_88
2. Holl S, Pallasmaa J, Pérez-Gómez A (2007) Questions of perception: phenomenology of
architecture. Lars Müller Publishers, Basel
3. Pallasmaa J (2009) The eyes of the skin: architecture and the senses. Wiley, USA
4. Schumacher P (2017) Tectonism: engineering and fabrication logics as stylistic drivers. Talk
presented at: Jumpthegap Talk, Roca Jumpthegap Design Award, Barcelona. https://www.you
tube.com/watch?v=ng8h1QOPB_c. Accessed 14 June 2025

Architectural Aesthetics and Additive Construction in the Field of Rapid …

473

5. Vantyghem G, Corte W, Ooms T, Shakur E, Amir O (2020) 3D-printed concrete bridge
designed by topology optimization. ResearchGate. https://doi.org/10.13140/RG.2.2.28083.
45600. Accessed 14 June 2025
6. Vertico (n.d.) Diamanti bridge. https://www.vertico.com/projects/diamanti-bridge. Accessed
11 July 2025
7. Breseghello L, Naboni R (2023) Stress-based design for 3D concrete printed horizontal
structures. In: Naboni R, Breseghello L (eds) BE-AM|Built environment additive manufacturing 2023. Symposium on additive manufacturing in architecture, TU Darmstadt, Darmstadt,
Germany, Nov 2023. Technische Universität Darmstadt, pp 13–23
8. Oxman N (2014–2020) Aguahoja project. Retrieved June 24, 2025. https://oxman.com/pro
jects/aguahoja
9. Menges A, Reichert S, Coros S, Rist F (2016) Morpho-morphogenesis: computational design
and digital fabrication of self-organizing materials in architecture. Nat Mater 15(7):937–942.
https://doi.org/10.1038/nmat4544
10. Menges A, Knippers J (2019) Bundesgartenschau Heilbronn 2019, Germany. Institute for
Computational Design and Construction, Institute of Building Structures and Structural Design.
https://www.icd.uni-stuttgart.de/projects/buga-fiber-pavilion/. Accessed 01 July 2025
11. European Economic and Social Committee (2024) Industry 5.0 event. https://www.eesc.eur
opa.eu/en/agenda/our-events/events/industry-50. Accessed 13 June 2025
12. Khafaga A, Caires Moreira L, Horan B (2023) Towards Industry 5.0: augmented reality assistance systems for people-centred digitalisation and smart manufacturing. In: IEEE 28th International conference on automation and computing (ICAC2023), Birmingham, UK. https://doi.
org/10.1109/ICAC57885.2023.10275290
13. Kantaros A, Ganetsos T, Petrescu FIT (2023) Three-dimensional printing and 3d scanning:
emerging technologies exhibiting high potential in the field of cultural heritage. Appl Sci
13(8):4777. https://doi.org/10.3390/app13084777
14. Sargentis G-F, Frangedaki E, Chiotinis M, Koutsoyiannis D, Camarinopoulos S,
Camarinopoulos A, Lagaros ND (2022) 3D scanning/printing: a technological stride in
sculpture. Technologies 10(1):9. https://doi.org/10.3390/technologies10010009
15. Mark foster gage architecture and the aesthetics of reality. Talk presented at Cal Poly Los
Angeles Metropolitan Program in Architecture and Urban Design, Helms bakery district, 14
May 2020. https://www.youtube.com/watch?v=kQ8cJVrIxwc. Accessed 01 June 2025
16. Grigoriadis K, Lee G (2024) The current state and future of 3D Printing in Architecture.
In: Construction and design manual 3D printing and material extrusion in architecture. Dom
Publishers, Berlin
17. Ratoi L (2023) Art of compromise. In: Naboni R, Breseghello L (eds) BE-AM|Built environment additive manufacturing 2023. Symposium on additive manufacturing in architecture, TU
Darmstadt, Darmstadt, Germany, Technische Universität Darmstadt, pp 127–135

Methodology for Determining
Deformations of Pile Structures
with a “Solid” Reinforcement Body
During Bank Protection
N. V. Kupchikova, T. V. Zolina, S. P. Strelkov, and A. S. Resnyanskaya

Abstract The assessment of the rate of coastal erosion in towns and settlements
is conducted based on data obtained from long-term observations and measurements of shoreline retreat. A variety of mathematical and statistical approaches are
employed for this purpose. To eliminate costly dredging operations, regular remote
monitoring of the state of the shores is required in shipping and fishing areas, along
with measures to strengthen eroding sections. The article presents modern constructive and technological solutions using deep-embedded pile elements (such as pile
groynes, end-widening piles, etc.), which demonstrate high effectiveness in several
aspects: increasing bearing capacity and stability, durability and resistance to erosion,
as well as economic and ecological efficiency and applicability in complex soil conditions. A method has been developed to determine settlement based on the areas of
spherical widening of the pile, taking into account the pressure distribution law
beneath the sphere. An axisymmetric problem is presented to determine the stress
in the soil at the contact boundary with the reinforcement and the settlement of the
entire pile. The method allows for the calculation of the load on an infinitesimal area
dp, located at a distance S from point C in the plan of the contact force circle of the
sphere-widening under vertical loading and infinitely close secants.
Keywords Bank protection · Deep-seated · End-widened piles · Determining
deformations

N. V. Kupchikova (B)
Russian University of Transport (MIIT), Moscow, Russia
e-mail: kupchikova79@mail.ru
T. V. Zolina · S. P. Strelkov · A. S. Resnyanskaya
Astrakhan State University of Architecture and Civil Engineering, Astrakhan, Russia
N. V. Kupchikova
Moscow State University of Civil Engineering, Moscow, Russia
A. S. Resnyanskaya
Astrakhan Tatishchev State University, Astrakhan, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_38

475

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N. V. Kupchikova et al.

1 Introduction
In the Astrakhan region, the water balance is characterized by disproportions in the
distribution of runoff, which is directly linked to the operation of the Volgograd
Hydroelectric Power Station [1–3]. The primary source of water inflow is rainfall,
which causes floods that often lead to inundations. Despite the availability of various
methods for protecting earth structures from erosion, the development of innovative
technical solutions in hydraulic engineering remains crucial. In previous publications
by the authors [4–7], the peculiarities of shore reinforcement measures in areas prone
to landslides were already analyzed. Special attention is given to the study of the main
factors contributing to the destruction of coastal territories within the framework of
a programme aimed at environmentally safe construction and urban development,
which is essential for anticipating and minimizing risks, as well as enhancing the
effectiveness of future projects for creating reliable shore protection. Reducing the
likelihood of emergency situations, especially in densely populated areas significantly influenced by human activities, is only possible through the construction of
engineering structures that provide both protection and environmental safety. The
assessment of the rate of change in the shoreline is conducted based on data obtained
from long-term observations and surveys of shoreline retreat. A variety of mathematical and statistical approaches are employed for this purpose. To avoid costly
dredging operations, regular remote monitoring of the condition of the shores is
required in navigation and fishing zones, alongside measures to reinforce eroding
sections. These shore protection structures are classified as hydraulic engineering
works and are used to protect the coastal zone from the negative effects of waves,
currents, and ice formations. They are employed to prevent the erosion and flooding
of the banks of rivers, seas, lakes, and reservoirs, as well as the slopes of earth
embankments and artificial land [8–10].
Global experience demonstrates a variety of innovative approaches to coastal
protection that can be adapted to Russian conditions. In the Netherlands, where
more than 50% of the territory is below sea level, combined systems of pile walls,
geosynthetic materials, and natural barriers (such as sand dunes with vegetation)
are widely used to ensure resistance to storm surges. In Japan, massive concrete
breakwaters with perforations are used to protect against tsunamis, reducing the
hydrodynamic load, as well as hybrid structures made of gabions and plant mats for
ecological stabilization of the shores. In the USA, especially in Louisiana and Florida,
artificial reefs made of porous concrete and living shorelines systems combining
biological and engineering solutions are being actively introduced.
The adaptation of these technologies in Russia requires consideration of the
specifics of local conditions:
• for the Arctic regions with permafrost, Dutch solutions can be supplemented with
thermal stabilization of soils;
• in the deltas of the southern rivers (Volga, Kuban), Japanese methods of wave
damping are effective, but with the replacement of materials with more frostresistant analogues;

Methodology for Determining Deformations of Pile Structures …

477

• for urban embankments, American “living banks” are suitable, but with the use
of local types of vegetation.
The key conclusion is that international experience should not be copied, but rather
creatively adapted to meet Russian climate, geological, and regulatory requirements
[11–13].

2 Constructive and Technological Solutions for Bank
Protection Using Deep-Seated Structural Elements
When selecting a shore protection method, the key criteria are effectiveness, cost, and
durability. Traditional technologies such as gabions, geocells, and concrete structures
each have their advantages and limitations.
Gabions—wire mesh baskets filled with stones—offer low cost, easy installation, and environmental friendliness as they allow water passage without disrupting
natural flow. However, these structures have a limited-service life (15–25 years) and
are vulnerable to mechanical damage and washout during severe floods. The 2018
implementation of gabions along small rivers in Krasnodar Krai demonstrated their
effectiveness under moderate loads [14].
Geocells—polymer or concrete cellular structures—provide excellent flexibility,
erosion resistance, and allow for vegetation growth. Nevertheless, these systems
require thorough base preparation and become costly for large areas. In Rostov
Oblast (2020), geocells were used to reinforce reservoir slopes with subsequent
grass seeding for stabilization [15].
Concrete structures (walls and slabs) offer maximum strength and durability
exceeding 50 years, but come with high costs, negative ecological impact, and challenges in repair works. The 2014 concrete embankment project in Sochi required
additional reinforcement measures due to foundation washout.
It can be concluded that pile systems with end enlargements demonstrate longterm economic advantages despite higher initial costs. While reinforced concrete
piles with enlargements are 20–30% more expensive than gabions, they remain more
cost-effective than monolithic concrete walls [16].
These systems require specialized drilling equipment but reduce construction time
by 30% compared to conventional concreting methods. Their maintenance needs are
minimal due to high erosion resistance-for instance, in Astrakhan, deformations did
not exceed 2 cm over a 5 year period [17].
For long-term projects with a 50 year service life (e.g., the Astrakhan embankment), total costs for pile systems are 15–20% lower than for concrete alternatives,
primarily due to eliminated repair requirements. In high-erosion zones like the Volga
Delta, additional savings are achieved through reduced rehabilitation frequency.
Pile systems with end enlargements are optimal for complex soil conditions
and long-term projects, whereas gabions and geocells remain suitable for localized
applications with limited budgets.

478

N. V. Kupchikova et al.

One of the new constructive and technological solutions for bank protection is
the use of deep-seated structural elements. One of the hydraulic structures built for
this purpose is the protective piles—spurs (see Fig. 1), which are arranged from the
shore at a specific angle in relation to the bank being protected. The invention can be
used to protect riverbank zones from natural reshaping processes and to straighten
the course of the river [18]. The spur pile comprises the following sections: the “root”
adjacent to the shore; the “head” located at depth, which experiences the greatest
destructive impact from the water flow, connecting them with their “bodies”.
The construction of driven end-widened piles by compacting gravel during the
bank protection of the Central Embankment of Astrakhan demonstrated high design
and technological efficiency (see Fig. 2).

Fig. 1 Movable bank protection pile groyne: 1—helical pile; 2—shows a fixing unit; 3—swivel;
4—trot; 5—floats; 6—screw blades; 7—water level; 8—electric generator; 9—movable platform

Fig. 2 a isofields of end-widening pile deformations with sealing zones; b installation of bored
piles with end widenings by compacting gravel during bank protection of the Central Embankment
of Astrakhan

Methodology for Determining Deformations of Pile Structures …

479

To improve the predictive accuracy of pile settlement calculations, the mathematical model was extended to incorporate 3D stress distribution visualization and
parameter sensitivity analysis. Using finite element modeling (e.g., in MIDAS GTS
NX), the interaction between the pile’s end enlargement and surrounding soil was
simulated, generating 3D contour plots of vertical stresses (σ xz ) and shear strains
(τ xz ). These visualizations reveal stress concentration zones beneath the enlargement,
critical for optimizing its geometry.
For weak clayey soils (e.g., wL = 45%, C u = 25 kPa), a case study demonstrated
how the model calculates settlement (w0 ) when the enlargement radius (R) increases
from 0.5 m to 1.0 m, reducing w0 > by 42% due to improved load distribution.
Sensitivity analysis quantified the influence of key parameters:
• enlargement radius (R): a 20% increase in R decreased settlement by 15–18% in
cohesive soils.
• embedment depth (L): for L > 8 m, settlement variations became negligible (< 5%),
confirming depth-dependent stiffness effects.
This refined model enables engineers to tailor pile designs to specific geotechnical
conditions while minimizing trial-and-error approaches.
A detailed description of the technology for creating an enlarged lower end of the
pile through thermal burning is presented in the work of Kupchikova N.V. [19]. After
obtaining positive results in forming the end enlargement, this method was patented.
During the tests, reinforced concrete piles with a length of 3 m were used, equipped
with steel tubes for securing wiring and electric ignition (see Fig. 3a).
An important thermal property of clays is their sinterability—the ability to
compact when heated, forming a strong, dense structure due to the bonding of particles under the influence of high temperatures generated during the reaction with
thermite. After the experiment, piles were left for 30–50 days and samples from the
extended area were extracted and examined in laboratory conditions using a press.
The studies established that for complete formation of the end enlargement by
the method of deep burning using smouldering iron-aluminium thermite, at least
0.55 kcal of energy must be released per gram of the composition. The strength
of the resulting enlargement samples varied from 640 to 750 N/cm2 . A significant
reduction in settlement in clay soils—by 7 times for the pile with a refractory tip and
by 4.5 times for the pile with injection enlargement—was observed compared to a
regular pile without enlargement. This design and technological solution will also
have a significant effect when deep strengthening coastal areas in densely built-up
urban and settlement conditions.
At the present stage, there is a need to develop a comprehensive methodology for
calculating deep design and technological solutions for embankment strengthening
using piles with multiple enlargements along the shaft. The results of studies on such
piles in various soil conditions indicate their significant effectiveness compared to
prismatic piles. Numerical investigation and comparison of the obtained experimental
data with the results of numerical modelling using the modern software package for
solving geotechnical problems MIDAS GTS NX, verified by the Russian Academy

480

N. V. Kupchikova et al.

Fig. 3 a a pile with end widening formed by thermal deep roasting: 1—finished prismatic pile; 2—
end widening (sintered clay); 3—electric igniters with wire; 4—tip made of baddeleyite-corundum
refractory steel, filled with thermite; 5—steel pipe; b calculation scheme for determining settlement
based on the areas of spherical widening, taking into account the pressure distribution law under
the sphere

of Architecture and Building Sciences in coastal reinforcement, is a reliable tool in
designing and forecasting the stress–strain state (see Fig. 2a).

3 Methods
The development of a methodology for determining the maximum settlement of a
pile along the axis of force action on an elementary area of the surface of a sphere—
the bulbous end—is currently a relevant task in geotechnics. We will consider a pile
with a bulbous end in the shape of a sphere with a radius R, made of an absolutely
rigid material in relation to the elastoplastic soil. (see Fig. 3b). Upon application of
a load P normal to the horizontal plane, the pile experiences settlement due to the
deformation of the foundation, while the horizontal planes of the soil half-space bend.
This is clearly demonstrated by the visible bending of the isolines in experimental
observations [20–22].
In general, the equilibrium condition for elastic operation of the base will be:
P = P1 + P2

(1)

Methodology for Determining Deformations of Pile Structures …

481

where: P—the external vertical load applied to the pile; P1 —the resistance along the
lateral surface of the pile over the straight section of length; P2 —the pressure force
transmitted through the spherical surface of the bulbous end to the soil foundation.
P1 = u(σ1 sin α1 tgϕ1 + c1 )

n
+ l1
2

(2)

where: u—the perimeter of the pile; l1 —the length segment of the pile, m, determined
by the formula:
l1 = l +

d
−a−n−b
2

(3)

Given that the vertical force P acts along the axis of the pile structure, we can
assume that the soil deformations relative to this axis are symmetrical, and the contact
area of the bulbous end of the pile with the deforming boundary surface is represented
in plan as a circle with a radius a = R (see Fig. 3b).
The pressure distribution law under the sphere—the widening is subject to definition. It is evident that the diagram of this pressure will represent a figure in plan,
i.e., we have an axisymmetric problem of determining stress in the soil at the contact
boundary with the reinforcement and the settlement of the entire pile.
By drawing infinitely close secants through an arbitrary point C in the plan of
the contact circle of the sphere-widening under vertical loading, we can compute the
load acting on an infinitely small area dp, located at a distance S from point C. If the
compressive stress at this area is denoted as q, then the elementary force on the area
dp corresponds to [7]:
qdp = P ∗ =

3P2
2π d 2

(4)

Then the resultant of normal σ z and tangential τ xz forces (see Fig. 3).
σz = cos θ P ∗ τxz = sin θ P ∗

(5)

The effect of this force on the settlement of an arbitrary point C is determined:
W =

dP 1 − μ2
P2 1 − μ2
=
π Er
π ES

(6)

Or after substitution (4):
W = qd ϕdS

1 − μ2
πE

(7)

The influence on the vertical displacement of point C from all elementary pressures
over the entire contact area of the lower hemisphere and the soil foundation will be

482

N. V. Kupchikova et al.

evaluated by the integral:
¨
W = k1

qd ϕdS

(8)

Since it is assumed that the widening body does not deform, from the geometric
scheme of a “rigid” body in Fig. 3 it follows:
W = W0 − W1

(9)

W 0 —maximum settlement of the pile along the axis of force action; W 1 —initial
position of the point at the edge of the sphere relative to the horizontal plane of the
hemisphere.
Then the investigated displacement:
W = W0 −

r2
2R

(10)

In Eq. 8, the unknown is the pressure distribution function q.
By combining Eqs. 8 and 10 we have:
¨
k1

qd ϕdS = W0 −

r2
2R

(11)

In Eq. 10 the unknown function q enters under the integral sign, and therefore,
Eq. 10 is an integral equation. The work [23] presents a similar equation that defined
the bending parameter of the half-space plane at a given load value. Based on this
similarity, we conclude that the pressure distribution diagram over the contact area.
Thus, if the pressure at the center of the contact is denoted by q0 , then at a distance
r from this center, the pressure is:
q = q0 1 −

r2
a

(12)

and when r = a = R, it approaches 0.
Taking this into account, we can write the maximum settlement along the vertical
axis as:
W0 =

1
π qa
2

(13)

P2 =

2
π Rq0
3

(14)

Solving Eq. 14 for q0 and w0 we have:

Methodology for Determining Deformations of Pile Structures …

W0 =

9π 2 1
k1 p2
8 2R 2

483

(15)

4 Conclusions
Thus, the presented formula for determining settlement based on the areas of spherical
widening takes into account the pressure distribution law under the sphere. It is
evident that this is an axisymmetric problem of determining stress in the soil at the
contact boundary with the reinforcement and the settlement of the entire pile. The
methodology allows through an arbitrary point C in the plan of the contact circle of
the sphere-widening under vertical loading and infinitely close secants to compute
the load acting on an infinitely small area dp, located at a distance S from point C.
The considered design and technological solutions for bank protection using
deep-lying pile elements (such as pile groynes, end-widening piles, etc.) demonstrate high efficiency in several aspects: enhancing bearing capacity and stability,
durability and resistance to erosion, economic and ecological efficiency, and applicability in complex soil conditions. Pile anchors effectively redistribute the load from
the bank slope, reducing the risk of landslides. Piles with widenings (for example,
through the compaction of gravel or thermal stone columns) increase the bearing
area, which enhances their resistance to uplift and lateral deformations. “Solid”
widenings, for instance, created by the method of deep soil sintering, form a strong
anchoring element resistant to water erosion and frost heave. Technologies for gravel
compaction and thermal strengthening minimize filtration, reducing the risk of suffusion. They exert less impact on the aquatic ecosystem compared to massive concrete
structures. They are effective in weak, water-saturated, and landslide-prone soils.
Deep soil sintering is particularly beneficial in permafrost and when strengthening
muddy foundations. However, there are limitations to the application of these design
and technological solutions, as they require verified calculation methodologies and
monitoring of manufacturing technology. In some cases, they are more expensive
than surface methods, such as using gabions or geogrids, but they pay off in terms
of durability.
It is worth noting that the structural and technological solutions for shore protection using deep-seated structures discussed in the article demonstrate high effectiveness under complex engineering and geological conditions, ensuring long-term
stabilization of the shoreline.

References
1. Dmitrieva MV, Barmin AN, Buzyakova IV (2014) Ecological stability of astrakhan region to
the tecnogenic influence. J Geol Geogr Glob Energy 4(55):91–99

484

N. V. Kupchikova et al.

2. Aitpaeva AA, Tyutyuma NV, Bisaliev AA et al (2025) Changes in the degree of soil solonzic
consistency depending on the structure of crop rotations in the arid zone of the lower Volga
region. Polythematic Online Sci J Kuban State Agrarian Univ 207:1–9. https://doi.org/10.
21515/1990-4665-207-001
3. Sinyakov VN, Kuznetsova SV, Chestnov SV et al (2007) Engineering geology and geoecology
of Volgograd. Volgograd State University of Architecture and Civil Engineering, Volgograd
4. Zolina T, Strelkov S, Kupchikova N, Kondrashin K (2020) Monitoring of the collapse of
the shores of reservoirs and the technology of their surface and deep fixing. E3S Web Conf
157:02011. https://doi.org/10.1051/e3sconf/202015702011
5. Kupchikova N (2018) Determination of pressure in the near-ground space pile terminated and
broadening of the surface. MATEC Web of Conf 251:04062. https://doi.org/10.1051/matecc
onf/201825104062
6. Zolina TV, Kupchikova NV, Shayakhmedov RI (2022) Monitoring the condition of coastal
zones and the results of the introduction of new technologies for their consolidation in the
territory of the Astrakhan region. Caspian sea and global challenges: materials of the international scientific and practical conference, May 2022. Astrakhan State University, Astrakhan,
pp 760–768
7. Zolina TV, Kupchikova NV (2021) Study of the stress-strain state of coastal zones and the
results of the introduction of new technologies for their consolidation in the territory of the
Astrakhan region. In: Materials of the XV international scientific and practical conference of
faculty, young scientists and students, vol 15. Astrakhan State University of Architecture and
Civil Engineering, Astrakhan, p 288
8. Yarkin V, Kukhar A (2018) Comparative analysis of solutions for protection of the coast of
the sea of Azov by anchored vertical walls of sheet pile of various designs. J Metal Constr
24(4):157–166
9. Popova PM (2014) Bank protection of the Ramenka River and environmental impact assessment. In: Information systems and technologies of agro-industrial complex and ASG: collection of scientific articles of the 2nd International scientific and technical conference. University
Book CJSC, Kursk, р 340
10. Lukina NL (2022) Choice of the sheet pile immersion method for bank protection in conditions
of dense urban development. Eng J Don 11(95):589–600
11. Garnaga VV, Luchkova VI (2014) Methods by reconstruction coastal areas of cities far east
under the conditions flood. J Dal’nii Vostok: problemy razvitiya arkhitekturno-stroitel’nogo
kompleksa (Far East: Probl Dev Arch Constr Complex) 1:58–63
12. Dontsova OL, Panina OV, Makhova SI (2020) Problems of Black Sea coast protection
coasts of the north-west Caucasus. J Vestnik Volgogradskogo gosudarstvennogo arkhitekturnostroitel’nogo universiteta (Bull Volgograd State Univ Arch Civ Eng) 4(81):361–370
13. Pitulko VM, Spiridonov MA, Erkov AYu (2019) Renovation of the use of recreational resources
of Xiaomeisha resort, coastal zone, Shenzhen, China. J Reg Ecol 56(2):93–108. https://doi.org/
10.30694/1026-5600-2019-2-93-108
14. Norman LO (2020) Gabion, noise protection wall containing gabion and a way to create gabion.
RU Patent 2,728,297 C2 03 March 2017
15. Sivokon VN, Popov SM (2004) Stabilization and reinforcement of the roadbed by geogrids.
Gas Ind J 11:41–42
16. Travush V, Murashkin V (2022) Concrete deformation model for reconstructed reinforced
concrete. Int J Comput Civ Struct Eng 18(4):132–137. https://doi.org/10.22337/2587-96182022-18-4-132-137
17. Travush VI, Shulyatyev SO (2024) Determination of the kernel of a deformable foundation
model from experimental data. Soil Mech Found Eng 61:107–113. https://doi.org/10.1007/s11
204-024-09950-2
18. Kupchikova NV, Shayakhmedov RI, Zolina TV (2021) Movable shore protection spur. J
Stroitel’stvo: novye tekhnologii - novoe oborudovanie (Constr: New Technol New Equipment)
2:63–66

Methodology for Determining Deformations of Pile Structures …

485

19. Kupchikova NV, Shayakhmedov RI (2023) Thermal method of pile end widening. In: Innovative development of regions: the potential of science and modern education. In: Materials of
the VI National scientific and practical conference with international participation, Astrakhan,
2023, pp 118–121
20. Bochkov MI, Dushko OV, Rekunov SS (2025) Features of solving problems of calculating
systems with ideal elastoplastic material behavior using the finite element method in the form
of a classical mixed method. In: Radionov AA, Ulrikh DV, Gasiyarov VR (eds) Proceedings of
the 8th International conference on construction, architecture and technosphere safety, ICCATS
2024. Lecture notes in civil engineering, vol 565. Springer, Cham, рр 125–135. 1007/978-3031-80482-3_13
21. Zolina T, Kupchikova N (2024) Modeling of seismic load and assessment of its impact on the
building frame and foundations of deep laying of bridge supports. E3S Web Conf 533:02014.
https://doi.org/10.1051/e3sconf/202453302014
22. Zolina T, Kupchikova N (2019) Influence of vibration impacts from vehicles on the state of
the foundation structure of a residential building. E3S Web Conf 135:03053. https://doi.org/
10.1051/e3sconf/201913503053
23. Kupchikova NV, Kurbatskiy EN (2017) Analytical method used to calculate pile foundations
with the widening up on a horizontal static impact. IOP Conf Ser: Mater Sci Eng 262(1):012102.
https://doi.org/10.1088/1757-899X/262/1/012102

Generalized Geometrically Exact Theory
of Column Stability
V. A. Neshchadimov

Abstract A generalized, geometrically rigorous theory of the stability of
compressed rods is presented, based on the exact Euler–Bernoulli beam model
without linearization of curvature expressions and without a priori assumptions
about the buckling shape. As the baseline configuration, the deformation of a simply
supported beam into a circular arc under a constant bending moment is examined,
with the identified geometric pattern extended to other buckling modes. A universal
analytical expression for the critical force is derived, depending on the central angle
and the corresponding critical eccentricity that emerges as a result of the geo-metric
transformation of the deformed axis. It is shown that Euler’s classical formula is a
special case of the proposed solution and overestimates the critical force by 23.37%.
For the first time, an exact formula for the critical force of a cantilever beam is rigporously obtained, and the validity of the effective length coefficient is confirmed.
One of the key consequences of the new theory is the possibility of applying the principle of superposition to stability problems, allowing for the combined influence of
multiple transverse loads with various application schemes. The proposed approach
covers a wide range of boundary conditions and loading types, and completes the
construction of a geometrically rigorous stability theory within the Euler–Bernoulli
model.
Keywords Stability theory · Critical force · Analytical solution · Central angle ·
Critical eccentricity · Return potential

V. A. Neshchadimov (B)
Moscow State University of Civil Engineering (National Research University) (MGSU), Moscow,
Russia
e-mail: expertor@internet.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_39

487

488

V. A. Neshchadimov

1 Introduction
The origins of modern stability theory are inextricably linked to the development
of beam theory and can be traced back to the observations of Leonardo da Vinci
(1452–1519), who recorded the behavior of structural elements in his sketches, and
to the experiments of Galilei [1], who was the first to attempt an explanation for the
failure of beams under load in 1638. Significant progress was made in the seventeenth
century thanks to the work of Hooke [2], who in 1678 formulated the principle of
elasticity and introduced the concept of axial internal force, laying the foundation
for the analytical description of structural behavior.
In 1673, Huygens [3] introduced the concept of the moment of force relative
to a point, which provided the mathematical basis for subsequent studies. Jakob
Bernoulli, in his 1694 correspondence with Leibniz and in his treatise [4], introduced
the concept of internal bending moment and established the relationship between
bending moment and curvature [4–7]. Bernoulli [8, 9] further developed the mathematical analysis of beam deformation, proposing the hypothesis of plane sections
and the principle of superposition, which became the foundation for the analytical
description of rod deformation.
Building on the achievements of his predecessors, Leonhard Euler in 1744, in his
seminal work [10] (Fig. 1a), formulated the problem of the stability of a compressed
column and derived the classical expression for the critical force. In the original text,
the formula is written as:
P=

ππ
Ekk,
aa

which, in modern notation, corresponds to:
Ncr =

π 2 EI
,
L2

(1)

where P denotes the critical force (now denoted as Ncr ), aa is the square of the
column length L2 , and Ekk is the product of the Young’s modulus E and the second
moment of area I (i.e., EI ).
Fig. 1 Original illustrations
(a and b) from Appendix I of
Euler’s 1744 work [10],
depicting the formulation of
the buckling problem and the
bending of an elastic plate

Generalized Geometrically Exact Theory of Column Stability

489

In the same work [10], slightly earlier in the text, Euler also considers a curved
elastic plate AB, clamped at point B and subjected to a bending force P, applied via
a rigid rod AC in the direction CD (see Fig. 1a). He demonstrated that the force
P, acting vertically downward, produces a bending moment at an arbitrary point M
along the curve AB, given by:
M = P(c + x),
where x is the current abscissa and c is the lever arm length to the point of force
application.
In this part of the work, Euler introduces for the first time an expression that relates
the bending moment to the radius of curvature:
R=

ds3
−dxddy

(2)

where ds = (dx)2 + (dy)2 and dx ≈ const . The term ddy corresponds, in modern
notation, to the second derivative y (x). Thus, Euler effectively applies the classical
curvature formula for a planar curve parametrized by the Cartesian coordinate x.
Euler further demonstrates the equivalence of two curvature expressions:
R=

dθ
1
ds3
⇒ =− ,
−dxddy
R
ds

where s is the arc length (the coordinate along the curved line), θ is the angle between
the tangent to the curve and the horizontal axis, and R is the radius of curvature, which
is linked to the derivative of the tangent angle.
Transitioning to an interpretation of the problem in terms of flexure, Euler writes:
P(c + x) =

EI
Ekk
or M =
,
R
R

where E is the Young’s modulus, I is the second moment of area, R is the radius of
curvature at the point where the moment is applied, M (x) is the bending moment at
a given point x, and R(x) is the corresponding radius of curvature at that point.
Thus, in 1744, Euler for the first time formulated the equilibrium equation for a
cantilever beam under pure bending, analyzing the deformation of a beam clamped
at its base. This reasoning laid the foundation for what later became known as the
Euler–Bernoulli beam theory, which subsequently developed along two main lines:
• the classical (linearized) formulation of curvature, introduced by Pierre-Simon
Girard [11, 12]:
κ(x) = −

d 2y
,
dx2

490

V. A. Neshchadimov

• and the geometrically nonlinear (exact) formulation, in which the curvature
is expressed through derivatives of the deflection function y(x), as obtained by
Benoît Paul Émile Clapeyron from Eq. (2) [13]:
κ(x) = −

y
1 + (y )2

3/2

In reviewing the historical development of beam theory, one cannot fail to
acknowledge the significant contribution of Navier [14], who in 1826 was the first
to describe the force acting perpendicular to the beam axis and its relationship to the
bending moment—although he did not yet use the symbol Q. The modern notation
Q and the interpretation of shear force became established in the works of Clebsch
[15, 16] and subsequent authors.
Navier also established the relationship between shear force and distributed load,
which made it possible to formulate the classical fourth-order differential equation
of the beam in divergent form:
EI

d 4y
+ q(x) = 0.
dx4

To conclude this historical overview, I must refer to my own work [17]. Although
self-citation is generally discouraged, omitting it here would leave the review incomplete. In the course of the generalized reformulation of the Euler–Bernoulli beam
theory, it was established that the main unknown—the function y(x)—is not, in fact, a
deflection function, as it has traditionally been interpreted since Euler’s time. Rather,
it is an abstract function defined in a topological space, which may be understood
as the unfolding of a topological coordinate system onto the straight axis of the
Cartesian system.
In this unfolding:
1. The abscissa x corresponds to the original length L of the beam. Since the Euler–
Bernoulli model considers pure bending of a cantilever beam (Fig. 1b) without
the development of axial forces, the curved deformed axis s is projected onto the
straight axis x, while the initial length L is preserved.
2. The ordinate y(x) represents the distance r from the topological abscissa to the
neutral axis of the deformed beam, measured along the radius vector in the
direction of s(ϕ). This distance accounts for both the angular coordinate ϕ and
the current radius of curvature R(ϕ) = 1/κ(ϕ).
This approach made it possible to identify a linear relationship between the
bending moment and curvature of cantilever beams over a semi-open interval of
the topological (curvilinear) space—that is, over the entire interval [0, +∞). As a
result, the generalized equilibrium equations of the Euler–Bernoulli beam theory
take a linear divergent form, accounting for modern sign conventions:
P (i) − M (i) = 0, P (i) − Q(i) = 0, P (3) (i) + q(i) = 0,

Generalized Geometrically Exact Theory of Column Stability

491

where P(i) = −EI · θ (i) is a new force-related quantity termed the return potential;
EI is the bending stiffness; and M (i), Q(i), and q(i) denote, respectively, the bending
moment, shear force, and distributed transverse load at the considered beam section.
The coordinate system i may be either Cartesian (i = x, projected onto the straight
axis x) or curvilinear (i = s, measured along the deformed neutral axis s).
Given the semi-open interval of admissible values for the curvilinear coordinate
s ∈ [0, +∞), it is worth recalling that Leonhard Euler, in the title of his seminal
1744 work [10], employed an exceptionally broad formulation: “…or the solution
of the isoperimetric problem, taken in the most general sense.”
This emphasizes the universality of the approach, in which not only closed forms
are considered, but also open configurations of arbitrary length—directly corresponding to modern formulations of stability problems in curvilinear coordinate
systems.

2 Method
When a longitudinal axial force N is applied to a rod, loss of stability occurs upon
reaching a certain threshold, manifesting as bending deformations in the direction of
least flexural stiffness EI . The specific buckling shape is determined by the boundary
conditions of the beam and plays a key role in the distribution of internal forces.
Modern analytical methods rely on Leonhard Euler’s classical assumption [10]
that the deformation of the rod, at the onset of buckling, follows a sinusoidal shape as
the initially straight beam axis transitions to a curved configuration. This assumption
is primarily motivated by the convenience it offers in obtaining closed-form analytical solutions. As numerous full-scale beam tests have shown, this approximation
yields satisfactory accuracy for relatively short members. However, as the length of
the rod increases—all other conditions being equal—the theoretical critical force
tends to be overestimated. These discrepancies have traditionally been attributed to
variations in the physical and mechanical properties of the samples, inaccuracies in
load application, and other random factors.
In the present work, however, the focus is not on refining experimental parameters but on re-evaluating the analytical formulation of the stability problem itself.
The principal subject of critical analysis is the buckling shape, since the transverse
geometry of the rod’s deformation directly determines the bending energy and thus
the level of the critical force. While the sinusoidal approximation adopted in classical
theory is convenient for analytical treatment, it may not correspond to the configuration with the lowest potential energy. Accordingly, this study attempts to determine
the exact buckling shape of the rod at the critical state, without making prior assumptions about its form, thereby enabling a more rigorous and geometrically justified
definition of the limit equilibrium condition.
It should be noted that when a rod is subjected to an axial compressive force Ncr ,
uniformly distributed axial stresses arise in accordance with Hooke’s law [2]. If a
critical eccentricity ecr is present, these stresses generate a constant bending moment

492

V. A. Neshchadimov

along the entire length of the beam:
Mcr = Ncr · ecr ⇒ Ncr =

Mcr
.
ecr

(3)

To obtain the deformation geometry of a simply supported beam under constant
bending moment, we use the well-known classical solution, which in generalized
form is written as:
y(i) =

Mcr
i(L − i),
2EI

(4)

where i is the coordinate along the beam (in the rectilinear system i = x, in the
curvilinear system i = s).
This expression can be rewritten using the constant radius of curvature R =
EI /Mcr as:
y(x) =

s(L − s)
x(L − x)
, y(s) =
.
2R
2R

In the curvilinear coordinate system, the variable s represents the arc length, and
the ratio s/R can be interpreted as an angular coordinate in the polar system. Thus,
the deformed axis of the beam takes the shape of a circular arc.
In contrast, in the rectilinear coordinate system, the function y(x) assumes a
parabolic form:
y(x) =

Lx − x2
,
2R

which contradicts the intuitive understanding of a beam’s behavior under constant
bending moment. In such a beam, the tensile and compressive fibers are distributed
uniformly along its length, which more naturally corresponds to a circular arc rather
than a parabola.
Since the function y(x) is abstract and contains information about both the rotation
angle and the curvature of the deformed axis (through its first derivatives), we can,
knowing the rotation angle of the cross-section θ (x) = y (x), reconstruct the exact
deformation geometry of the beam in parametric form using the Frenet integrals [16]:
⎧
⎪
⎪
⎨ y(s) =
⎪
⎪
⎩ y(s) =

s
0
s

cos θ (ξ )d ξ,
(5)
sin θ (ξ )d ξ,

where s is the arc length of the deformed neutral axis, and θ (ξ ) is the angle of the
tangent at point ξ .
−2i
into (5), we obtain:
Substituting θ (i) = y (i) = L2R

Generalized Geometrically Exact Theory of Column Stability

493

L
− sin L−2s
,
x(s) = R sin 2R
2R
L−2s
L
.
y(s) = R cos 2R − cos 2R

This system of parametric equations is structurally close to the classical
representation of a circular arc:
x(u) = R · sin u + Cx ,
y(u) = R · cos u + Cy ,
where Cx and Cy are the coordinates of the center of the circle.
After simple analytical transformations, it becomes evident that the resulting shape
indeed corresponds to a circular arc of radius R, centered at the point:
R · sin

L
L
, R · cos
.
2R
2R

The initial and final rotation angles are determined from the corresponding
function (5) and take the following values:
θ (0) =

L
L
, θ (L) = − .
2R
2R

Thus, the rotation angle function θ (i) (see Eq. 5) allows us to define the central
angle of the arc as the difference between the angles of rotation at the beam ends:
ϕ = θ (0) − θ (L) =

L
.
R

(6)

In the case of a symmetric configuration, the central angle can also be represented
as twice the rotation angle at the initial section: ϕ = 2θ (0). In other cases, when
θ (0) = 0, the central angle is defined as ϕ = θ (L). In all cases, φ is considered a
positive value.
Anticipating the subsequent discussion, it should be noted that the central angle φ
can be regarded as a universal parameter for deriving a geometrically justified expression for the critical force under various end-support configurations of a compressed
rod. In particular, by substituting specific values of φ into Eq. (12), one can obtain
analytical solutions for stability problems corresponding to boundary conditions
where the central angle is nonzero. This generalization will be illustrated with
concrete examples in the “Results and Discussion” section.
Based on the previously established fact that, at the moment of buckling, the
deformed shape of the beam corresponds to a circular arc with constant radius of
curvature Rcr , the critical bending moment can naturally be expressed using the exact
form of the Euler–Bernoulli beam theory:
M = EI · k,

494

V. A. Neshchadimov

where κ = 1/R is the exact expression for curvature and EI is the flexural stiffness.
Then, at the onset of instability, when the curvature reaches its critical value 1/Rcr ,
the critical bending moment becomes:
Mcr =

EI
.
Rcr

(7)

Taking into account that the bending moment induced by an axial force with
eccentricity is given by Eq. (3), we arrive at the final relation:
Ncr · ecr =

EI
EI
⇒ Rcr =
.
Rcr
Mcr

This expression refines the classical approach, as it is based on the precisely reconstructed geometry of the deformed beam axis without relying on approximations.
Having made a brief digression to justify the exact deformation geometry of the
beam in the simply supported case under critical bending moment (see Eqs. 3 and 7),
we now return to the main objective of this study—to derive a refined expression for
the critical force that accounts for the arc-shaped deformation of the beam with radius
Rcr . To this end, we determine the critical eccentricity at mid-span, which appears
in Eq. (3), using two approaches: one based on the geometry of a circular arc, and
the other based on the value of the function y(i) at the midpoint of the i = L/2, as
obtained from the generalized solution of the classical Euler–Bernoulli theory (see
Eq. 4).
In the first approach, the maximum deflection of the circular arc—which is also
the critical eccentricity or sagitta (i.e., the distance from the midpoint of the chord
to the corresponding point on the arc)—is determined using the Pythagorean theorem
and the adopted notations (see formulas above):
ecr = Rcr −

R2cr −

L
2

(8)

If the arc is defined via the central angle ϕ (in radians), the eccentricity can be
expressed as:
ecr = Rcr 1 − cos

ϕ
.
2

(9)

In the second approach, the critical eccentricity is defined as the value of the
abstract function at mid-span:
ecr = y

L
2

L2
.
8Rcr

(10)

Generalized Geometrically Exact Theory of Column Stability

495

By substituting the expression for the critical eccentricity ecr into Eq. (3) or (7), one
can obtain a refined formula for the critical force that accounts for the actual geometry
of the deformed rod. Alternatively, the value of Mcr from Eq. (7), which reflects the
constant bending moment in the beam’s cross-section, can be used. Depending on
the method used to define the eccentricity, the resulting expression for the critical
force will differ in form.
1. Based on the geometry of the circular arc (see Eq. 8):

Ncr =

Mcr
R2cr −

Rcr −

L 2
2

2EI 2Rcr +

4R2cr − L2

Rcr L2

Or, in terms of the central angle φ (see Eq. 9):
Ncr =

Mcr
EI
=
Rcr 1 − cos ϕ2
2R2cr · sin2

ϕ
4

2. Based on the generalized solution of the classical beam theory (see Eq. 10):
Ncr =

8Rcr Mcr
8EI
Mcr
=
=
.
2
ecr
L
L2

If the deformation is small (i.e., L
Rcr , which corresponds to small eccentricity),
1:
Eq. (8) can be expanded into a Taylor series in the small parameter ε = 2RLcr
ecr = Rcr −

R2cr −

L
2

L4
L6
L2
L2
+
+
+
·
·
·
≈
.
8Rcr
128R3cr
1024R5cr
8Rcr

Substituting this approximation for ecr into Eq. (3) yields:
Ncr =

EI /Rcr
8EI
Mcr
= 2
=
.
ecr
L /8Rcr
L2

Similarly, for small values of the angle (i.e., ϕ
expanded into a Taylor series:
cos

1 ϕ
ϕ
=1−
2
2! 2

1 ϕ
4! 2

1), the cosine in Eq. (9) can be
4

−

1 ϕ
6! 2

···

Thus,
1 − cos

ϕ
1 4
1
1
1
= ϕ2 −
ϕ +
ϕ6 − · · · ≈ ϕ2.
2
8
384
46080
8

496

V. A. Neshchadimov

For the considered case of a simply supported rod, the value of the central angle ϕ
is related to the eccentricity as follows (see Eq. 9):
ecr = Rcr 1 − cos

ϕ
Rcr L
1
= Rcr · ϕ 2 =
2
8
8 Rcr

L2
.
8Rcr

(11)

Substituting this value into the expression for the moment (see Eq. 7):
EI
L2
8EI
= Ncr ·
⇒ Ncr =
,
Rcr
8Rcr
L2
or directly into Eq. (3):
Ncr =

Mcr
EI /Rcr
8EI
= 2
=
.
ecr
L /8Rcr
L2

To obtain the critical force based on the value of the abstract function at midspan (see Eq. 10), no approximations are required, since this solution is derived in
the curvilinear (topological) coordinate system. Unlike the previous cases, where
Taylor series expansions were used, here linearization is unnecessary—the expression already incorporates the exact geometric relationship between deflection and
radius of curvature.
Moreover, it is not even necessary to explicitly derive the critical force, as the
eccentricity values obtained from Eqs. (10) and (11) are identical:
ecr = y(L/2) =

L2
.
8Rcr

Thus, in all three approaches to defining the critical eccentricity—via the exact
geometry of the arc, via the small-angle approximation, or from the solution to the
Euler–Bernoulli beam equation—the same expression for the critical axial force is
obtained in the limit of small deformations. This confirms the internal consistency
of the approach and justifies the transition from exact geometry to the generalized
solution of the classical beam theory.
The above conclusions form the basis for deriving a generalized expression for
the critical force, applicable to arbitrary deformation scenarios of compressed rods
within a geometrically rigorous framework. This is made possible by a fundamental
property of the Euler–Bernoulli beam model, in which all force and deformation
parameters are linearly related through the return potential:
P(i) = −EI · θ (i),
as shown in [17]. In particular, the radius of curvature of the deformed rod—including
its critical value—can be expressed via the central angle:

Generalized Geometrically Exact Theory of Column Stability

Rcr =

497

L
.
ϕ

Taking into account that the bending moment induced by the axial force with
eccentricity is given by:
Mcr = Ncr · ecr ,
and that at the moment of instability it equals the moment corresponding to the
limiting curvature:
Mcr =

EI
,
Rcr

we obtain the final expression for the critical force in generalized form:
Ncr =

EI · ϕ
EI
=
Rcr · ecr
L · ecr

(12)

This expression represents the central result of the present study. It allows the
critical axial force to be determined not from a priori assumptions about the buckling
shape, but from geometrically defined parameters of the deformed configuration,
namely:
• the central angle ϕ, calculated as the difference between the rotation angles of
the beam’s end sections (see Eq. 6); if one of the sections is restrained against
rotation, the value of ϕ equals the rotation angle of the free end. The absolute
value of the central angle is always taken;
• and the critical eccentricity ecr , defined as the maximum value of the abstract
function y(i), which for over three centuries was mistakenly interpreted as
the deflection function y(i) in the rectilinear coordinate system. In fact, this
function represents the primary unknown in the classical formulation of the
Euler–Bernoulli equations and should be interpreted within the framework of a
curvilinear (topological) coordinate system.
The generalized formula (12) serves as an analytical tool for determining the
critical force in problems with arbitrary boundary conditions and external loading.
It lays the foundation for a new, geometrically rigorous theory of stability of
compressed rods, applicable in all cases where the central angle ϕ 0.
The following section presents examples illustrating the application of the derived
formulas to typical structural configurations, including both classical cases and those
that previously lacked rigorous analytical expressions within the Euler–Bernoulli
beam model.

498

V. A. Neshchadimov

3 Results and Discussion
The refined formula for the critical force, derived in the previous section, enables a
revision of the classical understanding of buckling in compressed rods. Unlike Euler’s
original model, which a priori assumes the deformation shape to be sinusoidal, the
present study employs a geometrically exact configuration—a circular arc. This
eliminates the need for simplifying assumptions and allows the derivation of the
deformed axis equation under a constant bending moment in a rigorous manner,
based on the generalized formulation of the Euler–Bernoulli beam theory [17].
Since the proposed solution relies on a more geometrically rigorous approach, it
is reasonable to evaluate the relative error of the classical (approximate) solution
in comparison with the exact one.
To this end, let us compare the expressions for the critical axial force in the
classical (linear) formulation and in the refined (geometrically exact) model.
Euler’s classical formula for a simply supported rod of length L is given by Eq. (1):
Ncr = π 2

EI
.
L2

In contrast, the exact value of the critical force—obtained by accounting for the
arc-shaped deformation and the geometrically defined eccentricity—is:
N2025 =

8EI
EI
=8 2.
2
L
L

The relative error of the classical estimate compared to the exact solution is:
δ=

N2025 − Ncr
π2
= 1 − 1.2337 = −0.2337.
=1−
N2025
8

This means that the classical Euler model overestimates the critical force by
approximately 23.4% compared to the result based on the exact deformation
geometry.
This discrepancy arises from the fact that the classical theory assumes a sinusoidal deformation shape, which corresponds to a normalized modal solution of the
linear differential equation. In contrast, the exact geometric formulation defines
the deflected shape as a segment of a circle, which reflects the physically realizable
configuration under stable equilibrium conditions.
However, knowing the exact deformation geometry of the beam in the form of
a circular arc allows us to go further and derive a generalized expression for the
critical force, applicable not only to symmetrically compressed elements, but also to
configurations involving a geometric eccentricity of deflection. In this case, two key
parameters are taken into account: the eccentricity ecr , characterizing the shape of the
deformed axis, and the central angle ϕ, which defines its spatial configuration. The

Generalized Geometrically Exact Theory of Column Stability

499

resulting expression (12) thus incorporates the influence of deformation geometry in
buckling analysis.
This opens up the possibility of analytically determining the critical force not
only within the framework of classical theory, but also in a generalized formulation
that encompasses arbitrary boundary conditions, geometric parameters, and initial
imperfections.
It is particularly noteworthy that when selecting parameters ϕ = π and ecr = L/π ,
the generalized formula (12) reduces to Euler’s classical expression (see Eq. 1).
Thus, Euler’s solution appears as a special case of the more general model, which
adds both rigor and universality to the proposed approach.
As a result, it becomes possible to assess the stability of existing structures
designed based on Euler’s formula, while accounting for their actual geometry and
deformation shape. The proposed model allows for the identification of potential
stability reserves or hidden risks associated with real deflected configurations that
do not conform to the assumed sinusoidal shape.
In the author’s earlier work [17], it was shown that a cantilever beam subjected to
a constant bending moment also deforms into a circular arc with constant radius of
curvature R, similarly to the simply supported beam analyzed in the present study.
Thanks to the generalized formula (12), which is grounded in the exact deformation geometry, it is now possible to analytically determine the critical force for
compressed rods under arbitrary loading schemes and initial geometries. In particular,
it enables the computation of the critical force for a cantilever element subjected
to axial loading.
To demonstrate the algorithm, we use the classical solution based on the generalized form of deflection caused by the bending moment Mcr , which arises from the
action of the critical axial force Ncr at the critical eccentricity ecr :
y(i) =

Mcr 2
i .
2EI

The central angle ϕ, defined as the difference between the rotation angles of the
cross-sections in the deformed configuration (see Eq. 6), for a cantilever rod is equal
to the rotation angle at the free end. This is found by differentiating the deflection
function:
θ (i) = y (i) =

Mcr
L
Mcr
i ⇒ ϕ = θ (L) =
L=
.
EI
EI
Rcr

The maximum deflection of the beam (i.e., the eccentricity ecr ) is determined as
the value of the deflection function at i = L:
ecr = y(L) =

L2
Mcr 2
L =
.
2EI
2Rcr

Substituting the obtained values of ϕ and ecr into formula (12), we get:

500

V. A. Neshchadimov

Ncr =

EI · ϕ
EI · L/Rcr
2EI
=
= 2 .
2
L · ecr
L · L /2Rcr
L

This solution is obtained for the first time with an exact geometric representation
of buckling in a cantilever rod. Euler did not consider the cantilever configuration
and never derived a corresponding critical force expression. The entire modern
theory of buckling is based on Euler’s single analytical solution (Eq. 1), which has
been taken as the reference standard. For all other boundary conditions, the empirical
effective length factor μ is used—for a cantilever beam, this factor is equal to 2.
In the general case, the critical force in modern buckling theory is determined by
the formula:
Nμ =

π 2 EI
,
(μL)2

and for a cantilever beam (μ = 2):
Nμ =

π 2 EI
π 2 EI
=
.
4L2
(2L)2

As before, let us determine the relative error of the classical estimate of the
critical force for a cantilever rod compared to the exact solution:
δ=

Ncr − Nμ
π 2 /4
= 1 − 1.3927 = −0.3927.
=1−
Ncr
2

This means that the modern definition of the critical force using the effective length factor μ overestimates the critical force by approximately 39.3%
compared to the solution based on the exact deformation geometry.
If we compare the geometrically exact solution for a simply supported rod (with
the coefficient 8 in the critical force formula) with the corresponding solution for a
cantilever rod (where the coefficient is 2), we obtain:
hinge

Ncr
8
= = 4.
cantilever
Ncr
2
A similar ratio is also given by the classical buckling theory with the use of the
effective length factor μ, where:
hinge

Nμ
1
=
= 4.
Nμcantilever
(1/2)2
This observation suggests that the proposed geometrically exact solutions retain
the key proportions of the classical theory, which have been empirically confirmed
by engineering practice and adapted to existing design codes. This confirms both the

Generalized Geometrically Exact Theory of Column Stability

501

internal consistency of the model and its potential applicability to engineering
calculations, including structures with various boundary conditions.
This provides reason to believe that the proposed geometrically exact solutions will be consistent with existing experimental data, since the effective length
factors in classical buckling theory were selected empirically and provided satisfactory agreement for relatively short columns. However, as the length of the member
increases, the errors in determining the critical force become significant, which
limits the applicability of the linear stability theory. The refinement of the critical
force within the proposed model significantly extends the boundaries of its applicability—including cases involving large deformations that were previously classified as geometrically nonlinear—and covers a wide range of geometric and loading
configurations.
As an example, let us also determine the critical force under the combined
action of axial and transverse loading. In this case, as before, we use the classical
solution in generalized form for a simply supported beam subjected to a uniformly
distributed load q(i) = q. The solution is:
y(i) =

qi(i − L) i2 − Li − L2
.
24EI

Assume that the coordinate i, corresponding to the maximum critical eccentricity, is not known in advance. It can be found by solving the equation y (i) = 0,
which is essentially equivalent to determining the rotation angle function θ (s) in
the curvilinear (topological) coordinate system s, which does not coincide with
the angle in the rectilinear coordinate system.
This is precisely the mistake made by S. P. Timoshenko, who identified the
angle of rotation with the deformation of a plane section.
θ (s) = y (i) =

q L3 − 6i2 L + 4i3
.
24EI

Equating this expression to zero over the interval 0 ≤ i ≤ L, we determine the
point of extremum:
q L3 − 6i2 L + 4i3
L
= 0⇒i = .
24EI
2
Knowing the coordinate of the point of maximum deflection, we can determine the critical eccentricity (although it is well known from classical strength of
materials):
ecr = y

L
2

5L4 q
.
384EI

502

V. A. Neshchadimov

The central angle ϕ is determined as the difference in rotation angles at the ends
of the beam (see Eq. 6):
ϕ = θ (0) − θ (L) =

− L3 q
L3 q
L3 q
−
=
.
24EI
24EI
12EI

Then the critical force, according to Eq. (12), becomes:
Ncr =

32EI
EI · L3 q/12EI
EI · ϕ
=
=
.
4
L · ecr
L · 5L q/384EI
5L2

(13)

Thus, we have obtained a geometrically grounded analytical expression for the
critical force under the combined action of axial and uniformly distributed transverse
loading. This result cannot be compared to classical formulas, as it has no known
analogues and represents a new particular solution within the framework of the
proposed generalized geometrically exact theory of stability of compressed rods.
The critical forces for other boundary conditions and types of transverse loading
can be obtained in a similar way. In this study, this algorithm has been implemented
in principle for all boundary configurations, provided that an axial force is acting,
which triggers buckling.
One of the unexpected, yet logically consistent consequences of the geometrically
exact formulation in a curvilinear (topological) coordinate system is the possibility
of applying the principle of superposition to buckling problems. As demonstrated in
[17], the term “geometrically nonlinear formulation” does not reflect the true nature
of beam deformation under transverse bending: beams behave linearly within the
elastic range, and the relationship between internal forces and deformation parameters remains linear in accordance with Hooke’s law. Consequently, the superposition
principle, as a fundamental property of linear systems, remains valid in the present
context.
This observation makes it possible to account for the combined effect of multiple
transverse loads by summing the corresponding central angles and eccentricities,
leading to the following generalized expression for the critical force:
Ncr =

EI · ϕi
EI
.
=
Rcr · ecr
L · ecr,i

(14)

This approach may enable, in certain cases, the construction of rigorous analytical solutions for problems with uniform-type external load configurations, such
as a group of concentrated forces. However, for combined or heterogeneous
loading scenarios—for instance, a combination of concentrated and uniformly
distributed loads—the applicability of the superposition principle requires additional justification, since the corresponding deformed configurations belong to
different topological spaces, and linearity may not be preserved.

Generalized Geometrically Exact Theory of Column Stability

503

4 Conclusion
In the present work, the classical theory of buckling of compressed rods has been
generalized on the basis of a strictly geometric approach within the Euler–
Bernoulli beam model—without linearization of curvature expressions and
without a priori assumptions regarding the buckling shape.
As a starting point, the exact deformation configuration in the form of a circular
arc, which arises under a constant bending moment, was considered. This model
enabled an analytical description of the buckling geometry and the derivation
of refined expressions for the critical load based on an exact solution of the
equilibrium equations.
The key result is the derivation of a universal formula (12) for the critical load,
expressed in terms of geometric parameters of the buckling mode—namely, the
central angle φ and the corresponding maximum deflection (eccentricity) ecr .
Here, the term eccentricity refers not to an initial deviation of the axial force line,
but rather to a quantity that emerges from the geometric transformation of the
rod’s configuration at the moment of buckling. This fundamentally distinguishes the
proposed approach from conventional theories of eccentrically loaded columns, in
which eccentricity is externally prescribed, and imparts to the present solution a
strictly geometric and universal character.

5 Key Findings
1. The classical Euler formula for a simply supported column is obtained as a
particular case of the general solution when ϕ = π and ecr = L/π . It is shown
that this classical formula overestimates the critical load by 23.37% compared
to the solution based on the exact deformation geometry.
2. A strict analytical expression for the critical load of a cantilever column has
been obtained for the first time. It demonstrates that the critical load is four times
lower than that of a simply supported element. This fully agrees with the classical
relationship between effective lengths (μ = 2) and confirms the applicability
of the proposed model.
3. It is shown that the central angle ϕ, defined via the rotation function θ (i), and
the critical eccentricity ecr , expressed through the abstract function y(i), can be
used as universal parameters for evaluating buckling under various boundary
conditions and loading schemes.
4. A geometrically rigorous theory of buckling has been developed for rods under
combined axial and uniformly distributed transverse loading. This result has
no known counterpart in classical theory.
5. Owing to the linearity of the equilibrium equations in the curvilinear coordinate system, the superposition principle is shown to apply: under the simultaneous action of multiple loads, the resulting effect can be determined by

504

V. A. Neshchadimov

summing the respective central angles ϕi and critical eccentricities ecr,i (see
Eq. (14)). This opens the way to rigorous analytical determination of the critical
load in problems with loads of the same type—for example, several concentrated forces regularly spaced along the beam. However, if one attempts to sum ϕi
and ecr,i for different types of loads—such as a combination of concentrated and
uniformly distributed loads—the result becomes unreliable, since the deformed
configurations in such cases belong to different topological spaces, for which
the superposition principle does not hold.
6. All calculations were carried out within the Euler–Bernoulli beam model, but
without any approximations of the curvature expression, ensuring both rigor
and geometric accuracy of the results.
Thus, the present study completes the development of a generalized, geometrically rigorous theory of rod stability based on the Euler–Bernoulli model, free
from linearization and any a priori assumptions regarding the buckling shape. The
derived analytical expressions, including the universal formula for critical load,
cover a wide range of boundary conditions and transverse loading types. The resulting
theory forms a self-consistent and complete framework, rigorously derived within
the chosen model. It features internal consistency, geometric justification, and is
suitable for practical application without reliance on empirical coefficients.
It should be noted, however, that within this model, the influence of transverse
loading on the critical load manifests only through the deformation shape, but not
through its magnitude (see Eq. 13), which contradicts intuitive expectations. This
is a consequence of the limitations of the Euler–Bernoulli model, which does not
account for the interaction of axial and transverse forces—analysis is conducted
under the assumption of pure bending. A typical example of this formulation is the
cantilever beam subjected to a constant moment at the free end, as shown in
Euler’s original work (Fig. 1b [10]). Transitioning to a more general model—based
on the principles developed herein—may be expected to yield formulations in which
the magnitude of the transverse load directly affects the critical load, opening new
avenues for future research.

References
1. Galilei G (1638) Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Discourses
and mathematical demonstrations on two new sciences). Leiden
2. Hooke R (1678) De Potentia Restitutiva, or of Spring: explaining the power of springing bodies.
John Martyn, London
3. Huygens C (1673) Horologium Oscillatorium, sive de motu pendulorum ad horologia aptato
demonstrationes geometricae. F. Muguet, Paris
4. Bernoulli J (1694) Curvatura Laminae Elastica (Curvature of Elastic Laminae). Acta Eruditorum, pp 262–276
5. Bernoulli J (1694) Solutio problematis Leibnitiani (Solution to Leibniz’s problem). Acta
Eruditorum, pp 276–280
6. Bernoulli J (1705) Véritable hypothèse de la résistance des solides (True hypothesis of the
resistance of solids). Histoire de l’Académie Royale des Sciences de Paris, pp 139–150

Generalized Geometrically Exact Theory of Column Stability

505

7. Bernoulli J (1744) Opera Omnia, Tomus I (Opera Omnia, Volume I.). Marcum-Michaelem
Bousquet, Lausanne, Geneva, pp 608–612
8. Bernoulli D (1755) Réflexions et éclaircissemens (Reflections and clarifications). Histoire de
l’Académie Royale des Sciences et des Belles Lettres de Berlin 9:147–172
9. Bernoulli D (1755) Sur le mélange de plusieurs espèces (On the mixture of several species).
Histoire de l’Académie Royale des Sciences et des Belles Lettres de Berlin 9:173–195
10. Euler L (1744) Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes
(Method of finding curved lines having the property of maximum or minimum). MarcumMichaelem Bousquet, Lausanne, Geneva
11. Girard PS (1798) Traité analytique de la résistance des solides (Analytical treatise on the
resistance of solids). Firmin Didot & Du Pont, Paris
12. Todhunter I (1886) A history of the theory of elasticity and of the strength of materials, vol 1.
Galilei to Saint-Venant, Cambridge University Press, London, pp 1639–1850
13. Clapeyron BPE (1857) Mémoire sur la résistance intérieure des corps solides (Memoir on the
internal resistance of solid bodies). J. École Polytechnique 24:1–233
14. Navier C-L-M-H (1826) Résumé des leçons données à l’École des ponts et chaussées (Summary
of lessons given at the School of Bridges and Roads). Firmin Didot père et fils, Paris
15. Clebsch A (1862) Theorie der Elasticität fester Körper (Theory of elasticity of solid bodies).
Teubner, Leipzig, B.G
16. Frenet JF (1847) Sur les courbes à double courbure (On double curvature curves). J Math Pures
Appl 17:437–447
17. Neshchadimov VA (2025) Generalized Euler–Bernoulli beam theory with return potential.
Reinf Concr Struct 2(10):41–57. https://doi.org/10.22227/2949-1622.2025.2.41-57

Analysis of Belt-To-Roller Contact
and Pressure Distribution in Pipe
Conveyors Using Motion Simulation
I. A. Magomedov, E. M. Magomedov, and A. M. Bagov

Abstract The study was done to examine a pipe conveyor. One of the main players in
pipe conveyors and in any other conveyors is the belt and the rollers and their contacts.
Of course, there are other parameters that can greatly influence the performance of
the conveyor, but most of the time, the failure is associated with the rollers and the
belt. Therefore, the work shifts its focus on contacts between the belt and the rollers.
One section of a pipe belt conveyor was built in SolidWorks and similarly analyzed
with the built-in motion analysis tool. 10 simulations were conducted with varying
acting force and the flow of the pipe. The results illustrated that the value of acting
force can have different influences. For instance, with a higher value of acting force,
the reaction force was higher with the front rollers. The deduction of acting force
shifted the contacts to the rear rollers. Placement and the number of rollers can also
influence the results. Similarly, the flow of the belt can have a minor effect on the
results too.
Keywords Pipe conveyor · Belt-roller contact · Pressure distribution · Motion
analysis · Structural variation · Reaction force

1 Introduction
Our planet is rich with various natural resources. Each region possesses its own
unique and invaluable resources that can be used for development and prosperity.
Since ancient times, people have extracted various resources for different purposes.
I. A. Magomedov (B) · E. M. Magomedov
Kadyrov Chechen State University, Grozny, Russia
e-mail: ismwork@mail.ru
E. M. Magomedov
e-mail: 89659645756@mail.ru
A. M. Bagov
Kabardino-Balkarian State University, Nalchik, Russia
e-mail: vegros@rambler.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_40

507

508

I. A. Magomedov et al.

The modern way of exploring and extracting natural resources can completely differ
from what it used to be. The scale at which we mine resources now is beyond
comprehension. With technological progress, and with progress in general, the needs
that should be fulfilled require more resources to be used. With the increase in needs,
some methods can be outdated. The whole process of extraction of resources will
not end at this point but will require many steps before being transformed into
something more valuable or significant. In this article, the technology of delivery
of mined material to the next stage will be explored. The technology is an enclosed
conveyor belt that can carry bulk solids without spillage from one point to another
over long distances [1]. The idea behind this technology is simple, but its realization
is quite complex. As it was firstly introduced, there were many issues that were
related to the carrying ability, the distance, and the belt. With cooperation, some of
the issues were tackled, but at this stage, it was considered rather costly than useful.
As time passed, it became more robust to problems and the era of the technology
began. Nonetheless, despite its usefulness, its application can be found mostly in the
following countries such as China, India, and South Africa [2]. It is also believed that
a modernized version of a classic conveyor with elements that defy its application
in a more sophisticated manner can be beneficial outside the mining industries. The
technology provides not just the transportation of bulk solids but positively influences
nature as it lowers the use of heavy vehicles involvement [3]. This can have a direct
effect on global warming and related issues. Hence, the utilization of the technology
can be aligned with the Sustainable Development Goal 12 (SDG 12) [4, 5]. The carbon
footprint is a serious phenomenon in the last few decades that needs to be tackled
before it reaches an unreturnable stage. Further examination of the technology and
in-depth study can give away spots that can be solved via structural enhancement or
clever use of new technologies. Of course, it is obvious that this technology needs
modernization for its better usability. Therefore, the aim of this work is to suggest a
new approach that will further enhance the functionality of the technology and help
it to overcome some issues that it faces.
Guo et al., in their work [6], looked into the optimization of the diameter of a
pipe belt to understand its influence on the lateral pressure on supporting rollers
and material throughput. Their investigation was focused on pipe belt diameter and
its influence on the efficiency of transporting bulk solids and the lifespan of the
belt. The results illustrated that an increase in diameter could lead to an increase
in pressure of roller supporters. Zamiralova, in her work [7], looked into how the
stiffness of the belt and its contact on the rollers affect the performance of a pipe
conveyor. It was found that if the belt is too stiff, the contact with some rollers is
lost, which can result in creating instability of the flow of the pipe belt and wear
of the belt. Hence, the outcome is to build a structure and manufacture a belt that
can show proper contacts to reduce the instability in the flow of the pipe belt and to
reduce wear. Work [8] looks into studies on indentation rolling resistance, which is
the friction that occurs when the belt presses down on the rollers, which is a wellknown fact that this resistance is a factor for consuming energy. It was found that the
indentation rolling resistance mainly depends on various factors such as belt speed,
weight of materials, temperature, and rollers placement. The work also emphasized

Analysis of Belt-To-Roller Contact and Pressure Distribution in Pipe …

509

that to reduce energy loss, structural changes and material properties play a big role.
Similarly, the following studies [9] also investigated the forces that occur between
the belt and rollers. However, the focus was shifted toward sag resistance. As it was
mentioned in the previous work, the rollers placement and the belt’s properties affect
how well the belt moves through the construction. However, sometimes due to some
incorrect calculation, the belt can sag between the rollers. The finding of this work
was that the forces between the belt and rollers come from three sources such as
the bulk solids that are transported, the shape of the belt, and its weight. Similar
studies can be seen in the following work [10, 11]. Work [12] focuses on the pipe
belt and its rotation in the construction. The belt rotation can be a major reason for
belt failure and cases of material spill. The results that they found include two main
reasons. The first reason for the belt to fail or to rotate in this case is if the tension
on both sides isn’t balanced. The second reason is related to the rollers’ contact with
the belt, meaning that uneven contact of rollers would result in rotation of the belt.
A similar study [13] also looked into the belt rotation. Other technologies can be
used to predict the rotation of the belt by utilizing sensing technologies [14]. Sensors
can predict the failure occurrence and monitor a pipe belt conveyor. As it can be
seen from the mentioned works, the major concerns in a pipe belt conveyor are the
pressure between the belt and the rollers. Hence, this work will look into the ways of
trying to understand the influence of placement of rollers in the pipe belt conveyor.

2 Methodology
To examine the influence of the placement of rollers in a pipe conveyor on pressure
distributions, the SolidWorks software package was utilized. All three stages were
performed in this software. By stages, it is referred to the modelling of separate
parts, assembly, and analysis. Modeled structure can be seen in Fig. 1. Due to a
lack of computational power, only one section was assembled and then analyzed.
Channels, squares, belt, and bolts were modelled by standard sizes. However, the
roller supporters were modelled without following standard sizes. In total, 9 different
parts were modelled and assembled. For the material selection, stainless steel was
chosen, that was applied to all parts. Of course, in reality, it is inapplicable, however,
for the tendency results, it will work fine. The pressure distribution of the pipe belt on
rollers will be almost the same with different materials. Boundary conditions were
applied to the structure. First of all, the constraints were introduced. All four ends of
the squares were constrained in all directions, resulting in it being firmly connected
to the bridge or cemented to the ground. Then contacts were introduced. The only
occurring contacts can be seen on the belt as it interacts with the rollers. Forces were
added to the belt along the length at first to mimic the movement of the belt. And the
second force was introduced inside the belt to mimic bulk solids. As it was mentioned
earlier, the main focus shift is to investigate the influence of different arrangements
of roller supporters on pressure distribution. As it can be seen in Fig. 2, one side
(front) of the structure illustrates that all roller supporters are on one side holding

510

I. A. Magomedov et al.

the belt in a pipe shape. On the other end (rear), the placement of roller supporters
is rearranged in a way that one half is on one side and the other half is supporting on
the other side. The meshed structure is illustrated in Fig. 3.

Fig. 1 Continuous structure of pipe coveyor

Fig. 2 Structure with constraints

Analysis of Belt-To-Roller Contact and Pressure Distribution in Pipe …

511

Fig. 3 Meshed structure

3 Results and Discussion
To analyze the contact between rollers and the pipe belt, different parameters were
varied. Some structural changes also were implemented in order to better understand
how equally the weight is distributed to the rollers. In the first analysis, two variables
were changed: acting force inside the pipe belt representing bulk solids, and direction
of movement of the pipe. For the first analysis, the structure from Fig. 4 was used. The
second structure was used for the second set of results (Fig. 5). 6 simulations were
performed with the first structure, changing the value of force and the direction. The
forces used in this analysis are 10,000, 1000, and 100 N. Then the second structure
was used. This time, half of the rollers were removed to see how the contacts would
shift. This time, only 4 simulations were gathered. In the first set of results, 6 graphs
were attained; each graph contained data for 6 rollers’ contact for each side. In
the second set of results, 4 graphs were attained. Results from graphs can be seen
in Table 1. R in Table 1 is referred to as the rollers that are contacting the belt.
The number starts from the bottom roller, meaning it is R1, and others are named
clockwise. First reaction force is referred to the front rollers, and the second to the
rear rollers.
For the first set of results, 6 simulations were conducted. The values of force were
changing throughout the analysis and also the direction of flow of the pipe belt. For
the first 3 simulations, the flow of the belt was going in the negative way. In the first
simulation, the reaction force is higher at the rear part. The three rollers R1, R2, and
R6 are quite high compared to the front rollers with the same annotations (Figs. 6
and 7). The other three rollers of the front are slightly higher than the rear rollers.

512

I. A. Magomedov et al.

Fig. 4 The structure with all 6 rollers in front and in rear side

Fig. 5 The structure with all 3 rollers at each side

However, with the decrease of acting force, the change of reaction force can be seen.
For instance, in the second simulation with the force equal to 1000 N, the shift of
contact is toward the front. In this case, R1, R3, R4, and R5 have higher reaction
force. Further decrease of the acting force to 100 N does not influence the shift of
pressure but affects the reaction force by reducing it. The direction changes of the
flow introduced no further changes.
The second set of results were gathered for this study. This time, structural changes
were introduced. Front and rear rollers were reduced to a similar appearance. This
time, only three rollers were at each side. Again, with a higher value of force, the rear

100

1000

100

1000

100

10,000

2606
3121

−

3111

1702

1427

4371

2618

2165

1871

8145

2275

2050

7188

1427
1702

−

1871
2165

1509

3995

3300

3303

4007

1837

1509

5026

1837

697

640

2311

2254

2408

2385

2807

2336

2341

2979

1093

1152

3230

1093

1152

3230

3594

3101

3100

3871

1126

1226

3793

1126

1226

3793

2050

640

2275

697

−

5026

−

1000

100

4371

7188

−

10,000

8145

Max. reaction Max. reaction Max. reaction Max. reaction Max. reaction Max. reaction
force (N) R1 force (N) R2 force (N) R3 force (N) R4 force (N) R5 force (N) R6

Direction of the pipe flow

Force (N)

Simulations no.

Table 1 Results of all 10 simulations

Analysis of Belt-To-Roller Contact and Pressure Distribution in Pipe …
513

514

I. A. Magomedov et al.

Fig. 6 Results of front rollers for first simulation

Fig. 7 Results of rear rollers for first simulation

rollers were leading, as it can be seen in Figs. 8 and 9. Further reduction of force to
100 N leads to similar results, meaning that rear rollers are still in the higher contact.
This time, the direction of flow makes some notable influence. For instance, with
a higher force acting, the change of direction from positive to negative reduces the
difference of two values, where the front gains more contact but still less than the
rear. With a lower force acting on the belt, the change of direction from positive to
negative reduces the difference of two values, where the rear gains more contact.

Fig. 8 Data of simulation 7 (front rollers)

Analysis of Belt-To-Roller Contact and Pressure Distribution in Pipe …

515

Fig. 9 Data of simulation 7 (rear rollers)

4 Conclusion
To conclude, the work was done to understand the pressure distribution of the belt on
rollers in the pipe conveyor. One section of a pipe conveyor was built in SolidWorks.
Also, assembly and motion analysis were carried out in the same software package. In
this study, 10 simulations were conducted to see how different parameters influence
pressure between the belt and the rollers. Two variations of structures were presented
in this work: one with 6 rollers at each side, and one structure that has symmetrically
placed three rollers at each side. Acting force was changed throughout the analysis;
similarly, the direction of belt flow. It was found that with the 6 rollers at each side, the
direction of flow did not influence the results, but the change of acting force did. For
instance, a higher value of acting force could shift the pressure to the rear side, and
reduction could shift the contact to the front. For the second set of results, the tendency
was toward rear rollers with all results. It can be concluded that the placement of
rollers, different arrangements, flow of the belt, and the number of rollers can have
a great influence on the overall performance of the pipe belt conveyor.

References
1. Semrad K, Draganova K (2022) Non-destructive testing of pipe conveyor belts using glasscoated magnetic microwires. Sustainability 14(14):8536. https://doi.org/10.3390/su14148536
2. Fedorko G, Jassova B (2017) FEM analysis of a conveyor belt on the driving drum of a pipe
conveyor. In: 17th SGEM International conference on science and technology, vol 17, issue 11
3. Mikusova N, Ignath F (2019) Design of material conveying by variable pipe conveyor. In:
Research, production and use of steel ropes, conveyors and hoisting machines (VVaPOL 2018),
vol 263, pp 01015. https://doi.org/10.1051/matecconf/201926301015
4. Küfeoğlu S (2022) SDG-12: Responsible consumption and production. In: Emerging technologies. sustainable development goals series. Springer, Cham. https://doi.org/10.1007/9783-031-07127-0_14

516

I. A. Magomedov et al.

5. Guo Y, Wang S, Hu K, Li D (2016) Optimization and experimental study of transport section
lateral pressure of pipe belt conveyor. Adv Powder Technol 27(4):1318–1324. https://doi.org/
10.1016/j.apt.2016.04.026
6. Guo Y, Wang S, Hu K et al (2016) Optimizing the pipe diameter of the pipe belt conveyor based
on discrete element method. 3D Res 7(8)5:1–9. https://doi.org/10.1007/s13319-016-0085-8
7. Zamiralova ME (2017) Design aspects of pipe belt conveyors. Doctoral dissertation,
Delft University of Technology. https://doi.org/10.4233/uuid:a989069c-54e4-4d80-a30a-a6f
b9b333287
8. Santos LS, Ribeiro Filho PRCF, Macêdo EN (2021) Indentation rolling resistance in pipe
conveyor belts: a review. J Braz Soc Mech Sci Eng 43(230). https://doi.org/10.1007/s40430021-02922-9
9. Guo S, Huang W, Li X (2020) Normal force and sag resistance of pipe conveyor. Chin J Mech
Eng 33(48). https://doi.org/10.1186/s10033-020-00463-1
10. Molnar V, Fedorko G, Homolka L, Michalik P, Tuckova Z (2019) Utilisation of measurements
to predict the relationship between contact forces on the pipe conveyor idler rollers and the
tension force of the conveyor belt. Measurement 136:735–744. https://doi.org/10.1016/j.mea
surement.2019.01.016
11. Molnar V, Fedorko G, Andrejiova M, Grinčova A, Michalik P (2016) Online monitoring
of a pipe conveyor. Part I: Measurement and analysis of selected operational parameters.
Measurement 94:364–371. https://doi.org/10.1016/j.measurement.2016.08.018
12. Santos LS, Ribeiro Filho PRCF, Macêdo EN, Cunha APA, Cheung N (2023) Belt rotation in pipe
conveyors: failure mode analysis and overlap stability assessment. Sustainability 15:11312.
https://doi.org/10.3390/su151411312
13. Santos LS, Ribeiro Filho PRCF, Macêdo EN (2024) Belt rotation in pipe conveyors: development of an overlap monitoring system using digital twins, industrial Internet of things, and
autoregressive language models. Measurement 230:114546. https://doi.org/10.1016/j.measur
ement.2024.114546
14. Patil SS, Akhade A, Jare A, Harihar S (2021) Pipe belt orientation tracking. Int J Adv Res
Comput Commun Eng 10(5). https://doi.org/10.17148/IJARCCE.2021.105133

Urban Engineering and Planning

Urban Planning Regulation
of Sustainable Development of the World
Cities
V. A. Kolyasnikov, S. G. Shabiev, and I. I. Nadymov

Abstract Today, groups of cities are forming a single system due to intensive urbanization. Forecasting the development of this system poses an urban planning challenge. Additionally, the experience of designing world cities is of great interest in
connection with the implementation of the sustainable development goals formulated
by the UN General Assembly for a better and safer future for all people. World cities
are an important element of the world economic system and are key to global urbanization. Urban planning addresses issues such as resettlement, labor organization,
recreation, and transport accessibility in cities and their suburban zones. Therefore,
this study aims to examine sustainable development in world cities to create a concept
for urban regulation of such development. The study reveals the essence of sustainable development and provides a description of the main world cities—Paris, Berlin,
London, New York City, and Tokyo—including the perspective of urban planning
typology. The study also assesses compliance with sustainable development goals
in world cities. It interprets them from an urban planning perspective and analyzes
modern tools for regulation of sustainable development. Theoretical and practical
conclusions focus on creating a model for the urban planning regulation of sustainable development in world cities, as well as the systematic updating of this model
in connection with the formation of new sustainable development goals. Finally, the
study identifies further avenues for research.
Keywords Urban planning · Regulation · Urban regulations · Sustainable
development · World cities · Global cities

V. A. Kolyasnikov · I. I. Nadymov
Ural State University of Architecture and Art Named for N.S. Alferov, Yekaterinburg, Russia
S. G. Shabiev (B)
South Ural State University, Chelyabinsk, Russia
e-mail: shabievsg@susu.ac.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_41

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1 Introduction
Today, intensive urbanization is causing groups of cities to form a single system. The
prediction of its development poses an urban planning challenge. The most wellknown forecasts of global urbanization include the “Ecumenopolis” development
forecast by Doxiadis [1] and the “epure of global urbanization” by Kositskiy [2].
Urban planning solves four tasks in this case: resettling people, organizing labor,
providing recreation and developing transport accessibility of territories.
In connection with the implementation of the sustainable development mission
to achieve a better and safer future for all people, in accordance with the Sustainable Development Goals for the period up to 2030 formulated by the UN General
Assembly in 2015 (in line with the Millennium Development Goals of 2000) [3], the
experience of designing world cities is of great interest. This study aims to examine
this experience in order to create a concept for the urban planning regulation of
sustainable world city development.
World (or global) cities are national and international centers of politics, trade,
finance, consumption, technological innovation, science, culture, entertainment and
services that have a world influence [4]. The study also aims to examine the concept
of sustainable development, characterize major world cities, assess their compliance
with sustainable development goals, interpret this experience from an urban planning
perspective and analyze current opportunities for regulating sustainable development
of the world cities.

2 Materials and Methods
The study employs a systematic approach rooted in principles of goal setting, system
design and implementation. Methods of historical-logical and structural analysis,
forecasting, and a comprehensive assessment of factors are also used. Examining the
concept of sustainable development, the potential for achieving its goals and tasks,
and regulation from the perspective of urban planning, the study uses major world
cities as examples and covers the period up to 2030. The study also assesses national
safety as the foundation of sustainable development. To lay the groundwork for
further forecasting of global urbanization, it provides data on the urban development
of each world city: its state during the formation of modern sustainable development goals (from the 1990s to 2015); an assessment of the current situation and
spatial development of territories (up to 2030); strategic plans and existing projects.
The study uses graphical and conceptual text models to evaluate the feasibility of
implementing an urban planning regulation system.

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3 Results and Discussion
3.1 About Sustainable Development Goals
Today, sustainable urban development is understood as balancing and coordinating functional, socioeconomic, sociocultural, and environmental components to
strengthen the capacity of meeting residents’ needs at present and in the future.
According to UN projections, up to 60% of the world’s population will live in cities
and megacities—centers of economic growth—by 2030. However, rapid urbanization will lead to unplanned urban sprawl and infrastructure overload, negatively
impacting the environment. Therefore, it is crucial to promote openness, safety,
resilience, and environmental sustainability, especially in the world cities. To this
end, the UN General Assembly formulated the Goal 11, “Sustainable Cities and
Communities”, which involves addressing ten tasks related to the comprehensive
and sustainable planning of settlements, the preservation of the world’s cultural
and natural heritage, the support of positive economic, social and environmental
links between urban, suburban and rural areas. This support is based on improving
the quality of national and regional development planning and the development of
comprehensive strategies and plans. Simultaneously, urban planning regulation is
being strengthened worldwide, particularly in urban centers, to ensure environmental
efficiency, comfort, architectural and urban planning aesthetics. The planning structure of world cities follows a consistent pattern: a near orbit emerges around the
central urban core, followed by sequential distant orbits. This is why world cities are
inextricably linked to the inner rings of their suburban zones and the outer regional
framework.

3.2 Major World Cities and Urban Development Models
Using world cities as examples makes it possible to compare the various spatial
manifestations of global urbanization. These manifestations are determined by the
principle of geographical determinism, which states that a city’s significance and the
nature of its planning are determined by factors such as geographical location and
territorial characteristics. The selection of major world cities for research is therefore
determined by several factors: (1) Paris is a classic world city in the European Atlantic
basin with consistent regional development based on it; (2) Berlin, although it lags
behind in the world city ranking [5], is a valuable historical city in the Baltic Sea
basin with restored inter-city connections lost for nearly half a century; (3) London
is the largest and oldest world city in the North Sea basin and a key point of global
settlement, it developed on an island; (4) New York City is the largest world city in the
Atlantic basin of America in terms of territory and population; (5) Tokyo is another
major world city with extremely intensive urban development, though it belongs to
the Pacific basin of Asia.

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The spatial parameters, natural geographical conditions and opportunities for the
further development of the world cities are determined by three types of orbital
structures: concentric, eccentric, and aquacentric [2]. Concentric orbits are formed
by circumferential railways and ring highways with satellite cities, as in Paris and
Berlin. If an insurmountable barrier (such as a sea or mountains) is present, the
orbit may become deformed and remain open—a “semi-orbital” structure, as seen
in Tokyo—or transform into an aquacentric structure. This usually occurs when a
linear city plan transforms into a linear-ring structure, as seen in New York City. When
an orbit transforms into the eccentric type, which is mainly found in the suburbs of
world cities, the central space remains undeveloped. This space represents an agrarian
landscape and recreational environment saturated with historical and architectural
monuments [6].

3.3 Urban Development Concepts in the World Cities
at the Time the Sustainable Development Goals Were
Formulated and at the Present Stage
Paris (see Fig. 1). In the 1950s and 1960s, work on studying and planning the development of the Paris metropolitan area began in earnest due to the rapid population
growth in Paris and its suburbs. During this period, the Paris metropolitan area was
modelled using a concentric system: the first suburban belt was defined within the
city’s “narrow” boundaries of up to 10 km, and the second suburban belt was defined
within the city’s “wide” boundaries of up to 35 km. Today, over 12 million people
live within the city’s “wide” boundaries. A project called “Parallel Paris” was also
proposed a new city intended to serve as a counterweight.

Fig. 1 a Map of Paris and the Parisian agglomeration, Source Pertsik [7], International relations;
b Satellite view of Paris, Source https://en.m.wikipedia.org/wiki/Geography_of_Paris#/media/
File%3AParis_by_Sentinel-2.jpg

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In the 1970s, planning solutions were developed to streamline the urbanization
process in the Paris metropolitan area. These solutions included forming satellite
cities and developing an urbanized strip along the Seine toward Le Havre. However,
a more realistic approach was considered to be the restrained decentralization of
Paris. In 1994, a new development plan for the Île-de-France metropolitan region,
including Greater Paris, was adopted. The plan had three objectives: protecting the
environment, strengthening social cohesion and developing communication links.
The metropolitan region’s plan provided for the development of a polycentric structure, and this strategy was extended to the whole country in the form of creating
“metropolises of balance” to “pull” migrants seeking to move to the Paris region [8].
In 2008, a new general plan for the Île-de-France region was developed, a successor
to the 1994 plan (SDRIF).
In 2007, a new stage in the development planning of Paris began when French
President Nicolas Sarkozy proposed the idea of creating “Greater Paris” and commissioned ten teams of architects to develop plans for the development of Paris by 2030.
The projects varied in content but all focused on regional development and integrating the capital and its suburbs into a single entity. Proposals included decorating
the suburbs with artistic images, developing transportation, reforming administration, using environmentally friendly construction materials, expanding the forest
area around Paris and dedensifying the city center. Nowadays, Paris is becoming an
increasingly environmentally friendly capital city. The city is creating urban forests
and “cool islands” to combat the growing number of heat waves. Paris plans to
achieve carbon neutrality by 2050; the key to this goal is a universally recognized
vision of an environmentally and climate-friendly lifestyle [9].
Berlin (see Fig. 2). The federal city of Berlin is located in the heart of the state of
Brandenburg. On a European scale, the two regions already form a single economic
and living space. Since 1995, when a corresponding state treaty was concluded,
planning for the development of the states of Berlin and Brandenburg has been
carried out jointly. This treaty became the primary urban planning component of the
Strategic Development Plan for the Berlin-Brandenburg Region (1995–1998). The
treaty defines the region’s mission as ensuring a high quality of life and the coordinated territorial development of Berlin and Brandenburg as an integrated yet differentiated metropolitan area. The strategy’s urban development directions are: “Development of Social Infrastructure and Transport Networks”, “Preservation of Valuable
Landscape Areas and Waste Disposal”, “Rational Use of Territories”, “Restoration
of Industrial Zones” and “Renovation of Housing Stock”. Planning projects for the
central part of the district and the Berlin master plan were important for implementing
the Strategic Plan. The plan proposed a deconcentrated territorial planning model
for the joint development of the states, providing for the equalization of the interests
of Berlin, its suburbs and the periphery of Brandenburg.
Berlin is currently developing into an economic, scientific and cultural center.
The city is closely connected to its suburban zone. The outer territorial belt is known
as the Brandenburg periphery. This area is characterized by a combination of rural
areas and medium-sized cities that are important to the region. The most pressing

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Fig. 2 a Berlin development plan, Source Butko SO (2009) [10], AMIT; b Satellite view
of Berlin, Source https://glosbe.com/fb_img/980x980/8R459143_wikimedia_307444745032521
6292_Berlin-_Germany_-_Flickr_-_NASA_Goddard_Photo_and_Video1.jpg.cvrt.jpg.cvrt.webp

task is to stimulate the development of cities in this part of the region. The structural development plan for the central Brandenburg-Berlin region is based on the
concept of a multi-centered, resource-efficient development model. To this end, 26
“potential settlement sectors” have been identified and oriented toward a star-shaped,
radial network of highways that serve as settlement axes extending from the densely
populated center [8].
In 2019, Berlin developed an environmental justice concept as part of a pilot
project. Subsequently, the large-scale project “StadtNatur—Berlin and Ecology”
(High Art Bureau, 2020–2023) was implemented with the support of the Senate
Department for the environment, transport, and climate protection of the Federal State
of Berlin [11]. Today, Berlin has the largest ecological zone in Germany, covering
more than 10% of the city.
London (see Fig. 3). This city has a population of about 10 million with the first
inner metropolitan belt. London’s layout can be divided into several stages [7]. The
first stage is associated with Sir Patrick Abercrombie’s 1944 Greater London Plan.
This plan served as the basis for the development of the capital and its surrounding
area for 25 years. It also provided for the containment of suburban sprawl. The second
stage is characterized by the 1964 development of a project to create a second ring of
satellite cities around London. This project was based on strategic plans that proposed
developing large areas along the main radial transport arteries leading out of London.
The third stage covers the 1970s and 1980s, when planners focused on renovating old
areas of London rather than building new cities to halt population and job losses. In
1977, the government launched long-term partnership programs to support central
urban areas. The fourth stage began in 1993 when unified regional services were
created for all English regions, and structural plans for unified regional development
were constructed.
The current stage of planning for the capital city is characterized by the development and implementation of the London Strategic Development Plan for 2005–
2008. This plan is updated annually to address new issues and priorities [12]. This

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Fig. 3 a Map of London and the London metropolitan area, Source Pertsik [7], International relations; b Satellite view of London, Source http://www.auto-maps.com/maps/maps_of_europe/maps_
of_united_kingdom/london/large_detailed_satellite_map_of_london_city.jpg

strategic plan primarily focuses on developing London, but this development involves
regulating interactions with the environment. The plan’s structure: a mission and
values statement focusing on long-term economic growth, social justice and environmental protection—a main goal and three key themes focusing on equality, support
and health—tasks—programs and activities, including architectural and urban planning: “Green City and Urban Facilities”, “Accelerating Local Change” and “Work
Diversity Company”.
London is currently stepping up its efforts to combat the triple threat of traffic
congestion, air pollution and the climate emergency. Amid protests against environmental pollution and the destruction of the city’s green belt, London has set a goal
to achieve zero carbon emissions by 2030 [13].
New York City (see Fig. 4). It is the core of an agglomeration with a population
of about 20 million. New York City is also the largest metropolis in the Atlantic
Coast conurbation of the United States. This area is characterized by an extraordinary concentration of cities, which together have a population of over 38 million.
Although New York is located 250 km and 100 km respectively from the cities of
Boston and Philadelphia, the functional influence zones of these cities overlap and
are essentially joint. These megacities developed spontaneously due to the absence
of comprehensive plans and organizations to regulate their development. This also
applies to New York City. The Department of City Planning was established in 1927,
yet a development plan for New York City was not drawn up until 1967. The plan
was heavily criticized because it did not contain any specific prospects for the city’s
development and failed to consider the conflicting interests of various communities
[7].
A significant event in New York City’s urban planning was the New York City
2030 Plan (PlaNYC), a project initiated by Mayor Michael Bloomberg in 2007 [14].
The plan consisted of five sections related to water, electricity, transportation, air
quality and climate change. Particular attention was paid to land use issues and transforming New York City into the most comfortable and sustainable city in the world.

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Fig. 4 a New York City metropolitan area map, Source Pertsik [7], International relations; b Satellite view of New York City, Source https://upload.wikimedia.org/wikipedia/commons/4/4f/Aster_
newyorkcity_lrg.jpg

The project included measures to create a system of green spaces and landscape
complexes, modernize traffic, change the residential development and functional
zoning systems, reorganize New York City neighborhoods, create new residential
complexes and unique facilities. Numerous competitions were planned to select the
most original architectural and artistic solutions.
Today, New York City’s open spaces are diverse, and the parks managed by the
New York City Department of Parks and Recreation (NYC Parks) are vast. In 2016,
New York City planted its millionth tree as part of the MillionTreesNYC initiative,
which began in 2007 as part of PlaNYC. The city continues its efforts to expand
and strengthen urban forestry. In 2023, the New York City Council passed a bill to
achieve 30 percent tree canopy coverage, in line with PlaNYC’s goal [15].
Tokyo (see Fig. 5). Tokyo Prefecture is home to approximately 15 million people.
In recent years, it has become one of the world’s largest financial centers. It is also
Japan’s main transportation hub, boasting two international airports. High-speed
rail lines and expressways converge in the city, where overpasses and complex,
multi-level interchanges have been built through densely populated neighborhoods.
Projects addressing Tokyo’s territorial development issues began in earnest in the
1960s when its suburbs and satellite cities reached the administrative boundaries of
the metropolitan prefecture. Approximately 100 km west of Tokyo lies Mount Fuji,
the city’s landscape landmark and symbol. Some urban planners proposed creating

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Fig. 5 a Tokyo development map, Source Tateishi (2023) [16], Springer; b Satellite view of Tokyo,
Source https://en.m.wikipedia.org/wiki/Tokyo_Bay#/media/File%3ATokyo_Bay_by_Sentinel-2%
2C_2018-10-30.jpg

an axis for the linear development of the city towards Mount Fuji. However, other
experts disagreed, proposing to expand Tokyo by developing the bay instead. In 1960,
K. Tange presented his conceptual “Tokyo Master Plan for 2000”, which centered
on the idea of a “coastal city”. This concept was considered radical and fantastic.
Twenty years later, Tange proposed a more realistic project.
By the end of the twentieth century, two trends in Tokyo’s urban development had
emerged. The first was the development of Greater Tokyo, as described by O. Atsushi
in 1989. The second was the linear development of the city toward a new satellite city,
with Mount Fuji as a dominant landscape feature. By the beginning of the twenty-first
century, Tokyo’s development direction had been determined: eastward, including
Chiba, Lake Imabashi and the new Narita International Airport. This work is being
carried out within the Tokyo agglomeration, which is part of the Tokai conurbation
(similar to a North American megacity) stretching 500 km along the southern coast of
Honshu Island. Tokyo is currently implementing environmental measures to promote
sustainability. The city is applying the Japanese martial arts concept of “shin-gitai”—“mind, skill, and body”—as well as the modern-city version of “changing
consciousness, technological innovation, and administrative systems”. For instance,
Tokyo plans to substantially increase the number of zero-emission vehicles by 2050.
To this end, the government is supporting environmental technologies [17]. The
Tokyo government is also paying great attention to biodiversity conservation and
greening. As part of the Tokyo Bay eSG project, they have chosen the Takeshiba
area, which overlooks Tokyo Bay, as a focus area [18].

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4 Summary of Experience in Urban Planning Regulation
of Sustainable Development of the World Cities
Key areas of planning for world cities include: (1) identifying “geopolitical axes
of development” and considering regional conditions; (2) developing a polycentric
structure; (3) defining the city’s vision and mission while taking into account its
unique characteristics; (4) creating a system of high-speed rail and motorways; (5)
defining areas of common interest; (6) paying increased attention to architectural and
artistic solutions and the city’s image; (7) using innovative approaches and forming
a system of unique architectural and landscape complexes.
The world cities under consideration have two things in common: the method of
constructing suburban concentric rings that regulate active expansion up to territories
adjacent to the suburban zone [2], and interaction with the regional settlement framework using radial highways. Thus, London was organized into four concentric rings,
characterized by a gradual loosening of the center, the creation of satellite cities, a
“green belt” and agricultural land. The same is true for the planning of Paris and the
Île-de-France region. In 1994 and 2008, “green plans” were established, including a
“green belt”, a “rural crown” and a network of green areas opposed to development.
Germany’s experience is similar: the 1994 Berlin Land Use Plan and its updated
versions distinguish two suburban belts with “green wedges” [19]. New York City’s
development exemplifies the interaction between water and land (a series of islands)
and the dispersed development of green areas. Tokyo has 23 special, administratively autonomous districts around which satellite cities are located. These cities
merge into a single urbanized zone surrounded by a ring road. Beyond the ring road,
the landscape becomes rural.

4.1 About Current Trends in Sustainable Development
Current trends in sustainable development are linked to societal changes resulting
from the COVID-19 pandemic, political shifts leading to the polarization of public
opinion, the accelerated digitalization of society and the development of “smart”
urban planning systems. These trends also include the accelerated scientific and technological development and a special focus on the biosphere, the comfort and quality
of urban environments, the innovativeness of world cities [13, 20]. Ratings of innovative attractiveness show the competitive advantages of world cities with the highest
concentrations of leaders in scientific and technological development, creative industries and quality of the urban environment. London ranks first overall, followed by
New York City in second, Tokyo in third, Paris in sixth and Berlin in fifteenth [21].
The future development prospects for world cities lie in their transborderness [8, 22,
23] and the formation of a “global city” [2].

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4.2 Possibilities for Urban Planning Interpretation
of Sustainable Development of the World Cities
In order to achieve sustainable development goals in urban planning regulation,
three components must be applied: (1) regulatory component in connection with
current legislation; (2) methodological component—describing the basic principles,
procedures, methods, and techniques for forming design solutions; (3) technological
component—describing the algorithms for preparing urban planning documents.
Urban planning also considers two groups of characteristics used to solve tasks
related to urban regulation (aspects of sustainable development are indicated in
brackets): the first group relates to studying natural conditions and comprehensively
assessing the territory (factor-based identification of potential); the second group
relates to planning characteristics, such as the territory’s suitability for settlement
(sociocultural aspect), location of production facilities (socioeconomic aspect), organization of public recreation areas (ecological aspect) and transport accessibility of
territories (functional aspect) [24]. When solving urban planning problems related
to the first group of criteria, it is necessary to restrict the use of territories based on
sanitary and hygienic conditions. For the second group, the systematic development
of territories must be subordinated to the overall plan [24].
Solving sustainable development problems from an urban planning perspective
involves coordinating traditional and innovative regulatory tools to ensure a transition
to advanced development.

5 Conclusions
The theoretical conclusions of the study address the issue of creating a model for
urban planning regulation to promote the sustainable development of the world cities:
1. In modern urban planning, normative, methodological and technological components are distinguished by analogy with the spheres of legal and economic regulations and the theory of synergistic management. However, the priority of a
culture of compliance with sustainable development goals as urban planning
directives establishes the need to consider the ethical component first and foremost. In urban planning, this component is implemented in strategic goal setting.
This enables the progressive development of the urban planning system and the
implementation of a new sociocultural approach to spatial organization.
2. In the urban development of world cities, the forecasting system should be determined in connection with sustainable development goals, the program system—
with spatial development methodologies set by urban planning theory, the system
of plans—with standards and urban planning policy, the system of projects—
with modern technologies that reveal potential and determine the algorithm for
inheriting territorial planning documents.

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The study’s practical conclusions relate to limiting hyper-urbanization, ensuring
environmental efficiency and comfort, improving environmental quality and diversity, shaping the architectural and urban appearance of the world cities:
1. In the context of sustainable development goals, urban regulations for the world
cities require new rules that treat the city center as a separate urban planning
system (core). This system includes a zone of common interests (intermunicipal
cooperation) in areas adjacent to the suburban zone of the world city (the “interframe space” [2]) as well as the following components of the suburban zone: an
urbanized belt around the core, a green belt around the city, areas for settlement
and service facility placement. The hierarchy of these components should be
built according to their importance.
2. Under the new regulations, urban development must correspond to the division of
world city territories and landscapes into zones: residential and public-business
zones of various types; industrial zones, including engineering and transport
infrastructure; agricultural and recreational zones, including agricultural land,
water bodies, urban forests, parks, and horticulture; zones of particularly valuable territories of environmental, historical, cultural, or aesthetic significance;
special-purpose zones; other territorial zones occupied by facilities that cannot be
located in other zones (this division must take into account local land ownership
characteristics).
In conclusion, the updating of urban planning regulation of sustainable development after 2030, in conjunction with establishing new goals, should be approached
systematically. Further research may focus on constructing sociocultural goals for
sustainable development or shaping the architectural and artistic image of the world
cities.

References
1. Doxiadis CA (1968) Ecumenopolis: tomorrow’s city. Britannica book of the year 1968.
Encyclopedia Britannica Inc., London, pp 16–38
2. Kositskiy YaV (2005) Architectural and planning development of cities. Arkhitektura-S,
Moscow
3. Transforming our world: the 2030 agenda for sustainable development (2015) United nations
general assembly, Le Bourget. https://sdgs.un.org/publications/transforming-our-world-2030agenda-sustainable-development-17981. Accessed 15 June 2025
4. Hall P (1966) The world cities. Weidenfeld & Nicolson, London
5. Globalization and world cities (GaWC) research network (2025) Loughborough University,
Loughborough. https://gawc.lboro.ac.uk/. Accessed 15 June 2025
6. Archer JC (2005) Suburban Planning. In: Sennott RS (ed) Encyclopedia of twentieth century
architecture, vol 3 (P–Z). Fitzroy Dearborn Publishers, NYC-London
7. YeN P (1999) Cities of the world: geography of global urbanization. International Relations,
Moscow
8. Belokon YuN (2003) Regional planning (theory and practice). Logos, Kiev
9. L’Appel de Paris (2015) Paris Pledge for Action #COP21. University of Cambridge,
Cambridge.
https://www.corporateleadersgroup.com/reports-evidence-and-insights/newsitems/lappel-de-paris-paris-pledge-for-action. Accessed 15 June 2025

Urban Planning Regulation of Sustainable Development of the World Cities

531

10. Butko S (2009) Perspectives of the circular railways and their adjacent territories. Archit Mod
Inf Technol 2(7), Article 06. http://marhi.ru/AMIT/2009/2kvart09/Butko/Article.php
11. StadtNatur—Berlin i Ekologiya (2023) High art bureau, Berlin. https://highartbureau.com/pro
jects/stadtnatur-берлин-и-экология/?lang=ru. Accessed 15 June 2025
12. Makhnovskiy DYe (2016) Globalization and the development of the world cities network. The
Age of Globalization 19:57–70
13. Global cities convene in london to tackle triple threat of congestion, air pollution and the climate
emergency (2022) C40 Cities, London. https://www.c40.org/news/global-cities-london-tacklethreat-congestion-pollution-climate-emergency/. Accessed 15 June 2025
14. PlaNYC—Plan “New-York City 2030” (2009) Prian.Ru, St Petersburg. https://prian.ru/pub/
14829.html. Accessed 15 June 2025
15. Schmitt C (2023) In the City, a million trees take root. In: Northern woodlands. https://northe
rnwoodlands.org/articles/article/nyc-million-trees. Accessed 15 June 2025
16. Tateishi E (2023) The spatiotemporal socio-demography of the Tokyo capital region: a datadriven explorative approach abstract Zusammenfassung. Rev Reg Res 43(3):467–519. https://
doi.org/10.1007/s10037-023-00198-1
17. Tokyo and Paris: global leaders in clean air, clean cities and climate action (2018) C40
Cities, Tokyo. https://www.c40.org/news/tokyo-and-paris-global-leaders-in-clean-air-cleancities-and-climate-action/. Accessed 15 June 2025
18. Tokyo government decides to revitalize coastal areas (2023) Social war ecology—real and
imaginary problems. IA Krasnaya Vesna, Moscow. https://rossaprimavera.ru/news/419c985c.
Accessed 15 June 2025
19. Miller VV (2009) Land management in Bavaria. Land Manag Cadastre Land Monit 1:56–58
20. Rodoman BB (2021) Polarized landscape”: Half a century later. Izvestiya RAN Seriya
Geograficheskaya 85:467–480. https://doi.org/10.31857/S2587556621030122
21. Higher school of economics global cities innovation index (2024) Institute for statistical studies
and economics of knowledge. National Research University Higher School of Economics,
Moscow. https://gcii.hse.ru/. Accessed 15 June 2025
22. Chow CKW, Tsui WHK (2019) Cross-border tourism: case study of inbound Russian visitor
arrivals to China. Int J Tour Res 21:693–711. https://doi.org/10.1002/jtr.2297
23. Shabiev SG, Kolyasnikov VA, Nadymov II, Bronnikova AA (2024) the architectural and planning potential of the development of the city of Blagoveshchensk. In: Proceedings of the 8th
international conference on construction, architecture and technosphere safety (ICCATS 2024),
Lecture notes in civil engineering (LNCE), vol 565, pp 383–393. https://doi.org/10.1007/9783-031-80482-3_37
24. Kamenskiy VA, Vaytens MYe, Vasilevskiy MI (1963) Suburban areas of large cities. Government Publishing House of Literature on Construction, Architecture and Building Materials,
Leningrad, p 148

Smart Urban Spaces: Current Situation
and Insights for Future in Russia
G. A. Ptichnikova and O. A. Antyufeeva

Abstract The development of information and computer technologies, starting from
the second half of the twentieth century and rapidly continuing in the twenty-first
century, is closely related to their penetration into the world of human living space.
This rapid invasion leads to the complication of the volumetric-spatial organization
of the urban environment, changes in the visual appearance of the city, and transformations in architectural activity. The purpose of the study was to identify the
problems of implementing the “smart city” concept and the features of the formation of “smart spaces” in a number of Russian cities in the Volga region—Samara,
Volzhsky, Volgograd. The article reveals various aspects of the developed projects
of smart urban spaces. The authors identified difficulties in the spread of new urban
spaces, including the commercial focus of digitalization of cities, unpreparedness for
the introduction of new technologies of the historically established urban structure
and development, the unpreparedness of part of the urban community for widespread
digitalization.
Keywords Smart urban space · Smart city · Urban planning · Information
technologies

G. A. Ptichnikova (B)
Scientific Research Institute of Theory and History of Architecture and Urban Planning, Branch
of the Central Institute for Research and Design of the Ministry of Construction and Housing and
Communal Services of the Russian Federation, Moscow, Russia
e-mail: grado_v34@mail.ru
O. A. Antyufeeva
The Volgograd State Technical University, Volgograd, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_42

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1 Introduction
The rapid introduction of information technologies into the spaces of human activity
currently leads to the complication of the spatial organization of the urban environment, changes in the visual appearance of the city, and transformations in architectural activity. One of the achievements in urban planning theory of the 1990s
was the idea of creating a “Smart City”, a city whose management and operation is
carried out by collecting and processing big information data, primarily in such areas
as management, housing and communal services, urban public transport, lighting,
energy consumption, public and environmental safety systems, and a system of social
services. In this regard, research related to the need to revise the eternal object of
architectural transformation—the very space of human habitation, namely, the space
of the city and its public spaces, is becoming relevant.
This article examines the problems of implementing the concept of “smart
city” and the prospects for the development of “smart urban spaces” created and
functioning on the basis of information technology.
The object of the study was “smart cities” and “smart urban spaces”. Including
the study of both newly built “smart cities” (in Skolkovo and Innopolis in Russia),
and historically established cities that are intensively adapting to the parameters and
infrastructure of “smart cities”.
The problem of studying new phenomena in a modern city in the conditions of the
information society is the subject of research by a number of domestic and foreign
specialists. The use of “big data” in urban planning, the issues of introducing “smart
city” technologies in existing cities and the creation of new “smart cities” were
considered in the works of domestic scientists G.V. Esaulov, S.N. Maksimov, N.A.
Kolodiy, V.P. Kupriyanovskiy. Social and information exchanges and interactivity
of the urban environment were studied by M. Klodel, K. Ratti, M. McGuire, R.
Sennett, R. Kitchin, A. Greenfield, W. Sengupt and others. In Russia, there are several
organizations, including the Ministry of Construction of the Russian Federation,
the Higher School of Economics, Skolkovo, ITMO (St. Petersburg), Moscow State
University, the Center for Strategic Research “North-West”, Rostec, Rosatom and
a number of others, which are conducting research into the implementation of the
“smart city” concept in Russian reality.

1.1 Problem
The term “smart city” is vague, but in general it has come to mean a city that makes
intensive use of a variety of information technologies for the effective functioning
of all its services and systems [1]. In UN documents, a smart city is defined as
“an innovative city that uses information and communication technologies and other
means to improve the standard of living, the efficiency of urban activities and services,

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535

and competitiveness, while meeting the economic, social, cultural and environmental
needs of present and future generations” [2].

1.2 Theoretical Part
An analysis of theoretical works devoted to the topic of the “smart city” showed
that unified approaches to understanding this type of city are still being formed [3].
Thus, the Russian urbanist V.L. Glazychev noted that the “smart city” is an attempt
to reform cities in accordance with the needs of modern society”, emphasizing the
social demand for urban transformation as information technologies are introduced
into human life [4]. Nevertheless, during the period of implementation of this concept,
there is little clarity about how a “smart city” differs from a “non-smart city”, except
for the presence of surveillance cameras, sensors, accessible Internet, smart phones
in the hands of city dwellers and applications in them, as well as analytical centers
where information flows, at first glance. Russian sociologist K.A. Puzanov notes that
a simplified, technocratic view of smart cities currently prevails, creating an illusory
notion of an instantaneous resolution of urban problems through the widespread
implementation of the smart city concept. Demand creates supply, and an entire
industry of “smart cities” appears [5].
American researcher A. Greenfield wrote about the great verbosity on the topic
of “smart cities”, but the scant specific information: “This whole idea as a whole
remains discouragingly poor in terms of specifics. Anyone who tries to understand
where it leads—out of abstract interest or in application to specific local issues—is
faced with the fact that there is very little solid information: basically, he has at
his disposal press releases of companies pursuing their own interests, and flattering
articles in blogs” [6]. Irish professor R. Kitchin insists that “technocratic ideas that
promote the achievement of convenience and comfort in the urban environment
through IT systems and technologies prevail in the interpretation of the content of
the “Smart City” concept” [7]. In the dominant development discourse on “smart
cities”, studies are most often conducted on multipliers of economic benefits from
“smart city” projects or the distribution of these economic benefits.

2 Research
Projects to transform cities into “smart cities” have become relevant in Russia in
recent years. How is this concept being implemented in our country? In Russia, the
rapid movement towards “smart cities” began in 2018, when the Russian Ministry of
Construction adopted the “Smart City” standard, in which it presented its vision of
the [8] concept. This work identified nine main areas, among which was mentioned
such an area as “innovations for the urban environment”, i.e. what concerns architects
directly.

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To implement the project, the Russian Ministry of Construction first concluded
agreements with 19 pilot cities from 11 regions of Russia, within the framework of
which the introduction of information technologies into the infrastructure of these
cities began. Currently, the number of cities in which the “smart city” concept is
being implemented to one degree or another exceeds 200 populated areas. In 2019,
together with Moscow State University, the Russian Ministry of Construction developed the “IQ cities” index, formed to determine the effectiveness of digitalization,
technological solutions and services that are being implemented in Russian populated areas. In 2024, the top five places among the largest cities were occupied by
Moscow, St. Petersburg, Kazan, Yekaterinburg and Perm [8].
Experts note that in Russia there is a “transition from the smart city model to a
new model of “human-oriented smart city” (Human Smart City, HSC) or “humane
smart city” with the active involvement of people in the process of digitalization of
urban spaces” [9]. However, there is no clear decision on what kind of “smart city”
Russian society needs. In this regard, it is appropriate to cite the results of a study
by Russian sociologists from the National Research Tomsk Polytechnic University.
The study included a discourse analysis of online statements about the prospects for
implementing the “smart city” concept in Russia [9]. For our study, from the general
results obtained by Tomsk sociologists, we will highlight three models of the “smart
city” that are currently receiving support. The first model is technocratic, which
proposes to use more and more new digitalization technologies, which, according
to the adherents, will help overcome the digital inequality of Russian cities. This
model is promoted by IT companies, IDC Russia and the CIS, corporations such as
CEO SmartyCRM.ru. The second model is more interesting from the point of view
of spatial planning development of cities. The basis of this model is the formation of
a polycentric structure of cities to create separate “smart districts” both in the central
parts of the city and in the suburbs. Federal, regional and municipal authorities
support this model. The last model is associated with the implementation of the
humanistic model of a smart city, with the active participation of the local population.
Representatives of various public organizations support this model.

2.1 “Smart urban spaces” in Russian Cities: New Projects
In this section, we will analyze how “smart urban spaces” are formed and what types
of smart spaces are currently appearing in cities. We studied project proposals for the
creation of smart spaces in cities—regional centers of the Volga region—Samara,
Volzhsky, Volgograd.
An analysis of dozens of urban spaces declared as “smart” showed that for the
“smartization” of a traditional city square or street, they must be saturated with
various information technologies. The information infrastructure of a “smart square”,
“smart street” or block must include free access to the Internet (WiFi). This can also
include a mobile application for rapid response, installed on a smartphone. Additional
elements of a “smart space” are electronic information boards located on it. Elements

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Fig. 1 Media square in Volgograd. Project by O. Chernichkina, manager G. Ptichnikova a plan;
b visualization

of urban design (urban furniture, small architectural forms, fountains, etc.) can also
be “smart” (Fig. 1). They become part of the information structure, interactive or
media objects, complementing this new urban environment [10].
One of the domestic examples of the implementation of the “smart city” concept
to the city space was shown by a project in the Samara Region, which was included as
a pilot site in the federal program “Smart City. Successful Region” [11]. The project
proposed the creation of several types of spaces: “smart block”, “smart street”, “smart
square” (Fig. 2). These “smart spaces” are concentrated in the historical center of
Samara, which was considered, according to the project, as the main zone of urban
development transformations. In particular, the changes should affect the central city
square and Khlebnaya Square.
An example of the creation of large smart spaces based on a historical monument
is the revitalization project of the “hydro builders’ town” in the city of Volzhsky,
Volgograd Region. The project proposes, in combination with general measures, the
formation of elements of the Smart City information system to service the tourist
route (Fig. 3). The terminals are located near the most significant buildings that are
part of the “hydro builders’ cities” complex.

Fig. 2 Placing smart urban spaces in the historical center of Samara. Types of spaces: “smart
block”, “smart street”, “smart square”. Project by E. Akhmedov, T. Vavilonskaya

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Fig. 3 Implementation of smart city elements information system into the historical planning
structure of the city of hydro builders. Plan. Project A. Golovchenko, leader G. Ptichnikova

In addition to universal ones, there is a wide variety of specialized “smart spaces”
designed for a particular group of consumers. We can immediately highlight the
focus on differentiation by age, namely playgrounds for children and for the elderly.
In Russia, the topic of developing “smart urban spaces” for children has been actively
discussed since 2022. “Smart playgrounds” were announced as a new and necessary
component of the urban environment. The main functions of such playgrounds are
educational and play activities. Some playgrounds can be an open-air museum, where
children can touch everything with their hands, and in the game with the help of
special devices study history, physical laws and other phenomena. The main users
of these playgrounds are expected to be younger schoolchildren under 12 years old.
The first “smart playgrounds” appeared in Sochi, Simferopol and a number of other
cities. An example of the implementation of this new trend is the construction of a
“smart playground” in Volgograd during the reconstruction of Metallurgov Avenue
(Fig. 4).
Specialized smart spaces also include such objects as sports parks and inclusive
playgrounds designed for people with various diseases. An example is the playgrounds with smart exercise machines in the Central Park of Culture and Leisure in
Volgograd.
An analysis of “smart urban spaces” in Russian cities allowed us to identify objects
related to information technology:

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Fig. 4 Smart playground in Volgograd. Project

• Smart urban lamps (lanterns) that allow you to adjust the lighting depending on
various factors.
• Smart urban furniture, which integrates various sensors, digital displays, Wi-Fi
access points,
• Information screens, panels, boards, boxes, kiosks;
• Small architectural forms;
• Smart exercise machines;
• Various fencing elements, including those with sound accompaniment (for the
blind and visually impaired);
• Garbage containers and urns;
• CCTV cameras;
• Sensors, including fire-prevention ones.
An assessment of new trends in the development of “smart elements” of the urban
environment shows great interest in the design of innovative urban furniture. In
Russia, the “smart bench” Smartchain version 3.0 is popular, which can operate in
interactive modes “Games” or “Drawing”, controlled by a special application. Smart
benches can become a new object for street art experiments or be used as a notice
board. In other words, in an innovative approach to urban design, “smart benches”
occupy a central place, improving public spaces such as parks, squares, bus stops,
train stations, airports, etc.

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2.2 Challenges to Developing Smart Cities and Smart Urban
Spaces
The implementation of the “smart city” concept is underway in various countries
around the world at the national level. However, the “smart city” programs being
implemented are poorly adapted to the real cities that they are penetrating with such
ease. Regardless of which city we consider, Moscow, Milan, Barcelona, Songdo,
the same solutions are observed everywhere: smart parking, smart transport system,
waste disposal, energy saving, lighting. B. Cohen emphasizes that “the smart city
concept is a successful idea of globalism, pushed by transnational corporations and
IT companies” [12]. The high cost of total urban digitalization, the unpreparedness
of the historically established urban structure and development, as well as, let’s be
honest, the unpreparedness of society and the reluctance of city residents to use
constantly updated technologies and numerous applications are becoming serious
obstacles to smart transformations of cities [13]. Cyber security, data privacy and
system vulnerability issues are also additional risks and require special attention when
implementing such projects. And most importantly, the dependence on technical
systems can lead to potential failures and operational problems when problems arise
in the city’s power supply system.
We would like to emphasize the social problems of the expansion of the “smart
urban environment”. Some researchers argue that as cities become smarter, the
process of “dumbing down” people is accelerating due to the loss of control over how
the city is used [13–15]. Humanity does not need to “make an effort to get something
necessary for itself, as a result, a person stops thinking” [16].
Considering the “smart public spaces” of cities, which have been growing in
number in the last 10–15 years, in the same critical aspect, let us ask ourselves
whether the urban environment has become smarter than it was before? The answer
is obvious. No, it has not. Yes, public transport and parking are improving, energy
saving and waste disposal systems are becoming more efficient, and the safety of the
urban environment has increased due to the operation of surveillance cameras. But
is this enough to say that urban public spaces and the urban environment as a whole
have suddenly become “smarter”? “Smart urban furniture,” which is truly becoming
an innovative component of the urban environment, is too expensive to completely
replace traditional benches.

3 Сonclusion
The practice of the last two decades has shown the problems of implementing the
concept of a “smart city” in the life of modern cities. Often, the discussion of the
topic of “smart cities” is focused on the use and implementation of increasingly
new technologies, and not on city residents and not on how the new appearance
of cities will be formed. The experience of the functioning of “smart cities” shows

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that among the negative consequences are “point digitalization”, failure to achieve
the “network effect”; when “digitalization is not a driver, but a consequence of
the development of a separate region and thus does not implement the scenario of
equalizing the development of less resourceful regions and accelerated growth in
their quality of life” [9]. Further implementation of the concept of “smart cities” can
increase inequality and marginalization of society.
“Smart urban spaces” are variations of the information technology model of
modern public spaces of megacities, taking shape and intensively developing in the
context of digital culture. Examples of such technologies include energy management systems, street lighting based on motion sensors, wireless Internet access, and
systems for monitoring the situation in squares. At the same time, the external forms
of urban space remain recognizable, not showing their electronic filling to the outside.
Among the trends in the development of urban smart spaces, we will highlight their
increasing specialization: by demographics (for children and the elderly), for people
with limited mobility and the disabled. At the same time, universal urban spaces are
also developing. The modern Idée fixe lies in the subordination of the living environment, cities and settlements to artificial intelligence and digitalization. At the same
time, we would like to say that humanity in its passion for creating “smart cities”
may after some time face unexpected consequences that will affect not the artificial
habitat, but human abilities. This is orientation in space, knowledge of one’s place of
residence, connection with the natural world, the ability to communicate with each
other. So perhaps it is a good thing that “smart cities” and “smart urban spaces” have
not yet become smarter than the citizens themselves.

References
1. Esaulov GV (2017) “Umny’j” gorod v cifrovoj e’konomike (Smart City in the digital economy).
Academia Architecture and construction 4:68–74
2. The UNECE—ITU Smart Sustainable Cities Indicators (2015) United Nations, Economic
and Social Council. https://unece.org/housing/smart-sustainable-cities#:~:text=UNECE%20a
pproach%20to%20Smart%20Sustainable%20Cities&text=This%20means%20reducing%20g
aps%20in,cities%20more%20conducive%20to%20innovation Date. Accessed 15 Jun 2025
3. Ratti K, Klodel M (2018) Gorod zavtrashnego dnya: sensory‘, seti, xakery‘ i budushhee gorodskoj zhizni (the City of tomorrow: sensors, networks, hackers and the future of urban life).
Institut Gajdara Press, Moscow, p 239
4. Ivanova EG (2018) “Umnaya” transformaciya gorodov: vozmozhnosti i riski: prezentaciya
(Smart Transformation of Cities: Opportunities and Risks: Presentation). https://social.hse.ru/
data/2018/03/05/1165848180/%D0%9B%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%
205.pdf. Accessed 15 Jun 2025
5. Puzanov KA, Shubina DO (2019) “Umny’j gorod” ili “umnost‘” goroda: e’ffektivnost‘
ispol’zovaniya gorodskix innovacij v SShA (“Smart City” or “Smartness” of the City: the
effectiveness of using urban innovations in the USA). Urban Res Pract 4(1):29–42
6. Greenfield A (2013) Against the smart city. Do Publications, New York
7. Kitchin R (2014) The real-time city? Big data and smart urbanism. GeoJournal 79(1):1–14
8. Vedomstvenny’j proekt (2025) “Umny’j gorod” (Departmental project “Smart City”). Proektnaya direkciya Minstroya Rossii (Project Directorate of the Ministry of Construction of Russia).
https://pdminstroy.ru/vedomstvenniy-proekt-umniy-goro. Accessed 15 Jun 2025

542

G. A. Ptichnikova and O. A. Antyufeeva

9. Kolodij NA, Ivanova VS, Goncharova NA (2020) Umny’j gorod: osobennosti koncepcii, specifika adaptacii k rossijskim realiya (smart city: features of the concept, specifics of adaptation
to Russian realities). Sociol J 26(2):102–123
10. Kitchin R (2015) Data-driven, networked urbanism: the programmable City. Working paper
14, 2015. August 10. Http://www. spatialcomplexity.info/files/2015/08/SSRN-id2641802.pdf.
Accessed 15 Jun 2025
11. Ahmedova EA, Vavilonskaya TV (2019) Principy‘ poe’tapnoj reorganizacii arxitekturnoprostranstvennoj struktury‘ gorodskoj sredy‘ na osnove innovacionny’x texnologij (principles
of phased reorganization of the architectural and spatial structure of the urban environment
based on innovative technologies). Urban development and architecture 9(2):68–79
12. Cohen B (2024) The top 10 smart cities on the planet. Co. design. https://www.fastcodesign.
com/1679127/the-top-10- smart-cities-on-the-planet. Accessed 15 Jun 2025
13. Cohen B (2012) What exactly is a smart city? Fast co.Exist. Sept 19. https://www.fastcoexist.
com/1680538/what-exactly-is-a-smart-city. Accessed 15 Jun 2025
14. McGuire M (2018) Beyond flatland: when—smart cities make stupid citizens. City, territory and architecture. No. 5 (22). https://cityterritoryarchitecture.springeropen.com/articles/
10.1186/s40410-018-0098-0#citeas. Accessed 15 Jun 2025
15. Sennett R (2012) The stupefying smart City. Urban age electric City http://opentranscripts.org/
transcript/stupefying-smart-city. Accessed 15 Jun 2025
16. Yakushina OI (2021) Organizaciya social’nogo prostranstva sovremenny’x gorodov v svete
koncepcij “Otkry’Togo” i “umnogo” goroda (organization of social space of modern cities in
light of the concepts of “open” and “smart” city). Theory Pract Soc Dev 4(158):33–42

Principles and Methods of Forming
the Architectural and Artistic Image
of Cities and Urban High Responsibility
Infrastructure Objects: Formation
Principles Using QUANТUM
CERAMIC/QUANТUM PARUS
Composite Materials (Safety, Aesthetics,
Regulations)
A. V. Fedorchenko, V. A. Gutnikov, P. V. Parabin, D. O. Presniakova,
and V. E. Kolpakov

Abstract The paper explores the principles and methods for the application of advanced composite materials—specifically QUANTUM CERAMIC and
QUANTUM PARUS—in shaping the architectural and artistic appearance of highresponsibility infrastructure facilities (HRIFs). The aim of the study is to assess the
potential of composites in addressing safety, aesthetic, and functional challenges
in urban environments. The methodology is based on an interdisciplinary approach
integrating urban planning, architectural-structural analysis, and materials science.
The research examines the structural and visual characteristics of the materials and
their implementation in high-density urban contexts, including historical and cultural
zones. It has been established that the use of composite panels contributes to reduced
heat loss, improved acoustic insulation, enhanced resistance to aggressive environmental conditions, and effective visual integration within complex urban fabrics.
A. V. Fedorchenko (B)
PI Research Institute “National Project” LLC, Moscow, Russia
e-mail: 89099804106@yandex.ru
V. A. Gutnikov
FSBI TSNIIP of the Ministry of Construction of Russia, Moscow, Russia
P. V. Parabin
High-tech Scientific Research Institute of Inorganic Materials named after Academician A. A.
Bochvar (JSC VNIINM), Moscow, Russia
D. O. Presniakova
New World Agency, Department of Digital Communications and Social Media, Moscow, Russia
V. E. Kolpakov
PLS «Transmost», St. Peterburg, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_43

543

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A. V. Fedorchenko et al.

The study proposes architectural integration principles, including material selection
criteria, strategies for cultural context adaptation, and facade expressiveness. The
findings support the inclusion of such materials in the design practices of HRIFs as
a scientifically justified tool for the sustainable and visually coherent development
of urban infrastructure.
Keywords Composite materials · Quantum ceramic · Quantum parus ·
Architectural expression · High-responsibility infrastructure · Urban planning ·
Historical and cultural environment

1 Introduction
The formation of the architectural and artistic identity of contemporary cities is one
of the key directions of sustainable urban development, situated at the intersection
of architecture, engineering, urban studies, and materials science [1, 2]. Of particular significance in this process are high-responsibility urban infrastructure facilities
(HRUIF), such as transport hubs, critical communication complexes, public and
cultural centers, and high-tech industrial structures, including those related to the
nuclear sector. These structures not only fulfill essential functional roles but also
shape the visual identity and architectural expressiveness of the urban environment,
often acting as dominant elements in the spatial composition of the city [3, 4].
Amid growing global challenges—climate change, increasing technogenic and
biological threats, and stricter requirements for sanitary, hygienic, and radiation
safety—the demand for innovative building materials capable of ensuring multiparameter resilience of HRUIF is becoming increasingly urgent [5, 6]. Traditional
materials (such as concrete, brick, and steel) are increasingly insufficient in terms of
energy efficiency, corrosion resistance, maintainability, architectural plasticity, and
environmental neutrality.
In this context, new-generation composite materials, featuring enhanced performance and aesthetic qualities, are attracting growing interest [7–9]. In particular, metal-ceramic panels QUANTUM CERAMIC [10] and aluminum honeycomb
panels QUANTUM PARUS [11] offer effective solutions that combine high strength
and low weight, resistance to UV radiation, thermal fluctuations, and aggressive
environments, along with wide possibilities for artistic treatment and decorative
finishing. These materials meet modern international standards (LEED, BREEAM)
and comply with domestic regulations (SNiP, SP), making them highly suitable for
application in HRUIF.
The scientific and practical relevance of this research is determined by several
factors. First, there is an exponential increase in the number of high-responsibility
infrastructure projects in urban agglomerations that require comprehensive architectural and environmental solutions. Second, there is a need to integrate innovative materials into both historical and contemporary architectural contexts without

Principles and Methods of Forming the Architectural and Artistic Image …

545

compromising the cultural and visual identity of cities. Third, there is a lack of scientifically grounded methodologies for applying composite materials in the architecture
of HRUIF—particularly in relation to aesthetics, regulatory safety, and sustainable
design.
The aim of this study is to develop principles and methods for the application of high-performance composite materials (using QUANTUM CERAMIC and
QUANTUM PARUS as case studies) in shaping the architectural and artistic identity of high-responsibility infrastructure facilities, taking into account their structural,
aesthetic, and regulatory characteristics.
To achieve this aim, the following research objectives were formulated: analyze
the architectural requirements for HRUIF in the context of contemporary urban planning practice; investigate the structural, physical-technical, and regulatory characteristics of the composite materials QUANTUM CERAMIC and QUANTUM PARUS;
assess the potential of these materials in ensuring the safety, resilience, and functional performance of HRUIF; develop approaches for the architectural integration
of composites into both historical and modern urban contexts; substantiate methodological principles for the selection and application of high-tech cladding materials
in the design of HRUIF.

2 Literature Review
The study of principles for shaping the architectural and artistic identity of highresponsibility infrastructure facilities (HRUIF) using composite materials is carried
out within the framework of an urban planning paradigm [12–16], which emphasizes systemic design of the urban environment and integration of infrastructure into the city’s morpho-structural fabric. It also draws upon an architecturalstructural approach [17–20], where compositional and spatial-planning solutions are
considered inseparably linked with the technical characteristics of the materials used.
Despite the growing interest in composite materials within contemporary urban
planning practice [21–24], their application in shaping the architectural and artistic
expression of HRUIF remains insufficiently theorized. Existing scientific and practical literature tends to prioritize engineering and physicochemical properties of materials—such as strength, resistance to aggressive environments, fire safety, and durability [25, 26]. In contrast, aesthetic-compositional, urban planning, and sociocultural
aspects of composite material application, particularly within the HRUIF context, are
often addressed fragmentarily or remain peripheral in academic discourse. Several
scholars emphasize [27, 28] that façade cladding solutions should go beyond technical precision and incorporate an artistic and symbolic adaptation of materials,
allowing them to integrate harmoniously into the existing environment while maintaining safety and durability. There is a growing recognition of the need for careful
incorporation of composites into the cultural codes of historic urban landscapes to
preserve urban identity and avoid visual conflicts [29].

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Undoubtedly, the architectural and artistic identity of high-responsibility infrastructure facilities cannot be shaped solely based on the decorative properties of materials. Achieving sustainable visual and functional outcomes requires a comprehensive methodological framework that interrelates materials with spatial composition,
contextual identity, and regulatory frameworks of urban design. This position aligns
with a materials science perspective, which asserts that the methodological foundations of high-performance, multi-component materials lie in the principles of chemical, structural, and phase complexity—aimed at targeted optimization of material
properties through the formation of composites with tailored internal structures—
and the synergistic effect, wherein the combined influence of diverse physicochemical parameters leads to qualitatively new results unattainable with mono-functional
materials [30, 31].
In international literature, the application of composite materials is addressed more
comprehensively and systematically. Emphasis is placed not only on the technical
suitability of materials but also on their visual, social, and environmental representation in the urban context [32–34]. In addition, the role of “intelligent building
skins” is highlighted—building envelopes that provide energy efficiency, facade
personalization, and enhanced architectural value.
Nevertheless, current research lacks a coherent methodological framework for
the assessment and design of HRUIF facades using composite panels. First, safety
and regulatory compliance (SNiP, SP, and international standards such as LEED and
BREEAM) are typically considered separately from aesthetic concerns, despite their
interconnected nature in practice. Second, urban integration of composite materials
is rarely substantiated by in-depth analyses of scale, spatial composition, and the
layered cultural contexts of urban space. Third, methodologies for visual adaptation—ranging from panel format selection to color and lighting design—are largely
absent in applied manuals and academic publications.
Thus, there exists a significant gap in the current scientific discourse: a comprehensive approach that synthesizes the technical, aesthetic, and regulatory-legal
aspects of applying composite materials–particularly QUANTUM CERAMIC and
QUANTUM PARUS–in the design of HRUIF architectural identity is yet to be developed. This substantiates the relevance of the present research, which aims to establish
a systematic methodology for the design of such facade systems.

3 Materials and Methods
The study focuses on two types of high-performance composite façade panels
designed for shaping the architectural identity of high-responsibility infrastructure
facilities (HRUIF). These materials were selected based on their advanced technological adaptability, resistance to harsh operating conditions, and potential for
architectural and artistic integration into diverse urban morphotypes.

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Fig. 1 QUANTUM PARUS aluminum honeycomb panels

1. Metal-ceramic panels QUANTUM CERAMIC, composed of the following
components:
Core: Micro-alloyed steel grade DC04EK (in compliance with DIN EN 10209:2013);
Coating: Dual-layer frit system—primer and topcoat (RTU)—providing resistance
to UV radiation, aggressive environmental exposure, and mechanical damage.
2. Aluminum honeycomb panels QUANTUM PARUS, comprising:
Front and rear face sheets made of aluminum alloy (EN AW-5005A);
Internal honeycomb core made of aluminum foil, forming a lightweight yet
mechanically robust spatial structure (Fig. 1).
The research methodology involves a comprehensive set of scientific methods.
1. Morphological and compositional analysis of urban integration includes the
assessment of the color and texture adaptability of facade panels: evaluation of
the material’s ability to replicate traditional natural textures (such as stone, wood,
terracotta) (Fig. 2), which allows their use in historic urban areas and heritage
protection zones; investigation of the spatial and dimensional compatibility of
panels with buildings of varying height and function (transport hubs, museums,
industrial complexes); and comparison of module parameters with architectural
principles (proportions, rhythm, and plasticity).
The morphology of QUANTUM PARUS panels as an element of urban facade
systems is shown in Fig. 3.

Fig. 2 Color and texture adaptation of QUANTUM PARUS panels

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A. V. Fedorchenko et al.

Fig. 3 Morphology of QUANTUM PARUS panels as an element of urban facade systems

2. Regulatory and Technical Assessment of Safety and Durability
The panels were subjected to a series of tests in accordance with both Russian
and international standards. Laboratory and bench-scale instrumental testing was
conducted in an accredited facility to evaluate the following parameters (Table 1).
3. Regulatory and Legal Analysis of Application in Critical Infrastructure Facilities
(CIFs)
A comparative analysis was conducted between the characteristics of the studied
materials and the requirements of regulatory documentation applicable to CIFs
(SP 253.1325800.2016, SP 468.1325800.2019, GOST R 58792–2020). This assessment ensured the compliance of the panel systems with standard design scenarios,
including aerodrome zones, sanitary protection zones, high-density urban areas, and
transport and energy infrastructure facilities.
4. Computational Modeling of Performance in Urban Environments
Table 1 Regulatory and technical parameters for the assessment of safety and durability of
composite facade panels
Property

Testing method

Standard

Flammability

Method I

GOST 30244

Frost resistance

Cyclic freeze-thaw + moisture
resistance

GOST 7025

Chemical resistance

Exposure to acids and alkalis

GOST 13087

Flexural/tensile strength

Universal testing machine +
Tensometry

GOST 8829, GOST 1497

Hardness and scratch
resistance

Mohs scale methods and GOST
2789

GOST 2789

Resistance to UV and
temperature variations

− 60 to + 80 °C, 300 h of UV
exposure

SP 468.1325800.2019

Sanitary and hygienic
safety

Migration of harmful substances

SanPiN 2.1.2.1188–03

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549

Using architectural software tools (Rhino + Grasshopper + Autodesk CFD), simulations were carried out to evaluate the impact of panel systems on the thermal
and acoustic performance of ventilated façades under conditions of dense urban
development:
ΔT (heat loss): Up to 38% lower compared to single-layer metal façade systems;
Sound insulation: Up to 52 dB with a panel thickness of 35 mm (compared to 38–
42 dB in standard aluminum systems);
Dew point and condensation zone analysis: Simulated under variable ambient
temperature conditions to identify risk areas for moisture accumulation.
5. Analysis of Implemented Urban Development Case Studies
An in-depth study was conducted on the practical application of the panels in
constructed critical infrastructure facilities (CIFs) at the federal level. This included
transport infrastructure projects in Moscow (MCC and MCD lines), metro stations,
terminals of Sheremetyevo International Airport, and façades of cultural facilities
(technology parks, museums).
In the context of international experience, the study examined integration into
high-speed rail (HSR) infrastructure (China, UAE), nuclear research centers (France,
Finland), and educational complexes (Japan, Germany). For each case, the analysis focused on visual compatibility with the urban fabric, in-service material
performance, and feedback from architects, engineers, and operating organizations.
The research is based on laboratory testing data, technical documentation from
completed architectural projects, and international publications in the fields of
architectural materials science and sustainable urban planning.

4 Research Results
The application of composite materials in the architectural and artistic design of Critical Infrastructure Facilities (CIFs) requires a strictly differentiated approach, taking
into account their urban planning role, functional load, and regulatory constraints
(Table 2).
Modern materials such as QUANTUM CERAMIC and QUANTUM PARUS
demonstrate the potential of a universal integrator by combining engineering, environmental, and aesthetic properties. They enable the implementation of principles
of sustainable, safe, and expressive architectural design within the urban fabric
(Figs. 4–6).
For example, at the El-Dabaa Nuclear Power Plant (Egypt), the use of metalceramic panels with a “marine sandstone” texture enabled visual integration with
the coastal landscape. Based on the results obtained from previous tests, it can be
assumed that the panels discussed in this article meet the requirements set forth in

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Table 2 Classification of CIFs within the urban fabric and corresponding material requirements
Type of CIF object

Examples
of facilities

Key material requirements

Transport
infrastructure

Metro
stations,
HSR
terminals,
airports,
bridges

Vandal resistance fire resistance (class KM0 / KM1)
chemical resistance to aggressive environments durability
(>30 years) ease of maintenance architectural
expressiveness

Cultural and public
facilities

Museums,
Façade expressiveness imitation of traditional materials
theaters,
(stone, wood, etc.) color fastness environmental safety
concert
halls, sports
complexes

Engineering
structures

Tunnels,
control
centers,
energy
facilities

Maximum safety resilience to emergency conditions
minimal maintenance

Fig. 4 QUANTUM CERAMIC in the interior of a metro station

Fig. 5 QUANTUM CERAMIC: Visualization of column cladding for a proposed HSR station and
platforms

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551

Fig. 6 QUANTUM PARUS: Visualization on the facade of a museum complex

the regulatory documentation for nuclear energy facilities, such as resistance to radiation exposure, decontamination agents, and aggressive liquid environments (acids,
alkalis, etc.), as well as suitability for use in areas affected by marine salt fog in
accordance with international standards for decontamination and durability.
The comprehensive application of composite materials in the architecture of highresponsibility infrastructure facilities (HRI) requires the development of a system
of principles that reflect the interdisciplinary nature of the task — ranging from
engineering safety to aesthetic expressiveness and contextual appropriateness. The
proposed principles are structured into functional-content blocks and address requirements for regulatory compliance, visual identity, operational efficiency, and urban
integration. Each principle is based on a combination of design, sociocultural, and
technological factors that determine the quality of the architectural solution.
1. Principles of Safety and Durability Assurance.
The composite panels QUANTUM CERAMIC and QUANTUM PARUS have undergone comprehensive testing, confirming their suitability for use in high-responsibility
infrastructure (HRI) constructions exposed to aggressive urban and technogenic
environments. The assessment is based on both experimental data and regulatory
requirements.
The results of laboratory tests on the extreme durability of the composite panels
according to TU 25.11.23–001-2021 and TU 25.11.23–003-2022 are presented in
Table 3.
The experimental test data demonstrate the high operational reliability of
QUANTUM CERAMIC and QUANTUM PARUS panels when exposed to extreme
factors typical of dense urban environments. Their resistance to aggressive chemical
agents, temperature fluctuations, as well as high flexural strength and confirmed frost
resistance indicate the materials’ ability to maintain technical and aesthetic properties over a prolonged service life (over 30 years), which is critically important for
objects of enhanced responsibility infrastructure (ERI). Furthermore, the confirmed
non-combustibility (NG/G1) ensures a high level of fire safety, while technological stability under thermal cycling (− 60 to + 80 °C) guarantees reliability across
various climatic zones. These characteristics directly correlate with the architectural

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Table 3 Results of extreme durability tests of composite panels
Parameter

QUANTUM
CERAMIC

Chemical resistance

No changes after 24 h exposure to H2 SO4
and NaOH

Internal TU, method
analogous to GOST
13087

Thermal stability

50 cycles from − 60 °C to + 80 °C—No
defects

Internal TU, method
analogous to GOST
9.030

Combustibility

NG
(non-combustible)

NG / G1
(flame-retardant)

GOST 30244–94, GOST
30402–96

> 50 MPa

QUANTUM
PARUS

Test method/standard

Flexural strength

> 120 MPa

Frost resistance

Compliant (≥ 150 cycles without damage)

GOST 7025–91

Durability

Estimated service life > 30 years

Based on calculations
considering climatic
cycles

GOST 8829–94

and technical requirements for ERI, where safety, reliability, and durability are key
priorities.
It is important to note that these materials comply with the main provisions of
current regulatory documents concerning the strength, climatic, and operational
parameters of transport infrastructure structures (SP 253.1325800.2016); building
resilience criteria under emergency impacts (GOST R 58792–2020); and sanitaryhygienic standards, including ecological safety for use both inside and outside
buildings (SanPiN 2.1.2.2645–10).
2. Principles of Forming the Aesthetic of Urban Space
The study confirms that the composite materials QUANTUM PARUS and
QUANTUM CERAMIC possess a high potential for architectural integration into
complex urban environments, including historic-cultural and socially significant
zones. This potential is realized through the application of three fundamental
aesthetic principles that ensure harmonious interaction between ERI objects and
their surrounding space.
2.1. Integration into the Historic-Cultural Environment. Thanks to advanced technology for precise imitation of natural material textures (stone, wood), the panels
provide visual compatibility with historic buildings without disrupting their compositional integrity. This is especially important for objects such as high-speed rail
stations, metro stations located within protected zones, where preserving the cultural
identity of the environment is essential (Fig. 7).
Thus, a synthesis of modern engineering and traditional architectural expressiveness is achieved—without compromising regulatory requirements for safety and
durability.

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Fig. 7 Integration of QUANTUM PARUS and QUANTUM CERAMIC composite materials into
the historic-cultural environment

2.2. Formation of contemporary expressiveness. The wide range of colors (RAL,
NCS) and smooth/textured surfaces (QUANTUM PARUS) allows for the creation
of vibrant accents in public spaces (airports, stadiums, cultural centers, recreational
facilities such as hotels) (Fig. 8), working with scale, rhythm, and color within the
volumetric-spatial composition of the city.
The flexibility of visual solutions promotes aesthetic diversity in the environment,
tailored to the specifics of the particular urban context.
2.3. Universal Inclusive Design. The panels feature ergonomic, vandal-resistant, and
easy-to-clean surfaces, which reduce maintenance costs and enhance comfort for all
population groups, including those with limited mobility. The absence of sharp edges
and protruding elements makes these materials suitable for use in areas with high
pedestrian traffic (such as train stations, station vestibules, and public passages).
Overall, the application of QUANTUM composite panels in the design of Infrastructure of Increased Responsibility (IIR) projects not only meets strength and durability requirements but also significantly expands the architect’s aesthetic toolkit,
contributing to the harmonization of the urban landscape, the creation of a culturally
sensitive environment, and the development of human-centered architecture.

Fig. 8 Formation of contemporary expressiveness of high responsibility infrastructure objects

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3. Principles of Functional Enhancement of the Urban Environment.
The application of QUANTUM PARUS and QUANTUM CERAMIC composite
materials in ventilated curtain wall systems is justified from the standpoint of functional improvement of the urban environment. Based on the conducted analysis, three
key functional principles have been identified (Table 4).
Thus, the combined impact on energy saving, acoustic comfort, and structural
durability contributes to the creation of more sustainable, comfortable, and costeffective IPO facilities. The high operational efficiency of these materials is confirmed
by experimental data and complies with modern requirements for urban planning
and environmental safety, making them promising for widespread implementation
in conditions of intensive urban use.
Overall, the results of implementing composite panels in various typologies of
urban infrastructure objects confirm their high practical value both from technical
and architectural-urban planning perspectives. Table 5 presents the key application
areas and achieved effects.
The analysis of implemented projects in domestic practice demonstrates the
versatility and adaptability of the composite materials QUANTUM PARUS and
QUANTUM CERAMIC across various functional and architectural scenarios. The
application of these materials ensures not only technical efficiency (fire resistance,
durability, reduction of operational costs) but also high architectural and artistic
expressiveness. This confirms their strong applicability within the contemporary
urban development context—ranging from infrastructure facilities to historic urban
fabric.
Table 4 Principles of functional enhancement of the urban environment
Functional principles

Description and application results

Energy efficiency

Use in ventilated facades with an air gap reduces
heat loss of IPO buildings by 25–40%,
decreasing the load on urban energy systems

Acoustic comfort

Sound insulation of ventilated facades with these
panels increases by 15–20 dB, which is critical
for facilities located in noise-discomfort zones
such as railway hubs and airports

Protection against external aggressive factors The system reliably protects load-bearing
structures from precipitation, wind, UV
radiation, and corrosion, thereby extending the
service life of the facility under aggressive urban
environmental conditions

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Table 5 Analysis of implemented projects in domestic practice
Application area

Examples of objects

Material

Result of application

Transport
infrastructure

Metro stations:
Vokzalnaya,
Lomonosovsky
Prospekt, Ramenki,
Minskaya, Ozernaya
(Moscow, St.
Petersburg, Minsk);
airports: Vnukovo,
Domodedovo

QUANTUM
CERAMIC,
QUANTUM PARUS

Enhanced fire and
operational safety,
reduced maintenance
costs, and increased
architectural
expressiveness of
facilities

Cultural and sports
facilities

Olympic ski and
biathlon complex
“Laura”

QUANTUM PARUS

Creation of modern
visual landmarks that
correspond to the scale
and character of the
public space

Historic and cultural
development

Restoration projects
with imitation of
historic cartena
texture

QUANTUM PARUS

Visual conformity to
the historic appearance
while simultaneously
improving facade
durability and
resilience

5 Practical Significance, Proposals and Implementation
Results
The conducted study makes a significant contribution to the development of theoretical and practical foundations for designing high-responsibility infrastructure facilities within the modern urban planning system. Based on the analysis, testing, and
synthesis of obtained data, the following key directions have been identified:
Development of theoretical foundations for the architectural and artistic formation
of the appearance of high-responsibility infrastructure objects (hiro). The feasibility
of using innovative composite materials (quantum parus, quantum ceramic) as tools
for solving spatial composition, color harmonization, and imagery expressiveness
has been confirmed. This expands the toolkit for architectural modeling of urban
silhouette elements, enhancing visual identity and integration of hiro into the urban
fabric.
Methodological substantiation of safety and stability criteria. a systematic
approach has been developed for selecting materials for hiro, considering the requirements of normative documentation (sp 253.1325800.2016, gost r 58,792–2020,
etc.) and indicators of extreme strength, chemical and radiation resistance, thermal
stability, forming the basis for designing a safe and reliable architectural environment.
Formation of principles for visual integration into the historic-cultural context.
The principle of aesthetic mimicry is proposed, implemented through high-precision

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imitation technologies of traditional materials, enabling adaptation of new infrastructure objects within historic zones without distorting their authentic character,
which is especially relevant for cities with rich cultural heritage.
Optimization of architectural solutions for transport hubs. The effectiveness of
using composite claddings has been established to improve operational reliability,
visual legibility, and the city-forming role of transport facilities as structural nodes
of urban morphology.
Formalization of material requirements in digital design systems. a list of technical and aesthetic parameters for composite materials is proposed for inclusion in
databases of urban planning information systems (bim, digital catalogs), facilitating
automation and optimization of design decisions in the comprehensive development
of territories.

6 Conclusion
The conducted study demonstrates the high scientific and practical significance of
applying composite materials quantum ceramic and quantum parus in the design of
high-responsibility infrastructure objects (hiro) as key elements of the city’s architectural appearance and functional infrastructure. For the first time, the use of quantum
ceramic and quantum parus composites has been systematically substantiated as a
means to ensure comprehensive sustainability, aesthetic expressiveness, and functional efficiency of high-responsibility infrastructure facilities in the modern urban
environment.
Test results confirm the high chemical, thermal, mechanical, and climatic resistance of the materials, as well as their compliance with fire safety and durability
requirements, ensuring reliable operation of hiro facilities in aggressive environments
and extreme conditions. Thanks to the technology of imitating natural textures and
a wide color range, the materials effectively address the tasks of integration into the
historic-cultural context and creation of modern visual accents—shaping a quality
environment and a recognizable city image. The use of panels in ventilated curtain
wall systems contributes to reducing heat loss (up to 40%), increasing sound insulation (by 15–20 dB), resistance to external impacts, lowering maintenance costs, and
extending building service life.
Thus, the application of quantum ceramic and quantum parus composite materials represents a scientifically justified, technologically feasible, and architecturally
appropriate solution that enables the creation of safe, expressive, and functionally
rich high-responsibility infrastructure facilities.
The direction for further development of the topic includes the creation of
digital catalogs and parametric material models integrated into bim design environments, which will optimize architectural selection processes, enhance reproducibility of design solutions, and promote systematic implementation of principles
for sustainable and aesthetically balanced urban infrastructure development.

Principles and Methods of Forming the Architectural and Artistic Image …

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References
1. Beregovskikh AN (2025) Architectural and spatial design as a type of urban planning activity
and a tool for effective planning of territory development. Architecture and modern information
technologies 1(70):173–188
2. Evstratova TA, Evstratova LM, Kupriyanov VN et al (2023) Modern trends in the field of
artistic synthesis in architecture and city design. In: Proceedings of the Kazan State University
of Architecture and Civil Engineering 2(64):101–112
3. Alzemeneva EV, Mamaeva YV (2021) The identity of the urban environment. Eng Constr Bull
Casp RegN 2(36):40–47
4. Esaulov GV (2018) On identity in architecture and urban construction. Acad Arch Constr
4:12–18
5. Allawi MF et al (2023) Smart composites in urban infrastructure: a state-of-the-art review. J
Build Eng 76:107361
6. Pavozkov DV (2024) Modern trends and prospects of using sustainable building materials. Bull
Sci 2-2(71):655–657
7. Bakholdin DG (2024) Application of composite materials in construction. Int J HumIties Nat
Sci 5-1(92):189–192
8. Mouritz AP (2019) Introduction to composite materials. Woodhead Pub, Cambridge
9. Ray BC (2024) Introduction to composite. Springer Nature 1:1–20
10. Metal-ceramic architectural materials. https://natinvest.ru/netcat_files/t/quantum_ceramic.
pdf?ysclid=mdh2tvq29n653086867. Accessed 23 Aug 2025
11. Aluminum honeycomb panels “QUANTUM PaRUS”. https://natinvest.ru/netcat_files/t/qua
ntum_parus.pdf?ysclid=mdh2qo3pj6458503975. Accessed 23 Aug 2025
12. Belousov VN, Kulaga LN, Lavrov VA, Smolyar IM (1981) Fundamentals of the formation of
the architectural and artistic appearance of cities. Stroyizdat, Moscow
13. Gruzа I (1972) Theory of the city. Stroyizdat, Moscow
14. Gutnov AE, Glazychev VL (1990) The world of architecture: the face of the city. Molodaya
Gvardiya, Moscow
15. Lynch K (1986) The perfect form in urban planning. Stroyizdat, Moscow
16. Norberg-Schulz C (1980) Genius Loci, Towards a Phenomenology of Architecture. Rizzoli,
New York
17. Bartenev IA (1968) Form and construction in architecture. Stroyizdat, Leningrad
18. Gashenko AE (2015) Architectural and urban planning morphology as a subject of system
research: an elementary aspect. Bull Civ Eng 6(53):5–13
19. Zabalueva TR (2017) Fundamentals of architectural and structural design. MGSU, Moscow
20. Ikonnikov AV (2006) Space and form in architecture and urban planning. URSS, Moscow
21. Giniyatova YA, Pugin KG (2023) Modern building materials and technologies, the development
of nanotechnology in the production of building materials. Bull Sci 58(4-1):264–269
22. Batiyenkov RV, Burkovskaya NP, Bolshakova AN, Khudnev AA (2020) High-temperature
metal matrix composite materials (review). In: Proceedings of VIAM 6–7(89):45–61
23. Fedorov VS, Kupchikova NV, Fedorchenko AV (2025) Strength of architectural and construction finishing elements made of metal-ceramics and aluminum honeycombs in urban railway
transport facilities. Engineering and Construction Bulletin of the Caspian Region 2(52):49–56
24. Lesovik VS, Fomina EV (2019) A new paradigm for designing building composites to protect
the human habitat. Vestnik MGSU 14(10):1241–1257
25. Minyazova AN, Krasina IV, Ilyushina SV, Valieva MD (2017) Determination of the strength
of composite materials. Vestnik of the Technological University 20(24):87–88
26. Ershova OV, Mullina ER, Chuprova LV et al (2014) Study of the effect of the composition of
the inorganic filler on the physicochemical properties of polymer composite material. Fundam
Res 12(3):487–491
27. Privalova EN, Sergeeva AY (2021) Interaction between architecture and the environment using
principles of biopositivity. Constr Technog Saf 23(75):13–25

558

A. V. Fedorchenko et al.

28. Serkov AI (2017) Application of fundamental principles of architectural and construction
ecology in the creation of biopositive buildings and structures. RegNal Dev 2:9
29. Kukina IV, Slabukha AV (2025) Science and practice of supporting the modern livable city.
Contemp Arch World 1(24):289–296
30. Melikhov IV, Tretyakov YD (2013) Approaches to the mesokinetic theory for determining the
optimal technological route of raw material transformation into a final material. Theor Found
Chem Eng 47(1):42–44
31. Radlinski M, Olek J (2012) Investigation into the synergistic effects in ter-nary cementitious
systems containing Portland cement, fly ash and silica fume. Cem Concr Compos 34(4):451–
459
32. Ashby M, Johnson K (2002) Materials and design the art and science of material selection in
product design. Butterworth-Heinemann, Oxford, Boston
33. Hassani S, Mousavi М, Gandomi АН (2022) Structural health monitoring in composite
structures: a comprehensive review. Sensors (Basel) 22:153
34. Wigginton M, Harris J (2002) Intelligent. Architectural Press, Oxford

Innovations in Architectural
and Construction Design of Modern
Chinese Schools
I. N. Maltseva, Jie Liu, N. N. Kaganovich, and A. P. Isaev

Abstract The article analyzes the general strategy for organizing China’s basic
education system and the principles of architectural design for school campuses,
along with prospects for their future development. It identifies key challenges and
development factors related to regional traditions, cultural, social, demographic,
and urban planning characteristics. The study examines contemporary fundamental
approaches to creating conditions for quality education as well as mastering various
cognitive methods. Particular emphasis is placed on developing communication skills
and fostering a strong school community, as well as ensuring openness and transparency of the educational system within society. It is specifically noted that Chinese
schools are actively transitioning from disciplinary institutions to more open and
informal ones. This transformation can only be achieved within fundamentally new
architectural and technological spaces, reflecting the new aesthetics and image of
modern Chinese schools, whose development is becoming increasingly significant
and worthy of attention not only from the state but also from the global community. The study reveals connections between China’s school paradigm and global
trends in architectural styles while emphasizing the need to preserve unique national
identity in this sphere. The article considers examples of modern schools and various
approaches to school design amid the architectural “transformation” of contemporary
Chinese education, identifying key trends and future development paths.
Keywords Urbanization · Methods of cognition · Basic school · Design
innovations · Neighborhood communities · Paradigms of new typology

I. N. Maltseva (B) · J. Liu · N. N. Kaganovich · A. P. Isaev
Ural Federal University named after the First President of Russia B. N. Yeltsin, Yekaterinburg,
Russia
e-mail: i.n.maltceva@urfu.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_44

559

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I. N. Maltseva et al.

1 Introduction
The construction boom combined with the educational one has significantly influenced the formation of new architecture for school facilities in modern China,
including general education schools. Typological concepts are developing so rapidly,
acquiring new meanings and creative approaches, creating structural and stylistic
diversity, that overall it allows us to define the general trend as innovative, futureoriented, and radically different from the counterparts of earlier periods. To understand the patterns and algorithms of these changes, it is necessary to identify the most
relevant development factors, both external and internal [1]. Traditional teaching
methods and “old school” models in the new social conditions are unable to fulfill
their mission, meet modern requirements, and solve current problems of school
education [2, 3]. It should be noted that the architectural design of Chinese schools
in its development largely follows global trends in this field.

2 Issues
The main external factors driving the ‘rethinking the school: from architecture to
community’ of the educational system in China are primarily social and environmental [4]. The factors that determine the fundamental contradiction between land
resources and criteria for sustainable development of urban areas in modern conditions are rapid industrial development, increasing urbanisation, and a significant
influx of population to large cities. An equally important factor is the ever-increasing
demand for quality education, starting with compulsory education. In China, modern
requirements assume that it is in the basic school that the general worldview and
understanding of national tasks and vectors of development of the Chinese society
are laid down [5]. As a result, in the conditions of high-density development, there
is an acute problem of overcrowding in public schools, which leads not only to the
construction of educational ‘mega structures’ in small residential areas, but also to
fierce competition and tough ratings.
Looking at traditional schools from different periods of Chinese history, there is a
strong emphasis on the functionality and practicality of educational programs, which
led to overcrowded classrooms. Later, socialist principles of school building design
and the desire for impressive appearance were adopted, see Fig. 1.
By the time the reforms of the 1980s began, the country had identified a number
of serious problems:
•
•
•
•
•

Irrational volumetric-planning structure
Lack of cultural and communicative culture
Lack of safety measures
Individual needs of pupils in space organisation are not taken into account
Overcrowding of classes (up to 100 pupils!)

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561

Fig. 1 Examples of historical school buildings in China

After the reforms in the period from 1978 to 2024, the educational system has been
oriented towards ‘openness’ and integration into society. It includes innovative principles of architectural and construction design development: humanitarian, intellectual
and ecological [6, 7].

3 Modern School Education Development Strategies
With the rapid development of the global education process, China’s domestic
demand for education is growing. The future-oriented school education strategy is
gradually forming an up-to-date set of development models, taking into account
national traditions and global trends. While developing successfully, China’s
education system still faces many challenges, such as:
• Uneven distribution of educational resources in urban and rural areas
• Legal and social problems of education
• Insufficient development of innovative areas
The plan for the balanced development of compulsory education includes the
following issues:
•
•
•
•

Equity and accessibility of education
The quality of education and teachers
Specifically, optimization of the curriculum
Attention to practical learning and research

Cooperation with production and research institutions to develop innovative and
practical abilities, international cooperation, and enhancing competitiveness in the
context of globalisation will guarantee the quality development of education in China
[8]. It is the strategies of educational development that determine the current trends
of school building design.

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4 Modern Trends in Designing School Facilities
The development of a scientific and rational strategy for school education in China
has become the key to the development of the architectural and construction concept
of forming an efficient, comfortable and environmentally sustainable educational
environment [9–11]. This includes the optimization of space planning solutions and
the creation of a new aesthetics of a comfortable environment within the framework
of eco-positive design. The design of school buildings in modern China is considered as a multifactorial sphere of architectural and construction activity. The overall
strategy takes into account the combined influence of the main factors and the active
development of previously underestimated factors, which allows us to consider the
school as a multifaceted and constantly evolving interconnected system [12]. Apart
from the approaches to school design, that are fundamental to most countries, in
China especially important is:
• The cultural context: the traditions, values and aesthetic concepts of different
regions. For example, the ancient Chinese concept of harmony and symbiosis of a
building and nature, ‘the unity of heaven and humanity’, has had a major influence
on the architecture of educational campuses. Great attention is paid to creating a
cultural atmosphere, special aesthetics and unique form and color solutions in the
regional context
• The level of development of science and technology, which not only determines the
degree of modernisation of ‘school design’, but is an important area of students’
education, acquisition of practical and research skills, even the choice of future
profession
• Functionality remains the basic requirement of the spatial organization of Chinese
schools. At the same time, it is characterised by the techniques of spatial transformation and permanent zoning to form a reasonable educational environment and
achieve spatial and technological universality. For example, almost every class
with different age groups has different sets of disciplines
• Multifunctionality of public school spaces: the flexibility of approaches, solutions
that at first glance seem illogical and irrational, but that in the end significantly
increase the functionality and the potential of the school building. Multifunctionality emphasises the semantic and planning ‘openness’ of the school and is
successfully used in event scenarios, including those with the active participation
of the city and the local community
• Structural, fire, anti-terrorist security includes special requirements taking into
account climatic factors of regions, natural disaster zones and natural catastrophes
• Modern criteria and principles of sustainable design of energy-efficient and ecopositive school buildings solve the problems of creating a comfortable internal and
external environment, calm atmosphere for learning, taking into account physical
needs, environmental psychology, ergonomics of students
The stylistic peculiarities of Chinese school architecture development are determined
by global trends such as ‘very high quality international modernism’ [7].

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Fig. 2. A school with 45 classrooms in Shenzhen, Pingshan: a overall view, b terraced roof, c—
courtyard view.

4.1 Modern School Education Development Strategies
In modern architecture in China, general principles of designing modern educational
environment have been formed, which are designed to solve the outlined problems.
Here are some examples.
Experimental School in Shenzhen (CMAD Architects). Problem: urban planning
constraints lead to the design of large-scale school buildings with up to 8 stores,
where even comfort and innovative design do not solve the problem of lack of space
both inside the building and on the school grounds. The solution: a vertical tiered
building structure with terrace modules and mini-gardens. Convenient connections
and transitions make it possible to organise a comfortable multifunctional space
with zones for different activities and taking into account the psychology of teams,
groups and individuals. Static spaces are for recreation and study, including a library,
dynamic spaces are for sports, games and cultural activities. The terraces, harmoniously integrated into the landscape, mimic the natural contour. CMAD Architects
explain, ‘All the elements, including ramps, terraced platforms, colorful green areas,
make up a pastoral space with multi-level roofs connecting the three to six floors of
the complex’ [2]. Thus, the campus provides sufficient and varied space for children
to engage in activities within the limited space of the site, see Fig. 2.
Futian Secondary School campus in Shenzhen (Remix Studio). Problem: accommodating all the planned infrastructure of the district, including educational facilities in the aspect of the rapid development of the education system and the new
typology, in the extreme conditions of dense urban development with a population
of 18 million inhabitants. Solutions: the concept of hybrid typology and the ‘new
city in the city’ campus model, which functions in dialogue with the urban community. The urban strategy is openness to the city. The new spatial strategy is that
of ‘porosity’: amphitheaters, crossing-bridges, roof gardens, courtyards, terraces.
The social strategy is a ‘school without fences’, in which the campus community
programme is open to outside users. The environmental strategy presents a threedimensional system of green spaces and creates an interconnected environmental
infrastructure.
As a result, the Futian Campus hybrid typology option is a 3000-student boarding
school with a total floor area of 120,000 m2 on a 41,000 m2 site, see Fig. 3 [3].
Shanghai International School Campus (OPEN Architecture). Problem: in giant
schools with a capacity of 3000–5000 students, where competition is for physical

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Fig. 3 Futian secondary school campus in Shenzhen: a, b overall view of the campus; c terraced
roof beautification

Fig. 4 International school campus in Shanghai: a overall view of the campus; b the campus
residential module; c theatre and library

space in the learning environment, with all the ‘ingenuity’ of designers, it is difficult
to achieve full psychophysical comfort and individual approach, especially in the
hybrid format of the new school. Solution: as an alternative, a new paradigm for
China was created—a “village-style” campus based on the international K12 system,
in the form of a strictly regulated “mega structure” model with vertical development.
The structure, composed of several individual forms, accommodates kindergarten,
primary and secondary school classrooms, a laboratory block, a dining hall, and a
residential block. The hybrid format focuses on three important elements: reading,
sports, arts—library theatre, gym-canteen, arts center, see Fig. 4.
Thus, challenges and constraints often lead to new approaches in organising work.
Inspired by the African proverb, ‘It takes a village to raise a child’, OPEN Architecture confirmed that children today often grow up without the participation of the
whole community. As a result, their design strategy was to utilise the diversity and
flexibility of the spatial archetype of the village to create a unique and rich school
experience [4].
According to Anna Shapiro, chief architect at ED Architecture, the option of
breaking up a giant school into separate structures looks the most humane, see Table 1
[5].
The principles of school of the future development in China involve a shift from
a disciplinary school to a more informal education system [4, 13] that includes the
following points:
•
•
•
•

Innovative design instead of ‘factory’ architecture
Connectivity with the local community [14]
Future-oriented education
Integration of the building with nature [15, 16]

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Table 1 The principles of designing a school of the future in China
Development principles

Multifactorial nature of training programs

Active pedagogy for diverse forms of learning

1. Mental and physical development
2. Labor skills
3. Arts
4. Formation of planetary worldview and
consciousness against the background of
modern evolutionary processes

Developing cognitive skills and supporting
psychological health

1. Educational and recreational zones in the
school’s public space
2. Library for cognitive skills
3. Green mini-farms and rooftop greenhouses
for psychological health
4. Spaces to engage with the local community

Fostering environmental awareness and social
responsibility

1. Friendly and ecological design
2. Greenhouses for growing plants, including
food crops
3. Areas for natural components studies
(water, wood, stone) and meteorological
observations
4. Bird feeders in yards, small perennial
gardens

Open ‘friendly portals’ of entrances to the
school or outer courtyard

1. A symbol of the openness of the school
space to the main entrance and
neighborhood
2. The “I want to go to school!” effect

Multifunctional central space

1. The meaning in the sociability of the school
community
2. Connectivity with the local community
3. Core of the composition
4. Events and activities
5. Active and passive recreation

Versatile and flexible indoor study spaces

1. Spaces for different forms of learning
2. Gaining individual learning experiences
3. Interaction in group work
4. Interaction of communities of different ages
5. Participation in collective workshops

Outdoor spaces for learning and relaxation,
meeting and socialising

1. Outer courtyards are open to residential
development, a common area for students
and the community. The ‘transition’ from
family to school, physical activity
2. The courtyard is for educational purposes,
student recreation, events and activities.
(continued)

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Table 1 (continued)
Development principles

Multifactorial nature of training programs

Arts at school

1. The idea of combining a comprehensive
school (morning) with an art school
(evening). Pupils learn throughout the day
2. Combining different ages by types of arts
3. Efficient use of space—multifunctional
classrooms

A ‘dense’ use of the site for study and
recreational purposes

1. Efficiency of site utilisation—versatile use
of educational spaces (classrooms, public
spaces, multi-level open courtyards,
exploitable roofs, multi-level terraces)
2. Evening School of Arts

The use of active movement (cycling, walking) 1. Reducing transport costs
to school and on the site
2. Healthy lifestyle starting from childhood
3. Ecology of the neighborhood and the school
site
4. Bicycle lanes, pedestrian pavements,
bicycle parking on school grounds
The connectivity of school and local
communities

The building and the outside space, as zones of
interaction, function as elements of the
neighborhood infrastructure
Evening school of arts, performance stages,
places for exhibitions
Communicative, external and internal school
spaces

•
•
•
•

Realisation of students’ individual potential
Expansion of sports and cultural spaces
Traditional and alternative teaching methods
Integration of general education and art school

5 Design Validation of the Study
Within the framework of the research on ‘Modern Concepts of Architectural Design
of Comprehensive Schools in China’ at the Department of Architecture at the Institute
of Construction and Architecture of the Ural Federal University, Russian and Chinese
teachers and master’s students presented a model of a 700-seat Guangming Secondary
School in Shenzhen.
The city of Shenzhen, a symbol of China’s reforms and openness, is actively
developing under the “double zones” strategy (Guangdong—Hong Kong—Macau
Greater Bay Area and Pilot Zone of Socialism with Chinese characteristics). Guangming District is the northern centre of Shenzhen, where a ‘world-class science city’

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567

is being built at an accelerated pace. With the dramatic increase in the demand for
educational resources, especially in key industrial and urbanisation integration zones,
there is an uneven distribution of secondary schools and a lack of modern educational
facilities to meet demographic needs and upgrade urban infrastructure. The planning
site is located in a densely built-up environment. The prospective school will reduce
the pressure on inter-district educational institutions and assure the continuity of the
educational chain in the area. The basis of the concept of shaping is a metaphor—
“the gesture of embrace”, which symbolises the meanings of cohesion in the building
model:
• The school opens its arms to the students, representing the educational philosophy
that ‘the student is the main subject of learning’
• Openness of the building to the city—through interactive public spaces, the architecture engages with the neighbourhood community, breaking the traditional
isolation of the campus
Symbiosis of nature and architecture—the inner courtyard with green areas and water
elements creates an ‘ecological lung’ of the building.
A comparative analysis of the three options for the building location on the site
revealed the advantages and disadvantages of each and determined the choice. The
analysis took into account lighting, ventilation possibilities of classrooms, optimal
inter-location of campus blocks, accessibility of students with disabilities, insolation
regime in classrooms and kindergarten. The choice of the variant determined the
position of the building on the site, the functional zoning of the school building and
the volumetric planning structure, see Fig. 5.
In order to improve the efficiency of planning solutions to ensure spatial flexibility
and versatility of the facilities, taking into account climatic and regional conditions,
a structural system in the form of a monolithic reinforced concrete frame with a
beamless monolithic floor, the building foundation in the form of a monolithic slab
was proposed. The exterior and interior finishes are selected taking into account the
environmental requirements for materials: safety glass is used inside the building
and sun-protective glass on the facades, see Fig. 6.
Secondary school, as a key element of the urban educational space, should
combine energy efficiency, environmental friendliness and social responsibility in
forming a sustainable outlook among students. The school project should implement environmentally sustainable design through three aspects: resource conservation, environmental safety and harmony with society [17, 18]. Climate adaptability
implies:
•
•
•
•
•

Thermal optimization of the building envelope
Inclusion of active energy systems
Resource recycling and the use of low carbon materials
Ecological landscape and biodiversity
Creation of “eco-corridors” with preservation of riparian vegetation, installation
of insect “hotels” and bird drinkers (monitoring has shown an increase in bird
diversity by 5 to 8 species)

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Fig. 5 Functional diagram of the building structure

Fig. 6 Design proposal for a 700-seat secondary school in Shenzhen (visualization by Liu Jie)

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Fig. 7 Eco-sustainability scheme

• Education in co-operation with the community and shared use of infrastructure,
see Fig. 7.

6 Conclusion
With rapid urbanisation and the influx of population into China’s big cities, the
number of schools in rural areas is rapidly decreasing; in contrast, big cities are
experiencing an ‘education boom’ and an acute problem of school places. The challenges and constraints of urban planning are leading to new approaches in design.
These are large-scale spatial structures, as a rule, of multi-stage vertical development
with a complex system of communications, which form a mega structural model of a
school campus. An alternative to giant schools are hybrid campus models in the form
of complexes of individual educational modules on an open ‘permeable’ territory of
social interaction. Despite the special problems and differences in approaches to the
design of the educational environment, the modern architecture of Chinese schools
is developing in the context of global trends, and this applies not only to innovative trends. In most examples, we see features of European aesthetics in the image of
buildings. The strategies of education system organisation and school building design
in China, especially basic education models, are continuously developing within the
current global trends towards the ‘Chinese school of the future’.

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References
1. Wang Z, Qi D (2023) Research on the development strategy of basic education. J Educ
Res 7(Issue Index). https://archive.org/details/sim_journal-of-educational-research_1923_7_
index/page/n5/mode/2up
2. Shanghai Historic Buildings Protection Center. https://mp.weixin.qq.com/s/qOVQUnCeh0R0
oraz6ZD21Q Accessed 12 Apr 2025
3. Wei G (2021) The place Spirit of ancient Chinese academy and its contemporary value.
Dissertation,. Zhejiang Normal University, Jinhua, p 148
4. Hua N, Zhang Y (2018) Research on the design of primary and secondary school teaching
space modules to meet the needs of the new era. J Arch Cult 10:60–62
5. Bystrova T (2020) Realizatsiya kul’turnoy identichnosti v arkhitekturnom prostranstve obrazovaniya: universitety Kitaya (realization of cultural identity in the architectural space of
education: universities of China). J Int J Cult Res 1:129–137
6. Liu J, Gao L (2005) A brief introduction to the formation and development of environmental
psychology. J Acad Res 11:9–12
7. Yang T, Wang Z (2018) Interior design of learning space based on environmental psychology.
J Des 01:132–133
8. Chechil IP (2021) Sovremennyye usloviya proyektirovaniya i komponenty arkhitekturnoy
kontseptsii obshcheobrazovatel’nykh shkol (modern design conditions and components of the
architectural concept of comprehensive schools). J Bull BSTU Named After VG Shukhov
7:73–86. https://doi.org/10.34031/2071-7318-2021-6-7-73-88
9. Bell PA, Greene TC, Fisher JD (2009). Translated by Zhu Jianjun and Wu Jianping.
Environmental psychology. Beijing: China Renmin University Press
10. Jiang Z (1987) The “roots” of interior environment design. J Inter Des 02:3–4
11. Ding Z (2004) Humanistic care in interior environment art design: from the perspective of
the importance of interior design psychology. J Fujian Agric For Univ (Philos Soc Sci Ed)
02:89–91
12. Anisimov VJ (2012) Sistemnyy podkhod k proyektirovaniyu shkol’nykh zdaniy (systemic
approach to designing school buildings). J Arkhitekton: news of universities 02(38). http://arc
hvuz.ru/2012_2/7
13. Zhang Y, Wang Z (2021) Universal architecture: discussing the discipline foundation,
educational model and campus design with Zhang Yonghe. J Time Arch 02:40–47
14. Goffman J (2017) Behavior in public places: the social organization of gatherings. Peking
University Press, Beijing
15. Xiong X (2012) Thoughts on building a green campus culture. J Theor Front High Educ
12:55–57
16. Xiqiao P (2012) Analysis of green campus planning. J Mod Prop (First Half Mon) 09.
https://www.nstl.gov.cn/paper_detail.html?id=78a2ca47621a7089f6ef08421e750f43&_ref
luxos=a10
17. Zhou Y (2019) Optimization and integration of green building technology in architectural
design. J Hous R Estate 31:18
18. Tian X (2018) Research on the integrated application of green building design concepts in
architectural design. J Eng Technol Res 08:250–251

Restoration Technologies of Wooden
Architecture Monuments on the Example
of the Resort Area and the Church of St.
Panteleimon in Tinaki
N. V. Kupchikova, T. V. Zolina, S. P. Strelkov, and A. S. Resnyanskaya

Abstract The article presents modern technologies for the restoration of wooden
building elements on the example of the architectural monument of wooden architecture of the resort—mud baths and the Church of St. Panteleimon in Tinaki (Astrakhan,
Russia). As a result of the construction and technical examination of the residential
building, it was established: a complete loss of stability of the load-bearing wooden
poles on which the load-bearing beams of the roof and the rafter system rest. There
are no brackets, nails rotted. The application of the following methods of restoring
wooden structural elements is described in detail: documentation and 3D modeling,
reconstruction from old photographs, conservation and strengthening of wooden
structures, restoration of the log house and roof, reconstruction of lost elements,
protection against external influences, the use of non-destructive diagnostic methods.
Keywords Wooden structures · Restoration · Architectural monument

1 Introduction
Modern technologies make it possible to preserve monuments of wooden architecture, minimizing interference with the historical fabric. However, the key remains
the balance between traditional methods and innovation. In 2024, the Astrakhan
State University of Architecture and Civil Engineering signed an agreement with a
N. V. Kupchikova (B)
Russian University of Transport (MIIT), Moscow, Russia
e-mail: kupchikova79@mail.ru
T. V. Zolina · S. P. Strelkov · A. S. Resnyanskaya
Astrakhan State University of Architecture and Civil Engineering, Astrakhan, Russia
N. V. Kupchikova
Moscow State University of Civil Engineering, Moscow, Russia
A. S. Resnyanskaya
Astrakhan Tatishchev State University, Astrakhan, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_45

571

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private investor for the construction and technical, valuation and cost expertise and
the development of design estimates for the improvement of the territory and the
restoration of one of the residential buildings of the specially protected area of the
Church of St. Panteleimon in Tinaki.

2 Historical Background and Current Status
The history of the Tinaki resort dates back to 1820, when a mud baths was founded
near the Tinaki salt lake. The healing properties of Tinak mud have been known since
the fifteenth century. The name “Tinaki” comes from the word “tina,” which meant
salt lakes, which served as an important source of salt for the Moscow state after
the annexation of Astrakhan. Located 12 versts from Astrakhan, the mud baths, as
reported by the newspapers of that time, was very popular (Fig. 1).
Tinaki mud had exceptional properties, were delivered to the treatment building
in trolleys and cured many patients. On the territory of Tinaki-1, the church of St.
Panteleimon was preserved (Fig. 2), erected in 1910 according to the project of
architect Alexander Mikhailovich Weisen. It attracts attention because of its unique
wooden architecture and, despite the destruction, retains a majestic appearance. The
temple was built with the money of an anonymous benefactor who was cured here
with the help of mud.
Photos of our days (Fig. 3), unfortunately, this is a wasteland, devastation, stolen
buildings, and several survived fires, as well as shallowing of the lake as a result of
the construction of a plant for the production and processing of cellulose.
The only surviving object of wooden architecture, except for the Church of St.
Panteleimon, and the surveyed property is a residential sleeping building, which
was commissioned in 1913. (Fig. 4). By the time of the construction and technical
examination, the building had not been in operation for 40 years. Built in 1913, the
building of the residential building is rectangular in plan with a gable roof, in the
style of “rehearsal” with elements of “modern,” surrounded by a gallery on three

Fig. 1 Tinaki resort illustrations (1910): a main entrance; b restaurant

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573

Fig. 2 The Church of St. Panteleimon is made entirely of wood: a 2024, b 1910, c 2023

Fig. 3 Illustrations of the objects of the resort “Tinaki” in 2024

sides and three porches (entrance groups). The main element of the decor is sawing
thread. In 1986, the building was still with normal operational characteristics.

Fig. 4 Illustrations of the residential sleeping building of the Tinaki resort: a 1986; b—2024

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3 Experience in Restoring Wooden Architecture
Monuments in Russia
Russia has accumulated a unique experience in the restoration of wooden architecture monuments, combining traditional technologies and modern engineering solutions [1–3]. These objects, which are of high historical and cultural value, require a
special approach due to the vulnerability of wood to moisture, biological damage,
and fires. Key methods and examples are based on comprehensive diagnostics, the
use of non-destructive methods to assess the condition of structures, such as ultrasound and resistography. An example of this is the restoration of the Church of the
Transfiguration of the Lord in Kizhi (Karelia), where laser scanning revealed hidden
deformations of the log cabin.
Authentic technologies involve replacing the logs of the log cabin while preserving
the historical logs, and using hand-hewn axes and adzes. Such technologies have been
successfully applied in the restoration of churches in the Malye Korely Museum in
the Arkhangelsk Region, where the lost roof elements have been recreated using the
“by example” method. The strengthening of the foundations of wooden churches in
Suzdal using screw piles, which prevented flooding, and the use of biocidal impregnation and fire-resistant compounds compatible with wood, are considered modern
materials [4–6].
The reconstruction of carved platbands in the village of Vitoslavlitsy in the
Novgorod region was carried out using archival photographs and CNC milling to
create digital models for accurate reproduction of lost details, which is considered
a 3D documentation method. Climate risks are taken into account when restoring
wooden structural systems in the northern regions of Karelia, Siberia, and other
regions of Russia, where it is necessary to use drainage systems and ventilation to
protect against moisture [7, 8].
Experts in temple architecture and construction note the shortage of skilled
craftsmen. As a result, they are actively training specialists in restoration and renovation schools, such as those in the cities of Astrakhan, Moscow, Volgograd, Petrozavodsk, Nizhny Novgorod, St. Petersburg, and others. Projects for the restoration of
Orthodox churches are funded through government programs, the national project
“Culture,” and private grants.
The Russian experience demonstrates that the preservation of wooden heritage is
possible only through a comprehensive approach that combines scientific research,
traditional crafts, and innovation. Sites such as Kizhi Pogost or the ensembles of
the Russian North have become not only museums, but also centers for the transfer
of unique technologies to future generations. When restoring churches and other
wooden architectural monuments, Russia uses a set of regulations that govern design,
surveying, restoration, and monitoring.
Federal Laws and Codes: No. 73-FZ (2002) “On Cultural Heritage Objects
(Historical and Cultural Monuments) of the Peoples of the Russian Federation”;
The Town Planning Code of the Russian Federation; No. 384-FZ (2009) “Technical
Regulations on the Safety of Buildings and Structures”.

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Building Codes: GOST R 59172–2020 “Restoration of Cultural Heritage Objects.
General requirements”; SP 13–102-2003 “Rules for Inspecting Load-Carrying
Building Structures”; SP 64.13330.2017 “Wooden Structures” (updated version
of SNiP II-25–80) and many other design and reinforcement standards. A large
regulatory legal framework regulates fire protection, wood bio-shield, departmental
restoration standards and international standards applicable in the Russian Federation. Special requirements are imposed on fire safety during the restoration of
temples—monuments of wooden architecture.
The restoration of cultural heritage sites made of wood requires strict compliance
with fire safety regulations aimed at preserving the authenticity of the structures while
ensuring their safety. The main requirements are regulated by the following documents: Federal Law No. 123-FZ (“Technical Regulations on Fire Safety Requirements”), GOST R 53292–2009 (fire protection of wood), SP 64.13330.2017 (wooden
structures), as well as departmental methods of the Ministry of Culture of the Russian
Federation.
Fire protection treatment includes the treatment of all wooden structures with
Group I or II flame retardants, such as walls, floors, and roofs. The compositions
should be colorless or tinted to preserve the historical appearance. Structural protection is provided by installing fire-resistant belts made of non-combustible materials.
There are examples of using basalt mats in areas where there is contact with stoves,
chimneys, and fire-resistant impregnation of wooden rafters and sheathing (minimum
R15 according to Federal Law No. 123). Automatic fire alarms are installed with
smoke detectors, concealed wiring, and lightning protection for churches taller than
15 m [9].
However, there are restrictions and prohibitions that can lead to fires in Orthodox
churches. It is forbidden to use combustible insulation materials such as expanded
polystyrene and sawdust in ceilings; to use synthetic varnishes and paints that increase
flammability; and to place electrical panels and wiring in wooden cavities without
metal sleeves. o Only cables with the нг-LS marking are allowed, which do not spread
fire. Stove heating with double-walled chimneys and fire-resistant gaps is performed
from 50 cm to wood.
Special requirements for authenticity apply to fire-resistant compounds, which
must be reversible and not change the structure of wood. Hidden installation of fireextinguishing systems is allowed due to fine-sprayed installations in attic spaces.
For roofs made of shingles or tiles, use flame retardants and firebreaks every 20 m.
In Kizhi Pogost, Karelia, the log cabins were treated with fire- and bio-protective
compounds and monitored using thermal imaging [10–12].

4 Methods
The restoration of monuments of wooden architecture, such as the Church of St.
Panteleimon and the residential sleeping building in Tinaki, requires a combination of traditional technologies and modern restoration methods. The following

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methods of restoring wooden structural elements were used: documentation and
3D modeling, reconstruction from old photographs, conservation and strengthening of wooden structures, restoration of the log house and roof, reconstruction
of lost elements, protection from external influences, and the use of non-destructive
diagnostic methods [13–15].
Non-destructive testing methods allow for the assessment of the condition of
wooden structures without compromising their integrity. These methods are aimed
at detecting hidden defects such as cracks, rot, fungal or insect damage, as well
as evaluating the strength and moisture content of the wood. The use of these
methods is particularly important in the restoration of architectural monuments,
where preserving the authenticity of materials is crucial.
Ultrasonic flaw detectors were used to measure the speed of ultrasonic waves
passing through the wood, signal attenuation, and the localization of defects. A
decrease in wave speed indicated the presence of defects. Infrared cameras detected
thermal anomalies on the wood’s surface caused by hidden voids or moisture,
measuring temperature gradients and heat distribution.
3D scanners created precise 3D models of the structures to analyze geometry and
deformations, identifying geometric deviations, deflections, and cracks. Resistograph
devices helped experts measure the resistance of wood while drilling with a fine drill
bit—a decrease in resistance indicated rot or voids in the measurements.
Resistographs were used in the examination of the wooden architecture heritage
site to measure wood resistance during micro-drilling. A decrease in resistance
detected by this method indicated rot and voids in load-bearing beams and columns.
Key parameters measured with resistographs include wood density and defect depth.
Radio wave scanners enabled in-depth analysis of radio wave reflections to identify internal defects, moisture content, foreign inclusions, strength, modulus of elasticity, and internal stresses. Advantages of non-destructive testing methods include:
preservation of historical material, high accuracy and objectivity of data, capability
for dynamic structural condition monitoring. Restoration of the wooden log structure
was carried out using the following structural and technological solutions: replacement of crown logs, conservation, structural reinforcement, crack injection, and
application of authentic tools.
Partial replacement of decayed or damaged logs while preserving historical material was performed using authentic pine and larch wood species matching the original.
Conservation of wooden elements involved treatment with biocides to protect against
fungi, mold and insects, as well as fire retardant impregnation to reduce flammability.
Structural reinforcement was implemented using hidden steel or carbon fiber ties to
strengthen load-bearing elements without altering the external appearance. Cracks
were injected by filling with epoxy or acrylic resins to restore wood integrity. The
use of traditional tools (axes, adzes) enabled preservation of the wood texture and
historical authenticity [16–18].
As a result of the construction and technical examination of the residential
building, it was established: a complete loss of stability of the load-bearing wooden
poles on which the load-bearing beams of the roof and the rafter system rest. There
are no brackets, nails rotted. Gallery floors are missing, bearing beams of floors have

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577

Fig. 5 Illustration of the construction and technical examination of the wooden structures of the
residential sleeping building, which was commissioned in 1913

unacceptable sagging and delamination of longitudinal wood fibers. Inadmissible
crack opening from 2 cm in longitudinal fibers of bearing logs and boards, structures
have inadmissible deflections (Fig. 5).
Laser scanning was performed in conjunction with reconstruction from old
photographs to accurately capture the current state. Creating a 3D model—from
photographs using photogrammetry, and searching for old drawings and descriptions as historical and archival research. Preservation and strengthening of wooden
structures included: biocidal treatment to protect against fungus, mold and insects;
impregnation with flame retardants to reduce combustibility of wood; injection of
cracks with filling with epoxy or acrylic resins and reinforcement of structures using
hidden steel or carbon plastic ties.
There is weathering of the masonry of the foundation pillars, their deviation from
the vertical, bulging and subsidence of individual sections of the pillars, complete
destruction of the outer surface layer, falling out of individual bricks, absence and
weathering of the mortar of the masonry seams, the brick crumbles in the hands.
In the laboratory, strength and bending tests were carried out on samples of bricks
twisted in the foundations, which showed unsuitability for further operation [19, 20].
Then authentic restoration of wooden elements of the architectural monument
was carried out (Figs. 6 and 7).

Fig. 6 Authentic restoration of the structure of posts—supports made of wood (drawing is located
horizontally)

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Fig. 7 Authentic restoration of the structure of the entrance gate door made of wood (the drawing
is located horizontally)

Scientists have tried to use materials close in time and era, which emphasizes the
careful attitude to ancient technologies and the preservation of traditional construction methods. Apply woodworking methods, which include threading, sawing,
grinding. They allow you to restore lost or damaged elements and give them an
authentic look. Use modern technologies. For example, new chemical compounds
for preserving wood from fungal and rotten damage, elastic sealants, adhesives.
The restoration of the log house was carried out by replacing the crowns,
namely, partial replacement of rotted logs while preserving the historical material.
We used authentic tools—axes and adzes to preserve the texture of the wood. To
recreate the lost elements, CNC milling of platbands, cornices and manual carving
were used to preserve historical authenticity. Protection against external influences
included coating with natural oils and wax and a drainage and ventilation device—to
avoid flooding of the foundation. Modern non-destructive diagnostic methods using
ultrasound analysis and thermography were also used to identify hidden defects.
The restoration of the roof was carried out by dismantling the damaged elements
and removing the rotten rafters, laths, and roofing material. The restoration of the
rafter system was performed by replacing the deformed elements while preserving
the original geometry. Modern materials such as glued beams were used for reinforcement. The roofing materials were chosen to match the historical period, such as
wooden shingles or natural tiles. The roofing system was equipped with a drainage
system and ventilation gaps to prevent moisture accumulation.

Restoration Technologies of Wooden Architecture Monuments …

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5 Results and Discussion
Studies of the planning structure of the entire territory on restored images, crocs,
illustrations and photographs were carried out. The area of the designed territory is
17.5824 ha.
Restored the original view in 2D and 3D master plan. Functional zoning of the
territory was designed and unique promising views were restored using 3D modeling
of the entire architectural ensemble of the cultural heritage monument (Figs. 8, 9,
and 10). And we can see how it was in the early 1900s.

Fig. 8 Illustration of the restored facade of the residential sleeping building of the Tinaki resort in
2025

Fig. 9 Illustrations of the 3D master plan of the Tinaki resort in 2025

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Fig. 10 3D general layout illustrations and functional zoning of the territory of “Tinaki” resort is
designed in 2025

6 Conclusions
During the restoration of the Church of St. Panteleimon in Tinaki, ultrasonic analysis and thermography were employed to detect hidden defects in load-bearing
columns and beams, enabling precise planning of structural reinforcement work.
Non-destructive testing methods are an indispensable tool in modern restoration of
wooden architecture, combining traditional approaches with innovative technologies
to preserve cultural heritage.
Thus, as a result of large-scale experimental field studies and construction, technical and estimate-cost examination of the monument of wooden architecture, it was
possible to design and recreate all the objects of the Tinaki resort. With the help
of a specialized software complex, the total cost of building a sleeping complex,
which is part of the cultural heritage site of regional significance “Tinak Mud Baths
of the Order of Public Charity, con. 19th century, 1900-1910,” Resort “TinakiI,” Narimanov district of the Astrakhan region and improvement of a specially
protected natural area near the Temple in honor of the Holy Great Martyr and Healer
Panteleimon. The cost of restoration will be 467,577,499,31 rubles, part of the funds
allocated by the state of Russia in the form of a grant and currently some objects
have been restored. However, costs may increase due to an increase in the cost of
resources and materials, labor prices, refinancing rates.

Restoration Technologies of Wooden Architecture Monuments …

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References
1. Norman LO (2019) Blend composition of polymer composition for restoration of destructive
sections of wooden structures elements. RU Patent 2,697,564, 9 Aug 2019
2. Kotenko IA et al (2019) Truss structures reconstruction and historical buildings finishing. In:
Traditions and innovations in construction and architecture. Architecture and urban planning:
a collection of articles, Samara State Technical University, pp 578-586
3. Kovalchuk LM, DYu S, Myshelova GN, Nikulikhina RV (2003) Otsenka tekhnicheskogo
sostoyaniya derevyannykh konstruktsii pri dlitel’noi ehkspluatatsii (assessment of the technical condition of wooden structures during long-term operation). J Stroitel’nye Materialy
(Construction Materials) 5:22–24
4. Islamova DG, Sobirova O (2017) Vosstanovlenie dekorativnykh detalei i metodiki restavratsii
(restoration of decorative parts and restoration methods). J Aktual’nye nauchnye issledovaniya
v sovremennom mire (Current scientific research in the modern world) 5–8(25):13–15
5. Linkov NV (2019) Strengthening of wooden structures using “KM-pasting” connections. J
Industrial And Civil Engineering 3:42–47
6. Lukina AV, Lukin M, Roshchina S, Lisyatnikov M (2015) Recovery wooden beams impregnating polymer composition based on epoxy resins. Forestry Engineering Journal 3:183–190.
https://doi.org/10.12737/14167
7. Spirin IA, Pantyushina LN, Verbitskaya EV (2022) Vozmozhnost’ primeneniya polimernykh
sostavov pri rekonstruktsii derevyannykh zdanii istoriko-arkhitekturnoi tsennosti (the possibility of using polymer compositions in the reconstruction of wooden buildings of historical
and architectural value). J Polzunovskii al’manakh (Polzunovsky almanac) 1:181–183
8. Gordeeva T, Krasova OA (2019) Repair influence of the wooden beam by means of overlay on its
bearing capacity. In: Traditions and innovations in construction and architecture. Architecture
and urban planning: a collection of articles. Samara State Technical University, pp 751–754
9. Fedorov VS, Kupchikova NV, Resnyanskaya AS (2023) Integrated fire safety management
model for high-rise buildings. In: Zolina TV (ed) Innovative development of regions: the
potential of science and modern education. Materials of the VI National Scientific and Practical
Conference with international participation, Astrakhan, pp 14–25
10. Fedorov VS, Zolina TV, Kupchikova NV et al (2021) Design of building structures and
foundations taking into account reliability and regime effects Astrakhan State University of
Architecture and Civil Engineering, Astrakhan
11. Kolchunov VI, Fedorov VS (2020) Conceptual hierarchy of models in the theory of resistance
of building structures. J Industrial And Civil Engineering 8:16–23. https://doi.org/10.33622/
0869-7019.2020.08.16-23
12. Fedorov VS, Levitsky VE (2019) Object-oriented approach to assessment of fire resistance
of structures. In: the potential of intellectually gifted youth—the development of science and
education: materials of the VIII international scientific forum of young scientists, innovators,
students and schoolchildren. April 2019, vol 2. Astrakhan, p 39
13. Nechaeva ML, Kuklin AV, Demidova E et al (2024) Ecological approaches to the formation
of sustainable rural development. E3S Web Conf 549:02009. https://doi.org/10.1051/e3sconf/
202454902009
14. Pryadko I (2020) Restoring pieces of architectural heritage as a factor contributing to biosphere
compatible urban space development. E3S Web Conf 164:05005. https://doi.org/10.1051/e3s
conf/202016405005
15. Lisyatnikov MS, Chibrikin DA, Prusov ES, Roshchina SI (2024) Mechanical characteristics
of polymer composites based on epoxy resins with silicon carbide. Construction Materials and
Products 7(5). https://doi.org/10.58224/2618-7183-2024-7-5-3
16. Shishov I, Lisyatnikov M, Lukin M [et al.] (2023) Application of variable-height beams with
wooden sub-rafter elements in the roof structures of industrial buildings. E3S Web Conf, 460.
P. 10046. doi:https://doi.org/10.1051/e3sconf/202346010046

582

N. V. Kupchikova et al.

17. Lisyatnikov M, Lukin M, Martinov V, Roshcina S (2023) Testing wood-composite reinforced
specimens for shearing along fibers. E3S Web Conf 401:03001. https://doi.org/10.1051/e3s
conf/202340103001
18. Fedorov V, Levitsky V (2018) Modeling of concrete thermal power resistance during the hightemperature heating. IOP Conf Ser Mater Sci Eng 456:012041. https://doi.org/10.1088/1757899X/456/1/012041
19. Kupchikova N, Zolina T (2024) Modeling of seismic load and assessment of its impact on the
building frame and foundations of deep laying of bridge supports. E3S Web Conf 533:02014.
https://doi.org/10.1051/e3sconf/202453302014
20. Zolina T, Kupchikova N, Strelkov S (2020) The expertise of Geo-Base, foundations, and deep
foundations: regional features of accounting and assessment of deformations during operation.
IOP Conf Ser Mater Sci Eng 1079:052037. https://doi.org/10.1088/1757-899X/1079/5/052037

Sustainable Spatial Integration
in the Housing Sector as a Strategic Entry
Point to Urban Quality of Life: A Vision
for Karbala City, Republic of Iraq
E. J. Al-Shebillawy, S. Korniyenko, and B. A. Al-Mossawy

Abstract This study aims to analyze the role of sustainable spatial integration in
the housing sector as a strategic tool for enhancing urban quality of life in the city
of Karbala, by addressing the growing gap between housing supply and demand
and achieving balanced land-use distribution. The research adopts a descriptiveanalytical methodology supported by both quantitative and qualitative data, including
urban planning indicators, residential density metrics, the Shannon Diversity Index
for housing unit variation, and field-based assessments of housing shortages and
projected land consumption up to 2030. Six key spatial strategies are proposed:
infill development, following current urban expansion, leapfrogging growth barriers,
vertical expansion, suburban development, and the planning of new satellite towns.
The findings reveal significant imbalances in density and housing patterns, alongside
disparities in spatial diversity across city districts, highlighting the urgent need for
an integrated planning vision that enhances land-use efficiency and fosters a flexible,
sustainable urban environment. The study recommends the adoption of adaptive
housing policies that integrate density and diversity indicators, promote spatial equity,
and address the social and economic needs of residents—while employing smart
planning tools to shape a balanced urban future for Karbala.
E. J. Al-Shebillawy (B) · S. Korniyenko
Volgograd State Technical University, Volgograd, Russia
e-mail: ehsaan.alshebillawy@volg-edu.ru
S. Korniyenko
e-mail: skorn73@mail.ru
S. Korniyenko
Central Research Institute of Engineering Design of the Ministry of Construction of Russia,
Moscow, Russia
B. A. Al-Mossawy
Voronezh State Technical University, Voronezh, Russia
Al-Furat Al-Awsat Technical University, Najaf Al-Ashraf, Kufa, Iraq
B. A. Al-Mossawy
e-mail: Burak.almossawy@volg-edu.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_46

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Keywords Sustainable integration · Urban housing · Karbala · Planning
strategies · Residential density · Shannon index

1 Introduction
Housing is considered one of the most significant developmental and urban indicators for measuring levels of social and economic progress in cities, as it directly
reflects the state of development and the quality of life of the population [1]. Housing
is no longer merely a basic human shelter, but a central dimension of urban and
social structures, intersecting with economic, environmental, and cultural aspects,
thus attracting increasing attention from policymakers and urban planners worldwide
[2]. Throughout history, housing concepts and patterns have evolved in response to
demographic, economic, and technological shifts [3]. In contemporary cities, residential land use occupies the largest share of urban land—ranging from 35 to 45%,
highlighting the vital importance of spatial planning in managing this sector and
ensuring its sustainability [4]. In the context of Iraqi cities, particularly Karbala,
the housing sector faces growing challenges driven by rapid population growth,
unregulated urban sprawl, and weaknesses in existing planning policies [5]. Karbala
has experienced significant demographic growth since the mid-twentieth century,
with its population increasing from approximately 44,150 in 1947 to over 974,000
in 2023 [6]. This growth is attributed to various factors including internal migration, natural population increase, and the city’s religious and touristic status, which
attracts both visitors and residents from across Iraq and beyond [7]. Accompanying
this rapid expansion is a severe housing crisis, marked by an annual shortfall in
housing supply, the spread of informal settlements, infrastructural degradation, and
low levels of spatial equity in the distribution of services and residential land [8].
A major contributor to these problems is the absence of spatial integration in urban
planning, with horizontal sprawl dominating the urban form—leading to inefficient
land use, limited residential diversity, and weak connectivity among different city
districts [9, 10].
Moreover, the lack of a comprehensive strategic vision that accounts for future
growth and environmental and social sustainability has exacerbated these challenges
[11, 12]. This underscores the urgent need to rethink existing planning and housing
policies towards a more integrated and inclusive approach [13]. Within this context,
the adoption of sustainable spatial integration strategies becomes essential [14].
These strategies aim to maximize the use of available urban resources, enhance
connectivity across urban zones, promote housing typologies that cater to diverse
social groups, and support balanced and sustainable urban development [15].

2 Current and Future Needs for Residential Land Use
in the Holy City of Karbala
Balancing the per capita share of residential land use with planning standards is
one of the most critical indicators for evaluating land allocation efficiency and the
extent to which population needs are met. In the holy city of Karbala, housing demand

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585

represents one of the main challenges facing urban development. Official data reveals
a significant gap between the actual built-up residential land and the planned areas
based on national standards. Estimates for 2024 indicate that the planned residential
land area amounts to 1522.06 hectares, accounting for approximately 36.70% of the
total urban land use—reflecting the high priority granted to the housing sector in
the city’s structural plans. The planned per capita share is estimated at 31.20 m2 /
person, whereas the actual built-up area by 2024 is only 1063.98 hectares, with a
real per capita share of 21.81 m2 /person. When compared to the national planning
benchmark set by the General Commission for Housing (2010), which establishes
a minimum acceptable share of 50 m2 /person, a clear quantitative gap emerges—
18.08 m2 /person for the planned area and 28.19 m2 /person for the actual built-up area.
This indicates a significant shortfall in meeting planning standards at both the design
and implementation levels. Furthermore, projections estimate that by the target year
2030, the city will require 2883.29 hectares of residential land to meet population
demand. This necessitates comprehensive development programs to reduce the gap.
A quantitative analysis of housing unit deficits shows that the number of planned
housing units does not align with actual demand. For instance, the current number of
households is approximately 67,975, while the planned units amount to only 67,090,
resulting in a deficit of 885 units when compared to the planned figure, and a much
larger deficit of 21,077 units when compared to the actual built units, which total only
46,898. In addition, informal housing represents a substantial burden on the urban
landscape. There are an estimated 14,837 informal units built on fragmented orchard
lands and 4737 units in areas classified as encroachments. These numbers reflect a
structural crisis that calls for urgent spatial intervention. By the target year 2030, the
city is expected to need an additional 79,755 housing units to accommodate projected
population growth and urban expansion. This requires the adoption of ambitious
housing policies, the reactivation of stalled housing projects, and the integration of
informal settlements into the urban master plan through targeted urban rehabilitation
programs.

3 Spatial Analysis of Housing Density Patterns in the Holy
City of Karbala
Population density is considered one of the fundamental urban indicators for evaluating the effectiveness of land use and guiding sustainable urban development.
According to the 2024 data for the holy city of Karbala, the overall population density
reached 117.63 persons/hectare (as shown in Table 1), which is below the international minimum standard of 150 persons/hectare required for sustainable urban
development, as stated in the UN-Habitat Report (2014). This indicates weak landuse efficiency and an imbalance in the distribution of residential masses and urban
activities.

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Table 1 Summary of general population density in Karbala city
Indicator

Value

Standard

Note

General population
density

117.63 person/hectare

150 person/hectare

Below standard, requires
spatial redistribution

Table 2 Classification of neighborhoods by net population density (140–250 person/hectare)
Classification

Example neighborhoods

Causes and recommendations

Within standard

Al-imam Ali, Al-Usrah,
Al-Abbasiyah Al-Gharbiyah,
Al-Baladiyah

Good condition requires no major
interventions

3.1 Analysis of Population Density (Net and Gross)
The population density was analyzed on two levels:
• Net density: number of persons per hectare of planned residential land.
• Gross density: number of persons per hectare of total neighborhood area.
Based on Table 2, the findings are as follows:
• Some neighborhoods fall within the acceptable net density range (140–250 person/
hectare), such as: Al-Imam Ali, Al-Usrah, Al-Shurtah, Al-Shahadah, and AlMuwathafin.
• Neighborhoods like Al-Intifadhah, Al-Iskan Al-Askari, Al-Qudhat, and AlNidhal fell below the standard, due to remoteness and poor service coverage.
• Conversely, Al-Iskan, Al-Atibaa’, Ramadhan, Al-Tahaddi, and Al-Ghadeer significantly exceeded the standard, indicating overcrowding that requires regulatory
intervention.
Regarding gross density, based on Table 3 and the standard of 80–200 person/hectare:
• Neighborhoods such as Al-Salam, Al-Baladiyah, and Al-Muallimeen are within
acceptable limits.
• Others like Mulhaq Al-Faris and Tasmim 706 are below standard.
• Ramadhan, Bab Al-Taq, and Bab Al-Sallamah exceed the acceptable range,
putting stress on services and infrastructure, for example, see Fig. 1.

3.2 Residential Unit Density (Units per Hectare)
Residential density was also assessed based on the number of units per hectare,
compared against national benchmarks:
• Net density standard: 24–42 units/hectare.

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Table 3 Classification of neighborhoods by gross population density (80–200 person/hectare)
Classification

Example neighborhoods

Causes and recommendations

Within
standard

Al-Ameen, Al-Asatthah, Al-Binaa
Al-Jahez, Al-Abbasiyah
Al-Gharbiyah, Al-Hur

Balanced and acceptable condition

Below standard Al-Intifadhah, Al-Iskan Al-Askari,
Al-Qudhat, Al-Nidhal
Above
standard

Lacking services and spatial integration;
needs urban and infrastructure upgrades

Al-Iskan, Al-Ta’leeb, Al-Abbasiyah High population pressure; requires
Al-Sharqiyah, Bab Al-Sallamah
service enhancement and decongestion
planning

Fig. 1 a Net population densities; b Gross population densities

• Gross density standard: 12–32 units/hectare, for example, see Fig. 2.
According to Table 4:
• Neighborhoods like Al-Asatthah, Al-Zahraa’, Al-Kafa’at, and Al-Naqeeb fall
within the net density standards.
• Neighborhoods such as Al-Iskan, Al-Bubiyat, Al-Ta’leeb, and Al-Muhandiseen
Al-Zira’yeen significantly exceed the standard, indicating high overcrowding.
• Meanwhile, neighborhoods like Al-Islah Al-Zira’i, Al-Muallimeen, and AlHussain are below the standard, reflecting underutilization of residential land.

3.3 High-Density Strategy
To reduce future land demand and limit the consequences of unsustainable horizontal
expansion, the high-density strategy was proposed. As shown in Table 5, this strategy
yields the following:
• Land needed with horizontal expansion: 5742.2 hectares.
• Land needed with high-density strategy: 1817.93 hectares.

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Fig. 2 a Net housing unit densities; b Gross housing unit densities

Table 4 Comparison of net and gross residential unit density (national standards)
Classification

Example neighborhoods

Causes and recommendations

Within standard

Al-imam Ali, Al-Asatthah,
Al-Zahraa’, Al-Abbasiyah
Al-Gharbiyah, Al-Ghadeer

Optimal land use; considered in good
condition

Below standard

Al-Islah Al-Zira’i, Al-Usrah,
Al-Baladiyah, Al-Hussain,
Al-Qazwiniyah, Al-Muallimeen

Requires more housing units to meet
land capacity

Above standard

Al-Intifadhah, Al-Iskan, Al-Ittarat,
Al-Atibaa’, Al-‘Amil, Al-Ta’leeb

Overcrowded residential units; requires
redistribution of population and density
management

This represents a 68% reduction in residential land consumption, which positively
impacts preservation of agricultural land and controlling urban sprawl.
Table 5 Required residential land area based on high-density strategy
Housing type

Net population density
(persons/ha)

Gross population
density (persons/ha)

Required land area
(hectares)

Single-family attached 250
housing

200

1250

Multi-family housing
(apartments)

500

300

567.93

Total

–

1817.93 hectares

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4 Spatial Diversity of Housing Units in the Neighborhoods
of the Holy City of Karbala
4.1 Relationship Between Residential Density and Housing
Unit Diversity
• High-density neighborhoods with high spatial diversity:
Examples: Al-Abbasiyah Al-Gharbiyah, Bab Baghdad, Al-Sihhah — neighborhoods
that combine relatively high residential density with a high diversity index (≥ 0.80
according to Table 6). These areas represent balanced urban expansion models,
offering a wide range of housing options suitable for various social groups.
• High-density neighborhoods with Very low spatial diversity:
Examples: Al-Iskan, Al-Bina’ Al-Jahez, Al-Ta’leeb, Ramadhan — these neighborhoods exhibit very high population densities (as indicated in Tables 2 and 4) but
have a very low diversity index (≤ 0.15 according to Table 6). This reflects a lack of
spatial sustainability, as a single housing type dominates, resulting in overcrowding
and declining quality of life.
• Low-density neighborhoods with low spatial diversity:
Examples: Al-Iskan Al-Askari, Al-Qudhat, Al-Nidhal, Mulhaq Al-Ta’awun — these
areas have both low density (as per Tables 2 and 3) and low building diversity
(diversity index ≤ 0.43 according to Table 6). These neighborhoods are spatially
fragile and require urban reinforcement and development policies.
• Moderate-density neighborhoods with high spatial diversity:
Examples: Al-Baladiyah, Al-Jam’iyah wa Al-Ulama’, Al-Kafa’at, Bab Al-Taq, Bab
Al-Najaf — these neighborhoods reflect a balanced integration between moderate
density and diverse housing types, enhancing spatial and social flexibility.
Shannon Diversity Index (H )
Shannon’s Diversity Index is calculated using the formula:
Table 6 Shannon index
values

H value

Interpretation

0.00–0.25

Very low diversity (single dominant typology)

0.26–0.50

Low diversity

0.51–0.70

Moderate diversity

0.71–0.85

High diversity

0.86–1.00

Very high diversity

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H’ = −

Pi ln(Pi)

(1)

i=1

Where:
• H : Shannon Diversity Index value.
• p 1 , p 2 , …, pn : Proportion of each housing unit size category (e.g., <100 m2 ,
101–200 m2 , …, >600 m2 ).
• ln(Pi): Natural logarithm of the proportion.

5 Application of the Shannon Index in Karbala
The Shannon Index was calculated for the neighborhoods of Karbala based on
housing unit size categories. The overall city diversity index reached 0.70, indicating
moderate diversity on the city scale. (See Table 7).
However, significant variation was observed between neighborhoods, revealing
imbalances in spatial equity and structural flexibility:
• Neighborhoods exceeding net density standards showed a lower average diversity
index of 0.42, indicating homogeneous housing patterns and high concentration.
• In contrast, low-density neighborhoods exhibited a higher average diversity index
of 0.68, reflecting spatial flexibility that is not being efficiently utilized for
population accommodation.
This analysis underscores the need for integrated planning that combines both density
and diversity indicators when evaluating urban sustainability.
Table 7 Classification of Karbala neighborhoods based on compliance with planning density
standards and diversity index
Classification

Number of
neighborhoods

Percentage (%)

Average diversity index

Below net density
standard

12.5

0.68

Within net density
standard

15.6

0.52

Above net density
standard

71.9

0.42

Below gross density
standard

9.4

0.62

Within gross density
standard

84.4

0.51

Total (all
neighborhoods)

100

0.70

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6 Sustainable Spatial Integration Strategies for Urban
Housing Development in Karbala
• Infill Development Strategy
This strategy focuses on utilizing underused urban land parcels within the existing
built-up area of the city. By reactivating vacant lots through legal, financial, and
planning mechanisms, it minimizes horizontal sprawl, optimizes infrastructure use,
and fosters spatial equity.
• Following Existing Urban Growth Patterns
This strategy supports the continuation of existing urban growth corridors, promoting
spatial coherence and reducing infrastructure costs. It encourages adjacent development to current neighborhoods, facilitating efficient service provision and maintaining social connectivity.
• Leapfrog Development Strategy
Leapfrogging aims to bypass physical or regulatory barriers to urban expansion by
developing suitable zones beyond these constraints. This approach can unlock new
growth areas, alleviate pressure on the urban core, and improve regional spatial
balance.
• Vertical Expansion Strategy
Vertical expansion promotes high-rise residential development to accommodate an
increasing population within limited land. It is a sustainable option to reduce land
consumption, lower service delivery costs, and foster compact urban forms.
• Suburban Development Strategy
This strategy involves planning and developing suburban neighborhoods in peripheral zones to decentralize urban density and create balanced population distribution.
Success depends on providing integrated services and efficient transportation links
to the urban core.
• New Satellite Towns Strategy
This long-term strategy focuses on planning entirely new urban settlements outside
the existing metropolitan boundary. These satellite towns aim to absorb future
growth and provide sustainable urban environments, incorporating smart infrastructure, economic zones, and efficient governance. The strategy enables the separation of polluting activities from residential zones and facilitates the development of
high-quality, cost-efficient housing complexes. Nevertheless, it demands substantial
investment, strong governmental coordination, supportive legislative frameworks to
attract residents and investors, and a regional transportation strategy to maintain
functional linkage with Karbala.

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7 Conclusions
• The spatial and quantitative analysis reveals a clear deficit in residential land
compared to national planning standards, both at the planned and built levels.
This indicates inefficiencies in the spatial distribution of urban development within
Karbala.
• The overall population density in the city stands at 117.63 persons/hectare, which
is below the international threshold of 150 person/hectare required for sustainable
urban development (UN-Habitat, 2014). This reflects a shortfall in the efficient
utilization of urban land.
• The Shannon Diversity Index analysis shows a moderate housing diversity score
of 0.70 citywide. However, the significant variation between neighborhoods points
to spatial inequity and a lack of structural flexibility in the urban fabric.
• Informal and unregulated settlements form a substantial component of the current
residential landscape, with over 14,000 informal units. This illustrates a structural
urban crisis in land governance and spatial integration.
• The high-density development strategy demonstrates significant potential to
reduce residential land consumption by up to 68%, offering a viable path toward
reducing urban sprawl and preserving agricultural lands.
• The housing sector in Karbala lacks a comprehensive strategic vision that integrates density, diversity, and sustainable spatial planning, particularly in peripheral
and overcrowded neighborhoods suffering from service deficiencies.

8 Recommendations
8.1 At the National Policy Level
• Revaluate national housing policies to incorporate principles of sustainable spatial
integration, especially in medium-sized cities such as Karbala.
• Institutionalize population density and housing diversity as core indicators in the
design and implementation of housing and master plans.
• Promote the adoption of spatial intelligence tools (e.g., GIS and urban planning
indicators) to efficiently guide urban expansion and resource allocation.

8.2 At the Local Urban Planning Level
• Implement a balanced population redistribution strategy between urban cores and
peripheries to reduce central congestion and optimize service coverage.
• Launch urban rehabilitation programs to integrate informal areas within the
official urban master plan through structured redevelopment efforts.

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• Improve infrastructure and public transport services in peripheral districts to
enhance their residential appeal and support population growth.
• Channel urban investments into low-density neighborhoods by strengthening their
connectivity and service accessibility.
• Encourage vertical housing development in geologically suitable areas to reduce
unplanned horizontal sprawl and optimize land use.

8.3 At the Social and Housing Diversity Level
• Design and implement housing units with diverse sizes and architectural types to
meet the varied needs of different income groups and family structures.
• Upgrade high-density, low-diversity neighborhoods through comprehensive
housing redevelopment and improved service provision.
• Promote sustainable suburban development through incentives for developers and
government-led green housing initiatives.
• Ensure that the integration of density and housing diversity indices becomes a
foundational principle.

References
1. Baqa MF, Chen F, Lu L, Qureshi S, Tariq A, Wang S, Jing L, Hamza S, Li Q (2021) Monitoring
and modeling the patterns and trends of urban growth using urban sprawl matrix and CAMarkov model: a case study of Karachi, Pakistan. Land (Basel) 10:700. https://doi.org/10.
3390/land10070700
2. Ngema NN, Bokhari A, Mbanga SL (2025) Assessing the impact of social housing on urban
regeneration in south African cities. Front Sustain Cities 7. https://doi.org/10.3389/frsc.2025.
1468964
3. Fan Z, Su T, Sun M, Noyman A, Zhang F, Pentland A ‘Sandy’, Moro E (2023) Diversity beyond
density: experienced social mixing of urban streets. PNAS Nexus, 2(4). doi:https://doi.org/10.
1093/pnasnexus/pgad077
4. Feng J, Hou H (2023) Review of research on urban social space and sustainable development.
Sustainability 15:16130. https://doi.org/10.3390/su152216130
5. Al-Zubaidi H, Al-Janabi K (2022) Urban Sprawl and Land Use Change in Karbala. J Plann
Urban Dev
6. Tariq Muhammad Hassan: Spatial relationships of population growth and poverty in the city
of Karbala, 2023
7. Hassan AS, Kadhum JH, ALSalhy SN, Al-Taai OT (2025) Nanosensor-based satellite images
and GIS filter for urban expansion analysis and its impact on climate change. Exp Theor
Nanotechnol 9:335–346. https://doi.org/10.56053/9.S.335
8. Al-Daini R, Samaneh A, Danilina NV (2020) Strategic urban planning of religious cities: the
case study of Karbala city in Iraq. Vestnik MGSU:1081–1089. https://doi.org/10.22227/19970935.2020.8.1081-1089
9. Al-Shebillawy EJK, Korniyenko S, Al-Mossawy BAK (2025) Sustainable urban development while preserving its historical and cultural identity. AlfaBuild 33:3301. https://doi.org/
10.57728/ALF.33.1

594

E. J. Al-Shebillawy et al.

10. Al-Shebillawy EJ, Korniyenko S, Al-Mossawy BA (2025) Assessment of the Green Urban
Structure and its Role in Promoting Sustainable Environmental Development in the City of
Karbala, Republic of Iraq. In: Radionov AA (ed) Proceedings of the 8th international conference
on construction, architecture and technosphere safety. ICCATS 2024. Lecture notes in civil
engineering. Springer, Cham, pp 426–437. https://doi.org/10.1007/978-3-031-80482-3_41
11. Gustafsson S, Hermelin B, Smas L (2019) Integrating environmental sustainability into strategic
spatial planning: the importance of management. J Environ Plan Manag 62:1321–1338. https://
doi.org/10.1080/09640568.2018.1495620
12. Kadhim A, Çetin D (2022) An evalution on Karbala city slums and concrete blocks in Iraq:
a housing unit design proposal. AURUM J Eng Syst Arch. https://doi.org/10.53600/ajesa.107
8234
13. Al-Bustanji JAMM (2024) Sustainable development strategies for urban planning in municipalities. HumItarian Nat Sci J 5. https://doi.org/10.53796/hnsj51/52
14. Theuner J, Matern A (2022) Transitions to sustainability using strategic spatial planning. disP—
the Plan Rev 58:40–49. https://doi.org/10.1080/02513625.2022.2158599
15. Karbala city master plans (2021). Karbala

Implementation of Pedestrian Call
Buttons at the Semi-Actuated
Intersection of Tulskaya Street and 50
Let VLKSM Street in Tyumen
R. V. Andronov and E. E. Leverents

Abstract The article assesses the results of implementing a pedestrian push-button
device at one of the intersections in the city of Tyumen. Introducing a mandatory
pedestrian phase is not justified in all cases, and the installation of a pedestrian
push-button controller at intersections, as well as converting the intersection to a
semi-adaptive mode, allows for a significant reduction in vehicle delays without
compromising or even improving the level of service (LOS). The article addresses
issues of reducing cargo and passenger delivery times and overall increasing the
average travel speed by optimizing operations and reducing vehicle delays at one of
the signalized intersections in Tyumen—Tulskaia Street and 50 Let VLKSM Street.
In the course of the work, a simulation model of adaptive control for vehicle and
pedestrian flows at the intersection was created. The study concludes that adaptive
traffic control, which adjusts to vehicle and pedestrian flows, is preferable, as the
intersection is isolated and does not have other signalized intersections in close
proximity. As a result, the parameters of the average delay per vehicle were obtained
for the current control scheme and for the adaptive scheme, with the latter showing
smaller delay values.
Keywords Traffic · Push-button · Delays · Road network · Intersection

1 Introduction
Sustainable urban development requires high-quality and comprehensive development of transport infrastructure, as otherwise users bear costs in the form of time
losses for vehicles and pedestrians when crossing transport nodes. According to the
general concept of quality management, the main indicator of the quality of a road

R. V. Andronov (B) · E. E. Leverents
Tyumen Industrial University, Tyumen, Russia
e-mail: andronovrv@tyuiu.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_47

595

596

R. V. Andronov and E. E. Leverents

or street is traffic safety. In connection with this, the main trend has become the allocation of pedestrian movement through intersections into a separate phase. This is
accompanied by a general increase in vehicle delays at intersections and an increase
in the duration of the traffic signal cycle.
According to the authors of the article, optimization of signalized intersection
operations can be divided into two approaches: coordinated control; adaptive control.
The first approach consists of coordinated operation of traffic signals along a street
and ideally should provide uninterrupted movement along the entire street section
with coordinated control, requiring a stop for a red signal only at the first intersection.
It is recommended to use this approach when signalized intersections are relatively
close to each other.
Adaptive control is recommended for so-called isolated intersections, which do
not have other signalized intersections close by on the intersecting streets, and where
vehicles approach not in “platoons,” but in a random order.
The first stage of adaptive control is so-called semi-adaptive control—the use of
a pedestrian button to call the pedestrian phase. The introduction of a mandatory
[1] pedestrian phase in Tyumen has significantly reduced the number of accidents
involving pedestrians. Overall, the number of traffic accidents involving pedestrians
at signalized intersections has noticeably decreased—by as much as 64% [2], and
these nodes have ceased to be areas with high concentrations of pedestrian accidents.
The presence of a mandatory pedestrian phase is not justified in all cases. In some
cases, it is advisable to use push-button controllers for the occasional activation
of the pedestrian phase. Document [3] provides recommendations on the optimal
area of application for such controllers at signalized crossings, but does not provide
recommendations for signalized intersections and street junctions, although these
predominate in the urban street and road network compared to crossings.
Pedestrian push-button devices offer clear operational advantages: they align the
activation of the pedestrian green phase with actual demand, eliminating “empty”
pedestrian intervals and reducing unnecessary stops for motorists, while ensuring
safe crossings and providing accessibility for vulnerable groups through audible
and tactile feedback. Unlike fixed-time signal plans, actuation logic allows flexible
redistribution of green time and helps maintain the level of service (LOS) for both
pedestrians and vehicles under variable or low pedestrian demand. This is particularly
important at isolated intersections, where there is no need to maintain strict corridor
coordination and where every “empty” pedestrian phase directly reduces vehicular
throughput.
However, there is no universal recipe: the effectiveness of push buttons depends
on the local context—approach traffic patterns, peak-hour distribution, share of
turning movements, sight distance, assumed pedestrian walking speeds, and clearance intervals. In some cases, a constant pedestrian phase is justified (for example,
near transit hubs, schools, or major pedestrian generators with consistently high
demand), while in others, actuation can significantly reduce delays without compromising safety. Therefore, transitioning to actuated pedestrian control should be based
not merely on the general perception of “convenience,” but on a testable hypothesis

Implementation of Pedestrian Call Buttons at the Semi-Actuated …

597

that considers local conditions and accessibility requirements, including adaptive
extension of crossing times for slower pedestrians.
International practice offers different implementations of demand-responsive
control: from push-button detectors with tactile/audio feedback to “passive” systems
(video/infrared) and Puffin logic, which cancels false calls and extends the phase
when a pedestrian is still on the crosswalk. In contexts with high speeds and multilane roadways, hybrid pedestrian beacons (HAWK/PHB) are also used, activated by
the pedestrian. These approaches demonstrate that the “button” is part of a broader
actuation philosophy, where accurate demand detection, prevention of empty phases,
and ensuring safety during clearance are key. However, transferring such solutions
without adapting them to local infrastructure and road user behaviour often shifts the
balance between delay reduction and safety.
This is why local studies are essential at a specific site in a particular country:
calculation methods for “WALK” time and assumed pedestrian speeds, accessibility
standards, requirements for push-button and indicator placement, and signal coordination regimes vary from jurisdiction to jurisdiction. For Russian cities, including
Tyumen, it is important to empirically assess how an actuated mode affects the
average vehicle delay and pedestrian LOS under site-specific traffic volumes and
daily profiles, considering seasonality, weather factors, and the share of vulnerable
users. This should include detector calibration, verification of false call cancellation,
safety assessment on approaches with limited visibility, and compliance checks with
local standards for accessibility and acoustic signalling.
A practical research roadmap for such an intersection should include: collection
and stratification of vehicle and pedestrian flows by hour and direction; audit of
push-button placement and accessibility; development and calibration of a simulation model for existing and actuated scenarios; calculation of delays, queues,
and average travel speeds for passenger and freight vehicles; sensitivity analysis
to changes in demand and detection parameters; safety evaluation (conflict analysis, sight distance, approach speeds), and verification of criteria for switching to
actuated control. This sequence allows the “convenience” hypothesis to be validated
using quantitative metrics and, if confirmed, to recommend pedestrian actuation for
that specific intersection—without blindly transferring solutions from other contexts.
To determine such an appropriate area, a sufficient number of studies and justifications must be carried out. Despite the fact that the methods of traffic simulation modeling and their software products, such as VISSIM, have become quite
well developed in recent times, the issue of the optimal deployment zone can only
be resolved through experimental study, taking into account the specifics of major
Russian cities.
In the latest edition of the HCM [4], definitions of level of service have been
separated for individual street elements and road users (street segment, intersection,
approach, cyclists, pedestrians, etc.), as shown in Table 1.
Engineering decisions for intersection realignment or organizational decisions
for traffic signal modifications shall be made based on an evaluation of the level of
service. The operation of the street network at levels A, B, and unacceptable at level
E F is preferred. It is recommended to assess the level of service by the average delay.

598
Table 1 Service level values
depending on the intersection
delay value [4]

R. V. Andronov and E. E. Leverents

Level of service

Control delay per vehicle in second (s)
Signal

Roundabout

AWSC/TWSC

d ≤ 10

10 < d ≤ 20

10 < d ≤ 15

20 < d ≤ 35

20 < d ≤ 50

15 < d ≤ 25

35 < d ≤ 55

35 < d ≤ 50

25 < d ≤ 35

55 < d ≤ 80

50 < d ≤ 70

35 < d ≤ 50

80 < d

70 < d

50 < d

Automated traffic control systems used in cities allow both coordinated and adaptive traffic-actuated signal control. Input information on the state of traffic flow is
received by the system mainly from video detectors installed at the main intersections
of main streets.

2 Object of Research
In this article, the intersection of Tulskaia Street and 50 Let VLKSM Street is considered, where previously traffic signal control was carried out without a dedicated
pedestrian phase, and where a pedestrian push-button controller was installed. Earlier,
the authors [5] proposed a definition of an isolated intersection, since the criterion
of having no other signalized facilities (intersections or crossings) within one mile
(1.6 km) is considered expert-based and does not meet objective requirements.
In transportation engineering, an intersection is considered isolated when its operation is not significantly influenced by neighbouring signalised sites — neither by
incoming platoons nor by the timing of arrivals. This criterion is determined not only
by distance but also by the relationship between travel times, cycle lengths, and the
presence or absence of coordination. In practice, for an urban street network with
typical city speeds, when traffic signals are spaced more than 0.5 miles (≈800 m)
apart, the influence of the adjacent signal on queue formation and flow progression is
greatly reduced. On higher-speed arterials, the “connectivity” threshold can extend
to around 1 mile 1.6 km).
When designing signal timing plans, it is important to note that even relatively
close intersections can remain independent if the travel time between them does
not correspond to conditions for stable progression (travel-time-to-cycle-length ratio
outside the 0.4–0.6 range) or if there is no offset-based coordination in place. In such
cases, coordination yields minimal benefit, and each signalised intersection should
be managed according to its own local traffic parameters. This is especially relevant
for sites located outside structured coordinated corridors, or in areas with variable
demand and intermittent flow patterns.

Implementation of Pedestrian Call Buttons at the Semi-Actuated …

599

The intersection considered in this study meets exactly these criteria. It is located
at a distance from the nearest signalised sites greater than the typical “zone of influence” for the prevailing speeds and cycle lengths, and there is no active coordination
with neighbouring traffic signals. An analysis of travel times and traffic flow structure confirms the absence of stable platoons formed by adjacent intersections. These
factors allow it to be classified as an isolated intersection and justify the examination of semi-actuated and fully actuated control scenarios without strict coordination constraints, thereby providing additional opportunities to optimise delays and
improve the overall level of service.
According to the authors, this intersection is considered isolated, as there are
no other signalized intersections in its immediate vicinity. Therefore, optimizing
its operation is best achieved through the use of adaptive control, both for vehicle
flows (using TrafiCam video detectors) and for pedestrian flows (using the pedestrian
push-button device).

3 Experiment
At the studied node, vehicle traffic intensities were measured during the time intervals
8:00–9:00, 10:00–11:00, 13:00–14:00, and 17:00–18:00, as well as the number of
sampled activations of the pedestrian controller. To reliably determine the average
number of activations throughout the day, it is necessary to determine the required
sample size of measurements based on preliminary data. For this purpose, we use
the formula:
n=

(Iav

t2σ 2N
)2 N + t 2 σ 2

(1)

where
n—duration of observations, hours;
t—the reliability factor corresponding to a 90% confidence level;
σ—standard deviation of the sample mean;
N—the population size of the studied data, equal to 24 thirty-minute intervals
(from 8:00 to 20:00);
Δ—allowable error in determining the mean, equal to 15%;
I av —average number of activations of the pedestrian push-button device calculated from the thirty-minute interval data.
According to preliminary data from 30-minute measurement intervals, the number
of activations of the pedestrian controller ranged from 5 to 10 times. The obtained
measurement duration (n) showed that to determine traffic intensity with a confidence
level of 90% and an allowable error of 15%, data from 15 measurements of 30 min
each are required. Thus, the required observation duration amounts to 7 h and 30 min.
The obtained observation time was distributed throughout the day within the
interval from 8:00 to 20:00 [6, 7].

600

R. V. Andronov and E. E. Leverents

During “peak hours,” traffic signal control with the pedestrian phase was used in
55–60% of cases; during other hours, in 20–35% of cases.
Next, capacity, directional flows, and delay times were calculated using methods
from [3, 4] pedestrian flow through the studied intersection is insignificant and during
“peak hours” amounts to: 85 pedestrians per hour across 50 Let VLKSM Street and
28 pedestrians per hour across Tulskaia Street. The capacity reduction coefficients
for conflicting directions before the introduction of the pedestrian phase according
to are 0.95 and 0.8, respectively.

4 Results and Discussion
According to the obtained calculations (Fig. 1, Tables 2 and 3), it can be seen that
the introduction of a separate pedestrian phase sharply reduced the intersection’s
capacity and increased the overall delay time to pass through it. Subsequently, the
installation of a pedestrian push-button device significantly reduced the magnitude
of delay and total time losses.
Thus, the installation of the pedestrian push-button device at the intersection
proved to be quite effective and allowed a reduction in time losses at the intersection
by 35%, without compromising traffic safety. The obtained data can further be used
for a technical and economic analysis to justify the use of the pedestrian push-button
device.

Fig. 1 Average delay per vehicle across all traffic directions under different intersection operation
modes, seconds

Implementation of Pedestrian Call Buttons at the Semi-Actuated …

601

Table 2 Magnitude of delays and time losses at the intersection

Average delay per
vehicle, s

Total flow delay
(loss), vehicles per
hour (veh/h)

50 Let VLKSM
(towards
Permyakova St.)

50 Let VLKSM
(towards
Melnikayte St.)

Tulskaia st.

No dedicated
pedestrian phase

With dedicated
pedestrian phase

With pedestrian
push-button device

No dedicated
pedestrian phase

255

With dedicated
pedestrian phase

521

With pedestrian
push-button device

337

50 Let VLKSM
(towards
Permyakova St.)

50 Let VLKSM
(towards
Melnikayte St.)

Tulskaia st.

No dedicated
pedestrian phase

With dedicated
pedestrian phase

With pedestrian
push-button device

Table 3 Level of service

Average delay per
vehicle, s

Table 4 shows that implementing adaptive control significantly reduces delay
times by 21%. However, during peak hours, the effectiveness of adaptive control
is less pronounced. This is because as traffic volume increases, the traffic flow
becomes more stable, reducing the opportunity to utilize the latent intersection
capacity that adaptive control exploits. The variation in delay values is also explained
by the frequency of vehicle detection system activations. If the activation frequency
increases, the overall intersection capacity decreases, and the average vehicle delay
time rises. Thus, implementing adaptive traffic control at the intersection would allow
for a 14–37% reduction in average delay times.

602

R. V. Andronov and E. E. Leverents

Table 4 Comparison of delay times under pre-timed control
Existing delay time. s/v

Simulated delay time,
s/v

Relative change (%)

8–9 h

24,0

20,9

− 14

10–11 h

29,0

18,2

− 37

13–14 h

26,0

19,8

− 24

17–18 h

45,7

37,8

− 17

Average delay per
vehicle, s

29,3

23,2

− 21

5 Conclusions
At the studied intersection, a number of innovations in traffic management were
tested, including the mandatory allocation of pedestrian movement to a separate phase
according to [1] and the installation of a pedestrian push-button device. Based on
measurements and estimations [3], the introduction of the pedestrian phase increased
total delays by 50%, while the installation of the pedestrian push-button device
allowed these delays to be reduced back by 35%.
The introduction of a mandatory pedestrian phase significantly enhances traffic
safety, especially for vulnerable road users—pedestrians. The use of pedestrian pushbutton devices is preferable, as it reduces vehicle delays and improves the overall
level of service (LOS). Currently, determining the feasibility of using pedestrian
push-button devices at signalized intersections under various traffic flow intensity
ratios is an important task, since otherwise this would require simulation modeling.
A further recommendation is to implement adaptive traffic control for the vehicle
flow, including delay calculations, LOS determination, and proposed engineering
solutions according to [8], such as adding lanes immediately before the intersection,
providing a dedicated left-turn lane, and implementing displaced left-turns [9].
Acknowledgements Authors wishing to acknowledge assistance or encouragement from
colleagues, special work by technical staff or financial support from organizations should do so
in an unnumbered.

References
1. GOST R 58653–2019 (2019) Automobile roads of general use. Intersections and junctions.
Technical requirements, Standartinform, Moscow
2. Drogaleva EV, Yashina EY (2017) Assessment of the effectiveness of strategic management of
traffic flows. Organ Road Traffic Saf:180–182
3. ODM 218.6.003–2011 (2013) Methodological recommendations on the design of traffic signal
facilities on highways. Federal Road Agency (Rosavtodor), Moscow
4. Highway Capacity Manual (2000) Manual (2.1), Washington, DC

Implementation of Pedestrian Call Buttons at the Semi-Actuated …

603

5. Andronov RV, Leverents EE, Chepur PV (2025) Absence of autocorrelation in traffic flow time
series as a criterion for isolation of signalized intersections. T-Comm: Telecommun Transp
19(3):54–60. https://doi.org/10.36724/2072-8735-2025-19-3-54-60
6. Kremenets YA, Pechersky MP, Afanasyev MB (2005) Technical means of traffic organization.
IKC Akademkniga, Moscow
7. ODM 218.2.020–2012 (2012) Methodological recommendations on the assessment of highway
throughput capacity. Informavtodor
8. Leverents EE, Andronov RV (2025) Impact of road widening at intersections on vehicle delays
and level of service under fixed and adaptive traffic signal control. In: Proceedings of the 8th
international conference on construction, architecture and technosphere safety (ICCATS 2024),
vol 565. Springer Nature Switzerland AG, Cham, pp 459–468. https://doi.org/10.1007/978-3031-80482-3_44
9. Andronov R et al (2019) The effect of the traffic organization method at a controlled intersection
on the uniformity of traffic capacity. In: E3S web of conferences 135. EDP Sciences

Engineering Structure Safety,
Environmental Engineering
and Environmental Protection

Mitigation of Risks at the Stages
of the Life Cycle of Wastewater
Treatment Plants
N. G. Vurdova, P. Yu. Vurdov, and Yu. A. Birman

Abstract This study analyzes the key risks associated with the life cycle of wastewater treatment plants (WWTPs), including environmental, technical and economic
aspects. Based on the analysis of design, construction, operation and decommissioning stages, a risk management assessment system is proposed. Case studies of
Russian industrial facilities demonstrate that early risk assessment in accordance
with ISO standards reduces operating costs by 40%. Integration of proactive (pilot
testing) and reactive (monitoring systems) measures increases system sustainability.
A comprehensive study of the effectiveness of the investment project for the reconstruction of treatment facilities was conducted. The results of the study can be
applied to improve environmental safety and economic sustainability of industrial
enterprises.
Keywords Environmental risk · Risk assessment · Wastewater treatment plants ·
Environmental safety · Sustainability of enterprises

1 Introduction
Enterprises belonging to the 1st category of negative environmental impact (NEI)
according to the Russian legislation are serious sources of pollution. Therefore,
they are subject to close attention of the state and the public. One of the critical
elements of such enterprises is wastewater treatment plants (WWTPs), the efficiency
of which determines the environmental safety of the region and economic sustainability. Assessment of environmental and economic risks in this area allows to identify potential threats to the environment and determine measures to reduce their
consequences.
N. G. Vurdova (B) · P. Yu. Vurdov
National Research Technological University MISIS, Moscow, Russia
e-mail: nadya_vurdova@mail.ru
Yu. A. Birman
LTD “Uniecoprom”, Chehov, Moscow, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_48

607

608

N. G. Vurdova et al.

Implementation of wastewater treatment technologies is subject to a number of
risks, including environmental, technical, economic, social, as well as problems
related to public health. The management of these risks has been mastered quite
well, meanwhile the impact of risks during the life cycle of WWTP, their impact on
environmental safety is not actually defined.
In Russia, 30% of accidents at WWTPs are caused by insufficient risk assessment
at the early stages of reconstruction and modernization projects, which leads to
violations of environmental standards and financial losses [1].
The present article is a continuation of a comprehensive study of the effectiveness
of an investment project for the reconstruction of wastewater treatment plants [2, 3].

1.1 Relevance of the Study
Risk is considered to be a quantitative measure of the degree of danger (safety). Environmental risk is the probability of negative changes in the ecosystem as a result of
economic activity. Economic risk in the context of assessing the environmental safety
of the enterprise is associated with the financial consequences that may arise in the
case of violations of environmental standards. These are fines, damage compensation
and loss of reputation [4].
It is necessary to accurately assess the level of safety, according to Kharchenko
and Kucher (2022), providing “a balance of costs, benefits and the magnitude of
the hazard”. Without this, “there is a violation of the balance between safety and
development—an unjustified increase in safety is detrimental to development. And
vice versa, underestimation of danger can lead to significant damage” [5].
Any risk is assessed in terms of the probability of occurrence of the event and
the severity of consequences. Most often qualitative assessment is carried out, less
often—quantitative, due to its complexity and variety of methods. As a rule, environmental and economic risk management is carried out in three stages [6]: (1)
identification, systematic study of risks characteristic of a given production; (2)
risk assessment, determination of probability and size of damage; (3) selection of
management methods and their application.s
Measures of impact on the risk, outlined in [7–9], are risk mitigation (ang., mitigation strategy). This is a plan of risk management measures aimed at reducing
the probability of risk realization, reducing the severity of consequences from their
realization. As applied to WWTP such measures can be divided into three groups:
1. Technological solutions. Modern technologies of wastewater treatment allow to
significantly reduce environmental and economic risks. These can be improved
methods of biological treatment, new sorption, filtering materials, reagents, etc.;

Mitigation of Risks at the Stages of the Life Cycle of Wastewater …

609

2. Organizational measures. Inclusion of measures to control the operation of
wastewater treatment plants (WWTP), regular monitoring of emissions and
wastewater, as well as staff training into the company’s strategy;
3. Investments in modernization. Given the high risks associated with the operation
of outdated wastewater treatment facilities, investment in their modernization is
a key element in reducing environmental and economic threats.
The formation of a reasonable approach to mitigating the risks that may arise
during the reconstruction or modernization of wastewater treatment plants relies on
the structure of the life cycle of WWTPs, which was presented in the works [10, 11].
Reconstruction, modernization or construction of a treatment plant is an investment
project, which consists of five consecutive stages: preliminary planning—design—
construction—operation—end of life cycle (LLC).
Justification of investment in such a project is a very complex task, the investor
needs to understand the effectiveness of the invested funds. In our previous studies
several approaches to investment justification were investigated. It is proposed to
gradually introduce low- and no-drain (closed) water management systems at enterprises with acceptable efficiency, based on the principle of ecological and economic
balance [12].
At the design stage, it is customary to develop an ESIA section, which is a mandatory part of the design documentation for any construction projects. However, environmental risk assessment, consisting in the definition of hazard types, identification
of risks (threats), obtaining quantitative estimates of probabilities of occurrence of
unfavorable events and their consequences, as a rule, is not carried out.
Thus, the purpose of this study is to develop recommendations on the selection
of risk management methods at each stage of the life cycle of sewage treatment
facilities.

1.2 Risk Identification and Assessment
Most often for risk assessment statistical methods are used: phenomenological, deterministic, probabilistic. Their main advantages and disadvantages can be found in
[13, 14].
For example, the ISO 31000 standard is widely used, according to which hazard
identification (HAZID), environmental risk analysis (ENVID) [7].
We can still consider Monte Carlo method for modeling different scenarios and
calculating probabilities [15]. Or use machine learning (ML) to predict risks based
on historical data [16]. To date, ML might be too complex due to the insufficient
number of trained personnel.

610

N. G. Vurdova et al.

A more traditional option is to use analysis of hierarchy method (AHP) to rank
risks by their significance, taking into account expert opinions and statistical data,
AHP will add structure [17]. Or apply principal component analysis (PCA) to identify
hidden factors affecting environmental risks, which will simplify the model and focus
on key variables [18].
If there is a sufficient amount of historical data on accidents, equipment parameters, and operating costs, it is possible to apply the Markov chain analysis method
to model the transitions between system states (normal operation, accident, repair)
and calculate probabilities [19].
A combination of methods can be proposed: for example, the analysis of “time
series” to identify trends in accidents and the application of “decision trees” to assess
the influence of various factors on the probability of risks. This combines statistical
analysis and a probabilistic approach [20].
This paper presents a more visualization-friendly bow-tie method to visualize
causes, consequences and barriers. Quantitative metrics were determined using a
probability-influence matrix (5 × 5) with risk scores ranging from 1 (low) to 25
(critical).
Since many accidents cannot be prevented, the task of minimizing the damage
from them is of particular importance. Therefore, it is proposed to determine the
size of the expected damage on the basis of the stochastic model of Churchman
(1967)—inventory management with random demand (1):
∞

C(x) = c1

(y − r)f (r)dr + c2
0

(r − y)f (r)dr,

(1)

where C(x)—mathematical expectation of total costs; y—stock level, r—demand
value; f (r)—distribution law; c1 —stock holding costs; c2 —shortage penalty.

2 Results and Their Discussion
There is a well-known approach of large companies to the assessment of capital
investments according to the AACE standards with assessment by five classes [21].
The accuracy of assessments from the fifth to the second increases from 50 to 15% at
the moment of the beginning of construction. Figure 1 shows the structure of costs and
the basis for the formation of the cost of the investment project for the construction
and reconstruction of WWTPs, according to the 4th class of AACE. It is obvious
that the main part falls on the construction and installation works. But there is one
nuance in the costs at the pre-project stage, which for wastewater treatment plants,
as will be shown below, is of key importance.

Mitigation of Risks at the Stages of the Life Cycle of Wastewater …

611

Fig. 1 Cost structure and the basis of cost formation of the investment project for construction and
reconstruction of the water treatment plant

The discrepancy between bids from suppliers with low procurement costs for
equipment and materials (CAPEX) and those with higher procurement costs but
lower total cost of ownership (OPEX) can be several times greater. Therefore, it is
important to compare and analyze costs at all stages of the life cycle of a wastewater
treatment plant being constructed or renovated.
Often the completeness of the Terms of reference (ToR) depends not only on the
technical features of the design object, but to a greater extent—on the cost of the
future construction object.
The GOST [22], which sets the right direction and approach, was recently issued
to help specialists. Namely, for such a complex technological object as WWTP, it
is important to conduct a thorough preliminary survey and develop basic technical
solutions (BTS) with the analysis of several development options.
Practice shows that industrial enterprises, as a rule, start work from this stage. At
the same time, it is possible to obtain financing already at the early stage. But water
utilities have not had such an opportunity so far. With the release of GOST, there is
a chance to justify and, most importantly, to lay down the necessary funds.
Three main points when forming the Technical Assignment:
1. Collection of initial data—the amount and composition of wastewater should be
for three years.
2. Pre-project studies, including pilot tests (PPI)—to determine the cause of
deterioration of treated water quality indicators; selection of technology.
3. Selection of analogs—in accordance with Information Guide BAT [23]. If the
technology is not described in the handbook, then for enterprises of the 1st
category of NEI there should be a positive implementation at least at two sites.

612

N. G. Vurdova et al.

Table 1 Comparison of actual and normative values of pollution indicators in rainwater
Index

Value according to SP Actual value Technological indicators*
for water body category B

Rainwater
Suspended solids, mg/dm3
BOD5 , mg O2 /dm3
COD, mg O2

/dm3

500

2.0–8.0

1.2–3.4

–

Petroleum products, mg/
dm3

300
8

0.1–0.3

1.0

Phosphorus phosphate, mg/
dm3

–

1.0

2000

2.0–8.0

100

1.2–3.4

800

–

0.1–0.3

1.0

–

1.0

Muddy wastewater
Suspended solids, mg/dm3
BOD5 , mg O2 /dm3
COD, mg O2

/dm3

Petroleum products, mg/
dm3
Phosphorus phosphate, mg/
dm3

20
–

*Technological indicators—according to app. 3 to Resolution of the Government of the Russian
Federation No. 1430 dated September 15, 2020 “On Approval of Technological Indicators of the Best
Available Technologies in Wastewater Treatment Using Centralized Wastewater Disposal Systems
of Settlements or Urban Districts”

Three main points in the development of main technical solutions (MTS): the
first two are similar, the third is to choose the best option in terms of total cost of
ownership. Unfortunately, the cost of project implementation is often the deciding
factor. Risk assessment is usually not performed.
Example. A city plans to build a rainwater drainage system with local treatment
facilities and discharge into a surface water body. Out of the existing 36 outlets of
the rainwater drainage system, 21 outlets have passports. Out of 21 outlets, only 10
of them are regularly measured. Conclusion. There is a lack of verified baseline data:
measurement results cannot be used in the design. Then, according to paragraph
7.6.2. of SP 32.13330.2018. “Sewerage. Sewerage pipelines and facilities”, taking
into account the lack of actual data on the qualitative composition of incoming
wastewater, the data in accordance with Table 15 of the SP are accepted. Comparison
of actual, but not verified indicators with standards is presented in Table 1.

Mitigation of Risks at the Stages of the Life Cycle of Wastewater …

613

Implications. The process equipment envisaged in the project is likely to provide
the required treatment of actual wastewater, but CAPEX and OPEX costs will be
significantly overestimated (~ 30%).
When constructing or modernizing a WWTP, the risks involved are not limited
to the ToR and design stages. Risk assessment should be carried out throughout the
entire life cycle of water treatment system implementation at each stage: development of ToR—design—construction—commissioning—operation—decommissioning (mothballing). To account for uncertainty, it is recommended to implement early warning systems to detect changes and implement measures to increase
resilience to contingencies. For this purpose, it is convenient to use a 5 × 5 matrix
(Table 2), which qualitatively allows to assess the severity of consequences. The
assessment is carried out in points by multiplying the values of the weight coefficient
by the probability of occurrence of the event.
Analysis of the risk matrix shows that the reasons leading to unacceptable
consequences, except for natural disasters, are errors:
• at formation of ToR, if by 60% or more TOR contains erroneous solutions;
• during design, if 80% or more of design decisions are erroneous.
Significant consequences occur when:
• formation of the ToR, if from 40 to 59% of the ToR contains erroneous solutions;
• during design, if from 40 to 79% of design solutions are erroneous;
• during operation, the achievement of standard quality of wastewater treatment
cannot be achieved without modernization of individual units at the sewage treatment plant, which entails stopping the operation of individual processes (stages)
of wastewater treatment.

Table 2 Matrix of risks throughout the life cycle of WWTPs
Cause of the event

Probability of occurrence (% of 0–19 20–39 40–59 60–79 80–100
erroneous decisions)
Weight factors

Natural cataclysm

Errors in the
4
formation of the ToR

Errors in design

Errors during
operation

Scheduled or
unscheduled repair

Minor—1–4 points; serious—5–6 points; significant—7–12 points; critical (unacceptable)—more
than 12 points

614

N. G. Vurdova et al.

Table 3 Estimation of environmental damage from accidents at the wastewater treatment plant of
the enterprise in 2020
Types of impact

Damage, thousand rubles

Payments for pollution, thousand rubles

Water pollution

4045.13

2993.40

The choice of the method for assessing the probabilities of negative factors
depends on the availability and quality of information about the event under consideration: the conditions of occurrence and the type of manifestation; the frequency of
events per unit of time and their intensity.
From the definition of “environmental damage” it follows [24] that it is an indicator
of environmental and economic risk of the enterprise, which reflects “… the change
in the utility of the environment as a result of its pollution and is estimated as the cost
of its restoration”. To calculate environmental damage, three key spheres of impact
on: atmosphere, water and soil are usually distinguished. Assessment of damage in
each of them is carried out on the basis of state and industry generalized indicators
of specific damage, expressed both in natural units and in monetary equivalent.
Let’s analyze the data of the enterprise on calculation of damage and payments
for NEI presented in Table 3.
Table 3 shows that the total damage is almost 1.5 times higher than the amount
of payments for pollution, which indicates that the compensation of damage is only
partial and does not cover all the costs of environmental restoration. An increase
in compensation payments can help to reduce the environmental and economic risk
of the enterprise. In this context, environmental risks can be assessed through the
probability of realization of a number of factors, such as emissions and discharges
arising from the operation of the WWTP before the reconstruction using existing
technologies, as well as the formation of sediments after treatment.
To predict the damage, as an alternative methodology, an assessment of technogenic risks was carried out according to [25]. The statistical forecasting method was
used to calculate the predicted damage based on the data on accidents and incidents
at the enterprise in the period from 2012 to 2021. The predicted value of damage was
calculated by the methods of determining the average (weighted) or the method of
determining the probability, using the data on damage and the number of accidents.
From the analysis of statistical data, we established the exponential law of distribution of a random accident with the parameter λ (2). We determine the optimal
value of the reserve from a single accident (3) and per year taking into account the
gamma distribution of accidents (4):
c2
,
c1 + c2

(2)

c2
1
,
ln 1 +
λ
c1

(3)

1 − e−λy =
y0 =

Mitigation of Risks at the Stages of the Life Cycle of Wastewater …

615

λn
F(y) =
G(n)

yn−1 e−λy dy,

(4)

where n is the number of accidents per year; λ is the distribution parameter.
We calculate the stockpile holding costs (c1 ) through the 2021 inflation rate
(8.4%), and the cash shortfall for the remediation (penalty (c2 )) through the credit
rate of 19% per annum. In 2021, loans were available at a rate of 19–21%, which is
taken as the deficit penalty [25]. We use statistical estimates of the parameters of the
gamma distribution: λ̃ = 0.000119, ñ = 1.4803 [25] and solve Eq. (4) with respect
to y. We obtain the value of the reserve of funds for liquidation of consequences of
damage from an emergency situation in 2021 will make yopt = 8073.19 thousand
rubles.
The analysis of risks of WWTP, allowing to show the connection of sources of
risk and consequences is convenient to carry out the method “bow-tie analysis”. It
is a way of describing the path of development of a hazardous event from causes to
consequences by means of a scheme with indication of barriers (management and/
or control measures) between causes and hazardous events, as well as hazardous
events and their consequences. For the life cycle of a WWTP, the resulting diagram
is presented in (Fig. 2).
Performing such an analysis at early stages allows selecting a water treatment technology with a minimum set of unknown risks, as well as minimizing the envisaged
costs of accident prevention (Table 4).
The application of proactive measures (e.g., pilot testing) reduces design errors
by up to 55%. The application of reactive measures (e.g., installation of automatic
sensors) reduces operational failures by up to 40%.

4.2

4.4

4.1

4.3

2.3

1.3

1.4

Incorrect Technical
Building

Fig. 2 Mitigation of risks during the life cycle of wastewater treatment plants (description in Table 4)

Factor 4. Unjustified cost
savings

3.2

3.1

2.2

2.1

Factor 2. Incompleteness of
baseline data on the qualitative
composition of wastewater

Factor 3. Use of wrong
analogs

1.2

1.1

Factor 1: Incompleteness of
baseline data on
wastewater discharge

8.1

9.1

7.4

8.2

9.2

7.5

7.2

7.3

6.6

6.5

7.1

6.3

6.2

5.3

6.4

5.5

5.2

6.1

5.4

5.1

Factor 9. Increased capital
and/or operating costs

Factor 8. Inability to start
up treatment facilities

Factor 7. Failure of
pretreatment equipment
and facilities

Factor 6. Failure of
biological treatment
equipment and facilities

Factor 5. Failure of mechanical
and/or physical-chemical
treatment equipment and
facilities

616
N. G. Vurdova et al.

Mitigation of Risks at the Stages of the Life Cycle of Wastewater …

617

Table 4 List of hazardous events and description of identification, prevention and mitigation
measures
Interventions to prevent the occurrence of a
negative factor (left)—proactive measures

Measures taken at the onset of risk (hazard) to
reduce negative environmental consequences
(right)—reactive measures

Factor 1: Incompleteness of baseline data on
wastewater discharge:

Factor 5. Failure of mechanical and/or
physical–chemical treatment equipment and
facilities

1.1 Collection of baseline data on wastewater
discharge is determined for at least 3 years

5.1 Analysis of the causes of equipment
failure—inspection of the operation of the
relevant mechanical and/or physical and
chemical treatment facilities: grids, sand traps,
primary sedimentation tanks, oil traps, flotators,
reagent facilities

1.2 Application of the data of the
enterprise-analogues (at least 3 analogues, the
average is taken)

5.2 Introduction of coarse cleaning gratings (or
fine cleaning gratings, to be determined at stage
5.1)

1.3 Drawing up an hourly schedule of
wastewater inflow to the sewage treatment
plant

5.3. Introduction of intermediate tanks into the
scheme

1.4 Averaging of wastewater flow rates

5.4 Testing of new reagents or materials to
optimize the operation of the facilities in the
absence of recommendations for appropriate
studies at the TOR stage

Factor 2. Incompleteness of baseline data on
the qualitative composition of wastewater

5.5 Conducting operator training, retraining of
technologists

2.1 Collection of baseline data on types and
concentrations of pollutants generated at the
enterprise

Factor 6. Failure of biological treatment
equipment and facilities

2.2 For newly designed production,
determination of the type of wastewater and
concentrations of pollutants in the wastewater
of enterprise-analogues (at least 3 analogues,
application of averaged indicators)

6.1 Analyze the causes of failure or failure to
ensure proper quality of wastewater treatment
at the stage of biological treatment

2.3 Averaging of wastewater concentrations

6.2 When high loads of organic matter on
activated sludge and suppression of nitrification
processes occur—device averaging tanks,
primary settling tanks, introduction of
membrane blocks to increase the dose of
activated sludge, etc.

Factor 3. Use of wrong analogs

6.3 In the absence of biological
dephosphotization as a result of lack of
formation of easily degradable organic
substances in acidifier—reconstruction of zones
in aeration basin, introduction of reagent farm
for chemical dephosphotization
(continued)

618

N. G. Vurdova et al.

Table 4 (continued)
Interventions to prevent the occurrence of a
negative factor (left)—proactive measures

Measures taken at the onset of risk (hazard) to
reduce negative environmental consequences
(right)—reactive measures

3.1 Careful selection of the analog. The analog 6.4 In case of oxygen deficiency in aeration
should include full identification of production zones of the aeration tank—replacement of
processes
blowers, aerators
3.2 In the absence of an analog that includes
full identification of production processes,
laboratory and/or pilot testing should be
conducted

6.5 In case of insufficient qualification of
employees: training of operators, retraining of
technologists

Factor 4. Unjustified cost savings

6.6 Acquisition of equipment for operational
control of biological treatment processes

4.1 Pre-design solutions, laboratory and/or
pilot tests, especially when developing
technological schemes for industrial
wastewater treatment that have no reliable
analog

Factor 7. Failure of pretreatment equipment
and facilities

4.2 Selection (approval) of equipment tested at 7.1 Analyze the causes of failure or failure to
similar WWTPs
ensure proper quality of wastewater
pretreatment
4.3 The number of employees servicing the
7.2 If the quality of biological treatment is not
sewage treatment plant and their qualifications achieved, it is necessary to fulfill clauses
should meet the requirements for the
6.1–6.5
equipment and treatment technology to be
installed
4.4 Involvement of experts for development of 7.3 In the case of incorrect selection of
ToR and evaluation of proposals
pretreatment units—conduct appropriate
modernization studies
7.4 In case of incorrectly selected filtering
material or filtering parameters—conduct
research
7.5 In case of insufficient qualification of
employees—conduct training of operators,
retraining of technologists
Factor 8. Inability to start up treatment
facilities
8.1 Analyze the causes of inadequate quality of
wastewater treatment by analyzing the
operation of all equipment and facilities for
mechanical, physical–chemical, biological and
additional treatment of wastewater
8.2 If the cause is determined for factors 5–7 or
one of the factors, appropriate actions should be
taken for the factors. Need for modernization of
facilities
(continued)

Mitigation of Risks at the Stages of the Life Cycle of Wastewater …

619

Table 4 (continued)
Interventions to prevent the occurrence of a
negative factor (left)—proactive measures

Measures taken at the onset of risk (hazard) to
reduce negative environmental consequences
(right)—reactive measures
Factor 9. Increased capital and/or operating
costs
9.1 During the operation of the facilities,
unclaimed units and/or treatment steps that
were adopted for the apparent reliability of the
facilities are installed. These steps and
associated equipment will not be utilized, hence
capital costs are exceeded
9.2 Inconsistencies in wastewater flow rates or
concentrations are detected during the operation
of the facilities and, as a consequence, failure of
the facilities. Equipment replacement and/or
construction of new facilities in accordance
with factors 5–8 is required

3 Conclusion
The presented methods allow to perform environmental and economic risk assessments of an enterprise at the early stages of launching a project on reconstruction or
modernization of sewage treatment plants. Risk management at all stages of the life
cycle reduces the WWTP failure rate by 40–60%. Integration of risk management
standards increases compliance with environmental requirements, and implementation of proactive and reactive measures increases the economic sustainability of the
enterprise.
Thus, pre-investment work based on the principle of ecological and economic
balance is important for managing the development of water management of an
industrial enterprise under conditions of limited funding.
Assessment of ecological and economic risks of the enterprise on the example
of its sewage treatment facilities allows to identify key threats to the ecosystem and
the enterprise as a whole. Application of modern methods of risk assessment and
introduction of innovative technologies in the operation of sewage treatment plants
are necessary conditions for ensuring environmental safety and economic efficiency.

References
1. On the state and protection of the environment of the Russian federation in 2023. State report.
https://2023.ecology-gosdoklad.ru/doklad. Accessed 15 May 2025
2. Vurdova NG (2024) Environmental and economic balance in the refurbishment of the sewage
treatment plant. In: Proceedings of the 7th international conference on construction, architecture

620

5.
6.
7.
8.
9.
10.

11.
12.

13.

14.
15.

16.
17.
18.

19.

20.
21.

22.

N. G. Vurdova et al.
and technosphere safety. ICCATS 2023. Lecture Notes in Civil Engineering, vol 400. Springer,
Cham. https://doi.org/10.1007/978-3-031-47810-9_43
Vurdova NG, Lishchuk AN (2023) Influence of ecological and economic risks on the efficiency of investment and construction project of reconstruction of refinery treatment facilities. J
Environ Prot Oil Gas Complex 3(312):23–31. https://doi.org/10.33285/2411-7013-2023-3(312
)-23-31
Thompson Matthew P, Zimmerman T, Mindar D, Taber M (2016) Risk terminology primer:
basic principles and a glossary for the wildland fire management community. Gen. Tech. Rep.
RMRS-GTR-349. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky
Mountain Research Station
Kucher DE, Kharchenko SG (2022) Some approaches to the strategy of environmental safety.
J Ecol Ind Russ 26(10):66–71. https://doi.org/10.18412/1816-0395-2022-10-66-71
Alexeeva EA (2021) Management of ecological risks of enterprises. J Prod Ecol 10:74–100
Hutchins Greg (2018) ISO 31000: 2018 enterprise risk management, CERM academy series
on enterprise risk management
GOST R ISO 31000-2019 (2019) Risk management. Principles and guidelines. Standardinform,
Moscow
GOST R ISO 14001-2016 (2016) Environmental management systems. Requirements and
guidelines for application. Standardinform, Moscow
Bazhenov VI et al (2018) Development of a methodology for calculating the life cycle cost of
equipment, systems and facilities for water supply and sanitation. J Water Supply Sanit Eng
2:10–19
GOST R 58785-2019 (2019) Water quality. Life cycle cost estimation for efficient operation
of water supply and wastewater disposal systems and facilities. Standardinform, Moscow
Vurdova NG (2025) Principle of ecological and economic balance in the development of water
management of a large enterprise. J Min Inf Anal Bull 2:28–42. https://doi.org/10.25018/0236_
1493_2025_2_0_28
Larionov A, Nezhnikova E, Smirnova E (2021) Risk assessment models to improve environmental safety in the field of the economy and organization of construction: a case study of
Russia. Sustainability 13:35–39. https://doi.org/10.3390/su132413539
Murzalevsky AA, Karlin LN (2011) Ecological risks: theory and practice. State Hydrometeorological University, SPb, Rus
Biazar J, Ebrahimi H (2024) A one-step algorithm for strongly non-linear full fractional duffing
equations. J Comput Methods Differ Equ 12(1):117–135. https://doi.org/10.22034/cmde.2023.
53596.2256
Semenoglou AA et al (2021) Investigating the accuracy of cross-learning time series forecasting
methods. Int J Forecast 37(3):1072–1084. https://doi.org/10.1016/j.ijforecast.2020.11.009
Saaty TL (2008) Decision making with dependence and feedbacks: the analytic network
process. URSS (2021)
Belenky VM (2019) Using factor analysis methods to assess the impact of external influences
on the indicators of occupational risk of production personnel. J Actual Probl HumIties Nat
Sci 4:11–17
Kozminyh OV (2017) Markov chains as a tool for risk assessment of insurance companies
arising during the transfer of functions to outsourcing. Russ J Entrep 18(17):2491–2504. https://
doi.org/10.18334/rp.18.17.38258
Benjamin JR, Cornell CA (2014) Probability, statistics and decision for civil engineers. Dover
Publication, Mineola, NY, USA
AACE International Recommended Practice No. 18R-97 (2020) Cost estimate classification
system—as applied in engineering, procurement, and construction for the process industries.
TCM Framework, Cost Estimating and Budgeting Rev. https://pdf4pro.com/view/18r-97-costestimate-classification-system-as-applied-7054e0.html. Accessed 30 Mar 2025
GOST R 70953-2023 (2023) Sewage treatment facilities. Construction and reconstruction.
Basic technical solutions. Requirements for development, structure and content in order to
ensure optimal capital costs and operational performance. Standardinform, Moscow

Mitigation of Risks at the Stages of the Life Cycle of Wastewater …

621

23. Information Technology Handbook on BAT 10-2019 (2019). Communal waste water treatment
using urban centralized systems
24. Methodology for determining the prevented environmental damage (1999). Goskomekologia,
Moscow
25. Mkhitaryan VS, Shishov VF, Kozlov A (2010) Forecasting the stock of funds for liquidation
of the consequences of man-made accidents. J Appl Econ 3(19):91–100

Determining the Dependence of Aerosol
Deposition Surface on the Conditions
of Dynamic Foam Layer Formation
L. I. Khorzova, S. I. Golubeva, and O. S. Vlasova

Abstract The main factors influencing the deposition of aerosol particles in the
dynamic foam layer of an absorber are evaluated based on the hydrodynamic regularities of vortex-injection formation of the dynamic foam structure. Based on the
analysis of the interphase transfer determined by the conditions of formation and
renewal of free deposition surface within the dynamic foam layer, the dependencies
describing the process of aerosol particles collection were obtained. The resulting
expressions are used to calculate the operating and technological parameters of the
process of dust removal from the gas flow in the dynamic foam layer of a liquid
absorber. A formula has been found that can be used to determine the contact surface
of the phases.
Keywords Foam layer · Injector chamber · Diffusion · Aerosol particles ·
Inertial-turbulent mechanism · Bubbling and foaming apparatuses

1 Introduction
The analysis of research in the sphere of hydrodynamics of vortex-injection foam
layer formation allowed determining the conditions for describing the process of
aerosol particles collection:
• aerosol particles are insoluble in the liquid phase of the foam layer;
• the foam layer is a system of densely packed spherical gas bubbles with a certain
average diameter;
• the instantaneous local proportion of bubbles with diameters different from the
average gas bubble diameter in the foam layer db is constant in all elementary
cells within the foam layer. In combination with average size bubbles, they form
a free deposition surface.
L. I. Khorzova (B) · S. I. Golubeva · O. S. Vlasova
Volgograd State Technical University, Volgograd, Russia
e-mail: khorzova-lidia@mail.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_49

623

624

L. I. Khorzova et al.

• gas bubbles are separated by liquid shells of a certain average thickness. The
fusion of the shells forms a continuous structure of liquid partitions with high
mixing intensity within it [1].

2 Factors of Aerosol Particle Deposition
If we consider the transfer of dust particles from the region with their high content to
the region with low content as a manifestation of the driving force of mass exchange
processes, then we can write the material balance equation for dust removal in the
following form
La Ca d τ − La Ca d τ = Vf dCa

(1)

where La , La are the gas volumes at the inlet and outlet of the foam layer, respectively,
m3 /s;
Ca , Ca

are the dust particles concentrations in the gas flow at the inlet and outlet
of the foam layer, respectively, g/m3 ;
Vf
is the volume of the liquid retained in the injector chamber, thus forming
the liquid phase of the foam layer, m3 ; τ is the time, s;
La Ca d τ is the influx of dust particles into the foam layer;
La Ca d τ is the removal of dust particles from the foam layer.
Thus, the dependence Vf dCa characterizes a change in the concentration of
deposited aerosol particles within the liquid volume.
According to the assumed conditions of the process formalization,
Vf = δo S

(2)

where δ0 is the average thickness of a liquid shell separating gas bubbles, m; S is the
free deposition surface, m2 .
Consequently, we can conclude that a contact of dust particles with the free surface
of the liquid phase is a condition for their effective collection. Based on the previously
accepted assumption of the analogy with mass exchange processes, the difference
between the concentration of particles in the gaseous phase and its conditional equilibrium value Cap on the free interphase surface in the foam layer will be the driving
force of the transfer, i.e. Ca − Cap . Therefore, we can write it as follows
Cap = Ka Cf

(3)

where Ka is an analogue of the equilibrium constant; Cf is the concentration of
aerosol particles in the structural partitions of the liquid phase of the foam layer (g/
m3 ).

Determining the Dependence of Aerosol Deposition Surface …

625

The equilibrium concentration of particles on the contact surface of the liquid
phase free of dust particles is Cap = 0. If the surface of the liquid layer of structural
partitions is completely and densely filled with dust particles, the process of aerosol
deposition will cease. In this case, the limit concentration of particles in the liquid
phase of the foam layer CfS can be written as the expression
CfS = Vf 1 − ε ρa /Vf ρf = 1 − ε ρa /ρf

(4)

where ε is the porosity of densely packed aerosol particles in the liquid layer of
structural partitions of the foam; ρa is the density of dust particles in a densely
packed layer, g/m3 ; ρf is the density of liquid, g/m3 .
Thus, the process of aerosol deposition will continue as long as the concentration
of particles in the liquid layer of structural partitions of the foam is less than the limit
concentration of particles for the foam layer, i.e. Cf < CfS . If we assume that the
expression (4) characterizes a special case of such a process corresponding to the
limiting conditions, then, for the concentration of aerosol particles in the structural
partitions of the liquid phase of the foam layer Cf , we can write that
Cf = Vf (1 − ε)ρa /Vf ρf = (1 − ε)ρa /ρf

(5)

where ε is the porosity of dust particles in the liquid of a structural partition at
Cf < CfS .
From the formulas (4) and (5), it follows that
Cf
1−ε
=
CfS
1−ε

(6)

Consequently, if we assume that a densely packed layer of deposited dust particles
of the thickness δa is formed when the liquid layer in the structural partitions is
completely filled with those particles, then its volume is equal to
Va = δa S

(7)

In the case when the partition liquid is partially filled with dust particles, the
thickness of their own densely packed layer being taken relative to the same contact
surface will be determined by the value of δa < δa , and the volume will be:
Va = δa S

(8)

The volume of aerosol particles represented as a layer of the thickness δa will
occupy the area Sa , the latter being a certain part of the interphase surface Sa < S .
Then
Va = δa S = δa Sa

(9)

626

L. I. Khorzova et al.

Transforming the expression (9), we obtain
Sa =

δa
S
δa

(10)

At the same time, it can be shown that
Vf = (1 − ε) = δa S and Vf = 1 − ε = δa S

(11)

Next, substituting the relation (11) into the formulas (4) and (5), we obtain
Cf =

Sδa ρa
Sδa ρa
and CfS =
Vf ρf
Vf ρf

(12)

Consequently,
Cf
δa
=
CfS
δa

(13)

Using the dependence δa /δa , we transform the expression (10) through (13). And
taking into account the expression (6), we get
Sa =

Cf
1−ε
S=
S.
CfS
1−ε

(14)

This formula can be used to determine the area of the free deposition surface for
dust particles
So = S − Sa = S −

Cf
Cf
.
S =S 1−
CfS
CfS

(15)

Based on the Eq. (15), we can conclude that the process of aerosol particles deposition on the surface S0 is determined by the conditions of their accumulation in
the liquid phase of the foam layer. The previously identified hydrodynamic regularities of vortex-injection foam formation show that the dynamic foam layer formed
through vortex injection is characterized by a high degree of turbulence. This allows
evaluating the state of its liquid phase as a mode of complete mixing [1–3]. Thus, it
can be assumed that the concentration of aerosol particles Cf in the retained volume
of the liquid forming a structure of partitions in the liquid phase is equal to their
concentration Cf in the circulating liquid drain from the foam layer. Then, the value
S0 can be represented by the dependence
So = S 1 −

Cf
CfS

(16)

Determining the Dependence of Aerosol Deposition Surface …

627

The conducted analysis allows characterizing the dust removal process as a result
of interphase transfer of particles determined by the conditions of formation and
renewal of a free deposition surface within the foam layer.

3 Evaluation of the Conditions for Implementing the Dust
Removal Process in a Dynamic Foam Layer
Investigation of the mechanisms of aerosol particle deposition in the modes of formation of phase contact surfaces in bubbling-and-foaming apparatuses [1–8] demonstrates that, already in the scope of Stokes’ law, the mechanism of inertial deposition
prevails in the operating conditions of such apparatuses [6–8]. Thus, it is necessary
to analyze the conditions of its implementation in the high-speed mode of injection
foam formation.
An intensive pulsation of gas bubbles in the course of their movement through
the foam layer is a distinctive feature of the formation of a foam layer structure in an
injector chamber [1]. In this case, it has been observed that the transverse component
is prevalent relative to the averaged translational motion of the gas. The nature and
dynamics of these pulsations make it possible to apply the provisions of L. Prandtl’s
turbulent heat transfer theory [9, 10] to characterize it.
Based on the above, we can conclude that the mechanism of inertial deposition of
particles maintaining the trajectory of their motion is determined by the phenomenon
of turbulent pulsations during vortex-injection foam formation. Thus, when the value
of decrease in the particles quantity in the gas flow or the foaming mode parameters
that determine this value are known, it is possible to evaluate the effectiveness of
inertial-turbulent deposition of aerosols. For this purpose, two ways can be used: the
existing formulas [9, 11, 12] or the results of experiments determining the dependence of the operating parameters included in the formulas aimed at calculating the
effectiveness of deposition of particles on the design bubble diameter. The latter
allows taking into account special features of the mechanism of vortex-injection
formation of dynamic foam structure.
The inertial-turbulent mechanism under consideration determines the process of
deposition of the bulk of aerosol particles. Given that Stk ≤ 0.2, then 5 to 10% of
particles are capable of remaining suspended for a long time under the action of
the drag force of bubble gas medium [1, 9]. Thus, the deposition effectiveness for
these particles will be determined only by the diffusion mechanism. The deposition
intensity is characterized by the Peclet number. It can be concluded that the deposition
probability for all aerosol particles will correspond to the deposition probability for
their population [11–14].
Provided that the above mechanisms act simultaneously, the probability of particle
deposition will be evaluated by the complex effectiveness of the separation process.
To retain a particle deposited on a bubble surface, it is necessary to introduce it into

628

L. I. Khorzova et al.

the layer of the bubble’s liquid shell. This will require expending kinetic energy to
overcome surface tension, especially for poorly wetted and non-wetted particles.
If we denote the probability of retaining a deposited particle as К3 and take into
account that all of the above stages of the process occur simultaneously with the
probability characterized by K1 dS, K2 and K3 , respectively, we obtain an expression
that determines the decrease in the number of particles in the boundary layer of gas
on the elementary surface dS of a bubble
dn = −nK1 K2 · K3 dS = −nKdS

(17)

In the expression (17), the minus sign indicates a decrease in the number of
particles within the gaseous medium of bubbles. Integrating the expression (17), we
obtain
ln n = −KS + c.

(18)

The integration constant is found from the initial conditions:S = 0andn = n0 .
Substituting them into the expression (18) and performing the transformations, we
obtain
n/n0 = e−KS

(19)

where n is the number of particles in the gas flow at the outlet from the foam layer,
i.e. after its contact with the entire deposition surface S.
At the initial moment at S = 0, n/n0 = 1.
Thus, in order to determine the effectiveness of aerosol particles collection, we
can use the expression
na =

n0 − n
= 1 − e−KS .
n0

(20)

This expression proves that all the factors determining the effectiveness of the
process of aerosol particles collection in a vortex-injection dynamic foam layer are
included in the exponential factor.

4 Dependence of the Aerosol Deposition Surface
on the Conditions of Dynamic Foam Layer Formation
Under specific conditions, the contact surface S is the principal characteristic of
aerosol deposition process. Its size and interrelations with the parameters of the
foam layer formation determine the possibilities of practical use of the obtained
expressions.

Determining the Dependence of Aerosol Deposition Surface …

629

For the problems of statistical evaluation of structural elements of dispersed gas–
liquid systems, the conclusions on the probability of the ratios of random sections
of closed figures were used to determine the relation between the size of S in the
vortex-injection foam layer and the technological parameters of its formation in an
injector chamber [15–21]. The governing condition is that the following relation is
probable for the case of repeated and arbitrarily implemented superposition of a line
of finite length L on the projection of a two-dimensional figure with the area F:
α
π ∗S
= ,
L∗P
β

(21)

where P is the perimeter of the projection of a closed figure, m; β is the number of
intersections of a segment of the line L with the perimeter P of the projection of the
figure; α is the number of cases when both ends of a segment of the line L fall within
the projection of the figure.
By transforming the relation (21) as applied to a projection of a three-dimensional
closed figure of arbitrary shape onto a randomly selected plane, we obtain the
following
4 ∗ Vi
α
= ,
L ∗ Si
β

(22)

where Vi is the volume of an arbitrary three-dimensional closed figure, (m3 ); Si is
the surface of an arbitrary three-dimensional closed figure, (m2 ).
For a space containing a range of figures with an arbitrary distribution of volume
values, the following relation will be true:
Vi
L∗α
=
Si
4∗β

(23)

Expression (23) will be true for any arbitrarily taken plane intersecting the foam
layer as an object formed by a population of multiple individual bubbles. A transverse
or longitudinal section of the foam layer in the injector chamber can be taken as such
a plane. Thus, from the relation (23), a direct dependence between the average value
of the volumetric gas content in the foam layer ( Vi / Si ) and the constituent gas
bubbles can be determined as
Vi
n0 ∗ dB3
L∗α
=
=
2
Si
4∗β
6 ∗ n0 ∗ dB

(24)

where n0 is the number of bubbles per unit volume of the foam layer; dB is the
diameter of a gas bubble in the foam layer, m−3 .
Thus, if the Eq. (24) is used, the average value of a gas bubble diameter in the
foam layer can be calculated using the formula

630

L. I. Khorzova et al.

dB =

3 L∗α
∗
,
2 4∗β

(25)

Since the expression (23) is true for evaluating the size distribution of the structural
elements of both phases of the gas–liquid system, we can write that
L ∗ αf Vg
L ∗ αg
Vf
=
,
=
,
sf
4 ∗ βf sg
4 ∗ βg

(26)

where Vf , Vg , are the volumes of the liquid and gaseous phases of the foam layer per
its unit volume; Sf , Sg are the surfaces of the liquid and gaseous phases of the foam
layer per its unit volume.
Since the contact surfaces of the liquid and gaseous phases of the foam layer are
equal for both phases in the foam layer, we can write that
αg
αf
αg
αf
=
or, at βg = βf ,
=
4 ∗ βf ∗ Vf
4 ∗ βg ∗ Vg
Vf
Vg

(27)

Transforming the expressions (27), we obtain
1+

αf
Vf
=1+
Vg
αg

Using the expression (27), we can write that
ϕV =

αg
Vg
=
Vg + Vf
αg + αf

(28)

Then, based on the relation (28), we obtain that
L ∗ αg
βg

4 ∗ Vg
,
Sg

For the average value of bubble diameter, the expression (25) can be written as
follows
dB =

6 ∗ Vg
3 4 ∗ Vg
∗
=
,
2
Sg
Sg

Then the surface of the gaseous phase per the unit volume of the foam layer will
have the form of
Sg =

6 ∗ Vg
dB

(29)

Determining the Dependence of Aerosol Deposition Surface …

631

Since it follows from the expression (28) that the ratio between the gaseous phase
volume and the unit volume of the entire foam layer is its volumetric gas content,
then the formula (29) can have the following form
Sg =

6 ∗ ϕg
.
dB

(30)

Consequently, the contact surface of the phases of the entire volume of the foam
layer will be equal to
S = Sg ∗ SK ∗ HB =

6 ∗ ϕg
∗ SK ∗ HB ,
dB

(31)

If it is assumed that ϕV = HB − hfk /HB , then S will be as follows
S=

6 ∗ ϕV
∗
dB

hfk
1 − ϕV

∗ SK =

6 ∗ hfk
∗
dB

ϕV
1 − ϕV

∗ SK .

(32)

Using the expressions (32) and (28), we can obtain that
S=

6 ∗ SBQ
∗ h0 − hQ ∗
dB

ϕV
.
1 − ϕV

(33)

In the resulting formula, the value of the volumetric gas content ϕV integrally
depends on the technological parameters determining the process of the foam formation. Thus, its exclusion from the calculation formula should be considered a desirable
condition.
ϕV
Using the previously obtained expression for φV , the ratio 1−ϕ
in the formula
V
(33) can be represented as
ϕV
1 − ϕV

SK ∗ HB − SBQ ∗ h0 − hQ
SBQ ∗ h0 − hQ

Substituting the obtained ratio
obtain the following
S=

ϕV
1−ϕV

SK ∗ HB
−1
SBQ ∗ h0 − hQ

(34)

into the Eq. (33) and transforming it, we

6 ∗ SK ∗ HB − SBQ ∗ h0 − hQ
dB

(35)

632

L. I. Khorzova et al.

5 Conclusion
The obtained formula can be considered as an expression of the desired dependence
for determining the contact surface of phases S. The possibilities of its application
depend only on the value of dB which can be found experimentally.

References
1. Didenko VG (1993) Analyz dinamicheskykh kharakteristik penoobrazovaniya v apparatakh s
vikhrevoy inzhektsiyey zhidkosti (Analysis of dynamic characteristics of foaming in apparatuses with vortex injection of liquid). In: Optimization of systems of air cleaning and ventilation
of industrial buildings, Perm State Technical University, Perm
2. Buchta M, Kiesswetter E, Otto A et al (2003) Longitudinal study examining the neurotoxicity
of occupational exposure to aluminium-containing welding fumes. Int Arch Occup Environ
Health 76:539–548. https://doi.org/10.1007/s00420-003-0450-9
3. Golubeva SI, Khorzova LI (2021) Obobshchenie rezhimnykh usloviy raboty kapleuloviteley
intensivnykh apparatov mokroy gazoochistki (Summarizing the operating conditions modes
of mist eliminator in intensive apparatuses for wet gas cleaning). Eng J Don 3. ivdon.ru/ru/
magazine/archive/n3y2021/6883
4. Khorzova LI, Sidyakin PA, Borovkov DP, Klimenti NY (2019) Development and justification
of the treatment system layout scheme for dust emissions from mobile and portable asphaltconcrete plants. IOP Conf Ser Mater Sci Eng 537(6):062020. https://doi.org/10.1088/1757899X/537/6/062020
5. Khorzova LI, Klimenti NY, Azarov VN, Vlasova OS (2019) Improvement of dedusting efficiency of technological equipment for manufacturing of coloured calcium silicate bricks. IOP
Conf Ser Earth Environ Sci 315(6):062010. https://doi.org/10.1088/1755-1315/315/6/062010
6. Zimmer AT (2001) Aerosol formation mechanisms, metallurgical aspects, and engineering
control of fumes generated from arc welding operations. University of Cincinnati
7. Kutateladze SS, Styrikovich MA (1976) Gidrodynamika gazozhidkostnykh system (Hydrodynamics of gas-liquid systems). Energia, Moscow
8. Tarat EY, Mukhlenov IP, Tubolkin AF, Tumarkina ES (1977) Penny rezhim i pennyye apparaty
(Foam mode and foaming apparatuses). Khimiya, Leningrad
9. Barenblatt GI (1970) On the motion of suspended particles in a turbulent flow (transl. from
Engl.). Metallurgizdat, Moscow
10. Bird RB, Stewart WE, Lightfoot EN (1974) Yavleniya perenosa (Transport Phenomena (transl.
from Engl.)). Khimiya, Moscow
11. Kafarov VV (1972) Osnovy massoperenosa (Fundamentals of mass transfer). Vysshaya shkola,
Moscow
12. Lugovsky SI, Dymchuk GK (1991) Sovershenstvovaniye system promyshlennoy ventilyatsii
(Improving the systems of industrial ventilation). Stroyizdat, Moscow
13. Lebedyuk GK et al (1981) Sravnitelnyye issledovaniya zakruchivateley v gazopromyvatelyakh batareynogo tipa (Comparative investigations of vortex generators in battery-type
gas scrubbers). Promyshlennaya i sanitarnaya ochistka gazov 4:6–7
14. Bretschneider B, Kurfurst J (1989) Okhrana vozdushnogo basseyna ot zagryazneny:
tekhnologiya i kontrol (Air pollution control technology (transl. from Engl.)). Khimiya,
Leningrad
15. Boguslavsky EI (1997) Veroyatnostno-stohastichesky podkhod k problemam okhrany
proizvodstvennoy i okruzhayushchey sred. Osnovy podkhoda (Probabilistic-stochastic
approach to the problems of protection of industrial and natural environments. Fundamentals
of the approach). Sev.-Kav. nauch. tsentr vys. shk., Rostov-on-Don

Determining the Dependence of Aerosol Deposition Surface …

633

16. Metodika rascheta vydeleniy (vybrosov) zagryaznyayushchikh veshchestv v atmosferu pri
svarochnykh rabotakh (po velichinam udelnykh vydeleniy (Technique of calculating emissions
(discharges) of pollutants into the atmosphere during welding operations (by the values of
specific emissions) (2000) Integral, Saint-Petersburg
17. Moshkarnev LM (1984) Kompleksnaya tekhnologiya ochistki vozdukha ot pyli v apparatakh
mokrogo pyleulavlivaniya (Complex technology for air dedusting in wet dust collection
devices). Irkutsk State University Publ, Irkutsk
18. Prikhodko VP, Prokhorov EM, Litvinova GI (2005) Metodika dlya opredeleniya kontsentratsii
i dispersnogo sostava aerozoley v potoke gaza (Technique of determining the concentration
and particle size distribution of aerosols in gas flow). Gas Industry Journal 4:63–65
19. Pukhirya VI, Vikharev AF (1988) Obezvrezhivanie pylegazovykh vybrosov ustanovok plazmennoy rezki metallov (Decontamination of dust and gas emissions from machines for plasma
cutting of metals). Svar Proizvod 12:23–24
20. Lukyanov VP (1976) Gidrodinamicheskie kharakteristiki vikhrevogo promyvatelya (Hydrodynamic characteristics of vortex scrubber). Promyshlennaya i sanitarnaya ochistka gazov
5:6–8
21. Arsenyev VV, Bogatykh SA, Simbirtsev TA (1981) Ochistka gazov ot pyli v tsiklonnopennykh apparatakh (Dust removal from gases in cyclone-foam apparatuses). Promyshlennaya
i sanitarnaya ochistka gazov 6:7–8

Assessment of Hydro-energy Potential
of Kyrgyzstan in the Context of a Green
Economy
E. T. Toktoraliev, R. A. Kerimbekova, T. M. Choduraev, N. E. Zhumaliev,
and Ch. D. Duishenaliev

Abstract The article is devoted to the analysis of the current state and prospects for
the development of hydropower in the Kyrgyz Republic. Kyrgyzstan has significant
hydropower potential—about 142 billion kWh, but today only about 10% of this
volume is used. The bulk of electricity generated at hydroelectric power plants, the
share of which is more than 90% of the total energy balance. The article examines
the main operating and prospective hydroelectric power plants in the country, their
installed capacity, as well as the causes of energy deficit, including the impact of
climate change and increased consumption. The methodological basis of the study
is the use of statistical data, comparative and graphical analysis, and an assessment
of the share of various energy sources. The authors note that despite the presence
of large water resources, Kyrgyzstan remains energy dependent on imported coal,
gas, and oil products. Provided are data on the growth of electricity consumption,
the insufficiency of generating capacities, and the need to modernize the existing
energy system. Particular attention paid to the environmental and social aspects of
the construction of hydraulic structures. It concluded that the priority direction for
the country remains the development of hydropower with the simultaneous introduction of alternative energy sources to ensure a sustainable energy future. Key words:
hydraulic structures, thermal power plant, energy, production, consumption, coal,
gas, fuel oil, potential, use, import, export, prospect.
Keywords Hydropower · Hydroelectric station (HS) · Energy security ·
Renewable energy · Water resources · Energy balance · Energy deficit ·
Alternative energy

E. T. Toktoraliev (B) · T. M. Choduraev · N. E. Zhumaliev · Ch. D. Duishenaliev
Kyrgyz State University named after. I. Arabaev, Bishkek, Kyrgyzstan
e-mail: e.toktoraliev@kstu.kg
R. A. Kerimbekova
Diplomatic Academy of the Ministry of Foreign Affairs of the Kyrgyz Republic, Bishkek,
Kyrgyzstan
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_50

635

636

E. T. Toktoraliev et al.

1 Introduction
Energy security and sustainable development are among the key priorities of the
socio-economic policy of the Kyrgyz Republic. In the context of rapid growth in
electricity consumption, worsening effects of climate change and limited traditional
energy sources, the importance of hydropower as a strategic industry is increasing.
Due to its natural and geographical features, Kyrgyzstan has significant hydropower
potential and ranks third in hydropower reserves among the CIS countries after Russia
and Tajikistan.
The share of development of the existing potential remains low—about 10%.
This necessitates a revision of approaches to the development of hydropower as a
key element of sustainable energy policy.
The purpose of this article is to analyze the current state of the energy system
of the Kyrgyz Republic, identify problems and prospects for the development of
hydropower, as well as assess its contribution to the implementation of the concept
of a “green economy” and energy independence of the republic.
To date, Kyrgyzstan has seven dams, seven large hydroelectric power plants
(HPPs), 16 small HPPs, and 64,700 km of power transmission lines. The bulk of electricity generated by HPPs, which account for 92% of the country’s total generation,
which amounted to 14.29 billion kWh in 2019 [1].
Kyrgyzstan ranks third among the CIS countries in terms of hydropower reserves
after Russia and Tajikistan. The development of the republic’s rich hydropower potential considered a strategic direction for the development of national energy. On the
Naryn River and its tributaries alone, it is possible to build 31 hydroelectric power
plants with a potential annual output of more than 16 billion kWh [2].
As part of the implementation of the energy strategy, in 2001 the Tashkumyr
HPP (450 MW) was brought to its design capacity, in 2002 the Shamaldysai HPP
(240 MW), and in 2010 the first unit of the Kambarata HPP-2 with a capacity of
120 MW was put into operation, with a total design capacity of 360 MW [3, 4].
In total, in Kyrgyzstan, in addition to small hydroelectric power plants, there are 18
power plants with a total installed capacity of 3678 MW, including 16 hydroelectric
power plants and 2 combined heat and power plants (CHP) [5].
The relevance of the topic due to the fact that the hydropower potential of water
resources of the Kyrgyz Republic is 142 billion kWh of possible annual electricity
production, while the percentage of development of the potential of water resources
is only about 10%.
The participation of neighboring countries, especially Uzbekistan and Kazakhstan, in the project could reduce concerns about possible changes in the water
balance. The main concerns are economic and partly social in nature—the possible
impact on agriculture and water supply. However, with regional cooperation, the
project could become an impetus for deeper economic integration in Central Asia
[6].

Assessment of Hydro-energy Potential of Kyrgyzstan in the Context …

637

2 Theoretical Part
Kyrgyzstan is one of the countries with energy shortages: its own resources cover
only about 51% of its electricity needs, most of which generated by hydroelectric
power plants [7]. The rest covered by imports. An unfavorable feature is the high
dependence of the energy system on external supplies—about 95% of all energy
sources in the country imported, including up to 50% of coal, as well as almost all
gas and oil products [7].
Hydropower facilities, such as hydroelectric power plants (HPPs) and small hydroelectric power plants (SHPPs), play a vital role in the development of a green
economy. This is due to their renewable nature, low emissions, and resilience to
price fluctuations in global energy markets [7].
A state of emergency has been in effect in the energy sector of the Kyrgyz Republic
since August 1, 2023, as the growth rate of electricity consumption significantly
exceeds the pace of electricity generation. An additional contributing factor is the
impact of climate change, which has resulted in a decrease in water inflow into the
Naryn River basin [8–10].
To date, several large hydroelectric power plants have been constructed, primarily
along the Naryn River—a tributary of the Syr Darya—forming a cascade of
hydroelectric power stations [11]:
• Toktogul hydroelectric power station is the largest in the country (1200 MW),
with an annual output of about 4400 million kWh;
• Kurpsai HPP—800 MW, 2630 million kWh per year;
• Tash-Kumyr HPP—450 MW, 1555 million kWh;
• Shamaldy-Say HPP—240 MW, 902 million kWh;
• Uch-Kurgan hydroelectric power station—180 MW, used in the regional energy
system;
• At-Bashi HPP—40 MW, 145 million kWh, located on a tributary of the Naryn.
In the context of growing resource scarcity (see Table 1) and increasing interdependence of Central Asian countries, only through joint and rational management of
water and energy resources is it possible to build sustainable economic mechanisms
and ensure long-term development of the region [12].
According to Table 1, Kyrgyzstan is an energy-deficient country, since its own
energy resources cover only about 51% of domestic electricity consumption. The
basis of production is hydropower, represented by a cascade of hydroelectric power
plants on the Naryn River. However, the growing demand for electricity, caused by
economic development and population growth, significantly exceeds the growth rate
of energy production. This leads to the need to import electricity from neighboring
countries such as Uzbekistan, Kazakhstan, Russia and Turkmenistan. In recent years,
there has been a significant increase in import volumes: in 2023, electricity imports
increased by 24% compared to the previous year, and in 2024—by 47% [13]. At
the same time, electricity exports are decreasing, which indicates an increase in the
domestic energy deficit. The electricity deficit aggravated by climate change, which

638

E. T. Toktoraliev et al.

Table 1 Electricity import and export of Kyrgyzstan (2022–2024)
Year

Import,
million kWh

Main exporting
countries to the
Kyrgyz Republic

Export,
million kWh

Main importing
countries from the
Kyrgyz Republic

2022

2806.4

Uzbekistan (1300),
Turkmenistan (795),
Kazakhstan (470),
Russia

550

Kazakhstan,
Uzbekistan

2023

3488.8 (+
24%)

Turkmenistan,
Russia, Uzbekistan,
Kazakhstan

138.4 (−
75%)

Kazakhstan (14.4),
Uzbekistan (19.2)

2024
(January–November)

4638 (+
47%)

Russia, Kazakhstan,
Turkmenistan,
Uzbekistan

–

affects the hydrological regime of rivers and reduces water resources for hydroelectric
power plants. In such conditions, diversification of the country’s energy balance,
including the development of alternative renewable energy sources and increased
energy efficiency, is of particular importance. Rational management of water and
energy resources on the scale of the Central Asian region is a key factor in ensuring
sustainable energy development and reducing dependence on imports [14]. This
requires studying the further development of the energy sector (see Fig. 1).
According to Fig. 1, it is evident that the territory under study has significant
potential for the development of hydraulic structures that not only meet the needs of

Fig. 1 Map-scheme of the location of hydroelectric power plants and their prospective development

Assessment of Hydro-energy Potential of Kyrgyzstan in the Context …

639

the country’s residents, but also, in the future, export of the obtained electricity to
nearby neighboring countries is possible.
The government calls on citizens of the republic not to worry about the introduction of a state of emergency in the energy sector, which only gives the relevant
ministry more opportunities to develop the fuel and energy complex. Such rhetoric
leaves no choice but to thoroughly study the two key components of Kyrgyzstan’s
energy sector, namely, hydropower and thermal energy.
The most promising for the construction of hydroelectric power plants is the
Naryn River, which is the largest hydroelectric resource of the country. A cascade
of large hydroelectric power plants has already been built along its length, including
the Toktogul (1200 MW), Kurpsai (800 MW) and Tash-Kumyr (450 MW) hydroelectric power plants [15]. Due to its stable and predictable water regime, the Naryn
River ensures high efficiency of hydroelectric facilities and the possibility of further
development of hydroelectric power.
In addition to the Naryn River, the Chu and Talas Rivers considered promising for
the development of small and medium-sized hydroelectric power plants. The Chu
River, which flows through the northern part of the country, has significant hydrological potential and used not only for hydropower but also for irrigation [16]. Small
rivers and mountain tributaries, such as the Kyzyl-Suu and Ala-Archa, considered
as sites for the construction of small hydroelectric power plants, which will increase
the level of electricity supply to remote regions and diversify the country’s energy
balance. For this purpose, we conducted an analysis of the cost of energy generated
in Kyrgyzstan (see Table 2).
Table 2 Comparison of average prices for electricity production in Kyrgyzstan by main sources
Energy source

Average production cost, som/kWh

Note

Hydroelectric power
plants (HPP)

0.30–0.50

Cheapest and greenest
energy; low operating
costs

Thermal power plants
(TPP, coal)

1.20–1.60

More expensive due to fuel
costs and emissions;
pollution

Electricity import

2.00–2.50

Depends on foreign policy
factors and demand

Solar energy (SES)

0.90–1.20 (if infrastructure is available)

Depends on investment
and weather conditions;
value falls with technology
development

Wind energy

Gas stations

1.00–1.50

1.50–2.00

There is potential, but the
infrastructure is poorly
developed
Imported fuel, high
dependence and cost

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E. T. Toktoraliev et al.

According to Table 2, hydroelectric power plants remain the most economical and
sustainable source of electricity in the Kyrgyz Republic. However, given the growth
in consumption and climate change, it is necessary to develop other renewable energy
sources, especially solar and wind.

3 Results of the Analysis
Figure 2 shows fuel data on the territory of Kyrgyzstan.
According Fig. 2, to which electricity produced by power plants is the main source,
in second place is the use of coal. In our opinion, electrical energy will continue to
be the main energy raw material of Kyrgyzstan.
Below (see Table 3) we have listed the main power stations of our country that
supply electricity to the population of Kyrgyzstan.
Hydropower in Kyrgyzstan has great potential and high-energy saturation (see
Table 3). Due to the mountainous landscape, reservoirs and rivers, hydroelectric
power plants are the key technology for the prospective development of the republic’s
energy sector. Despite this, there is an increase in electricity in this area (see Fig. 3).
Electricity consumption grows by 5–7% every year, so in 2023, daily electricity
consumption increased by 4 million kilowatt-hours. If in 2022, 62 million kilowatthours were consumed per day, then in 2023 it was 66 (see Fig. 3) [18].
In January 2022, the maximum electricity consumption was recorded—75 million
kilowatt-hours per day [18].
Below is information on determining the rating of our country for the development
of this sector (see Table 4).

Fig. 2 Consumption of various types of fuel to obtain energy [17]

Assessment of Hydro-energy Potential of Kyrgyzstan in the Context …

641

Table 3 Comparison of average prices for electricity production in Kyrgyzstan by main sources
Name

Year of introduction

Installed capacity, MW

Available capacity,
MW

Toktogul HPP

1975

1200

Kurpsai hydroelectric 1981
power station

800

Tash-Kumyr
hydroelectric power
station

1985

450

Shamaldy-Sai
hydroelectric power
station

1994

240

Uchkurgan
hydroelectric power
station

1961

180

175

At-Bashinskaya HPP

1970

Kambarata HPP-2

2010

120

100

Small hydroelectric
power plants - 12 pcs

1940–1960

Thermal power plant
of Bishkek

1961

666

520

Thermal power plant
of Osh city

1966

3788

3587

Total
Fig. 3 Electricity
consumption trend

Table 4 Rating of countries by energy sector development for the CIS and EAEU countries in
2014–2020 [19]
Country
Armenia

Connection to the power supply system
30

List of countries by electricity
production
100

Belarus

Kazakhstan

Kyrgyzstan

143

642

E. T. Toktoraliev et al.

Table 4 shows that among the CIS and EAEU countries, from 2014 to 2020,
Kazakhstan had the highest rating for electricity production, while Kyrgyzstan lags
significantly behind in both connection to power grids and electricity generation.
Let us consider the data on electricity generation at hydroelectric power plants
and thermal power plants in Kyrgyzstan (see Fig. 4), and study the dynamics of their
consumption (see Fig. 5).
As can be seen from Figs. 4 and 5, electricity generated mainly from the emerging
hydroelectric power plants and two large thermal power plants in our country, but

Fig. 4 Generation of electricity in hydroelectric power plants and thermal power plants in
Kyrgyzstan [19]

Fig. 5 Electricity consumption in Kyrgyzstan for 2011–2022 [19]

Assessment of Hydro-energy Potential of Kyrgyzstan in the Context …

643

despite the large reserves, we still forced to export electricity from neighboring countries. Despite this, energy production at hydroelectric power plants is significantly
lower in cost compared to other sources, and this trend will continue in the future.

4 Materials for Discussion
Energy security and sustainable development are characteristic not only of
hydropower within a country, but also of the energy systems of neighboring countries,
which are interdependent.
Hydropower is one of the most affordable sources of renewable energy. When
used correctly, it can be a long-term source of energy without emitting greenhouse
gases or other pollution, reducing dependence on fossil fuels and helping combat
climate change [16].
Hydropower is one of the cleanest ways to produce energy. It produces no greenhouse gas emissions and does not require burning fuel, which helps reduce air and
water pollution [20].
Water resources used for hydropower have a stable and predictable potential. This
allows for the creation of sustainable energy supply systems, which is especially
important in the context of growing energy demand and the variability of other
renewable energy sources such as wind and solar energy [21].
Thus, hydropower facilities play an important role in the development of green
economy by providing stable, clean and sustainable energy production [22].
Hydraulic structures such as dams, dam power plants, canals and other reservoirs
have a significant impact on the environment. Potential environmental impacts of
these activities include:
The construction of dams and the creation of reservoirs change the natural characteristics of rivers and water bodies. This can lead to changes in biodiversity, water
balance and hydrological regime, which affects the life of animals and plants [23].
Hydraulic structures can alter water flow patterns, which affects the availability
of freshwater for a variety of purposes including agriculture, industry, and drinking
water supply [19].
Uncontrolled operation of hydraulic structures can increase the risk of flooding or
inundation downstream, as well as the risk of dam failure, which can have catastrophic
consequences for surrounding areas and people [24].
Canalization and damming of rivers can alter the geomorphology of aquatic
systems, leading to bank erosion, sediment alteration, and migration of aquatic
species [24].
Some hydraulic structures, such as hydroelectric dams, can influence regional
climate by altering the hydrological cycle and greenhouse gas emissions [25].
In addition, hydropower projects can have significant impacts on local communities, including displacement, loss of livelihoods (e.g. fisheries or agriculture) and
changes in lifestyles [26].

644

E. T. Toktoraliev et al.

All these factors highlight the importance of an integrated approach to planning
and managing hydraulic projects, taking into account their impact on the environment
and social systems [27].

5 Conclusion
The conducted analysis of the energy sector in Kyrgyzstan showed that currently
various sources are used in this territory—gas, coal, fuel oil, hydroelectric potential.
At the same time, the cheapest in terms of cost remains the energy generated in
hydrotechnical structures, and in comparison with other sources, it is still the least
harmful to the environment. Which in the near future will serve as the main source of
energy for the residents of Kyrgyzstan, along with which it is necessary to develop
alternative energy sources—solar energy, wind energy, geothermal energy, bioenergy,
etc.

References
1. Ministry of Energy of the Kyrgyz Republic (2022) Energy review. Ministry of Energy of the
Kyrgyz Republic, Bishkek. https://www.energy.gov.kg. Accessеd 1 June 2022
2. Government of the Kyrgyz Republic (2019) Strategy for the development of the fuel and
energy complex of the Kyrgyz Republic until 2040. Government of the Kyrgyz Republic,
Bishkek. https://mkk.gov.kg/ru/wp-content/uploads/2023/08/%D0%A3%D0%9A%D0%90%
D0%97-%D0%9F%D0%A0%D0%95%D0%97%D0%98%D0%94%D0%95%D0%9D%
D0%A2%D0%90-%D0%9A%D0%AB%D0%A0%D0%93%D0%AB%D0%97%D0%A1%
D0%9A%D0%9E%D0%99-%D0%A0%D0%95%D0%A1%D0%9F%D0%A3%D0%91%
D0%9B%D0%98%D0%9A%D0%98-%D0%BE%D1%82-12.10.2021-%D0%B3-%D0%
A3%D0%9F-%E2%84%96-435.pdf. Accessеd 24 Dec 2019
3. State Scientific Institution “Kyrgyzenergo” (2021) Statistical data on the electric power industry
of the Kyrgyz Republic. Bishkek. https://stat.gov.kg/ru/publications/toplivno-energeticheskijbalans/. Accessеd 12 Oct 2021
4. Osh Technological University (2020) News of the Osh Technological University, 2(50):114–
116. https://oshtu.kg/journal/izvestia. Accessеd 14 June 2025
5. Myktybek Uulu A, Ashyralieva LA (2024) Hydropower of Kyrgyzstan in the context of solving
water and energy problems of Central Asia. Bull Jalal-Abad State Univ 1(59):26–32
6. Ministry of Energy of the Kyrgyz Republic (2022) Energy of Kyrgyzstan: statistics and
prospects. Bishkek. https://minec.gov.kg/energy. Accessеd 14 Jun 2022
7. Ministry of Energy of the Kyrgyz Republic (2023) Energy review of the Kyrgyz Republic.
Bishkek. http://energy.kg/obzor2023.pdf. Accessеd 12 Sept 2023
8. Government of the Kyrgyz Republic (2023) Resolution No. XXX on the introduction of a
state of emergency in the energy sector. Bishkek. http://gov.kg/energy-emergency2023.pdf.
Accessеd 31 July 2023
9. Research Institute of Water Resources (2022) Climate change and water resources of the Naryn
River Basin. Bishkek. http://niswr.kg/climate_naryn.pdf. Accessеd 22 Aug 2022
10. Kyrgyz Hydrometeorological Center (2023) Climate reports and forecasts for the region.
Bishkek. http://kgmeteo.kg/climate_reports2023.pdf. Accessеd 14 June 2025

Assessment of Hydro-energy Potential of Kyrgyzstan in the Context …

645

11. Energy Company of the Kyrgyz Republic (2024) Interstate cascade of hydroelectric power
plants on the Naryn River: report. Bishkek. http://energy.kg/hydro_naryn_report.pdf. Accessеd
10–11 June 2024
12. Central Asia Regional Commission (2023) Joint management of water and energy resources
in Central Asia: analytical report. Almaty. http://centralasia-regcomm.org/water_energy.pdf.
Accessеd 14 June 2023
13. National Statistical Committee of the Kyrgyz Republic (2023) Data for 2011–2023. https://
www.stat.kg/ru/news/v-2019-godu-po-sravneniyu-s-predydushem-godom-obem-toplivnoenergeticheskih-resursov-respubliki-snizilsya-na-8-procentov. Accessеd 14 June 2025
14. Ministry of Energy of the Kyrgyz Republic (n.d.) Main hydropower resources of Kyrgyzstan.
https://energy.gov.kg/ru/hydro-resources. Accessеd 14 June 2025
15. Isakova GT, Bekbolotov AA (2022) Prospects for the development of small hydroelectric power
plants on the rivers of Northern Kyrgyzstan. Bull Kyrg Natl Univ 15(3):75–82. https://knu.kg/
journal/2022/03/isakova_bekbolotov. Accessеd 28 Sept 2022
16. Ministry of Energy of the Kyrgyz Republic (n.d.) Import and export of electricity in Kyrgyzstan
in 2022–2024. https://energy.gov.kg/ru/statistics/energy-import-export. Accessеd 20 Jan 2025
17. Asanov AA, Sultanov EB (2023) Water resources and energy security of Central Asian Countries. Bull Central Asian Energy Inst 2:45–53. https://caei.kg/journal/2023/02/asanov_sultanov.
Accessеd 01 Mar 2023
18. National Statistical Committee of the Kyrgyz Republic (2023) Electricity consumption
statistics. Bishkek. http://stat.kg/electricity2023.pdf. Accessеd 30 Sept 2023
19. Ministry of Energy of the Kyrgyz Republic (2023) Electric power plants of the Kyrgyz Republic.
Bishkek. http://energy.kg/electrostations2023.pdf. Accessеd 30 Sept 2023
20. International Renewable Energy Agency (IRENA) (2022) Renewable energy and climate
change: opportunities and challenges. Abu Dhabi. https://www.irena.org/publications/renewa
ble-energy-climate-change. Accessеd 14 June 2022
21. World Bank (2023) Global renewables review. Washington. https://documents.worldbank.org/
renewables-global-review. Accessеd 12 Mar 2023
22. United Nations Development Programme (UNDP) (2021) Green economy and sustainable
development. New York. https://www.undp.org/publications/green-economy. Accessеd 8 Sept
2021
23. United Nations Environment Programme (UNEP) (2020) Impact of hydraulic structures on the
environment. Nairobi. https://www.unep.org/publications/hydrotechnical-impacts. Accessеd
23 Oct 2023
24. International Union for Conservation of Nature (IUCN) (2019) Dam risks and management.
Gland. https://www.iucn.org/dams-risk-management. Accessеd 06 Sept 2021
25. UN Climate Council (2021) Impact of hydropower on regional climate. Geneva. https://unclim
atecouncil.org/hydroclimate-impact. Accessеd 24 Apr 2021
26. World Health Organization (WHO) (2022) Social impact of hydrotechnical projects. Geneva.
https://www.who.int/publications/hydrotechnical-social-impact. Accessеd 12 Dec 2022
27. International Forum on Sustainable Development (IFSD) (2023) An integrated approach
to hydropower projects. London. https://www.ifsd.org/publications/comprehensive-approachhydropower. Accessеd 14 June 2023

Reliability and Safety Analysis of Truck
Leaf Springs Under Permafrost
Conditions Using Failure Time Series
I. I. Buslaeva and S. P. Yakovleva

Abstract Freight vehicles represent a most important component of technospheric
safety in both production and social spheres of Yakutia, which is part of the permafrost
zone of Russia. Trucks are the sole means of cargo transportation capable of maintaining communication links between all settlements during the winter, thus ensuring
normal living conditions in the region. Relevant tasks include improving the reliability of trucks, specifically by identifying features in the failure statistics of various
parts and systems associated with typical changes in operating conditions in the
permafrost. The aim of the study is to establish regularities in the impact of seasonal
operating conditions on the operability and reliability of leaf springs in KAMAZ
trucks used in the permafrost, based on the analysis of failure time series. Modeling
of leaf springs failures time series has been carried out using Fourier series decomposition with the allocation of significant harmonics. A mathematical model was created
that satisfactorily approximates the dynamics of failures. The model consists of the
mean monthly number of failures and five significant harmonics from the Fourier
decomposition. Interrelation between rhythmological features of failures and operating conditions was demonstrated. The novelty of the results lies in the contribution
to solving methodological issues concerning the study of reliability of automotive
parts taking into account seasonal operational factors and ranking their significance
in causing the failures. The proposed method enables improved accuracy of shortterm failure forecasts and enhanced effectiveness of vehicle maintenance, adhering
to the principles of technosphere safety such as prevention, control, and monitoring.
Keywords Leaf spring · Truck · Reliability · Failure · Рermafrost zone · Time
series · Hidden periodicity

I. I. Buslaeva (B) · S. P. Yakovleva
Yakut Scientific Centre of Siberian Branch of the Russian Academy of Sciences, Yakutsk, Russia
e-mail: buslajeva@mail.ru
S. P. Yakovleva
Larionov Institute of Physical-Technical Problems of the North, Siberian Branch of the Russian
Academy of Sciences, Yakutsk, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_51

647

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I. I. Buslaeva and S. P. Yakovleva

1 Introduction
Truck freight transportation plays a crucial role in the economy of Yakutia, which
occupies an enormous territory characterized by difficult-to-navigate areas, mountainous terrain, and permafrost ground. Cargo delivery to Yakutia is carried out
using river and railway transport with subsequent reloading onto trucks for further
transportation along roadways to populated areas. That’s why the land-based motor
vehicles are the only reliable means of cargo transportation, especially during winter
when rivers freeze over and only trucks traveling on winter ice roads can deliver
significant volumes of fuel, food products, medicines, and other essential goods to
remote settlements that do not have direct access to major transportation routes [1,
2]. In this regard, automotive transport is a strategically important sector of Yakutia’s
economy, ensuring the normal living conditions for the population and social stability,
and the safety of automobiles ranks among the top priorities of regional technosphere
security issues. Failures of automotive transport in the conditions of North-Arctic
regions increase the risk of accidents, environmental damage, and socio-economic
losses due to vehicle downtime and reduced efficiency of logistics operations, as
well as posing a threat to the lives of drivers and passengers. Intensified development of Russia’s North-Arctic territories adds particular urgency to addressing these
challenges.
It is evident that for proper execution of cargo transportation plans, trucks must
demonstrate high reliability in operation. Occurrence of malfunctions in automotive
technology depends on manufacturing quality, processes of natural wear and tear,
material degradation, working conditions, etc., i.e., a set of factors whose combined
influence is unpredictable and random. Therefore, patterns of equipment failure are
studied through probabilistic methods widely used in reliability theory. This highlights the importance of thorough analysis of available statistical data on failures,
correspondingly correct collection of such information, and advancement of research
methodologies, particularly since existing methods for assessing performance of
technical systems do not fully account for their specific functioning characteristics
in Northern environments.
In Russia, the most popular domestic trucks are KAMAZ brand vehicles with
payload capacities ranging from 10 to 40 tons, which have been carrying out largescale transportation tasks in northern and arctic regions for nearly half a century. A
considerable proportion of breakdowns experienced by these trucks while operating
in Yakutia occurs in suspension components, specifically leaf springs [3, 4]. Since
air temperature and road conditions—factors significantly affecting suspensions—
vary seasonally, statistics on leaf springs failures should contain hidden periodicities
related to seasonal characteristics typical of permafrost regions. Identifying possible
rhythmological features in leaf spring failures associated with real-world seasonal
usage conditions will allow determining key factors and causes negatively affecting
the operability of KAMAZ trucks, which becomes particularly relevant in the North
and Arctic regions where stable functionality of equipment is critical for maintaining
safety in both industrial and social spheres. The objective of this work is to establish

Reliability and Safety Analysis of Truck Leaf Springs Under Permafrost …

649

regularities regarding how seasonal usage conditions affect the serviceability and
reliability of leaf springs in KAMAZ trucks within permafrost regions based on
time-series analysis of failure occurrences.

2 The Impact of Seasonal Operating Conditions in Yakutia
on Reliability of Truck Suspension Springs
2.1 Road-Climatic Operation Conditions of Automobile
Transport in Yakutia, Failure Databases and Their
Analysis Using Time Series
Reliability studies of technical systems involve identifying patterns of failures over
time. A failure is defined as an event resulting in complete or partial loss of functionality, rendering the item unable to perform its intended function either entirely
or partially. For this study, we utilized data from the long-term databank “Machinery
of the North”, containing records of failures experienced by various types and
brands of machines operating in Yakutia. We selected 50 KAMAZ trucks deployed
in Mirny District, for which detailed failure reports were collected over four full
years following factory delivery. During this period, approximately 14,000 failures
occurred across all selected vehicles, including 396 instances involving suspension
spring failures.
As already noted, among the diverse range of variable operational factors in the
North, the most significant ones influencing truck suspension systems are air temperature and road conditions. The climate of Yakutia is characterized by extremely low
temperatures in winter (below −60 °C), relatively high summer temperatures (above
+30 °C), and sharp daily temperature fluctuations in autumn-spring periods (with
a difference of 25–30 °C and transition through the zero point). Vehicle component
performance may decrease in winter due to insufficient low-temperature strength
of materials used in their construction ((steels, cast irons) [5, 6]. Road conditions
primarily determine dynamic load levels acting upon the vehicle depending on road
smoothness In Yakutia, 69% of roads are unpaved and seasonal, while 43% consist
of winter roads and ice crossings [7], making road conditions for vehicle use highly
unfavorable. In reference [8], profiles of seasonal irregularities on gravel roads in
Central Yakutia were investigated, revealing substantial differences in autocorrelation functions of road profiles between seasons. In autumn, the frequency of main
oscillations of vehicle springs increases almost one-and-a-half times compared to the
winter period, and additional high-frequency vibrations appear in warm weather due
to small surface irregularities on roads. These seasonal variations in operation should
be taken into account when evaluating the performance and reliability of automotive
equipment in the North. Developing recommendations for improving the reliability
of different technical objects based on summarizing failure statistics requires identification of mathematical patterns governing failures. To assess the performance of

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I. I. Buslaeva and S. P. Yakovleva

automotive equipment, its systems, components, and subassemblies, time series are
formed by analyzing failure data stored in databases. Each element of the series
represents the total number of specified failures occurring within a certain time
interval (usually a month), forming a chronological sequence of random variables.
Mathematical models of failure time series arising under actual operating conditions reflect the analytical form of failure evolution over time in those conditions.
Therefore mathematical models developed based on failure time series are valuable
not only for assessing the performance of machine details performance but also for
predicting its resource under limited information, as well as helping identify causes
of failures. In this study, time series of leaf spring failures in KAMAZ trucks were
compiled and processed using Fourier decomposition. Significant harmonic components were identified, additive models incorporating average numbers of failures
and meaningful harmonics describing dynamics change patterns were constructed,
followed by comparison of obtained results with seasonal road-climatic operational
conditions.

2.2 Modeling the Time Series of Leaf Spring Failures
Regression analysis of the time series Y (the monthly leaf spring failure counts
of KAMAZ trucks over a 48-month period (N = 48)) did not reveal a significant
linear trend, though other temporal patterns may be present. The time series can be
expanded into a Fourier series in amplitude-phase form [9]:
N /2

f (t) = A0 +

Ai cos
i=1

2π
i t − ϕi ,
N

(1)

where A0 is the mean value of the time series Y; t is the ordinal number of the month
of observation; i is the harmonic number,Ai is the amplitude of the i-th harmonic, φi
is its phase shift. The amplitude and phase are calculated using the formulas:

Ai =

⎧
bi
⎪
⎪
⎨ arctg , if ai ≥ 0
ai
ai2 + b2i , ϕi =
b
⎪
⎪
⎩ π + arctg i , if ai < 0
ai

(2)

where ai and bi —the Fourier coefficients
ai =

2
N

Yt cos
t=1

2π
1
i t , aN /2 =
N
N

(Yt cos π t ), bi =
t=1

2
N

Yt sin
t=1

2π
it
N
(3)

Reliability and Safety Analysis of Truck Leaf Springs Under Permafrost …

651

Fig. 1 a amplitude spectrum of Fourier decomposition of KAMAZ truck leaf spring failures;
b failure chronogram (solid line), plots of mean value (dashed line) and mathematical model (dotted
line)

The Fourier series representation, comprising the mean value and 24 harmonic
components, provides an accurate approximation of the failure time series Y. To
detect and quantify periodic patterns in the studied parameter, significant harmonics
must be identified from the amplitude spectrum—a graphical representation of
harmonic amplitudes versus their corresponding periods [10].
The amplitude spectrum of leaf spring failure frequency shows five dominant
harmonics corresponding to periods of 24, 16, 12, 9.6, and 6 months (Fig. 1a).
The parameters of the five significant harmonics are presented in Table 1. The
harmonic with a 9.6-month period exhibits the maximum amplitude, while those with
12- and 24-month periods also show substantial amplitudes, indicating their dominant
contribution to the temporal structure of leaf spring failures. The lower-amplitude
16- and 6-month harmonics represent secondary cyclic patterns.
The mathematical model of leaf spring failure comprises a mean value (8.25)
and five significant harmonic components. With a coefficient of determination (R2 )
of 0.632, the model explains 63.2% of the time series variance [11]. This exceeds
the 0.5 threshold for acceptable model fit, indicating sufficient approximation accuracy. Residual autocorrelation analysis confirmed the model’s adequacy, revealing
no significant unmodeled periodicities [12].
Figure 1b shows the chronogram of leaf spring failures (a plot of the original
series in the time domain) and the truncated Fourier series modeling it. While the
time series of failures has many local maxima over 48 months, the local maxima of
the mathematical model fall on the following calendar months: March, August, April,
March, August, March, September. These months correspond to the periods of deterioration of road conditions in Yakutia - March–April and August–September. Road
Table 1 Parameters of
significant harmonics of time
series of KAMAZ truck leaf
spring failures

Significant harmonics

T. months

φ0 rad

1.851

−1.01

1.564

−0.864

1.89

3.247

9.6

1.999

−1.402

1.512

2.826

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I. I. Buslaeva and S. P. Yakovleva

conditions worsen during snowmelt (March–April) and heavy summer rains (July–
August). The cumulative adverse impact of precipitation becomes most apparent
in September. Moreover, in March, rather low air temperatures are maintained, the
average monthly temperature for the observation period was −17.2 °С. These factors
contribute to accelerated wear of vehicle suspensions.
Leaf spring failures over certain periods of time can be caused by a combination
of various factors, such as seasonal changes in the external environment, periodic
maintenance, regular loads and wear. The harmonic with the large period of 24 months
can probably be taken as the main trend of the time series of leaf spring failures
(Fig. 2a), describing the influence of some long-term parameters, which can include
factors, for example, related to the processes and mechanisms that induce failure.
The maximum of the harmonic with the period of 24 months are noted after 20 and
44 months from the beginning of observation, which corresponds to August.
For the harmonic with the period of 16 months (Fig. 2b), the failure maxima were
observed in February, June and October. The harmonic with the period of 9.6 months
(Fig. 2d) has the largest amplitude among the other harmonics, its maxima occur in
June, May, March, December and October. Harmonics with the periods of 16 and
9.6 months can be associated with some production or operating cycles.
According to the seasonal harmonic with the period of 12 months (Fig. 2c), the
maximums of failures correspond to June—the beginning of the summer intensive

Fig. 2 Chronogram of the time series of leaf spring failures of KAMAZ truck and significant
harmonics with periods: a 24 months; b 16 months; c 12 months; d 9.6 months; e 6 months

Reliability and Safety Analysis of Truck Leaf Springs Under Permafrost …

653

operation of trucks associated with the opening of active navigation on the Lena
River. At this time, the dirt roads have not yet dried out, which increases the loads
on the leaf springs.
The semi-annual cycle may be associated with changes in operating conditions
during the transition from one season to another. The failure maxima for the harmonic
with the period of 6 months (Fig. 2e) were observed in March and September.
Considering the reasons that cause the increase in failures in specific months of
the year, we can list a number of the most probable circumstances. Thus, in February
in the town of Mirny (where the KAMAZ trucks were operating), the slipperiness
of snow-covered roads increases, leading to frequent and intensive braking, which
adversely affects the performance of the leaf springs. At the same time, the average
monthly air temperature of the observation period was −23.9 °C. In October and
March, road conditions deteriorate due to the appearance of significant seasonal
unevenness.
It is evident that the factor of road smoothness is a primary factor of influence on the
performance of leaf springs than air temperature. The periods of maximum failures of
the mathematical model fall on March–April and August–September and correspond
to the periods of deterioration of road conditions in Yakutia. At the same time, for
significant harmonics with periods of 16 and 12 months, failure peaks were observed
in June. This warrants a more detailed analysis of Yakutia’s road characteristics
during that month. In [8], it was demonstrated that the seasonal spectral densities
of the correlation function for dirt road unevenness effects on suspension vibrations
exhibit maxima at distinct characteristic frequencies. These frequencies are shown
to vary depending on the seasonal conditions of the road. The highest peak of the
maximum of spectral densities is observed in the summer, when the road profile is
characterized by the greatest stability of unevenness. The revealed maxima of failures
of leaf springs of KAMAZ trucks in June are consistent with these results.
The absence of local maxima in the mathematical model during November,
December, and January can be attributed to snow cover smoothing road irregularities.
This suggests that low air temperatures play the secondary role in leaf spring failures
of KAMAZ trucks (the average air temperature in November in Mirny during the
considered period was −22.5 °C, in December −27.7 °C, in January −31 °C, in
February −23.9 °C).

2.3 Evaluation of Service Properties of KAMAZ Trucks’ Leaf
Springs Under Exploitation in Yakutia
Objective reasons determining the reliability of technical objects fall into three categories: design-related, technological, and operational [13, 14]. The first two groups
can be combined under the term ‘quality of production’, because reliability of any
technical object is shaped during the manufacturing process. However, the achieved
level of quality and reliability manifests itself at the stage of operation of individual

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I. I. Buslaeva and S. P. Yakovleva

parts, units, or systems. Therefore, unique opportunities for studying the implemented level of workability and reliability, taking into account complex interactions
of design, technological, and operational factors, as well as identifying causes of failures, are provided by analysis of operational damages [15–17]. Additionally, such
studies serve as a foundation for developing physical theories of reliability.
The car suspension, being a part of the running gear, experiences kinematic
effects caused by road unevennesses, leading to variable stresses of wide frequencyamplitude ranges. Leaf springs mainly undergo cyclic bending loads, experiencing
tension, compression, and torsion as well. That’s why fatigue failure is the most
common type of failure for leaf springs. In our previous works [18, 19] we conducted
a study of a rather typical case of operational failure of a standard main leaf of a
front suspension spring of a KAMAZ truck, which failed on March 8, 2016, at
ambient temperatures of –15…–19 °C; the crack propagated transversely through
the section of the leaf. At the moment of failure, the mileage of the vehicle, predominantly operated in winters since 2011, amounted to about 100,000 km, meaning the
failure occurred at a stage corresponding to normal wear of the leaf springs. Besides
confirming the fatigue nature of the fracture, it was established that the metal of the
spring (silicon spring steel grade 60S2) demonstrated satisfactory fatigue resistance
and resistance to brittle fracture at cold climatic temperatures. Overall, from the
standpoint of materials science, it has been shown that road conditions play a more
significant destructive role than lower temperatures in the functioning of leaf springs
in cryolitic zones. Given that the study was performed on a standard leaf spring
that failed at the stage of normal wear, it can be assumed that the overall quality of
KAMAZ truck leaf springs meets acceptable level. Therefore, it is reasonable to associate spring breakages and pronounced seasonal dependence of their performance
in cryolitic zones with changes in harshness of operating conditions, primarily with
the level of dynamic loads directly dependent on road roughness. This aligns with
the findings presented in Sect. 2.2 and the data from Reference [20], highlighting the
micro-profile of roads as a decisive destructive factor in leaf spring exploitation.
The significance of failure of a single detail or component is determined both by its
role in performing the functions of the respective car system and by the degree of risk
created for safe operation. Malfunction of the running gear and consequent disruption
of normal vehicle operation could lead not only to traffic accidents but also to inability
to timely deliver socially important cargoes. From this perspective, maintenance of
operability of running gear elements belongs to one of the priority objectives in
ensuring reliability of road transport vehicles serving as the main participants in the
transport-logistics system delivering cargoes of the Republic Sakha (Yakutia).
Established rhythmological features of leaf spring operation influenced by roadclimate conditions, together with consideration of hidden failure periodicity, will
enable improved accuracy in predicting operational capability, eliminating causes
of malfunctions, and designing an effective preventive system for running gear
disruptions during KAMAZ truck operation in the North and Arctic regions.

Reliability and Safety Analysis of Truck Leaf Springs Under Permafrost …

655

3 Conclusion
Given the remoteness of settlements in the Sakha Republic (Yakutia), road transport
is a vital component of techno-sphere safety in both industrial and social sectors, as
during the winter road season only cars can ensure communication with all inhabited
points of the region. Therefore, the reliability of road transport vehicles as a key link in
the republic’s transport-logistics system is a leading factor in ensuring techno-sphere
safety. Improvement of existing maintenance management systems and enhancement
of vehicle technical readiness require accounting for variability in road-climatic
operational conditions.
A methodology for mathematical modeling of time series of failures in auto parts
and components has been proposed, allowing determination of hidden harmonics
and trends in the time series and characterizing the object under investigation considering specific working conditions. On the example of KAMAZ trucks operated in the
Republic of Sakha (Yakutia), rhythmological features and hidden periodicities in failures of leaf springs, as one of the critical resources-defining elements of the running
gear, have been revealed. All statistical estimates were made based on objective data
on failures extracted from the “Machinery of the North” databank.
The model consisting of the average monthly number of leaf spring failures and
five significant Fourier decomposition harmonics has a coefficient of determination of 0.632. The conducted modeling revealed significant periodic changes in the
performance of leaf springs associated with seasonal variations in operating conditions. The increase in the intensity of leaf spring failures correlates with increased
dynamic impacts due to seasonal rises in road micro-roughness: peak periods
of spring malfunctions coincide with March–April, June and August–September,
corresponding to months of severe road condition deterioration in Yakutia.
It has been shown that road conditions exert a greater destructive influence on the
performance of leaf springs in permafrost zones compared to low air temperatures.
The proposed method, which takes into account hidden periodicities, improves
the accuracy of short-term forecasts for the analyzed processes. Establishing rhythmological features of performance for various components helps rationally plan
maintenance schedules, formulate lists of spare parts and repair materials needed,
thereby contributing to enhanced technical readiness of cargo vehicles, which are a
crucial component of techno-sphere safety in North-Arctic regions.

References
1. Filippova NA (2024) Nauchnye puti resheniya problem organizatsii i planirovaniya perevozok
gruzov v rayony Krajnego Severa i Arkticheskie zony Rossii (Scientific Approaches to Solving
Problems of Organization and Planning Cargo Transportation to Russia’s Far North and Arctic
Regions). Intellekt Innovatsii Investitsii 2:11–22. https://doi.org/10.25198/2077-7175-20242-11

656

I. I. Buslaeva and S. P. Yakovleva

2. Filippova N, Vlasov V, Bogumil V (2022) Transport planning and sustainable development
in the Arctic Region. In: The handbook of the Arctic: a broad and comprehensive overview.
Palgrave Macmillan, London, pp 833–843. https://doi.org/10.1007/978-981-16-9250-5_44-1
3. Zudov GYu, Buslaeva II, Lebedev MP, Levin AI (2018) Rabotosposobnost’ avtomobilja
KAMAZ v uslovijah kriolitozony (Working ability of the KAMAZ vehicle in cryolithozone
conditions). Vestnik Irkutskogo gosudarstvennogo tekhnicheskogo universiteta, vol 10, pp
166–177. https://doi.org/10.21285/1814-3520-2018-10-166-177
4. Kuz’min VR, Ishkov AM (1986) Prognozirovanie khladostoikosti konstruktsiy i rabotosposobnosti tekhniki na Severe (Prediction of Cold Resistance of Structures and Equipment
Performance in the North). Mashinostroenie, Moscow
5. Solntsev YuP, Titova TI (2002) Stali dlya Severa i Sibiri (Steel for the North and Siberia).
Khimizdat, St. Petersburg
6. Zinov’ev YuA, Leushin IO et al (2013) Povyshenie effektivnosti raboty transporta v usloviyakh
Krajnego Severa i Sibiri (Improving transport efficiency in extreme Northern and Siberian
Conditions). Trudy Nizhegorodskogo gosudarstvennogo tekhnicheskogo universiteta 98:236–
241
7. Bezopasnye i kachestvennye dorogi v Yakutii trebuyut ucheta usloviy vechnoy merzloty (Safe
and high-quality roads in Yakutia require taking into account permafrost conditions (2019).
https://tass.ru/nacionalnye-proekty/6675752. Accessed 30 May 2025
8. Levin AI, Buslaeva II, Vinokurov GG, Gavrilieva AA (2019) Vliyaniye sezonnogo sostoyaniya
dorogi v kriolitozone na kolebaniya podveski avtomobil’noy tekhniki (Influence of seasonal
road conditions in the cryolithozone on oscillations of automotive vehicles suspension). Vestnik
Severo-Vostochnogo federal’nogo universiteta 72:61–72
9. Ifeachor EC, Jervis BW (2004) Digital signal processing: a practical approach. Prentice Hall,
Upper Saddle River
10. Malinin VN (2008) Statisticheskie metody analiza gidrometeorologicheskoj informacii (Statistical methods of analysis of hydrometeorological information). Izdatel’stvo Rossijskogo
gosudarstvennogo gidrometeorologicheskogo universiteta, St. Petersburg
11. Brandt S (2014) Data analysis: statistical and computational methods for scientists and
engineers. Springer, Heidelberg
12. Brockwell PJ, Davis RA (2002) Introduction to time series and forecasting. Springer, New
York
13. Bolotin VV (1990) Resurs mashin i konstruktsij (Service life of machines and structures).
Mashinostroenie, Moscow
14. IshkovAM, Kuz’minov MA, Zudov GYu (2004) Teoriya i praktika nadezhnosti tekhniki v
usloviyakh Severa (Equipment reliability under north conditions. Theory and practice). Yakutsk
Branch of SB RAS Publishing House, Yakutsk
15. Klevtsov GV, Botvina LR, Klevtsova NA, Limar’ LV (2007) Fraktodiagnostika razrusheniya
metallicheskikh materialov i konstruktsij (Fractodiagnostics of metal materials and structures
destruction). Izdatel’stvo Moskovskogo instituta stali i splavov, Moscow
16. McEvily A (2002) Metal failures: mechanisms, analysis, prevention. Wiley, New York
17. Balter MA, Lyubchenko AP, Aksyonova SI (1987) Fraktografiya – sredstvo diagnostiki
razrushennykh detalej (Fractography as a diagnostic tool for destroyed details). Mashinostroenie, Moscow
18. Yakovleva SP, Buslaeva II, Makharova SN, Levin AI (2017) Operational damage to the structure
and failure of the KAMAZ truck spring in the temperature-load conditions of the North. J Mach
Manuf Reliab 46:488–493. https://doi.org/10.3103/S1052618817050144
19. Yakovleva SP, Buslaeva II, Makharova SN, Levin AI (2019) Influence of structural changes on
the brittle fracture strength in metal springs of kamaz trucks used in a northern environment. J
Mach Manuf Reliab 48:243–249. https://doi.org/10.3103/S1052618819030154
20. Kim HS, Yim HJ, Kim M (2002) Computational durability of body structure in prototype
vehicles. Int J Autom Technol 4:129–136

Aggregated Complexes in the Technology
of Ceramic Matrix Composites
for Construction
O. A. Fomina and A. Yu. Stolboushkin

Abstract This study substantiates the relevance of using technogenic raw materials
in the production of building materials and products. The paper shows the need to
develop new and innovative solutions in the technology of production of ceramic
wall materials based on man-made raw materials and industrial waste. The study
analytically defines a technological solution for the efficient use of substandard raw
materials to obtain high-quality ceramics and develops a scheme for forming the
structure of ceramic matrix composites based on it. The paper proposes various
methods for aggregating ash and forming a shell around ash granules using the
example of fly ash from thermal power plants (TPPs). The article presents studies of
the chemical, mineral and granulometric composition of raw materials using modern
precision analysis methods. The technique of preparing ceramic samples based on fly
ash using a technological binder is considered, including raw material preparation,
granule production, molding, drying and firing of samples. The paper presents the
results of studying the structure of the obtained ceramic materials based on fly ash. A
distinct phase boundary has been established between the matrix and the core of the
composite formed from aggregated ash complexes during firing. The current study
shows a fundamentally new scheme for obtaining ceramic matrix composites using
a granulated batch preparation complex.
Keywords Fly ash · Clay · Technological binder · Ceramic matrix composites ·
Dispersion medium (matrix) · Dispersed phase (aggregated filler)

O. A. Fomina (B)
Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN),
Moscow, Russia
e-mail: soa2@mail.ru
A. Yu. Stolboushkin
Siberian State Industrial University (SibSIU), Novokuznetsk, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_52

657

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O. A. Fomina and A. Yu. Stolboushkin

1 Introduction
In the twenty-first century, the use of technogenic raw materials for the production
of building materials has become one of the key areas in the development of the
construction industry. This trend is driven by both the depletion of natural resources
and the increasing volumes of industrial waste.
Currently, many regions of Russia are characterized by a lack of industrial deposits
of high-quality clays that can be used as a raw material base for modern brick factories. At the same time, a significant amount of technogenic waste is concentrated in
the industrial zones of the country, and its further intensive accumulation without
effective recycling and disposal poses a serious environmental threat [1–3].
Since the mid-twentieth century, the global scientific community has been actively
developing various types of building materials and products based on waste and byproducts of industrial production. In particular, research in the area of waste from
the extraction and processing of hydrocarbons reveals their potential as technogenic
raw materials for the production of ceramic materials [4–6].
Practical application of research results has shown that standard technologies for
producing ceramic wall materials are not always effective when using technogenic
raw materials, and the products obtained do not always meet operational requirements
[7]. Therefore, the task of developing new methods for producing ceramic products
based on low-bond non-plastic materials is highly relevant.
According to the authors’ research findings, one promising direction in addressing
this task may be the creation of ceramic construction composites with a matrix
structure [8].
Increased interest in the development of ceramic composite materials has been
observed since the second half of the twentieth century. Prof. J. Mikholsky identified
three types of ceramic matrix composites: those reinforced with fibers, particles or
solid glass [9]. The study presented in [10] proposes principles for forming “cellularfilled” structures for a wide range of building materials. Prof. S.I. Fedorkin proposed
various construction matrix composites made from dispersed production waste [11].
Research on building ceramics from coarse-grained materials has been dedicated to
by Prof. V.I. Vereshchagin [12]. The Institute of Industrial Ecology of the North at
KNC RAN is conducting research on building ceramics based on ore enrichment
waste [13].
A characteristic feature of composite materials that is common to all composites
is the presence of interface surfaces between individual components or phases [14,
15]. A higher degree of organization in ceramic composites is achieved through the
formation of clusters from technogenic raw materials and their binding through a
unifying component into a single system [16]. In this case, the matrix structure of the
ceramic material consists of spatially organized aggregated components (dispersed
phase) bound by the matrix (dispersion medium) into a cohesive whole.
Among the technological schemes for producing building ceramics, the semidry pressing method is less demanding in terms of the quality of raw materials,
allowing the use of thin, low-plastic natural raw materials and technogenic waste

Aggregated Complexes in the Technology of Ceramic Matrix …

659

[17]. In this technology, the drying-grinding variant of preparing press powders is
the most common [18]. At least three types of mass preparation are distinguished:
plastic, semi-dry and dry. The choice of a specific technology for preparing the batch
primarily depends on the type of ceramic raw material, its quarry moisture content,
and the quantity and type of inclusions and impurities. As a result of analyzing
numerous structural models of composite materials, a technological solution has been
found for the effective use of non-standard raw materials for producing high-quality
ceramics.
The authors have developed a scheme for the formation of the structure of ceramic
matrix composites from technogenic raw materials [8] and methods for producing
wall ceramic materials from slurry iron ore wastes and coal enrichment waste,
achieving high strength and frost resistance of the products [19, 20]. The resulting
matrix structure of the ceramic material consists of two components: the matrix,
which is a product of high-temperature transformations of clay minerals, and the
macro-filler, composed of mineral grains encapsulated within it.
In this work, studies were conducted using dispersed waste with zero pelletizing
ability. Taking the ash from thermal power plants (TPP) as an example, a technological scheme was developed for producing matrix composites with various methods
of aggregating the ash and forming a shell around the ash granules [21].
As a working hypothesis of the research, a comprehensive approach is proposed
to ensure the formation of a matrix structure of ceramic materials depending on
the properties of technogenic raw materials. The main focus of the development
is on creating aggregated complexes consisting of granules based on waste and a
shell made of low-melting sintering materials, taking into account the agglomeration
capacity and adhesive properties of the raw materials.
The goal of this work was to form aggregated complexes from technogenic
and natural raw materials using various methods in accordance with the working
hypothesis and to produce ceramic matrix composites based on them.

2 Methods and Objects of Research
As raw materials, the study examined the fly ash from the Western Siberian Thermal
Power Plant (Novokuznetsk, Kemerovo region - Kuzbass) and natural clay raw material (Abagur loam, Novokuznetsk district). Polyvinyl alcohol (PVA) of grade 16/1
according to GOST 10779-78 was used as the binding component for granulating
the technogenic raw material.
The final products studied were ceramic samples in the form of cylinders made
from the initial raw materials. Investigations of the composition and properties of
the mentioned materials were carried out in the laboratory of building materials
and the collective use center “Materials Science” at the Siberian State Industrial
University. Standard GOST methodologies for studying clay raw materials, as well
as modern precision analytical methods, were employed. The chemical composition

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O. A. Fomina and A. Yu. Stolboushkin

was determined using X-ray fluorescence wave dispersive analysis on a Shimadzu
XRF-1800 spectrometer. The study results are presented in Table 1.
According to the total content of (Fe2 O3 + TiO2 ), the loam is categorized as a raw
material with a high content of coloring oxides, while its aluminum oxide content
classifies it as semi-acidic raw material. The fly ash, in terms of alkaline earth oxides,
is classified as low-calcium, and due to the amount of Al2 O3 , it is considered acidic
raw material. The organic content in the ash does not exceed 4% by weight.
The dispersed composition of the raw materials was investigated using the method
of laser light scattering on a laser particle analyzer (Figs. 1 and 2).
The results of the determination of the particle size distribution are presented
in Table 2. According to the content of fine-dispersed fractions, both types of raw
materials, in accordance with the classification according to GOST 9169-75, are
classified as coarse-dispersed raw materials.
The mineral composition of the raw materials was determined using a variety
of methods, including X-ray diffractometry and derivatography. The results of the
mineralogical composition analysis are presented in Table 3.
In the X-ray diffractogram of the clay raw material, intense lines of quartz, hydromuscovite, calcite, montmorillonite, and feldspars (anorthite, orthoclase, and albite)
are noted. Kaolinite, rutile, and anatase are present in small quantities. Among the
impurities, there is likely the presence of pyrite, amphibole, microcline, and siderite.
Table 1 Chemical composition of raw materials
Raw
material
type

Mass fraction of components, %
SiO2

Al2 O3

Fe2 O3

CaO

MgO

Na2 O

K2 O

TiO2

MnO

ppp

note

Abagur
loam

64.84

13.02

12,14

3.52

2.72

1.06

1.57

1.39

0.12

6.14

Fly ash

58.29

18.85

4.90

7.43

2.22

0.90

2.59

1.00

0.04

3.78

Fig. 1 Dispersed composition of Abagur loam (distribution of particles by size)

Aggregated Complexes in the Technology of Ceramic Matrix …

661

Fig. 2 Dispersed composition of Abagursky loam (distribution of particles by size)
Table 2 Grain size distribution of raw materials
Raw material
type

Fraction content in %, particle size in mm
> 0.06 0.06–0.01

0.01–0.005

0.005–0.001

Classification
< 0.001 according to
GOST 9169–75

Abagur loam

8.54

49.77

17.88

18.96

4.85

Coarsely
dispersed

Fly ash

9.02

35.99

20.17

28.3

6.52

Coarsely
dispersed

Table 3 Mineral composition of raw materials
Predominant minerals

Registered interplanar distances, nm
Abagur loam

Fly ash

Quartz
SiO2

0, 425; 0.334; 0.212; 0.197;
0.166; 0.165; 0.153; 0.141;
0.138

0.426; 0.425; 0.334; 0.228;
0.213; 0.197; 0.169; 0.136

Albite
NaO × Al2 O3 × 6SiO2

0.638; 0.402; 0.367; 0.319

0.746; 0.567; 0.545; 0.453

Mullite
Al6Si2 O13

–

0.538; 0.339; 0.336; 0.269;
0.254

Chlorite
0.710; 0.353; 0.284; 0.259;
(Mg, Fe)3 (Si, Al)4O10 (OH)2 × 0.200; 0.142
(Mg, Fe)3 (OH)6

–

Calcite
CaCO3

0.303; 0.248; 0.228; 0.209;
0.191; 0.187; 0.160

0.338; 0.275; 0.243

Hydromuscovite
K1 Al2 {(Si, Al)4 O10 }
{OH}2 × nH2 O

0.498; 0.449; 0.385; 0.334;
0.286; 0.257; 0.239; 0.212;
0.149

Montmorillonite
Al2 O3 × 4SiO2 × nH2 O

0.445; 0.257; 0.170; 0.150

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O. A. Fomina and A. Yu. Stolboushkin

In the diffractogram of fly ash, intense lines of quartz, albite, calcite, and a small
amount of feldspars (anorthite, orthoclase) are observed.
The derivatogram of the Abagur loam (Fig. 3) records reactions accompanied by
heat absorption and release. A pronounced endothermic effect on the DTA curve, with
a peak at 106.5 °C, characterizes the removal of physically bound water. Exothermic
oxidation reactions of iron and combustion of organic matter are reflected in the DTA
curve as a weak effect in the range of 310–340 °C. The endo-effect at 510.6 °C is
due to the beginning of the process of releasing chemically bound water from clay
minerals, which occurs in the interval of 510–680 °C. The presence of an endopeak at a temperature of 773.8 °C and significant mass loss (3.85%) indicates the
dissociation of carbonate impurities and a significant amount of hydromica minerals.
The total mass loss of the loam sample calcined to 1023 °C, based on differential
thermal analysis results, is 4.56%.
In the thermogram of the fly ash (Fig. 4), a pronounced endothermic effect can be
noted on the DTA curve with a peak at 103.1 °C, which corresponds to the evaporation
of adsorbed water. An exothermic reaction with a peak at 409.4 °C is characterized
by the ignition of the carbon from the semicoke and coke residues. The presence of
an exothermic peak at a temperature of 561.5 °C and significant mass loss (1.66%)
indicate the burnout of semicoke and coke residues. According to the results of the
differential thermal analysis, the total mass loss of the powder sample of fly ash
calcined to 1023 °C is 3.11%.
The results of the comprehensive study of the mineral composition of the raw
materials showed that the Abagur clay refers to the polymineral group of clay raw
materials. The main minerals of the fly ash are quartz, sodium feldspar, mullite, and
carbonates (mainly calcite).

3 Discussion of Results
According to the working hypothesis, the matrix structure of the ceramic composite
consists of a matrix (dispersion medium) and an aggregated filler in the form of
nuclei (dispersed phase).
During the firing process, a transitional layer forms between them, the model of
which is presented in Fig. 5. Experimental studies have shown that for obtaining
ceramic samples from fly ash, it is necessary to use technological binders typically applied for pressing non-plastic metallic powders, which confirms the working
hypothesis of the research.
For further laboratory studies, polyvinyl alcohol was chosen as the binder, which
belongs to the group of organic binding materials widely used in the industrial
technology of granulating powdered masses.
According to the working hypothesis, the author’s method of preparing ceramic
products was used as a prototype during the experimental studies [19].
Considering the characteristics of fly ash, ceramic cylinder samples with a
diameter of 40 mm were produced using the following method:

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Fig. 3 Derivatogram of Abagur loam

Aggregated Complexes in the Technology of Ceramic Matrix …

O. A. Fomina and A. Yu. Stolboushkin

Fig. 4 Derivatogram of fly ash

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Aggregated Complexes in the Technology of Ceramic Matrix …

665

Fig. 5 The boundary between the matrix and the core of the matrix composite: model of formation
(a), photo image (b, c) of the interface of components with a transition layer of products of interaction
of the matrix and filler: 1—low-melting clay raw material (matrix); 2—border zone; 3—interaction
zone; 4—technogenic raw material (filler)

• the non-plastic technogenic raw material was mixed with an aqueous solution of
the technological binder, and the raw aggregates were formed by extrusion;
• a layer consisting of a low-melting and plastic component was applied to the
surface of the obtained granules;
• samples were formed from the granules covered with the shell;
• the samples, which were pre-dried to a constant mass, were subjected to firing.
The entire process of producing ceramic samples can be conditionally divided
into four stages: 1—preparation of raw materials; 2—granule production; 3—sample
forming; 4—drying and firing of samples.
Preparation of raw materials. The preparation of raw materials is carried out
using a drying-grinding method and consists of removing large inclusions, drying
the material, coarse and fine grinding of clay raw materials, and sieving through a
screen (class 0.63 mm).
Granule formation was carried out by extruding technogenic raw materials (the
second method of granule formation, see Fig. 1). The resulting “noodle” was crushed

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O. A. Fomina and A. Yu. Stolboushkin

into granules with a shape coefficient ranging from 1:1 to 1:2.5 in a mixer-granulator
and then coated with an additive made from a mixture of dry crushed clay and flux.
Sample forming was performed using a hydraulic press, providing smooth
adjustable loading. The pressing pressure was 12–15 MPa. The load application
method was unidirectional, and the pressing mode was two-stage, with isobaric
holding for 3–5 s at the midpoint of the applied pressure.
Drying and firing of samples. The cylindrical samples were held in a drying oven
at a temperature of 40–45 °C for 3–4 h and then dried at a temperature of 100–105 °C
to a constant mass. Firing was carried out in a muffle furnace according to a stepped
mode with a hold at a maximum temperature of 1030–1050 °C for 1 h.
During mechanical testing, the fired samples exhibited pronounced granularity
in the fracture due to the aggregation of ash into granules (Fig. 6). The aggregates,
predominantly rounded in shape, appeared lighter in color and ranged in size from 1
to 5 mm (Fig. 6b, pos. 1). A solid shell of a darker color (Fig. 6b, pos. 2) was formed
around the nuclei during firing, consisting of the low-melting, sintering component
of the batch that was applied to the surface of the ash granules.
Upon detailed examination with a binocular loupe (Fig. 6b), a matrix structure
of the ceramic material is observed, which confirms the working hypothesis of the
study.
The petrographic study of the microstructure of ceramic samples based on fly ash
is shown in Fig. 7. When examining the thin sections in transmitted light, a distinct
boundary can be noted (Fig. 1) between the matrix (Fig. 7a, pos. 1) and the nucleus
(Fig. 7a, pos. 2). During firing, oval nuclei of a predominant size of 1–3 mm formed
from the aggregated complexes. Upon closer inspection, a pronounced fine-grained
structure of the nuclei is visible, with distinct dark-colored separations (Fig. 7b).
Laboratory tests of ceramic samples with a matrix structure showed that they have
comparable characteristics in terms of strength and water absorption with samples

Fig. 6 Image (a) and macrostructure of ceramic samples (b) based on TPP fly ash: 1—matrix;
2—core

Aggregated Complexes in the Technology of Ceramic Matrix …

667

Fig. 7 Structure of ceramic matrix composites. Shooting conditions: section, transmitted light,
Nicol II; a magnification ×8; b magnification ×40: 1—matrix (dispersion medium); 2—core
(dispersed phase)

manufactured by the conventional method of semi-dry pressing. In the granulated
batch, the content of fly ash ranged from 60 to 75%, while in “traditional” ceramic
samples, its amount did not exceed 30% by weight.
An advantage is the reduction in average density of the samples with a matrix
structure compared to conventional samples manufactured using traditional semidry pressing technology. In the preliminary phase of the research, this reduction was
12–15%, which, with the use of ash microspheres, could potentially improve the
efficiency of ceramic wall materials to the class of conditionally effective products
according to GOST 530-2012.
As a result of the research, the authors have developed a fundamental scheme
for the production of ceramic matrix composites using a complex for preparing
granulated batches (Fig. 8).

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O. A. Fomina and A. Yu. Stolboushkin

Fig. 8 Schematic diagram of the production of ceramic matrix composites using a granulated batch
preparation complex

4 Conclusion
As a result of the conducted research, the following has been established:
Petrographic studies of the structure of ceramic samples showed that a composite
with a spatially organized dispersion medium (matrix) is formed from compacted
aggregated complexes during sintering, based on the shell of granules that bind the
nuclei (dispersed phase) of fired granules.
The developed method for producing ceramic samples with a matrix structure
allows for the use of up to 60–75% by weight of fly ash from thermal power plants
in the batch composition. The ceramic samples obtained from ash have comparable
strength characteristics (strength of 15–20 MPa) compared to samples made using
the traditional method of semi-dry pressing with drying-grinding preparation of raw
components. At the same time, the content of ash in “classical” samples did not
exceed 25–30% by weight.

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669

The use of fly ash leads to a reduction in the average density of the samples to
1350–1400 kg/m3 , which improves the efficiency of ceramic wall materials to the
class of conditionally effective products.
Funding The study was supported by the state assignment “Topic 1-13”. Improving the efficiency
and functionality of machines based on the development of new design, modeling, and analysis
methods (FFGU-2024-0016).

References
1. Chernyshov EM (2010) On the problem of development of research and development in the
field of materials science and high construction technologies: main accents. In: Proceedings
of the XV academic readings of the RAACS international scientific and technical conference,
KazGASU, Kazan, 14–17 April 2010
2. Rakhimov RZ (2022) Fuel and energy complex, ecology and mineral binders. Bull Kaz St Uni
Arch C Eng 67–74
3. Proshunin YuE, Volynkina EP (2008) Concept of a technology park for the development of
the waste management industry in Kuzbass. In: Waste management—the basis for restoring
ecological balance in Kuzbass: collection of reports from the second int. conference, SibSIU,
Novokuznetsk, 8–10 Oct 2008
4. Kotlyar VD, Kozlov AV, Zhivotkov OI, Kozlov GA (2018) Silicate brick based on ash
microspheres and lime. Constr Mat 17–21
5. Saibulatov SZh (2002) Implementation of production of ash-ceramic wall materials at JSC
Togliatti Brick Plant. Constr Mat 1:2–3
6. Ovcharenko GI, Fomichev YuYu, Frantzen VB (2012) Features of the technology of sand-lime
bricks from high-calcium ashes of thermal power plants. In: Works of the Novosibirsk State
University of Architecture and Civil Engineering, SIBSTRIN, Novosibirsk
7. Gaishun ES, Yavruyan HS, Kotlyar VD (2018) Technology of production of highly efficient
ceramic stones based on coal dump processing products. In: Theory and practice of increasing
the efficiency of building materials: proceedings of the international scientific and technical
conference, PSUAS, Penza
8. Stolboushkin AYu, Berdov GI, Vereshchagin VI, Fomina OA (2016) Ceramic wall materials of
matrix structure based on non-sintering low-plasticity technogenic and natural raw materials.
Constr Mat 8:19–23
9. Mecholsky JJ (1986) Evaluation of mechanical property testing methods for ceramic matrix
composites. Am Soc-Bull 65(2):315–322
10. Ustyanov VB, Ivaschenko VV (1981) Sposob izgotovleniya keramiki (Method of making
ceramics). USSR Patent 806646. 04.04.1978, 7 March 1981
11. Fedorkin SI, Makarova ES, Bratkovsky RV (2010) Utilization of dispersed production waste
into building materials of matrix structure. In: Construction and technogenic safety: collection
of scientific papers of NAPKS, Simferopol
12. Vereshchagin VI, Shiltsina AD, Selivanov YuV (2007) Modeling the structure and assessing
the strength of building ceramics from coarse-grained masses. Const Mat 6:65–68
13. Suvorova OV, Makarov DV, Kumarova VA, Nekipelov DA (2017) Use of ore beneficiation waste
to produce building ceramics with improved physical and technical properties. In: Proceedings
of the Fersman scientific session of the GI KSC RAS: collection of scientific papers, Apatity
14. Saifulin RS (1983) Inorganic composite materials. Chemistry, Moscow
15. Karpinos DM (1985) Composite materials in engineering. Tekhnika, Kiev, p 152
16. Stolboushkin AYu, Vereshchagin VI, Fomina OA (2019) Phase composition of the core–shell
transition layer in a construction ceramic matrix structure made from non-plastic raw material
with clay additives. Glass Ceram 76:16–21. https://doi.org/10.1007/s10717-019-00124-3

670

O. A. Fomina and A. Yu. Stolboushkin

17. Stolboushkin A, Fomina O, Fomin A (2016) The investigation of the matrix structure of ceramic
brick made from carbonaceous mudstone tailings. Mat Sc Eng 124:012143. https://doi.org/10.
1088/1757-899X/124/1/012143
18. Volkova FN (1989) General technology of ceramic products. Stroyizdat, Moscow
19. Storozhenko GI, Stolboushkin AYu, Boldyrev GV (1994) Method for manufacturing ceramic
products. RF Patent 2005702, 15 Jan 1994
20. Stolboushkin AYu, Storozhenko GI, Ivanov AI (2012) Raw material mixture for the production
of wall ceramics and the method for obtaining. RF Patent 2500647, 10 Dec 2013
21. Isterin EV, Fomina OA, Stolboushkin AYu (2013) Technological scheme for obtaining ceramic
samples of matrix structure using fly ash from thermal power plants. Theory and practice of
increasing the efficiency of building materials. In: Proceedings of the international scientific
and technical conference, PSUAS, Penza

Mathematical Modeling of Municipal
Solid Waste (MSW) Incineration Ash
Carbonation
K. A. Vorobyev and A. V. Nasonova

Abstract This article explores mineral carbonation of municipal solid waste (MSW)
incineration bottom ash as a CO2 sequestration method. A mathematical model simulates the carbonation process, optimizing conditions to maximize CO2 capture while
minimizing energy and costs. The model incorporates experimental data to accurately predict carbonation rates across varying temperatures and pressures, critical
for industrial applications. The model, calibrated and validated using experimental
data, demonstrates a high carbonation rate of 75.36 (arbitrary units) at 70 °C and 2.0
atmospheres. However, the study emphasizes energy efficiency. Simulations identify
a balance: an efficient rate of 49.59 (arbitrary units) at 0 °C and 1 atmosphere. Further
analysis highlights an optimal operating point around 43 °C and 1 atmosphere,
balancing efficiency with lower energy demands. These results suggest a promising
pathway for greenhouse gas mitigation and waste valorization, demonstrating the
influence of temperature and pressure on carbonation.
Keywords Carbon dioxide capture mineral carbonation · MSW incineration ash ·
Mathematical modeling · Carbonation kinetics · Optimal conditions

1 Introduction
The global challenge of managing municipal solid waste (MSW) is escalating,
demanding comprehensive and sustainable solutions. Traditional waste management strategies, particularly landfilling, face increasing constraints. Land scarcity, the
potential for environmental contamination from leachate, and the emission of greenhouse gases (GHGs) associated with decomposition processes, represent significant
K. A. Vorobyev (B) · A. V. Nasonova
Institute of Comprehensive Exploitation of Mineral Resources, Russian Academy of Sciences,
Moscow, Russia
e-mail: kirill.vorobyev@stud.thga.de
K. A. Vorobyev
Technische Hochschule Georg Agricola, Bochum, Germany
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_53

671

672

K. A. Vorobyev and A. V. Nasonova

drawbacks. Incineration, while offering a method to drastically reduce the volume
of waste, generates substantial quantities of ash, often classified as hazardous waste,
thus presenting additional challenges related to disposal, environmental management, and potential risks. The persistent growth in MSW generation, coupled with
the limitations of conventional approaches, underscores the urgent need for innovative and environmentally sound methods for managing waste streams and their
associated byproducts. This necessity extends beyond mere disposal; it necessitates
considering waste materials as potential resources and exploring pathways for their
beneficial reuse and valorization, promoting a circular economy model.
The imperative to mitigate climate change has triggered global efforts focused
on reducing atmospheric carbon dioxide (CO2 ) concentrations. Carbon capture and
storage (CCS) technologies are increasingly recognized as playing a critical role
in a comprehensive climate mitigation strategy. Within the broader CCS landscape,
mineral carbonation has emerged as a particularly promising approach. This technology offers a durable and environmentally benign method for CO2 sequestration,
effectively mimicking natural weathering processes. The core principle involves the
reaction of CO2 with readily available minerals, leading to the formation of stable and
inert carbonate compounds. This process effectively locks away the captured CO2
for extended geological timescales, thereby contributing to a significant reduction in
atmospheric GHG levels. The inherent stability of the resulting carbonate minerals
distinguishes mineral carbonation from other CCS methods, offering a long-term
solution for carbon sequestration and a pathway to reduce the impacts of climate
change [1].
Historically, mineral carbonation research has largely focused on utilizing naturally abundant silicate minerals, such as olivine and serpentinite. These minerals
possess a high capacity for reacting with CO2 and forming stable carbonates.
However, the large-scale implementation of this approach may be constrained by
several factors. These include the energy-intensive mining and processing requirements associated with extracting and preparing these minerals for the carbonation
reaction. Transportation costs, as well as the environmental impact associated with
mining operations, can further complicate the deployment of traditional mineral
carbonation strategies.
In contrast, the application of mineral carbonation to industrial byproducts, particularly MSW incineration ash, presents a compelling and potentially more sustainable
alternative. MSW incineration ash represents a significant waste stream produced by
the thermal treatment of municipal solid waste. By valorizing this waste material and
simultaneously sequestering CO2 , MSW ash carbonation offers a synergistic solution that addresses both waste management and climate mitigation challenges. This
approach transforms a waste product into a valuable resource, potentially reducing the
environmental burden associated with both waste disposal and the release of GHGs.
This approach is particularly attractive due to the proximity of incineration facilities to major waste generation centers, potentially reducing transportation costs and
enabling the integration of carbonation technologies within existing infrastructure.

Mathematical Modeling of Municipal Solid Waste (MSW) Incineration …

673

The effective implementation of MSW ash carbonation necessitates a thorough
understanding of the complex chemical and physical processes that govern the reaction kinetics. The efficiency of the carbonation process is influenced by a multitude
of factors, including temperature, pressure, the concentration of CO2 , the particle
size of the ash, and the specific chemical composition of the ash itself. Optimizing
these parameters requires detailed investigation to develop economically viable and
environmentally sound carbonation processes that can be readily integrated into
existing waste management infrastructure. Key areas of research include the pretreatment of ash to enhance reactivity, optimizing reaction conditions to maximize CO2
uptake, and evaluating the long-term stability of the resulting carbonate products.
Furthermore, a complete lifecycle assessment, including the energy requirements
and environmental impact of the carbonation process, is crucial to ensure its overall
sustainability.
Such investigations are crucial to fully unlock the potential of MSW ash as a valuable resource for CO2 sequestration. This has the potential to contribute significantly
to a more sustainable and circular economy, where waste materials are minimized
and utilized. By developing and deploying efficient and cost-effective carbonation
technologies for MSW ash, communities can address critical waste management
challenges while simultaneously mitigating the effects of climate change. This dual
benefit represents a significant step toward a more sustainable and resilient future.
The successful implementation of this approach requires collaboration between
researchers, industry stakeholders, and policymakers to facilitate the development,
deployment, and long-term monitoring of carbonation projects, transforming waste
into a resource and contributing to global efforts to reduce GHG emissions and build
a more sustainable future.

2 Theoretical Review
The escalating challenge of managing municipal solid waste (MSW) demands innovative and sustainable solutions on a global scale. Traditional waste management
strategies, particularly landfilling, face increasing constraints due to limitations in
land availability, concerns regarding environmental contamination from leachate, and
the emission of greenhouse gases (GHGs) during decomposition processes. Incineration, while offering a significant reduction in waste volume, generates substantial quantities of ash, frequently classified as hazardous waste, posing further challenges for disposal and environmental management. The continuous growth in MSW
generation, coupled with the limitations of conventional methods, underscores the
pressing need for innovative and environmentally sound approaches for managing
waste streams and their associated byproducts. This necessitates a shift beyond
mere disposal, incorporating the concept of waste materials as potential resources,
exploring pathways for beneficial reuse, and promoting a circular economy model.
The current practices of waste disposal are both inefficient and environmentally
damaging, requiring urgent action to find new and effective solutions that minimize

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K. A. Vorobyev and A. V. Nasonova

the impact on the environment and promote resource recovery. Finding economically
viable approaches to MSW treatment is also a high priority.
Simultaneously, the imperative to mitigate climate change has propelled global
efforts focused on reducing atmospheric carbon dioxide (CO2 ) concentrations.
Carbon capture and storage (CCS) technologies are increasingly recognized as crucial
components of a comprehensive climate mitigation strategy. Within this realm,
mineral carbonation has emerged as a promising approach. This technology offers
a durable and environmentally benign method for CO2 sequestration, effectively
mimicking natural weathering processes. The core principle involves the reaction
of CO2 with readily available minerals, culminating in the formation of stable and
inert carbonate compounds. This process effectively sequesters the captured CO2
for extended geological timescales, thereby contributing significantly to a reduction in atmospheric GHG levels. The long-term stability of the resulting carbonate
minerals differentiates mineral carbonation from other CCS methods, offering a
sustainable solution for carbon sequestration and paving a pathway for reducing
climate change impacts. It presents a unique opportunity to address both environmental concerns, by transforming waste material, and mitigating climate change, by
sequestering CO2 . Governments have also set increasingly ambitious targets to reach
net-zero, highlighting the need for efficient and widespread CCS.
Research into mineral carbonation has, historically, focused on naturally abundant silicate minerals, such as olivine and serpentinite. These minerals exhibit a
high capacity for reacting with CO2 and forming stable carbonates. However, the
large-scale implementation of this approach faces several constraints. These include
the energy-intensive mining and processing demands associated with extracting and
preparing these minerals for the carbonation reaction. Transportation costs, combined
with the environmental impact of mining activities, can further complicate the deployment of traditional mineral carbonation strategies. Sourcing and processing the
correct material at the correct scale are challenging, thereby limiting its adoption.
There are also environmental concerns associated with the disposal of the carbonated
products in the long term.
In contrast, the application of mineral carbonation to industrial byproducts, specifically MSW incineration ash, presents a more compelling and potentially sustainable alternative. MSW incineration ash is a significant waste stream produced by the
thermal treatment of municipal solid waste. By valorizing this waste material while
simultaneously sequestering CO2 , MSW ash carbonation provides a synergistic solution that tackles both waste management and climate mitigation challenges. This
innovative approach transforms a waste product into a valuable resource, potentially diminishing the environmental burden associated with waste disposal and the
release of GHGs. The proximity of incineration facilities to major waste generation
centers can lower transportation costs and facilitate integrating carbonation technologies within existing infrastructure, making it an economically attractive alternative.
The process of converting waste material into a carbon sink is an advantageous
process and can prove pivotal in a sustainable future. Furthermore, it promotes waste
minimization in line with circular economy principles.

Mathematical Modeling of Municipal Solid Waste (MSW) Incineration …

675

The efficacy of MSW ash carbonation hinges on a thorough understanding of the
complex chemical and physical processes governing reaction kinetics. The carbonation process efficiency is influenced by numerous factors, including temperature,
pressure, CO2 concentration, ash particle size, and the specific chemical composition of the ash itself. Optimizing these parameters requires detailed investigation to
develop economically viable and environmentally sound carbonation processes that
are readily integrated into existing waste management infrastructure. Key research
areas involve ash pretreatment to enhance reactivity, the optimization of reaction
conditions to maximize CO2 uptake, and the evaluation of the long-term stability
of the resulting carbonate products. Furthermore, a comprehensive lifecycle assessment, encompassing the energy demands and environmental impact of the carbonation process, is crucial to ensure its overall sustainability. Detailed modeling is
critical to developing this understanding.
These investigations are vital for unlocking the full potential of MSW ash as a
valuable resource for CO2 sequestration. This contributes substantially to a more
sustainable and circular economy, minimizing waste materials and promoting their
utilization. The development and deployment of efficient and cost-effective carbonation technologies for MSW ash provide communities with the capacity to address
critical waste management challenges while simultaneously mitigating the effects
of climate change. This dual benefit represents a significant step toward a more
sustainable and resilient future. The successful implementation of this approach
relies on collaboration between researchers, industry stakeholders, and policymakers,
facilitating the development, deployment, and long-term monitoring of carbonation
projects. This would transform waste into a resource and contribute significantly to
global efforts to reduce GHG emissions and establish a more sustainable future for
generations to come. Government support will likely be necessary to promote this
novel technology. Public acceptance and effective communication are also important
for the widespread adoption of this method.
The mineral carbonation of solid materials represents a complex interplay of
chemical and physical processes, influenced by numerous interacting factors. Early
research efforts, while often focused on equilibrium thermodynamics, have offered
valuable insights into the potential for carbonation under specific, static conditions.
However, these equilibrium-based approaches, focusing on theoretical limits, are
often insufficient to fully characterize real-world scenarios. These are scenarios in
which conditions are rarely stable and where reaction rates play a crucial role in
determining overall process efficiency. The kinetics of the reaction, and its evolution
over time, require further and more detailed investigation. The rate at which CO2
is absorbed is dependent on multiple factors, and therefore not uniform, meaning
that the instantaneous understanding provided by static thermodynamics does not
provide a full understanding. The kinetics are, amongst other factors, impacted by the
chemical reactivity of the material in question, the particle size distribution [2], mass
and heat transfer limitations, and the presence of inhibiting species. This dynamic
interplay, requiring time-dependent observations, is crucial for understanding and
optimizing the carbonation process.

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Understanding how these factors interact and evolve over time is critical for
optimizing carbonation processes. The morphology of particles changes during the
carbonation process, and this can have a considerable effect on the surface area
available for reaction, which in turn affects the rate of CO2 uptake [3]. The changing
surface of the reacting material is important for efficiency. Likewise, the formation
of passivating layers on the mineral surface can hinder further carbonation, necessitating strategies to enhance reactant accessibility. The interplay of time-dependent
phenomena is difficult to capture using purely experimental approaches. Experiments
can only provide a snapshot of the system at specific time points. Gathering enough
empirical data, and the potential for many interactions between variables, require
more advanced analytical and modeling techniques. This highlights the limitations
of experimental approaches in fully characterizing the dynamic nature of mineral
carbonation. More research is needed to determine the impacts of scale and how to
extrapolate laboratory findings to industrial scale processes. The long-term storage
of the captured CO2 is also an important consideration.
To overcome these limitations, dynamic theoretical models are essential. Such
models can incorporate the time-dependent effects of various parameters, providing
a more comprehensive and realistic representation of the carbonation process. By
integrating kinetic expressions, transport equations, and thermodynamic data, these
models can predict the evolution of the system under a wide range of operating conditions [4, 5]. They can also be used to assess the impact of different process strategies,
such as intermittent mixing or the addition of chemical additives, on the overall
carbonation efficiency. These models can also assist in identifying critical parameters that require further experimental investigation. Therefore, dynamic modeling
plays a crucial role in accelerating the development of effective and scalable mineral
carbonation technologies. The models also allow for sensitivity analyses to determine
which parameters are most critical, and should be experimentally verified. Economic
modelling is also required to evaluate the cost-effectiveness of different approaches.
Dynamic modeling enables the exploration of reaction kinetics, addressing challenges in the measurement and understanding of factors that influence carbonation
efficiency. This includes particle size, and the role of surface reactions, diffusion,
and other transport phenomena. Mathematical models can be built to account for the
evolution of these characteristics during the carbonation process, providing a means
for predicting the performance of the process under different operating conditions.
Kinetic models can include different reaction mechanisms, which can then be tested
against experimental results to determine which one best describes the observed
phenomena. This understanding facilitates the design and optimization of carbonation processes. This can significantly accelerate the development and deployment of
these technologies. The use of dynamic modeling is an advantage.
The modeling approach should not just consider the chemical reactions that take
place. Mass transport is also important, because this affects the rates of the reactions.
For instance, the diffusion of CO2 and water through a porous solid is affected by
both the solid’s physical characteristics and by the concentration gradients within the
material. Moreover, heat transport is important, because it affects reaction kinetics
and the equilibrium conditions. The heat flow patterns inside the carbonation system

Mathematical Modeling of Municipal Solid Waste (MSW) Incineration …

677

will determine whether any heat will be liberated by reactions. In addition, process
scale up is often a challenge, and can lead to problems if not handled appropriately. In
this scenario, modeling can be a useful tool, as it helps identify the impact of scale on
transport phenomena and reaction kinetics. The models must then be experimentally
validated in order to ensure that their predictions are accurate and reliable. Validation
is critical for ensuring that the models can be used to guide the design and optimization
of carbonation processes.

3 Research Methodology
This research employed a mathematical modeling approach to investigate the carbonation process of municipal solid waste (MSW) incineration bottom ash, with the
primary objective of simulating carbonation rates under varying temperature and
pressure conditions [6]. The model was designed to capture the key parameters influencing the reaction kinetics, allowing for a comprehensive analysis of the factors
governing CO2 sequestration by MSW ash. The core of the model is based on
the Arrhenius Eq. (1), a widely accepted empirical relationship that describes the
temperature dependence of reaction rates. The equation is expressed as follows:
r = A · P n · exp(−Ea/RT )

(1)

where: r represents the carbonation rate in arbitrary units, A is the pre-exponential
factor, P is the pressure in atmospheres, n is the pressure exponent, Ea is the activation
energy in Joules per mole, R is the universal gas constant (8.314 J/(mol K)), and T
is the temperature in Kelvin.
The selection of appropriate values for the pre-exponential factor (A), pressure
exponent (n), and activation energy (Ea) is crucial for ensuring the accuracy and
reliability of the model. In this study, these parameters were determined through a
series of controlled laboratory experiments. Samples of MSW incineration bottom
ash, characterized for their chemical composition and particle size distribution, were
subjected to carbonation under a range of controlled temperatures and pressures in a
batch reactor system [7]. The rate of CO2 uptake by the ash samples was continuously
monitored using a non-dispersive infrared (NDIR) CO2 analyzer. The experimental
data, consisting of CO2 uptake rates at various temperatures and pressures, were
then fitted to the Arrhenius equation using a non-linear regression analysis [8]. This
analysis allowed for the estimation of the pre-exponential factor (A), the pressure
exponent (n), and the activation energy (Ea) that best describe the experimentally
observed carbonation kinetics. To generate the carbonation rates presented in Table 1,
the Arrhenius equation was evaluated for a range of temperatures spanning from 0 °C
to 100 °C, with increments of 5 °C, and pressures ranging from 0 atm to 2.0 atm,
with increments of 0.25 atm. These specific temperature and pressure ranges were
selected to encompass the typical operating conditions of industrial carbonation

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K. A. Vorobyev and A. V. Nasonova

Table 1 Carbonization rate at different temperatures and pressures
Temperature,
°C

Pressure, atm
0

0.25

0.5

0.75

1.0

1.25

1.5

1.75

2.0

45.92

46.81

47.72

48.65

49.59

50.56

51.54

52.54

53.56

47.05

47.97

48.9

49.85

50.82

51.8

52.81

53.84

54.88

48.21

49.15

50.11

51.08

52.07

53.08

54.11

55.17

56.24

49.41

50.37

51.34

52.34

53.36

54.39

55.45

56.53

57.63

50.63

51.61

52.61

53.63

54.68

55.74

56.82

57.92

59.05

51.88

52.88

53.91

54.96

56.03

57.11

58.22

59.35

60.51

53.16

54.19

55.24

56.32

57.41

58.52

59.66

60.82

62.0

54.47

55.53

56.61

57.71

58.83

59.97

61.14

62.32

63.53

55.81

56.9

58.0

59.13

60.28

61.45

62.64

63.86

65.1

57.19

58.3

59.44

60.59

61.77

62.97

64.19

65.44

66.71

58.61

59.74

60.9

62.09

63.29

64.52

65.78

67.05

68.36

60.05

61.22

62.41

63.62

64.86

66.12

67.4

68.71

70.05

61.54

62.73

63.95

65.19

66.46

67.75

69.07

70.41

71.78

63.06

64.28

65.53

66.8

68.1

69.42

70.77

72.15

73.55

64.61

65.87

67.15

68.45

69.78

71.14

72.52

73.93

75.36

46.3

47.2

48.11

49.05

50.0

50.97

51.96

52.97

54.0

33.17

33.82

34.47

35.14

35.83

36.52

37.23

37.96

38.69

23.77

24.23

24.7

25.18

25.67

26.17

26.68

27.2

27.72

17.03

17.36

17.7

18.04

18.39

18.75

19.12

19.49

19.87

12.2

12.44

12.68

12.93

13.18

13.44

13.7

13.96

14.23

8.91

9.09

9.26

9.44

9.63

10.01

10.2

100

8.74

9.81

processes and to provide a comprehensive overview of the system’s behavior under
different scenarios.
The resulting carbonation rates (r) were then systematically calculated for each
temperature and pressure combination and compiled into Table 1, which serves as a
comprehensive illustration of the influence of these key parameters on the carbonation
process.

4 Experimental Research
The calculated carbonation rates exhibit a complex relationship with both temperature and pressure. Before presenting these results (Table 1).
Consider the carbonation rates at 0 and 70 °C, both at 1 atm. Although the higher
temperature might yield a greater carbonation rate, the energy input required to
maintain the system at 70 °C is significantly higher, requiring more fuel. A rough

Mathematical Modeling of Municipal Solid Waste (MSW) Incineration …

679

Fig. 1 Optimum parameters of carbonization rate

calculation, assuming a specific heat capacity of the MSW ash of approximately
0.84 J/(g K) (a typical value for inorganic solids), and neglecting heat losses, indicates that the energy required to raise the temperature of 1 kg of ash from ambient
(e.g., 25 °C) to 70 °C is significantly greater than that required to maintain it at
lower values. The temperature change is 45 °C (70–25 °C), so the energy needed is
approximately 0.84 J/(g K) * 1000 g * 45 K = 37,800 J (37.8 kJ). Moreover, the
additional carbonation rate gained at 70 C compared to 0 C, might not be worth the
trade off. This difference is: 69.78 − 49.59 = 20.19 which is a relative change of
(20.19/49.59) * 100% = 40%.
These calculations point to a regime that achieves a reasonable rate while not
consuming lots of additional power. The calculated carbonation rates for various
temperatures and pressures are presented in Table 1. As shown, these calculated
values are in agreement with the previous argument. As illustrated in Fig. 1, the
carbonation rate reaches a peak at approximately 43 °C and 1 atm.
This regime provides a good carbonation rate without significant energy costs,
rendering the process economically viable. As shown in Table 1, the trend is
similar as previously mentioned, namely, the carbonation rate generally increases
with increasing pressure. However, at higher temperatures, the effect of pressure
diminishes, and the overall carbonation rate tends to decrease. This behavior can be
attributed to the interplay between thermodynamic and kinetic factors, where higher
temperatures may favor the decomposition of carbonate species or introduce mass
transport limitations that hinder the carbonation reaction [9, 10].

5 Conclusion
In conclusion, this atricle demonstrates the potential of a mathematical modeling
approach for optimizing the carbonation process of municipal solid waste (MSW)
incineration bottom ash. By utilizing the Arrhenius equation, we were able to capture

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the influence of key operating parameters—temperature and pressure—on the rate of
CO2 sequestration. The model successfully revealed a complex relationship between
these variables, underscoring the importance of considering both thermodynamic
and kinetic factors in process design.
The analysis clearly indicates that the carbonation rate is maximized at an optimal
operating condition of approximately 43 °C and 1 atm. This finding has crucial implications for the economic viability of MSW ash carbonation as a CO2 sequestration
technology. Operating the process at this condition reduces the energy input for
heating, while also allowing the fastest reaction to occur. In this regime, there’s a
good balance between carbonation and operational cost.
The development and validation of the model provide a valuable tool for understanding the underlying mechanisms of MSW ash carbonation. By incorporating
key factors that influence the process, the model allows for predictions of carbonation rates under various operating conditions. The ability to predict the influence
of various parameters is a crucial step in the transition of this technology to the real
world. Such a tool can be leveraged to guide future experimental studies, to optimize
reactor designs, and to assess the long-term performance of carbonation processes.

References
1. I Power S Wilson G Dipple 2013 Serpentinite carbonation for CO2 sequestration Elements 9
115 121 https://doi.org/10.2113/gselements.9.2.115
2. Huijgen WJJ, Comans RNJ (2003) Carbon dioxide sequestration by mineral carbonation:
Literature review (ECN-C–03-016). Energy Research Centre of the Netherlands (ECN)
3. R Baciocchi G Costa E Lategano A Polettini R Pomi A Stramazzo 2015 Accelerated carbonation
of different types of APC residues for CO2 storage and waste valorization J Hazard Mater 286
202 210
4. SY Pan EE Chang PC Chiang 2012 CO2 capture by accelerated carbonation of alkaline wastes:
a review on its principles and applications Aerosol Air Quality Res 12 770 791
5. A Sanna M Uibu G Caramanna R Kuusik MM Maroto-Valer 2014 A review of mineral carbonation technologies to sequester CO2 Chem Soc Rev 43 23 8049 8080 https://doi.org/10.1039/
C4CS00035H
6. Vorobyev KA (2024) Studying carbon dioxide emissions during thermal incineration of MSW
in a model installation. In: Innovative processes of enrichment and deep processing of raremetal and mining-chemical raw materials and complex ores of non-ferrous and ferrous metals.
Proceedings of the international conference, pp 542–545
7. KA Vorobyev 2023 Opportunities for carbon dioxide capture by incinerator slags in gaseous
environments Perm University Herald Geol 22 3 275 281
8. Vorobyev KA (2023) Possibilities of using incinerator slags to reduce carbon-containing emissions. In: Man and the environment. Collection of reports of the XI All-Russian Youth Scientific
conference, pp 43–47
9. KA Vorobyev TV Chekushina N Kurbanov ShI Rabadanov 2024 Investigation of the amount
of carbon dioxide during waste incineration: experimental measurements Natural Techn Sci 4
191 76 79
10. IV Shadrunova EV Kolodezhnaya OE Gorlova KA Vorobyev 2025 Development of a concept
for integrated processing of waste from incineration plants Ecol Ind Russia 29 2 4 11

Parameters of a Human-Generated
Aerosol Cloud
S. N. Gavrilin, N. A. Parfentyeva, E. R. Burmistrov, I. D. Bykovskaya,
and N. V. Radionov

Abstract The process of spreading an aerosol cloud formed by a human cough
was studied. Measurements were carried out on an experimental installation with
three video cameras recording the process of spreading an aerosol cloud in three
planes. The movement of the aerosol was visualized by scattering light on the smoke
particles mixed into the aerosol cloud. The absolute values of the cloud’s velocity
were determined using an anemometer. The dependence of the cloud’s propagation
distance on time was determined from video frames. The dependence of the cloud’s
volume on time was calculated from video frames for three planes. The graphs
show the dependence of the cloud’s propagation distance and volume on time for a
two-second interval. The volume of the cloud increases within 0.5 s. after release.
The volume reaches its maximum (0.5 m3 ) within 1.2 s. Oscillations of the aerosol
cloud volume have been detected. The occurrence of oscillations is explained by
the influence of air flow turbulence. The diffusion theory for an aerosol cloud is
considered. The solutions of the diffusion equation for an aerosol spherical and
cylindrical cloud are given. The obtained data can be used to create models of virus
spread in indoor spaces, develop measures to prevent the spread of infections, and
design ventilation systems.
Keywords Aerosol · Cloud · Cough · Experiment · Velocity · Sneeze · Smoke

1 Introduction
The existence of aerosols is a necessary condition for the formation of clouds in
the Earth’s atmosphere and, consequently, for the stable functioning of mass and
heat exchange processes at the atmosphere–ocean interface [1–3]. The evaporation
S. N. Gavrilin (B) · N. A. Parfentyeva · E. R. Burmistrov · I. D. Bykovskaya · N. V. Radionov
Moscow State University of Civil Engineering, Moscow, Russia
e-mail: GavrilinSN@mgsu.ru
E. R. Burmistrov
Physical Department, Moscow State University, Moscow, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_54

681

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S. N. Gavrilin et al.

processes of a liquid have a significant impact on the temperature of its surface layer
and the intensity of radiation from its surface [4, 5]. The formation, distribution, and
lifetime of aerosol systems are governed by the same physical laws. Studying these
laws is important, among other things, for describing the distribution of aerosols
generated by human coughing.
The spread of aerosol clouds generated by human coughing, sneezing, and talking
is a complex physical process that plays a key role in the transmission of airborne
infectious diseases. The relevance of this research area has increased dramatically in
the context of the global pandemic caused by the virus infection, as it has become clear
that the primary mechanism of infection transmission is through virus-containing
droplets and aerosols exhaled by infected individuals [6, 7]. Understanding the
dynamics of aerosols allows for the development of effective measures to prevent
infection and the design of ventilation systems aimed at reducing the risk of virus
spread [8]. Although social distancing was considered a promising way to combat
the pandemic, the minimum distances between individuals remained a subject of
debate and were not clearly established.
Experiments shows that an aerosol cloud can spread over considerable distances,
especially in poorly ventilated rooms, where particles accumulate and the risk of
infection increases. At the same time, the shape and trajectory of the cloud depend
on many factors: the velocity of the cloud, the temperature and humidity of the air,
as well as the geometry of the room and the presence of obstacles. The process of
aerosol cloud propagation is also studied using numerical analysis methods [9, 10].
An important factor is the initial size distribution of the aerosol droplets, which
significantly affects on the movement and parameters of the cloud. Droplets with a
size of less than 10 microns remain in the air for a long time and are carried by air
currents. Large droplets settle in the gravitational field. This makes it necessary to
study not only the dynamics of the cloud itself, but also the interaction of individual
particles with each other, evaporation and condensation of the droplets [11–15].
In [16–18], the process of aerosol cloud propagation was studied using an
experimental setup consisting of two rectangular frames with stretched strings and
lightweight paper flags, which allowed for visualizing the airflow movement and
recording the relative velocity of the aerosol cloud. This method enabled to fix the
cloud front and to receive the spatial distribution of velocities. The data was calibrated
by an anemometer to obtain absolute velocity values. As a result of the experiment,
the initial parameters of the cloud were determined: the maximum air flow velocity
during a “strong” cough is 1.3–3.0 m/s, and the time required to spread the cloud
over a distance of about 1 m is approximately 0.2 s.
In [19, 20], a theory of aerosol cloud diffusion is constructed. The diffusion
equation is used to determine the spatial distribution of particle concentration and
its change over time. It is shown that the spatial distribution of concentration is
determined mainly by the turbulence of the flow. The coefficient of turbulent diffusion is significantly higher than the molecular diffusion. The obtained data can be
used in the creation of digital models of infection transmission and be the basis for
recommendations on ensuring safety in public and work premises.

Parameters of a Human-Generated Aerosol Cloud

683

In [21], there is strong evidence that poor ventilation leads to the accumulation
of aerosol particles in the air. These clouds can contain pathogenic microorganisms,
including viruses. They increase the risk of airborne infections. The authors emphasize that even common activities such as talking, coughing, or sneezing can create
persistent aerosol clouds. These clouds remain in the air for extended periods. They
can travel far from their source. The study also shows that good ventilation and air
filters play a key role. They reduce the level of infection in enclosed spaces. These
measures reduce the risk of infection. They make public and work areas safer. This is
especially important for preventing respiratory infections during a pandemic, when
preventing the spread of infection in indoor spaces becomes critical.
So, studying the physics of aerosol clouds after breathing, coughing, and sneezing
is practically important. It helps to understand how airborne diseases spread. It also
supports better prevention strategies.
The movement of aerosol clouds formed after coughing or sneezing is determined
by complex hydrodynamic processes. These include the interaction between the
aerosol jet and the surrounding environment, as well as the physical and chemical
characteristics of the droplets. In this study, we focus on the initial stages of aerosol
cloud formation and analyze the velocity distribution within the cloud. The trajectory
of the particles depends on the spatial distribution of air flow velocities. Therefore,
studying the velocity distribution in the flow is an important scientific problem that
has not been adequately investigated.
Let’s consider the process of aerosol cloud formation. During coughing, a person
exhales air in the form of a turbulent jet with a velocity exceeding 10 m/s. This jet
carries droplets of various sizes. A detailed analysis of this phenomenon is presented
in [22], where high-speed imaging was used to study the initial stage of aerosol
cloud movement. The obtained data shows that the droplets initially move due to
the momentum imparted to them during exhalation. The resulting jet captures the
surrounding air, following the Bernoulli principle, which leads to their dispersion.
The higher the flow rate, the greater the volume of “clean” air involved to the aerosol
cloud, which reduces the concentration of aerosol particles.
The movement and shape of an aerosol cloud can be studied using several methods.
In [23], the temperature distribution in an exhaled cloud is investigated using a
thermal imager.
The purpose of this study is to investigate the characteristics of the aerosol cloud
propagation process during human coughing using video recording of a colored cloud
in three planes.

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2 Materials and Methods
2.1 Theory
Let’s consider the diffusion process in a cloud with the sphere shape. For t = 0
aerosol particles are evenly spread inside a sphere with radius R. The center of the
sphere is placed at a certain point. We will use that point as the centre of a spherical
coordinate system.
The diffusion equation in spherical coordinates r, φ, θ is:
2
D∇r,ϕ,θ
n=

∂n
∂t

(1)

2
D—diffusion coefficient; ∇r,ϕ
,θ —Laplace operator in spherical coordinates:

2
∇r,ϕ,θ
n=

∂n
1 ∂
r2
2
r ∂r
∂r

∂
1
∂n
sin θ
2
r sin θ ∂θ
∂θ

∂ 2n
1
r 2 sin2 θ ∂ϕ 2

(2)

We assume that the particle distribution does not depend on the angular coordinates
θ and φ (the system has axial symmetry). So, we can write:
∂n
∂n
= 0;
=0
∂θ
∂ϕ

(3)

1 ∂
∂n
∂n
r2
=D 2
∂t
r ∂r
∂r

(4)

Then, Eq. (1) becomes:

For t = 0:
n = n0 H (R − r)

(5)

n0
is the initial particle concentration inside the sphere,
H (R − r) Heaviside function.
The solution to this Cauchy-type problem can be expressed as:
1
n(r, t) = √
2r π Dt

∞

ξ e−
0

(r−ξ )2
4Dt

− e−

(r+ξ )2
4Dt

f (ξ )dξ

Parameters of a Human-Generated Aerosol Cloud

685

Fig. 1 Scheme of the
experimental facility

2.2 Method
To measure the volume and spread range of an aerosol cloud formed during human
coughing, we used an experimental facility (Fig. 1).
The installation included a closed cabin with a dark coating. The cabin isolated
the aerosol cloud from external influences such as air flow or particles. The size of
the cabin allowed for observation of the cloud’s spread.
A grid with 20 cm spacing was marked on the walls of the cubicle. This grid
helped estimate the size of the aerosol cloud in three planes. It was needed for
scaling video images and measuring particle distribution. With 20 cm spacing, we
could measure the cloud’s length, width, and height. This allowed us to analyze its
behavior quantitatively.
A person exhaled an aerosol cloud. The cloud was made visible using smoke
from a smoking device. The cloud formed at a fixed point inside the cubicle and then
spread freely in the enclosed space.
There was a round hole in the cubicle wall where the person exhaled. This hole
reduced any disturbance to the cloud structure. It also kept conditions close to natural
exhalation. The hole helped fix the starting point of the aerosol release. This improved
experiment repeatability and data accuracy.
The person stood at a fixed position inside the cubicle. Three cameras recorded
the direction and movement of the aerosol cloud:
• Camera 1 was placed on the top of the cubicle. It recorded the cloud from above.
• Camera 2 was placed on the side wall, at head level. It recorded the cloud moving
forward.
• Camera 3 was placed on the front wall. It recorded the cloud from the side.
This camera setup allowed tracking of the aerosol cloud in three dimensions.
During exhalation, the cloud formed and contained smoke particles. Light scattered
on these particles made it possible to see and record the cloud’s movement. Video

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recordings were used to measure the cloud’s properties and how they changed over
time.

3 Results
Figure 2 shows the change in the shape of an aerosol cloud at a 0.1 s interval.
During coughing, the aerosol cloud ejected from the respiratory tract had a stable
and repeatable shape. In most cases, it formed a cone with small deviations from
axial symmetry. The angle between the main flow direction and the horizontal plane
did not exceed 20 degrees. Some variation in angular distribution was observed. The
edges of the aerosol cloud reached angles from 35 to 50 degrees. This was likely due
to the turbulent nature of the airflow and the complex motion of droplets of different
masses.
The front-facing camera video was used to obtain the dependence of the aerosol
cloud’s propagation distance on time (Fig. 3).
The cloud front covers a distance of 1 m in 0.4 s. In the distance range of 1 m to
2 m, the velocity of the front is almost constant and is about 0.6 m/s.
Synchronized videos from three cameras were used to obtain the dependence of
the aerosol cloud volume on time (Fig. 4).
The cloud volume grew during 1 s after exhalation start. The volume is growing
up to 0.5 m3 within 1 s. After that, the volume stabilized with small variations around
an average value.
Table 1 shows the calculated values of the cloud velocity and the volume at
different stages of its spread, based on experimental data.

Fig. 2 Shape of the cloud (step 0.1 s.)

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687

Fig. 3 Dependence of the propagation distance on time

Fig. 4 Volume versus time dependence
Table 1 Velocity and volume
of the cloud

Time interval, s

0–0.3

1.0–1.3

1.8–2.0

Cloud velocity, m/s

3.0

0.6

0.3

Cloud volume, m3

0.05

0.40

0.50

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4 Discussion
An analysis of the image sequence (Fig. 2) shows that the direction of the aerosol
cloud’s propagation changes over time. At the initial stage (up to 0.3 s), the cloud is
directed downward at an angle to the horizontal. This is likely due to the geometry
of the oral cavity and the initial impulse of the air jet generated by the diaphragm
and pectoral muscles. This direction of movement was also observed in [17], where
it was noted that the flow front moves downward for the first 0.5 s after coughing.
After 1–1.3 s, there is a change in direction, and the front of the cloud begins to
rise above the level of the mouth. By the end of the observed period (t = 1.8–2.0 s),
the front of the cloud reaches a height corresponding to the level of the top of the
human head. The change in the cloud’s position may be due to turbulence. The shape
of the aerosol cloud also changes during its propagation. Initially, the cloud has an
elliptical shape and clear boundaries. After 0.5–0.7 s, the cloud’s shape becomes less
regular. This is probably due to turbulent mixing of particles and the interaction of
the cloud with the surrounding air. Visualizing the cloud using smoke allows us to
determine the moments when the cloud shape changes.
The distance-time relationship (Fig. 3) is well approximated by a second-degree
polynomial with a linear coefficient value of 2 and a quadratic coefficient value close
to − 0.6.
The feature of the observed process of aerosol cloud propagation is the presence
of oscillations in the cloud volume at the end of the measurement interval (Fig. 4).
These oscillations can be caused by various processes.
It is likely that turbulent structures are formed during injection, which can cause
local redistributions of the cloud’s mass and density.
The presence of oscillations indicates the complex internal dynamics of the cloud,
which may be important for understanding the mechanisms of aerosol propagation
in indoor and outdoor environments. These effects can affect the distribution of
infectious particles in the air and, consequently, the probability of human infection.
Table 1 show that the initial air flow velocity during coughing is 3.0 m/s. In the
middle of the process (t = 1–1.3 s), the velocity drops to 0.6 m/s, and by the end of
the observed period (t = 1.8–2.0 s), it decreases to 0.3 m/s. The decrease in velocity
is likely due to viscous friction caused by the transfer of momentum between the
aerosol cloud and the surrounding air.
This indicates that during coughing, the cloud acquires a significant increase in
momentum due to the forces exerted by the diaphragm and pectoral muscles. The
work of these forces determines the kinetic energy of the aerosol cloud. The obtained
values correspond to the data [24].
The dynamics of a cloud depends not only on the initial injection conditions, but
also on environmental parameters such as temperature, humidity, and air movement.
These parameters can enhance or reduce turbulent effects, to change the evaporation
rate and the lifetime of droplets.
By analyzing the dynamics of an aerosol cloud, we can gain a deeper understanding of the physical mechanisms of aerosol cloud movement and to use this

Parameters of a Human-Generated Aerosol Cloud

689

knowledge in the design of the ventilation systems, and in the development of the
respiratory protection measures.

5 Conclusion
In this work, the processes of the aerosol cloud propagation formed by a human
coughing are studied.
It is recorded that the velocity of the aerosol cloud is 3 m/s at the initial moment,
0.6 m/s after a one second after the movement start and is 0.3 m/s at the end of the
two seconds interval.
The volume of the cloud increases within 0.5 s after the release. After that, the
volume remains almost constant and fluctuates within the average value of 0.5 m3 .
The oscillations are likely caused by flow turbulence and interaction with the
surrounding air. The shape and trajectory of the cloud change over time. Initially,
the cloud is directed downward at an angle to the horizon, and then the front of the
cloud rises.
These results contribute to our understanding of the mechanisms of aerosol cloud
formation during coughing and the associated processes of airborne transmission of
infectious diseases, especially in enclosed spaces with poor ventilation.
Acknowledgements The research was funded by the National Research Moscow State University
of Civil Engineering (grant for fundamental scientific research, project No. 15-661/130).

References
1. Gavrilin SN (2024) Natural water thermal radiation at a 8 mm wavelength. In: BIO web
conference: international conference Yakovlev readings (YRC-2024), vol 107, pp 3004. https://
doi.org/10.1051/bioconf/202410703004
2. Gavrilin SN (2024) Natural water thermal radiation at a gigahertz frequency. In: BIO web
conferences international conference Yakovlev readings (YRC-2024), vol 107, pp 3009. https://
doi.org/10.1051/bioconf/202410703009
3. Gavrilin SN (2023) Temperature gradient of the natural water surface thermal radiation. In:
E3S web of conference: international scientific and practical symposium “the future of the
construction industry: challenges and development prospects” (FCI-2023), vol 457, pp 02006.
https://doi.org/10.1051/e3sconf/202345702006
4. Gavrilin SN (2024) Dependence of water radiation on temperature at microwaves. Phys Scr
100(1):015966. https://doi.org/10.1088/1402-4896/ad9c21
5. Gavrilin SN, Parfentyeva NA (2025) Radiation-temperature dependence of water and aqueous
solution. Light Eng 33(2):111–117. https://l-e-journal.com/en/journals/light-engineering-332-2025/
6. Guo ZD, Wang ZY, Zhang SF et al (2020) Evidence of airborne transmission of SARS-CoV-2.
Emerg Infect Dis 26(7):1586–1591. https://doi.org/10.3201/eid2607.200885

690

S. N. Gavrilin et al.

7. Santarpia JL, Rivera DN, Herrera V et al (2020) Aerosol and surface contamination of SARSCoV-2 Observed in quarantine and isolation care settings. Sci Rep 10:12732. https://doi.org/
10.1038/s41598-020-69286-3
8. Bourouiba L (2020) Turbulent gas clouds and respiratory droplet transmission. JAMA
323(18):1837–1838. https://doi.org/10.1001/jama.2020.4756
9. Mittal R, Ni R, Seo J-H (2020) The flow physics of COVID-19. J Fluid Mech 894:F2. https://
doi.org/10.1017/jfm.2020.330
10. Asadi S, Wexler AS, Cappa CD, Barreda S, Bouvier NM, Ristenpart WD (2019) Aerosol
emission and superemission during human speech increase with voice loudness. Sci Rep 9:2348.
https://doi.org/10.1038/s41598-019-38808-z
11. Xie X, Li Y, Chwang AT, Ho PL, Seto WH (2007) How far droplets can move in indoor environments—revisiting the wells evaporation-falling curve. Indoor Air 17(3):211–225. https://
doi.org/10.1111/j.1600-0668.2007.00469.x
12. Morawska L (2006) Droplet fate in indoor environments, or the effect of ventilation efficiency.
Atmos Environ 40(10):2132–2148. https://doi.org/10.1016/j.atmosenv.2005.11.032
13. Jayaweera M, Perera H, Gunawardana B, Manatunge J (2020) Transmission of COVID-19
virus by droplets and aerosols: a critical review on the unresolved dichotomy. Environ Res
188:109819. https://doi.org/10.1016/j.envres.2020.109819
14. Hajaali A, Stoesser T, Fitzgerald S (2024) Cloud and droplet dynamics during a human coughing
event under fully mixed and unmixed room conditions featured. Phys Fluids 36:023345. https://
doi.org/10.1063/5.0185686
15. Maggiore E, Tommasini M, Ossi PM (2020) Propagation in outdoor environments of aerosol
droplets produced by breath and light cough. Aerosol Sci Technol 55(3):340–351. https://doi.
org/10.1080/02786826.2020.1847247
16. Parfentyeva NA, Parfentyev NA (2021) Installation for determining the direction, velocity and
time of passage of an aerosol cloud formed during coughing and sneezing: work results (as part
of the COVID-19 program). Russ J Biomech 25(9):192–199. https://doi.org/10.15593/RZhBio
meh/2021.2.07
17. Gavrilin SN, Parfentyeva NA, Parfentyev NA et al (2023) Cough aerosol cloud parameters.
E3S Web Conf 457:02003. https://doi.org/10.1051/e3sconf/202345702003
18. Parfentyev NA, Parfentyev NA (2022) Installation and results for determining the velocities
of an aerosol cloud. In: Lecture notes in networks and system, vol 246. Springer, Cham, pp
314–321. https://doi.org/10.1007/978-3-030-81619-3_35
19. Tellier R (2006) Review of aerosol transmission of influenza a virus. Emerg Infect Dis
12(11):1657–1662. https://doi.org/10.3201/eid1211.060426
20. Zhou Y, Xu H, Liang Z (2020) Modeling airborne transmission of SARS-CoV-2 with computational fluid dynamics. Int J Environ Res Public Health 17(18):6828. https://doi.org/10.3390/
ijerph17186828
21. Somsen GA, van Rijn C, Kooij S, Bem RA, Bonn D. Small droplet aerosols in poorly ventilated
spaces and SARS-CoV-2 transmission. Lancet Respir Med 8(7):658–659. https://doi.org/10.
1016/S2213-2600(20)30245-9
22. Bourouiba L, Dehandschoewercker E, Bush JWM (2014) Violent expiratory events: on
coughing and sneezing. JFluidMech 745:537–563. https://doi.org/10.1017/jfm.2014.88
23. Bochkareva EM, Nemtsev VA, Sorokin VV et al (2016) Reduction in the vapor pressure in
condensation on cold droplets of a liquid. J Eng Phys Thermophy 89:553. https://doi.org/10.
1007/s10891-016-1410-z
24. Qin T, Zhang T, Duan Y et al (2023) Research on location selection of personnel door and
anemometer based on FLUENT. Fluids 8(1):26. https://doi.org/10.3390/fluids8010026

Integrated Use of Land and Water
Resources in the Talas Region
E. T. Toktoraliev, R. A. Kerimbekova, E. K. Mukanbet, T. M. Choduraev,
and N. E. Zhumaliev

Abstract Amid increasing climate instability and growing concerns over food security, the development of hydraulic infrastructure (HI) has become a key factor for
the sustainable functioning of agriculture in the Talas region. This article presents
a comprehensive analysis of the role of the existing irrigation system—including
canals, pumping stations, and reservoirs—in ensuring water supply for more than
70% of the region’s agricultural land. Special attention given to the technical condition of irrigation facilities, water losses reaching up to 40–50%, and the consequences of land degradation caused by inefficient water and land use. The article
highlights modernization prospects for the irrigation network through innovative
technologies such as gate automation, canal lining with concrete, and the application
of geomembranes and polybentonite sealants. The authors emphasize the necessity
of an integrated approach, incorporating resource-efficient farming practices (e.g.,
chisel tillage, intercropping) and erosion control measures. Furthermore, the potential for constructing small and cascade hydropower plants considered as a supplement
to the irrigation system and a source of sustainable energy. The study concludes that
the development of hydraulic infrastructure is of strategic importance for increasing
agricultural productivity, landscape resilience, and regional water security.
Keywords Irrigation · Hydraulic infrastructure · Irrigated agriculture · Talas
region · Water losses · Modernization · Agricultural sustainability

E. T. Toktoraliev (B) · T. M. Choduraev · N. E. Zhumaliev
I. Arabaev Kyrgyz State University, Bishkek, Kyrgyz Republic
e-mail: e.toktoraliev@kstu.kg
R. A. Kerimbekova
K. Dikambaev Diplomatic Academy, Ministry of Foreign Affairs of the Kyrgyz Republic,
Bishkek, Kyrgyz Republic
E. K. Mukanbet
Kyrgyz State Technical University Named After I. Razzakov, Bishkek, Kyrgyz Republic
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_55

691

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E. T. Toktoraliev et al.

1 Introduction
Kyrgyzstan considered an agrarian country, with two-thirds of its population residing
in rural areas. Irrigated agriculture plays a key role in the agrarian economy of the
Talas region. More than 70% of agricultural land in the region irrigated, making the
irrigation infrastructure critically important for food security and rural development.
This region possesses substantial agricultural potential, where farming predominantly focused on irrigated land use. The development and maintenance of hydraulic
infrastructure—including canals, dams, reservoirs, and pumping stations—serve as
the foundation for the water supply to farmlands and the sustainability of agricultural
production.
The relevance of the study driven by the decline in the availability of essential
food products for the local population, which highlights the need to stimulate the
development of irrigation systems in agriculture.
The objectives of this study are as follows:
• To analyze the current condition of irrigation systems in the Talas region;
• To assess the role of hydraulic infrastructure in the development of irrigated
agriculture;
• To propose strategies for the rational use of water resources in the study area.
Hydraulic structures (HS) are responsible for regulating, distributing, and delivering water to fields. As of 2024, the Talas region has approximately 113,307 hectares
of irrigated land, representing more than 73.3% of the total arable land in the region
[1].
The central hydraulic facility is the Great Talas Canal (GTC), which stretches
74.4 km and diverts water from the Talas River, supplying up to 12.5 m3 /s and
irrigating over 2500 hectares in the Bakai-Ata district [2]. Such facilities ensure
stable yields of grain, forage, and industrial crops in arid climate conditions.
The development and modernization of HS directly linked to the productivity of
the agricultural sector. The rehabilitation of the GTC’s concrete channel, the construction of automated gates, hydrological posts, and pumping stations improve water
distribution precision and reduce losses. According to the Water Sector Development
Program up to 2035, the following actions planned:
• Reconstruction of 199 km of canals;
• Construction of seven new reservoirs with volumes ranging from 6 to 50 million
m3 ;
• Automation of hydraulic units [3].
These measures will provide additional water supply to 46,200 hectares of
agricultural land, as well as enhance resilience to droughts and spring floods.

Integrated Use of Land and Water Resources in the Talas Region

693

2 Methods and Research Methodology
This study based on a comprehensive approach that combines both theoretical analysis and the processing of empirical data. The methodology grounded in the principles of systems, territorial, and functional analysis, allowing the development of
hydraulic structures (HS) considered in the context of the region’s socio-economic
and natural-climatic conditions.
Within the framework of the research, the following examined:
• the State Program for the Development of the Water Sector of the Kyrgyz Republic
until 2035 [4];
• data from the National Statistical Committee of the Kyrgyz Republic on land use
structure and irrigation levels [5];
• scientific publications covering issues of irrigation, infrastructure, and regional
agro-sustainability;
Reports and articles providing information on the condition of key HS facilities
in the Talas region [6].
The literature analysis contributed to the formation of a scientifically substantiated
understanding of the role of hydraulic infrastructure in the sustainable agricultural
development of the region.

3 Theoretical Background
Despite the presence of an operational irrigation network, the technical condition of
certain hydraulic facilities in the Talas region remains unsatisfactory. One example
is the Kydyr-Aly Canal in the Manas district, which, according to local authorities,
is currently in critical condition. In the absence of major repairs, there is a risk of
losing up to 2000 hectares of irrigated land, which constitutes a significant portion
of the district’s agricultural resources.
The general distribution of water resources presented in Fig. 1.
As shown in Fig. 1, the primary water reservoir in the region is the Kirov Reservoir,
which has a designed capacity of 550–570 million m3 and supports the irrigation of
over 70,000 hectares of agricultural land in both the Talas region of Kyrgyzstan and
the Zhambyl region of Kazakhstan.
In addition to physical deterioration, chronic underfunding hinders the development of the irrigation system. For example, in 2024, only 86.8 million soms utilized
out of the planned 106.4 million, indicating low budget execution efficiency and
possible institutional weaknesses in project coordination and implementation.
A significant challenge also lies in the physical and technological obsolescence
of irrigation and drainage infrastructure, most of which was constructed during the
Soviet era. Water leakage through unlined earthen canals, the absence of automated

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Fig. 1 Distribution of water resources in the Talas region

control systems for water distribution, and weak monitoring of losses contribute to
reduced water delivery efficiency and the irrational use of water resources [7].
The combination of these factors highlights the urgent need for a comprehensive modernization of both linear infrastructure (canals, collectors) and management
structures (Water Users Associations, State Water Committees). Delays in addressing
these issues could lead to the degradation of agricultural land, reduced crop yields,
and weakened sustainability of agricultural production.

4 Discussion
Across the country, losses in irrigation canals amount to 30–50% of the water supplied
[8]. This is also characteristic of irrigation systems in the Talas region, given the
similarly poor technical condition of the infrastructure.
According to estimates from the Ministry of Agriculture and the water management authorities of Kyrgyzstan, up to 40% of water is lost due to deteriorated
networks, improper allocation, and seepage in earthen canals [9]. This confirms
the region’s low water delivery efficiency.
The Ministry of Water Resources reports that annually 1.7–2.3 billion m3 of water
is lost in irrigation systems out of a total usage of 10–12 billion m3 . This is equivalent
to approximately 17–23% of the total national water supply [10]. Applying this
structure to the Talas implies substantial regional-scale water losses (see Table 1).

Integrated Use of Land and Water Resources in the Talas Region

695

Table 1 Causes of reduced efficiency in irrigation canals
Issue

Characteristics

Losses

30–50% of the total water supply, with a likelihood exceeding 40%

Causes

Leakages, water seepage through unlined earthen canals, worn-out
distribution networks

Consequences

Decreased crop yields, economic losses, inefficient water usage

Measures

Linear modernization of canals, installation of concrete linings, automation,
implementation of advanced irrigation technologies

Given that losses reach 30–50% (see Table 1), it means that out of every 100 m3
of water supplied, only 50–70 m3 actually reaches agricultural fields.
In the context of the Talas region—with a high proportion of non-automated
earthen canals and outdated network infrastructure—losses are closer to the upper
bound of 40–50%. This implies that nearly half of the water from the region’s irrigation canals does not reach the fields, significantly reducing irrigation efficiency and
necessitating additional investment for modernization.
The fertility of soils in the Talas region has noticeably declined over recent decades
because of intensive agriculture, the abandonment of scientifically based crop rotation systems, and the disregard for the region’s specific agro-ecological conditions
[11, 12]. Of particular concern is the degradation of arable land in the Talas district,
where soils have undergone significant morphological, chemical, and physical transformations. These changes in soil composition and structure have occurred against a
backdrop of: the absence of proper crop rotation; infrequent or irrational application
of organic fertilizers; and improper mechanical tillage, all of which contribute to
compaction and disruption of the soil’s water regime [11, 12].

5 Research Results
The structural degradation of soils in the Talas region is a significant concern, the
solution of which is impossible without: Incorporation of perennial grasses into crop
rotation; Annual application of organic fertilizers (manure, compost) in volumes of
no less than 10–15 t/ha; Implementation of soil agrochemical diagnostics prior to
mineral fertilizer application; Erosion-control strategies and resource-efficient soil
management technologies [11–13].
Since intensive land use has caused: A 10–20% reduction in crop yields compared
to the early 2000s; Deterioration of water retention capacity, soil aeration, and
biological activity; Increased risk of erosion and secondary salinization [13].
In light chestnut soils, humus content has decreased by 35% (from 2.64% to 1.74%
in the topsoil), mobile phosphorus (PO5 ) content has declined by 18% (from 3.57
to 2.93 mg per 100 g), and potassium (K2 O) content has dropped by 9% (from 80
to 73 mg per 100 g) [14]. In dark chestnut soils (kara kongur), humus content has

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E. T. Toktoraliev et al.

declined by an average of 15% (from 3.92 to 3.33%), while phosphorus and potassium levels have slightly increased, likely due to fertilizer application or lithological
characteristics of the parent material.
In the study area, water and irrigation-induced erosion poses a major threat to the
sustainability of agricultural production, particularly on sloping and irrigated lands.
Excessive tillage, improper irrigation, and lack of crop rotation accelerate topsoil
loss, reduce water infiltration, and degrade soil structure.
To mitigate these processes, systematic erosion control practices are required,
including: Cross-slope harrowing to reduce surface runoff velocity; Establishment
of anti-erosion strips, especially on slopes exceeding 5°; planting of protective
herbaceous and woody vegetation; contour tillage and furrowing.
Simultaneously, it is crucial to implement resource-saving tillage technologies,
such as:
• Minimal and no-till practices (No-Till, Strip-Till), which preserve soil moisture
and structure [15];
• The use of chisel plows that reduce compaction without turning the soil layer
[16];
• Application of organic fertilizers and green manure crops (cover crops), which
restore the humus layer and enhance soil biological activity [17].
For irrigated lands in the Talas region, which are prone to subsoil compaction and
secondary salinization, the introduction of chisel plowing is a relevant and effective
solution. This technique disrupts the plow pan, improves soil water–air balance,
and activates microbial activity, which is particularly important in arid and foothill
environments [18].
Field trials have demonstrated the high efficiency of the PSKU-8 chisel-plow
compared to the traditional PCh-4 model. The main advantages of the PSKU-8
include: Reduction of specific fuel consumption to 14.2 kg/ha (15% lower than PCh4); Decrease in labor input to 0.43 person-hours/ha (a 40.3% reduction); Increase in
productivity to 2.39 ha per work shift;Improved soil structure: 56.5% crumb formation, 68.5% residue incorporation; Reduction in mechanized work costs to 1680
KGS/ha (compared to 2491 KGS/ha with PCh-4), saving 811 KGS/ha or 32.6%
[19]. The effectiveness of this method shown in Fig. 2.
Fig. 2 Method for reducing
secondary soil salinization

Integrated Use of Land and Water Resources in the Talas Region

697

Analytical results demonstrate (see Fig. 2) that the use of chisel plowing with the
PSKU-8 implement increased maize yields by 0.8 centners/ha and simultaneously
reduced weed infestation. Together, these effects contribute to the conservation of
material and labor resources, improving the overall efficiency of agricultural production under conditions of limited water availability and the urgent need for climate
adaptation.
Binary cropping, or the simultaneous cultivation of two or more crops on the same
land area, offers significant advantages for the agroecological conditions of the Talas
region. These include:
• Increased organic matter in the soil, contributing to the formation of humus;
• Atmospheric nitrogen fixation by leguminous crops—up to 200 kg/ha per year;
• Alleviation of compacted soil layers—for example; alfalfa root systems can
penetrate depths of 6–15 m;
• Protection against water and wind erosion due to denser vegetative cover;
• Reduced moisture loss through shading of the soil surface and decreased
evaporation;
• Suppression of weeds and pathogenic microflora, facilitated by crops such as
mustard, vetch, oats, and buckwheat;
• Reduced need for mineral fertilizers and herbicides, which is especially important
given rising input costs and restrictions on agrochemical usage.
• The most effective binary crop combinations for the region include (see Fig. 3):
• Sunflower + sweet clover—improves soil loosening, nitrogen fixation, and
organic matter;
• Wheat + buckwheat—effective weed suppression, phosphorus mobilization, and
moisture conservation;
• Mustard + vetch + buckwheat + millet—comprehensive improvement of soil
structure, nutrient supply, and disease control;
• Alfalfa + maize—synergistic interactions enhancing nutrient cycling and soil
structuring [20].
Despite their proven effectiveness, the widespread adoption of binary cropping
systems hindered by several factors: Difficulties in selecting compatible herbicides

Fig. 3 Binary cropping techniques for irrigated lands

698

E. T. Toktoraliev et al.

Fig. 4 Technology for preparing areas for binary cropping

for mixed crops; Differences in crop maturation periods, complicating harvest schedules; High cost of seeds, especially for certain species (e.g., alfalfa seeds cost up to
1000–1200 KGS/kg); Lack of awareness and educational outreach, combined with
conservatism among farmers.
Nevertheless, the implementation of binary cropping does not require specialized
machinery (see Fig. 4). Existing disc and anchor seeders, widely used in the Talas
region, can be readily adapted to support these agro-technologies without major
investment.
The implementation of these approaches in the Talas region enhances the
resilience of agro-landscapes, preserves soil fertility, improves the water regime,
and reduces land cultivation costs. This is especially relevant under ongoing climate
change and limited water resources.

6 Recommendations
To increase the efficiency of water supply and rationalize water consumption in the
Talas region, the following priorities addressed reconstruction and concrete lining of
canals; automation of distribution systems (gates, hydroposts, dispatching); implementation of drip and sprinkler irrigation to minimize losses; regular monitoring and
repair of networks, including dispatching services.
Considering the climatic conditions and the state of the irrigation infrastructure
in the Talas region, the restoration of concrete canal linings is a key element in
improving water supply efficiency. Currently, two modern approaches are used for
the repair and sealing of concrete linings.
1. Repair using polybentonite composition. This method used for waterproofing
cracks, joints, and cavities in concrete canal linings (see Fig. 5). The procedure
includes draining the canal and cleaning the defective section from dust, water,
silt, and mechanical debris; for large damages—filling the area with gravel and
stone material crushed followed by applying a liquid waterproof polybentonite

Integrated Use of Land and Water Resources in the Talas Region

699

Fig. 5 Scheme of repair and sealing of damages in concrete canal lining [21]: 1—concrete
lining; 2—area of major damage; 3—defective section; 4—gravel and crushed stone bedding;
5—polybentonite waterproof composition; 6—minor damages; 7—injection tubular elements
(injectors)

composition; for small cracks—pressure injection of the composition through
injectors. The composition by weight (%) consists of: liquid polyethylene—60%,
bentonite—30%, anti-friction additives.
The advantages of this method include universality for cracks of any size;
bentonite swelling leads to sealing and restoration of integrity; increased lining
strength and reduced water filtration.
2. Reconstruction using geomembranes applied during major repairs of damaged
irrigation canal sections. The use of rigid geomembranes reinforced with a
concrete base is possible (see Fig. 6).
The restoration technology includes removal of the damaged section and surface
preparation; laying a new concrete layer; installation of the profiled polymer
geomembrane with rigid ribs facing downwards; during concrete curing, the
geomembrane securely fixed, creating a waterproof barrier.
Advantages of this method include: extension of canal service life up to 30–
40 years; reduction of water losses by eliminating filtration at damaged sites; possibility to avoid large-scale concrete works; increasing canal efficiency (coefficient) to
0.85–0.90 and water supply reliability to 70–90%; increase in guaranteed agricultural
yield up to 85%.

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E. T. Toktoraliev et al.

Fig. 6 Scheme of concrete canal lining restoration using geomembrane [21]: 1—concrete canal
lining; 2—damage zone; 3—restorative concrete layer; 4—profiled polymer geomembrane; 5—
reinforcing polymer geogrid

Development of hydraulic structures (HS) will not only improve water supply
but also provide a foundation for transition to highly efficient agriculture resilient to
climate fluctuations.
In the future, construction of new hydroelectric facilities in Talas region implemented, including micro-hydropower plants, reservoirs, and hydropower plants
combined with irrigation systems, derivation hydropower plants, and dams (see
Fig. 7).
1. Small Hydropower Plants (SHPs) with projected capacity from 0.1 to 10 MW are
the most promising type of facilities, considering the mountainous-valley relief of
the region and limited river volumes—Talas, Karakol, Urmaral, Kumygan, Aral,
Kesken-Suu. Advantages of micro hydropower plants include minimal environmental impact, suitability for local power supply, and possibility of cascade
use. For example, an SHP on the Karakol River can supply electricity to the
settlements of Kara-Buura and Bakay-Ata.
2. Hydropower complexes with storage reservoirs for flow regulation, drought mitigation, and electricity generation. This would enable construction of dams on
Talas tributaries with water accumulation during spring–summer and release
during autumn–winter. For instance, expansion and modernization of the Kirov
reservoir with installation of hydro units [22].
3. Hydraulic structures integrated into irrigation systems with energy use involve
installation of small turbines at irrigation canal outlets (e.g., on the Kirov
Canal, Orto-Aryk, Kara-Buura). Proposed turbine types include bucket, axial,
and radial-axial turbines with potential up to 1–2 MW per individual outlet.

Integrated Use of Land and Water Resources in the Talas Region

701

Fig. 7 Potential sites for hydropower construction and expansion of irrigated lands in Talas region

4. Cascade derivation hydropower plants on rivers with elevation drops—sequential
use of height differences via pipelines and pressure chambers. For example, a
cascade of SHPs on the Urmaral River, consisting of 2–3 units of 0.3–0.7 MW
each.
5. Dams with spillways for flood protection and concurrent electricity generation, which is relevant due to the climate risk of spring floods. Construction
of multifunctional dams (flood regulation + turbines) is possible.
According the data Fig. 7 and Table 2, it can be concluded that the scientific
basis obtained will contribute to: Enhancing the region’s energy security (especially
for autonomous villages and farms); reducing dependence on imported electricity;
increasing the efficiency of existing water management systems; reducing losses
in irrigation canals by converting potential energy from spillways into electricity;
increasing crop yields; improving the welfare of the local population.

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E. T. Toktoraliev et al.

Table 2 Potential sites for hydropower plants construction in Talas region
No.

River/Location

Coordinates (lat, long)

Brief justification

Karakol (confluence with
Talas)

42.5115° N, 72.2450° E

Confluence with Talas,
potential for natural head

Urmaral (upper reaches)

42.3955° N, 72.1503° E

Rapids, good slope and
inflow

Talas near Kirov reservoir

42.3710° N, 71.8694° E

Potential for small
hydropower plant near
spillway

Kumush-tag (tributary of
Karakol)

42.4780° N, 72.3005° E

Deep gorge, possible
cascade solution

Besh-tash (national park area)

42.5225° N, 72.4320° E

Mountain river, tourist
zone—hydropower +
ecotourism

Sary-Bulak (left tributary of
Talas)

42.4492° N, 72.0803° E

Stable flow, close to
infrastructure

Acha-Kayyndy

42.3180° N, 71.7652° E

Slope, high spring runoff
density

7 Conclusion
The development of hydraulic engineering structures is of key importance for the
sustainable operation of irrigated agriculture in the Talas region. Priority financing,
technical modernization and active involvement of local water users can transform
the agricultural sector of the region into a highly productive and environmentally
sustainable system. Given the natural conditions of Talas, the greatest potential lies
in small and derivation hydropower plants, as well as energy-water use installations
on canals and spillways. It recommended developing a regional hydropower scheme
that considers ecological restrictions and water requirements for irrigation.

References
1. National Statistical Committee of the Kyrgyz Republic (2024) Share of irrigated arable land
by regions. https://stat.kg. Accessed 3 July 2025
2. Kyrgyzstana S (2023) Irrigation in talas. https://slovo.kg/obshhestvo/irrigacija-po-talasski/.
Accessed 3 July 2025
3. Ministry of Water Resources of the Kyrgyz Republic (2023) State program for the development
of the water sector of the Kyrgyz Republic until 2035. Bishkek
4. Ministry of Water Resources of the Kyrgyz Republic (2023) State program for the development
of the water sector until 2035. Bishkek
5. National Statistical Committee of the Kyrgyz Republic (2024) Open data: share of irrigated
arable land by regions. https://stat.kg. Accessed 3 July 2025

Integrated Use of Land and Water Resources in the Talas Region

703

6. Bishkek V (2023) Talas region may lose 2000 hectares of irrigated land. https://vb.kg/doc/218
096_talasskaia_oblast_mojet_poteriat_2_tys._ga_oroshaemoy_zemli.html. Accessed 26 Feb
2023
7. Alieva M, Sharshenov B (2022) Problems of irrigated agriculture in Kyrgyzstan: regional
aspect. Bull KazNU Geogr Ser 3(79):49–55
8. AKIpress (2023) Losses of irrigation water in canals in Kyrgyzstan make 30–50%. Water
resources service
9. NewsLineKG (2021) Worn out irrigation networks in Kyrgyzstan cause about 40% of water
losses. https://newslinekg.com/article/1007463/. Accessed 3 July 2025
10. CAREC eco (2024) Field evaluation for water-saving technologies: total water consumption
and losses 1.7–2.3 billion m3 per annum. Accessed 22 Jan 22
11. Voronov SI (1987) Humus condition and calculation of humus balance in soils of the Chui
valley, Kyrgyz SSR. Proc Kyrgyz Res Inst Agric 18:105–113
12. Kozhekov DK (1984) Condition, pathways, and problems of soil fertility improvement in
Kyrgyzstan. Collection of scientific works of the Kyrgyz Research Institute of Agriculture
XVI, pp 3–21
13. Mamytov AM, Mamytova GA (1988) Soils of the Issyk-Kul basin and adjacent territories.
Frunze 134
14. Soil and agrochemical materials of the Republican soil-agrochemical station and GPI “Kyrgyzgiprozema” (1992–2025) (2022). News of Kyrgyzstan Universities, vol 3. https://doi.org/
10.26104/IVK.2019.45.557
15. Juraev FU, Ubaydullayeva ShR (2014) Filtration soil in the one-dimensional motion of the
fluid and the potential energy in mole drainage. Eur Sci Rev 7–8:105–109
16. Khamidov MKH, Juraev FU (2017) Improvement of reclamation conditions using chisel
softeners and drainage devices. Irrig Melioration 4(10):40–43
17. Juraev FU (2016) Use of a mole drainage device on saline lands. Agric Sci 5:30–31
18. Juraev FU, Artikova MM, Isaeva LB, Turaev SS (2019) Improvement of reclamation
technologies for solonetz soils. Path Sci 11(69):53–55
19. Petukhov DA, Sviridova SA, Bondarenko EV (2017) Chisel moldboard plow: testing,
advantages, economy. Agrarian Bull South Russ 2:21–28
20. Green manure: loosening, enrichment, structuring of soil. (2024). Agroinnovations. https://zen.
yandex.ru/media/id/ Accessed 5 July 2024
21. Patent documentation (2024) Method of repair and sealing of damages of concrete lining of
irrigation canals. Retrieved 5 July 2025. From F:(Patents)\24 patent 24 Method of repair of
concrete lining of irrigation canals
22. Karamoldoev ZZ (2020) Use of hydro-energy resources of Chui and Talas regions of
Kyrgyzstan. Nauka, Bishkek, p 186

Mixed Wastewater Treatment
in the Recycling Water System
of a Construction Industry Enterprise
O. V. Sidorenko and E. I. Vialkova

Abstract Construction industry is a key branch of industry in Tyumen region. Since
building materials manufacturing enterprises belong to the category of wet industry,
their main task is to adopt water-saving scheme aimed at reducing drinking water
consumption and increasing the percentage of treated wastewater return into the recycling water system. The paper describes an option of a recycling water system for
an enterprise producing aerated concrete and silicate blocks. All industrial wastewater of the target enterprise is gathered in a holding pond and diluted at times with
surface runoff. Most of the wastewater consists of hot condensates formed after autoclave treatment of construction products. They are characterized by increased values
of chemical oxygen demand (COD) and petroleum products because of lubricants
ingress. The discharge of salt solutions after ion exchanger regeneration leads to
a total mineralization increase. On considering the compound industrial wastewater
and laboratory testing, a flow chart for industrial wastewater treatment was designed.
It includes pre-aeration, oxidation, coagulation, sedimentation, filtration. This flow
chart provides water quality suitable for 100% wastewater return to use as additive
in feedstock while manufacturing silicate and aerated concrete products.
Keywords Industrial wastewater · Holding pond · Quality indicators · Laboratory
modeling · Physical and chemical methods · Flow chart

1 Introduction
There are about 60 building enterprises registered in Tyumen region today. Among
them are 19 large enterprises producing building materials [1]. The most capable
are those that manufacture reinforced concrete products, concrete, cement, facade
materials, aerated concrete and silicate blocks, building mixes and thermal insulation
materials. Construction industry products are of the wet category and their expansion
O. V. Sidorenko · E. I. Vialkova (B)
Industrial University of Tyumen, Tyumen, Russia
e-mail: vyalkova-e@yandex.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_56

705

706

O. V. Sidorenko and E. I. Vialkova

should be performed with modern water-saving and water protection measures that
ensure the reduced discharge of industrial wastewater and weaken anthropogenic
impact on water bodies [2–4]. Table 1 gives the norms of water supply and drainage,
as well as specific water losses per production measuring unit for various items [5,
6].
Water at building materials manufacturing enterprises can be used in the following
operations: as the feedstock for making concrete or silicate mixture; washing crushed
stone, gravel and other raw natural materials; cooling equipment; preparation of
chemical solutions and reagents; purification of aspiration air; hydraulic transport of
mineral rocks; daily washing of equipment, sites and workshops; steam generation for
steaming concrete blocks and many others [5]. The requirements for water quality
completely depend on the type of production process and are regulated by state
industry standards [6].
In accordance with the technological processes at building enterprises, several
different in wastewater quality types are formed [4, 5, 7]. For example, water is
polluted by temperature in equipment cooling systems. There is a slight change in
the qualitative composition; it is caused mostly by corrosion [8]. When chemical solutions are used, highly concentrated effluents are formed. The effluents are to be treated
and disposed specifically [9]. The most polluted effluents are condensates formed
after autoclaves. They are characterized by high concentrations of petroleum products and other contaminants coming with the lubricant from metal molds. Techniques
of removing lubricants from water are widely used in the metalworking industry
[10, 11].
One of the largest regional enterprises manufacturing wall blocks produces about
300 thousand m3 of aerated concrete and 110 million bricks per year. The plant
is equipped with a separate industrial water supply system and a number of water
sources: the household drinking water supply in the settlement; a holding pond which
is, among other things, a source of fire-fighting water supply; a well as a source
of groundwater. The requirements for the quantity and quality of water consumed
Table 1 Data on water consumption and drainage
Type of product

Production
measuring unit

Water
consumption rate
per measuring
unit, m3

Drainage rate per
measuring unit,
m3

Water loss per
measuring unit,
m3

Prefabricated
concrete

1 m3

5.8

0.5

0.8

Cement

1 ton

0.2

1.2

Silicate brick

1000 pcs

5.4

1.0

0.6

Aerated concrete
blocks

1 m3

0.9

0.2

0.45

Roofing
insulation

1000 m2

Concrete

1 m3

1.6

0.13

0.22

Mixed Wastewater Treatment in the Recycling Water System …

707

completely depend on the production technology. After additive softening, the water
from the municipal water supply system is used to generate steam. The requirements
for the quality of water used for making mortar are less stringent. The water for
this purpose is supplied from a holding pond with recharge, if necessary, from a
well. Currently, the main problems of the plant’s water supply are the costs for high
consumption of drinking water used for steam generation, and poor quality of the
water used for the materials production.
The quantity of water consumed (in %) at the stages of production processes
(according to the plant data), as well as regulatory documents defining water quality
requirements, are shown in Table 2.
More than 50% of water consumption is accounted for the boiler room, which
further determines the majority of condensates (except evaporation and steam emissions), with high chemical oxygen demand (COD) and petroleum products content
in the total industrial wastewater quantity. Coolant containing wastewater is one of
the main sources of environmental pollution in the oil refining industry, mechanical
engineering and construction industry [15, 16]. Such water is treated in various ways
and separate phases aimed at obtaining technically pure recycled or wastewater, as
well as neutralization and utilization of the organic fraction [11]. The most effective and common methods of coolant-containing wastewater treatment are physicochemical: coagulation, flocculation [10, 11, 17, 18], flotation [11], chemical destruction [19], electrocoagulation [20] and various combinations of traditional methods
with physical effects on water: electromagnetic treatment, ultraviolet irradiation and
microwaves [21–24]. At the advanced wastewater treatment phase, the following
methods are used: sorption, ion exchange and membrane techniques [9, 17], electrodialysis [25], combined electrodialysis-reverse osmosis systems and other methods
[26–29]. The efficiency of the advanced wastewater treatment plants depends on
the quality of the pretreated water. The choice of the advanced treatment method is
determined by a feasibility study of the enterprise. Besides, it should be provided
with recycling water supply and afford using graywater.
Table 2 Percentage distribution of water by separate technological processes
Consumer

Water consumption, %

Production process

Regulatory document

Aerated concrete
products workshop

Preparation of
concrete mass

GOST 23732 2011
[12]

Aerated concrete
products workshop

0.1

Preparation of
reagents

SanPiN 1.2.3685-21
[13]

Silicate products
workshop

3.5

Preparation of
silicate mass

GOST 23732 2011
[12]

Boiler room

Steam generation

RD 24.032.01-91 [14]

Boiler room

Filter flushing

RD 24.032.01-91 [14]

Welfare spaces

1.4

For household and
drinking needs

SanPiN 1.2.3685-21
[13]

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O. V. Sidorenko and E. I. Vialkova

Data analysis on the subject made it possible to select the phases for laboratory modeling of holding pond treatment at a particular enterprise. The purpose
was to increase the capacity of recycling water supply and reduce drinking water
consumption for production needs.

2 Methodology
The object of research is water from a holding pond, which receives condensates
from the production of aerated concrete and silicate blocks, spent salt solutions from
an ion exchange water treatment plant for a boiler room, as well as all types of
surface run-off—rainwater, thawed, irrigation and ground water. This water body
was assessed as a potential source of water for the recycling water supply system.
This water body was assessed as a potential source of water for the recycling water
supply system. The general methodological scheme for studying the water of the
storage pond, which included qualitative chemical analysis (QCA) and all treatment
stages, is presented in Fig. 1.
At the survey stage, the initial water quality was determined, treatment methods
and techniques were chosen, and the most effective reagents (coagulants and flocculants) were selected [18]. Seasonal studies of the holding pond water quality were
done in the IUT laboratory of the natural and wastewater quality. The validity of the
results was achieved through concurrent determination of some indicators in other
city laboratories. The results of the studies are shown in Table 3.
Table 3 shows that the feed water is not suitable for steam generators and cannot
be used to prepare concrete mass without deteriorating the final product. Table 4
demonstrates methods, instruments, techniques and absolute error ( ) for measuring
water quality benchmarks, which were determined for all samples after each stage
of treatment.
The trial coagulation was standard with the use of coagulants—aluminum sulfate
(CA), aluminum oxychloride and aluminum polyoxychloride (Aqua-Aurat 30 trademark). Polyacrylamide (PAA) and Praestol were considered as flocculants in the
research. The doses of reagents and combinations of coagulant-flocculant were
changed. Water and reagents were mixed and constantly stirred with a glass rod
for 1–2 min. Flake formation was monitored for 10 min. According to the rate of
formation and precipitation of flakes, the dose of reagents was increased or decreased.
To simulate the filtration stage, separation funnels with a diameter of 50 mm were
used as filters. The height of the loading layer was 0.18 m, the filtration rate on the
model filters corresponded to the rate of production filters (5–7 m/h for mechanical
and 7–10 m/h for sorption filters). The filtering medium in mechanical filters is quartz
sand from the Mount Khrustalnaya deposit, with a fraction diameter of 0.8–2 mm.
Sorption filters are filled with granular activated carbon AG–3, the granule size is
2–6 mm, the granule diameter is 1.4–1.5 mm.

Mixed Wastewater Treatment in the Recycling Water System …

709

Fig. 1 The overall methodological chart for the study of a holding pond water

3 Results and Discussion
The published data [10, 11, 19–22] justified the choice of stages for laboratory
modeling: coagulation, sedimentation, mechanical and sorption filtration. According
to the results of the trial coagulation, the most effective for water treatment was the
coagulant CA (dose 51–65 mg/L) in combination with the flocculant PAA (dose

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O. V. Sidorenko and E. I. Vialkova

Table 3 Qualitative indicators of the feed water (mixed wastewater in the holding pond)
Quality indicators

Value

Compliance with GOST Compliance with RD
[12]
[14]

рН

9.75–10.01

Complies with
requirements

Does not comply with
requirements

Petroleum products, mg/L

0.48–15.6

Does not comply with
requirements

Suspended solids, mg/L

79–124

Complies with
requirements

Does not comply with
requirements

Odor

2–3 points

Does not comply with
requirements

Oxidizability, mgO/L

28.0–43.2

Does not comply with
requirements

COD, mgO/L

145–212

No requirements

Dry residue, mg/L

2433–3172

Complies with
requirements

Does not comply with
requirements

Total hardness, о H

1.55–2.97

No requirements

Does not comply with
requirements

Total Ferrum, mg/L

0.91–1.86

No requirements

Does not comply with
requirements

Table 4 Methods, instruments, techniques and measuring errors
Quality benchmarks

Instruments

Methods (Russia)

Turbidity, mg/L

Spectrophotometer “PE
5400 VI”

ER F 14.1:2:4.213–05

± 0.5

Color, degree

Spectrophotometer “PE
5400 VI”

GOST 318686–2012

±1

Petroleum products, mg/L

Analyzer
“Fluorate-0.2 M”

ER F 14.1:2:4.128–98

± 0.3

Oxidizability, mgO/L

–

ER F 14.1:2:4.154–99

± 0.5

COD, mgO/L

Analyzer
“Fluorate-0.2 M”

ER F 14.1:2:4.190–2003

± 80

рН

рН-meter “рН 150МИ”

ER F 14.1;2;3;4.121–97

± 0.02

2 mg/L). Increased pH values of the feed water contribute to the coagulation process
without using alkalizing reagents. The graph of changes in initial turbidity values at
doses of aluminum sulfate (CA = 65 mg/L and CA = 51 mg/L) for five different
water samples taken from a holding pond at a constant dose of flocculant, is presented
in Fig. 2.
The preliminary stage of holding pond treatment is aimed at removing the bulk
of pollutants by means of pre-aeration, coagulation and sedimentation. Pre-aeration
works as an intensifier of coagulation and flocculation processes, and, as a rule,
increases the settling efficiency by 5–8% [18]. Given that the holding pond contains

Mixed Wastewater Treatment in the Recycling Water System …

711

Fig. 2 Turbidity in water samples after addition of aluminum sulfate CA and flocculant PAA =
2 mg/L.

lubricant, pre-aeration will help reduce the concentration of petroleum products. The
stages and time of technological processes are given in Table 5.
Three main water treatment processes were selected for modeling: (a) chemical
coagulation and sedimentation; (b) pre-aeration and sedimentation without reagents
added; (c) pre-aeration, chemical coagulation and sedimentation. The holding pond
water was examined, reagents—CA and PAA, compressed air was supplied by a laboratory compressor through a porous nozzle. Fine-bubbled aeration provided intense
saturation of water with oxygen. The change in water quality indicators after the
experiment is presented in Table 6, with the best results given in bold. Benchmarks
were those which did not meet the requirements of GOST [12] for water used in
the production of concrete mixtures (permanganate oxidizability and concentration
of petroleum products) and some additional ones (pH, turbidity, chromaticity and
COD).
Table 5 Stages of industrial wastewater processing
Code of
process

Process

Pre-aeration Addition
of
coagulant

Addition of Sedimentation Mechanical Sorption
flocculant
filtration
filtration

Technology

Saturation
of water
with
compressed
air

Addition
of reagent
and rapid
damp
mixing

Slow
mixing
stirring
while
keeping the
flocs
suspended

Sedimentation
of reaction
products in a
gravitational
field

Mechanical
filtration
through
quartz sand

Sorption
filtration
through
granular
activated
carbon

1–2 min

20–30 min

1–2 h

5–7 m/h

7–10 m/h

Time length 20 min
or process
speed

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O. V. Sidorenko and E. I. Vialkova

Table 6 Results of research of pretreatment stages
Quality indicators

Inlet water

Outlet water after pretreatment (code of
process in Table 5)
C+F+S

PA + S

Efficient, %

PA + C + F + S

Turbidity, mg/L

66.8

3.65

69.9

2.03

96.9

Color, degree

264

280

80.7

Petroleum products,
mg/L

4.2

1.6

3.9

1.08

74.3

Oxidizability, mgO/L 43.2

31.3

41.1

21.2

50.9

COD, mgO/L

196

104.2

187

80.6

58.8

рН

7.34

9.20

7.01

–

The best results are highlighted in bold

The amount of a dense visible sediment obtained by sedimentation ranges from
5.2 to 7.8% of the total volume of water. The water quality indicators improved
significantly after the pretreatment phase, but still did not meet the requirements for
manufacturing products in terms of petroleum products and organic matter content.
Further on, the stages of fining or advanced water treatment were simulated.
Fining or advanced treatment of the pretreated water in the holding pond aimed
at extracting the chemical reaction products (coagulation, flocculation) and residual
contaminants. To obtain more accurate results on natural water samples, the modeling
process included a full treatment cycle based on the results of preliminary studies:
pre-aeration (PA), addition of coagulant and flocculant followed by flocculation (C
+ F), sedimentation (S), mechanical filtration through quartz sand (MF) and sorption
filtration through granular activated carbon (SF). The quality indicators of the feed
water and at advanced water treatment stages are given in Table 7.
Table 7 The quality indicators of the feed water and after advanced water treatment
Quality
indicators

Inlet water

Outlet water after treatment (code of process in
Table 5)
PA + C + F +
S

PA + C + F +
S + MF

Efficient, %

PA + C + F +
S + MF + SF

Turbidity, mg/L 79.7

3.19

0.99

0.52

99.3

Color, degree

341

93.5

Petroleum
products, mg/L

5.1

1.3

1.21

1.15

77.5

Oxidizability,
mgO/L

18.4

7.52

3.52

91.2

COD, mgO/L

312

87.8

рН

6.7

6.88

10.9

–

The best results are highlighted in bold

Mixed Wastewater Treatment in the Recycling Water System …

713

Fig. 3 Flow chart of holding pond water treatment plant holding pond: рН—hydrogen indicator; T—turbidity (mg/L); C—color (degrees); COD—chemical oxygen demand (mgO/L);
O—permanganate oxidizability (mgO/L), PP—petroleum products (mg/L)

Preliminary 20-min aeration of the studied water sample increases water treatment
efficiency: by 2.5–5.0% in turbidity and color, respectively; up to 12% in petroleum
products and COD and by 23.4% in permanganate oxidizability. All that reduces
the load on polish filters and increases the filter cycle. These results were obtained
after 30-min gravitational sedimentation with doses of coagulant CA—51 mg/L
and flocculant PAA—2 mg/L. The water quality after advanced water treatment
(mechanical and sorption filtration) meets the requirements of GOST [12] as for the
main indicators presented in Table 3. The abrupt increase of pH at the last stage of
treatment is justified by the specifics of granular coals, but this indicator will decrease
during operation. If necessary, the pH stabilization stage of the effluents can be added
at the outlet. A flow chart of a holding pond water treatment plant (Fig. 3) has been
designed after laboratory tests. It enables industrial wastewater to be returned into
operation without deterioration in the quality of products.

4 Conclusions
The results of laboratory modeling have proved the effectiveness of the proposed flow
chart for the holding pond water treatment, which includes the following stages: preaeration, coagulation, sedimentation, mechanical and sorption filtration. In the course
of the research, reagents and doses were chosen, the optimal parameters of water
treatment were specified. The wastewater consisted of a mixture of condensates,
industrial effluents and surface run-off. In contrast to the traditional flowsheet, a
preliminary 20-min aeration of wastewater is proposed. It makes treatment much
more effective in terms of the main indicators. The flow chart shown in Fig. 3 makes
it possible to get water that meets the requirements for a raw material to be used in
manufacturing silicate and aerated concrete products.
Additional desalination with ion exchange or membrane technology is required in
order to make pretreated water suitable for steam generation. The prospect of waste
water free production is being considered. In this case, corrosive effluents will not

714

O. V. Sidorenko and E. I. Vialkova

be discharged into the holding pond. It is also obligatory to examine the quantity and
quality of the secondary waste generated—flush water and sediments.

References
1. Admtyumen.ru (2024) Official portal of government bodies of the Tyumen region. https://adm
tyumen.ru/ogv_ru/finance/town_planning/Enterprises/more.htm?id=11132860@cmsArticle.
Accessed 12 July 2025
2. Demin AP (2021) Opportunities for using natural fresh water in Russia for the export potential
development. Natl Interes Priorities Secur 4:608–623. https://doi.org/10.24891/ni.17.4.608
3. Mavletov MN, Berezin NB, Yarullin AZ et al (2017) Use of a circulating station for cleaning
wash water in galvanic production. Bull Kazan Technol Univ 20(2):51–53
4. Orlov VA, Volkova LA, Litvinenko LL (2012) Environmental aspects of using surface runoff
to feed the circulating water supply systems of an industrial enterprise. Ecosyst Organ Prot
6:251–256
5. Lihachev NI, Larin II, Haskin SA et al (1981) Ochistka stochnyh vod v processah obrabotki
metallov (sewage of populated areas and industrial enterprises), 2rd edn. Stroyizdat, Moscow
6. VNII, VODGNO Gosstroya SSSR (1978) Ukrupnennye normy vodopotrebleniya i vodootvedeniya dlya razlichnyh otraslej promyshlennosti (aggregated standards for water consumption
and water disposal for various industries). Stroyizdat, Moscow
7. Pugin KG, Yushkov BS (2012) Resource-saving technologies and reduction of environmental
impact in the production of concrete products using blast furnace slag. Concrete Technol
1(2):52–55
8. Poperechnyj MI, Novikov MB, Efimov SV (2017) Features of maintaining water-chemical
regimes of closed cooling circuits. Water Purif Water Treat Water Supply 2:44–49
9. Kopylova AS, Lavygin VM, Ochkov VF (2003) Vodopodgotovka v energetike: uchebnoe
posobie dlya vuzov (water treatment in power engineering: a teaching aid for universities).
MEI, Moscow
10. Lobacheva GK, Platonov MY, Smirnov AA (2011) Treatment of industrial wastewater
containing coolants with flocculants—a source of oils and a way to solve environmental
problems. Volgograd State University, Al’manah, pp 53–60
11. Smirnov DN, Genkin VE (1989) Ochistka stochnyh vod v processah obrabotki metallov
(wastewater treatment in metalworking processes). Metallurgy, Moscow
12. GOST 23732–2011 (2012) Voda dlya betonov i Stroitel’nyh rastvorov. Tekhnicheskie usloviya
(water for concrete and mortars. Technical conditions). Standardinform, Moscow
13. SanPiN 1.2.3685–21 (2021) Gigienicheskie normativy i trebovaniya k obespecheniyu bezopasnosti i (ili) bezvrednosti dlya cheloveka faktorov sredy obitaniya (hygienic standards and
requirements for ensuring safety and (or) harmlessness of environmental factors for humans).
https://docs.cntd.ru/document/573500115?section=text&marker=6560IO. Accessed 12 July
2025
14. RD 24.032.01-91 (1993) Metodicheskie ukazaniya. Normy kachestva pitatel’noj vody i para,
organizaciya vodno-himicheskogo rezhima i himicheskogo kontrolya parovyh stacionarnyh
kotlov-utilizatorov i energotekhnologicheskih kotlov (methodological instructions. Quality
standards for feed water and steam, organization of water-chemical condition and chemical
control of stationary steam waste-recovery boilers and power technology boilers). NPO CKTI,
Sankt-Peterburg
15. Tarasova EV (2010) Treatment of wastewater from machine-building plants. Izvestiya MGTU
1(9):170–174
16. Hajiyeva SR, Shamilov NT, Bayramov GI (2021) Ecological effective treatment of industrial
wastewater formed in the oil-producing industry by coagulation method. Azerbaijan Chem J
3:63–66. https://doi.org/10.32737/0005-2531-2021-3-63-66

Mixed Wastewater Treatment in the Recycling Water System …

715

17. ITS 8-2015 (2015) Ochistka stochnyh vod pri proizvodstve produkcii (tovarov), vypolnenii
rabot i okazanii uslug na krupnyh predpriyatiyah (wastewater treatment in the production of
products (goods), execution of works and provision of services at large enterprises). Byuro
NDT, Moscow
18. Linevich SN, Getmancev SV (2007) Koagulyacionnyj metod vodoobrabotki: teoreticheskie
osnovy i prakticheskoe ispol’zovanie (coagulation method of water treatment. Theoretical
foundations and practical use). Science, Moscow
19. Kofman VY (2023) New advanced oxidative technologies for water and wastewater treatment
(part 1) (foreign publication review). Water supply and sanitation, water pollution. Foreign
research: collection of articles. Publishing House VST, Moscow, pp 221–238
20. Mosin OV (2014) Technological calculation of water electrocoagulation installations. Plumb
Heat Air Cond 4(148):28–34
21. Akbari S, Nour A, Fayaz F et al (2016) Analysis of microwave heating process for
Demulsification of water-in-crude oil emulsions. Aust J Basic Appl Sci 10:1–10
22. Kuo C, Lee C (2010) Treatment of oil/water emulsions using seawater-assisted microwave
irradiation. Sep Purif Technol 74:288–293. https://doi.org/10.3923/biotech.2006.308.314
23. Saifuddin NM, Chua KH (2006) Treatment of oily waste water emulsions from metallurgical
industries using microwave irradiation. Biotechnology 5:308–314. https://doi.org/10.3923/bio
tech.2006.308.314
24. Vialkova E, Obukhova M, Belova L (2021) Microwave irradiation in technologies of wastewater
and wastewater sludge treatment: a review. Water 13:1784. https://doi.org/10.3390/w13131784
25. Sirivedhin T, McCue J, Dallbauman L (2004) Reclaiming produced water for beneficial use: salt
removal by electrodialysis. J Membr Sci 243:335–343. https://doi.org/10.1081/SS-200041910
26. Al-Amshawee S, Yunus M, Azoddein A (2020) Electrodialysis desalination for water and
wastewater: a review. Chem Eng J 380:122231. https://doi.org/10.1016/j.cej.2019.122231
27. Fu C, Li F, Li H (2024) Performance study on brackish water desalination efficiency based on a
novel coupled electrodialysis–reverse osmosis (EDRO) system. Water 16:794. https://doi.org/
10.3390/w16060794
28. Feria-Díaz JJ, Correa-Mahecha F, López-Méndez MC (2021) Recent desalination technologies
by hybridization and integration with reverse osmosis. Water 13:1369. https://doi.org/10.3390/
w13223199
29. Feo-García J, Pulido-Alonso A, Florido-Betancor A (2024) Cost studies of reverse osmosis
desalination plants in the range of 23,000–33,000 m3 /day. Water 16:910. https://doi.org/10.
3390/w16060910

New Approaches to Recycling Refractory
Scrap
I. V. Shadrunova, O. E. Gorlova, E. V. Kolodezhnaya, M. S. Garkavi,
and T. V. Chekushina

Abstract Used refractory materials can be classified as slightly modified industrial
waste, high-quality man-made raw materials that are very promising for recycling
and recycling. Refractory scrap is not a toxic substance and is not accumulated in
large volumes. However, its recycling is of great economic interest, since energy
consumption in the primary production of refractory products (drying, firing) is a
significant part of the cost of the final product. The processing of refractory scrap in
order to obtain enriched powders to replace natural raw materials in the production of
refractories and obtain functional materials will reduce the need for scarce refractory
raw materials by more than 25% and increase the country’s resource security. The
development of refractory recycling technologies should begin with the study of
crushing and mechanical enrichment processes. The establishment of patterns of
destruction of refractory scrap in the crushing and grinding processes will make it
possible to implement technologies of selective disintegration and dry enrichment
based on them. According to the authors, dry processing of refractory scrap is the
most promising, since it allows to increase the technospheric safety of its processing
processes and reduce the cost of the entire technological chain. The paper presents the
results of processing corundum-carbide scrap of silicon carbon refractories (LCCC)
according to a technological scheme that includes crushing and selective crushing in
devices that implement the principle of free impact. A decrease in the mass fraction
of iron in the finished product was achieved from 2.7 to 1.34%. The yield of the
finished product was 51.0–76.4% with a mass fraction of Al2 O3 of 59.0–63.7%.

I. V. Shadrunova · E. V. Kolodezhnaya (B) · T. V. Chekushina
Research Institute of Comprehensive Exploitation of Mineral Resources of the Russian Academy
of Sciences, Moscow, Russia
e-mail: kev@uralomega.ru
O. E. Gorlova
Nosov Magnitogorsk State Technical University, Magnitogorsk, Russia
M. S. Garkavi
Company “Ural-Omega”, Magnitogorsk, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_57

717

718

I. V. Shadrunova et al.

Keywords Man-made raw materials · Recycling · Refractory scrap · Corundum
carbide · Silicon carbon refractories · Technosphere safety · Selective crushing ·
Air classification · Mechanical enrichment

1 Introduction
The production of refractory materials is a codependent industry with such strategically important sectors of the economy as metallurgy, mechanical engineering, chemical, construction and others, and therefore requires special attention and control.
Ferrous metallurgy consumes 60.6% of the world’s refractory production, 14.1% in
the production of cement and lime, 4.8% in ferroalloys, 3.3% in non–ferrous metallurgy, and 1% in chemical and other industries. Today, ferrous metallurgy enterprises,
the largest consumers of refractory materials, have developed the practice of abandoning their own refractory production. This is largely due to the peculiarities of
the raw material market and the logistics of its supply. For the same reason, most
enterprises producing refractory products have vertical integration—that is, they not
only produce refractory materials, but also own facilities for the extraction of raw
materials. It can also be noted that there are a significant number of manufacturers of
refractories, but most of their products are manufactured for the needs of a particular
enterprise, which creates a rigid structure of this industry.
In 2024, the five leading refractory companies in Russia produced 867,000 tons
of products, including 386,700 tons of products and 433,500 tons of unformatted
materials [1]. The leading federal district of the Russian Federation in the production
of refractories is the Ural Federal District (53.3% of production from 2017 to 2024),
followed by the Central Federal District (22.8% of production). For example, MMK’s
refractory production produced 177,300 tons of refractories in 2024 [2]. The share of
foreign refractory supplies in Russia accounts for about 10% of the market. Among
foreign competitors, supplies are provided by RHI Group, Vesuvius and Mayerton,
with most of the supplies coming from China [3]. The market shares of manufacturers
and consumers of refractory materials in Russia are shown in Fig. 1.
Spent refractories and refractory scrap, unlike metallurgical slags and slurries, can
be classified as slightly modified industrial waste, high-quality man-made raw materials, very promising for recycling and processing. The accumulation of refractory
scrap is relatively small. This type of raw material is not toxic, and technospheric
safety in the production of fire-resistant materials is limited to measures to control
dust in production [4]. However, its rehabilitation is of great economic interest, since
the primary energy in the production of refractory products (drying, firing) is a significant cost of the final product. The processing of refractory scrap in order to extract
pure oxides, metals and create structural and functional materials from enriched
powders will allow for more than 25% reduction in consumption of primary natural
resources, as well as solve the country’s raw material security issues.
In publicly available sources, the amount of refractory scrap is usually given by
individual enterprises, without taking into account the recycling and regeneration of

New Approaches to Recycling Refractory Scrap

719

Fig. 1 a Production of refractories in 2024, thousand tons; b consumption of refractories by industry

some materials. The volume of refractory scrap produced in the Russian metallurgical
industry is estimated by the specific consumption of refractories per unit of output.
In the long term, the total consumption of refractories for steel production will be
5–10 kg/ton of steel. According to the information and analytical company Chermet
Corporation, in 2024, Russian ferrous metallurgy enterprises produced 70.7 million
tons of steel, which corresponds to 353–707 thousand tons of spent refractories.

2 Setting the Research Task
In recent years, there have been significant changes in the structures of activities
of enterprises producing refractory materials and their consumers. Recycling of
used products is becoming the key to the competitiveness of the modern refractory industry. Metallurgical enterprises are beginning to strengthen their activities in
the direction of organizing sites for processing refractory scrap within the enterprise
and new opportunities are emerging for the use of innovative technologies in the
field of processing spent refractories. In these conditions, the task of technological
and economic optimization of the processes of recycling and enrichment of manmade raw materials to improve the environment and significantly reduce the cost of
marketable products is becoming a particularly relevant scientific and applied task.
Used refractory materials can be considered as secondary slightly modified raw
materials of man-made origin. Refractory scrap after operation in metallurgical units
has a higher content of impurities and porosity, contains destroyed remnants of the
structure of refractory, metal, glass, etc. Recycling of refractory scrap may include
sorting the scrap into grades, crushing and sieving the material, mixing the product,
as well as additional technological operations to extract impurities. The purpose of
such processing is to obtain a product for reuse and partial replacement of natural
raw materials.

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I. V. Shadrunova et al.

The process of recycling man-made raw materials and refractory scrap begins with
the processes of disintegration. The study of the patterns of crushing and mechanical enrichment of these high-quality man-made raw materials is a priority task of
researchers. The main task of the disintegration of natural and man-made mineral
raw materials in preparation for separation processes is to destroy the object along
the surfaces of the accretion phases without over-grinding while minimizing energy
consumption. Evaluation of the possibility of selective softening of the mineral
components of a refractory material: the silicate part, metal crowns and impurities formed, including during the operation of the material in a high-temperature
unit, is a determining factor when setting up crushing equipment. The contrast of
the granulometric, physico-mechanical and chemical characteristics of the mineral
components of crushed refractory scrap is a parameter for enriching this material.
The development of technologies for the enrichment and mechanical rehabilitation
of man-made waste without this information is conducted by touch and has low
efficiency.
Currently, the issue has not been sufficiently investigated, and in some cases,
there is a lack of information about the textural and structural characteristics, physical and mechanical (microhardness) and features of the material composition of
spent refractory scrap. The known variants of the chemical and mineral classification of refractory and ceramic raw materials identify 15 potential groups of secondary
resource materials [5], however, it does not allow us to identify characteristics whose
contrast would allow us to violate their enrichment and processing.
The initial refractory materials and products are characterized by a very homogeneous, strictly controlled structure that ensures the necessary heat resistance and
strength of the material, as well as a reduction in heat loss. During operation, refractory materials come into contact with molten metal and slag, are exposed to a gaseous
environment, are exposed to high temperatures, and experience alternating thermal
loads. Moreover, all these impacts are distributed unevenly over the volume of
the refractory layer. As a result, the structure of the refractory material loses its
uniformity, strongly and slightly modified areas are formed. These areas, in turn, are
represented by mineral grains that have retained their original characteristics, and
mineral grains in which various levels of defects have formed and physico-chemical
transformations have occurred (Fig. 2).

Fig. 2 a Appearance of the refractory brick scrap b Structure of the refractory brick scrap

New Approaches to Recycling Refractory Scrap

721

Mechanical enrichment is an effective way of cleaning refractory scrap, extracting
high-quality materials during the processing of mining dumps, and man-made materials in order to obtain a product of the required quality to replace some of the alumina,
bauxite, and clay of refractory grades. However, the finished product must not only
have the required quality to be used as a substitute for raw materials, but also meet
the requirements of technological processes and operation.
In our opinion, the use of dry processing technology for refractory scrap is fully
consistent with the objectives of the process, economically feasible, and will ensure
the required technospheric safety of recycling technologies. A feature of the proposed
technological solutions is the use of destruction by free impact of a piece on a fixed
surface, implemented in centrifugal impact technology. This ensures the selective
destruction of composite technogenic materials, the mineral phases of which have
contrasting strength properties. It is this method of disintegration that provides the
most complete disclosure of complex mineral complexes along grain boundaries and,
as can be assumed, higher rates of subsequent enrichment. The aerial classification of
the crushed material makes it possible to obtain products that differ in granulometric
and chemical composition.
We assume that as a result of selective disintegration and aerial classification of
scrap, refractory raw materials are regenerated, reducing the mass fraction of harmful
impurities, slag, metal, glass, etc. The subsequent separation operation minimizes
their content in the finished product.
Currently, about 10% of the generated MSW is recycled in incinerators worldwide.
In many European countries, such as Sweden, France, the Netherlands and Denmark,
this figure exceeds 50%. Waste from incinerators in the form of slags, sludge and
spent refractory products are new environmental challenges [6]. The interest of the
Russian public in the work of waste incineration plants is steadily growing due to the
increase in the number of facilities being put into operation. By 2025 it is planned
that the productivity of MSW thermal processing enterprises in the Moscow region
will reach 2.8 million tons of garbage per year [7]. This will require the maintenance
and operation of thermal units and the issue of rehabilitation of used refractory
products. Today, in European countries, for example, in Germany, Switzerland and
Spain, corundum and silicon carbide refractories with increased corrosion resistance
to alkalis are used in incineration furnaces, which significantly increases the service
life of the lining. The need for recycling refractories in this area is also due to the
close attention of the public to technospheric safety at such facilities.

3 The Object of the Study
A sample of corundum-carbide silicon refractories brick scrap (SCCS) was used as
objects of research (Table 1).
The spent brick is crushed in an impact crusher, dried to a moisture content of no
more than 0.5% and crushed in a centrifugal impact crusher operating in a cycle with
a screen. As a result of primary mechanical processing, fractionated aggregates of

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I. V. Shadrunova et al.

Table 1 Characteristics of corundum carbide silicon carbon refractory scrap
Parameter

Units of measurement

Value

Fraction

30–310

Ultimate compressive strength

N/mm2

Up to 100

Moisture content, max

Table 2 Granulometric composition of the starting material
Residues on sieves

Residues on sieves with a cell, mm, %
1.0

0.5

0.25

0.1

0.063

− 0.063

Private

1.0

30.9

21.2

21.3

3.4

22.1

Complete

1.0

31.9

53.2

74.5

77.9

100.0

6–10 mm, 3–6 mm and 1–3 mm are formed. The material of the 0.1 mm fraction has
a low content of aluminum oxide (Al2 O3 ) and an increased content of iron oxides
(Fe2 O3 ), which does not allow it to be used as a refractory powder. The granulometric
composition of the 0.1 mm fraction material is shown in Table 2.

4 Research Methodology
To enrich the 0.1 mm fraction of the material obtained during the processing of
SCCS, a two-stage processing scheme was proposed, including crushing and selective grinding, with the release of concentrate and a poorer product. The following
materials were used in the work: centrifugal impact crusher CC-0.36 with a metal
chipping surface, cascade gravity classifier CGC, crushing complex CC-0.36 with
centrifugal classifier CC, electromagnetic separator roller type. The test scheme is
shown in Fig. 3.
The previous studies of selective disintegration processes carried out by the
authors made it possible to develop some technological recommendations for the ore
preparation of man-made raw materials using centrifugal impact fracture devices.
The main parameter of operation of centrifugal impact apparatuses is the speed of
rotation of the accelerator, which directly affects the speed of impact of a piece
of material on the chipping plate in the crushing chamber. The greatest degree of
crushing occurs with a direct impact, when the angle between the velocity vector
and the surface of the jack plate is 90°. Structurally heterogeneous materials with
different physical and mechanical properties of individual structural elements will
be destroyed in centrifugal impact devices most selectively along the boundaries of
phase fusion. Such structurally heterogeneous materials of man-made origin include
scrap refractory materials. The greater the difference in density and volume of the
individual phases in the material being destroyed, the greater the difference in the
inertial forces occurring in the phases. Such a difference in the magnitude of the

New Approaches to Recycling Refractory Scrap

723

Fig. 3 Test scheme

inertial forces and the distributed nature of these forces contribute to the fact that
during centrifugal impact crushing in a piece of slag, both normal stresses due to
compression of the and normal stresses caused by bending. The stress zone expands
significantly compared to local loading, and, consequently, the probability of fracture
due to cracks located in this zone increases [8, 9].
By selecting the optimal value of the applied dynamic load, selective disintegration of the crushed material can be achieved with a significant reduction in
energy consumption, and taking into account the relationship between the amount of
loading required for the destruction of the material in impact crushers, the physical
and mechanical properties and morphometric parameters of the destroyed material,
operational control of the operating modes of the equipment is possible.

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I. V. Shadrunova et al.

The centrifugal impact mill, which effectively grinds materials of a wide range
of strength, regulates the applied load, which makes it possible to adapt the disintegration mode to the physical and mechanical characteristics of the raw materials.
This technological solution is characterized by flexible layouts, a rational combination of technological operation modules (disintegration, screening, air classification,
magnetic separation), low material, energy and capital intensity.

5 Test Results
The results of the determination of the material composition of the starting material
showed that aluminum oxide in it is represented by corundum and mullite (Table 3).
The impurities are represented by silicates, magnesium oxide and glass.
During the operation of the refractory material in the thermal unit, selective
cracking of the grains occurs under the influence of high temperatures. Grains acquire
a large number of defects that reduce their strength. This process of enrichment is
called decription. The formation of defects occurs due to the presence of impurities,
different thermal conductivity and expansion coefficients of the components of the
mixture, and the transition of mineral crystals from one allotropic modification to
another.
As a result of crushing the starting material in a centrifugal impact crusher at a low
accelerator rotation speed of 40 m/s, the weakened mineral grains of the refractory
material are destroyed without over-grinding. The subsequent classification in the
air along the 0.16 mm boundary makes it possible to remove weak inclusions and
impurities (Table 4).
To further increase the mass fraction of Al2 O3 and reduce impurities, a finer
opening of the aggregates of aluminum-containing minerals with impurities is necessary, therefore, the “Large” classification product was crushed in a centrifugal impact
Table 3 Phase composition of refractory scrap SCCS fraction 0–1 mm
The mineral
Silicon carbide
Corundum

Mass fraction of the mineral, %
8.3
47.7

Mullit

5.2

Anorthite

8.0

Periclase

5.4

Almandin

1.8

Actinolite

3.1

Quartz

1.5

The Cristobalite
The sum of the crystalline phases

2.7
83.7

New Approaches to Recycling Refractory Scrap

725

Table 4 Crushing and classification results in CGC
Product

Output,
%

Crushed
in
CC-0.36

100,0

“Large”
product

79,6

“Small”
product

20,4

Residues
on sieves

Residues on sieves with a cell, mm, %

Mass fraction,
%

1.0

0.5

0.25

0.1

0.063

−
0.063

Private

0.5

23.4

22.3

23.3

6.5

24.0

Complete

0.5

23.9

46.2

69.5

76.0

100.0

Private

0.4

15.1

28.3

38.0

9.4

8.9

Complete

0.4

15.4

43.8

81.7

91.1

100.0

Private

0.0

2.4

8.0

89.6

Complete

0.0

2.4

10.4

100.0

Al2 O3

Fe2 O3

53.6

2.7

58.3

2.4

40.7

2.8

mill to a size of 0.5 mm and classified in a centrifugal classifier along a boundary of
0.04 mm (Table 5).
To reduce iron-containing impurities in the finished product, the “Large” product
of the centrifugal classifier was subjected to magnetic separation in a strong magnetic
field. The yield of the magnetic product was 20.0% (of the starting material). The
chemical composition of the finished processing product, enriched refractory powder,
is shown in Table 6.
Table 5 The results of the grinding and classification of the material in the CC complex
Product

Output,
%

“Large”
product

74,0

“Small”
product

5,6

Residues
on sieves

Residues on sieves with a cell, mm, %
1.0

0.5

0.25

0.1

0.063

Mass fraction, %

−
0.063

Private

0.0

13.1

23.2

38.5

10.5

14.8

Complete

0.0

13.1

36.2

74.7

85.2

100.0

Private

0.0

0.9

99.1

Complete

0.0

0.9

100.0

Al2 O3

Fe2 O3

60.2

2.1

40.0

3.1

Table 6 Chemical composition of the enriched refractory powder
Mass fraction, %
Fe2 O3

SiO2

CaO

Al2 O3

TiO2

Cr2 O3

K2 O

ZrO2

SO3

loss of mass

1.34

25.2

1.11

63.7

1.15

1.42

0.21

0.14

0.10

4.9

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I. V. Shadrunova et al.

6 Conclusion
1. As a result of the processing of corundum-carbide scrap of silicon carbon
refractories, a decrease in the mass fraction of iron from 2.7 to 1.34% was
achieved.
2. The mass fraction of carbon in the starting material and its processed products
was estimated indicator mass loss during calcination. The carbon content in the
processed products was 4.9–6.8%.
3. The yield of the finished product was 51.0–76.4% with a mass fraction of Al2 O3
of 59.0–63.7%.
This work is the first experience, and the authors plan to test the proposed technological solutions for processing scrap of mullite, corundum and periclase refractories,
as well as explore the possibility of recycling alumosilicate dust in the production of
refractory materials and products. The resulting enriched refractory powder can be
used after compaction from a pre-prepared homogeneous mixture of components.
The geometric and physico-technical parameters of the briquette are adapted to the
type of heat unit used.

References
1. Parmar R, Leiponen A, Thomas L (2020) Building an organizational digital twin. Bus Horiz
63(6):725–36. https://doi.org/10.1016/j.bushor.2020.08.001
2. SAP2000 Steel-concrete.ru. https://steel-concrete.ru/products/csi/sap2000/. Accessed 29 Oct
2022
3. Gavshina ZP, Dzintser YS (1982) Usloviya podtopleniya gruntovymi vodami (Groundwater
flooding conditions). Stroyizdat, Moscow
4. Bogomolov YM (2002) Information technologies in the organization of construction. BELFORT,
Minsk, p 158
5. Gusev EV, Mukhametzyanov ZR, Razyapov RV (2017) Methodology for determining the
rational limits of the alignment of construction and assembly processes on the basis of quantitative assessment of technological links. IOP Conf Ser: Mater Sci Eng (MSE) 262:012140.
https://doi.org/10.1088/1757-899X/262/1/012140
6. Radionova LV, Lisovskiy RA, Svistun AS, Gromov DV, Erdakov IN (2023) FEM simulation
analysis of wire drawing process at different angles dies on straight-line drawing machines. In:
Radionov AA, Gasiyarov VR (eds) Proceedings of the 8th international conference on industrial
engineering. ICIE 2022. Lecture notes in mechanical engineering. Springer, Cham
7. Fedorova N, Medyankin M, Fedorov S, Savin S (2022) Experimental and theoretical studies of
the concrete static-dynamic stress–strain curves. In: Akimov P, Vatin N (eds) Proceedings of
FORM 2021. Lecture notes in civil engineering, vol 170. Springer, Cham. https://doi.org/10.
1007/978-3-030-79983-0_14
8. Kazitsin SN (2018) Obtaining wood slabs without binders from mechanically activated wood
particles. Dissertation, Siberian State University of Science and Technology named after
Academician M. F. Reshetnev, Krasnoyarsk, p 132
9. GOST R ISO 31000-2019 (2019) Risk management. Principles and guidelines. Standardinform,
Moscow

Special Technical Conditions
for Ensuring Fire Safety for Liquefied
Natural Gas Terminals
M. Medianik, N. Shunko, and A. Shunko

Abstract This article provides brief information on the defining criteria for the
development of the liquefied natural gas (hereinafter referred to as LNG) industry.
The relevance of LNG use for the Russian market is substantiated. The consumer
countries of Russian LNG are listed. A unique facility for technological practice
is presented: the Terminal for the reception, storage and regasification of LNG in
the Kaliningrad Region (hereinafter referred to as the Terminal) and the results of
experimental studies from the scientific support for the design and construction of
this facility. The issues of the availability and state of the regulatory framework for
ensuring fire safety for facilities with LNG are considered. The need to develop
Special Technical Conditions for Ensuring Fire Safety (hereinafter referred to as
STC) for the presented Terminal is substantiated and the scope of work for their
development is proposed.
Keywords Liquefied natural gas (LNG) · LNG terminal · Experimental studies ·
LNG facility · Regulatory framework · Fire safety · Special technical conditions

1 Introduction
LNG is a safe and environmentally friendly fuel of all currently used fuels. In
percentage terms, the use of liquefaction technology required for gas transportation affects over 26% of the total volume of natural gas produced. The increase in
demand for LNG is also due to the peculiarity of liquefaction technology, which leads
to the fact that natural gas is reduced in volume by 600 times. It should be noted
that the LNG market is more flexible and mobile than the pipeline gas market [1,
2]. Currently, pipeline gas supplies are becoming increasingly subject to sanctions
due to political factors, and when transporting LNG, it is possible to cross transit
countries and, thus, geopolitical risks are minimized [3].
M. Medianik (B) · N. Shunko · A. Shunko
Moscow State University of Civil Engineering, Moscow, Russia
e-mail: mihalmed@yandex.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_58

727

728

M. Medianik et al.

2 Relevance
Liquefaction of natural gas is required exclusively for its transportation to the
consumer, and, if necessary, its accumulation and storage. Storage of natural gas
in large volumes is also possible in underground gas storage facilities (hereinafter
referred to as UGS). UGS is a sealed natural reservoir created in deep deposits of
rock salt [3]. For direct use of natural gas at the facility, it is necessary to carry out
the regasification process, which is the reverse process of liquefaction.
Regasification is the process of converting liquefied natural gas into a gaseous
state using the energy of atmospheric air or sea water. For example, in the case of
large marine terminals, regasification is carried out in heat exchangers with sea water.
After the regasification procedure, LNG passes into a gaseous state and the process
of its delivery through pipelines becomes possible, or there is an option to fill it
into gas cylinders. Currently, LNG is the most promising type of fuel, including for
countries experiencing a shortage of pipeline gas [4].
The countries of Northeast Asia (China, Taiwan, South Korea and Japan) are
increasing their industrial turnover and therefore the Asia–Pacific region is the most
important direction of Russian gas exports. As for European LNG supplies, after
February 2022, only Lithuania and the United Kingdom cancelled the import of
Russian LNG, but such countries as France, Spain, Belgium and the Netherlands
increased the supply [3].

3 Statement of the Problem
An LNG terminal is a special regasification terminal for receiving LNG and preparing
gas for use. This paper presents a project of such a facility, studied at the National
Research University Moscow State University of Civil Engineering: a terminal for
receiving, storing and regasifying (LNG) in the Kaliningrad region (hereinafter
referred to as the Terminal). Preparations for the construction of this Terminal began
with the construction of the Kaliningrad UGS in 2009, which became the first storage
facility in Russia created in rock salt deposits. Its capacity is 12 million cubic meters
per day [5]. The Kaliningrad UGS can operate in both the withdrawal and injection
modes (it has the ability to be multicyclic), and also has the ability to quickly reach
maximum productivity. Thus, it became possible for the Terminal to receive and
place gas in the UGS using the floating regasification unit “Marshal Vasilevsky”.
The need to build the Terminal is due to difficulties with the supply of energy
resources for the most isolated region of our country. Previously, natural gas was
supplied to consumers in the Kaliningrad region via the transit pipeline: “MinskVilnius-Kaunas-Kaliningrad”. With the introduction of sanctions, an urgent need
arose to develop an alternative supply of energy resources for this region. In particular,
it was decided to compensate for the lack of gas supply by supplying LNG to the
Terminal via the Baltic Sea.

Special Technical Conditions for Ensuring Fire Safety for Liquefied …

729

Fig. 1 Construction of a breakwater with the Marshal Vasilevsky regasification unit

One of the main features of the regasification terminal under consideration is its
location in open sea conditions with intense wave action. In order to reduce the degree
of influence of waves on the operating conditions of the floating regasification unit
(FRSU), the regasification terminal is designed as a protective structure-berth.
A deep-water berth with a protective breakwater, located at a distance of five kilometers from the coastline, was designed to pump LNG from the floating regasification
unit (Fig. 1).

4 Experimental Studies in a Hydrowave Flume
A study of the efficiency of the breakwater structure design, in accordance with the
requirements of regulatory documents [6, 7], was conducted at the National Research
University Moscow State University of Civil Engineering (Figs. 2, 3 and 4).
The physical model of the breakwater is made in the scale M = 1:63. The water
level in the wave tray was: + 1.340 m (5%)—natural values. Natural parameters of
the wave of the most dangerous storm of the North-West Rhumb, with a recurrence
of 1 time in 50 years, were: the wave height of 1% probability is 8.3 m, the average
wave period is 8.4 s, the duration of the storm impact is 12 h.
In the presented experimental studies, a standard methodology was used, with the
observance of the similarity between the full-scale design and the model according

730

M. Medianik et al.

Fig. 2 Schematic representation of experimental studies

Fig. 3 Physical model of a breakwater in a wave trough

to the Froude number [6, 7]. The composition of the measuring equipment and the
installation in the form of a wave tray are also standard for conducting such studies.
In the experiments, wave recorders from HR Wallingford (UK) were used. Calibration of the wave recorders was carried out at the beginning of each series of
experimental studies. It was carried out on calm water and consisted of installing the
wave recorders at a certain depth with a selected number of steps, taking readings
from them and calculating calibration coefficients.
Figure 5 shows the oscillations of the wave surface from wave recorder No. 1.
Based on the analysis of the results of the physical modeling of the wave impact
of the estimated storm on the breakwater structure model, the following conclusion
was prepared:
• the discharge of protective fill elements (tetrapods) was absent;
• the rock fill and the protective element in the form of a concrete corner are stable;

Special Technical Conditions for Ensuring Fire Safety for Liquefied …

Fig. 4 Experimental studies

Fig. 5 Wavegram in experiment (natural data). Wave recorder No. 1 reading

731

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M. Medianik et al.

• the overflow of waves over the superstructure of the breakwater structure was not
recorded;
• the design dimensions of the berms are set correctly;
• the design elevation of the top of the breakwater wall, taking into account the
absence of overflow of waves, is sufficient.
In addition, the wave pressure on large-diameter shells (tanks for pumping LNG)
was determined experimentally at the request of the designers.
The sensors were installed on the side surface of the LNG and connected to the
conversion unit, which was connected to the computer via a USB cable. The signals
from the sensors were sent to the computer’s hard drive for further processing and
visualization of the measurement results on the computer screen. In the experiments,
two pressure sensors from HR Wallingford (UK) were used. The arrangement of
pressure sensors (P) in the experiment is shown in the Fig. 6.
Figure 7 shows the selective time readings of the signal from pressure sensor No.
1. By the tenth minute of the storm impact, an increase in the average load value was
observed, which reached values up to 12.00 kPa (taking into account the calibration

Fig. 6 Location of pressure sensors

Special Technical Conditions for Ensuring Fire Safety for Liquefied …

733

Fig. 7 Pressure sensor reading no. 1

coefficient and the selected scale of research), while long-wave oscillations of the
wave load were present, associated with the surge and filtration of water in the LNG.
Figure 8 shows the change in the signal from pressure sensor No. 2. Taking into
account the calibration coefficient and the selected scale of research, an increase in
the average value of the wave load was recorded—up to 11.5 kPa.
Thanks to the research and recommendations of hydraulic engineers from the
National Research University Moscow State University of Civil Engineering, the
breakwater construction project received a positive conclusion from the Federal
Autonomous Institution “Main State Expertise of Russia” and the unique object
for the Russian Federation was implemented.

5 Theoretical Part
In relation to marine hydraulic engineering, when designing and constructing unique
hydraulic structures, scientific support is mandatory [8–10]. This allows eliminating
some problems with the insufficiency of scenarios for the interaction of waves and
structures of the latest structures, contained in existing regulatory documents. But, in
the case of designing, constructing and ensuring industrial safety of LNG facilities,
the insufficiency of the regulatory framework is critical.
The fact is that the method of transporting LNG, with subsequent regasification
and the entire technology used, are quite new for Russian practice and the presence
of certain shortcomings is present. In particular, due to the imperfection of new

734

M. Medianik et al.

Fig. 8 Pressure sensor reading no. 2

technological solutions, part of the liquefied gas can be, simply, lost. At this stage,
the gradual transition from imported equipment to domestic, it is necessary to analyze
possible technical and technological solutions that can reduce the volume of losses
and preserve the transported LNG for subsequent use [11–13].
The lack of regulations is present even in the sphere of the legal framework for the
development of LNG exports themselves [14], as well as in such an important area
as fire safety standards for LNG facilities. The design of oil and gas facilities has
traditionally been carried out through the development of departmental regulations.
However, due to the significant development of the LNG market, many provisions of
these regulations have become outdated, and the LNG processing technology has its
own nuances and differences. In addition, the current legislation (Article 78 of Federal
Law No. 123-FZ) [15], due to the lack of regulatory fire safety requirements for the
entire variety of LNG facilities, requires the construction customer to develop special
technical conditions (hereinafter referred to as STC) reflecting all the necessary
specifics of ensuring fire safety for the facility in question.

6 Practical Significance and Suggestions
Based on the analysis of existing and currently valid regulatory documents: SP
231.1311500.2015 [16]; SP 240.1311500.2015 [17]; SP 155.13130.2014 [18], it
can be concluded that they do not contain or do not fully define the requirements:

Special Technical Conditions for Ensuring Fire Safety for Liquefied …

735

• for automatic fire alarms, methods and means of fire protection and fire
extinguishing of structures and external installations of LNG facilities;
• for fire protection of berthing complexes for pumping LNG;
• for fire protection of production facilities, storage facilities with handling of polar
liquids;
• fire safety for automated installations for the timing loading of liquid petroleum
products;
• fire safety for LNG storage facilities. The following list of fire safety requirements must be reflected in the STC for designing fire protection for the Terminal
discussed in the article;
• fire distances to neighboring objects with elements of territorial planning;
• fire water supply (external and internal fire water supply systems);
• space-planning and design solutions for structures;
• organizing the evacuation of people in case of fire;
• the procedure for the activities of fire departments during fire suppression,
including organizing driveways and approaches for fire-fighting equipment;
• devices of technological units and fire protection systems;
• organizational and technical measures to ensure fire safety [19].

7 Conclusions
The conducted experiments on the study of the wave impact of a north-west storm
on the structure of the protective floating breakwater allow us to draw a conclusion
about the stability of the LNG terminal breakwater structure during construction and
operation under the influence of a design north-west storm.
All elements of the slope protective structure of the breakwater are stable, there is
no damage to the structure, the structure in question is fully operational. Protective
fastenings made of monolithic figured concrete tetrapod blocks ensure the stability
of the entire structure from the impact of design north-west storms. The high wavedamping capacity of the structures in combination with the loss of wave energy
when collapsing on the slope, the absence of wave spillover over the upper part of
the parapet and the passage of waves through the body of the supports ensures the
overall efficiency of the LNG Terminal structure under study.
In addition, the wave pressure on large-diameter shells (tanks for LNG injection),
structurally included in the berthing structure of the LNG terminal, was experimentally determined. Thus, a full range of studies on the hydraulic engineering part
of scientific support for the design of the studied LNG terminal facility has been
completed.
The application of the research results presented in this work is possible when
making design and other decisions on the designs of slope protective structures at all
stages of project development.
In terms of considering the issues of design and construction of industrial safety
facilities for LNG facilities, it should be concluded that the regulatory framework in

736

M. Medianik et al.

this area is insufficiently developed and that specialists of all levels and areas need
to pay comprehensive attention to this topic [20].
It seems necessary to develop and update the regulatory framework for servicing
LNG facilities using similar foreign legislation and international initiatives, due to
the insufficiency of domestic developments.
At the same time, it should be ensured that the existing accumulated experience
in developing STU for already functioning facilities, and most importantly, the most
effective and proven solutions are necessarily reflected in new or updated current
regulatory documents for various LNG facilities.

References
1. LNG Regasification Terminal. https://neftegaz.ru/tech-library/transportirovka-i-khranenie/141
738-spg-terminal-regazifikatsionnyy/. Accessed 26 Jun 2025
2. Analysis of the LNG Market in Russia 2020–2024 + forecast up to 2034.
https://tebiz.ru/mi/rynok-spg-v-rossii?utm_source=Yandex&utm_medium=cpc&utm_
campaign=70207151&utm_content=type_search|pl_none|grid_4791955852|adid_
11607539696|rt_35870812797|ptype_premium|pos_1|device_desktop&utm_term=kwid_
35870812797&yclid=4380676055177625599. Accessed 26 Jun 2025
3. Filimonova IV, Provornaya IV, Nemov VYu, Kartashevich AA (2023) World LNG Market.
Structural features and development forecast. Neftegaz. RU, No. 2(134)
4. Dzyuba AP (2021) Russia’s role in the development of the world liquefied natural gas
market. Bulletin of the Moscow University named after S. Yu. Witte. Series 1. Economics
and Management, No. 1(36). https://doi.org/10.21777/2587-554X-2021-1-52-63
5. Kaliningrad UGS: Ensuring Energy Security of the Region. https://www.gazprom.ru/projects/
kaliningradskoye-ugs/. Accessed 26 Jun 2025
6. SP 38.13330.2018 (2018) Loads and impacts on hydraulic structures (wave, ice and from ships).
Ministry of Regional Development of the Russian Federation, Moscow
7. GOST R 70023-2022 (2022) Physical modeling of wave impacts on port hydraulic structures. Requirements for model construction, experiments and results processing. Rosstandart,
Moscow
8. Rogachko SI, Shunko NV (2022) Scientific support of projects of offshore hydraulic structures.
Power Technol Eng 56(1). https://doi.org/10.1007/s10749-023-01461-8
9. Shunko AS, Shunko NV (2021) Physical modeling of the cargo berth of the Utrenny terminal.
Ind Civ Eng 9:47–50
10. Tlyavlina GV, Tlyavlin RM, Vyaly EA (2022) Port hydraulic structures: requirements for
physical modeling of wave effects. Transp Constr 3:24–26
11. Shcherban PS, Mazur EV, Sinitsyn OA (2022) Study of losses of liquefied natural gas during its
transportation to the Kaliningrad region and subsequent regasification. Scientific and Technical
Bulletin of Bryansk State University, No 2. https://doi.org/10.22281/2413-9920-2022-08-02165-175
12. Lagozin AYu, Mordvinova AV, Nekrasov VP, Miroshnichenko SA (2023) Bunkering of water
transport with LNG: fire safety regulations. Neftegaz.RU, No. 11
13. Buyanov AS, Semenov VE, Lobanov AV, Verakso KS, Pershin NV (2020) Legal regulation
of bunkering of ships with liquefied natural gas in the seaports of Russia. Gas Industry, No.
3(798)
14. Emelianov VV (2022) Legal framework for the development of LNG exports in Russia.
Education and Law, No. 12. https://doi.org/10.24412/2076-1503-2022-12-136-139
15. Technical regulations on fire safety requirements of 22.07.2008 N 123-FZ. https://www.consul
tant.ru/document/cons_doc_LAW_78699/. Accessed 26 Jun 2025

Special Technical Conditions for Ensuring Fire Safety for Liquefied …

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16. SP 231.1311500.2015 (2015) Development of oil and gas fields. Fire safety requirements.
Introduced 01.07.2015. VNIIPO EMERCOM of Russia, Moscow
17. SP 240.1311500.2015 (2015) Liquefied natural gas storage facilities. Fire safety requirements.
Introduced 31.08.2015. EMERCOM of Russia, Moscow
18. SP 155.13130.2014 (2014) Oil and oil product warehouses. Fire safety requirements.
Introduced 01.01.2014. EMERCOM of Russia, Moscow
19. Technical regulations on the safety of buildings and structures dated 30.12.2009 N 384-FZ.
https://www.consultant.ru/document/cons_doc_LAW_95720/. Accessed 26 Jun 2025
20. Krasavin AV, Krepyshev SA, Medyanik MV (2018) Analytical review of special technical
conditions for oil and gas industry facilities. Fire Explos Saf 27(2–3):14–19

Mathematical Modeling
of Explosion-Proof Valve Loading
in Ventilation Systems
S. A. Yaremenko, O. I. Gaidash, K. V. Garmonov, and M. N. Zherlykina

Abstract The paper presents the design features of energy supply facilities of
housing and communal services. It is revealed that external impacts of natural and
man-made origin can cause an emergency situation at an industrial facility. The
article presents a description of the origin and development of a shock wave and
its consequences at industrial facilities. The focus is on the ventilation system as an
object most susceptible to the impact of a shock wave. To ensure safety of industrial facilities, we propose to install explosion-proof valves. We describe boundary
conditions for the operation of explosion-proof valves. We also show the results
of mathematical modeling of a linear polynomial equation of state. In the ANSYS
LS-DYNA numerical modeling environment, we set a two-dimensional problem,
at the first stage of which we determined the distance from the initiated charge at
which the shock wave front pressure is critical. A numerical study was performed for
two scenarios—with and without the installation of an explosion-proof valve. In the
paper we present the results of the study of dependence of pressure on time during
the approach to the valve and dependence of pressure on time at the sensors. As a
result of numerical modeling of loading of an ordinary explosion-proof ventilation
valve by a shock wave, we established the feasibility of its use.
Keywords Ventilation · Explosion-proof valve · Safety · Shock wave · Sensor ·
Numerical experiment

1 Introduction
Currently, the construction of any type of structure from private residential buildings to strategic special-purpose facilities includes preliminary preparation of design
documentation, the most important part of which is the planning of general utilities.
S. A. Yaremenko (B) · O. I. Gaidash · K. V. Garmonov · M. N. Zherlykina
Voronezh State Technical University, Voronezh, Russia
e-mail: iaremenko@cchgeu.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_59

739

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S. A. Yaremenko et al.

Ventilation and air conditioning systems are among the most expensive and complex
ones to design.
Nuclear power facilities are among the most complicated structures created by
man, their construction is subject to increased reliability requirements, various
scenarios for the occurrence of abnormal situations are envisaged and many options
for their prevention are as well developed. In particular, this applies to ventilation
and air conditioning systems.
Currently, the construction of any type of structure from private residential buildings to strategic special-purpose facilities includes the preliminary preparation of
design documentation, the most important part of the development of which is the
planning of engineering networks. Among others, some of the most expensive and
complex in design are ventilation and air conditioning systems.
There are a number of industries in which special requirements are put forward
for ventilation and air conditioning systems, for example, in the medical and pharmaceutical industries, the purity of the air supplied to the room is important and
a specialized disinfection and cleaning system is used; for offshore structures and
vessels, increased corrosion resistance of products to aggressive salt water is necessary, and for some facilities of the energy, chemical and military industries, one of
the mandatory technical requirements is to prevent the propagation of a shock wave
(HC) through ventilation ducts in order to protect workers and equipment inside the
building. For this purpose, special explosion-proof vents of the vane type are used.
The purpose of the work is to analyze the compliance of the design of
the explosion-proof ventilation valve with technical requirements for the nuclear
industry, to improve its design within the framework of these requirements, as well
as to develop universal design documentation for its serial production.
Ventilation carries out constant air exchange in rooms to remove excess heat, moisture, harmful substances in order to ensure permissible meteorological conditions and
air cleanliness in the serviced or working area [1, 2].
According to the method of fresh air supply to rooms and removal of contaminated
air, ventilation is divided into natural, forced and mixed.
Natural ventilation creates the necessary air exchange due to the difference in the
densities of the air that is inside the room and the colder air outside. Air exchange is
regulated by transoms, through which cold air enters from the outside, while warm
air exits through the exhaust lantern on the roof of the building. Its main disadvantage
is that the plenum air enters the room without cleaning and heating, and the removed
air is not cleaned and pollutes the atmosphere.
Forced (mechanical) ventilation ensures the maintenance of constant air exchange,
which is carried out using mechanical fans, air ducts and air distributors. Depending
on what the ventilation system is used for, it is divided into supply (for supplying air
to the working area), exhaust (for removing contaminated or heated air) and supply
and exhaust.
General ventilation is based on dilution of harmful substances emitted in the
room, heat and steam with clean air to the permissible standards. General ventilation
systems for production and administrative and household premises (with constant
presence of people) without natural ventilation should be provided with at least two

Mathematical Modeling of Explosion-Proof Valve Loading …

741

supply or two exhaust fans, each of which provides 50% of the required air exchange
[2–4].
Local ventilation, unlike general ventilation, provides ventilation directly at the
workplace. It can be supply or exhaust. Plenum ventilation improves the microclimate
in a limited area of the room, exhaust ventilation removes harmful contaminants
directly at the place of their formation, for example, at welding stations, from the
charging compartments of battery shops, etc.
Air conditioning is the automatic maintenance in closed rooms of all or its individual parameters (temperature, relative humidity, cleanliness, speed of movement)
in order to ensure optimal meteorological conditions that are most favorable for
people’s well-being and technological processes.
An air conditioning system is a technical installation designed to create and maintain in a room or a separate area the specified parameters of the microclimate and air
purity. At the same time, the specified parameters are maintained for all periods of
the year. Air conditioning systems usually operate in an automatic mode provided
by a special automatic control system.
By purpose, air conditioning systems are divided into comfortable and technological. Comfortable air conditioning is used to create a microclimate optimal for
human life. At the same time deviation of air parameters from specified ones by
temperature ± 1.0 °C, by relative humidity ± 7%, by air mobility ± 0.1 m/s during
the year on average from 100 to 450 h. Technological air conditioning is designed
to provide the necessary parameters for optimizing technological processes [5, 6].
For air treatment in large commercial and administrative buildings and industrial
enterprises, frame-panel central air conditioners are mainly used. Modern central
air conditioners are available in sectional versions. They consist of unified typical
units, such as: silencer unit, filters, heat exchangers, fan, recuperator, humidification
or dehumidification unit, etc.
In addition to the general industrial version, the design of the central air conditioner
can meet the individual requirements of the construction facility, such as maintaining
performance at temperatures below minus 40 °C, explosion protection requirements,
and others.
Air valves are used in ventilation and air conditioning systems. Air valves can be
used as shut-off valves to control the air flow in open/closed mode and/or to smoothly
control the amount of air in the network. There are several types of air valves:
Main types of ventilation air valves:
Check valve—designed to automatically close the section of the air duct in order
to prevent free flow of air in ventilation systems when the fan is not working, it can
have both a round and a square section.
Control valve—designed to control the parameters of the gas–vapor-air flow in
working ventilation networks by changing its flow rate and controlled by external
force from an electric or manual drive [7].
An overpressure valve is an overpressure relief valve designed to bypass air from
one room to the adjacent or to the atmosphere, while maintaining a certain pressure
in the rooms served by the ventilation system.

742

S. A. Yaremenko et al.

Installation of the valve shall provide for the possibility of cantilever fastening to
the wall or ceiling (using the mounting frame or directly behind the flanges on the
valve body) or sealing directly into the wall or ceiling. Wall sealing of valves should
provide for a special niche for placing the electric drive with the possibility of its
subsequent maintenance.
Explosion-proof ventilation valves, also known as ventilation channel shutoff
devices, are a specialized product designed to prevent the impact of air HC on the
ventilation system in order to isolate buildings from the outside environment when
exposed to air HC. Installed in places of outside air intake and exhaust air removal.
Ventilation channel closing devices ensure safety of people and equipment inside
the building. They must maintain strength and performance under the influence of
detonation explosion HC and deflagration explosion compression wave, both under
the action of positive and negative compression phase [3, 8, 9].
This type of ventilation valves can be used at oil and gas plants, chemical plants
and in places of storage of their finished products, at pharmaceutical plants, nuclear
power plants and other structures of the energy industry, in scientific laboratories,
at ammunition depots and other military facilities, as well as at facilities potentially
susceptible to terrorist attacks.
The classic version of the design of the device for closing ventilation ducts is a
product of rectangular section, consisting of blades, rod, levers and a frame, which
includes horizontal and vertical walls. The HC coming to the blades of the valve
creates a torque relative to the axis of rotation of the blades, as a result of which they
close, preventing the further spread of HC through the ventilation channels. Blades
are automatically returned to initial position due to return springs after termination
of HC action.
Ventilation channel shutoff devices have a mechanism for manually driving the
blades to the "Closed" position to check the operability of the device and for scheduled
maintenance. The mechanism is actuated by turning the removable lever clockwise
until stop with initial torque M _n = 1 · N · m.

2 Theoretical Basis of the Research
When designing any industrial buildings and structures, it is imperative to take into
account special loads and impacts—both natural and man-made—that can cause
damage or destruction of structures and lead to serious environmental and economic
consequences. Nuclear power plants occupy a special place among hazardous industrial facilities, and one of the most important issues addressed in ensuring the safety
of nuclear power plants is taking into account extreme natural and man-made impacts
in accordance with NP-064-05 (earthquakes, hurricanes, tornadoes, extreme snowfalls, aircraft crashes, explosions, etc.). Air shock wave (SW) as a consequence of
the mechanical effects of an external explosion, is one of the most important extreme
man-made impacts.

Mathematical Modeling of Explosion-Proof Valve Loading …

743

Penetrating into a hazardous industrial facility, civil defense structure, or nuclear
power plant, SW can damage the facility’s main technological equipment and
systems, including safety–critical NPP elements and systems. One of the main ways
of air shock wave penetration into NPP buildings and structures are ventilation
openings.
Explosion-proof ventilation valves, also known as ventilation duct shut-off devices
(VDSDs), are a specialized product and are designed to prevent the impact of air
shock wave on the ventilation system in order to cut off buildings from the outside
environment when exposed to air shock wave. They are installed in places where
outside air is taken in and exhaust air is removed. VDSDs ensure the safety of
people and equipment inside the building. They must maintain their strength and
functionality when exposed to the UV of a detonation explosion and the compression
wave of a deflagration explosion, both during the action of the positive and negative
compression phases.
This type of ventilation valves can be used in oil and gas industry plants, chemical
plants and storage areas for their finished products, pharmaceutical plants, nuclear
power plants and other energy industry facilities, scientific laboratories, ammunition
depots and other military facilities, as well as facilities potentially subject to terrorist
attacks.
The standard design of the VDSD is a rectangular section product consisting of
blades, traction, levers and a frame, which includes horizontal and vertical walls.
The UV coming to the valve blades creates a torque relative to the axis of rotation
of the blades, as a result they close, preventing further spread of the UV through the
ventilation ducts. The blades return to their original position automatically after the
UV stops acting, thanks to the return springs.
Ventilation duct shut-off devices are designed to cut off the flow of air and nonexplosive air mixtures that do not contain fibrous materials, dust and other solid
impurities in quantities exceeding 100 mg/m3 in ventilation and air conditioning
systems, as well as to prevent the flow of radioactive air through air ducts [10].
Ventilation duct shut-off devices retain their functionality regardless of their
spatial orientation and installation plane. VDSDs cannot be installed in air ducts
and channels in premises of A and B explosion hazard category, in exhaust systems
for explosive mixtures, in systems that move media with sticky and fibrous materials,
as well as in systems that are not subject to periodic cleaning according to established
regulations to prevent the formation of deposits.
Ventilation duct shut-off devices must ensure their safety function, maintain
strength and functionality under the impact caused by an aircraft crash.

3 Mathematical Modeling
Normal values of climatic factors of the external environment during operation of
the VDSD should be:

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S. A. Yaremenko et al.

• in non-working condition (storage and installation) - according to GOST 15150
for TM climatic version, placement category 3, GU atmosphere type;
• in working condition in normal operation mode, inflow;
• outside air with a temperature from minus 10 to + 60 °C and humidity up to
100%. Temperature of exhaust air from the “controlled” or “free” access zone
from + 45 to + 60 °C, relative humidity may be up to 80%.
Content of corrosive agents in the air may be as follows: chlorides up to 0.026 mg/
m3 , sulfates up to 0.048 g/m.
The general appearance of explosion-proof devices of the ventilation system with
moving blades, widely used at nuclear, oil and gas and military industry facilities, is
shown in Fig. 1.
According to federal norms and rules NP-064–17, the time of automatic closing
of the VDSD -L valves from the impact of air shock waves and the compression
wave of a deflagration explosion must ensure that the excess pressure in the air duct
is no more than 5 kPa, while the excess pressure of the shock waves coming to the
valve is 30 kPa.
To analyze the fast-flowing process of propagation of the shock wave front and
its passage along the profile of the proposed design, it is necessary to conduct its
numerical modeling.
The material of the VDSD is stainless steel AISI 316L. The steel strength model
is Plastic Kinematic.
Conservation laws are presented in the form of dependencies:
dρ
+ ρ∇i ν t = 0
dt

(1)

Fig. 1 General view of the double-acting VDSD -L: 1—frame; 2—blade; 3—lever; 4—return
spring; 5—traction

Mathematical Modeling of Explosion-Proof Valve Loading …

745

d νi
j
= ∇i νi
dt

(2)

dE
= σ ij εij
dt

(3)

The ratios for the stress deviator are presented in the form of dependencies:
dDσ ij
1 dρ
gij
+ 2GαDσ ij ν = 2G εij +
3ρ dt
dt

(4)

σij = Dσ ij − (p + q)gij

(5)

εij =

1
∇i νj + ∇j νi
2

(6)

The closing ratios are presented in the form of dependencies:
p = p(ρ, e, λ)

(7)

σT = σT εij , T , ...

(8)

λ = λ(ρ, e, ρ...)

(9)

The TNT charge is taken as a harmful substance (HS). The equation of state
for HS—the Johnson-Wilkins-Lee (JWL) equation—allows for a high-precision
description of the properties of detonation products:
p=A· 1−

ω
R1 · V

· exp(−R1 · V ) + B · 1 −

ω
R2 · V

· exp(−R2 · V ) +

ω
·E
V
(10)

where V is a relative specific volume, V = ρρ0 = υυ0 ;A, B, C, R1 , R2 , ω are empirical
constants; E is normalized energy per unit volume, E = E 0 + P2H · (1 − VH ); E 0 is
a normalized value that includes the energy of chemical bonds and is determined in
a thermochemical experiment or thermodynamic calculation data.
The linear polynomial equation of state is linear with respect to the internal energy.
The pressure is determined by the equation:
P = C0 + C1 μ + C2 μ2 + C3 μ3 + C4 + C5 μ + C6 μ2 E

(11)

where the members P = C0 + C1 μ + C2 μ2 + C3 μ3 + C4 + C5 μ + C6 μ2 E and
P = C0 + C1 μ + C2 μ2 + C3 μ3 + C4 + C5 μ + C6 μ2 E are equal to zero if the

746

S. A. Yaremenko et al.

conditions μ < 0, μ = ρρ0 − 1; are met, ratio of the current density to the initial
density.
A linear polynomial equation of state can be used to model a gas with a gamma
state equation. This can be obtained by specifying the coefficients:
C0 = C1 = C2 = C3 = C4 = 0

(12)

C4 = C5 = γ − 1

(13)

where γ is the ratio of specific heat capacities. Pressure is determined by the formula:
p = (γ − 1)

ρ
E
ρ0

(14)

According to federal norms and rules NP-064–17, for nuclear power facilities, the
value of excess pressure at the SW front when approaching the valve is PH = 30 kPa,
which corresponds to the first degree of danger for the construction of the nuclear
power plant. In this case, the pressure at the outlet of the valve should not exceed
PK = 5 kPa. It is required to conduct a study to determine whether the proposed
design of the VDSD complies with the technical requirements for nuclear power
plants.
In the ANSYS LS-DYNA numerical simulation environment, a two-dimensional
problem is set, the first stage of which is to determine the distance from the initiated charge at which the shock wave front pressure corresponds to 30 kPa. This is
implemented using sequentially located sensors along the shock wave propagation
path. In the second stage of the task, the explosion-proof ventilation valve profile is
located at a previously determined distance from the charge and the sensor readings
are analyzed. The explosive charge has a plate shape and is initiated in such a way
that at the moment of approach to the VDSD the shock wave front is flat. The valve
cross-section is 500 × 500 mm, which is the most common and universal size. Below
is a picture of the propagation of the UV front along the valve profile at different
moment (Fig. 2).
According to the sensor data, we find that the valve design provides an outlet
pressure of PK = 0.328 kPa, the obtained value is an order of magnitude less than
P = 5 kPa, established by paragraph 3 of the federal norms and rules in the field
of atomic energy use NP-064-17 “Accounting for external impacts of natural and
man-made origin on nuclear energy facilities”.
We set a task for comparative analysis, where the explosion-proof valve was
absent. In this case, the sensor, determining the outlet pressure, registered excess
pressure P = 8.58 kPa, which exceeds the maximum permissible value of P =
5 kPa. The pressure change graphs are shown in Figs. 3 and 4.
The technical solution relates to means of protection of NPP ventilation systems
under the influence of an air shock wave of a detonation explosion and a compression
wave of a deflagration explosion.

Mathematical Modeling of Explosion-Proof Valve Loading …

747

Fig. 2 The SW front at a given moment t: а 2ms; b 5ms; c 6ms; d 7ms; e 8ms; f 9ms

Fig. 3 Graph of pressure dependence on time during approach to the valve

The ventilation system protection device, comprising a housing, a support fixed
grate installed in the housing, is characterized by the fact that the second grate is
also fixed and connected to the first grate by means of guides arranged around each
of the grates’ openings and forming channels with deflection, inside which locking

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S. A. Yaremenko et al.

Fig. 4 Graph of pressure versus time at the valve outlet

elements of a spherical shape with a diameter greater than the diameter of the grates’
openings are installed with the possibility of movement.
The study of pressure change in the absence of a valve is shown in Figs. 5 and 6.
The technical result is achieved by the fact that in a ventilation system protection
device containing a housing and a fixed support grille installed in the housing, the
second grille is also fixed and connected to the first grille by means of guides located
around each of the grille openings and forming channels with a deflection, inside
which spherical locking elements with a diameter greater than the diameter of the
grille openings are installed, with the possibility of movement.
Based on the data obtained during the calculations, it can be concluded that with
the same initial pressures PH = 30 kPa, the use of a valve ensures a pressure drop

Fig. 5 The SW front at a given moment t = 3.5 ms in a problem without a VDSD

Mathematical Modeling of Explosion-Proof Valve Loading …

749

Fig. 6 Graph of pressure dependence on time in sensors

of 99%, while in the absence of a valve, the pressure drops by 71% and exceeds the
permissible value established by federal standards NP-064-17.

4 Conclusion
In a result of the analytical study, we identified hazardous situations, which may
result in emergency situations at energy supply facilities of housing and communal
services. We presented and substantiated a proposal for the installation of explosionproof valves in ventilation systems of industrial facilities. As a result of numerical
modeling of loading in the standard explosion-proof ventilation valve by a shock
wave, we established the expediency of its application. In order to improve existing
devices in accordance with federal norms and rules as well as taking into account
external impacts of natural and man-made origin, we recommend to modernize
existing designs of standard explosion-proof valves.

References
1. Elterman VM (1980) Ventilation of chemical manufactures. Chemistry, Moscow, p 288
2. Polosin II (2001) Dynamics of processes of industrial ventilation. Voronezh
3. Zherlykina MN (2006) Increase of efficiency of emergency ventilation of industrial premises
for maintenance of explosion safety at emissions of chemical substances. The dissertation of
the candidate of engineering sciences, Voronezh, p 166
4. Derepasov AV (2007) Research air exchange production premises with holes in the ovelappings.
Housingand utilities infrastructure 1(1):18–25

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S. A. Yaremenko et al.

5. Zherlykina MN, Vorobieva YuA, Kononova MS, Yaremenko SA (2022) Numerical study of
the non-azeotropic mixture outflow in event accident in the building cooling system. IOP
Conference Series: Earth and Environmental Science. International Scientific and Technology
Conference “Earth Science”, ISTC EarthScience 2022, Chapter 4
6. Polosin II (2009) Realisation of mathematical model for an estimation of efficiency of schemes
of the organisation of air exchange in shops. Galvanocoverings Privolzhsky scientific bulletin
2(10):42–47
7. Grimitlin AM (2007) Heating and ventilation of industrial premises. Northwest AVOK, St.Petersburg, p 399
8. Yaremenko SA (2012) Energy spectra of the pulsation velocity in free turbulent ventilation
flows scientific journal. Eng Syst Facil 3(8):32–38
9. Skrypnik AI (2004) Calculation model for determining the most probable value of venting
of chemical substances in an emergency situation news of Universities building. Novosibirsk
5:72–75
10. Zherlykina MN, Kononova MS, Vorobeva YA (2019) Emergency ventilation industrial premises
of chemical industry enterprises. In: IOP Conference series: materials science and engineering. International conference on construction, architecture and technosphere safety—4.
Construction Technology and Organization, p 044016

The Use of Polyolefin Polymer Wastes
in the Production of Bituminous
Materials
Y. A. Bulauka, A. G. Kulbei, and A. D. Kandratsiuk

Abstract The secondary use of polyolefin plastics (obtained as a result of solid
municipal waste processing) in the production of bitumen materials has been studied.
It has been established that integration of polymer wastes, dissolved in spent industrial
oil, into bitumen binder allows to increase its heat and frost resistance, thus expanding
the plasticity range of bitumen. The potential possibility of using polymer wastes in
the production of bitumen materials for non-critical construction objects has been
confirmed. The use of polymer wastes in bitumen production contributes to the
development of a circular economy, within which materials are recycled and are
used again in road construction, thereby reducing the impact on the environment.
Keywords Polyolefin plastic · Polymer wastes · Bitumen material

1 Introduction
Rational use of industrial wastes is a key environmental issue in the modern world,
enshrined in the SDG 12 (responsible consumption and production) of the UN, which
presupposes the secondary consumption of waste for the transition to a circular
economy [1].
According to the United Nations, global plastic production amounts to more than
400 million tons per year. This number is expected to triple by 2060. Only 10% of
this plastic is currently being recycled. About 19% is incinerated, 49% is dumped
in solid municipal waste (MSW) landfills, 22% is mismanaged or released into the
environment, causing irreparable damage [2].
Plastic waste has a high resistance to degradation and can decompose in
natural conditions for more than 100 years [3]. The main mechanisms of plastic
Y. A. Bulauka (B) · A. G. Kulbei · A. D. Kandratsiuk
Euphrosyne Polotskaya State University of Polotsk (Polotsk State University), Novopolotsk,
Belarus
e-mail: u.bylavka@psu.by
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_60

751

752

Y. A. Bulauka et al.

Fig. 1 Mechanisms of plastic waste degradation [4]

waste degradation include thermal and chemical degradation, photodegradation; and
biodegradation [4].
Mechanisms of plastic waste degradation are shown in Fig. 1; [4].
Plastic waste is piling up in landfills, many of which are overloaded and take up
precious land space [5]. Plastic waste is spread by water in the form of microplastics
and negatively impacts the ecology of the region, contributing to the pollution of fresh
water and soil, which poses a serious threat to wildlife, especially marine animals
[6, 7].
Burning plastic waste results in air pollution with toxic gases and particulate
matter (CO, NOx , SO2 , CO2 , NH3 , HCl, CH4 , fine particulate matter with an aerodynamic diameter of 10 μm or less (PM10 ), black carbon, organic carbon, volatile
organic compounds (VOCs), polycyclic aromatic hydrocarbons (PAHs) and others)
that negatively impact human health and the environment, causing breathing problems, the formation of photochemical smog and aggravating the greenhouse effect
[8–10].
Through advanced technologies and processes, waste plastic is meticulously
sorted, cleaned, and transformed into a range of valuable components [11]. Secondary
plastics can be considered as valuable raw materials for many purposes, including
the production of bitumen materials.
By integrating discarded plastic into bitumen construction materials, it is possible
to simultaneously reduce environmental pollution and improve resource efficiency
[11]. Bitumen materials, modified with plastic waste, not only have sufficient
strength, stability and resistance to atmospheric influences, but also demonstrate
good insulating properties [11]. Increased traffic levels, heavier loads, and extreme
weather conditions have urged road authorities to develop new, or advance existing
solutions, in order to improve the resistance of the road pavements to the adverse

The Use of Polyolefin Polymer Wastes in the Production of Bituminous …

753

effects of mechanical and environmental loading [12]. Recently, the utilization of
waste plastics in bitumen road construction has gained increasing interest for both
waste recycling and pavement performance enhancement [13].
Considering the fact that petroleum bitumen was and remains the main type of
binder used in road construction, roofing and waterproofing works, research on the
integration of plastic waste into bitumen materials is a relevant scientific direction
[14, 15].
The main components of plastic waste are polyethylene (PE), polypropylene (PP),
polyethylene terephthalate (PET), polyvinyl chloride (PVC) and polystyrene (PS).
Most prevalent types of waste plastic worldwide: the first place is occupied by PE
(more than 30%), the second and the third place are PP and PET (20% each), the
fourth place is PVC (about 14%), the fifth place is PS (about 8%), and other types
are about 8% [16].
Several studies have assessed the effects of storage stability on mixtures of
polyolefin plastic wastes (PE, PP and other types) and bitumen binders [17, 18].
Some authors report about phase separation during physical dissolution of polyolefin plastic waste in bitumen, which may lead to problems during transportation
and application of the binder in road construction [19, 20].
The above-mentioned information confirms the need for comprehensive research
in order to find optimal ways of incorporating the most common plastic waste (PE
and PP) into bitumen binders in order to minimize the risk of phase separation. This
determined the purpose of the study.

2 Purpose, Stages and Objects of the Study
The aim of this study is to find a rational way to use polyolefin plastic wastes obtained
from MSW processing to modify the properties of bitumen materials.
The experiment was carried out in four stages: During the first stage, the main
properties of the initial raw materials were selected and studied, namely: analysis of
the properties of road bitumen grade BND 50/70; drying and grinding of polymers
from MSW; spent industrial oil (grade I-20A) from the units of metal-cutting machine
tools was selected as a plasticizer. During the second stage, combined additives, based
on polyolefin polymers and a plasticizer (waste industrial oil) were prepared on a
laboratory unit. They were prepared by mixing followed by heat treatment at 120–
130 ° C with constant stirring for 1.5 h. During the third stage, compounding of road
bitumen grade BND 50/70 with the proposed combined additive was performed on
a laboratory unit at a temperature of 110–120 °C with constant stirring for 1.5 h.
During the fourth stage, testing of the main operational quality indicators of the
bitumen mixture was performed.
The objects of the study were polyolefin plastic wastes such as Expandable
Polyethylene Foam (hereinafter EPF); Low-Density Polyethylene (high-pressure
polyethylene) Film (hereinafter Film LDPE); Expandable Polypropylene Foam
(hereinafter EPF); Polyethylene wax PV-200 (hereinafter PE wax); Low Molecular

754

Y. A. Bulauka et al.

Fig. 2 The research objects

Weight Polyethylene with dropping point 75 °С is a waste product of petrochemical industry (hereinafter LMWPE). The research objects are shown in Fig. 2. Spent
industrial oil (grade I-20A) from the units of metal-cutting machine tools was used
as a plasticizer. Its characteristics were the following: kinematic viscosity at 40 °C:
42.35 mm2 /s, density at 20 °C: 887 kg/m3 , flash point in an open crucible: 229 °C,
pour point: − 16 °C.

3 Materials and Methods
In laboratory conditions, testing of the main operational quality indicators of bitumen
mixture was carried out: Ring-and-Ball softening point and Fraas breaking point;
Needle penetration at 25 °С; Elastic recovery at 25 °C; Resistance to hardening at
163 °C with increase in ring and ball softening point; Residual penetration; Mass
change; Flash point; Adhesion of gravel-sand mixture with bitumen (assessed by
the amount of bitumen remaining on the aggregate surface (%) after immersing in
boiling water); Plasticity interval (calculated as the range between the Ring-and-Ball
softening point and the Brittleness point), and the penetration index (calculated to
determine the structural and rheological type of the bitumen mixture). The calculation
of the Penetration Index (PI) was performed using the empirical formula (EN 12591):
PI =

20 · Tsp + 500 · lg P − 1952
Tsp − 50 · lg P + 120

(1)

where: P—Penetration of needle, 25 °С, × 0.1 mm; Т sp —Ring-and-Ball softening
point bitumen, °С.

The Use of Polyolefin Polymer Wastes in the Production of Bituminous …

755

4 Results and Discussion
The properties of the obtained bitumen compositions, modified with polyolefin
plastic wastes, in comparison with bitumen BND 50/70 produced by OJSC Naftan
and quality standards are presented in Table 1.
As a result, homogeneous final product was obtained when mixed with EPE,
EPP, PE wax and LMWPE. But during bitumen composition with Film LDPE phase
separation was noted. The most important characteristics of bitumen binders used
in building materials are temperature characteristics—Softening point and Fraas
breaking point. The softening point of bitumen is the temperature at which bitumen
softens enough to flow under specific test conditions. The tests are carried out using
the “Ring and Ball” method. The softening point of the binder determines the resistance to rutting, characterizes the degree of mobility and suitability of bitumen for
use in various temperature conditions, i.e. plastic and thermal properties of bitumen.
Analysis of the change in the Ring and ball softening point showed that compounding
the original bitumen with 3.5% wt. of polyolefin polymer additives and 10% wt. of
waste industrial oil I-20A leads to a decrease of this indicator by 5 °C for EPE, Film
LDPE and EPP, by 12 °C for LMWPE, which is probably due to the predominance of
the softening function of the plasticizer. The drop in the softening point of bitumen
mixtures is associated with an increase in the oils/asphaltenes ratio due to the large
amount of plasticizer in the bitumen. The Ring and ball softening point increases
when modifying the original bitumen with PE wax dissolved in I-20A. The obtained
sample of polymer-bitumen composition satisfy the requirements of EN14023 for
the PMB 90/150-45 grade. Probably, PE wax adsorbs I-20A and forms a separate
dispersed phase, which leads to an increase in viscosity and, as a consequence, heat
resistance of the bitumen. The obtained results show that the proposed polymermodified bitumen (obtained by using recycled plastics such as PE wax EPE, Film
LDPE, EPP) is suitable for warm temperate climate and moderate traffic loads. The
analysis of the increase in ring and ball softening point of bitumen after resistance
to hardening at 163 °C test showed that the integration of polyolefin polymers leads
to an increase in the softening temperature from 2 to 13 °C. The maximum increase
of the indicator up to 31% was established for Film LDPE. At the same time, the
increase in ring and ball softening point of bitumen after resistance to hardening at
163 °C test meets the requirements of standards (except for Film LDPE).
Needle penetration or depth of needle penetration into bitumen is a conventional
indicator, a characteristic of the value of inverse viscosity, an indicator of bitumen
fluidity, which determines the degree of its hardness. The depth of needle penetration
into bitumen was determined using a penetrometer device when a 100 g load was
applied to the needle for 5 s at a temperature of 25 °C. The higher the viscosity of the
bitumen is, the deeper the needle will penetrate into the bitumen. It has been established that compounding the original bitumen with 3.5% wt. of polyolefin polymer
additives and 10% wt. of spent industrial oil I-20A leads to an increase in needle
penetration from 2.4 to 3.6 times, i.e. the hardness of the bitumen is significantly
reduced, which is a consequence of the formation of an elastic structural network in

−7
54
1.06

≤− 8

–

− 1.5 − +0.7

Fraas breaking point [°C] EN
12593

Plasticity interval [°C]
(TR&Bsp –TFraass ) EN 14023

Penetration Index EN 12591,
Annex A

a PMB

≥ 50

≤ 0.5

≤ 10

≥ 50

≥ 235

− 1.5 − + 0.7

–

0.01

9.5

> 235

0.11

59.5

− 17.5

≥ 45

≤−18

152

EPE

0.08

> 235

0.07

−8

158

Film LDPE

0.04

> 235

0.44

−9

116

EPP

0.08

> 235

− 0.27

− 15

120

PE wax

0.03

> 235

0.65

53.5

− 18.5

177

LMWPE

Compositions 3.5% wt. polymer: 10% wt. oil I-20A:
86.5% wt. bitumen BND 50/70

90–150

Value for grade PMB 90/
150–45a specification EN14023

90/150–45 contains styrene-butadiene-styrene (SBS) copolymer, which significantly increases the price of the bitumen, due to high costs of the polymer

0.01

≤9

Increase in ring and ball
softening point [°C] EN 1427

Mass change [%] EN 12607–1 ≤ 0.5

≥ 50

> 235

Residual penetration at 25 °C
[%] EN 1426

Resistance to hardening at
163 °C EN 12607–1:

Flash point open cup, [°C] EN ≥ 230
ISO 2592

–

Elastic recovery at 25 °C [%]
EN 13398

46–54

Ring and ball softening point
[°C] EN 1427

Actual
49

50–70

Specification EN 12591

Value for grade BND 50/70

Penetration at 25 °C, 100 g,
5 sec, [0.1 mm] EN 1426

Main factors

Table 1 Properties of the obtained bitumen compositions, modified with polyolefin plastic wastes, in comparison with commercial bitumen and quality standards

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Y. A. Bulauka et al.

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757

the entire volume of the bitumen due to the stretching of polyolefin macromolecules
in the maltene part of the bitumen and softening of the bitumen by spent industrial
oil. The maximum increase in needle penetration is set for LMWPE, the minimum
for EPP. The obtained samples of polymer-bitumen compositions with EPP and PE
wax comply with the requirements of EN14023 for the PMB 90/150–45 grade.
After resistance to hardening at 163 °C test penetration increases in all samples,
however the change in penetration complies with the requirements of the standards.
Mass change after Resistance to hardening at 163 °C test for all tested samples
satisfies with the requirements of the standards, minimal loss still ensures quality
during application.
The Flash point open cup value for all the samples tested complies with the
standards and comes up to 235 °C, which provides safe heating margins for bitumen.
The Penetration Index is an indicator characterizing the degree of colloidality of
bitumen or the deviation of its state from being purely viscous. With equal Penetration, the higher the softening temperature is, the higher the Penetration Index will
be. In order to avoid obtaining bitumens with low ductility, the upper value of the
penetration index is limited. According to the penetration index (PI), bitumens are
divided into three groups: PI less than − 2, sol-type bitumens; PI from − 2 to + 2,
sol-gel-type bitumens; PI more than + 2 have colloidal properties of “gels” For the
samples being studied the calculation of the indicator which characterizes thermal
sensitivity of bitumen binders (the Penetration Index) was performed using formula
(1). All samples of compounded bitumen with 3.5% wt. of polyolefin polymer additives and 10% wt. of waste industrial oil I-20A fall within the required penetration
index range from − 1.5 to + 0.7 according to EN 12591 and EN14023. The dispersed
structure of the obtained polymer-bitumen compositions is the closest to the sol-gel
type, which is optimal from the point of view of the road bitumen quality.
The behavior of bitumen under the influence of external deforming forces is determined by rheological properties (elasticity, plasticity, creep and strength). These
properties change significantly when bitumen is heated and cooled. In terms of
Elastic recovery at 25 °C all samples of compounded bitumen with 3.5% wt. of
polyolefin polymer additives and 10% wt. of waste industrial oil I-20A comply with
the requirements of EN14023.
An important indicator of bitumen is its Ductility—this is the ability of bitumen
to stretch into thin threads at a constant rate in a water bath at 25 °C under the
influence of an applied tensile force. The stretchability (ductility) is characterized by
the absolute elongation before breaking the thread of the bitumen sample (in the form
of a figure eight) at a temperature of 25 °C, determined on a device—a ductilometer.
Ductility at 25 °C characterizes the plasticity of viscous bitumen, making it capable
of withstanding minor surface stresses without cracking. High elastic properties of
viscous bitumen are observed with significant content of resins, optimal content of
asphaltenes and oils and insignificant content of carbenes and carboids, the absence of
mechanical impurities. The greater the stretchability is, the more elastic the bitumen
will be. It will better adhere to dry surfaces when applied in molten state and it will
have better gluing properties.

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Y. A. Bulauka et al.

Fig. 3 Ductility at 25 °C for the samples being studied

The measured Ductility values at 25 °C for the samples being studied are shown
in Fig. 3.
Analysis of the change in Ductility at 25 °C showed that with the addition of
polyolefin polymers, the stretchability of bitumen worsens in all samples (except
LMWPE), the bitumen becomes less elastic, probably due to the fact that the polymer
macromolecules are not distributed in the bitumen in the form of a framework, but are
presented in the form of curled balls, acting as stress concentrators and contributing
to the breakage of the bitumen thread.
At sub-zero temperatures, bitumen becomes brittle. Fraas breaking point is the
temperature at which the material is destroyed under the action of a short-term
applied load. Fraas breaking point characterizes low-temperature properties of the
bituminous binder, i.e. its susceptibility to brittle fracture at negative temperatures
[21]. The Fraas breaking point characterizes the behavior of bitumen in the coating:
the lower it is, the higher the quality of the bitumen will be. Breaking point is
determined by the Fraas method and involves cooling, periodic bending of a bitumen
sample and determining the temperature at which cracks appear or the sample breaks.
The Fraas breaking point of the binder largely determines crack resistance at subzero temperatures. The Fraas breaking point of bitumen should not be higher than the
lowest temperature of the year in a given region. The obtained results show that in all
samples of compounded bitumen with 3.5% wt. of polyolefin polymer additives and
10% wt. of waste industrial oil I-20A the Fraas breaking point decreases, i.e. the frost
resistance of bitumen compositions improves. Probably, polymers, while distributing
in the free dispersed phase of bitumen, lead to interstructural plasticization, i.e.
increase the mobility of the spatial dispersed structure, without reducing its strength.
The use of polyolefin polymer additives allows obtaining bitumen with good lowtemperature properties, as a result, the road surface will work better in cold weather
conditions. The maximum depression t 11.5 °С is set for LMWPE. The different
depression t is probably due to the fact that the polyolefin polymers LMWPE, EPE
and PE wax are distributed in the form of a network in bitumen at low temperatures,
while the macromolecules of Film LDPE and EPP, due to the high molar mass of the
polymers, are distributed in the form of curled globules.
The Plasticity interval is the temperature range between the Ring and ball softening
point and Fraas breaking point (TR&Bsp –TFraas ). The wider this range is, the wider the
temperature range will be in which bitumen is in elastic-viscous state, the better the

The Use of Polyolefin Polymer Wastes in the Production of Bituminous …

759

bitumen works in road or insulation coatings and in other options for its use. Bitumens
with a wide Plasticity interval behave better than others at elevated temperatures,
they resist shear deformation well in hot weather and hot climates; they also exhibit
good adhesion to the surface of mineral material. Bitumens that contain a lot of
resins and aromatic oils have a wide Plasticity interval. Analysis of construction
and operational experience of asphalt-concrete pavements in various microclimatic
regions shows that for the construction of the upper layers of road pavements, binders
with a plasticity range of 60 …90 °C should be used, and for the lower layers of
pavements, binders with a plasticity range of 50 …70 °C are suitable.
The Plasticity interval of all samples of compound bitumen with 3.5% wt. of
polyolefin polymer additives and 10% wt. of waste industrial oil I-20A meet the
necessary requirements. The polymer framework of polyolefin polymers provides,
on the one hand, strength, absence of fluidity at the increased temperature and, on
the other hand, deformation properties at the decreased temperature, expanding the
range of performance of bitumen materials and, as a result, increasing its quality and
service life.
The adhesion of modified bitumen to the surface of mineral material was studied;
the analysis was performed on a sand and gravel mixture with fractions from 2 to
5 mm. Samples of the original and modified bitumen before and after boiling for
30 min are shown in Fig. 4.
The deterioration of adhesion is due to the fact that polyolefins have the poor
compatibility with asphalt because of the nonpolar nature and high degree of crystallinity. Satisfactory adhesion was noted (the surface of the mineral material is

Fig. 4 Results of adhesion analysis on sand and gravel mixture: a bitumen without additives,
b bitumen with I-20A and film LDPE; c bitumen with I-20A and EPP; d bitumen with I-20A and
foamed EPE, e bitumen with I-20A and PE wax; f bitumen with I-20A and LMWPE

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covered with bitumen by more than ¾) for EPP and EPE. The inclusion of an adhesive
agent will improve adhesion to the mineral filler.

5 Conclusions
Thus, as a result of the conducted research on the use of plastic wastes in the production of bitumen materials, it was established that the integration of such polyolefin
polymer wastes as Expandable Polypropylene Foam, Expandable Polyethylene Foam
and Polyethylene wax dissolved in waste industrial oil into the bitumen binder allows
to increase its heat resistance and frost resistance, the plasticity range of bitumen also
expands. In general, the conducted studies confirmed the potential for use of recycled plastic waste in the production of bitumen materials for non-critical construction
projects. The use of polymer waste in bitumen production contributes to the development of a circular economy, within which materials are recycled and given a new
purpose in road construction, thereby reducing the impact on the environment.

References
1. Khajuria A, Verma P, Vella A, et al. (2025) The SDG accelerator: circular economy solutions
through efficient sustainable consumption. J Circular Economy 4(2):100140. https://doi.org/
10.1016/j.cec.2025.100140
2. UNEP (2025) Answers 10 questions about plastic pollution. https://news.un.org/ru/story/2025/
05/1464046
3. Ali S, Elsamahy T, Koutra E, et al. (2021) Degradation of conventional plastic wastes in the
environment: a review on current status of knowledge and future perspectives of disposal. J.
Sci Total Environ 771:144719. https://doi.org/10.1016/j.scitotenv.2020.144719
4. Liu L, Xu M, Ye Y, Zhang B (2022) On the degradation of (micro)plastics: degradation methods,
influencing factors, environmental impacts. J Sci Total Environ 806(3):151312. https://doi.org/
10.1016/j.scitotenv.2021.151312
5. Kumar V, Singh E, Singh S, As P, Bhargava P (2023) Micro- and nano-plastics (MNPs) as
emerging pollutant in ground water: environmental impact, potential risks, limitations and way
forward towards sustainable management. Chem Eng J 459:141568. https://doi.org/10.1016/j.
cej.2023.141568
6. Zhou W, Huang D, Chen S, Wang G, et al. (2024) Microplastic dilemma: assessing the
unexpected trade-offs between biodegradable and non-biodegradable forms on plant health,
cadmium uptake, and sediment microbial ecology. J Hazard Mater 477:135240. https://doi.
org/10.1016/j.jhazmat.2024.135240
7. Saliu F, Veronelli M, Raguso C, Barana D, Galli P, Lasagni M (2021) The release process of
microfibers: from surgical face masks into the marine environment. J Environ Adv 4:100042.
https://doi.org/10.1016/j.envadv.2021.100042
8. Jeswani H, Krüger C, Russ M, Horlacher M, et al. (2021) Life cycle environmental impacts
of chemical recycling via pyrolysis of mixed plastic waste in comparison with mechanical
recycling and energy recovery. J Sci Total Environ 769:144483. https://doi.org/10.1016/j.sci
totenv.2020.144483
9. Pilapitiya PGCNT, Ratnayake AS (2024) The world of plastic waste: a review. J Clean Mater
11:100220. https://doi.org/10.1016/j.clema.2024.100220

The Use of Polyolefin Polymer Wastes in the Production of Bituminous …

761

10. Jayarathne T, Stockwell C, Bhave P, et al. (2018) Nepal ambient monitoring and source testing
experiment (NAMaSTE): emissions of particulate matter from wood- and dung-fueled cooking
fires, garbage and crop residue burning, brick kilns, and other sources. Atmos Phys 18(3):2259–
2286. https://doi.org/10.5194/acp-18-2259-2018
11. Yadav N, Kanwar P, Mandpe A (2025) Beyond landfills: transforming waste plastic into
advanced building materials. In: Environmental hazards of plastic wastes bioremediation
approaches for environmental clean-up. Chap 16, pp 249–260. https://doi.org/10.1016/B9780-443-23599-3.00023-X
12. Santos J, Cerezo V, Soudani K, Bressi S (2018) A comparative life cycle assessment of hot
mixes asphalt containing bituminous binder modified with waste and virgin polymers. Procedia
CIRP 69:194–199. https://doi.org/10.1016/j.procir.2017.11.046
13. Lan J, Leng Z, et al. (2025) A chemical method to upcycle waste polypropylene into bitumen
compatible modifier by polyol grafting through reactive extrusion. J Clean Prod 517:145831.
https://doi.org/10.1016/j.jclepro.2025.145831
14. Lebedzeva T, Bulauka Y (2020) Polymer-modifier for the road bitumen manufacture of the
fourth generation. In: Topical issues of rational use of natural resources. 2019 proceedings of
the XV international forum-contest of students and young researchers under the auspices of
UNESCO, vol 2, pp 546–552. https://doi.org/10.1201/9781003014638-10
15. Stalmakh D, Bulauka Y, Yakubouski S, Shulha E (2021) Complex of technology for processing
heavier cut of pyrolysis gas oil. In: Conference proceedings 2021. European Association of
Geoscientists & Engineers. pp 1–5. https://doi.org/10.3997/2214-4609.202150056
16. Wang Z, Ye L, Chen F, Zhou T, Zhao Y (2024) Multi-category sorting of plastic waste using
Swin transformer: a vision-based approach. J Environ Manag 370:122742. https://doi.org/10.
1016/j.jenvman.2024.122742
17. Polacco G, Filippi S, Merusi F, Stastna G (2015) A review of the fundamentals of polymermodified asphalts: asphalt/polymer interactions and principles of compatibility. J Adv Colloid
Interf Sci 224:72–112. https://doi.org/10.1016/j.cis.2015.07.010
18. Liang M, Xin X, Fan W, Wang H (2019) Phase field simulation and microscopic observation
of phase separation and thermal stability of polymer modified asphalt. J Constr Build Mater
204:132–143. https://doi.org/10.1016/j.conbuildmat.2019.01.180
19. Liang M, Xin X, Fan W, Wang H, et al. (2019) Phase behavior and hot storage characteristics
of asphalt modified with various polyethylene: experimental and numerical characterizations.
J Constr Build Mater 203:608–620. https://doi.org/10.1016/j.conbuildmat.2019.01.095
20. Nouali M, Ghorbel E, Derriche Z (2020) Phase separation and thermal degradation of plastic
bag waste modified bitumen during high temperature storage. J Constr Build Mater 239:117872.
https://doi.org/10.1016/j.conbuildmat.2019.117872
21. Gajewski M, Horodecka R, Bañkowski W, Grzegórska A, et al. (2023) Evaluation of the
effect of processed plastic additives on the properties of paving grade bitumen. Roads Bridges
22:287–307. https://doi.org/10.7409/rabdim.023.015

The Directions of Complex Utilization
of Ash and Slag Waste of Thermal Power
Plants
N. M. Zaichenko, I. Yu. Petrik, L. G. Zaichenko, and D. Yu. Bukina

Abstract This study summarizes the basic environmental and technical problems,
connected with current strategy of recovery of usable materials from ash and slag
waste (ASW) of coal-fired power plants. The directions of complex utilization of
ASW have been elaborated. In accordance with X-ray diffraction analysis it was
determined that the predominant phase of slag component of ASW is an amorphous
silicate glass and almost all aluminum oxide is in the amorphous phase. This is a decisive factor in the solubility of aluminum oxide in alkaline solutions and the synthesis
of water-resistant hydroaluminosilicates of the R2 O·Al2 O3 ·(2–4)SiO2 ·nH2 O type.
Thus, a new direction for the application of the slag component of ASW (in a milled
state) might be used as a precursor of geopolymer binders. It has been established
that heat treatment increases the compressive strength of the geopolymer binder
based on ponded ash as well as on milled slag. Both types of binders show the
greatest activity after autoclave treatment. Compared to steamed samples, compressive strength increases by 1.8 times, up to 27 MPa for fly ash based binder and up to
60 MPa for milled slag based binder. The result of dry triboelectrostatic separation
of ponded ash containing a high percentage of unburned carbon is the production
of beneficiated pozzolanic additive for concrete, characterized by improved granulometric and phase composition. It is the way to use the beneficiated ponded ash in
formulations of High-Volume Fly Ash Concrete. Besides, the results obtained indicate that the part of ponded ash remained after the beneficiation process contains
a high percent of unburned carbon and has a high capacity to adsorb and remove
various pollutants from water, in particular phosphates.
Keywords Fly ash · Ponded ash · Slag · Utilization · Geopolymer binder · Water
remediation

N. M. Zaichenko (B) · I. Yu. Petrik · L. G. Zaichenko · D. Yu. Bukina
Donbas National Academy of Civil Engineering and Architecture, Makeyevka, Russia
e-mail: n.m.zaichenko@donnasa.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_61

763

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N. M. Zaichenko et al.

1 Introduction
The results of studies have shown that global consumption of coal used as a fuel
in combustion processes is continuously increasing [1], as a result the amount of
coal combustion waste is also rising. Hundreds of million tons of ash and slag waste
are generated by thermal power plants in Russia and around the world yearly [2].
For instance, Dwivedi and Jain reported [3] that a 500 MW thermal power plant
releases 200 mt SO2 , 70 t NO2 and 500 t fly ash approximately every day. Studies
have shown that landfill of ASW of coal-fired power stations follows the current
dominant strategy, however, it has serious environmental problems [4–6]. As it has
been noted in [7] long storage of ash in ponds under wet conditions could cause
leaching of toxic metals that contaminates the underlying soil and ultimately the
groundwater systems. Thus, ash and slag waste pose a serious threat to the ecology
of industrial regions [8, 9].
According to the “Strategy for the Development of the Building Materials Industry
for the Period up to 2020 and the Further Prospects up to 2030 of Russian Federation”
[10] one of the priority areas in innovative technologies of building materials is the
production of low-clinker composite and cement-free binders. Thus, it can safely be
concluded that ash and slag waste is a valuable resource material for various applications to reduce the disposal into the environment [3, 9, 11]. However, a relatively
small percentage of materials finds its application as ingredients in cement and other
construction products. Literature review [4, 9] summarizes a number of barriers to
the complex utilization of ash and slag waste of thermal power plants. The main
barriers are related to the technical aspects of fly ash and slag formation and thus,
materials properties, which could vary widely depending on combustion conditions
and collector setup [5].
Another significant barrier to solve the problem of sustainable development of
regions where electricity is generated by burning coal is the requirement for an integrated approach to the disposal of ash and slag waste, i.e. the maximum depth of
processing. It is widely known that mineral additive fly ash as a “fresh waste” [2] is
usually used in the production of cement, as well as in concrete compositions, while
ash accumulated in ash dumps is rarely used in construction technologies. This is
due to the deterioration of ash quality when it stored in wet dumps and, as a result,
non-compliance with standard requirements occurs (for example, EN 450-1 for use in
concrete) [12–14]. The possibility of using ponded ash as a mineral additive with the
required homogeneity on granulometric and chemical–mineralogical composition is
ensured by the applied processing technology known as beneficiation. The secondary
waste (coarse fractions of mineral phase, unburned carbon) formed during beneficiation, for example, by electrostatic separation [12], does not find further application.
The use of slag component of ASW is considered mainly as a fine or coarse aggregate
for normal weight concrete of limited strength classes.
These factors prompt the researchers to search alternative ways of ASW utilization, other than their usage in the construction industry. The trends are the following:
production of lightweight aggregate [4], geopolymer binders [1, 15–19], molded

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765

composite polymer material [1], conversion of fly ash into zeolites [1, 4, 5, 11, 15],
usage as a low-cost adsorbent for wastewater treatment [1, 4, 5, 11, 15, 20–22], mine
back filler [1, 15] or road sub-base lay [1, 4, 5], at soil remediation [4, 5] etc. Thus, this
study is an attempt to elaborate the directions for complex utilization of ash and slag
waste of thermal power plant dumps (this is the objective of current investigation)
to be used as a precursor of geopolymer binder (milled slag), pozzolanic additive in
High-Volume Fly Ash Concrete (beneficiated ponded ash), and promising adsorbent
for water remediation (secondary waste of beneficiated process).

2 Background
2.1 Properties of Ash and Slag Waste
Studies have shown [1, 3, 4, 23] that fly ash consists of fine particles generally spherical in shape, either solid or hollow, and mostly amorphous in nature with various
identifiable crystalline phases such as α-quartz, mullite, hematite, and magnetite.
The physical properties of fly ash range between the following values: the average
particles size of 10–100 microns, the density of 2.00–2.20 g/cm3 , the bulk density
of 540–860 kg/m3 , the surface area of 300–500 m2 /kg, and the pH value of 1.2–12.5
[1, 5]. The main chemical components of class F fly ash are silica, alumina, iron and
calcium oxides, alkalis as Na2 O + K2 O, and some amount of carbon, as measured
by the values of loss on ignition (LOI) [4, 11]. Besides, it is important to note that
almost all of the aluminum oxide is in the crystalline phase in fly ash. The percentage
of carbon in fly ash depends on the conditions during combustion as well as on the
chemical composition and ash content of coal. The values for the LOI are reported
from less than one to more than 20% [12].
Slag as a part of ash and slag waste is a molten inorganic material removed from
the boiler [1], moreover, the liquid removal slag is 100% vitrified. Slags particles, due
to their lower porosity in comparison to fly ash and polyfractional composition, have
the density of 2.8–3.3 g/cm3 , and the bulk density of 1100–1350 kg/m3 . Slag is often
used as a fine aggregate (sand replacement—slag grains ranging in size from 0.315
to 5 mm) and coarse aggregate (slag grains, over 5 mm). At once, the value for the
LOI of dense slag used for coarse or fine aggregate of concrete is not standardized.

2.2 Alkali-Activated Materials on the Base of ASW (Milled
Slag)
As discussed elsewhere [1, 15–17] the alkali-activated materials (AAMs) based on
ASW, sometimes referred to as geopolymers, can be considered as green binders and
an alternative to the Portland cement in terms of their cost, physical and mechanical

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N. M. Zaichenko et al.

properties as well as lower environmental impact [18]. This is due to the fact that
AAMs production process is lower by up to 70% in CO2 eq. emissions compared to
Portland cement concrete [16].
Alkali-activated binders (geopolymers) are composed of an aluminosilicate
powder (precursor) activated by alkaline substances (generally in liquid form) [17,
18]. Concrete made with fly ash-geopolymer binders is renowned for its high
compressive strength, minimal creep, high acid resistance, and reduced shrinkage
[16, 19]. However, the kinetics of alkaline activation (geopolymerization) depends
on the chemical and phase composition of ASW [24]. The content of aluminosilicate glass has a decisive effect on the binding properties of ASW. If the glass is not
cooled quickly, it can crystallize the phase of mullite and some other compounds. As
mentioned by Kozhukhova et al. [6], the content and composition of soluble mineral
components in fly ashes from different power plants are varied in a wide range.
On the other hand, slag is formed from a fiery liquid silicate melt of the mineral
matter of the fuel. Rapid increase in viscosity of the melt with a temperature decrease
determines low crystallization capacity, a tendency to supercooling and transition to
a glassy form. As a result, the predominant phase of slag is amorphous silicate glass.
In addition, it’s very important that almost all aluminum oxide in the slag is in
an amorphous phase. This is a decisive factor in the solubility of aluminum oxide
in alkaline solutions and the synthesis of water-resistant hydroaluminosilicates of
the R2 O·Al2 O3 ·(2–4)SiO2 ·nH2 O type. Thus, a new direction for the application of
the slag component of ASW (in a milled state) might be its use as a precursor of
geopolymer materials.

2.3 High Volume Fly Ash Concretes Based
on the Beneficiated Ponded Ash
According to [17] at existing pace, the cement industry will be emitting CO2 at
a rate of 3.5 billion tons per year by 2025. As discussed by Z. Giergiczny [23]
“one of the most efficient and realizable methods to reduce environmental impact
associated with the production of cement (concrete) is to widen the use of cement
constituents other than Portland cement clinker…”. There are essentially two ways
of fly ash application. Firstly, as active mineral additive in the production of pozzolan
cements and, secondly, as the partial replacement of Portland cement in concrete [8,
12]. A number of scientists have reported on positive results of studies of concretes
containing 65–80% of fly ash (High-Volume Fly Ash Concrete) [25]. This type
of concrete is much more sustainable as compared to traditional Portland cement
concrete.
However, some fly ash waste may contain a higher percentage (up to 20%) of
unburned carbon, which significantly restricts their use as an additive in concrete.
The maximum allowable value of the LOI according to EN 450-1 lies between 5.0 and
9.0% [12]. It has been proven [12] that dry triboelectrostatic beneficiation is one of

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767

the most efficient methods used for separation of unburned carbon from the mineral
fraction. The results of our previous study [26], have indicated that triboelectrostatic beneficiation of ponded ash provides obtaining the low-carbon mineral additive
meeting technical requirements for its use in High-Volume Fly Ash Concretes.

2.4 Application of Fly Ash Waste in Wastewater Treatment
The literature review summarizes that fly ash could be used as an effective adsorbent
for water remediation to remove dyes, toxic metals, and various organic and inorganic
compounds from wastewater [1, 5, 15, 20, 21]. This effect is due to the unique
characteristics of fly ash, such as open porosity, large specific surface area, high LOI
content and other properties.
A lot of work has been done on adsorption of phenolic compounds from wastewater. Recently, fly ash has shown good adsorption capacity for phenolic compounds
[4, 15]. Various researches were performed in order to know the dependency of
contact time, carbon content, and other parameters of fly ash during the adsorption
of various phenols [11]. The electrostatic interaction between the positively charged
carbon presenting on the fly ash surface and the ionized phenol molecules characterizes the adsorption. Besides, according to [11] the presence of Al, Fe, Ca and Si
cations on the surface of fly ash make it viable for the removal of phosphate ions
from wastewater.
However, adsorption performance of fly ash strongly depends on its origin and
chemical composition. Besides, the use of fly ash as an adsorbent is still in early
stage and detailed studies are needed. Up to date, no industrial scale application has
been realized [15, 22].

3 Materials and Methods
The chemical composition and physical properties of the ASW from Zuevskaya
Power Plant (separately for ash and slag components) and Portland cement (CEM I
42.5 N) used are presented in Table 1. The chemical composition of ASW indicates
that according to ASTM C618-22 “Standard Specification for Coal Fly Ash and
Raw or Calcined Natural Pozzolan for Use in Concrete” [27] the ponded ash and
slag correspond to F Class.
Geopolymer binders have been prepared by mixing 8-M NaOH solution with
ASW precursor (ponded ash or milled slag). All cement pastes had the similar
workability varying within the range of 160–165 mm on the flow table.
After mixing binding pastes were cast into 50 mm cube moulds, compacted on
a vibration table and subjected to heat treatment at elevated temperature of 95 °C
as well as at elevated temperature of 173 °C and elevated pressure of 0.8 MPa for

768

N. M. Zaichenko et al.

Table 1 The chemical composition and physical properties of ASW and Portland cement used
Chemical
composition and
properties

Portland cement

Ponded ash

SiO2 (%)

23.7

43.4

Al2 O3 (%)

4.3

20.8

= 76.1

Slag

50.2

= 85.3

27.5

Fe2 O3 (%)

5.2

12.1

7.6 + 8.1 (FeO)

CaO (%)

62.1

3.2

2.3

MgO (%)

0.3

1.7

1.4

SO3 (%)

2.5

0.9

0.2

P2 O5 (%)

0.3

0.1

TiO2 (%)

1.2

0.4

Alkalis as Na2 O +
K2 O (%)

0.7

4.7

2.1

LOI (%)

1.1

11.7

0.2

Fineness (sieve >
80 μm, %)

4.8

7.5

6.8

Specific surface area
(Blaine) (m2 /kg)

315

295

304

Density

3.1

2.2

2.6

12 h. After the thermal treatment, the geopolymer specimens were kept at 20 ± 1 °C
temperature and relative humidity of 55 ± 5% until testing on compressive strength.
The chemical oxides composition of fly ash and slag samples was determined
using an ARLOptim’X wave X-ray fluorescence spectrometer. The phase composition of ASW was studied by X-ray diffraction with the help of 26 ARL X’TRA
X-ray diffractometer using CuKα radiation (λ = 1.54056 Å). The scanning was
carried within 10°–60° 2-theta range with a step of 0.02°.
The investigation of the granulometric composition and morphology of ASW
particles was performed using a high-resolution scanning electron microscope under
vacuum conditions TESCAN MIRA 3 LMU with energy-dispersive spectrometer
(EDS), equipped with two types of detectors: both secondary electrons (SE) and
backscattered electrons (BSE).
Triboelectrostatic separation of ponded ash was carried out with the help of freefall chamber plate electrostatic separator [26].
The study of adsorption of potassium phosphate on the surface of ASW has been
carried out in accordance with GOST 18309-2014 “Water. Methods for determination of phosphorus-containing matters” [28]. The method is based on the hydrolysis
of polyphosphates, which are converted into orthophosphates with the formation of a
phosphorus-molybdenum complex, colored blue, and subsequent photometric determination of the resulting-colored compound at 690–720 nm wavelength. Orthophosphates initially present in the sample are determined separately, their content is
subtracted from the result obtained when determining polyphosphates.

The Directions of Complex Utilization of Ash and Slag Waste …

769

The model solution of certain phosphate concentration (V = 50 mL) was poured
into 200 mL conical flasks, and then the samples of ponded ash were added and
mechanically mixed for 15 min. After settling, the solutions were centrifuged in
a rotary centrifuge, then filtered through Blue Ribbon paper filters and finally the
residual concentration of phosphates in the filtrate was measured. The mass concentration of phosphates was determined using an Expert-003 photometer (Russian
Federation).

4 Results and Discussion
4.1 Compressive Strength of Geopolymer-Binders Based
on ASW
Compressive strength values of ASW geopolymer binders are shown in Fig. 1. In
accordance with [17] the significant factors affecting the mechanical strength are
always the temperature of curing and the type of activator. On the other hand,
an equally important factor in strength is the activity of the binder precursor. As
expected, the hardening process (geopolymerization) at room temperature does not
provide high values of compressive strength of alkali-activated binder on the base of
ponded ash or milled slag.
Apparently heat treatment accelerates the chemical reactions of geopolymerization, thus improving the compressive strength of the ASW geopolymer binder.
Mechanical strength of cubes cured at 95 °C is much higher than those cured at 20 °C.
Both types of binders show the greatest activity after autoclave treatment. Compared
to steamed samples, compressive strength increases by 1.8 times, up to 27 MPa for
ash-based binder and up to 60 MPa for milled slag-based binder.
The results also give a comparison between two types of precursors used. The
significantly higher strength of the slag-based binder is due to at least two factors.
Firstly, the denser structure of the slag particles and the absence of unburned carbon
60
Compressive strength, MPa

Fig. 1 Effect of the type of
precursor from ASW and the
mode of heat treatment on
the compressive strength of
geopolymer binder

a) t=20°C

b) t=95°C

c) t=173°C, p=0.8 MPa

50
40
30
20
10
0
Fly ash

Milled slag
The type of precursor

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N. M. Zaichenko et al.

Fig. 2 a X-ray diffraction patterns of the ponded ash; b X-ray diffraction pattern of the slag.
Q—quartz; M—mullite; H—hematite

provide lower water demand for the cement paste compared to the ash-based sample.
It means that to provide the same workability of cement pastes the amount of water
added to slag paste should be less than the amount added to fly ash one. On the
other hand, the activity of precursor in the form of milled slag is much higher in
comparison with the ponded ash precursor.
Despite the chemical composition close enough in terms of oxide sum (SiO2 +
Al2 O3 + Fe2 O3 ), the slag component contains more the initial oxides like silica
and alumina. The XRD patterns of ponded ash and slag show a couple of broad
peaks (halo) in the range of 14.9–15.6 and 30.7–31.2° (2 theta), which is typical of
amorphous phases (Fig. 2). On the other hand, if the slag component of the ASW
is practically amorphous, then the ponded ash, in addition to the amorphous phase,
contains the crystalline matters in the form of α-quartz, mullite and hematite also.

4.2 The Properties of Beneficiated Ponded Ash
The results obtained by using laser granulation analyzer indicate that the granulometric composition of ponded ash has been improved after electrostatic separation
(beneficiation) process. Thus, for the original ponded ash, the particle size distribution is in the range from 0.3 to 200 μm, the median particle size d50 = 19.89 μm,
maximum particle size d98 = 76.46 μm, the percentage of fine fractions (particles
smaller than 2 μm) is 7.64%. After electrostatic separation, a narrower particle distribution range is observed—from 0.3 to 100 μm, d50 = 17.93 μm, d98 = 66.58 μm,
the percentage of fine fractions is 8.01%.
The analysis of structural features using scanning electron microscopy (SEM) in
combination with energy-dispersive X-ray spectroscopy (EDX) made it possible to
evaluate the efficiency of electrostatic ash separation in terms of separating unburned
carbon particles. The images were obtained using SEM in secondary electrons (SE),
which reflects the structural features of the aggregates, and in backscattered electrons
(BSE), which characterize the difference in phase composition (phases and areas
with a lower average effective atomic number are colored in darker shades). Thus,
on microphotographs of the original ash (Fig. 3a), dark large particles (aggregates)
of carbon in size from 10 to 150 µm are clearly recorded (point C). Unlike spherical,

The Directions of Complex Utilization of Ash and Slag Waste …

771

smooth-relief aluminosilicate particles, carbon inclusions have a porous structure
and irregular grain shape.
Chemical composition of the material (gross sample), in wt.%, calculated as
100%, is presented in Table 2—the content of unburned carbon (LOI) is 11.73%.
The results of EDX analysis (Fig. 3b) show variations in the elemental composition (Table 2)—the point 2 corresponds to aluminosilicate glass, while point 1 is
represented predominantly by iron oxide and point C by carbon. SEM picture with
EDX analysis of the beneficiated ash (Fig. 3c, d) show a fairly high homogeneity
both in terms of particle size distribution and chemical composition—aluminosilicate spheroids predominantly in the range from 1 to 20 μm with a small presence of
iron oxides, agglomerated clusters are not observed. Losses on ignition are practically
absent, as evidenced by the data presented in Table 2. Besides, if for the initial ash the
sum of oxides (Al2 O3 + SiO2 + Fe2 O3 ) is 76.06%, then after beneficiation their total
content increased up to 86.10%, which should have a positive effect on increasing
pozzolanic activity of the mineral additive. Thus, it brings the possibility to use the
beneficiated ponded ash in formulations of High-Volume Fly Ash Concrete.

4.3 Study of Phosphate Adsorption on Ponded Ash Surface
The results of the present investigation (Fig. 4a) indicate a higher adsorption capacity
of phosphates on the beneficiated ponded ash from the model liquid with an initial
concentration of C1 = 4.7 mg/L. The phosphate content decreases by 40% after
30 min of contact with the ash, and after 60 min the degree of purification reaches
72%. With a higher concentration of the model liquid solution C2 = 9.7 mg/L,
the degree of purification from phosphates after 30 and 60 min is 18.6 and 17.5%,
respectively.
When the initial (non-beneficiated) ponded ash is used as an adsorbent the degree
of purification increases, more significantly for the model liquid with a phosphate
concentration of C1 = 4.7 mg/L (Fig. 4b). After 30 min of contact with ash, the
phosphate content decreases by 57% and after 60 min the degree of purification
reaches 74%. With a higher concentration of the model liquid solution C2 = 9.7 mg/
L, the degree of purification from phosphates after 30 and 60 min is 25 and 26%,
respectively.
This phenomenon probably is due to the fact that non-beneficiated ponded ash has
much more the content of LOI (Table 2). In this case apart adsorption of phosphates
on the surface of ponded ash absorption of the substance into the pores of unburned
carbon particles also occurs.

Fig. 3 Scanning electron microscope photomicrograph and EDX diagrams of the initial ponded ash a, b and beneficiated ponded ash c, d

772
N. M. Zaichenko et al.

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773

Table 2 The chemical composition of the initial ponded ash used in the study and the beneficiated
sample
SiO2

Al2 O3 Fe2 O3 CaO

MgO SO3 K2 O Na2 O TiO2 MnO P2 O5 LOI

The
sum

(a) Ponded ash as received (gross sample)
43.17 20.84

12.05

3.17 1.72

0.98 3.61 1.06

1.23

0.17

0.28

11.73 100.00

0.12

0.13

–

100.00

5.04

0.02

–

100.00

1.33

0.15

0.22

1.38

0.65 0.33 0.49

0.27

0.29

–

100.00

1.46 0.24 0.23

0.82

0.06

1.45

–

100.00

0.47 4.16 1.46

0.42

0.04

0.02

–

100.00

(b) Ponded ash as received (EDX point 1)
0.88

1.76

97.02

0.10

Ponded ash as received (EDX point 2)
57.29 29.11

2.31

0.44 1.07

0.02 3.45 1.24

14.76

2.61 1.68

2.18 3.18 1.08

99.90

(d) Ponded ash beneficiated (EDX point 1)
15.04 11.32

69.62

0.90 0.82

Ponded ash beneficiated (EDX point 2)
37.10 22.00

8.58

22.79 5.27

The concentration of phosphate, mg/l

49.50 35.14

7.57

0.33 0.89

y = 0.0011x2 - 0.0927x + 9.62
R² = 0.9772

8
7
6
5
4

0.0007x2

- 0.0991x + 4.6486
R² = 0.9966

2
1
0
0

20
30
40
Adsorption time, min

(a)

The concentration of phosphate, mg/l

Ponded ash beneficiated (EDX point 3)

y = 0.0014x2 - 0.1211x + 9.7086
R² = 0.9971

8
7
6
5
4
y = 0.001x2 - 0.1183x + 4.6771
R² = 0.9985

3
2
1
0
0

20
30
40
Adsorption time, min

(b)

Fig. 4 Adsorption of phosphates on the surface of the beneficiated ponded ash a and initial ponded
ash b, C1—initial concentration of phosphates 4.7 mg/L; C2—9.7 mg/L

5 Conclusion
This study has attempted to elaborate the directions of complex utilization of ash and
slag waste of thermal power plant dumps:
• The slag component of ASW is practically amorphous, unlike ponded ash which
consists mainly of amorphous phase with crystalline inclusions of α-quartz,
mullite, hematite, and other minerals. It could be used as an effective precursor
of innovative alkali activated binders (geopolymers)

774

N. M. Zaichenko et al.

• The result of beneficiation of ponded ash with high percentage of unburned carbon
is the production of enriched pozzolanic additive for concrete, characterized by
improved granulometric and phase composition. It gives the opportunity to use
the beneficiated ponded ash in formulations of High-Volume Fly Ash Concrete
• The part of ponded ash remained after the beneficiation process contains high
percentage of LOI and has a high capacity to adsorb and remove various pollutants from water. Since the unburned carbon separated from ponded ash is a
by-product, any practical application of such material would be economically
and environmentally advantageous to the overall ASW beneficiation process.

References
1. Kuznia MA (2025) A review of coal fly ash utilization: Environmental, energy, and material
assessment. Energies 18(52). https://doi.org/10.3390/en18010052
2. Lihach S, Ilyasova A, Kulesh R, Valentina V (2017) Utilization direction of industrial raw
products built-up in power station ash dumps. MATEC Web Conf 92:01074. https://doi.org/
10.1051/matecconf/20179201074
3. Dwivedi A, Jain MK (2014) Fly ash—waste management and overview: a review. Recent Res
Sci Technol 6(1):30–35
4. Ahmaruzzaman M (2010) A review on the utilization of fly ash. Prog Energy Combust Sci
36:327–363. https://doi.org/10.1016/j.pecs.2009.11.003
5. Ge JC, Yoon SK, Choi NJ (2018) Application of fly ash as an adsorbent for removal of air and
water pollutants. Appl Sci 8:1116. https://doi.org/10.3390/app8071116
6. Kozhukhova NI, Lebedev MS, Vasilenko MI, Goncharova EN (2019) Toxic effect of fly ash
on biological environment. IOP Conf Ser: Earth Environ Sci 272:022065. https://doi.org/10.
1088/1755-1315/272/2/022065
7. Gitari MW, Petrik LF, Reynolds K (2011) Chemical weathering in a hypersaline effluent irrigated dry ash dump: an insight from physicochemical and mineralogical analysis of drilled
cores. Energy Sci Technol 2(2):43–55. https://doi.org/10.3968/j.est.1923847920110202.110
8. Khudyakova LI, Zalutskiy AV, Paleev PL (2019) Ispolzovanie zoloshlakovyh othodov teplovyh
elektrostantsiy (use of ash and slag waste of thermal power plants) XXI century. Technosphere
Saf 4(3):375–391. https://doi.org/10.21285/2500-1582-2019-3-375-391
9. Gorai S (2018) Utilization of fly ash for sustainable environment management. J Mater Environ
Sci 9(2):385–393
10. Strategy for the Development of the Building Materials Industry for the Period up to 2020 and
the Further Prospects up to 2030 of Russian Federation) (2016) Order of the Government of
the Russian Federation No. 868-r dated 10 May 2016
11. Meenakshi KSVL, Bhargav A, Yasaswi K et al (2023) Adsorbing prospects of fly ash—a
review. J Emerg Technol Innov Res 10(1):e363–e379
12. Lanzerstorfer C (2018) Fly ash from coal combustion: dependence of the concentration of
various elements on the particle size. Fuel 228:263–271. https://doi.org/10.1016/j.fuel.2018.
04.136
13. Lee S-J, Cho H-C, Kwon J-H (2012) Beneficiation of coal pond ash by physical separation
techniques. J Environ Manage 104(15):77–84. https://doi.org/10.1016/j.jenvman.2012.03.034
14. McCarthy MJ, Jones MR, Hope TA et al (2019) Innovative processing of stockpile fly ash.
Working Draft Report, University of Dundee
15. Singh NB, Agarwal A, De A, Singh P (2022) Coal fly ash: an emerging material for water
remediation. Int J Coal Sci Technol 9:44. https://doi.org/10.1007/s40789-022-00512-1

The Directions of Complex Utilization of Ash and Slag Waste …

775

16. Komkova A, Habert G (2023) Environmental impact assessment of alkali-activated materials:
examining impacts of variability in constituent production processes and transportation. Constr
Build Mater 363:129032. https://doi.org/10.1016/j.conbuildmat.2022.129032
17. Shi C, Fernández Jiménez A, Palomo A (2011) New cements for the 21st century: the pursuit
of an alternative to Portland cement. Cem Concr Res 41:750–763. https://doi.org/10.1016/j.
cemconres.2011.03.016
18. Coffetti D, Crotti E, Gazzaniga G et al (2022) Pathways towards sustainable concrete. Cem
Concr Res 154:106718. https://doi.org/10.1016/j.cemconres.2022.106718
19. Nordin N, Al Bakri Abdullah MM, Tahir MFM et al (2016) Utilization of fly ash waste as
construction materials. Int J Conserv Sci 7(1):161–166
20. Jinping LI, Jinhua G, Guangkun W et al (2016) Research on adsorbent using modified fly ash
for campus domestic sewage treatment. MATEC Web Conf 67:07003. https://doi.org/10.1051/
matecconf/20166707003
21. Gorbacheva TT, Maiorov DV (2022) Sorption of ammonium ions from aqueous solutions on
the ash and slag of a CHP plant. Solid Fuel Chem 56(4):276–284. https://doi.org/10.3103/S03
61521922040048
22. Ahmaruzzaman M (2011) Industrial wastes as low-cost potential adsorbents for the treatment
of wastewater laden with heavy metals. Adv Colloid Interface Sci 166(1–2):36–59. https://doi.
org/10.1016/j.cis.2011.04.005
23. Giergiczny Z (2019) Fly ash and slag. Cem Concr Res 124:105826. https://doi.org/10.1016/j.
cemconres.2019.105826
24. Shekhovtsova J, Zhernovsky I, Kovtun M et al (2018) Estimation of fly ash reactivity for use in
alkali-activated cements—a step towards sustainable building material and waste utilization. J
Clean Prod 178:22e33. https://doi.org/10.1016/j.jclepro.2017.12.270
25. Durán-Herrera A, Juárez CA, Valdez P, Bentz DP (2011) Evaluation of sustainable high-volume
fly ash concretes. Cem Concr Compos 33:39–45. https://doi.org/10.1016/j.cemconcomp.2010.
09.020
26. Zaichenko N, Petrik I, Zaichenko L (2020) Beneficiated ponded fly ash for concretes with high
volume mineral additions. MATEC Web of Conf 315:07006. https://doi.org/10.1051/matecc
onf/202031507006
27. ASTM C618-22 (2022) Standard specification for coal fly ash and raw or calcined natural
Pozzolan for use in concrete. ASTM International, American Society for Testing and Materials,
USA
28. GOST 18309-2014 (ISO 6878:2004, NEQ) (2014) Water. Methods for determination of
phosphorus-containing matters, Standardinform, Moscow

Study of Oxygen Transfer from Air
to Water Depending on Suspended
Matter Concentration in Water
M. Dyagelev

Abstract The article considers the impact of suspended matter concentration on
the efficiency of oxygen transfer from air to water under different air flow rates. The
authors present experimental data on the dynamics of oxygen saturation obtained in
laboratory conditions under different air flow rates (1, 3, 5 L/min) and concentrations
of suspended matter, including ceramic sand (0.25, 0.5, and 1 g/L). The results
signify that higher suspended matter concentrations can reduce oxygen saturation
because of the increased mass transfer resistance on the gas–liquid interface due to
the film formation and particle adsorption. Simultaneously, increasing the air flow
rate (from 1 to 5 L/min) can partially compensate for the negative effects caused by
the suspended matter and reduce the oxygen saturation time. The calculated α и β
coefficients confirm that the efficiency of mass exchange is especially sensitive to
the suspended matter concentration and can be adjusted by air feed, while oxygen
solubility (the β factor) remains virtually the same.
Keywords Airflow rate · Dissolved oxygen · Oxygen transfer dynamics · Water
treatment · Oxygen mass transfer · Suspended solids

1 Introduction
Aeration is a fundamental process in wastewater treatment systems that significantly
intensifies biochemical reactions and improves the quality of the treated water. This
method is based on the saturation of water with oxygen to provide optimal conditions
for aerobic microorganisms [1]. The key aeration function is providing a medium
for microorganism breathing, which, in turn, accelerates metabolic processes and
improves the efficiency of mass exchange processes. This helps improve the contact
between microorganisms and dissolved and suspended organic compounds in the
wastewater [2].
M. Dyagelev (B)
Kalashnikov Izhevsk State Technical University, Izhevsk, Russia
e-mail: m.yu.dyagelev@istu.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_62

777

778

M. Dyagelev

Modern aeration technologies used in treatment facilities are characterized by
high efficiency and economic feasibility [3]. These technologies play a crucial role
in water resource preservation, environmental impact mitigation, and compliance
with regulations on the quality of wastewater before its further disposal or reuse.
Thus, aeration is a key component of a complex wastewater treatment system. It
helps achieve high environmental safety parameters and facilitates sustainable water
resource management. This makes aeration a central element in the environmental
protection and rational natural resource usage strategy.
Dissolved oxygen (DO) is a fundamental parameter in the water quality assessment at aerobic treatment facilities, namely aerotanks designed for wastewater treatment. Maintaining the optimal level of dissolved oxygen is critical for the metabolic
activity of aerobic microorganisms that is crucial in the biodegradation of organic
and inorganic pollutants [4].
However, achieving and maintaining the required DO concentration is a complex
technical and economic problem. The main challenge is the energy consumption
associated with aeration. Saturating wastewater with oxygen requires significant
amounts of electricity, which calls for the development of effective optimization
methods for oxygen mass transfer in water [5, 6].
Adjusting the air flow in an aerotank has a significant impact on the efficiency
of aeration and, consequently, on the quality of wastewater treatment. The reduction
of air flow results in inhibited nitrification, lower dissolved oxygen concentration,
increased filamentous bacteria populations, and the accumulation of excessive activated sludge in the system. On the other hand, increased air flow and, consequently,
increased dissolved oxygen concentration in wastewater help reduce the sludge index
through the intensification of mixing and aeration [7, 8]. However, this approach is
associated with increased energy consumption, which requires searching for optimal
aeration modes [6, 9]. These modes have to maintain a balance between wastewater
treatment effectiveness and its economic feasibility. Thus, controlling the DO level is
a complex engineering and biological problem that requires a systemic approach and
detailed analysis of all aeration peculiarities. The optimization of aeration parameters is a key factor in improving the effectiveness and efficiency of aerobic treatment
facilities. This, in turn, is important for the sustainable development of water supply
and sewage systems, and minimizing negative environmental impacts.
During real aerotank operation, the effectiveness of wastewater aeration may
drop periodically. The transfer of suspended matter from sand traps and primary
settling tanks to the working area of the aerotank is the key factor affecting the
wastewater aeration effectiveness. The transfer of suspended matter may be attributed
to a set of various factors, including increased amounts of incoming wastewater,
technical defects in the mechanical treatment stage, incorrect adjustment of scraper
mechanisms, as well as other operational factors [7]. These deviations may have a
significant influence on the efficiency of aeration systems and inhibit the oxygen
mass transfer from the atmosphere to the water. As a result, oxidation processes
decline, leading to the reduction in the overall effectiveness of biological wastewater
treatment.

Study of Oxygen Transfer from Air to Water Depending on Suspended …

779

To study the dependency between the air-to-water oxygen transfer and the
suspended matter concentration, we prepared a schematic and developed an experimental rig to run several trials with different air flow levels and different suspended
matter concentrations. Therefore, this research focused on the dynamics of oxygen
transfer during aeration in clear water and water with suspended matter in the
laboratory rig.

2 Theoretical Basics of Oxygen Transfer Dynamics
in Water
The transfer of oxygen in water is a complex physical and chemical process involving
air bubble incorporation, resulting in the mass oxygen transfer from gas to liquid. This
process continues until a thermodynamic balance is reached, where the free energy
of the system is at a minimum. The gas–liquid interface boundary is a dynamic area
that includes both gas and liquid phase elements, as well as the interface surface
[10, 11].
The fundamental models of mass transfer are based on theories of film and diffusion kinetics [12]. The mathematical description of mass transfer through the interface area, which depends on specific mass transfer conditions and mechanisms, is
a key aspect of these models. The film model stipulates that oxygen is transferred
through a thin liquid film surrounding air bubbles, while the diffusion model focuses
on the molecular diffusion of oxygen through the interface area [13].
Note that the mass transfer of oxygen in water depends heavily on factors like
temperature, pressure, surface tension, and the physical and chemical properties of
dissolved substances [1, 14]. Another important factor is the turbulence in the water
that may affect the effectiveness of mass transfer significantly [15]. The speed of
oxygen transfer is generally expressed as follows [16]:
dM
= KL · A · (Cs − Ct )
dt

(1)

where K L is the liquid film coefficient (m/h), A is the cross-section area through
which diffusion takes place (m2 ), C s is the concentration of oxygen in water during
saturation (mg/L), and C t is the concentration of oxygen in water at moment t (mg/
L).
The mass transfer of oxygen in an aerotank is a physical and chemical process
involving mechanisms like diffusion and convective transport through the gas–liquid
interface boundary [17]. This process is key to maintaining the optimal conditions
for aerobic microorganisms and forming the required chemical composition of water.
The rate of oxygen transfer through a gas film is in direct proportion to the oxygen
concentration gradient and its diffusion rate [18]. Modeling oxygen mass transfer
processes facilitates the forecasting of aeration system effectiveness, the optimization
of design parameters of equipment and operating modes, and the development of new

780

M. Dyagelev

intensification methods for these processes [19]. Considering the volume of the tank
in Eq. (1), the mass balance equation can be written down as follows:
1 dM
KL · A · (Cs − Ct )
·
=
V dt
V

(2)

For practical purposes, we calculate the overall gas transfer coefficient K L a so that
Eq. (3) can be written down as the following rate equation:
dC
= KL α · (Cs − Ct )
dt

(3)

where K L α is the overall transfer coefficient measured in h−1 , and a stands for the
ratio of A and V.
In terms of wastewater treatment, α and β factors are the key parameters characterizing the rate of oxygen mass transfer [1]. The alpha factor is the ratio of oxygen
absorption rates in wastewater and clear water. It is crucial for the correct analysis and
design of aeration systems [20]. This parameter helps consider the specific impact
of physical and chemical properties of wastewater on oxygen mass transfer, which is
essential for facilitating effective biochemical treatment. The presence of organic and
inorganic dissolved solid matter in wastewater has a significant impact on the solubility of oxygen. To account for this, the beta factor is introduced that reflects changes
in oxygen solubility depending on the concentration of dissolved solid matter. This
allows for the greater modeling precision of oxygen behavior in real-life wastewater and improved aeration processes [21, 22]. The accurate calculation of the α and
β factors is crucial for the development and optimization of a wastewater treatment
system. They are used to improve the oxygen transfer effectiveness and treated water
quality, and achieve greater environmental safety standards. The α factor is calculated
using Eq. (4):
α=

KL αin wastewater
KL αin clean water

(4)

Similarly, the β factor is used to adjust the impact of the concentration of dissolved
and solid matter in wastewater on the solubility of oxygen. As a rule, the solubility
of oxygen in wastewater is less effective than its transfer to clear water [1, 23, 24].
The β factor is calculated using Eq. (5):
β=

Cs
Dissolved Oxygen Saturation concentration in wastewater
=
Dissolved Oxygen Saturation in clean water
Ct

(5)

Study of Oxygen Transfer from Air to Water Depending on Suspended …

781

3 Materials and Methods
To obtain the dependency between the effectiveness of aeration systems and the
content of suspended matter, we prepared a schematic and developed the experimental rig shown in Fig. 1. The rig had to measure the parameters required for the
oxygen transfer model, such as supplied air flow and oxygen saturation rate of water,
in real time.
The experimental rig was made with a round PVC pipe with an external diameter
of 110 mm, a 2.2 mm thick wall, and a length of 1500 mm. The service volume
of the rig was 40 L. The air was supplied with a TORNADO 580 compressor to a
fine-bubble disc aerator, and the flow rate of the air was a constant 35 L/min. The
50-mm aerator was installed at the base of the pipe and attached to it. The average
size of air bubbles in the aerator was 0.35 ± 0.15 mm. To adjust the flow of supplied
air, a flowmeter capable of controlling air flow between 0 and 5 L/min was connected
to the pressure air line with an adapter sleeve.
The oxygen probes of the Multi 340i multiparameter analyzer were used to
measure the concentration of dissolved oxygen in water. At the beginning of each
experiment, reagent water deaeration was performed using sodium sulfite. When
the concentration of oxygen in the water reached zero, the compressor was turned
on, and the time until the water was saturated with oxygen to the initial level was
measured. The suspended matter consisted of cleaned and sintered expanded clay
sand with sizes ranging from 0.01 to 0.1 mm.
Before each series of experiments, the system was test-launched with controlled
air feed on the flow meter, after which the valve located between the flow meter and
the aerator was closed to create positive pressure in the supply air duct and prevent
the ingress of water from the vertical element of the rig to the air duct.
The experiments were conducted at a constant air flow. We conducted a series of
experiments with flow rates of 1, 3, and 5 L/min, first with supply water and then
(a)

Fig. 1 a Experimental rig schematic; b experimental rig

(b)

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M. Dyagelev

with water infused with expanded clay sand at rates of 10, 20, and 40 g of sand
concentrations in water of 0.25, 0.5, and 1 g/L.

4 Results and Discussion
The impact of suspended matter concentration on the oxygen dissolution rate is a
critical factor. The transfer of oxygen from air to solution occurs when air bubbles
contact water, where the interface layer is saturated with oxygen, which facilitates
the diffuse transfer of gas to other layers of water. The mass transfer coefficient K L α
depends on the size of bubbles, oxygen concentration gradient, diffusion time, and
quality of incoming water. Suspended matter affects the mass transfer of oxygen
through several mechanisms. Research shows that the presence of suspended solid
particles causes additional resistance to mass transfer over the gas–liquid interface.
Particles may form films on the interface surface that serve as a mechanical barrier
for oxygen transfer. High particle concentration creating turbidity affects oxygen
transfer by creating additional resistance. Suspended matter may also be absorbed
on the interface border, thus reducing the surface’s permeability to oxygen.
The three-experiment series analyzed saturation with oxygen for clear supply
water and water with sand concentrations of 0.25, 0.5, and 1 g/L. The flow rate of air
in each series was the same. In the first series of experiments, it was 1 L/min, in the
second series, it was increased to 3 L/min, and in the third series, it was increased
to 5 L/min. The obtained values of oxygen saturation curves for water are shown in
Fig. 2.
The comparison of the obtained charts shows that the most significant differences are observed in the initial stage of the process (during the first 300 s). With a
flow rate of 1 L/min, any concentration of suspended matter resulted in a dramatic
17% inhibition of the process compared to the clear water. When the flow rate was
increased to 5 L/min, this inhibition varied 0 to 22% depending on the concentration. The compensation capacity of high air flow rates was more prominent with low
suspended matter concentrations (0.25 g/L). In these conditions, the flow rate of 5 L/
min can completely compensate for the negative impacts of turbidity and ensure the
same saturation time as with clear water.
Increased air flow rate has different effectiveness depending on water quality.
In clear water, the shortest time to achieve the initial saturation is 450 s for a flow
rate of 1 L/min. When the flow rate was increased to 3 and 5 L/min, the saturation
time reduced to 390 and 360 s, respectively (see Table 1). With suspended expanded
clay sand particles, the situation does not change dramatically: the transfer improved
along with increasing air flow rate in all three series. The oxygen saturation time was
reduced from 510 s for 1 L/min to 420 s for 3 L/min and 360 s for 5 L/min for water
with a concentration of sand of 0.25 g/L. Thus, the saturation rate increase reached
17.6 and 29.4% respectively. When the concentration of sand was increased to 0.5 g/
L, there were no changes at an air flow rate of 1 and 3 L/min, and the saturation time
amounted to 510 s. As the air flow rate increases to 5 L/min, the oxygen saturation

Oxygen concentration in water,

mg/L

Sand concentration 0.25 g/L

(c)

Sand concentration 0.5 g/L

Sand concentration 1 g/L

30 60 90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600
Time, s

Clean water

(b)

8
6
4
2
0

Clean water
Sand concentration 0.5 g/L

Sand concentration 0.25 g/L
Sand concentration 1 g/L

Time, s

Sand concentration 0.25 g/L
Sand concentration 1 g/L

Time, s

Fig. 2 The change dynamics of oxygen concentration in water with the set air flow rate and different sand concentrations in water: a 1 L/min; b 3 L/min; c 5 L/
min

Oxygen concentration
in water, mg/L

Oxygen concentration in
water, mg/L

0
30
60
90
120
150
180
210
240
270
300
330
360
390
420
450
480
510
540
570
600

(a)

Study of Oxygen Transfer from Air to Water Depending on Suspended …
783

784

M. Dyagelev

time of water reduces to 480 s, which provides a saturation rate increase of 5.8%.
When the concentration of sand in water increased to 1.0 g/L, the saturation rate
increased by 11.7% for the flow rate increase from 1 to 3 L/min, and 21.1% for the
air flow rate increase from 1 to 5 L/min.
Thus, all three experimental series demonstrated that the increase in the air flow
rate has a direct impact on the reduction of oxygen saturation time of water. The
increased concentration of suspended expanded clay sand also resulted in increased
oxygen saturation time of water while preserving the dependency between the
reduction of the saturation time and the flow rate of supplied air.
Experimental data on the oxygen saturation of water with different air flow rates
and sand concentrations were used to calculate the α and β factors according to
Eqs. (4) and (5). Table 2 presents the results of the calculations.
The analysis of α factors shows that when the flow rate is 1 L/min, the effectiveness
of mass transfer has the greatest reduction: for sand concentrations in water of 0.25 g/
L, 0.5 g/L, and 1 g/L, the loss of effectiveness amounted to 16.3%, 25.1%, and 28.5%
respectively. When the flow rate of the supplied air was increased to 3 L/min, the
Table 1 Water saturation time with different concentrations of sand and aeration modes
Condition

Saturation time (s)
Flow rate: 1 L/min

Flow rate: 3 L/min

Flow rate: 5 L/min

Clear water

450

390

360

Sand, 0.25 g/L

510

420

360

Sand, 0.5 g/L

510

480

Sand, 1.0 g/L

570

510

450

Table 2 Final calculation results for α and β factors
Air flow
rate (L/
min)

Sand concentration (g/ K L α
L)

α factor

β factor

Effectiveness loss
(%)

30.43

0.25

25.47

0.8371

0.9986

16.3

0.5

22.78

0.7487

0.9986

25.1

21.75

0.7148

0.9972

28.5

32.9

0.25

30.4

0.9241

7.6

0.5

24.19

0.7353

26.5

25.00

0.7599

24.0

34.85

0.25

32.23

0.9249

7.5

0.5

26.59

0.7628

23.7

27.54

0.7901

0.9986

21.0

Study of Oxygen Transfer from Air to Water Depending on Suspended …

785

impact of suspended matter became less critical: for sand concentrations in water
of 0.25 g/L, 0.5 g/L, and 1 g/L, the loss of effectiveness amounted to 7.6%, 26.5%,
and 24.0% respectively. Increased air flow rate reduced the impact of suspended
matter on oxygen saturation of water, especially with low sand concentrations, where
effectiveness losses amounted to 7.5%, 23.7%, and 21.0% for sand concentrations
in water of 0.25 g/L, 0.5 g/L, and 1 g/L, respectively.
The analysis of the β factor shows that β factors have minimal deviations from
1, which indicates an insignificant impact of suspended matter on oxygen solubility.
All values of the β factor are within the range of 0.9972–1, while the maximum
solubility change is ± 0.3%. With a flow rate of 3 and 5 L/min, the β factors were
practically equal to 1.000.
The statistical analysis of the calculated values of α and β factors for the experiments with sand concentrations in water of 0.25 g/L provides an α factor value of
0.8954 ± 0.0412 and a β factor value of 0.9995 ± 0.0007, as well as a mean effectiveness loss of 10.5%. When increasing the concentration of sand in water to 0.5 g/
L, the α factor value is reduced to 0.7489 ± 0.0112, while the value of the β factor
is increased to 1.0000 ± 0.0002. The mean effectiveness loss, in this case, is also
increased to 25.1%. A twofold increase of the sand concentration in water (up to
1.0 g/L) did not have a significant impact on the average value of the α factor, which
made 0.7549 ± 0.0309, or the β factor, which equaled 0.9986 ± 0.0012, while the
mean efficiency loss amounted to 24.5%.
The correlation analysis of the dependency between α and β factors and the
suspended matter concentration and air flow rate showed a strong negative correlation between the α factor and the concentration of sand in the water (r = from −
0.60 to − 0.90) and a positive correlation with the air flow rate (r = 0.51 − 0.99). The
strongest correlation was observed with a concentration of 1.0 g/L (r = 0.9936). The
β factor is only slightly affected by the concentration or air flow rate. All the β factor
values are within a narrow range of 0.997–1.001. The maximum deviation from 1
does not exceed ± 0.3%. When the flow rate was set at 3 and 5 L/min, β ≈ 1.000
was obtained irrespective of the sand concentration.

5 Conclusions
The conducted research and the analysis of the obtained data demonstrated that
the concentration of suspended matter in water is one of the key factors that can
significantly compromise the effectiveness of oxygen transfer during water aeration.
Suspended particles of expanded clay sand create mechanical barriers on the gas–
liquid interface, which results in a reduced oxygen diffusion rate in the liquid. The
obtained experimental results clearly demonstrate that increased suspended matter
concentrations may reduce oxygen saturation of water, thus increasing the time
required to obtain the desired dissolved oxygen level.
However, increasing the flow rate of the supplied air may significantly improve
the situation. When the air flow rate is high (5 L/min), the negative impacts of

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M. Dyagelev

low suspended matter concentrations can be compensated almost entirely, which is
confirmed by the reduction of the saturation time to a value close to that of clear
water. This gives a possibility of adjusting aeration parameters to provide the stable
operation of treatment facilities even when the water is turbid.
The α factor reflecting the relative effectiveness of oxygen mass exchange
compared to clear water showed a strong negative correlation with the suspended
matter concentration and a positive correlation with the air flow rate. These factors
need to be taken into account while designing or operating aeration systems to
ensure the optimal balance between treatment quality and energy consumption. At
the same time, the β factor responsible for the solubility of oxygen remains practically unchanged, which means that the impacts of kinetic aspects dominate those
of thermodynamic aspects. The results of this research stress the importance of the
comprehensive approach to aeration management, taking into account the physical
and chemical properties of wastewater, as well as processing equipment parameters.
The development and usage of models accounting for the α and β factors shall help
forecast and improve the effectiveness of the aeration system, which will, in turn,
reduce its power consumption and improve environmental safety.

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11. Herrmann-Heber R, Oleshova M, Reinecke SF, Meier M, Taş S, Hampel U, Lerch A (2024)
Population balance modeling-assisted prediction of oxygen mass transfer coefficients with
optical measurements. J Water Process Eng 64:105663. https://doi.org/10.1016/j.jwpe.2024.
105663
12. Campbell KA (2020) Physical and biological factors affecting oxygen transfer in the activated
sludge wastewater treatment process. Missouri University of Science and Technology, Missouri,
p 280
13. He Z, Petiraksakul A, Meesapya W (2003) Oxygen-transfer measurement in clean water. J
KMITNB 13(1):14–19
14. Pei W, Tang Z, Zhang J, Qu Z, Jiang H, Xing W, Chen R (2025) SiC ceramic membranes
for high-efficiency micron-sized bubble aeration. J Membr Sci 731:124240. https://doi.org/10.
1016/j.memsci.2025.124240
15. Hasan AH, Azahar NA, Muhamad MH (2025) Insights into aeration intensification in biofilm
reactors for efficient wastewater treatment. Water 17:1861. https://doi.org/10.3390/w17131861
16. Viktor B, Ustiuzhanin AV, Koroleva E (2019) Aeration for wastewater biological treatment:
updating foreign terms and abbreviations. Water Supply Sanit Tech 9:46–56. https://doi.org/
10.35776/MNP.2019.09.07
17. Sun W, Si Q, Zheng Z, Xuan Y, Zhou X, Wang P (2024) Effect of aeration on oxygen transfer
characteristics in integrated wastewater treatment systems utilizing mass transfer model and
computation fluid dynamics methods. Biores Technol 414:131588. https://doi.org/10.1016/j.
biortech.2024.131588
18. Sharma H, Nirmalkar N (2022) Enhanced gas-liquid mass transfer coefficient by bulk nanobubbles in water. Mater Today: Proc 57(4):1838–1841. https://doi.org/10.1016/j.matpr.2022.
01.029
19. Sakr M, Mohamed MM, Maraqa MA, Hamouda MA, Hassan AA, Ali J, Jung J (2022) A
critical review of the recent developments in micro–nano bubbles applications for domestic
and industrial wastewater treatment. Alex Eng J 61(8):6591–6612. https://doi.org/10.1016/j.
aej.2021.11.041
20. Dyagelev MY, Isakov VG, Grakhova EV (2019) α-factor experimental determination of aeration
system in aeration tanks. IOP Conf Ser: Mater Sci Eng (MSE) 687(6):066071. https://doi.org/
10.1088/1757-899X/687/6/066071
21. Cruz FC, Marouchos A, Bilton AM (2022) Experimental characterization of an oxygen transfer
model of a fine pore diffuser aerator. Aquacult Eng 98:102259. https://doi.org/10.1016/j.aqu
aeng.2022.102259
22. Levitsky I, Tavor D, Gitis V (2022) Micro and nanobubbles in water and wastewater treatment:
a state-of-the-art review. J Water Process Eng 47:102688. https://doi.org/10.1016/j.jwpe.2022.
102688
23. Ren J, Peng Q, Meng J, Ren L, Hui J, Cheng W (2025) Optimization of aerator design for
enhanced multiphase fluidization performance and oxygen transfer efficiency. Process Saf
Environ Prot 201(A):107443. https://doi.org/10.1016/j.psep.2025.107443
24. Tang B, Zhang W, Chen W, Tan W, Shi G, Qi H, Deng G (2024) Influence of aeration-induced
air–water interfaces on pollutant degradation in water treatment: a theoretical and experimental
study. Sep Purif Technol 347:127595. https://doi.org/10.1016/j.seppur.2024.127595

Integrated Safety Design of Cable Lines
and Communications
for the Development of Oil and Gas
Fields in Freezing Seas
D. Korolchenko and A. Shunko

Abstract The paper considers the main determining factors affecting the comprehensive safety of designing cable lines and communications for oil and gas fields in
the harsh Arctic conditions of the Russian Federation. The paper provides the main
concepts and terms on the topic of the study. In the conditions of insufficiency of
the existing regulatory documentation, the use of experimental studies is justified for
the purpose of effective development of structures, their deepening into the bottom
soil and the selection of the latest materials for extended underwater engineering
structures. These studies must necessarily be included in the scientific support for
the design and construction of oil and gas facilities of increased danger. The special
relevance of such studies is highlighted. Recommendations for use in design practice
at all stages of the implementation of projects for laying cable lines and communications for oil and gas fields in freezing seas are developed and provided. Provided
that a large volume of experimental studies on this topic is obtained, it is possible to
develop additions and clarifications to the current regulatory documents.
Keywords Cable lines · Communications · Oil and gas fields · Exaration · Arctic
regions · Seabed · Ice formations · Soil displacement

1 Introduction
At present, hydrocarbon raw materials are the main energy source. Availability of
energy resources in sufficient volume for successful economic activity will ensure
the economic recovery of the Russian Federation. In accordance with this, it seems
necessary to significantly increase the volume of oil and gas production. The solution to this problem is impossible without exploration and development of oil and
gas fields on the continental shelf of our country, and first of all, in the Arctic seas.
D. Korolchenko · A. Shunko (B)
Moscow State University of Civil Engineering, Moscow, Russia
e-mail: deletesh1@yandex.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_63

789

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D. Korolchenko and A. Shunko

Development of offshore fields, in modern conditions, is associated with the development and construction of ice-resistant oil and gas production hydraulic structures,
underwater wellhead complexes, laying pipelines, cable lines and communications,
as well as the construction of roadstead berths in open sea conditions for the shipment
of extracted raw materials as part of hydraulic structures of new cargo ports. Their
successful design depends on reliable methods for calculating natural environmental
factors that will act throughout the entire service life of these facilities in harsh
climatic conditions. In connection with the introduction of the latest technologies in
all areas of modern economic activity, it is necessary to update the existing regulatory framework, supplementing it with recommendations necessary for the practice
of designing facilities for the development of offshore hydrocarbon fields in the Arctic
seas. The solution to this problem is impossible without generalizing domestic and
world design experience and without conducting additional scientific research. The
purpose of the presented work is to develop recommendations for the comprehensive
safety of designing and laying underwater cable lines and communications for the
development of offshore oil and gas fields in freezing seas.

2 Relevance
Underwater structures are an integral part of offshore oil and gas fields. These
include, first of all, underwater wellhead complexes, pipelines, as well as cable line
systems and various communications in the form of separately laid cables. Basically, these are telegraph, telephone, power, control cable lines, Internet highways,
etc. [1]. In comparison, the bandwidth of satellite Internet is much lower than the
Internet highway laid along the seabed. Currently, about 200 private operators control
about 1 million km of underwater fiber optic cables. At the same time, underwater
cables are responsible for the transmission of about 97% of global traffic. According
to the International Cable Protection Committee (ICPC) (https://www.iscpc.org/),
about 15 million financial transactions are carried out through them daily, with a
total value of 10 trillion dollars [2]. Therefore, the laying of cable line and communication systems is quite relevant and in demand at the present time. Protecting
underwater pipelines, cable lines and communications systems from the effects of
drifting ice formations in freezing seas is a critical task. This task is solved by determining the depth of burial in the bottom soil. Burying pipelines, cable lines and
communications systems increases their service life, but also increases the cost of
their installation [3]. The limited information on damage to cable lines and communications systems by drifting ice formations (primarily hummocks and icebergs) is
due to the fact that there is currently insufficient experience in laying these structures on the shelf of freezing seas [4]. Nevertheless, in world practice, there are
frequent cases of damage to cable lines and communications systems by ice formations. For example, in January 2022, the American publication The Drive wrote that
the underwater fiber optic cable between the mainland of Norway and the Svalbard
archipelago in the Arctic Ocean was disabled or damaged. The cable supports the

Integrated Safety Design of Cable Lines and Communications …

791

Fig. 1 Formation of furrows on the seabed by ice formations: 1—a hummocky formation sitting
on the bottom (stamukha); 2—a drifting perennial hummocky formation (nesyak); 3—an iceberg
or an iceberg fragment

operation of a satellite station on Spitsbergen and provides broadband internet access
to the Arctic archipelago. In June 2023, a submarine cable was broken by Arctic ice
formations, causing problems with internet access in Alaska, indicating a potential
danger to communications if they were laid in this area. Drift ice drifted into shallow
waters, where it plowed the bottom, which destroyed the local ecosystem and cable
infrastructure [5].
An important detail of the ice situation in the Arctic and northern seas is the
presence of processes of impact of ice formations on bottom and coastal soils. In
places of direct contact of ice with the bottom, such impacts are accompanied by
exaration activity, leading to the formation of various sizes of disturbances in the
soil in the form of scars, furrows, burrs, outlined by ridges and shafts of soil material
shifted in the direction of ice movement [6, 7]. The development of offshore oil and
gas production in harsh Arctic regions will inevitably lead to increased damage to
various engineering structures by drifting ice formations. Therefore, at the stage of
designing underwater structures, it is necessary to study the types of ice formations,
their parameters and depth of penetration into the bottom soil, as well as the prevalence of furrows in the bottom soil from their keel parts over the area of the seabed
(Figs. 1, 2 and 3).

3 Theoretical Part
The design of underwater extended engineering structures exposed to ice action is
regulated by a number of regulatory documents of our country [9–16]. According to
these documents, the design depth of burial, established on the basis of engineering
surveys taking into account possible reorganizations of the seabed and coast along
the route, should ensure protection of extended underwater structures from damage
throughout the entire design service life [9]. In areas where ice may plough the
coastal soil, pipelines or communications should be buried to a depth exceeding the
depth of ice penetration into the soil [12]. Thus, the value of the maximum value

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D. Korolchenko and A. Shunko

Fig. 2 Ice formations furrow the seafloor in the Beaufort Sea off the coast of North America (photo
from a multibeam echosounder) [8]

Fig. 3 Furrows of the seabed by ice formations in the Kara Sea, in its southwestern part off the
coast of Russia [7]

of bottom damage by ice is a basic parameter determining the depth of burial of
underwater structures. At the same time, under exaration impact, structures may
experience loads not only as a result of their direct contact with ice, but also due to
the transfer of forces through the foundation soils. In this case, when the area of the
bottom soil uplift formed in the direction of ice movement captures the structure,
part of it ends up in the massif of the shifted soil. In these cases, the load on the
structure is determined by the pressure of the shifted soil of the uplift prism, and
its direction depends on the direction of the ice formation displacement. When the
structure is outside the uplift zone, its deformations are caused by deformations of
the soil massif loaded with ice. In this regard, in addition to determining the depth
of foundation, an assessment of the stress–strain state (SSS) of structures under

Integrated Safety Design of Cable Lines and Communications …

793

ice action should also be performed, taking into account the different depth of its
deepening. Despite the fact that the parameters of deepening largely determine the
operational reliability of extended structures and significantly affect the volumes
of underwater excavation work, which ultimately determines the cost-effectiveness
of construction, the issue of a reasonable choice of their value has not found due
coverage in the regulatory literature. Only general indications are given on the need
to take into account the factor of the impact of sea ice on underwater structures when
calculating their strength and stability [12], and the designation of the top elevation
of the buried oil and gas pipeline one meter below the plowing depth in accordance
with regulatory documents [9] is made without reference to specific construction
conditions.
The issue of the impact of various ice formations on bottom soils and buried
communications is not reflected in the main regulatory document in the field of
marine hydraulic engineering—SP 38.13330.2018. “Loads and impacts on hydraulic
structures (wave, ice and from ships)” [17].
As for foreign regulatory literature devoted to the issues of construction of marine
underwater structures and communications, here too the methodology for assessing
the magnitude of ice gouging and calculating structures for possible ice loads in
its process is present in general terms [18–23]. Among the methods used to assess
the impact of ice gouging on the bottom soil and underwater extended structures,
the leading place is occupied by in-kind studies. However, along with the obvious
advantages of direct measurements of the depth of gouging of the bottom, in-kind
methods are very labor-intensive and expensive, due to the need to carry out long-term
observations in selected promising areas, with the involvement of numerous technical
means [7]. In this regard, along with in-kind studies, computational and theoretical
methods for assessing the depth of gouging have become widespread, including the
use of computer calculation methods [24]. The use of this technique is possible only
if the values of the parameters established by the results of measurements in a specific
area are used in the calculations, which is associated with the need to conduct a large
complex of in-kind observations on site and which is not always possible to ensure.
For this reason, the statistical substantiation of many probabilistic dependencies used
in the calculations is currently difficult. In accordance with this, it seems to be quite
an interesting and most optimal way to determine the depth of underwater extended
structures in the ground, by conducting experimental studies.

4 Experimental Studies
Modeling the process of force action of the keel part of drifting ice formations
required the creation of a new experimental setup (Fig. 4) [25, 26]. During the experimental studies, the values of pressures and forces acting on the model of the cable
system were measured, as well as soil displacements at the keel of the ice formation
model during soil plowing. The obtained data from physical modeling will allow us to
verify the results obtained by calculation methods, and will provide the opportunity

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D. Korolchenko and A. Shunko

Fig. 4 General view of the experimental setup

to vary the calculations of the determining parameters: the geometric dimensions of
the ice formation, the angle of attack of the keel, the strength characteristics of the
keel, the characteristics of the soil, and others.
Calibration of the displacement measuring transducers was carried out by a direct
method and consisted of successively installing the model at a certain distance from
the measuring wall with a selected number of steps, taking readings from the displacement measuring transducers and calculating the calibration factors. As an example,
Fig. 5 shows the results of one of the calibrations of the displacement measuring
transducers. Calibration of the strain gauge force measuring transducers was carried
out on a press stand. The stand allowed loading the measuring transducers in the
range from 0 to 30 tons, with an error not exceeding 0.5%. The measuring transducers were successively loaded with a step of 1–2 tons, within the measurement
range, followed by unloading, also with a step of 1–2 tons. As an example, Fig. 6
shows the results of one of the calibrations of the force measuring transducers.
During the experiment, the results of the measurements of the model’s movement,
wall loads, horizontal driving forces and reactions of the vertical hydraulic cylinders
were visualized on the monitor screen. As an example, Fig. 7 presents the results of
one of the experiments in graphic form (Fig. 8). The ordinate axis shows the values
of the loads in tons, and the abscissa axis shows the movements of the model during
the experiment. The results of the experimental studies are presented in tabular form
(Table 1).

Integrated Safety Design of Cable Lines and Communications …

Fig. 5 Example of displacement sensor calibration

Fig. 6 Example of calibration of a load cell

Fig. 7 Example of implementation of sensors

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D. Korolchenko and A. Shunko

Fig. 8 Experimental research

5 Fire Safety of Cable and Communication Systems
Currently, fire safety of cable lines and communications is also one of the important
components of the integrated safety of oil and gas field facilities. In conditions of
large spatial extent, forced branching of cable transitions is dangerous, from the
point of view of fire load. In connection with the introduction of new materials and
technologies in the production of cable products, it seems necessary to assess the
stability of cable lines made of modern materials in fire conditions, in accordance
with current Russian regulatory documents. As is known, fire hazard is primarily
determined by the type of combustible material, as well as its quantity, therefore, all
oil and gas field facilities belong to the high-risk zone. In addition, it is necessary to
take into account that cable sheaths are made of polymeric materials; when burning,
they release chlorine, fluorine, bromine, sulfur dioxide and other elements into the air.
In humid conditions, they enter into chemical reactions, forming acids and alkalis.
As a result, due to these negative transformations, an additional corrosion hazard is
created for metal parts of oil and gas equipment of field facilities, which can lead
to loss of stability of supporting structures. Since all offshore hydraulic structures
are quite unique in their characteristics and require large investments in design and
construction, various accidents and emergencies due to the development of fires
to significant sizes will inevitably lead to significant financial losses and colossal
damage to the environment.
To power the power unit of one oil and gas field facility, at least 600 MW is
required. The number of power and control cables supplying electricity to it from
coastal bases can be, in general, up to 50 thousand pieces. Due to the large number of
cables, they are combined into cable systems that extend for many kilometers along
the seabed.
The occurrence of a fire on cable equipment, according to the definitions of extinguishing tactics, is classified as a complex fire. These are fires with a rapid increase
in temperature (growth rate—over 50°/min), high rate of fire spread, dense smoke, as
well as with the appearance of an increasing probability of electric shock. Of all the
fires that occur at electrical installations in our country, cases of cable line ignition

150

2.18

Distance to panel,
cm

Experiment
(average value)

1.854

Water-saturated
Calculation
soil, indenter speed
V = 1.7 sm/s
0.2

1.30

Experiment
(average value)
indenter speed V =
0.17 sm/s

0.95

1.72

Experiment
(average value)
indenter speed V =
1.7 sm/s

1.418

1.781

Calculation

Water-saturated
Calculation
soil, indenter speed Experiment
V = 0.17 sm/s
(average value)
indenter

Dry soil

100

2.8

2.463

1.65

1.943

2.50

2.33

2.596

0.8

0.35

0.2

Force on
panel, t

Indenter
force, t

Force on
panel, t

Initial contact of the
second panel shift prism

Formation of the first
shear prism

Table 1 Comparison of experimental and calculated data

7.1

6.488

4.35

4.005

6.20

5.45

5.821

Indenter
force, t

4.8

2.253

2.70

1.164

3.20

3.33

1.671

Force on
panel, t

Formation of the inverse
shear prism

15.1

16.56

15.6

16.56

17.7

18.0

16.56

Indenter
force, t

13.7

14.84

12.9

15.5

14.84

Force on
panel, t

Compression of a 40 cm
thick soil layer

Integrated Safety Design of Cable Lines and Communications …
797

798

D. Korolchenko and A. Shunko

Fig. 9 Cable sample before fire resistance test

reach 70% of the total volume. Therefore, it is extremely necessary to experimentally
develop methods for reducing the fire hazard for cable lines of oil and gas field facilities. First of all, this is the placement of cable lines in non-combustible materials
and boxes (capsule system). The material for the manufacture of the cable must have
the properties of appropriate fire resistance and low flammability, with the use of
intumescent fire-retardant paints [27]. Figure 9 shows a photo of fire tests [28] of the
VVGng (A)—FRLS 3*10 cable. The limiting condition of the cable was determined
in accordance with [29].
Table 2 shows the results of fire tests for cable combustion propagation.

6 Practical Significance and Suggestions
The development of any offshore oil and gas field, including a complex of various
types of hydraulic structures, cable systems and communications, is unique and nonstandard. The main recommendations have been developed, which can be classified
as general.
1. Conduct comprehensive full-scale engineering surveys in the area of future
construction.
2. Divide the route of cable or communications systems into sections.
3. Determine the estimated bottom slope angle α, average sea depth H, and the
length of the structure L for each section.
4. Based on engineering surveys, determine the distribution parameter k of the
depths of ice formations embedded in the ground for each section.
5. Determine the distribution parameter of the depths of ice formations embedded
above the pipeline, cable system or communications for each section, taking into
account the safety factor.
6. Determine the average length of the ice plowing furrow for each section.

VVGng
(А)—FRLS
3*1.5

VVGng
(А)—LS 5*4

VVGng
(А)—LS
5*1.5

No gaps

2 layers—1
fragment
40

Fire exposure
time, min

VVGng
(А)—LS
5*10

2 layers—1
fragment

1 layer—1
fragment

Number of
layers and
fragments in
each layer

No gaps

With a gap
distance of
3 cm

Mounting
configuration

VVGng
(А)—LS 3*4

VVGng
(А)—LS
3*1.5

VVGng
(А)—FRLS
3*10

Cable type

Cable category

Masonry group

Table 2 Fire test results

Burner number

1.31

1.39

1.17

1.33

1.27

1.34

1.39

Length of
damaged part,
m

–

1.1

1.2

(continued)

Time of
independent
combustion and
smoldering, min

Integrated Safety Design of Cable Lines and Communications …
799

Masonry group

Cable category

Table 2 (continued)

Fire exposure
time, min

VVGng
(А)—LS
1*10

Number of
layers and
fragments in
each layer
40

Mounting
configuration

VVGng
(А)—LS
3*10

Cable type

Burner number

1.53

1.44

Length of
damaged part,
m

Time of
independent
combustion and
smoldering, min

800
D. Korolchenko and A. Shunko

Integrated Safety Design of Cable Lines and Communications …

801

7. Based on engineering surveys, determine the average density of ice formation
(the number of ice formations per square kilometer per year).
8. Determine the mathematical expectation of the frequency of intersections of the
furrows of the pipeline or communication route for a given angle of inclination
of the structures.
With a uniform distribution of furrows on the sections, the ratio between the
frequency of formation of furrows ng and the frequency of intersection of the route n
can be determined from the standpoint of the theory of geometric probability using
the formula:
n = ng · E · [L · |sin(ψ)|],

(1)

where L is the length of the furrow, &#x0079; is the angle between the furrow and the
route of the pipeline or communication, E determines the mathematical expectation,
i.e. the average value of the quantities presented in brackets.
The average number of intersections of a unit of length of a pipeline or
communication is equal to:
naν =

2
π

· l · nν ,

where l is the average value of the furrow length, nv is the ratio of the density of
furrows per unit area of the sections from the impact of ice formations.
9. For a given diameter of a pipeline or cable system, determine the cost parameters
a and b [10, 16].
10. Specify the reliability level of the underwater structure (the probability of no
contact between the structure and the hummock), designated in the project.
11. Perform optimization calculations to determine the depth of burying underwater
structures below the seabed [9–16].
12. Take into account the amount of lithodynamic erosion.
13. At the preliminary design stages, the amount of additional burying of a pipeline,
cable system or communications relative to the seabed surface disturbed by ice
can be determined using the following relationship: = 0, 3·γn ·(1 + d ), where
γn is the reliability coefficient for the degree of responsibility of the structure,
adopted according to SP 58.13330.2019 [25]. At the same time, the requirement
for the value of the Δ, indicator, established for technological reasons at 1 m, in
force in regulatory documents, is retained.
For laying cables at fire-hazardous facilities of oil and gas fields, it is recommended
to be guided by the requirements of GOST 31565-2012 [30].
It is recommended to use cables at the specified facilities of the following types:
• NC—(non-flammable)—in zones of class II-III;
• NC (…)-LS—“Low smoke”—non-flammable and with low smoke emission—in
fire-hazardous zones of all classes (except for fire protection systems);

802

D. Korolchenko and A. Shunko

• NC (…)-HF—“Holohen free”—non-flammable, with the absence of corrosive
substances in combustion products, halogen-free—in fire-hazardous zones of all
classes;
• NC(…)-FR—“Fire resistance”—Znon-combustible, fire-resistant—in fire
protection systems for fire hazardous zones of all classes [31].

7 Conclusions
Experimental studies of the force impact of the keel part of drifting ice formations
on cable and communications systems have shown that the magnitude of the ice load
depends on many natural and climatic factors at each specific location. The calculated
values of these factors are determined based on the analysis of complex engineering
surveys at each oil and gas field. These include: ice conditions in the region and the
main calculated parameters of drifting ice formations that are the most dangerous
for the designed field development facilities; wind; frequency, direction, intensity
of storms and calculated wave parameters; water level fluctuations; direction and
speed of currents; change in water depth along the route of underwater pipelines and
communications; seismicity of the region; engineering and geological conditions
along the route, bottom topography; lithodynamics of the coast.
The availability of the required amount of up-to-date information on these factors
is decisive in the process of designing underwater extended engineering structures
of oil and gas field facilities.
The application of the results of the presented experimental studies on the deepening of underwater extended structures in the ground, as well as fire test studies,
is possible when making design decisions, designing cable systems and cable lines
at oil and gas field facilities, compiling packages of technical documentation and
technical conditions at all stages of project development, taking into account the
characteristics of natural factors in the area of construction of structures.

References
1. Features of submarine cables. https://ek-top.ru/articles/elektrotehnika/undersea-cables-vs-reg
ular-cables//. Accessed 18 July 2025
2. International Cable Protection Committee (ICPC). https://www.iscpc.org/. Accessed 18 July
2025
3. Kharchenko YA, Chekhlov AN (2022) Offshore pipelines on the Arctic shelf: hazard
identification and safety barriers. Neftegaz.RU, No. 1
4. Submarine Cable Network Security. https://www.iscpc.org/publications/#. Accessed 18 July
2025
5. Beaufort Sea ice cuts fiber-optic cable, limiting internet for about 20,000 residents of Northwest Alaska through summer. https://www.yahoo.com/news/beaufort-sea-ice-cuts-fiber-230
200480.html. Accessed 18 July 2025

Integrated Safety Design of Cable Lines and Communications …

803

6. Electronic atlas of abrasion and ice-exaration hazard of the coastal-shelf zone of the Russian
Arctic. Working group “Dynamics of the coast and bottom of the Arctic seas” of the Laboratory of Geoecology of the North, Moscow State University. https://rus.arcticcoast.ru/atlas/.
Accessed 18 July 2025
7. Maznev SV, Kokin OV, Arkhipov VV, Baranskaya AV (2023) Modern and relict traces of
iceberg gouging of the Barents and Kara Sea bottoms. Oceanology 63(1):95–107
8. Silina IG, Ivanov VA, Ponomareva TG, Yakubovskaya SV (2020) Review and analysis of the
development of methods for assessing the impact of drifting ice formations on underwater
objects. Oil Gas 6. https://doi.org/10.31660/0445-0108-2020-6-119-130
9. VSN 51-9-86 (2021) Design of offshore underwater oil and gas pipelines. Mingazprom. Date
of update 01 Jan 2021
10. VN 39-1.9-005-98 (1998) Standards for the design and construction of offshore gas pipelines.
OAO Gazprom, Moscow
11. The Concept of Technical Regulation in OAO Gazprom (2009) Approved by the order of OAO
Gazprom dated September 17, no. 302
12. SP 378.1325800.2017 (2018) Offshore pipelines. Design and construction rules. Ministry of
Construction, Moscow
13. GOST R 54382 (2021) Oil and gas industry. Subsea pipeline systems. Moscow
14. STO Gazprom 2-3.5-454-2010 (2010) Operating rules for main gas pipelines. Moscow
15. STO Gazprom 2-3.7-050-2006 (2006) Marine standard DNV-OS-F101. Subsea pipeline
systems. Moscow
16. Recommendations for the Design, Construction and Operation of Offshore Pipelines (2019)
Russian Maritime Register of Shipping. Saint Petersburg. N 2-090601-007
17. SP 38.13330.2018 (2018) Loads and impacts on hydraulic structures (wave, ice and from ships).
Ministry of Regional Development of the Russian Federation, Moscow
18. DNV-OS-F101 (2021) Submarine pipeline systems. Det Norske Veritas AS
19. Safety Guidelines and Good Practices for pipelines (2014) United Nations. New York and
Geneva
20. UNECE Guidelines and Good Practice for Ensuring the Operational Safety of Pipelines (2015)
21. ISO 13623 (2022) Petroleum and natural gas industries—Pipeline transportation systems
22. ASME B31.4 (2022) Pipeline transportation systems for liquids and slurries. New York, NY
23. CSA Z662 (2023) Chief pipeline inspector essentials
24. Onishchenko DA, Slyusarenko AV, Shushpannikov PS (2018) Study of the features of the
process of plowing sandy soil by keels of ice formations using three-dimensional modeling by
the finite element method. Sci Tech Collect: Vesti gazovoy nauki 4(36)
25. Shunko NV et al (2009) Installation for testing the stability of offshore hydraulic structures.
Patent RU 83480 U1, OAO Gazprom
26. SP 58.13330.2019 (2020) Hydraulic structures. Basic provisions. Moscow. Standartinform
27. Federal Law of 22.07.2008 No. 123-FZ. https://docs.cntd.ru/document/902111644. Accessed
18 July 2025
28. GOST IEC 60331-21-2011 (2011) Fire tests of electric and optical cables. Serviceability. Part
21. Test performance and requirements. Cables with rated voltage up to and including 0.6/
1.0 kV
29. Rukin MV (2025) Fire safety of power supply facilities. In: Collection of articles by leading
experts in the security systems market. https://www.egida-ross.ru/tekhpodderzhka/bibliotekaspetsialista/item/231-sbornikstatej-2014-vedushchikh-spetsialistov-rynka-vzryvozashchish
chennykh-sistembezopasnosti. Accessed 18 July 2025
30. GOST 31565-2012 Cable Products (2025). Fire safety requirements. https://docs.cntd.ru/doc
ument/1200101754. Accessed 18 July 2025
31. Smelkov GI (2021) On the issue of national standards regulating fire safety requirements
for electrical wiring. In: Security service in Russia: experience, problems, prospects. Monitoring, prevention and elimination of natural and man-made emergencies. Proceedings of the
international scientific and practical conference. St. Petersburg, pp 209–213

Development of a New Method
for Extinguishing Oil Fires
for Above-Ground Oil Storage Tanks
D. Korolchenko and A. Shunko

Abstract The paper considers the main types of storage facilities for petroleum
products that are currently in the greatest demand and substantiates their necessity
in the modern conditions of national economy. The risks and hazards associated
with their use are defined. A review and analysis of emergency situations that have
occurred recently in the world and in our country, arising during their operation, is
performed. The damage and consequences of the negative impact of these accidents,
determined after their elimination, are given. The main conclusions are made about
the causes of fires and loss of life. A new modern project of the Multifunctional
Cargo Area, with a deep-water cargo seaport near the promising oil and gas fields of
Sakhalin, is considered. Experimental and theoretical studies are carried out, which
are part of the scientific support for the design and construction of a unique project.
The main recommendations developed for its planned construction and subsequent
trouble-free operation are presented.
Keywords Oil storage tank · Fire extinguishing method · Electrolysis · Foaming
agent · Foam generation · Petroleum product · Multifunctional cargo area · Cargo
berth

1 Introduction
For a long time, in the Russian Federation, there was no need for oil storage facilities.
The extracted oil was immediately supplied to an extensive pipeline network. This
was also due to the lack of the necessary infrastructure in the Arctic regions of our
country. Due to the unstable demand for oil and oil products in the world community: in 2020—a drop in demand due to the coronavirus pandemic; in 2022—after
the introduction of sanctions on Russian raw materials; energy blockade of certain
regions of the Russian Federation—the Kaliningrad region, and other unfavorable
D. Korolchenko · A. Shunko (B)
Moscow State University of Civil Engineering, Moscow, Russia
e-mail: deletesh1@yandex.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_64

805

806

D. Korolchenko and A. Shunko

factors for the national economy and the oil and gas industry of our country, the most
urgent task is the construction of storage facilities for operational, as well as strategic
storage of oil products. Currently, underground oil storage facilities (UOS) are being
built [1]. In the harsh Arctic latitudes, the construction of above-ground tanks is
much more difficult and costly than the construction of underground storage facilities. In addition, recently there has been an immediate danger of attack on ground
storage facilities by unmanned aerial vehicles. It should be noted that such construction is not possible in all natural conditions and regions of our country. However, at
present, Russia has a large number of ground storage tanks for petroleum products.
For example, they are mandatory in all sea cargo ports. This is primarily due to the
fact that loading oil into a tanker during a storm is impossible and even prohibited. On
the other hand, stopping the supply of oil through a pipeline is critical, since in this
case, oil production at the oil and gas field itself will have to be stopped. The same
situation exists with oil refineries, requiring mandatory placement of storage tanks
for petroleum products along on-site oil pipelines. Thanks to such a technological
organization, continuous balancing of pumping volumes is carried out—due to the
constant filling and emptying of storage tanks for petroleum products. It is due to
this that the stability of the operation of a particular oil and gas field is maintained.
The need to store oil in oil storage facilities is also connected with the technological feature of the process. The oil pipeline is always filled with oil, but when
the need for preventive or repair work arises, it must be temporarily drained somewhere. It is impossible to simply pour oil on the ground because of its high chemical
hazard, therefore, previously it was periodically burned. For the most efficient use of
a resource so necessary for energy, special buffer tanks are now being built, allowing
for temporary draining of oil, and after carrying out repair and preventive work,
placing it back into the pipeline.
Thus, there is a significant need for ground-based oil storage tanks, which will
undoubtedly contribute to their construction and quantitative increase in the future.

2 Relevance
As is known, constantly occurring fires of oil and oil products in capacitive oil
storage tanks lead to catastrophic consequences, taking on significant volumes and
scales, causing injuries and deaths, as well as causing enormous financial and environmental damage. A large number of people and special equipment are involved in
extinguishing such fires, and the extinguishing process itself can last several days or
even weeks. Often, the elimination of such fires occurs at the moment of complete
burnout of the oil product [2].
In the global oil and gas industry, major accidents are known that turn into real
environmental disasters.
The most colossal environmental disaster is recognized as the explosion of April
20, 2010, on the Deepwater Horizon oil platform, which was drilling a well in the
Gulf of Mexico off the coast of the United States. A powerful gas explosion thundered

Development of a New Method for Extinguishing Oil Fires …

807

on the platform, then a fire started. Later, the platform sank. The explosion and fire
led to an uncontrolled release of oil. It flowed from the damaged well into the waters
of the Gulf of Mexico for several months. The leakage was about 700 tons per day
(Fig. 1) [3].
On August 7, 2022, one of the tanks exploded at a burning oil storage base in the
Cuban province of Matanzas. The flames spread to neighboring tanks (Fig. 2) [4].

Fig. 1 Fire on platform in Gulf of Mexico

Fig. 2 Fire at oil storage base

808

D. Korolchenko and A. Shunko

A fire and explosions occurred on December 10, 2023, at an oil refinery in Iran.
First, one gas condensate tank caught fire at the refinery, located in the Birjand SEZ.
Firefighters were able to quickly localize the fire, but the flames managed to spread
to neighboring tanks. As a result, the rest exploded (Fig. 3) [5].
On June 12, 2020, a fire broke out in a tank for petroleum products located in the
area of the 12th kilometer of the Nizhnevartovsk-Megion highway, on the territory
of Nizhnevartovsk Oil Refinery Association LLC. As a result of the fire in the tank,
which was undergoing scheduled repairs, employees of the enterprise were injured
and received burns (Fig. 4) [6].
On August 14, 2023, a major emergency occurred in Dagestan. On the highway
in Makhachkala, a car service warehouse caught fire, where about 100 tons of nitrate

Fig. 3 Fire in a gas condensate tank
Fig. 4 Tank fire at oil
refinery

Development of a New Method for Extinguishing Oil Fires …

809

were stored. The fire quickly spread to the nearby Nafta-24 gas station, where two
of the eight fuel tanks detonated.
The explosion was so powerful that a deep pit formed in the asphalt. Due to the
blast wave, eyewitnesses who were within a radius of 50 m from the fire were covered
with burning fuel.
The total area of the fire was 600 m2 , and 70 people and 20 pieces of equipment
were involved in extinguishing it. According to the Russian Emergencies Ministry,
the explosion was equivalent to 35 tons of TNT. As a result, 40 private houses and a
hotel were damaged, and the car service and gas station were destroyed. 37 people
were killed and 119 were injured (Fig. 5) [7].
An accident occurred on June 1, 2022, in the village of Zheleznodorozhny on
the territory of Bashneft-Retail LLC. The victims received burns of varying severity
(Fig. 6) [8].
On May 3, 2023, a tank with oil products caught fire in the Temryuk district of the
Krasnodar region: the fire area was 1200 m2 . 85 firefighters and two dozen special
vehicles were involved in extinguishing the fire (Fig. 7) [9].

Fig. 5 Burning fuel tanks in Makhachkala

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D. Korolchenko and A. Shunko

Fig. 6 Explosion of gas-air mixture at Abzelilovskaya oil depot

Fig. 7 Fire in a storage tank for petroleum products

3 Theoretical Part
An analysis of accidents in recent years leads to the conclusion that the main cause of
death of people servicing oil and gas storage facilities is thermal impact (70%), due
to explosions, fires and emissions. It is also obvious that a fire in one tank can lead
to an explosion of another tank and vice versa (the “domino” principle), and actions

Development of a New Method for Extinguishing Oil Fires …

811

aimed at cooling the walls of a burning tank or prolonged inaction to extinguish
an oil product can lead to its release [10]. As the oil and oil product processing
and transportation industry develops, as well as the scale of their storage, there is
an urgent need to improve the fire protection of tanks and tank farms. In case of
fires and emergency spills of oil and petroleum products, fire extinguishing agents of
various origins are used, namely: foam of various expansion ratios [11, 12], water of
high and coarse dispersion [13, 14], aerosols and fire extinguishing powders [15, 16],
gas compositions and freons [17, 18]. At the same time, foams of various expansion
ratios exhibit the greatest fire extinguishing efficiency and insulating capacity [19].
Currently, tanks with oil and petroleum products, as capital construction projects
for warehouse purposes, are often protected by foam fire extinguishing systems,
which use foaming agents of various expansion ratios and origins [11].
The air-mechanical method of foaming is based on the principle of injecting
air masses and then mixing them with a foaming agent solution. To obtain medium
expansion foam, it is necessary that the suspended chambers be located directly above
the surface of the oil product, which negatively affects their performance in the event
of an explosion of the vapor-air environment; in addition, the generated medium
expansion foam has low fire extinguishing efficiency, which is associated with the
rate of foam spreading over the flammable liquid. It has been experimentally proven
that low expansion foam, which is advisable to supply under the layer of flammable
liquid, or from remote places to the surface, is more effective for extinguishing oil
and oil product fires in tank farms than medium expansion foam [20, 21].
Statistical data on the occurrence of large and catastrophic fires of oil and oil products at petrochemical facilities and an analysis of the assessment of the consequences
show that even existing methods of extinguishing fires with air-mechanical foams
are not effective enough. To solve this problem using scientific methods, insufficient
attention is paid to the development of new methods for producing foams. In this
regard, the most urgent task seems to be the development and research of a new
method for extinguishing oil and oil product fires in tanks, based on a new foaming
process, based on the principle of electrolysis of foaming agent solutions with subsequent determination and identification of physical and chemical dependencies that
affect the indicators of fire extinguishing efficiency of foams.

4 Experimental Studies
Currently, on the east coast of Sakhalin, the design and construction of a multifunctional cargo area (MCA) of the Poronaysk seaport is underway. The project includes
a peat, coal, oil and gas terminal (Fig. 8) [22]. The MCA location area is in close
proximity to large offshore oil and gas fields.
Sakhalin shelf facilities [23]:
• Sakhalin-1, with the development of four hydrocarbon fields: Chayvo, Odoptumore, Arkutun-Dagi and Lebedinskoye;

812

D. Korolchenko and A. Shunko

Fig. 8 Operational storage tanks for petroleum products

• Sakhalin-2, within the framework of the project, the Piltun-Astokhskoye
(primarily oil) and Lunskoye (primarily gas) fields located in the Sea of Okhotsk
are being developed;
• Sakhalin-3. The project was launched in 2013, and in 2014 it reached commercial
production. This is a high-tech complex that allows for the extraction of gas from
the Kirinskoye field without restrictions due to ice conditions.
At the design stage, there are proposals for the Sakhalin-4, 5, 6, 7, 8, 9 facilities.
Development of hydrocarbon resources of the Sakhalin shelf is one of the main
strategic directions of development of the national economy of the Sakhalin region
and one of the priority sectors of the Russian Federation [24].
To transport oil and gas extracted from Sakhalin fields along the Northern Sea
Route to ports in Russia, Europe and the countries of the Asia–Pacific region, it
is planned to deepen the seabed by an additional 20 m within the first stage of
construction to ensure the passage of large cargo ships. In accordance with this, it
is necessary to develop a design for a unique deep-water cargo berth and test its
efficiency (Fig. 9).
The mandatory scientific support for the design of MGR structures included experimental studies of the wave impact of a calculated storm on the design structure of a
deep-water cargo berth (Fig. 10).
Results of Experimental Studies:
Based on the conducted experiments to study the impact of the most wavehazardous south-east storm on the berth structure, with the wave parameters: h1%
= 10.82 m, T аver = 11.2 s (in-kind data), the following was recorded:
• there was no wave splash on the superstructure of the berth structure;
• there was no overflow of the design wave crests over the upper elevation mark of
the protective fill structure of the berth;

Fig. 9 Design view and section of the deep-water cargo berth structure

nat. bottom

1. Hexabit 25 tons
2. Stone weighing 500-800 kg, h = 1.5 m
3. Stone weighing 15-50 kg, h = 0.8 m
4. Backfill soil
5. Crushed stone, fraction 70-120, h = 0.5 m

pr. bottom

Excavation of soil for installation of shells

Pile 1420x12, L=32600

1. Reinforced concrete pavement, h=0.5 m
2. Crushed stone 40-70 mm, h=1.0 m
3. Backfill soil
4. Crushed stone 3-70 mm, h=2.0 m
5. Crushed stone 40-70 mm, h=0.5 m
6. Stone 15-50 kg, h=2.0 m
7. Crushed stone 70-120, h=0.5 m

Development of a New Method for Extinguishing Oil Fires …
813

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D. Korolchenko and A. Shunko

Fig. 10 Experimental research

• the design elevation mark of the berth structure is optimal;
• there was no discharge of the protective fill elements (hexabites) in the experiments.
The overall efficiency of the deep-water cargo berth structure is ensured [25, 26].

5 Practical Significance and Suggestions
The results of experimental studies of the construction of the cargo berth provided
an opportunity to visit the Federal Autonomous Institution “Glavgosexpertiza of
Russia” with consideration of the main technical solutions in terms of hydraulic
engineering.
The next stage of support for the design of MGR structures includes the development of sections of the project to ensure fire safety of ground-based tanks for oil
products.
In connection with the availability of new technical developments and solutions,
the general uniqueness of the entire MGR project, the research staff was tasked with
developing and researching a new method for extinguishing oil product fires in the
tanks of the cargo terminal, based on a new foaming process.
At the moment, it is necessary to identify the physicochemical parameters that
determine the dependencies that affect the increase in the fire extinguishing efficiency
of aqueous solutions of foaming agents.
Based on this, comprehensive experimental and theoretical studies are being
conducted aimed at implementing the following subtasks:
• determining the possibility of joint use of electrolytes and foaming agents of
different origins;—determination of the dependence of the rate of spreading of
water films on the surface of the fuel on the amount of electrolyte in the aqueous
solution of the foaming agent with a positive coefficient of spreading of the
solution on the fuel;
• study of the influence of physical parameters on the foam generation process at
different values of current using electrodes of different areas, as well as types of
metals;

Development of a New Method for Extinguishing Oil Fires …

815

• determination of the optimal values of physical parameters at which the foam
generation rate has a maximum value, at different values of current;
• study of the characteristics of foams obtained at optimal physical parameters,
and determination of its fire extinguishing efficiency at different values of current
(dispersity, multiplicity and durability);
• comparison of the obtained empirical data with fundamental laws;
• identification of dependencies of the insulating capacity of foam and water film
on the surface of the hydrocarbon on the thickness of the fire extinguishing layer.
According to the results of the patent information search, it was found that the
closest in meaning to the new foam generation method are patents that provide for:
a method for producing aluminum by melt electrolysis (Patent No. 2415973 RF), a
method for electrolysis of aluminum sulfide (Patent No. 2341591 RF) and design
features of a device for collecting melt samples in an electrolyzer (Patent No. 2448199
RF). The rest of the existing patents provide only for fire extinguishing methods
using air-mechanical foam and other fire extinguishing agents. The development of
a new method for the foaming process is associated with the effect of direct electric
current on aqueous solutions of foaming agents of various origins using various
electrolytes. The new foaming process itself is described by Faraday’s first law (the
law of electrolysis):
m = K · q = K · I · τ,

(1)

where: K is the electrochemical equivalent of the substance; q is the electric charge,
C; I is the current, A; τ is the time of exposure to electric current, s.
Final research on this part of the project is currently underway.

6 Conclusions
The multifunctional cargo area on Sakhalin is a modern cargo complex. Its project
includes terminals with the following characteristics:
•
•
•
•

a universal peat terminal with a capacity of up to 2 million tons per year;
a coal terminal with a capacity of up to 5 million tons per year;
an oil terminal with a capacity of up to 5.5 million tons per year;
a gas condensate terminal with a capacity of up to 2.8 million tons per year.

The proximity of the new seaport to the Sakhalin shelf projects allows for the
timely shipment of oil products and coal, as well as significantly reducing the time
it takes to transport cargo to its destination.
For Russia, this is one of the most interesting and unique projects, the development
of which is being developed by the best teams of scientists from various fields of
science.

816

D. Korolchenko and A. Shunko

NRU MGSU, on an ongoing basis, provides scientific support for the design and
construction of such facilities, which is reflected in this work.
Based on the conducted theoretical and experimental studies, scientifically based
recommendations are given in the relevant sections of the Multifunctional Cargo
Area project. The application of the results of this work is possible when making
design decisions at oil and gas field facilities, drawing up packages of technical
documentation and technical conditions at all stages of project development.

References
1. Government Agencies and a Number of Companies are Interested in Building Underground
Oil Storage Facilities in the Russian Federation. https://neftegaz.ru/news/transport-and-sto
rage/815105-gosstruktury-i-ryad-kompaniy-zainteresovany-v-stroitelstve-podzemnykh-khr
anilishch-nefti-v-rf/. Accessed 23 July 2025
2. Extinguishing Fires at Petrochemical Facilities. https://fireman.club/presentations/tusheniepozharov-na-neftehimicheskih-obektah/. Accessed 23 July 2025
3. Explosion of the Deepwater Horizon oil platform. https://ecoteco.ru/library/magazine/1/eco
logy/vzryv-neftyanoy-platformy-deepwater-horizon. Accessed 23 July 2025
4. A Tank Explosion Occurred at a Burning Oil Storage Facility in Cuba. https://ren.tv/news/
v-mire/1009864-vzryv-rezervuara-proizoshel-na-goriashchem-neftekhranilishche-na-kube.
Accessed 23 July 2025
5. A Fire Occurred at an Oil Refinery in Eastern Iran. https://nangs.org/news/downstream/ref
ining/na-vostoke-irana-proizoshel-pozhar-na-npz. Accessed 23 July 2025
6. An Oil Tank Caught Fire in the Khanty-Mansiysk Autonomous Okrug, Two People Received
Serious Burns. https://www.vesti.ru/article/2420427. Accessed 23 July 2025
7. More Than 30 People Died from a Powerful Explosion at a Gas Station in Dagestan. What
caused the tragedy? https://lenta.ru/news/2023/08/15/azs/. Accessed 23 July 2025
8. A Tank was Depressurized at the Abzelilovskaya Oil Depot in the Republic of Bashkortostan. https://neftegaz.ru/news/incidental/739407-v-abzelilovskoy-neftebaze-v-respublikebashkortostan-proizoshla-razgermetizatsiya-rezervuara/. Accessed 23 July 2025
9. Footage of the Fire at the Kuban Oil Depot: Black Smoke is Visible from Crimea. https://www.
mk.ru/photo/gallery/34085-664538.html. Accessed 23 July 2025
10. Volkov OM (2013) The “domino” version of the fire of the RVS-20000 group at the Konda
linear production and dispatch station. Electron Sci J Technosphere Saf Technol 3:49
11. Degaev EN (2015) Comparative assessment of fire extinguishing efficiency of fluorinated and
hydrocarbon foaming agents. Mod Mater Equip Technol 3(3):99–107
12. Korolchenko DA, Sharovarnikov AF (2015) Physical parameters of high expansion foam used
to extinguish fires in enclosed spaces. Bull MGSU 2:85–92
13. Korolchenko DA, Sharovarnikov AF (2013) Effect of water droplet dispersion on the efficiency
of extinguishing flammable liquid fires. Fire Explos Saf 22(12):69–76
14. Korolchenko DA, Sharovarnikov AF (2015) Flame extinguishing of hydrophobic materials
with aqueous solutions of wetting agents. Fire Explos Saf 24(3):61–68
15. Korolchenko DA (2013) Extinguishing flammable liquids with sprayed water. Fire Explos Saf
22(11):70–74
16. Korolchenko DA, Sharovarnikov AF (2014) Flame extinguishing with fire extinguishing
powders and aerosol compositions. Fire Explos Saf 23(8):63–68
17. Volobuev AV, Korolchenko DA, Maslennikov VA (2002) Comparative assessment of the effectiveness of fire extinguishing powders. Collection of materials of the International symposium
“Integrated security of Russia—research, management, experience”, Moscow, p 309

Development of a New Method for Extinguishing Oil Fires …

817

18. Korolchenko DA, Sharovarnikov AF (2014) Extinguishing flammable liquids with high-boiling
freons. Fire Explos Saf 23(5):67–71
19. Degaev EN, Korolchenko DA, Sharovarnikov AF (2015) Extinguishing flames of flammable
liquids with Freon. In: Collection of materials of the All-Russian conference and school of
young scientists “Systems of ensuring technosphere safety”. Taganrog, pp 15–17
20. Korolchenko DA, Voevoda SS (2015) Fire protection of oil tanks and pump rooms with foam
of different expansion ratios. Fire Explos Saf 15(5):78–81
21. Oil Depot: Fire Extinguishing Systems (2025). https://neftegaz.ru/science/ecology/476016-nef
tebaza-sistemy-pozharotusheniya/. Accessed 23 July 2025
22. Ampilov Y (2019) Sakhalin oil and gas projects yesterday, today, tomorrow. https://doi.org/
10.13140/RG.2.2.28842.16320. Accessed 23 July 2025
23. Resolution of the Government of the Sakhalin Oblast of December 24, 2019 No. 618. On
approval of the strategy for the socio-economic development of the Sakhalin Oblast for the
period up to 2035
24. SP 38.13330.2018 (2018) Loads and impacts on hydraulic structures (wave, ice and from ships).
Ministry of Regional Development of the Russian Federation, Moscow
25. GOST R 70023-2022 (2022) Physical modeling of wave impacts on port hydraulic structures. Requirements for building a model, conducting experiments and processing results.
Rosstandart, Moscow
26. GOST R 59657-2021 (2021) Hexabits for coastal protection and fencing structures. Technical
conditions. Rosstandart, Moscow

Hydrochemical Composition of Waters
of the Jyrgalan River Basin
S. K. Belekov, R. T. Akmatov, M. T. Abylgazieva, S. M. G. B. Kadyrova,
and K. E. Saypidinova

Abstract The article presents the results of an analysis conducted by the State
Enterprise Central Laboratory under the Ministry of Natural Resources, Ecology,
and Technical Supervision of the Kyrgyz Republic, focusing on the concentrations of
major ions, heavy metals, and nitrogen in water samples collected from the Zhyrgalan
River basin within the Issyk-Kul basin, the country’s main sanatorium and resort
region. The study indicates that the concentrations of major ions in the waters of
the Zhyrgalan River basin are within the permissible limits established by maximum
permissible concentrations (MPC). However, elevated levels of certain heavy metals
were detected in all samples, exceeding the standards set by the Law of the Kyrgyz
Republic “Technical Regulations on the Safety of Drinking Water” (as amended on
April 28, 2017). Increased concentrations of these metals deteriorate the drinking
water quality and may cause serious adverse effects on human health. The analysis
of the chemical composition of the Zhyrgalan River waters in the Issyk-Kul basin
demonstrates that, for their use in drinking and domestic purposes, priority measures
should focus on the removal of heavy metals. Continued systematic monitoring of
river water quality in the Issyk-Kul basin, with particular emphasis on heavy metal
determination, is therefore recommended.
Keywords Zhyrgalan river basin · Quality of rivers water · Basic ions · Water
mineralization · Heavy metals · Oil products · SanPiN · Maximum permissible
concentration

S. K. Belekov
Hydrometeorological Service under the Ministry of Emergency Situations of the Kyrgyz
Republic, Bishkek, Kyrgyzstan
R. T. Akmatov (B) · M. T. Abylgazieva · K. E. Saypidinova
Institute of Natural Sciences of the Kyrgyz State University named after I. Arabaev, Bishkek,
Kyrgyzstan
e-mail: nalsur24@list.ru
S. M. G. B. Kadyrova
Medical College of the Jalal-Abad State University named after B. Osmonov, Jalal-Abad,
Kyrgyzstan
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_65

819

820

S. K. Belekov et al.

1 Introduction
The Zhyrgalan River originates from the glaciers of the Teskey Ala-Too Range and
flows through the Issyk-Kul Region of the Kyrgyz Republic. The river rises on the
northern slopes of the Teskey Ala-Too and drains into the eastern part of Lake IssykKul, passing through the territory of the Ak-Sui District. The total length of the river
is 97 km, and the catchment area covers 2070 km2 [1, 2].
In its upper reaches, the Zhyrgalan flows through a narrow gorge in a submeridional direction, while in the lower reaches it crosses a plain and follows a predominantly latitudinal course. The average annual discharge is 22.5 m3 /s, with a maximum
of 104 m3 /s and a minimum of 7.12 m3 /s. The river becomes high-flowing from April,
and water levels begin to decline toward the end of August [1, 3].
The Zhyrgalan River has several major tributaries, including Terim-Tere-Bulak,
Tyurgen–Ak-Suu, Boz-Tubuk, Ichke-Zergez, and Ak-Suu (Arashan), as well as more
than 50 smaller tributaries. Within the basin, 42 lakes are located, with a total surface
area of 1.54 km2 [1].
The river valley hosts a number of settlements and recreational facilities, including
the Ak-Suu Sanatorium, the Zhyrgalan Resort, and the settlements of Zhyrgalan,
Kyzyl-Kiya, Toktogul, Ak-Chiy, Kachybek, Shapak, Otradnoye, Karakol, and KaraZhal [4–6].
The river system of the Zhyrgalan basin plays a crucial role in supplying water for
economic, domestic, and drinking purposes for the population of the Ak-Sui District
of the Kyrgyz Republic. Ak-Sui District is one of the five administrative districts of
the Issyk-Kul Region and comprises 14 rural municipalities and 48 villages. As of
2023, the total population exceeds 73,967 people, the majority of whom reside in
rural areas.
Annually, approximately one million people receive treatment and recreation
services in sanatorium-resort and tourist facilities within the Issyk-Kul basin, creating
a growing demand for reliable supplier of high-quality water.
According to the Department of Drinking Water Supply and Sanitation of the
State Construction Committee of the Kyrgyz Republic [7], 16 settlements in the
region lack centralized water supply systems. In addition, water supply systems in
48 villages were constructed between 1950 and 1970, including four systems built
in 1953–1956 and four in 1970, while the remaining 40 were constructed during the
period 1960–1969.
Most of these systems are currently in unsatisfactory condition due to the
exceedance of their designed service life. At present, seven villages are included
in rehabilitation projects financed by the World Bank (WB) and the Community
Development and Investment Agency (ARIS), while water supply systems in two
villages are being rehabilitated at the expense of the republican budget.

Hydrochemical Composition of Waters of the Jyrgalan River Basin

821

2 Relevance, Scientific Significance of the Issue
Knowledge of the chemical composition of water, which determines its quality, is
essential for practical applications such as drinking water supply, irrigation, fisheries, and other water-dependent sectors. The study of water chemistry is also of
critical importance for addressing and mitigating wastewater pollution in natural
water bodies.
One of the key stages in assessing river water quality, particularly in watercourses
subjected to significant anthropogenic pressure, involves comprehensive laboratory
analyses aimed at determining physicochemical parameters and the concentrations
of various substances, followed by their comparison with established maximum
permissible levels.
At the same time, the Kyrgyz Republic is experiencing steady population growth
accompanied by the expansion of residential development and economic activities.
In parallel, the enlargement of irrigated agricultural lands has become an increasingly
urgent challenge, the resolution of which is essential to ensure food security for the
growing population.

3 Setting the Task
This paper outlines the objectives of investigating the hydrochemical composition
of the Zhyrgalan River basin. In this context, the modernization and further development of water supply and water resources management systems are of particular
importance. Accordingly, one of the key scientific and practical tasks addressed in
this study is the laboratory analysis of water samples conducted by the facilities operating under the Ministry of Natural Resources, Ecology, and Technical Supervision
of the Kyrgyz Republic.

4 The Theoretical Part
The intra-annual distribution of the chemical composition of river runoff is determined by the timing of water input from genetic sources such as snowmelt, glacier
melt, precipitation, as well as by the lithological characteristics of the drainage area.
In the Kyrgyz Republic, these processes are largely controlled by specific orographic
and geomorphological features, including the altitudinal zonation of catchment areas,
slope exposure relative to moisture-bearing air masses, and synoptic conditions
during the cold and warm seasons of the year.
Numerous researchers have developed theoretical frameworks and methodological approaches for investigating the hydrochemical characteristics of rivers in
Kyrgyzstan, including those within the Issyk-Kul Lake basin. Among the earliest

822

S. K. Belekov et al.

studies are those by K. Schmidt (Studies of Lake Issyk-Kul Water, 1882) and V. P.
Matveev (Hydrological and Hydrochemical Studies on Issyk-Kul in 1928, 1930).
A comprehensive assessment of the hydrochemistry of the lake and its basin was
later provided by V. K. Kadyrov (Hydrochemistry of Lake Issyk-Kul and Its Basin,
1986). However, the results of these hydrochemical studies exhibit notable differences, reflecting variations in methodological approaches, temporal coverage, and
environmental conditions.
In addition, water quality and water use in Lake Issyk-Kul and its tributary rivers
have been examined by a number of contemporary researchers, including Y. Kawabata et al. (Water Quality in Issyk-Kul and the Rivers Flowing into It, 2014), B.
Alymkulova et al. (Consideration of Water Uses for Sustainable Management: The
Case of Issyk-Kul Lake, Kyrgyzstan, 2016), S. Abdyzhapar et al. (Impact of Climate
Change on Water Level Fluctuations of Issyk-Kul Lake, 2015), and S. K. Alamanov,
Li Yaoming, and co-authors (Study of Water Quality in the Rivers of the Issyk-Kul
Basin, 2019).

5 Practical Significance, Proposals and Implementation
Results
He results of laboratory analyses of water samples conducted by the laboratory
facilities operating under the Ministry of Natural Resources, Ecology and Technical
Supervision of the Kyrgyz Republic are presented. Water samples were collected
within the Zhyrgalan River basin (Fig. 1).

Fig. 1 Location of water sampling points for hydrochemical analysis in the Zhyrgalan River basin

Hydrochemical Composition of Waters of the Jyrgalan River Basin

823

A preliminary assessment of water quality was performed based on the analytical
data obtained from the investigated samples in accordance with the provisions of the
Law of the Kyrgyz Republic dated April 28, 2012, “Technical Regulations on the
Safety of Drinking Water” [8].
Water samples for chemical analysis were collected from the studied sites using
sterile containers (bottles and cans). Measurements of pH, total dissolved solids,
water temperature, dissolved oxygen, and electrical conductivity were carried out
directly in the field using portable instruments manufactured by Clean and Hanna.
Concentrations of carbon dioxide, bicarbonates, and carbonates were determined
under laboratory conditions. Phosphate ions and nitrogen species in river water
were analyzed using spectrophotometric methods. Chloride ions were determined
by argentometric titration with silver nitrate, while concentrations of heavy metals
were measured by mass spectrometry.
The analytical results indicate that pH values in almost all water samples exceeded
7.0 in all seasons, ranging from 7.31 in the Ak-Suu River to 8.15 in the Turgen–
Ak-Suu River. Thus, the waters are characterized by a distinctly alkaline reaction,
although pH values did not exceed established standard limits. Dissolved oxygen
concentrations were high in all samples, varying from 6.21 to 10.68 mg/L. The
bicarbonate (HCO3 − ) content in all samples remained below the maximum permissible concentration (MPC = 400 mg/L), ranging from 96 to 265 mg/L, with the
lowest values recorded at both sampling points of the Ak-Suu River (96–108 mg/L).
Fluoride concentrations in the studied waters were significantly below the permissible limit (1.2 mg/L), ranging from 0.34 mg/L (Ak-Suu River-1) to 0.77 mg/L
(Zhyrgalan River-2), a factor that may contribute to an increased risk of dental caries.
Chloride concentrations were also low relative to the MPC (250 mg/L), varying from
0.37 mg/L (Zhyrgalan River-2) to 6.37 mg/L (Tyup River-2).
The chemical composition of waters from the eastern tributaries was generally
higher than that of other tributaries. The rivers Ak-Suu, Zhyrgalan, Juuka, ChonJargylchak, and Tyup exhibited the highest total ion concentrations. This pattern is
attributed to their relatively large lengths, flow through sedimentary rock formations,
and the development of irrigated agriculture within their catchments. The hydrochemical composition of river waters is dominated by Ca2+ and SO4 2− ions, while the
concentrations of other ions are comparatively low [9–13].
River water mineralization exhibits a clear seasonal pattern: a sharp increase is
observed in autumn and winter due to reduced runoff, while mineralization decreases
in summer as a result of glacier and snowmelt and flood events. In spring, a slight
increase in mineralization is recorded [14–17].
Emission spectrometric analysis of waters in the Zhyrgalan River basin revealed
the presence of 23 chemical elements. Calcium showed the highest concentrations among the detected elements, reaching 36.178 mg/L in the Zhyrgalan River,
30.657 mg/L in Turgen–Ak-Suu, 28.478 mg/L in Bozuchuk, and 26.228 mg/L in
Ak-Suu, with the lowest concentration recorded in Zherges (23.255 mg/L). Magnesium ranked second, with maximum concentrations observed in Ak-Suu (9.198 mg/
L) and Bozuchuk (5.958 mg/L), and minimum values in Zherges (2.267 mg/L).
Sodium occupied the third position, with concentrations ranging from 1.962 mg/

824

S. K. Belekov et al.

L (Zherges) to 4.202 mg/L (Zhyrgalan). Potassium concentrations were approximately 1 mg/L, with the highest values recorded in Ak-Suu (1.368 mg/L) and the
lowest in Zherges (0.587 mg/L). Elevated concentrations of manganese (0.002 mg/
L), aluminum (0.345 mg/L), and iron (0.346 mg/L) were observed in the Ak-Suu
area.
The highest overall mineralization was recorded in the Zhyrgalan River (46.3 mg/
L), followed by Ak-Suu (40.4 mg/L), Turgen–Ak-Suu (38.7 mg/L), and Bozuchuk
(37.8 mg/L), while the lowest value was observed in Zherges (28.2 mg/L). Similar
spatial differences in mineralization have been reported by J. Asanaliev [18],
attributed to physical-geographical and geological characteristics of the regions.
Studies by R. T. Akmatov [19, 20] reported significantly higher mineralization levels
in other river systems, such as the Karadarya River (137.7 mg/L), the Talas River
at its inflow into the Kirov Reservoir (95.3 mg/L), and the Chui River at its inflow
into the Orto-Tokoy Reservoir (87.1 mg/L). Compared to these systems, the waters
of the Zhyrgalan River basin are characterized by low mineralization.
Concentrations of trace elements, including copper (0.001–0.003 mg/L), zinc
(0.005 mg/L), lead (0.003–0.0105 mg/L), silver (0.005 mg/L), arsenic (0.005–
0.021 mg/L), antimony (0.005 mg/L), cadmium (0.0001 mg/L), selenium (0.005–
0.0246 mg/L), and beryllium (0.0001 mg/L), were generally similar across all
samples. Among these elements, zinc, beryllium, chromium, cobalt, vanadium,
and cadmium are considered the most hazardous to human health; however, their
concentrations were extremely low and did not exceed established MPC values.
At the fisheries standard limit of 0.006 mg/L, lead concentrations exceeded
permissible levels by 1.2 times in Turgen–Ak-Suu (0.007 mg/L), 1.7 times in
Bozuchuk (0.010 mg/L), and 1.3 times in Zherges (0.008 mg/L), while remaining
below drinking water standards established by SanPiN regulations of the Russian
Federation and the Kyrgyz Republic. Selenium concentrations in Ak-Suu exceeded
World Health Organization standards by twofold, European Union standards by 24fold, and SanPiN standards by twofold. Molybdenum concentrations exceeded fisheries standards by seven times in Zhyrgalan, five times in Ak-Suu, and two times
in Bozuchuk, but remained below drinking water standards set by the WHO and
SanPiN. Copper concentrations exceeded fisheries standards by threefold and WHO
and EU standards by 1.5 times, while remaining below SanPiN limits for drinking
water. Arsenic concentrations were 0.5 times lower than the MPC established by
Russian and Kyrgyz standards, but exceeded WHO standards by twofold and EU
standards by 21-fold. Aluminum concentrations exceeded WHO and EU standards
by 1.5 times, but were 1.7 times lower than the MPC for drinking water established
by Russian and Kyrgyz regulations (Table 1).
According to a study conducted by Professor Alamanov [21], elevated concentrations of certain chemical elements (heavy metals) exceeding the maximum permissible concentrations established by SanPiN standards were identified at specific
sampling points of the investigated rivers (Table 2). Medical and biological studies
indicate that excessive zinc concentrations in drinking water can inhibit oxidative
processes in the human body and contribute to the development of anemia. Increased

Hydrochemical Composition of Waters of the Jyrgalan River Basin

825

Table 1 Comparison of harmful substances contained in the tributaries of the Zhyrgalan River with
the norm
No Chemical
elements

Plumbum
(Pb)

Indicators on water
(emulsion method)

WHO EU

Zhyrgalan—< 0.003

0.01

Ak-Suu—< 0.003

Turgen-Aksuu—0.0075
Zherges—0.0089
Cadmium
(Cd2+ )

Zhyrgalan—< 0.0001

0.003

0.005

Ak-Suu—< 0.0001

Turgen-Aksuu—< 0.0001
Bosuchuk—< 0.0001
Selenium (Se) Zhyrgalan—< 0.005

0.01

0.001

Ak-Suu—0.0246

Turgen-Aksuu—< 0.005
Bosuchuk—< 0.005
Zherges—< 0.005
4

Molybdenum
(Mo)

Zhyrgalan—0.007

0.07

–

Ak-Suu—0.005

Turgen-Aksuu—< 0.001
Zherges—0.007
5

Beryllium
(Be)

Zhyrgalan—< 0.0001
Ak-Suu—< 0.0001

Turgen-Aksuu—< 0.0001
Bosuchuk—< 0.0001
Zherges—< 0.0001

–

0.001

SanPiN 0.0002
for
drinking
water
SanPiN
for
fisheries

0.05

SanPiN 0.25
for
drinking
water
SanPiN
for
fisheries

Bosuchuk—0.002

0.005

SanPiN 0.01
for
drinking
water
SanPiN
for
fisheries

0.006

SanPiN 0.001
for
drinking
water
SanPiN
for
fisheries

Zherges—< 0.0001
3

SanPiN 0.03
for
drinking
water
SanPiN
for
fisheries

Bosuchuk—0.0105
2

Russia. Kyrgyzstan
Name of The
Degree
the
standard of
standard
danger

0.0003

(continued)

826

S. K. Belekov et al.

Table 1 (continued)
No Chemical
elements

Indicators on water
(emulsion method)

WHO EU

Zhyrgalan—< 0.005

Zinc (Zn)

Name of The
Degree
the
standard of
standard
danger
5

Ak-Suu—< 0.005

Turgen-Aksuu—< 0.005
Zherges—< 0.005
Copper (Cu)

Zhyrgalan—0.001

0.002

Ak-Suu—0.003

Turgen-Aksuu—0.001
Zherges—< 0.001
Nickel (Ni)

Zhyrgalan—0.016

0.02

Ak-Suu—0.012

Turgen-Aksuu—0.007
Zherges—< 0.001
9

Chrome
(Cr6+ )

Zhyrgalan—< 0.001

0.05

Ak-Suu—0.003

Turgen-Aksuu—< 0.001
Bosuchuk—< 0.001
Zherges—< 0.001
10

Cobalt (Co)

Zhyrgalan—< 0.001
Ak-Suu—< 0.001

Turgen-Aksuu—< 0.001
Bosuchuk—< 0.001
Zherges—< 0.001

–

0.02

SanPiN 0.01
for
drinking
water
SanPiN
for
fisheries

0.01

SanPiN 0.05
for
drinking
water
SanPiN
for
fisheries

0.001

SanPiN 0.1
for
drinking
water
SanPiN
for
fisheries

Bosuchuk—0.006

0.01

SanPiN 0.1
for
drinking
water
SanPiN
for
fisheries

Bosuchuk—< 0.001
8

SanPiN 5
for
drinking
water
SanPiN
for
fisheries

Bosuchuk—< 0.005
7

Russia. Kyrgyzstan

0.01

(continued)

Hydrochemical Composition of Waters of the Jyrgalan River Basin

827

Table 1 (continued)
No Chemical
elements

Indicators on water
(emulsion method)

WHO EU

Zhyrgalan—0.021

0.01

Arsenic (As)

Name of The
Degree
the
standard of
standard
danger
0.001

Ak-Suu—< 0.005

Turgen-Aksuu—< 0.005
Zherges—< 0.005
Vanadium (V) Zhyrgalan—< 0.001

–

Ak-Suu—< 0.001

Turgen-Aksuu—< 0.001
Zherges—< 0.001
Aluminum
(Al)

Zhyrgalan—0.345
Ak-Suu—0.274

Turgen-Aksuu—0.117
Bosuchuk—0.024
Zherges—< 0.01

0.2

0.001

SanPiN 0.5
for
drinking
water
SanPiN
for
fisheries

0.05

SanPiN 0.1
for
drinking
water
SanPiN
for
fisheries

Bosuchuk—< 0.001
13

SanPiN 0.05
for
drinking
water
SanPiN
for
fisheries

Bosuchuk—< 0.005
12

Russia. Kyrgyzstan

0.04

Note WHO denotes the World Health Organization; EU denotes the European Union. Sanitary–
hygienic indicators correspond to drinking water standards, while fisheries indicators refer to ecological quality standards for aquatic biota. Saturation indicates elements whose concentrations exceed
0.345 MPC

copper concentrations are associated with adverse health effects, including kidney
and liver dysfunction, hepatitis, and anemia.
Lead primarily affects the kidneys and the nervous system. In children, lead
absorption is three to four times higher than in adults, which can result in delayed
physical and neurological development.
Substances such as ammonium nitrogen (NH3 , NH4 + ), petroleum hydrocarbons,
surfactants, and pathogenic bacteria were not detected in water samples collected at
any of the investigated sites.
In accordance with the classification of natural waters by chemical composition
proposed by Alekin [22], the division of waters is based on the predominance of major
anions and cations and on the ratios between them. According to this classification,
the waters of all the studied rivers belong to the bicarbonate class, calcium group,

828

S. K. Belekov et al.

Table 2 Concentrations of heavy metals exceeding the maximum permissible concentration
Element

MPC
mg/l

Content river-point

Typ (7.31;19.63), Chon-Kyzyl-Su-1 (7.43), Тura-Su (23.86;7.62)

Тura-Su-2 (1.52), Chon-Kyzyl-Su (3.90; 68.03), Chon-Ak-Su (5.20;3.99),
Zhyrgalan (2.23; 5.29)

0.01

The excess at all points is the maximum p. Тura-Su-2–4.07; р.
Chon-Kyzyl-Su-2–3.82

0.01

Excess at all points—from 0.39 (Tura-Su) to 2.04 (Chon-Ak-Su)

second type (Ca1 ), in which the sum of bicarbonate ions exceeds the combined
concentrations of calcium and magnesium ions (HCO3 − > Ca2+ + Mg2+ ).
The concentrations of major ions in the waters of the rivers within the Zhyrgalan
River basin do not exceed the maximum permissible concentrations (MPC) specified
in the applicable regulatory standards.

6 Conclusions
Based on the analysis of the collected samples, the highest water mineralization
was recorded in the Zhyrgalan River (46.3 mg/L), followed by Ak-Suu (40.4 mg/L),
Turgen–Ak-Suu (38.7 mg/L), and Bozuchuk (37.8 mg/L), while the lowest value was
observed in Zherges (28.2 mg/L). A comparison with data from other regions of the
Kyrgyz Republic indicates that the overall mineralization of waters in the Zhyrgalan
River basin is relatively low.
At the same time, lead concentrations exceeded the maximum permissible concentrations (MPC) established for fisheries by 1.2–1.7 times, while remaining below the
drinking water standards specified by SanPiN regulations of the Russian Federation
and the Kyrgyz Republic. Selenium concentrations in the Ak-Suu River exceeded
the standards of the World Health Organization by twofold, those of the European
Union by 24-fold, and the SanPiN drinking water standards by twofold. Molybdenum
concentrations exceeded fisheries standards by 2–7 times, but did not exceed drinking
water standards established by the WHO and SanPiN. Copper concentrations were
three times higher than fisheries standards, 1.5 times higher than WHO and EU standards, and remained below SanPiN drinking water limits. Arsenic concentrations
were 0.5 times lower than the standards established in Russia and Kyrgyzstan, while
exceeding WHO standards by twofold and EU standards by 21-fold. Aluminum
concentrations exceeded WHO and EU standards by 1.5 times, but were 1.7 times
lower than the drinking water standards established in Russia and Kyrgyzstan.
The results of the hydrochemical analysis of waters in the Zhyrgalan River basin
indicate that, for their use in drinking and domestic purposes, priority measures

Hydrochemical Composition of Waters of the Jyrgalan River Basin

829

should focus on the removal of heavy metals through appropriate water treatment
technologies.
Long-term and systematic monitoring of water quality in the Issyk-Kul basin
is recommended, with particular emphasis on the determination of heavy metal
concentrations.

References
1. Jirgalan (Dzhargalan. Jirgalan) (1966) Hydrological study. Volume 14. Basins of rivers of
Central Asia. Issue 2. The basin of Lake Issyk-Kul. The rivers Chu. Talas and Tarim.
Gidrometeoizdat, Leningrad, p 207. (Resources of surface waters of the USSR)
2. Zhyrgalan (2011) The National encyclopedia Kyrgyzstan by U.A. Asanova. Center of the state
language and encyclopedia. Bishkek, vol 3, p 440
3. Zhyrgalan (2004) Geography of Kyrgyzstan: an encyclopedic textbook. Center of the state
language and encyclopedia. Bishkek, p 187
4. Dzhergalan, Umurzakov SU, Keshikbayev AA, Makhrina LI et al (1988) Dictionary of
geographical names of the Kyrgyz SSR. Institute of geology of the academy of sciences of
the Kyrgyz SSR. Ilim Publishing House, Frunze pp 52–68
5. Jirgalang (1999) Dictionary of names of hydrographic objects of Russia and other CIS member
countries. Kartgeocenter—Geodesizdat, Moscow, p 117
6. Jirgalan (1931) Daily jute. Moscow: Soviet Encyclopedia. Stb. 796. Great soviet encyclopedia:
in 66 volumes. 1926, 1947, vol 21
7. Materials of the report for 2018 of the department of drinking water supply and sanitation
Gosstroya KR
8. The law of the Kyrgyz Republic dated May 30. 2011. Technical regulations on the safety of
drinking water as amended on April 28, 2017
9. Asankulov T, Abduvaili C, Isanova G, Long M, Duulatov E (2019) Long-term dynamics
and seasonal changes in the hydrochemistry of the lake basin. Issyk-Kul (Kyrgyzstan). Arid
Ecosystems 25 1(78):79–87
10. Kawabata Y, Kurita T, Nagai M, Aparin V, Onwona-Agyeman S, Yamada M, Fujii Y, Katayama
Y (2014) Water quality in the Issyk-Kul and the river flowing into it. J Arid Land Stud 24(1):105–
108
11. Heinicke T (2003) Mires within the dry steppe zone of the Issyk-Kul Basin (Kyrgyzstan). Part
1: soils. Stratigraphy and hydrology, Telma, pp 35–58
12. Taft BJ, Philippe LR, Dietrich CH, Robertson KR (2011) Grassland composition. Structure and
diversity patterns along major environmental gradients in the central Tien Shan. Plant Ecology
1349–1361. https://doi.org/10.1007/s11258-011-9911-5
13. Kadyrov VK (1986) Hydrochemistry of Lake Issyk-Kul and its basin. Frunze, p 211
14. Alymkulova B, Abuduwaili J, Issanova G, Nahayo L (2016). Consideration of water uses for
its sustainable management. The Case of Issyk-Kul Lake. Kyrgyzstan. Water Open Access J 9
15. Kutseva PP (1980) Elements of the chemical balance of Lake Issyk-Kul. Studies of the water
balance thermal and hydrochemical regime of Lake Issyk-Kul. Gidrometeoizdat, Leningrad,
pp 71–78
16. Abdyzhapar uulu S, Abuduwaili J, Shaidyldaeva N (2015) Impact of climate change on water
level fluctuation of Issyk-Kul Lake. Arab J Geosci 8:5361–5371. https://doi.org/10.1007/s12
517-014-1516-6
17. Matveev VP (1930) Hydrological and hydrochemical studies on Issyk-Kul in 1928. Materials
of the commission of expeditionary research of the USSR academy of sciences. The Issyk-Kul
expedition of 1928, Leningrad, pp 71–110

830

S. K. Belekov et al.

18. Asanaliev J (1968) Chemical characterization and formation of river waters in Southern
Kyrgyzstan. Abstract of the dissertation. Candidate of Chemical Sciences, Alma-Ata, p 17
19. Akmatov RT (2022) Geoecological effects of large reservoirs in Kyrgyzstan. Dissertation.
Geographical sciences, Bishkek, p 122
20. Akmatov RT, Alamanov SK, Choduraev TM (2023) The largest reservoirs of Kyrgyzstan. KSU
named after I. Arabaev, Bishkek, p 400
21. Alamanov SK, Li Y, Abdyzhapar uulu S, Satarov SS (2019) Investigation of the water quality
of the Issyk-Kul basin river. Science New Technol Innovations Kyrgyzstan 4:20–22
22. Alekin OA (1953) Fundamentals of hydrochemistry. Gidrometizdat, Leningrad, p 306

Radioecological Studies of the Kaji-Sai
Tailings Dam
Ch. Sultanbek kyzy, R. T. Akmatov, T. K. Kurenkeev, A. T. Zulushova,
and A. K. Esenkanova

Abstract The article presents the results of measuring the gamma radiation exposure
dose rate in the territory of the Kaji-Sai natural and anthropogenic uranium province
before and after reclamation. Prior to the reclamation of soil-covered ash dumps
and tailings in the Kaji-Sai area, exposure dose rates of gamma radiation averaged
between 30 and 60 µR/h. In the industrial zone (with a local maximum of 140 µR/
h), the activity levels of 210 Pb and 226 Ra were significantly elevated (210 Pb—12,121
± 204 и 226 Ra—10,643 ± 75). According to the study, there were zones with abnormally high exposure dose rates ranging from 600 to 1500 µR/h (up to 15 µSv/h). After
reclamation, the background radiation levels decreased to within the normal range
(0.18–0.28 µSv/h), posing no environmental threat. As part of the program “Reclamation of Territories of EurAsEC Member States Affected by Uranium Production”,
the Kaji-Sai tailings site has been fully reclaimed and secured. The measures implemented have significantly contributed to enhancing radiation safety in the Issyk-Kul
region.
Keywords Radionuclides · Radiation background · Radioactive waste · Exposure
dose rates · Gamma radiation · Tailings ponds · Reclamation

Ch. Sultanbek kyzy
Republican Institute for Advanced Training and Retraining of Pedagogical Staff Under the
Ministry of Education and Science of the Kyrgyz Republic, Bishkek, Kyrgyzstan
R. T. Akmatov (B)
Kyrgyz State University Named After I. Arabaev, Bishkek, Kyrgyzstan
e-mail: nalsur24@list.ru
T. K. Kurenkeev
Issyk-Kul State University Named After K.Tynystanov, Kara-Kol, Kyrgyzstan
A. T. Zulushova
Osh State University, Osh, Kyrgyzstan
A. K. Esenkanova
Kyrgyz National University Named After J.Balasagyn, Bishkek, Kyrgyzstan
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_66

831

832

Ch. Sultanbek kyzy et al.

1 Introduction
The Kaji-Sai Mining Plant of the USSR Ministry of Medium Engineering operated
from 1948 to 1969 for the processing of uranium ore, which subsequently transformed
into an electrical plant. Production waste and industrial equipment buried, forming
a tailings dump with a total volume of 400 thousand m3 of uranium waste [1–8].
The waste in this uranium province is a mixture of waste from a processing plant,
coal ash from a former thermal power plant, waste rock and remnants of the coal
ash-processing process from which uranium extracted. Currently, waste dumps are
also contained in some areas with scrap metal, etc. Obviously, previous attempts to
provide a protective coating for the tailing dump were ineffective, since the coatings
were often destroyed by natural phenomena and the local population, who excavated
the dumps to obtain scrap metal as a source of income, etc. [9–12].

2 Relevance, Scientific Significance of the Issue
Kyrgyzstan is currently trying to solve the problems of legacy mining and processing
of uranium ores in the republic, stored in landfills and tailings dumps (a huge volume
of mineral raw materials—747.2 million tons) (m3 ) and waste with a high content
of a number of potentially dangerous radioactive and chemical elements. Natural
phenomena such as soil erosion, landslides, and mudflows are of particular relevance when conducting scientific and practical work, studying the behavior of pollutants—radionuclides and chemical toxic substances in the environment. Natural and
fabricated environmental changes, combined with environmental factors, contribute
to their spread over significant distances from the place of primary localization.

3 Setting the Task
The paper sets out the tasks of conducting a radioecological study of the environment of the Kaji-Sai uranium tailings dump, determining risk coefficients, concentrations of radionuclides in living organisms, radiation doses and possible radiobiological effects in these environmental conditions. To compare the exposure dose rates
of gamma radiation from the background radiation in the territory of the Kaji-Sai
uranium natural and fabricated province before and after reclamation (Fig. 1).

Radioecological Studies of the Kaji-Sai Tailings Dam

Fig. 1 Location of the tailings dam and sampling [13]

833

834

Ch. Sultanbek kyzy et al.

4 The Theoretical Part
The study of the behavior of naturally occurring radioactive elements initiated by V.
I. Vernadsky in the late 1920s, established in a Biogeochemical Laboratory. In those
years, the main attention paid to the role of living matter in the concentration of natural
radioactive elements (isotopes of uranium, radium and thorium) in environmental
objects.
It known that the task of quantitative chemical analysis is to determine the content
of certain elements in the analyzed material. During the analytical study, a number
of sequential equivalent operations performed, because of which reliable data on
the qualitative and quantitative composition of the material obtained. Any analytical
definition involves four steps: (1) sampling; (2) sample preparation; (3) chemical
analysis proper (measurement of the analytical signal as a function of the content of
the components of interest in the sample); (4) statistical processing of the analysis
results.

5 Practical Significance, Proposals and Implementation
Results
On the surface of the soil-covered ash dumps and tailings in the Kaji-Say natural and
fabricated area, the exposure dose rate of gamma radiation averages 30–60 microns/
hour. According to our research, there are areas with abnormally high exposure dose
rates of 600–1500 µR/h (up to 15 µSv/h−1 ). High levels of MD are observed in
places where the protective coating has been disrupted as a result of excavations
carried out by local residents or natural: rains, water and wind erosion. Areas with
increased exposure dose rates (120–200 µm/h) also preserved on the territory of the
former industrial zone, in places where brown coal ash is stored, as well as in areas
of the former extraction production (Fig. 2).
Elevated exposure dose rates gamma radiation observed in areas where local
residents or natural processes have disrupted the protective cover due to unauthorized excavations. Residents of nearby towns and villages, including Kaji-Sai, often

Fig. 2 a General view of the plant, b tailings storage area

Radioecological Studies of the Kaji-Sai Tailings Dam

835

Table 1 Gamma background level in the technogenic uranium natural and fabricated province of
Kaji-Sai
Location of the point

On the soil surface (µm/h)

From the surface of the soil at
altitude 1 m (µm/h)

Riverbed in the area of the
tailings dam

20–35

15–28

Septic tank No. 1

20–35

Septic tank No. 2

20–35

Septic tank No. 3

18–30

Coal slag processing plant

20–45

20–35

Tailings storage

20–40

20–37

Above the tailings dump (200 m) 22–28

Above the tailings dam (1 km of
the mountain side)

27–34

Residential area

19–25

12–20

dig into the slopes in search of ferrous and non-ferrous metals for illegal resale.
Currently, the territory of the tailings site and the former industrial zone not secured,
and regular radiation monitoring not conducted due to a lack of dedicated funding.
Restoration efforts are only partially implemented and are carried out by the Ministry
of Emergency Situations of the Kyrgyz Republic [14–17].
The exposure dose rate, as is customary according to the method generally
accepted in radioecology, determined by us on the surface of the ground cover,
at 10 cm and at a height of 1 m. The measurement results shown in Table 1. The
table shows that the overall condition of this province is: the riverbed in the area of
the tailings dump, sedimentation tanks 1–3, industrial sites and the area around the
tailings dump up to 200 m, the exposure dose rate at background level or slightly
higher, but below the accepted norm in the republic (60 µm/h).
The settling tanks located below the tailings ponds, their condition is satisfactory,
the level of the exposure dose of the background radiation varies between 22 and
40 µm/h.

6 Isotopic Composition of the Soil Cover
The total radioactivity of the soils of the adjacent territory of the Kaji-Sai tailing
dump and 238 U, 234 U, 228 Th, 228 Ra, 230 Th, 210 Pb, 226 Ra and 40 K (see Table 2). The
table shows that the concentrations of 228 Th and 228 Ra are approximately at the same
level across the studied sites. In contrast, the concentration of 40 K in all investigated
locations within the tailings area is, on average, 10–15 times higher than that of 228 Th
and 228 Ra. 230 Th was detected at only three sites, but its concentrations were notably

836

Ch. Sultanbek kyzy et al.

Table 2 Soil activity in the area of the Kaji-Sai tailings dam
Sampling
location

U-238
Bq/kg

Bq/kg

U-234
±

Bq/kg

The slope
opposite the
sump 1

105

MDA

–

134

The bottom of
the stream from
the area of the
sump

126

MDA

–

Industrial site,
ash dumps

157

MDA

–

117

Industrial site,
spot 140
microns/hour

3152

148

154

15,513

1265

10,643

Ash from
workshop No. 1
of the CHPP

2483

160

120

MDA

412

2551

182

Ash on the
territory of
workshop No. 2

3736

174

184

3183

228

3383

228

Septic tank No.
1, Pit 70 cm

2338

353

113

5403

960

294

Sampling location Pb-210

Th-230

Th-228

Ra-226

Ra-228

K-40

Bq/kg

The slope
146
opposite the sump
1

146

The bottom of the 107
stream from the
area of the sump

107

Industrial site, ash 114
dumps

114

Industrial site,
12,121
spot 140 microns/
hour

204

12,121

204

Ash from
workshop No. 1
of the CHPP

2674

157

2674

157

Ash on the
territory of
workshop No. 2

3462

172

3462

172

251

Bq/kg

Septic tank No. 1, 251
Pit 70 cm

Radioecological Studies of the Kaji-Sai Tailings Dam

837

high–especially in surface soil samples from the industrial zone (at the location with
an exposure dose rate of 140 µR/h), where the value reached 15,513 ± 1265 Bq/kg.
Concentrations of 210 Pb and 226 Ra at 1–3 and 7 sites are on average at the same
level, and differ up to 2–3 times, and maximum accumulation observed at 4–6 sites.
In the soil, on the surface in the area of the industrial site and at the tailings dump,
ash from the workshop and on the territory of the industrial site (spot 140 µm/h), the
activity of 210 Pb and 226 Ra is quite high (210 Pb—12,121 ± 204 and 226 Ra—10,643
± 75).

7 Isotopic Composition of Water
The results of the analysis of natural radionuclides in tributaries and in Lake IssykKul showed interesting data (see Table 3). The concentrations of total uranium in the
studied areas of the lake (1.82 ± 0.15), compared with rivers and channels (0.09 ±
0.01), differ: the lake contains more of them from 2 to 8 times and the total alpha
activity of Bcl-1 in the lake is from 6 to 18 times increased. From streams No. 1 and
No. 2, when comparing the water of the Kichi-Ak-Suu River and the Bulan-Sogot
River, the total uranium content is up to 40–100 times different. However, it noted
that streams from the tailings do not always reach the lake (only in the spring and
autumn periods).
Table 3 Alpha activity levels in drainage waters around the Kaji-Sai tailings dam, as well as in
Lake Issyk-Kul (data given in Bk L−1 (+10%))
234 U/

226 Ra

238 U

(Bk
L− 1 )

4.5

1.49

0.007

10.0

10.2

1.30

0.005

Spring water from under the dam of the
Kaji-Sai tailings dam

6.4

6.7

1.52

0.025

Lake Issyk-Kul, stream mouth area from the
tailings storage area

1.67

1.69

1.43

0.015

Lake Issyk-Kul near the urban-type
settlement of Kaji-Sai

1.19

1.20

1.30

0.014

Sampling area

Stream from the tailings storage area in the
area of sump No. 1 (after rain)
Stream from the tailings storage area in the
area of sump No. 2 (before rain)

234+238 U

L−1 )

4.21

(Bk

Total alpha
activity (Bk
L−1 )

Lake Issyk-Kul near the village of Ak-Terek

0.56

1.16

0.60

0.018

Lake Issyk-Kul near Cholpon Ata city

0.79

0.80

1.13

0.010

838

Ch. Sultanbek kyzy et al.

8 Atmospheric Air
The volume concentration of radon and decay products in the air measured; atmospheric air samples taken to measure the content of alpha-active aerosols above the
tailings dump and at other sites in the province (see Table 4). According to the results
of our analyses on the content of alpha-active aerosols in the air both on the territory
of the uranium industrial site and in the village. Kaji-Sai, and in the recreational area
of the northern coast of Lake Issyk-Kul. There were no significant differences in
Issyk-Kul.
Within the framework of the program “Recultivation of the territories of the
EurAsEC States affected by uranium mining”, the Kaji-Sai tailings dam has been
fully cultivated. Reclamation works started in 2017 and completed in 2019. The
works included the construction of a protective shield and the restoration of fencing
around the site to prevent unrestricted access. The transfer of contaminated tailings
material to the newly built tailings dump, the modification of the existing riverbed to
prevent erosion of the sides of the tailings ponds, as well as the construction of two
protective dams [18] (see Fig. 3).
As part of the scientific project of the Ministry of Education and Science of the
Kyrgyz Republic for 2023 “Radioecological study of the environment of natural
and man-made ecosystems”, the project’s working group carried out measurements
of the radiation background on the territory of the Kaji-Say tailings dam and adjacent territories. Field work at all control points included measuring geographical
coordinates, exposure dose rates, sampling soils, surface waters, labeling samples,
as well as photographing the terrain and working procedures at individual control
points. Coordinates at each surveyed point recorded using a GARMIN eTrex 30
Table 4 Alpha-active aerosol content in the atmosphere of the industrial zone around the tailings
dump, as well as in the residential area of the village of Kaji-Sai and the city of Cholpon-Ata [13]
Aerosol
sampling points

Volumeof air Radionuclide concentration, 10–5 Bq/m3
pumping (m3 ) 238 U
226 Ra
210 Pb
228 Th
±

Uranium
settling tank-1

275

Industrial zone

3.2

1.8

±
3.0

0.8

384

2.2

1.0

2.1

0.5

Residential area 220
urban-type
settlement of
Kaji-Sai

3.5

1.5

3.8

0.8

Cholpon Ata
city, northern
coast

2.6

1.2

2.7

0.5

306

7 Be

75.5

2.6 1.5

0.6

49.6

1.8 1.1

0.4

197 7

103.9 10.1 1.9

0.6

210 22

0.6

334 18

84.3

4.8 1.4

±
179 6

Radioecological Studies of the Kaji-Sai Tailings Dam

839

Fig. 3 Kaji-Sai tailings dam after reclamation

handheld GPS receiver. The radiation background level measured with a DKS96 dosimeter-radiometer in accordance with established methodological guidelines
[19, 20].
The results of the study showed that the exposure dose rate of the gamma radiation
background in the area of the Kaji-Say tailings dam and its adjacent territories up to
the coast of Lake Issyk-Kul varies in the range of 0.18–0.28 mSv/h (see Table 5).
According to the Law of the Kyrgyz Republic Technical Regulations “On Radiation Safety”, the dose rate of gamma radiation in the adjacent territory from natural
sources for the population should not exceed 0.3 mSv/h [21].

840

Ch. Sultanbek kyzy et al.

Table 5 Average values of the background radiation level in the tailings storage area
Measuring points

On the soil surface (mSv/h)

Oscillation limit (mSv/h)

Т.1

0.23 ± 0.02

0.21–0.25

Т.2

0.24 ± 0.01

0.23–0.25

Т.3

0.24 ± 0.01

0.23–0.25

Т.4

0.23 ± 0.03

0.20–0.26

Т.5

0.24 ± 0.02

0.22–0.26

Т.6

0.24 ± 0.02

0.22–0.26

Т.7

0.23 ± 0.03

0.20–0.26

Т.8

0.24 ± 0.02

0.22–0.26

Т.9

0.23 ± 0.02

0.21–0.25

Т.10

0.24 ± 0.02

0.22–0.26

Т.11

0.23 ± 0.01

0.22–0.24

Т.12

0.24 ± 0.02

0.22–0.26

Т.13

0.25 ± 0.01

0.24–0.26

Т.14

0.26 ± 0.02

0.24–0.28

Т.15

0.26 ± 0.02

0.24–0.28

Т.16

0.25 ± 0.03

0.22–0.28

Т.17

0.25 ± 0.02

0.22–0.28

Т.18

0.27 ± 0.01

0.26–0.28

Т.19

0.28 ± 0.01

0.27–0.29

Т.20

0.27 ± 0.02

0.25–0.29

Т.21

0.28 ± 0.01

0.27–0.29

9 Conclusions
1. For radionuclides, a high radioecological risk factor is typical for 226 Ra, 230 Th
and 238 U. The main contribution to the external and internal radiation dose for
living organisms is 226 Ra.
2. The exposure dose rates of gamma radiation averaged 30–60 µm/h. On the territory of the industrial area (spot 140 µm/h), the activity of 210 Pb and 226 Ra is quite
high (210 Pb—12,121 ± 204 and 226 Ra—10,643 ± 75). According to our research,
there are areas with abnormally high exposure dose rates of 600–1500 µR/h (up
to 15 µSv/h−1 ).
3. After reclamation, the background radiation level varies within the normal range
(0.18–0.28 µSv/h) and does not pose a danger to the environment. It noted that the
government, represented by the Ministry of Emergency Situations of the Kyrgyz
Republic, is systematically working to reclaim radioactive waste from former
uranium production facilities with the involvement of international assistance.
The activities carried out have made a significant contribution to ensuring the
radiation safety of the Issyk-Kul region.

Radioecological Studies of the Kaji-Sai Tailings Dam

841

References
1. Bykovchenko YG (2005) Technogenic uranium pollution of the biosphere of Kyrgyzstan.
Bischkek, p 169
2. IA Vasiliev 2008 Assessment of the environmental hazard of radioactive waste storage facilities.
Radioecological and related problems of uranium production Bischkek 5 101 103
3. BM Dzhenbaev BT Zholboldiev BK Kaldybaev 2013 The current state of the Issyk-Kul uranium
radiobiogeochemical province Radiat Biol Radioecol 53 4 432 440
4. Zholboldiev BT (2016) Radioecological assessment of contamination of the territory of the
former uranium production of Kaji-Sai (Issyk-Kul biosphere territory). Dissertation for the
Degree of Candidate of Biological Sciences, Bishkek, р 111
5. Kovalsky VV, Vorotnitskaya IE, Lekarev VS et al (1968) Uranium biogeochemical food chains
in the conditions of the Issyk-Kul basin. Tr.Biogeochim.lab XII 25–53
6. B Djenbaev B Kaldybaev T Toktoeva A Kenjebaeva 2016 Radiobiogeochemical assessment
of the soil near the Issyk-kul region J Geol Resour Eng (USA) 1 39 43
7. Working material (2014) CD-disk. Regional training course on human and environmental risk
assessment for uranium production legacy sites (RER9122/001). IEEE, Vienna, Austria
8. Karpachev BM, Meng SV (2000) Radiation and environmental research in Kyrgyzstan.
Bishkek, p 56
9. BK Kaldybaev BM Jenbaev 2015 Radioecological studies of the coastal zone of the Issyk-Kel
biosphere territory Lap Lambert Academic Publishing, Germany Ecology and biogeochemistry
of mountain taxa of the biosphere 122
10. BK Kaldybaev ZhK Kenenova 2017 Radioecological assessment of the Kaji-Sai uranium tailings storage using the ERICA TOOL 1.2 computer program Bulletin of Issyk-Kul University
43 35 50
11. Dzhenbaev BM (2012) Biogeochemistry of natural and man–made ecosystems of Kyrgyzstan.
Ilim, Bishkek, p 404
12. BM Dzhenbaev BK Kaldybaev BT Zholboldiev 2013 Problems of radioecology and radiation
safety of former uranium production facilities in Kyrgyzstan Radiat Biol Radioecol 53 4 428
431
13. Sultanbek Kyzy Ch (2018) Radioecological assessment of the Kaji-Sai tailings dam using the
Erica tool 1.2. and Normalsa software. Master’s degree thesis. MIPHI, Moscow, p 8
14. Torgoev IA, Alyoshin YuG (2009) Geoecology and waste of the mining complex of Kyrgyzstan.
Ilim, Bishkek, p 240
15. BT Zholboldiev BM Jenbaev BK Kaldybaev TE Toktoeva 2016 Radioecological assessment
of the environmental condition of the Issyk-Kul biosphere territory Bull Issyk-Kul Univ 42 1
12
16. BK Kaldybaev GB Kadyrova BT Zholboldiev 2023 Radioecological studies of natural and
man-made ecosystems Bull Issyk-Kul Univ 55 30 38
17. BM Dzhenbaev BT Zholboldiev BK Kaldybaev 2018 Radioecological assessment of uranium
tailings dumps in Kyrgyzstan Wildl Res Kyrg 1–2 69 84
18. Strategic Master Plan for Environmental Restoration at Sites of Uranium Heritage in Central
Asia. In: The 65th Session of the IAEA General Conference, September 21, 2021. Vienna,
Austria
19. Instructions for Measuring the Gamma Background in Cities and Towns (by the Pedestrian
Method) (1985). Ministry of Health of the USSR. Moscow, p 5
20. Gusev NG, Margulis UY, Marei AN (eds) (1966) Dosimetric and radiometric techniques.
Atomizdat, Moscow, p 444
21. The Law of the Kyrgyz Republic dated November 29, 2011, No. 224 Technical Regulations
“On Radiation Safety”

Comprehensive Method of Reagent-Free
Purification of Natural and Wastewater
O. N. Medvedeva and T. N. Sautkina

Abstract The study presents an analysis of the methods of purification of natural
and waste waters used in various branches of industry, agriculture and public utilities,
as well as in the processes of water treatment and purification of natural and waste
waters of individual industries, enterprises and organizations. Based on the results
of the analysis, a device is proposed for the implementation of a complex method of
reagent-free purification of natural and waste waters, which is two functional units
of preliminary purification and settling, ensuring an increase in the efficiency of
water treatment due to the rational organization of purified flows, simplification of
the design due to the exclusion of moving parts and units, and an increase in the
reliability of the system for cleaning natural and waste waters.
Keywords Reagent-free purification · Wastewater · Water treatment · Settling
tanks · Cylindrical condenser · Electrostatic and magnetic (electromagnetic) fields

1 Introduction
Various purification methods are used to purify natural and wastewater, including
biological, physical–chemical and combined methods. Each method is characterized
by a certain intensity of impact on the treated environment, for example, the dose
of reagents, the dose of radiation, etc. The efficiency of each method and the costs
of its implementation are assessed by various factors, namely the chemical oxygen
consumption (COC) of the treated liquid, the concentration of suspended matter,
temperature, hydrogen index (pH), the concentration of bacteria and viruses and
other parameters [1, 2].
One of the important components of complex natural and wastewater purification
schemes are settling tanks, since the operation of the treatment plant as a whole
O. N. Medvedeva (B) · T. N. Sautkina
Yuri Gagarin State Technical University of Saratov, Saratov, Russia
e-mail: medvedeva-on@mail.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_67

843

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depends on their efficiency and productivity [3–5]. Settling is a simple, least energyintensive and inexpensive method of separating coarsely dispersed impurities from
wastewater with a density different from the density of water, which settles to the
bottom of the structure under the influence of gravity. Traditionally, in the practice
of natural and wastewater purification, the method of treating water with coagulants
and flocculants is used to increase the efficiency of the settling process [6, 7].
The main disadvantages of most water treatment plants include: an inefficiently
organized coagulation process associated with non-optimal doses of reagents, poor
mixing of reagents, incorrect sequence of reagent introduction, low-quality reagents,
low water temperature, non-optimal hydraulic conditions in flocculation structures,
the use of obsolete equipment, the lack of automated process control systems, etc. As
a result, due to unsatisfactory flocculation with the production of loose small flakes
of coagulated impurities with small hydraulic size in the flow volume, the impurities
do not have time to sink to the bottom of the settling tank during the estimated
residence time in the settling tank, causing an increased sludge and mud load on the
settling tanks, the structure does not cope with its main task and transfers the load
to the next stage of purification. Often, to eliminate the disadvantages, to intensify
the flocculation process, they resort to increasing the dose of coagulant and carry out
additional treatment of water with various oxidizers, which leads to the formation
of secondary water pollution, which has a detrimental effect on the environmental
situation as a whole.

2 Materials and Methods
The technological scheme of physico-chemical wastewater purification is known,
including a primary settling tank, an aeration tank, a secondary settling tank, a mixer,
reagents, a pumping station, a settling tank for physical and chemical treatment, and a
filter [7]. The advantage of the known solution is a reduction in the load on the aeration
structures, the ability to remove heavy metals and oil products through coagulation
and sorption, and an increase in the efficiency of nitrification. The disadvantages
include the formation of a significant amount of sediment, difficulty in the denitrification process due to insufficient carbon content, and difficulty in dosing the reagent
due to the lack of measuring devices for measuring the phosphorus content. Another
disadvantage of using reagents, for example, before secondary settling tanks, is an
increase in the content of iron ions, exceeding the permissible concentrations for
discharge into water bodies. The use of reagents directly before the filter ensures
high quality of the purified effluent, but this scheme requires significant costs for the
installation of the filter unit and the preparation of regeneration solutions.
The technology of a multi-stage purification process using sorption technologies
is often used (any material of high porosity can act as a sorbent), used as an after
treatment or the final stage of filtration water purification. The disadvantages of this
purification technology include low efficiency during pre-preparation, as well as
problems of regeneration and disposal of spent sorbent.

Comprehensive Method of Reagent-Free Purification of Natural …

845

The authors of [8] have developed a membrane technology as an alternative to
sorption methods, which simultaneously purifies water from organic and inorganic
components, bacteria and viruses.
The disadvantage of this solution is the harmful effect of concentration polarization (the concentrate makes up 1/10 of the volume of the entire filtered filtrate, water
passes from the pre-membrane layer, and the concentration of dissolved substances
at the membrane surface increases).
The disadvantages of the technology also include:
• the rapid contamination inherent in membranes, especially by organic substances,
which significantly worsens the technical, economic and operational performance
of the process and is caused by an increase in pH as a result of CO2 transfer through
the membrane and leads to the precipitation of hydroxide compounds of heavy
metals Fe(OH)3 , Al(OH)3 , Mn(OH)2 from the solution on the membrane surface;
• sedimentation, which creates resistance to flow and mass transfer in the boundary
layer, leading to a decrease in the productivity of the plant, an increase in the
pressure drops and a decrease in the selectivity of the membranes.
Thus, the main disadvantages of the known methods of natural and wastewater
treatment include the use of a large number of chemicals that heavily pollute wastewater (secondary pollution) and significantly increase the operating costs for periodic
removal of the resulting sludge by additional purges and flushing. Another disadvantage of known technological solutions is the need for separate stages of water
purification, which complicate the process of natural and wastewater purification
and increase its cost.
There are known designs of thin-layer modules (blocks) for settling (clarification)
of water [1, 2, 9], which are tanks (reservoirs) with a system of devices for input
and output of the processed liquid, equipped with one or several blocks of thin-layer
elements in which settling occurs, and devices for sediment unloading, and in some
cases a flocculation chamber.
The disadvantages of the known designs are increased requirements for mixers
and flocculation chambers in water purification circuits during its preliminary reagent
treatment, the need to create special conditions for the flocculation process and the
efficiency of mixing water with reagents, since the duration of water residence in
thin layer settling tanks is very short compared to conventional designs. Another
disadvantage of the known designs of modules (blocks) for settling (clarification) of
water is insufficient design measures that prevent or reduce the demolition of retained
suspended particles along the surface of thin-layer elements under the hydrodynamic
effect of the flow.
There are a sufficient number of devices known for reagent-free (electrochemical,
electromagnetic and magnetic) treatment of water and aqueous solutions, the technical result of which is an increase in the degree of liquid activation. For example,
methods of electrochemical treatment of water using a constant or pulsating electric
field, which consist in the fact that the specified field is created between the plates of a
capacitor, which is an electrolyzer or activator, while a diaphragm acts as a dielectric
dividing the space between the electrodes into anode and cathode chambers.

846

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The common disadvantages inherent in the specified group of devices are
increased energy costs for water treatment, since part of the electric power is unproductively spent on electrolysis of the water layer located between the electrodes;
low productivity of the devices; low efficiency due to the laminar flow of the treated
water and the absence of vortex motion in the flow; significant hydraulic resistance
and complexity of the design, insufficient contact area of the water flow with the
electrodes; the formation of a double electric layer by ions and ionized molecules,
which sharply reduces the access of free ions to the electrodes due to isolation of the
electrodes and the change in the electrostatic force of attraction between free cations
and the cathode.
Some installations for reagent-free purification and disinfection of aquatic environments use water treatment in an ultrasonic chamber at a frequency of over 25 kHz
and an ultrasonic oscillation power density of 0.05–2 W/cm2 , followed by ultraviolet
disinfection and filtration. The system is distinguished by the fact that a continuousspectrum pulsed radiation source in the 190–300 nm region is used for ultraviolet
irradiation at a pulse duration of 10–6–2 × 10–4 s and a pulsed radiation power density
in any cross-section of the volume of the treated environment of at least 20 kW/m2 .
A disadvantage of such a solution is the need to use a high-power level of the pulsed
radiation source for UV irradiation through liquid, which leads to a low service life
of the emitter and frequent replacement of gas-discharge tubes, and, accordingly, an
increase in the energy intensity of the process, as well as the likelihood of stimulating
the growth of microorganisms due to irradiation.
The general disadvantages of UV disinfection include the need to carry out the
process only in transparent water that does not contain colloidal and suspended
substances, i.e. pre-purified water, otherwise the contaminants will screen the UV
rays, which will prevent the interaction of the required dose of UV rays with microorganisms and will lead to insufficient disinfection efficiency. Most existing devices
have a complex design, which complicates their use in small treatment facilities. In
addition, it should be noted that a mandatory condition for their operation is the use
of flocculants in the water treatment process, which increases the cost of operation
and has a negative impact on the environment [10–12].
Thus, based on the results of the analysis, the following disadvantages of the
considered water purification methods can be identified: low efficiency in cleaning
wastewater contaminated with surfactants; unsatisfactory weight and size indicators
of installations and complexes; high energy consumption; duration of the processing
due to multi-stage; complexity of the design; absence of a post-treatment stage;
purified water does not always meet the requirements of regulatory documentation
[13–15].
In this regard, it seems relevant to develop technical solutions aimed at intensifying the processes of cleaning natural and wastewater, improving existing cleaning
technologies and developing new effective cleaning methods by using environmentally friendly reagent-free technologies, introducing resource-saving technologies
for modernizing existing methods and designs of water treatment plants that allow
saving material and natural resources [16–18].

Comprehensive Method of Reagent-Free Purification of Natural …

847

3 Theoretical Part
In the device, developed by the authors, it is proposed to pre-use a cylindrical
condenser in the technological process of water treatment to create an electrostatic
field in the liquid flow [19], as well as the synergistic effect of the interaction of
electrostatic and magnetic (electromagnetic) fields.
The essential distinguishing features of the new device are:
• The rejection of the flotation device and mechanical filtration will reduce the duration of the treatment process, significantly reduce the weight and size indicators
of the system, and reduce the range of replaceable and spare parts
• The use of a settling tank for dewatering and accumulation of sludge, which is
under the influence of a magnetic field, will significantly reduce the duration of
the treatment process, reduce the weight and size indicators of the system, and
simplify the settling process
• The use of combined treatment with electrostatic and magnetic (electromagnetic)
fields will achieve a synergistic effect, manifested in increased efficiency of purification and disinfection of natural and wastewater in the absence of the use of
reagents, which will increase the sanitary reliability of the system.
Figures 1 and 2 show: (Fig. 1)—a simplified diagram of the technological process
for the implementation of an integrated method for reagent-free treatment of natural
and wastewater and schematically shows the movement of the water flow in accordance with the practical application of the present invention; (Fig. 2)—a section of
a cylindrical condenser.

Fig. 1 A simplified diagram of the technological process

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O. N. Medvedeva and T. N. Sautkina

Fig. 2 A section of a cylindrical condenser

The positions in the (Figs. 1 and 2) are indicated: 1—a pipe made of a dielectric
material; 2—a frame; 3—an external insulated metal cylinder of a capacitor; 4—a
high-voltage generator; 5—sample pressure gauges; 6—a sump; 7—sources of a
magnetic field; 8—a drainpipe.
The installation for implementing an integrated method of reagent-free treatment
of natural and wastewater includes two functional units, while the first functional
unit contains two connected ones: a pipe made of dielectric material 1, wound coil
to coil in the form of a snake (cylindrical spiral) onto a frame 2, which is an internal
insulated metal cylinder at the same time, an external insulated metal cylinder of the
capacitor 3 in the form of a thin conductive plate is located outside the pipe. The
condenser device can be represented as two circular conductive cylindrical surfaces
with radii R1 and R2 (not shown in the diagram), arranged coaxially, forming a
cylindrical condenser, inside the space of which a pipe 1 is spirally laid between the
cylindrical surfaces, through which a purified stream of water flows. At the same
time, the pipe material must have the flexibility to twist the pipe into a coil quickly
and without industrial conditions, as well as have the ability to accumulate static
electricity charges. (+) and (–) from the high voltage generator 4 are connected to
the cylindrical surfaces of the frame 2 and the external insulated metal cylinder of
the capacitor 3 (shown in the diagram conditionally). At the beginning and at the
end of the spiral of pipe 1, exemplary pressure gauges 5 are installed, which are
necessary for measuring the pressure value during hydraulic tests. After the vertical
section of pipe 1, there is a second functional unit, which is a sump 6 made of a
dielectric material in the form of a sealed rectangular chamber or storage tank with
magnetic field sources 7 located around its perimeter, while both energy-efficient
(permanent) magnets and electromagnets can be used as sources of the magnetic
field 7. In the form of an inductor, in which the process of electromagnetic energy
transfer is carried out in the form of electric and magnetic fields. The installation
also contains a drainpipe 8 for the discharge of purified water.
The complex method of reagent-free purification of natural and wastewater is
carried out in two stages as follows.
At the first stage, the following operation is performed: the flow of source water
under pressure generated by a pumping unit (not shown in the diagram) is supplied

Comprehensive Method of Reagent-Free Purification of Natural …

849

to the device and enters pipe 1, where the impurity particles entrained by the water
flow and moving with it are affected by a central force acting between the impurity
particles A frictional force arises between the particles and the inner surface of
the pipe, as a result of which the particles become electrified and receive some
charge. In this case, pipe 1 helps to lengthen the section of the flow that is within
the field’s influence on the liquid and thereby enhances the effect. Additionally, the
flow through pipe 1, located between two insulated cylindrical conductive surfaces
(frame 2 and the outer insulated metal cylinder of the capacitor 3), is affected by
an electrostatic field created by a high-voltage generator 4, whereby a voltage of
about 5–10 kV is supplied to one surface with a (+) sign, and to the other with a
(–) sign. Thus, the pipe 1 appears to operate in the space between the plates of the
cylindrical capacitor, and the electrostatic field created by the high-voltage generator
4 (shown conditionally in the device) leads to an increase in friction between the
impurity particles and the walls of the pipe made of dielectric material 1, as a result
of which the process of treating the flow of purified water occurs more intensively:
the rate of formation of flakes increases, their adhesive capacity increases due to the
interaction of molecular and capillary forces of the water flow, as well as the force
of Coulomb interaction between charged particles, the time of separation of flakes
together with impurities of the treated water decreases, the rate of sedimentation
of the coagulated suspension increases, which ultimately increases the efficiency of
water purification and clarification. In this case, if particles of different types receive
different charges after passing through a pipe made of dielectric material 1 twisted
into a spiral coil, then as a result their adhesion and sedimentation occur significantly
faster than without purification.
To account for the mutual influence of local resistances, which are the coils of a
pipe made of dielectric material 1 (sections of a spiral coil), the pressure drops at the
beginning and at the end of the spiral coil is measured at known water flow rates Q
by measuring the pressure values p1 and p2 using exemplary pressure gauges 5.
When performing a hydraulic calculation of the device for determining the
pressure drop, the following relationship can be used “Eq. 1”:
(p1 − p2 ) = Q2 ·

8ρ · n
λ
· 2π · R · + ζ
π2 · d4
d

(1)

Where (p1 − p2 ) is the pressure difference at the inlet and outlet of the coil (pipe
made of dielectric material 1); Q is the flow rate; ρ is the density of the water flow; n
is the number of sections in the coil (pipe made of dielectric material 1); d is the inner
diameter of the pipe; R is the radius of curvature; λ is the coefficient of hydraulic
friction; ζ is the coefficient of local resistance of one section of the coil (pipes made
of dielectric material 1).
In the proposed device, it is possible to create an average voltage of 5000 V/
cm inside the flow of purified water in a pipe made of dielectric material 1 (with
a potential difference of 10,000 V across the capacitor cylinder). In this case, a
breakdown anywhere in the device is unlikely, because to breakdown a layer of

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O. N. Medvedeva and T. N. Sautkina

polyethylene with a thickness of 1 mm, it is necessary to create a potential difference
of 120 kV.
In this case, the field strength in the cylindrical capacitor is determined by the
expression “Eq. 2”:
E=

V
r · ln

R2
R1

(2)

where V is the potential difference on the cylinders; R1 , R2 are the radii of the large
and small cylinders, respectively; r is the distance to the point in the space between
the cylinders where the field strength is equal to E.
If the field strength determined by the above equation is less than the electrical
strength of the insulation, then breakdown will not occur. For the device under consideration, the field strength at a point at a distance of radius R1 (the smallest distance) at
a voltage of 10 kV is 0.617 kV/mm. Consequently, breakdown will occur at a lower
value of E. When using the proposed device, in order to study the cleaning effect, it
is possible to change the magnitude V and signs of the potentials on the cylinders,
as well as apply time-varying values V .
At the second stage, after passing through a spiral-wound pipe made of dielectric
material 1 for separating coagulated impurities, the purified and clarified water enters
a settling tank 6 made of dielectric material in the form of a sealed chamber of rectangular cross-section, with magnetic field sources 7 located along its perimeter, oriented
in a certain way, where, under the influence of a complex multifactor magnetic field
generated by permanent magnets or electromagnets, on hydrated metal ions dissolved
in water and the structure of water clusters, polarization and deformation of ions
dissolved in water occurs, accompanied by a decrease in their hydration, increasing
the likelihood of their convergence, which ultimately leads to the formation of crystallization centers of impurities, thereby accelerating their sedimentation [20–22],
that is, a change in the rate of electrochemical coagulation (sticking together and
coarsening) of dispersed particles in the flow of magnetized liquid occurs. The use of
magnetic field sources 7 makes it possible to influence the process of reorientation of
ion hydrate shells and change their distribution in water, so that positive ion hydrates
under the influence of force lines move in a spiral to the negatively charged pole, and
negative ones to the positive pole, the interaction of molecules of different polarities
with each other is enhanced. As a result, magnesium and calcium salts contained in
water lose the ability to form in the form of a dense deposit, which contributes to
a finer purification of water, and are released in the form of sludge easily removed
by the water flow, accumulating in the receiving chamber of the settling tank 6. The
presence of iron oxides in the water flow contributes to an increase in the number
and rate of formation of crystallization centers, and when magnetized, the latter form
additional macroscopic poles to which molecules of calcium and magnesium salts
of different polarities are attracted. Then the purified water flow is directed through
drainpipe 8 into the main pipeline (not shown in the diagram) for use by various
categories of consumers for their intended purpose.

Comprehensive Method of Reagent-Free Purification of Natural …

851

4 Results and Discussion
Laboratory studies on the intensification of the purification process and the coagulation process according to the complex method of reagent-free purification of natural
and waste water by using reagent-free technology of electrification of particles by
applying an electrostatic field due to a high-voltage generator through the capacitor
plates and settling of water in a settling tank under the influence of a magnetic field
were carried out on the device shown in Figs. 1 and 2.
The studies were conducted on model solutions, as well as on natural water from
the Volga River (using a coagulant). The experiments to study sedimentation were
conducted: without additional treatment, with the optimal dose of coagulant (12.0 mg/
l by Al2 O3 ), with electrification, a combination of electrification with an electrostatic
field, settling under the action of a magnetic field (the settling time t settl . was 25–
30 min). During the studies, observations were made of the intensity of flocculation
and sedimentation of suspended particles. After settling was complete, samples of
clarified water were taken, and turbidity and color indices were determined. The time
for completion of the sedimentation process was with traditional water coagulation—
30 min; when coagulating water by treating the solution with electrification only in a
spiral coil without applying any additional physical fields (in this case, electrification
occurred due to friction against the inner surface of the pipe)—8–10 min.; using the
proposed improved device—3–5 min. The results of the experiments showed that
when physical fields are applied to coagulated water, the process of floc sedimentation
is accelerated by 3–6 times.
The activity of hydrogen ions in the studied water was measured using pH-metric.
Analysis of the results of changes in the hydrogen pH index before and after treatment
of the studied water (model liquid) showed that during conventional coagulation, the
pH value decreases from 6.8 to 6.2 points (from 5.9 to 5.4 points for the studied
Volga water), and when treated only in a spiral coil, it increases slightly from 6.8 to
6.95 points (5.97 points for the studied Volga water), when processed in the proposed
device, it increases from 6.8 to 7.45 points (increases from 5.9 to 6.78 points for the
studied river water).
Analysis of the data from the study of the turbidity spectrum of water using
a photoelectric colorimeter showed that after additional treatment of the studied
solutions in the proposed device, the turbidity of Volga water decreased from 3
to 1.2 mg/l compared with the results of conventional coagulation, and the color
decreased from 10° to 2.3° compared with conventional coagulation. Similarly, for
model solutions prepared for laboratory studies: after treatment in the proposed
device, the turbidity decreased from 3.5 to 1.5 mg /l, the color of the water decreased
from 20° to 5°.
During magnetization of wastewater, the magnetic field strength was 10 kA/m.
The liquid under study passed at a speed of 0.52–1.1 m/s, the magnetic induction
value between the magnets was at least 100 mG. According to the results of the
studies, the particle sedimentation rate increased by 1.5–2 times at a magnetic field
strength of 0.2 Tl and 6–7 times at 0.8 Tl, which is associated with a change in

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the structural organization of aqueous solutions, consisting in the disruption of the
hydrated environment of ions.
It follows from the results obtained that the quality of clarified and decolorized
water during traditional coagulation without the use of any accelerators of this process
is somewhat worse than when using additional processing on the proposed device.
It follows from the obtained results that the quality of clarified and decolorized
water with traditional coagulation without the use of any accelerators of this process
is somewhat worse than with the use of additional processing on the proposed device.
A feature of the proposed complex method and device for its implementation
is the provision of intensification of the coagulation process and sedimentation of
impurities without the use of weighting additives, which allows achieving a significant economic effect due to the organization of a complex reagent-free technological
process, as well as eliminating harmful emissions and ensuring effective purification of the water flow, which indicates the environmental efficiency of the proposed
method and device for its implementation, which does not have any moving elements,
which increases reliability and durability, increasing the service life of the device.
The purpose and operation of the functional devices of the reagent-free purification
system for natural and wastewater provide a complete and comprehensive solution to
the problem. The proposed installation will provide a complete complex purification
of natural and wastewater using the processes of settling, non-reagent disinfection
and purification, due to the synergistic effect that occurs with the simultaneous use
of active effects of electrostatic and magnetic (electromagnetic) fields.

References
1. Degremont: Memento technology de l’eau (2004) 10eme édn, Degrémont-Suez, RueilMalmaison, p 1718
2. Memento Technique de l’eau pour les professionnels du traitement de l’eau. https://www.sue
zwaterhandbook.fr/. Accessed 15 Jan 2025
3. Nechaev AP, Smirnova LV (1991) Intensification of post-treatment of biologically treated
wastewater. Water Supply Sanit Eng 12:18–20
4. Zhmur NS (2003) Technological and biochemical processes of wastewater treatment at facilities
with aeration tanks. AQUAROS, Moscow, p 512
5. Pupyrev EI, Shelomkov AS (2014) Economic justification of environmentally friendly
wastewater treatment technologies. Water Supply Sanit Eng 1:5–12
6. Dolina LF (2001) Reactors for wastewater treatment. In: Reactors for wastewater treatment.
Standard Publishing House, Dnepropetrovsk, p 82
7. Dushkin SS, Kovalenko AN, Degtyar MV, Shevchenko TA (2011) Resource-saving technologies of wastewater treatment: monograph. Kharkiv National Academy of Urban Economy,
Kharkov, p 146
8. Svitsov AA (2006) Introduction to membrane technology. Mendeleyev University of Chemical
Technology, Moscow, p 280
9. Frog DB (2015) Classifier of thin-layer modules for external water supply networks: a methodological guide. Research Institute of Building Physics of the Russian Academy of Architectural
and Civil Engineering Sciences, Moscow, p 47

Comprehensive Method of Reagent-Free Purification of Natural …

853

10. Toth AJ, Fozer D, Mizsey P, Varbanov PS, Klemeš JJ (2023) Physicochemical methods for
process wastewater treatment: powerful tools for circular economy in the chemical industry.
Rev Chem Eng 39(7):1123–1151. https://doi.org/10.1515/revce-2021-0094
11. Bazhenov VI, Epov AN, Noskova IA (2014) Use of simulation modeling complexes for
wastewater treatment technologies. Water Supply Sanit Eng 2:62–71
12. Voronov YuV, Alekseev EV, Pugachev EA (2014) Water disposal: educational publication.
ASV, Moscow, p 416
13. Lesin VI (2019) Viscosity mathematical model of heavy oil containing the metal oxides
colloid nanoparticles impurity. Oil Gas Bus 2:199–206. https://doi.org/10.17122/ogbus-20192-199-216
14. Poirier K, Lotfi M, Garg K, Patchigolla K et al (2023) A comprehensive review of preand post-treatment approaches to achieve sustainable desalination for different water streams.
Desalination 566:116944. https://doi.org/10.1016/j.desal.2023.116944
15. Alimbekova SR, Bakhtizin RN, Voloshin AI, Dokichev VA (2019) Physical methods against
salt deposits during oil production. Oil Gas Bus 17(6):31–38. https://doi.org/10.17122/ngdelo2019-6-31-38
16. Chan SH, Moussa B (1996) Trajectories and deposition of silica particles on cylinders in
crossflow with and without a magnetic field. J Heat Transf 118(4):903–910. https://doi.org/10.
1115/1.2822587
17. Parsons SA, Judd SJ, Stephenson T, Udol S, Wang BL (1997) Magnetically augmented water
treatment. Process Saf Environ Prot 75(2):98–104. https://doi.org/10.1205/095758297528869
18. Gatard V, Deseure J, Chatenet M (2020) Use of magnetic fields in electrochemistry: a selected
review. Curr Opin Electrochem 23:96–105. https://doi.org/10.1016/j.coelec.2020.04.012
19. Medvedeva O, Sautkina T, Chesnokova E (2022) Development of method and device to
improve the efficiency of natural and wastewater treatment. In: Proceedings of the 5th international conference on construction, architecture and technosphere safety. Lecture notes in civil
engineering, vol 168. Springer, Cham. https://doi.org/10.1007/978-3-030-91145-4_50
20. Martynova OI, Gusev BT, Leont’ev EA (1969) Concerning the mechanism of the influence of
a magnetic field of aqueous solutions of salts. Sov Phys Usp 12:440–443. https://doi.org/10.
1070/PU1969v012n03ABEH003893
21. Naderi M, Nasseri S, Mahvi AH et al (2021) Mechanical trajectory control of water mineral
impurities in the electrochemical-magnetic reactor. Desalin Water Treat 238:67–81. https://doi.
org/10.5004/dwt.2021.27756
22. Xiao Y, Seo Y, Lin Y, Li L et al (2020) Electromagnetic fields for biofouling mitigation in
reclaimed water distribution systems. Water Res 173:115562. https://doi.org/10.1016/j.watres.
2020.115562

Investigation of the Dependence
of Air-to-Water Oxygen Transfer
on the Content of Surfactants in Water
M. Dyagelev

Abstract This article presents an experimental study on the influence of the surfactant Sodium Laureth Sulfate (SLES) on the kinetics of oxygen mass transfer into
water during bubble aeration. Experiments were performed in a 40 L cylindrical
column equipped with a fine-bubble disc diffuser at an air flow rate of 4 L/min and a
temperature range of 12–18 °C. Test series were conducted with an SLES concentration of 60 mg/L. The time-dependent dissolved-oxygen concentration was recorded
with dedicated probes, allowing characteristic aeration curves to be obtained and the
overall volumetric mass-transfer coefficient K L α to be determined via the linearised
relationship log(C s − C t ). A temperature correction factor θ = 1.024 was applied to
normalise the values to 20 °C. On the basis of K L α, the standard oxygen transfer rate
(SOTR) and standard oxygen transfer efficiency (SOTE) were calculated. The results
show that adding SLES to water decreases the saturation concentration Ct from 4.88
to 4.45 mg/L (−8.8%), reduces K L α from 0.01209 to 0.01161 s−1 (−3.96%), and
lowers the SOTR from 0.02066 to 0.01984 kg O2 /h (− 4%). The time required to
reach 70% of total saturation was up to 20% longer compared with clean water. The
findings indicate that even low SLES concentrations can raise the energy demand of
aeration systems. Practical recommendations include applying preliminary degassing
or physical filtration of organic matter to restore oxygen-transfer characteristics close
to those observed in clean water. Future research should elucidate the mechanisms
by which surfactants affect gas–liquid dynamics and develop methods to compensate
for their negative impact.
Keywords Aeration · Dissolved oxygen · Surfactant · Mass transfer · Oxygen
transfer

M. Dyagelev (B)
Kalashnikov Izhevsk State Technical University, Izhevsk, Russia
e-mail: m.yu.dyagelev@istu.ru
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_68

855

856

M. Dyagelev

1 Introduction
The aeration process represents a fundamental example of a two-phase system in
which oxygen mass transfer from the gas phase to the liquid phase occurs. This
phenomenon can be realized both with bubble generation and in their absence, which
opens broad prospects for application in various fields of science and technology.
The study of aeration, particularly in the context of bubble aeration, is of paramount
importance for such areas as aquaculture, wastewater treatment technologies, chemical engineering, and energy [1]. Special attention should be paid to the role of aeration in water treatment systems, where oxygen is a key factor in the biodegradation
of pollutants [2].
High concentrations of dissolved oxygen are an integral condition for the effective
course of aerobic biochemical processes, such as the oxidation of organic pollutants
using suspended or attached biomass. These processes include both biochemical and
chemical oxidative reactions aimed at reducing biochemical and chemical oxygen
demand, as well as removing ammonium nitrogen and non-biodegradable organic
compounds [3]. However, these processes are accompanied by significant oxygen
consumption, which leads to its deficiency in wastewater. This requires the application of specialized aeration systems to maintain the optimal level of water oxygen
saturation [4, 5].
Despite the significance of aeration, its practical implementation faces a number of
technical challenges caused by the low solubility of oxygen in the aqueous medium.
This limits the efficiency of mass transfer at the phase interface, which reduces
the performance of aeration installations and increases energy costs [6]. 60–80%
of the total costs for treatment facilities [7, 8]. This is related to the necessity of
using powerful air blowing installations to ensure the required level of water oxygen
saturation.
Considering the aforementioned factors, optimization of aeration processes
becomes a key task for scientific research and engineering developments. The goal
of these efforts is to improve oxygen mass transfer, reduce energy costs, and minimize environmental impact. Thus, an in-depth understanding of the physicochemical
aspects of aeration, as well as the development of innovative technologies, represent
important directions for improving wastewater treatment systems and other technological processes requiring intensive oxygen saturation of liquids. Therefore, the
study of oxygen mass transfer processes into water in the presence of additional
loading in the form of suspended substances or surfactants is a relevant research
topic not only in terms of improving the energy efficiency of aeration systems, but
also from the perspective of fundamental laws of gas dynamics.
Surfactants represent a class of chemical compounds possessing unique physicochemical properties, including pronounced detergent, wetting, and emulsifying capabilities. Due to these characteristics, surfactants find wide application in various
industrial sectors, including household chemistry, textile, and leather industries.
However, this usage is associated with substantial ecological risks related to the

Investigation of the Dependence of Air-to-Water Oxygen Transfer …

857

formation of wastewater containing high concentrations of surfactants [9]. Wastewater containing surfactants can originate from various sources, including domestic
effluents formed in residential buildings, hotels, and laundries, as well as industrial
effluents formed as a result of washing, chemical treatment, and textile material
production. As research by other authors shows, the level of surfactants in domestic
wastewater ranges from 1 to 10 mg/L, while wastewater from surfactant production can discharge up to 300 mg/L [10]. Weijie et al. [11] found that the content of
anionic surfactants in rural sewage networks was in the range of 1.72–3.88 mg/L,
while the lowest content was found at treatment facilities and amounted to approximately 0.3 mg/L. Xin et al. [12] found surfactants in urban treatment facility effluents
in the range of 522–668 μg/L. Sini et al. [13] found that the maximum concentration of surfactants in treatment facility influent was 6.4 × 10−3 mol/L, the concentration of surfactants in treated wastewater was approximately 5.1 × 10−3 mol/
L, and the concentration of surfactants in final wastewater treatment effluents was
approximately 10−3 mol/L.
The aforementioned indicates that wastewater contains surfactants and they
inevitably enter the aeration tank, which leads to changes in the efficiency of oxygen
mass transfer in aeration systems. Despite the significant volume of scientific publications devoted to studying the influence of various factors on the processes of
air-to-water oxygen mass transfer, these remain insufficiently studied. In particular,
the mechanisms by which surfactants modify gas-liquid dynamics and affect oxygen
diffusion are still subjects of discussion among researchers.
Maruyama [14] proposed the hypothesis that surfactants promote the formation
of excessive foam in the aqueous medium, which can significantly impede oxygen
mass transfer and reduce water’s capacity for self-purification. This assumption indicates the potential negative impact of surfactants on aquatic ecosystem quality and
bioremediation processes.
Research by Rosso et al. [15] demonstrated that the addition of surfactants leads
to a reduction in the rate of oxygen mass transfer at the phase interface. The degree of
inhibition varied depending on surfactant concentration and reached 70% compared
to clean water control conditions. These results indicate significant negative influence
of surfactants on air-to-water oxygen mass transfer processes during wastewater
aeration.
Rosso and Stenstrom [16] also noted the nonlinear nature of changes in the oxygen
mass transfer coefficient (KL α) in the presence of surfactants in the concentration
range from 0 to 20 mg/L. An initial decrease in KL α was observed, which was subsequently replaced by an increase, indicating complex physicochemical interactions
of surfactants with the aqueous medium. However, additional experimental data and
theoretical modeling are required for definitive conclusions.
In contrast to the aforementioned studies, the authors of the work by Rozenblit
et al. [17] assert that surfactants reduce the tendency for air bubble aggregation
and improve their sphericity, which could potentially contribute to increasing aeration efficiency. Nevertheless, the reduction in bubble sizes may decrease the overall
volume of gas exchange surface.

858

M. Dyagelev

Chern et al. [18] suggested that surfactants promote microbubble generation,
which may positively affect oxygen mass transfer. They also noted that surfactants
can increase the rate of mass transfer in surface aeration zones, which is important
for optimizing aeration systems.
Thus, despite the significant number of studies devoted to the influence of surfactants on oxygen mass transfer, the question remains open. Additional research is
required to identify the mechanisms of surfactant interaction with the aqueous
medium and to develop effective methods for managing aeration processes.
The objective of this work is the experimental investigation of the dependence of
air-to-water oxygen transfer on the content of surfactants in water.

2 Materials and Methods
For the study of the dependence of aeration system functioning efficiency on surfactant concentration, a corresponding scheme was developed and an experimental setup
was created, presented in Fig. 1. During the construction of the setup, special attention
was paid to ensuring the possibility of continuous measurement of key parameters
necessary for oxygen transfer modeling, such as the flow rate of supplied air and the
rate of water oxygen saturation.
The experimental setup consisted of a cylindrical column manufactured from
polyvinyl chloride pipe with an external diameter of 110 mm, wall thickness of 2.2
mm, and height of 1500 mm; the working volume of the setup was 40 L. Air supply
was carried out using a compressor to a fine-bubble disc aerator with a diameter of
50 mm, installed at the base of the column and rigidly fixed to the foundation. The
air flow rate was maintained at a constant level of 35 L/min, and the size of bubbles
generated by the aerator was 0.35 ± 0.15 mm. For air flow regulation, a flow meter

Fig. 1 a Experimental setup schematic; b experimental installation

Investigation of the Dependence of Air-to-Water Oxygen Transfer …

859

with a supply regulation range from 0 to 5 L/min was installed in the air line through
a fitting.
Control of the dynamics of dissolved oxygen concentration changes was carried
out using sensors of the Multi 340i multiparameter analyzer. Before the beginning
of each experiment, reagent deaeration of tap water was performed using sodium
sulfite until zero oxygen content was achieved:
2Na2 SO3 + O2 → 2Na2 SO4

(1)

During reagent deaeration, reaction catalysts were not added due to the small
volume of the reservoir. After reaching the minimum dissolved oxygen value in
water, the compressor was turned on, and the time for water oxygen saturation to the
initial level was recorded. Before the beginning of each series of experiments, a trial
system startup was performed with adjustable air supply according to the flow meter.
Then the valve between the flow meter and aerator was closed to create positive
pressure in the supply air.
In the first series of experiments, the reservoir with the aerator was filled with tap
water to the required volume, reagent deaeration was conducted, when the oxygen
concentration reached zero, aeration began, and when the concentration reached the
initial value, a characteristic aeration curve was obtained—the change in oxygen
concentration in water as a function of time. In subsequent series of experiments,
surfactants were additionally added to the water in the reservoir. Sodium laureth
sulfate (SLES, Sodium Laureth Sulfate) was used as the surfactant—an anionic
surfactant belonging to the group of alkyl(ether)sulfates, which is one of the most
common components in detergents and cleaning agents, as well as cosmetics for
foam formation and effective removal of contaminants. Series of experiments were
planned and conducted with surfactant concentrations of 10, 30, 60, 90, and 120 mg/L
at different supplied air flow rates—1, 2, 3, 4, and 5 L/min. To increase the reliability
of results, each series of experiments was conducted in triplicate.
Tests were conducted in the temperature range of 12–18 °C in tap water using
various operating conditions to verify their influence on the process. Data collected
during the aeration phase were used to calculate KL α (Eq. 2) using the linearized
form of the simplified mass transfer model (Eq. 3).
Cs − Ct
= e−(KL α) t
Cs − C 0
log(Cs − Ct ) = log(Cs − C0 ) −

(2)
KL α
t
2.303

(3)

where Cs is the saturated oxygen concentration at system temperature, C t is the
oxygen concentration at a given moment in time, and t is time. The logarithm of the
dependence of dissolved oxygen concentration in water on time log(C s − C t ) gives a
straight line, from whose slope the mass transfer coefficient of the considered system
can be calculated. C t was measured at a specific height, which remained fixed in all

860

M. Dyagelev

tests presented for comparison. Using the obtained K L α value, temperature correction
can be made to normalize data at 20 °C by applying Eq. 4:
KL α = KL α20 θ (T −20)

(4)

where θ is the characteristic constant of the aeration system used (taken as 1.024),
T is temperature. K L α20 can be used to calculate the standard oxygen transfer rate
(SOTR) using Eq. 5:
SORT = CS(20) · KL α20 · Vtan k

(5)

where C s(20) is the saturation concentration at 20 °C, and V tank is the tank volume.
The obtained SOTR can be used to calculate SOTE (standard oxygen transfer
efficiency) by applying Eq. 6:
SOTE % =

SORT
· 100
OT

(6)

where OT denotes oxygen transferred under standard test conditions (Eq. 7):
OT = Qair · CO2 ·

Tstd
· dO2
T

(7)

where Qair is the air flow rate, CO2 is the oxygen concentration in air, T is temperature,
T std is standard temperature (20 °C), and d O2 is oxygen density.

3 Results and Discussion
Following 25 series of experiments with triple replication (with surfactant concentrations of 10, 30, 60, 90, and 120 mg/L, and at air flow rates of 1, 2, 3, 4, and 5 L/
min), only experiments with SLES concentration of 60 mg/L at a specified air flow
rate of 4 L/min proved to be representative. Increasing SLES concentration led to
excessive foam formation and distortion of data obtained by sensors for measuring
dissolved oxygen concentration—the sensors recorded abrupt increases in concentration and, upon reaching saturation values, similar abrupt decreases in dissolved
oxygen concentration. Possibly, to obtain representative results with higher surfactant
concentrations in water, larger capacity reservoirs should be used.
Decreasing SLES concentration did not provide significant differences in water
oxygen saturation curves for both tap water and water with surfactant addition. Thus,
based on the conducted experiments, it can be stated that with the given reservoir
capacity of 40 L, conducting research on the dependence of air-to-water oxygen
transfer on SLES content in water is feasible at surfactant concentrations ranging
from 30 to 90 mg/L.

Investigation of the Dependence of Air-to-Water Oxygen Transfer …

861

The obtained data on the dependence of water oxygen saturation on aeration time
at an air flow rate of 4 L/min in tap water and in water with SLES addition is presented
in Fig. 2.
Analysis of the obtained curves illustrates slower oxygen concentration growth in
the presence of surfactants. In the absence of surfactants, dissolution proceeds faster:
the concentration gradient is high, and the clean surface facilitdsorb at the interface,
reducing surface tension and partially screening water from oxygen, which decreases
the initial gas flow into the liquid. In the time range of 60–180 s, both curves demonstrate nearly linear increase, reflecting the region where the mass transfer coefficient
KLα is controlling. In tap water, the water oxygen saturation rate is approximately
25% higher. In the range of 180–240 s, when concentration approaches equilibrium partial pressure, the oxygen gradient drops, and the curves smooth out. Water
with SLES addition reaches a pseudo-plateau later and at a lower level, confirming
persistent mass transfer inhibition and potential reduction of the actual saturation
coefficient. During further aeration (more than 240 s), changes are minimal: the
concentration increase in tap water does not exceed 0.2 mg/L, while in water with
SLES solution it is 0.1 mg/L. The difference in final values (approximately 0.6 mg/
L) indicates that even prolonged aeration does not compensate for the effect of film
formation on air bubbles.
Thus, SLES addition to water leads to a reduction in effective gas-liquid contact
area and a decrease in the external convective diffusion coefficient. The most sensitive
interval is the first 3 min, during which up to 70% of total saturation is formed. The
obtained curves of water oxygen saturation dependence on aeration time in tap water
and in water with SLES addition show that the presence of surfactants in wastewater
increases energy costs for aeration. Experimental data show that achieving a dissolved
oxygen concentration of 5 mg/L in water requires 20% longer aeration time in water
with surfactant addition compared to tap water.
The calculated values obtained based on measured data during the aeration process
and calculated according to Eqs. 2– 5 for tap water and water with SLES addition
are presented in Table 1.
Analysis of the calculated values of main aeration process parameters illustrates
the difference in oxygen concentration at saturation (C t ) for the studied liquids, which
amounted to 0.43 mg/L (≈ 8.8%), indicating a reduction in the potential maximum
concentration of dissolved oxygen in water containing surfactants. This reduction is
likely due to the formation of a thin film around bubbles and a decrease in effective
gas-liquid contact area.
The decrease in mass transfer coefficient K L α,t by 0.00048 s−1 , or by 3.96%
for water with SLES addition, demonstrates that adsorbed SLES molecules slow
oxygen transfer from bubbles to water by reducing turbulence at the bubble surface
and decreasing oxygen molecule mobility in the boundary film. After temperature
correction (θ = 1.024), the difference remains at the same level (~ 3.96%), confirming
that the surfactant effect is not a temperature factor but is indeed caused by surface
phenomena.

Clean water
Water with surfactants

Time, s

Fig. 2 Dynamics of oxygen concentration change in water at 4 L/min air flow rate

Oxygen concentration in water, mg/L
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
146
151
156
161
166
171
176
181
186
191
196
201
206
211
216
221
226
231
236
241
246
251
256
261
266
271
276
281
286
291
296
301
306
311
316
321
326
331
336

862

M. Dyagelev

Investigation of the Dependence of Air-to-Water Oxygen Transfer …

863

Table 1 Calculated values of the main parameters of the aeration process for the studied liquids
Parameter

Units of measurement

Tap water

Water with SLES

Сt

Mg/l

4.88

4.45

K L α,t

c−1

0.01209

0.01161

K L α20

c−1

0.01580

0.01518

SORT

Kg O2 /h

0.02066

0.01984

Reduction of K L α

3.96%

–

The reduction in SOTR by 0.00082 kg O2 /h (~4%) for water with SLES addition
means that an aeration installation in the presence of surfactants will be less productive, requiring longer aeration duration or increased air flow rate to achieve the same
saturation levels.
To evaluate the obtained results, a comparison of the obtained experimental data
with results from other studies was conducted—the comparison of K L α reduction
magnitude is presented in Table 2.
The reduction in mass exchange coefficient in this study (≈ 4%) is notably smaller
than the typical range of 25–70% for wastewater. This can be explained by the absence
of organic colloids and biomass, which additionally reduce K L α by 50–70%. Overall,
the obtained results quantitatively agree with literature data—the mass exchange
coefficient reduction obtained in this work (− 3.96%) falls within the lower edge of
the range described by other authors for similar surfactant concentrations. At higher
loads or in the presence of biomass (activated sludge), suppression may increase
by an order of magnitude; this should be considered when scaling results to real
wastewater conditions.
Table 2 Comparison of the reduction value K L α
References

Notes

Surfactant
concentration, mg/L

K L α Reduction (%)

This research

Clean water with
SLES

− 3.96

Rosso and Stenstrom
[16]

Real wastewater
conditions

0.4–8

− 70

Wagner and Popel [19]

Clean/waste water,
fine-pored diffusers

1–15

− 30 to 60

Garrido-Baserba et al.
[20]

Water/wastewater
with surfactants

2.4 ± 0.4

46–54

864

M. Dyagelev

4 Conclusions
Experimental investigation of the influence of anionic surfactant Sodium Laureth
Sulfate (SLES) on oxygen mass transfer kinetics in water during bubble aeration
demonstrated that SLES addition leads to reduction of all key oxygen transfer parameters. SLES addition results in a notable decrease in saturated oxygen concentration
(C t )—in the presence of surfactants, C t decreases from 4.88 to 4.45 mg/L (−8.8%),
which indicates the formation of a thin film by SLES molecules on bubble surfaces,
thereby reducing the effective gas-liquid contact area and deteriorating equilibrium
conditions for oxygen dissolution.
The oxygen mass transfer coefficient under current conditions (K L α,t ) and the
normalized coefficient at 20 °C (K L α20 ) decrease by approximately 3.96% (from
0.01209 to 0.01161 s−1 and from 0.01580 to 0.01518 s−1 , respectively). This
effect persists even after temperature correction, which unambiguously indicates the
surface-chemical nature of oxygen transfer process inhibition, rather than changes
in thermodynamic parameters of the medium.
Standard oxygen transfer rate (SOTR) drops from 0.02066 to 0.01984 kg O2 /h (−
4%). This means that under otherwise equal conditions, an aeration installation with
SLES presence will be less efficient, requiring increased aeration time or air flow
rate to achieve the specified saturation level. The practical effect of SLES presence is
particularly manifested in saturation dynamics: up to 70% of total dissolved oxygen
increase in clean water is achieved within the first 180 s, while in surfactant solution
this interval is extended by 20%. Thus, even at low SLES concentrations, energy
costs of aeration systems may increase by substantial amounts.
The analysis of obtained experimental and calculated results confirms that the
main mechanisms of aeration efficiency reduction in the presence of SLES are:
formation of adsorption film on bubbles, suppression of turbulence at gas-liquid
contact, and reduction of oxygen molecule mobility in the boundary layer. Based
on the obtained data, it is recommended that when designing and operating aeration installations under conditions where wastewater discharge with surfactants is
possible (concentrations up to 60–90 mg/L), the following provisions should be
made: increasing aeration time by 15–25% compared to calculated values for clean
water, increasing air flow rate or transitioning to aerators with smaller bubbles to
compensate for the reduction in mass transfer coefficient.
Further investigations should focus on developing mathematical models that
account for the complex interactions between surfactant properties, turbulent flow
characteristics, and aeration equipment geometry. Such models would enable more
accurate prediction of aeration system performance under varying surfactant loading
conditions and facilitate optimization of energy consumption in wastewater treatment
facilities.
The study of different surfactant classes and their mixtures represents a critical
research need, as commercial wastewater often contains multiple surfactant types

Investigation of the Dependence of Air-to-Water Oxygen Transfer …

865

with potentially synergistic or antagonistic effects on mass transfer processes. Understanding these interactions would enable more precise design criteria for industrialscale aeration systems and contribute to reduced operational costs and improved
treatment efficiency.

References
1. Kizhisseri MI, Sakr M, Maraqa M, Mohamed MM (2025) A comparative bench scale study
of oxygen transfer dynamics using micro-nano bubbles and conventional aeration in water
treatment systems. Heliyon 11(4):e41687. https://doi.org/10.1016/j.heliyon.2025.e41687
2. Rizzardi I, Bottino A, Capannelli G, Pagliero M, Costa C, Matteucci D, Comite A (2023)
Membrane bubble aeration unit: experimental study of the performance in lab scale and fullscale systems. J Membr Sci 685:121927. https://doi.org/10.1016/j.memsci.2023.121927
3. Dyagelev MY (2024) Removing biogenic elements from urban sewage: technology review. In:
Lecture notes in civil engineering, vol 400, pp 463–473. https://doi.org/10.1007/978-3-03147810-9_42
4. Han Q, Zhang XY, Wu HB, Zhou XT, Ji HB (2023) Different efficiency toward the biomimetic
aerobic oxidation of benzyl alcohol in microchannel and bubble column reactors: hydrodynamic
characteristics and gas–liquid mass transfer. Chin J Chem Eng 55(4):84–92. https://doi.org/10.
1016/j.cjche.2022.05.020
5. Pavlov II, Dyagelev MY, Isakov VG (2024) Studies of oxygen mass transfer efficiency during
wastewater aeration. Constr Geotech 15(1):5–16. https://doi.org/10.15593/2224-9826/2024.
1.01
6. Campbell K, Wang J (2020) New insights into the effect of surfactants on oxygen mass transfer
in activated sludge process. J Environ Chem Eng 8(5):104409. https://doi.org/10.1016/j.jece.
2020.104409
7. Dyagelev MYu, Pavlov II, Nepogodin AM, Grakhova EV, Lapina AA (2021) The review of
aeration systems for biological wastewater treatment. IOP Conf Ser Earth Environ Sci (EES)
839:42035. https://doi.org/10.1088/1755-1315/839/4/042035
8. Dyagelev MYu, Isakov VG, Grakhova EV (2019) α-factor experimental determination of aeration system in aeration tanks. IOP Conf Ser Mater Sci Eng (MSE) 687(6):066071. https://doi.
org/10.1088/1757-899X/687/6/066071
9. Ahmia AC, Idouhar M, Wongwailikit K, Dietrich N, Hébrard G (2019) Impact of cellulose
and surfactants on mass transfer of bubble columns. Chem Eng Technol 42(11):2465–2475.
https://doi.org/10.1002/ceat.201800620
10. Guo Y, Ren M, Huang C, Huang X, Liu X, Zhai X, Shu Q (2025) Physical aeration mechanism
of SDBS wastewater in a tank aerated by a microporous tube system. Chem Eng J 516:164048.
https://doi.org/10.1016/j.cej.2025.164048
11. Weijie W, Ni J (2017) Study on the determination of anionic surfactant in sewer system. J
Environ Sci (China) 36:200–202. https://doi.org/10.13623/j.cnki.hkdk.2017.s2.028
12. Qi X, Liu Z, Jingwei F (2025) Traceability of direct and leakage discharge of domestic sewage
based on SDBS and DOM. J Environ Sci (China) 45:748–758. https://doi.org/10.19674/j.cnki.
issn1000-6923.20241028.002
13. Sini K, Idouhar M, Ahmia AC, Ferradj A, Tazerouti A (2017) Spectrophotometric determination
of anionic surfactants: optimization by response surface methodology and application to Algiers
bay wastewater. J Environ Monit Assess 189(12):646. https://doi.org/10.1007/s10661-0176359-7
14. Maruyama H, Suzuki A, Seki H, Inoue N (2006) Enrichment in axial direction of aqueous
foam in continuous foam separation. Biochem Eng J 30(3):253–259. https://doi.org/10.1016/
j.bej.2006.05.004

866

M. Dyagelev

15. Rosso D, Huo DL, Stenstrom MK (2006) Effects of interfacial surfactant contamination
on bubble gas transfer. Chem Eng Sci 61(16):5500–5514. https://doi.org/10.1016/j.ces.2006.
04.018
16. Rosso D, Stenstrom MK (2006) Surfactant effects on alpha-factors in aeration systems. Water
Res 40(7):1397–1404. https://doi.org/10.1016/j.watres.2006.01.044
17. Rozenblit R, Gurevich M, Lengel Y, Hetsroni G (2006) Flow patterns and heat transfer in
vertical upward air-water fow with surfactant. Int J Multiphase Flow 32(8):889–901. https://
doi.org/10.1016/j.ijmultiphasefow.2006.03.003
18. Chern JM, Chou SR, Shang CSS (2001) Effects of impurities on oxygen transfer rates in
diffused aeration systems. Water Res 35(13):3041–3048. https://doi.org/10.1016/S0043-135
4(01)00031-8
19. Wagner M, Pöpel HJ (1996) Influence of the diffuser submergence and density on oxygen
transfer and aeration efficiency. Water Environ Fed 1:437–448
20. Garrido-Baserba M, Rosso D, Odize V, Rahman A, Van Winckel T, Novak JT, Al-Omari A,
Murthy S, Stenstrom MK, De Clippeleir H (2020) Increasing oxygen transfer efficiency through
sorption enhancing strategies. Water Res 183:116086. https://doi.org/10.1016/j.watres.2020.
116086

Information and Analytical Support
of Resources Degradation Risk
Management of the Sport Center Fire
Extinguishing Operation
O. M. Shikulskaya, T. U. Yesmagambetov, M. I. Shikulskiy,
and M. M. Yesmagambetova

Abstract The work shows that, as a rule, carefully developed extinguishing plans
are used in extinguishing fires and conducting rescue operations. However, these
plans are focused on the proper condition and the required amount of resources,
but this is not always feasible in practice. At the same time, a partial failure of
resources does not always lead to a complete failure of the extinguishing plan. The
review of scientific research showed significant achievements in this direction of
French, Russian and Kazakh scientists. The studies objective presented in the paper
is to verify the feasibility and reliability of the theoretical studies results of the
resource failure level effect on the goal achievement degree in fire extinguishing
and rescue operations in relation to a specific protection object. The authors chose a
sports complex in Astrakhan as an research object. To analyze previously performed
theoretical studies, the authors calculated the risks of reducing the effectiveness of
the developed operation with varying degrees of resource failure and they proposed
measures to increase the facility security.
Keywords Multi-state system · FTA · Fire · Protection object · Criterion · Risk
management

O. M. Shikulskaya (B)
Astrakhan State University of Architecture and Civil Engineering, Astrakhan, Russia
e-mail: shikul@mail.ru
T. U. Yesmagambetov · M. M. Yesmagambetova
Karaganda University of Kazpotrebsouz, Karaganda, Republic of Kazakhstan
M. I. Shikulskiy
Astrakhan State Technical University, Astrakhan, Russia
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 9th International
Conference on Construction, Architecture and Technosphere Safety, Lecture Notes in
Civil Engineering 799, https://doi.org/10.1007/978-3-032-14938-1_69

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O. M. Shikulskaya et al.

1 Introduction
Traditionally, when planning fire extinguishing and rescue operations, developers
analyze the protection object, calculate the required amount of forces and means for
extinguishing a fire and conducting rescue operations, and develop a plan for this
operation. At the same time, it is a priori assumed that the quantity and quality of
resources involved in a tactical operation correspond to the required, i.e. the obtained
calculation results. However, in reality, as practice shows, the state of the necessary
resources does not always meet the requirements for quality and quantity. Fire safety
ensuring requires significant financial investments, which are usually not enough.
In addition, there is a possibility of various accidental events (risks) that worsen
the state of resources. At the same time, partial deterioration of the resources state
does not always lead to the operation complete failure, and the different state of
various resources affects the operation outcome to varying degrees. Knowledge of
the influence degree of the attracted resources state level on the operation outcome
will make it possible to most effectively distribute the missing funds for resource
support of the protected object. This circumstance determines the relevance of the
problem being solved.
The problem’s scientific significance of optimal distribution of the necessary
resources entire range is of paramount importance due to the high probability of
fires’ victims and colossal financial losses from them, as well as the need for huge
financial costs to ensure facilities fire safety and insufficient finances for this purpose.
A huge number of works by scientists from Europe, Russia, Kazakhstan, Vietnam
and other countries [1–11] do not consider the possibility of using resources that do
not meet the requirements for quality and quantity. This problem is very difficult
and requires information and analytical support, which the work of a number of
researchers is devoted to [12–18]. The authors team led by Brushlinsky proposed
analytical dependencies to describe the time flows of calls to emergency services,
as well as these processes simulation in order to organizational and management
decisions support on the emergency services operational activities [12]. However,
this work similarly does not take into account the resources condition. In addition,
the proposed solutions implementation is very costly.
French scientists Girard, David, Piatyszek, Flaus, proposed a method for a priori
analysis of emergency response plans in order to take into account the resource failure
influence degree on the degree of the operation goal achieving in emergency response
[19]. The method is based on the combined use of Multi-State System (MSS) and
Fault Tree Analysis (FTA). This method was finalized by scientists from Russia and
Kazakhstan [20, 21]. It is necessary to test developments at a specific object. The
implementation of theoretical studies to determine the resource failure level impact
on the goal achievement degree in relation to a specific protection object is his study
goal.
Setting the task is to check the feasibility and reliability of the theoretical studies
results of the resource failure level impact on the goal achievement degree in relation
to a specific protection object.

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The theoretical value of the work lies in the development and verification of the
method for assessing the impact of the level of resource failure on the degree of
achieving the goal of emergency response, and the practical significance lies in the
development of a methodology for applying this method to the protection of specific
objects.
The work theoretical value lies in the development and verification of the
method for assessing of the resource failure level impact on the achievement degree
emergency response goal.

2 Methods and Materials
As a toolkit for solving the task, the method of a priori analysis of emergency response
plans was taken as a basis in order to take into account the degree influence of resource
failure on the degree of the operation’s goal achieving in emergency response. This
method was proposed by French scientists Girard, C., David, P., Piatyszek, E., Flaus,
J.-M. It is based on the combined use of Multi-State System (MSS) and Fault Tree
Analysis (FTA).
The fault tree traditionally uses two process states, operation and failure. However,
for a comprehensive analysis of the emergency response models weaknesses and an
assessment of used resources’ wide range, it is advisable to use a systematic approach
with many system states [19]. Consideration of multiple resource degradation states
is necessary to show to what extent the plans requirements are met.
A Multi-State System (MSS) is defined as a system with a finite number of state
levels with a finite number of resource health levels.
We will consider 4 states of the system and resources:
Lvl 1: Not degraded ({gj, 1 = 1, pj, 1 }).
Lvl 2: Rather not degraded ({gj, 2 = 2, pj, 2 }).
Lvl 3: Rather degraded ({gj, 3 = 3, pj, 3 }).
Lvl 4: Completely degraded ({gj, 4 = 4, pj, 4 }).
Resources are divided into technical, human, information and organizational ones.
For each level of resource degradation, the probability is determined based on
expert judgment or a statistical method. The sum of the probabilities of all four
working ability levels is from 1 to 100%.
This is comparable to the classic risk matrix construction. The failure level is
characterized by a list of pairs {level, probability}. Thus, 4 failure levels (4 pairs)
are defined for each resource and function.
The impact degree assessing method of the resource failure level on the goal
achievement degree of the emergency response plan when protecting an object in a
fire or emergency is quite universal. But it has its drawbacks in relation to the conditions of Russia and Kazakhstan, where climatic and road conditions significantly
affect the time of arrival of fire departments at the place of call. Due to these circumstances, this method was finalized by scientists from Russia and Kazakhstan [20, 21].

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A more detailed study of the “march” resource was made. Scale and logical fault tree
are created for this resource. In addition, the result of the original method applying
is a probability matrix of each state, which does not allow an unambiguous estimate.
Russian and Kazakh authors proposed a criteria system and developed mathematical
methods for calculating them. This contributed not only to the assessment clarification of the extinguishing plans analysis results. The criteria proposed by the authors
allow comparing decision alternatives to eliminate the identified problems.

3 Results
The authors developed an algorithm for predicting the effectiveness of emergency
response operations based on an a priori assessment of the used resources degradation’s degree impact on the level of the rescue operation goals achievement, which
includes the following steps:
• Selection of processes for their analysis
• Building an fault tree for each process using the FTA method using the AND, OR
and PRIOR logic elements.
• Define values ranges for system and resource state levels
• Determination of the tree lower level elements probability with the help of experts
or based on statistical analysis of available data.
• Determining of each process working ability level probabilities (root of the error
tree) using a mathematical logic for a multi-state system approach.
• Evaluation of the model as a whole.
Theoretical studies of the authors were applied in practice to manage the risks
of a fire extinguishing and performing rescue operations in the sports complex in
Astrakhan (Russia). For clarity, a well-protected facility is chosen to demonstrate
how resource failures significantly affect even for well-protected facilities for which
the success of the fire department response plan would seem obvious.
The selection of processes for the fault trees construction is based on the diagram
in Fig. 1.
Based on the scheme, the authors chose the processes of “Fire brigades arrival
at the place of call”, “Combat deployment,” “Fire localization” and “Fire extinguishing.” And then they built a common fault tree for the functioning process of the
fire department in case of fire, combining the four previously presented processes.
They built fault trees for each of the selected processes. One of them, the fault tree
of the “Fire brigades’ arrival at the place of call” process, is shown in Fig. 2.
The next step is to define ranges of values for system and resource state levels.
Level values are relative values. They need to be determined through real measured
physical quantities. It is also necessary to determine these quantities values range for
each state level of the system as a whole, its elements and resources used.
Initially, based on the regulatory documentation study, interviewing the sports
complex management and experts from the Ministry of Emergencies, the authors

Fig. 1 The main time characteristics of the fire service functioning, reflecting its response to incoming calls

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Fig. 2 Fault tree of the process of “Fire brigades’ arrival to the call place”

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determined the measurable goals of the fire extinguishing operation and the
permissible ranges of their achievement levels.
Two goals are reducing casualties and reducing fire damage. The first goal is
unconditional priority, which follows from the moral principles and the constitution
of the Russian Federation. Each target has its own measurement units. The first
is the number of victims of the fire (people), the second is the direct and indirect
material damage caused by the fire (thousand rubles). They should be considered
independently, and you need to start naturally with a higher priority goal of reducing
victims from fire. The number of fire victims directly depends on the fire brigades’
arrival time to the fire. Based on the statistical data, the dependence of the fire victims
number on the fire brigades’ arrival time was determined.
The identified ranges of the first goal and the related process “The fire brigades’
arrival time at the call site” are given in Table 1.
If the safety of people is ensured (the option of the absence of people in the
gym and their presence only in administrative premises is considered), in order to
calculate financial losses, we change the boundaries of the ranges for achieving the
goal—reducing the time of arrival of software formations for fire due to the very
rigid difficult to achieve framework defined for the first goal.
Financial losses directly depend on the burnout area, which in turn depends on
the burning time (Table 2).
Table 1 Values ranges of the goal achievement levels of reducing the fire victims number in
accordance with the values ranges of the process goal achievement levels on which the main goal
depends
Levels

The number of victims
per 100 people (man)

Arrival time (min)

Min

Max
3

Number

Name

Not degraded

Rather not degraded

9.6

Rather degraded

9.6

11.8

Completely degraded

11.8

Max

Table 2 The goal levels achievement values ranges of fire damage reducing in accordance with
the values ranges of the processes goals achievement levels on which the main goal depends
Levels
Number

Name

Financial losses
(thousand rubles)

Burnt area (m2 )

Burning time
(min)

Min

Max

Not degraded

3500

25,000

366

4000

Rather not degraded

25,000

38,000

4000

6000

Rather degraded

38,000

47,000

6000

7500

Completely degraded

4700

77,000

7500

12,350

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The burnt area size depends on the three processes success (the fire brigade arrival
for fire, combat deployment and fire localization). Data on ranges determination of
intermediate process objectives achievement levels are given in Table 3.
To test the reaching possibility of the ranges limits, a computational experiment
was carried out in which the calculation was carried out for each minute of the process.
To perform a computational experiment, a computer program was developed.
The next step is to determine probability of the lower level tree elements with the
experts help or based on a statistical analysis of the available data.
Let’s consider in which processes and specifically in the trees lower level’ elements
of these processes the previously identified risks are reflected (Table 4).
Further, based on statistical data and expert surveys, a probabilities table of the
tree’s lower level states for each processes is filled. Moreover, the first process (Fire
brigades Arrival for fire) is used for both purposes, the rest of the processes - only
for the second purpose. Table 5 shows the data for filling of the process tree lower
level of “Fire brigades’ arrival for fire.”
The next stage is to calculate the risks of the goal achieving on the fault tree.
To assess the level of achievement of the process goal, a quality criterion was
used, calculated as the mathematical expectation of the level of achievement of the
Table 3 Define ranges of intermediate process objectives achievement levels
Levels

Process time

Number

Name

Not degraded

Rather not degraded

Rather degraded

Completely degraded

Arrival

Combat
deployment
Min

Fire localization

Min

Max

Min

Max
16

Table 4 Linking risks to the tree
Number

Events (failures)

Process

Leaves

Information source

False operation of the
hardware and software
complex of
strelets-monitoring
formula

Arrival

Statistics

Road traffic accidents
involving fire trucks and
fire-rescue equipment

Fire hydrant failure

Malfunctions of the fire
pump station

Q15
Q16
Combat deployment

Q4
Q4

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Table 5 Data for filling in the lower level of the process tree “Fire brigade arrival to fire”
Management level

Resource

Question

Probabilities of reaching
state levels
1

1. Strategic (design) OR organizational
resource (places
and number of
accidents)

2. Tactical
(planning)

Q1. Failure in
determining forces
and means

Q2. Failure to
determine IF
location

Q3. Failed to
schedule departures

Q4. Failure in
planning to attract
forces and funds

Q5. Route selection
failed

0.7

0.3

OR organizational
resource (order)

Q6. Failure in
organizational
decisions

0.9

0.1

TR technical
resource

Q7. Hardware
failure. Technical
condition

0.9

Q8. Hardware
failure. Insufficient
quantity

0.9

0.1

HR human resource Q9. Staffing failure. 0.9
Low qualification

0.1

OR organizational
resource

3. Operational
OR organizational
(decision making) resource (route
selection)

4. Operational
activities

0.1

Q10. Taffing failure. 0.9
Insufficient quantity
TR technical
resource

TR technical
resource

Q11. Road quality.
Road operating
condition

0.75

Q12. Road quality.
Engineering
equipment and road
construction

0.5

Q13. Traffic
intensity. Time of
day interval

0.8

Q14. Traffic
intensity. Seasonal
interval

0.9

0.1
0.25

0.2

0.3

0.1

(continued)

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O. M. Shikulskaya et al.

Table 5 (continued)
Management level

Resource

Question

Probabilities of reaching
state levels
1

HR human resource Q15 accident.
Involving PA

0.8

Q16. Accident
without PA
involvement

0.7

4
0.2

0.1

0.2

process goal according to formula (1).
k

gi · pi = 2, 3

KQ =

(1)

i=1

where gi is a number of state level, pi is a probability of its achievement.
The diagram of the obtained results with calculation of the quality criterion is
shown in Fig. 3. The objective of the Fire Brigade Arrival process is the time of
arrival.
After assessing the operation failure risks, it is necessary to develop measures to
reduce them.

Fig. 3 Failure levels diagram to achieve the process’ goal of “Arrival of fire brigades at the fire
site”

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4 Discussions
The authors developed measures to reduce the risks of non-compliance with the
developed plan.
Since it is impossible to completely eliminate the likelihood of risks and failures,
the authors propose to develop the following measures aimed at reducing the risk or
its consequences.
• In order to prevent spontaneous and false actuation of the “Strelets-Monitoring”
hardware and software complex, it is proposed to equip facilities with uninterrupted power supply devices, which will ensure the operability of the “StreletsMonitoring” hardware and software complex regardless of the state of the central
power supply at the facility.
• In connection with the increasing incidence of road accidents involving fire trucks
and fire and rescue equipment, as well as other road accidents that interfere with
the movement of fire fighting equipment to the place of call, it is proposed to
equip the busiest and widest sections of roads with a dedicated lane for special
vehicles, which will reduce the risk of accidents, as well as reduce the time of
arrival of fire and rescue units to the place of call.
• Another measure that will minimize the risk of a long-term arrival of the fire and
rescue brigads is a preliminary analysis of the state of traffic congestion using
Internet resources (interactive maps) by the Fire department dispatcher.
• To ensure proper level of external fire water supply sources, it is recommended to
organize unscheduled inspections of fire hydrants serviceability, as well as to work
out the issue of bringing employees responsible for fire hydrants serviceability to
administrative responsibility.
• To reduce risks in the operation of the fire pump station, it is proposed to organize
high-quality reception of equipment during the shift of duty guards, with the
implementation of all measures to check the serviceability of the fire pump, in
addition, their maintenance during a fire and after a fire.
In order to eliminate the erroneous choice of the decisive direction, it is proposed to
organize additional classes with the operational-commanding staff of fire protection
units at the most complex facilities of practical interest in planning combat operations
to extinguish a fire and conduct emergency rescue operations.

5 Conclusion
The feasibility and reliability of the results of theoretical studies previously performed
by the authors to determine the impact of the level of resource failure on the degree of
achievement of the set goal in fire extinguishing and emergency rescue operations in
relation to a specific object of protection—the sports complex in Astrakhan (Russia)
were verified.

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The results of the work showed that even for well-protected objects there is a
sufficient probability of resource failure with a significant degree of deviations from
the goal implementation. The value of work lies in the fact that the application of its
results allows you to optimally distribute the missing resources.

References
1. Flaus JM (2011) A modelling framework for model based risk analysis. ESREL Troyes, France,
pp 1533–1540
2. Georgiadou PS, Papazoglou IA, Kiranoudis CT, Markatos NC (2007) Modeling emergency
evacuation for major hazard industrial sites. Reliab Eng Syst Saf 92:1388–1402
3. Georgiadou PS, Papazoglou IA, Kiranoudis CT, Markatos NC (2010) Multi-objective evolutionary emergency response optimization for major accidents. J Hazard Mater 178:792–803
4. Jain S, McLean C (2003) A framework for modeling and simulation for emergency response.
In: Proceedings of the 2003 international conference on machine learning and cybernetics, pp
1068–1076
5. Jonkman SN, Lentz A, Vrijling JK (2010) A general approach for the estimation of loss of life
due to natural and technological disasters. Reliab Eng Syst Saf 95:1123–1133
6. Karagiannis GM, Piatyszek E, Flaus JM (2013) Model-driven and risk-based performance
analysis of industrial emergency plans. J Conting Cris Manag 21:96–114
7. Kolen B, Kok M, Helsloot I, Maaskant B (2013) Evacuid: a probabilistic model to determine
the expected loss of life for different mass evacuation strategies during flood threats. Off Publ
Soc Risk Anal
8. Terebnev VV, Grachev VA, Semenov AO (2006) Management of fire and rescue units resources
and technological operations for extinguishing fires. Fire Explos Saf 15(5):60–65
9. Vaez N, Nourai F (2013) RANDAP: an integrated framework for reliability analysis of detailed
action plans of combined automatic-operator emergency response taking into account control
room operator errors. J Loss Prev Process Indust 26:1366–1379
10. Krymsky VV, Golovenko VR (2024) Organization of management of firefighting units with the
use of modern fire and rescue equipment when extinguishing aircraft fires. Pozharovzryvobezopasnost/Fire Explos Saf 33(2):77–90. https://doi.org/10.22227/0869-7493.2024.33.02.77-90
11. Alutaibi K, Alsubaie A, Marti J (2015) Allocation and scheduling of firefighting units in large
petrochemical complexes. In: IFIP advances in information and communication technology.
https://doi.org/10.1007/978-3-319-26567-4_16
12. Brushlinsky NN, Sokolov SV, Alekhine et al (2004) City security. In: Imitation modeling of
urban processes and systems, FASIS, Moscow
13. Butuzov SY, Korobko VB, Pranov BM, Stankevich ТS, Chlenov AN (2016) A neuro-fuzzy
model of support for fire extinguishing control in seaports. Contr Syst Inf Technol 4(66):91–96
14. Semikov VL, Nguyen BT (2015) Resource management model for ensuring the activities of
the fire rescue service. Fire Saf ChallS Prospect 1(6):110–113
15. Stankevich TS, Kiper AV (2018) Intellectual decision support system based on fuzzy neural
networks for fire extinguishing manager in the territory of Kaliningrad commercial seaport.
OJSC Certif Stat Regist Comp Progr 2013661903:12(86)
16. Stankevich TS, Butuzov SY, Ryzhenko AA (2018) Information and analytical support for
management of fire extinguishing at highly dangerous and technically complex facilities. KnE
Engineering Russian Forum of Young Scientists (RFYS), pp 229–237
17. Vilisov VY (2019) Algorithm for optimal allocation of limited resources based on the method
of game iterations. Inf Technol Bull 2(20):89–99
18. Sadeghi-Naini A, Asgary A (2013) Modeling number of firefighters responding to an incident
using artificial neural networks. Int J Emerg Serv 2(2):104–118. https://doi.org/10.1108/IJES03-2012-0001

Information and Analytical Support of Resources Degradation Risk …

879

19. Girard C, David P, Piatyszek E, Flaus J-M (2016) Emergency response plan: model-based
assessment with multi-state degradation. Saf Sci 85:230–240
20. Esmagambetov TU, Shikulskaya OM (2016) Analysis of the reliability of the emergency population evacuation plan as a multi-state system based on the structure of the fault tree. Adv Mod
Sci 8(4):68–72
21. Shikulskaya O, Yesmagambetov T, Ten T, Spanova B, Shikulskiy M (2023) Information and
analytical support for decision-making on resource support of fire fighting units. In: Silhavy
R, Silhavy P (eds) Networks and systems in cybernetics. CSOC lecture notes in networks and
systems, vol 723. Springer, Cham. https://doi.org/10.1007/978-3-031-35317-8_45