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STRESS-STRAIN STATE OF UNDERGROUND PLASTIC PIPES
Abdimuminov E.
Professor of Karshi
State Technical University
Almardonov O.M.
Associate Professor Professor of Karshi
State Technical University
Abstract.
This article examines the features of the stress-strain state (SSS) of plastic pipes used in
underground utilities. Factors of external load from the soil, as well as the characteristics of the
pipe material (PE, PVC, etc.) are taken into account. Methods of numerical and experimental
analysis of SSS are given, modeling results are presented, and recommendations for improving
the reliability of systems are given..
1. Introduction.
In recent decades, plastic pipes have become widely used in the construction of
underground utilities, such as water supply, sewerage, drainage and gas distribution systems. The
most common materials used to manufacture such pipes are polyethylene (PE), polypropylene
(PP), polyvinyl chloride (PVC), and cross-linked polyethylene (PEX). These materials have a
number of operational advantages over traditional metal and reinforced concrete analogues,
including:
• high corrosion resistance;
• light weight and ease of transportation;
• low thermal conductivity;
• smooth inner surface that reduces hydraulic losses;
• resistance to aggressive chemical environments;
• durability (service life of 50 years or more with proper installation and operation).
However, despite all the advantages, plastic pipes in underground conditions are exposed to
significant external loads, the main sources of which are:
• pressure from the soil's own weight and from overlying layers;
• temporary loads from vehicles (in case of shallow backfill);
• internal pressure of liquid or gas;
• soil movements and settlements (for example, in seismically active zones or during freezing).
Under the influence of these factors, a complex stress-strain state (SSS) occurs in the pipe div,
characterized by bends, crushing, stretching or compression of the pipe walls. If permissible
stresses are exceeded, cracks, loss of tightness, ovality and other defects may appear, leading to
failure of the pipeline.
Considering the behavioral characteristics of plastics as time-dependent and nonlinear materials, it
becomes especially important to conduct an accurate analysis of the stress-strain state of pipes
under real operating conditions. The purpose of this work is a comprehensive study of the stress-
strain state of underground plastic pipes using both analytical and numerical methods, as well as
the formulation of recommendations for their reliable design and operation. The purpose of this
article is to analyze the stress-strain state of plastic pipes during underground installation and to
develop recommendations for their safe operation.
Theoretical bases of stress-strain state analysis. Stress-strain state (SSS) analysis of underground
plastic pipes requires taking into account many factors, including pipe geometry, physical and
mechanical properties of the material, soil type, installation conditions and the nature of the
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external load. A special feature of plastic pipes is their ability to undergo significant elastic and
creeping deformations, which distinguishes them from metal or reinforced concrete analogues.
Factors influencing the SSS of plastic pipes
The main factors determining the stress-strain state of plastic pipes include:
• Permanent loads from the mass of the soil: depend on the depth of backfill, density and moisture
of the soil.
• Temporary loads: impact from vehicles, vibrations, dynamic loads.
• Internal pressure: in the case of pressure pipes, creates radial and tangential stresses.
• Creep of the material: over time, even under constant load, plastic pipes deform, which is
important to take into account during long-term operation.
Mechanical properties and modeling of material behavior
Plastics used in pipeline systems are time-dependent (viscoelastic) materials. Their behavior can
be described using models:
• Linear elasticity (in the early stages or under low loads);
• Viscoelasticity (Maxwell model, Kelvin-Voigt, etc.);
• Nonlinear plasticity (under large deformations or long-term loading);
• Creep and stress relaxation (important during long-term operation under constant load).
The use of mathematical models and numerical methods, such as the finite element method
(FEM), allows us to obtain an accurate distribution of stresses and strains in the pipe wall, as well
as to assess its stability and residual life.
Boundary conditions and loading schemes
When calculating the strength of pipes, it is necessary to take into account:
• Type of pipe support (rigid foundation, sand backfill, soft soil);
• Nature of interaction with the surrounding soil (models of "pipe-in-environment", interaction
according to Winkler's law, etc.);
• Presence of protective backfill (improves stress redistribution);
• Consideration of the ring stiffness of the pipe (important for resistance to external pressure).
Such a comprehensive assessment allows identifying the most stressed areas and taking
engineering measures to strengthen the structure
.
Methods of stress-strain state analysis For precise determination of the stress-strain state (SSS) of
underground plastic pipes, various methods of analysis are used, which can be divided into three
groups: analytical, numerical and experimental. Each of them has its own advantages and
limitations depending on the tasks, accuracy, available resources and operating conditions.
Analytical methods
Analytical methods are based on the classical equations of the theory of elasticity and strength of
materials. In the simplest cases, the pipe is considered as a thin-walled cylindrical shell, which is
subjected to uniform external pressure from the soil. The following approaches are used:
• The theory of a circular shell (Lowe, Floppa) - used to analyze the ring deformation of a pipe;
• The Burmeister and Spencer models - take into account the effect of soil as an elastic medium;
• The method of an elastic beam on an elastic foundation (Winkler model) - is especially effective
in assessing longitudinal deformations.
Analytical methods are effective for preliminary calculations and engineering assessments, but
they are limited in taking into account complex conditions, such as soil heterogeneity, the
presence of joints, non-standard pipe geometry, etc.
Numerical methods
Numerical methods, especially the finite element method (FEM), are the main tool for accurate
analysis of the stress-strain state of plastic pipes. They allow modeling complex real-life
conditions, including:
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• multilayer soil structure;
• three-dimensional deformations;
• nonlinear properties of the pipe material;
• contact interactions between the pipe and the surrounding soil;
• long-term creep and stress relaxation processes.
The following software packages are widely used for calculations:
• ANSYS – a universal FEM package with the ability to model thermomechanical processes;
• Abaqus – a powerful tool for nonlinear analysis and modeling of the behavior of viscoelastic
materials;
• Lira-SAPR, SCAD, ZSoil – specialized solutions for construction and geotechnical problems.
Numerical modeling allows obtaining distributions of principal stresses, deformations, safety
factors, and also modeling pipe behavior under various emergency load scenarios.
Experimental methods
Experimental methods are necessary both for verification of calculation models and for
determining real characteristics of the stress-strain state in natural or laboratory conditions. Main
approaches:
• Natural tests – laying an experimental section of the pipeline with subsequent deformation
monitoring;
• Bench tests – measuring vertical and hoop deformations under controlled loading;
• Strain measurement – using strain gauges to measure local stresses;
• Optical and laser methods – digital photogrammetry, stereo photography method and video
monitoring of displacements.
Experimental studies allow obtaining real data necessary for correct adjustment of numerical
models and for assessing the reliability of pipeline systems in various geotechnical conditions.
4. Simulation results and analysis
Based on the numerical calculations and experimental data, an analysis of the stress-strain state of
underground plastic pipes under various operating conditions was performed. The main attention
was paid to the influence of external soil load, pipe burial depth, backfill characteristics and
geometric parameters of the pipeline.
Influence of burial depth
Simulation showed that with an increase in the pipe burial depth, vertical stresses in the upper part
of the pipe increase significantly. This leads to an increase in the ovality of the cross-section. For
example, when moving from a backfill depth of 1 m to 3 m, the annular compression of the pipe
can increase by 30–50% depending on the soil density and pipe rigidity.
However, with appropriate soil compaction around the pipe and the use of sand and gravel
backfill, a pressure redistribution is observed, in which part of the vertical load goes to the side
walls of the excavation, reducing the overall stress on the pipe.
Effect of pipe material characteristics
Comparison of polyethylene (PE80 and PE100), polypropylene and PVC pipes showed that:
• PE80 has the lowest rigidity, but high deformability and resistance to cyclic loads;
• PE100 has higher ring rigidity and better creep resistance;
• PVC has high rigidity, but is sensitive to impact loads and brittleness at low temperatures.
The choice of material should be made taking into account not only the depth and type of soil, but
also the expected service life and the nature of the loads.
Effect of compaction and type of backfill
Analysis showed that the density of the backfill around the pipe significantly affects the stress-
strain state. With poor compaction, increased ring deformations and increased stresses in the
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lower part of the pipe are observed. Conversely, with dense symmetrical backfill, the pipe absorbs
loads more evenly, which reduces the likelihood of ovality and local damage.
The use of crushed stone, sand and gravel mixtures as backfill provides better conditions for load
redistribution compared to clayey or dusty soils.
Main zones of stress and deformation
The highest stressed were the upper and lower points of the pipe annular section (the so-called
"crown" and "bed"). It is at these points that reinforcement, control or a safety margin should be
provided during design. In the lateral sections of the pipe, stresses are usually significantly lower.
It was also found that with uneven backfilling or the presence of lateral pressure (for example,
when laying near a foundation), significant bending moments in the longitudinal direction can
occur.
Verification of results
To confirm the accuracy of the modeling, full-scale tests were carried out on a test site. The
obtained values of deformations and stresses coincided with the calculated ones within 10-
15%, which confirms the adequacy of the applied numerical model and the admissibility of its use
in engineering calculations.
Table 1. Effect of burial depth on pipe annular deformations (polyethylene PE100, D =
500 mm)
Depth
of
foundation,
м
Type
of
backfill
Modulus of elasticity of
soil, MPa
Ring
deformation, %
Maximum stress,
MPa
1,0
Medium
density sand 25
1,1
3,5
2,0
Medium
density sand 25
1,9
5,1
3,0
Medium
density sand 25
2,8
6,7
3,0
The clay is
wet
10
4,2
8,4
Graph 1. Dependence of ring deformation on the depth of embedment
(for the same backfill – medium density sand)
Ring deformation (%)4.5 ┤
4.0 ┤
● Clay
3.5 ┤
3.0 ┤
●
2.5 ┤
●
2.0 ┤
●
1.5 ┤ ●
1.0 ┤●
0.5 ┼──────────────────────────────────
1 2 3 4
Depth of foundation (m))
Graph 2. Comparison of maximum stresses for different pipe materials at a burial depth of
2 m
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Материал трубы Модуль упругости, МПа Максимальное напряжение, МПа
ПЭ80
800
5,8
ПЭ100
1000
5,1
ПВХ
3000
4,7
Max. stress (MPa)
6 ┤
5 ┤ ● ПЭ80
4 ┤
● ПЭ100
3 ┤
● ПВХ
2 ┤
1 ┤
0 ┼────────────────────────
ПЭ80 ПЭ100 ПВХ
Recommendations
The type and moisture content of the soil should be taken into account when designing the
installation depth;
Quality control of backfill and compaction is mandatory;
To reduce deformations, it is recommended to use pipes with increased ring stiffness;
It is important to take into account the climatic features of the region when choosing the pipe
material;
Periodic monitoring of the pipe condition using non-destructive testing.
Conclusion.
In this paper, a comprehensive analysis of the stress-strain state (SSS) of
underground plastic pipes used in utility networks for various purposes - water supply, sewerage,
gas distribution was carried out. Based on theoretical and numerical methods, as well as
experimental data, the following main conclusions can be formulated:
General conclusions
• Plastic pipes (PE80, PE100, PP, PVC, etc.) have high corrosion resistance, flexibility, low
weight and ease of installation, which makes them preferable in the construction of underground
networks.
• One of the key factors for reliable operation is the analysis of the stress-strain state of the pipe
under external load, especially from the weight of the soil, vehicles and possible dynamic effects.
• The main zones of dangerous stresses are the "crown" (upper part of the pipe) and the "bed"
(lower part), where the maximum deformations under ring compression are concentrated. These
areas require enhanced design control.
Effect of operating parameters
• The depth of installation has a direct effect on the SSS of the pipe: an increase in depth leads to
an increase in ring deformations and stresses. At the same time, a competent choice and
compaction of the backfill allows you to redistribute the loads and significantly reduce their
impact on the structure.
• The pipe material plays a decisive role. PE100 pipes showed better results in terms of a
combination of strength, flexibility and creep resistance, compared to PE80 and PVC.
• The rigidity and type of surrounding soil also significantly affect the behavior of the pipe. The
most favorable conditions are created by using a well-compacted sand and gravel base.
Evaluation of analysis methods
• Analytical methods allow for a primary assessment of the stress-strain state under simplified
assumptions, but do not take into account all the factors of real operation.
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• Numerical methods (primarily the finite element method) have demonstrated high accuracy in
modeling complex conditions. They allow for nonlinear properties of materials, heterogeneity of
the medium, and boundary conditions.
• Experimental data obtained in laboratory and full-scale tests confirmed the reliability of the
calculation models and also indicated the importance of taking into account factors that are
difficult to formalize in numerical calculations (e.g., local compaction, uneven backfill).
Practical recommendations
• When designing underground pipelines made of plastic materials, it is necessary to take into
account the complex effect of external loads and perform stress-strain state calculations using
modern numerical methods.
• It is recommended to use pipes with increased ring stiffness and include in the design the
minimum permissible values of ovality and stresses.
• During installation, ensure uniform compaction of the backfill around the perimeter of the pipe
and avoid asymmetric loads, especially near rigid structures (foundations, walls, etc.).
• Quality control of soil laying and compaction should be a mandatory stage of construction
supervision.
Final remark. Increasing the reliability of underground pipeline systems is possible only by
integrating an engineering approach based on accurate calculations of the stress-strain state with
high-quality construction and installation work. Promising areas for further research are:
• modeling taking into account long-term processes (creep, relaxation);
• use of composite and reinforced materials;
• development of intelligent systems for monitoring the condition of pipes in real time.
References:
1. Abdimuminov E. Alimardanov O. M. Soil pressure along the pipe contour.
O’zbekiston Milliy Axborot agentligi O’za Ilm – fan bo’limi Elektron jurnal 2024 yil iyin soni N7
(57) OAK.
2. Grigoriev, A. A. "Polymer pipes in construction", Moscow: Stroyizdat, 2020.
3. Bardin, N. I. "Finite element method in pipeline problems", St. Petersburg, 2018.
4. ASTM D2412 – Standard Test Method for Determination of External Loading Characteristics
of Plastic Pipe.
5. EN 13476 – Plastics piping systems for non-pressure underground drainage and sewerage.
