This paper investigates the response of a flexible buried pipe to traffic load using laboratory experiments and numerical analysis. A series of laboratory tests and numerical simulations were performed to examine the effect of surface pressure, loading width, pipe type, pipe thickness, and burial depth on model response. In the experiments, a load was applied to the surface of a tank in which a pipe was buried. To gain a better understanding of the pipe's behavior, numerical simulations were performed using the finite element method; PLAXIS 2-D software. The results show that there is a good agreement between numerical and experimental test results. Furthermore, experimental and numerical analysis show that increasing burial depth reduces pipe deflection, increases soil surface settlement, and decreases pipe pressure, whereas increasing surface pressure increases all of the above parameters. Finally, equations were developed based on all numerical and experimental results to predict maximum stress on the pipe crown.
Introduction
Buried pipes are one of the most secure, efficient, and cost-effective ways of transporting, distributing, and delivering natural resources. They are widely used as a protective infrastructure for electrical and telecommunications cables, as well as a transportation system for water, oil, and gas products. The integrity of these latter systems is especially important, as failures of such infrastructure have significant economic consequences as well as serious environmental and public safety implications.
Damage to such infrastructure may occur due to corrosion, external loading, construction defects, or ground movement, depending on the material types of buried pipes. Surface loads, particularly those caused by traffic movement, can have a significant impact on the performance of buried pipes. Many experimental and numerical studies have thus been carried out to investigate the responses of buried pipes to soil types and moisture contents, geometrical conditions such as burial depth, and ground conditions such as movement during and after construction. However, identifying the responses of buried pipes under specific surfaces or traffic loads is limited and poorly understood.
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Several researchers have investigated the experimental behaviors of buried pipes under various loadings. Arockiasamy et al. [1] conducted a full-scale field test on the flexible pipe under live load application. They looked into the behavior of pipe deflection during installation and live load application for various pipes.
They also measured pressure around the pipe during the live load application with various pipe-buried depths. They discovered that the pressure on the crown of the smaller diameter HDPE pipe (914 mm) is greater than the pressure on the crown of the larger diameter HDPE pipe (1208 mm).
In a full-scale plate load test, Cao et al. [2] investigated the effects of cyclic traffic loading on the behaviors of a flexible pipe buried at a shallow depth, evaluating the pipe's permanent deformation. They discovered that the buried pipe deflected very little under cyclic traffic loading and that as the stiffness of the buried pipe increased in the parametric study under numerical analysis, the permanent deformation of the road surface was magnified; similarly, the road surface deformation decreased as the pipe embedment depth increased.
Culvert 1976 and Hager 1985 were the first to use the finite element method to simulate problems in pipe–soil interaction analysis. Since then, many numerical studies have been conducted using finite element methods to investigate pipe–soil interaction. Mosadegh and Nikraz [3] conducted a parametric study on both 2D and 3D models using ABAQUS to demonstrate the impact of surface pressure, loading area, boundary conditions, pipe material properties, internal pressure, and pipe–soil interaction properties on buried pipe response and soil surface settlement.
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They found that surface pressure, burial depth, and loading area all had the greatest influence on the model response. The impact of cycles was not considered in their research, and traffic load was applied to the soil surface as the static load. Previous research has been restricted to either experimental or numerical analysis. Therefore, a combined experimental and numerical study of the impact of traffic load on buried pipe response is required.
The specific objectives of this study are to investigate the response of buried pipelines subjected to traffic load through experimental and numerical investigations while taking into account changes in deflection and increases in the earth pressure on the pipe. A series of tests were carried out to investigate the effect of traffic load and burial depth on model response. A numerical simulation of a laboratory model was created to examine the impact of those parameters on model response in parallel with experimental tests. Finally, a relationship between pipe behavior parameters and pressure on the pipe due to traffic load was developed.
Experimental studies
A rigid steel box with dimensions 210 mm wide, 1000 mm long, and 680 mm deep was designed and built as a testing tank. The sizes chosen are due to load-applying machine limitations. The footing was designed as a steel plate with dimensions of 250 mm long, 200 mm wide, and 20 mm thick. To maintain the plain strain condition, the width of the footing is nearly equal to the width of the tank. The footing is centered in the tank to apply the load, and its width is parallel to the width of the tank and buried pipe.
It should be noted that the tank wall was painted with epoxy to reduce friction between soil and steel. In this study, sand soil was used, and the grain size distribution is shown in Fig. 1. According to the Unified Soil Classification System, the sand soil is classified as SP or poorly graded sand (USCS). Table 1 shows the soil properties used in this study.
Fig. 1
Grain size distribution curve of sand
Table 1
Physical properties of soils
Description
Sand soil
Coefficient of uniformity (Cu)
2.61
Coefficient of curvature (Cc)
1.17
Max. dry unit weight (kN/m3)
18.9 kN/m3
Optimum moisture (%)
7.9%
×
The pipe was 150 mm in diameter and made of HDPE (high-density polyethylene) and fiberglass. Pipe diameters vary widely in urban services such as drainage sewer applications; however, a reasonable dimension representing a common small pipe diameter has been chosen. The pipes are 6, 5, and 4 mm thick with 200 mm long, and have standard dimension ratios (SDR) or D/t values of 25, 30, and 37.5. According to the manufacturer's specifications, the pipe density is 9.5 (kN/m3), and the Young modulus is 810 MPA for HDPE pipe and 11,000 MPA for fiberglass pipe.
To avoid binding against the end walls and boundary condition impacts, the pipe is 10 mm shorter than the width of the tank. Furthermore, to prevent sand particles from entering the pipe, the two ends of the pipe were covered with a sponge, as shown in Fig. 2. Each test's tank sample was prepared separately by placing granular soil in a U shape at the bottom and lateral sides of the tank.
Fig. 2
a Photograph of test setup b Digital photogrammetry program
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The pipe should be in place before placing trench material, and pressure cells should be attached to the pipe in appropriate positions. Following the placement of the pipe, backfill sand soil was to be placed and compacted in the trench area. The trench width of 550 mm was chosen in accordance with AASHTO recommendations, which state that the trench width should not be less than the greater of 1.5 times the pipe outside diameter plus 305 mm or the pipe outside diameter plus 406 mm. Trench depth varied between 350 and 550 mm in different tests, which is the sum of burial depth plus pipe diameter soil compaction was performed with an appropriate hammer to simulate compaction in the field to achieve 95% and 85% maximum dry density. Finally, the soil's surface was leveled. In the final step, the loading cell and loading plate were centered in the tank, as shown in Fig. 2.
The deflection of the buried pipes was measured using a digital photogrammetry technique package designed specifically for geotechnical applications. The images were processed using an image analysis technique known as digital photogrammetry, which allows targets on test material to be tracked by comparing images taken, while the pipe is under load to an initial image taken before loading, known as the reference image, throughout the test. Desired monitored data in the current experiment program include pipe deflection VDS and increased vertical pressure distribution on pipe–soil interaction.
Finite element modeling
In most geotechnical engineering, finite element (FE) methods are used to evaluate complex problems where traditional analysis is time-consuming and complicated, and using laboratory models requires more effort and budget. As a result, the finite element software of PLAXIS 2D foundation version 2019 is the selected program in this paper.
The depth and width of the models in this study are chosen to be sufficient to simulate real-world behavior. The models have a soil volume of 0.21 × 1 m plan area and a depth of 0.68 m. The pipe used in the analysis has a diameter of 150 mm and a wall thickness of 6 mm, with negative interfaces added around the pipes to account for soil–pipe interaction. The model's side boundaries were fixed in a horizontal direction, while the bottom was fixed in both vertical and horizontal directions. The backfill was modeled using fifteen nodded plane strain triangular elements, and the soil is assumed to follow the hardening soil model. The soil elements inside the pipe were excavated to be void after the pipe was created and groundwater was not considered in this study. On the ground surface, a strip surface load ranging from 0 to 200 kN/m2 was applied along the length of the pipe at 0.25 m width, and the plane strain condition is represented by the model. The pipe embedment ratio (H/D) varied between 1, 1.67, and 2.4. where H is the distance between the pipe crown and the ground surface, and D is the pipe's external diameter. The model's backfill material, native soil, and pipe material properties are listed separately.
Characteristics of sandy soil
Hardening soil models were used in this study to represent the sand soil materials. The soil-hardening model incorporates two types of soil hardening: shear hardening and compression hardening. Shear hardening is used to simulate irreversible strains caused by deviator loading [5]. Compression hardening can be used to simulate irreversible strains caused by compressive loading. The hardening soil model includes the following eight parameters:
Pressure-dependent stiffness as a function of power, m;
Plastic strain due to deviator loading described by reference elastic modulus (\({E}_{50}^{{\text{ref}}}\));
Plastic strain due to compression loading as described by the reference compressive modulus at 100 kPa (\({E}_{{\text{oed}}}^{{\text{ref}}}\));
Elastic unloading and reloading as defined by the reference unloading–reloading modulus (\({E}_{{\text{ur}}}^{{\text{ref}}}\)) and the reference unloading–reloading Poisson's ratio (vur); and.
Failure according to the Mohr–Coulomb model, with cohesion (c), friction angle (Φ), and dilation angle (ψ).
where Eoed = modulus of soil with respect to compressive loading (Table 2). The Poisson’s ratio of soil for unloading vur is usually taken as 0.2 Schanz and Vermeer [5] suggested \({E}_{{\text{oed}}}^{{\text{ref}}}\) =\({E}_{50}^{{\text{ref}}}\) and \({E}_{{\text{ur}}}^{{\text{ref}}}\) = (3 – 5)\({E}_{50}^{{\text{ref}}}\).
Table 2
Hardening Soil Model Parameters of the Sand Soil
Parameter
Sand soil
Dense sand
Medium sand
Unit weight, γ (kN/m3)
18.6
16.4
Cohesion, c (kN/m2)
1
1
Friction angle, ϕ (degree)
36.5
34
M
0.5
0.5
\({E}_{50}^{{\text{ref}}}\)
32,000
27,000
\({E}_{{\text{oed}}}^{{\text{ref}}}\)
32,000
27,000
(\({E}_{{\text{ur}}}^{{\text{ref}}}\))
96,000
81,000
ѵur
0.2
0.2
ψ (degree)
6.5
4
HDPE pipe properties and modeling
The finite element PLAXIS 2D software includes a tunnel designer tool for modeling tunnels and pipes. The tunnel designer, in fact, generates plate element segments to form a circular structure. The internal forces of the plate elements can be plotted after they have been calculated. The plate element has five parameters: (1) normal stiffness, EA; (2) flexural rigidity, EI; (3) equivalent thickness, t, which can be calculated automatically from EA and EI; (4) unit weight, and (5) Poisson's ratio, v, which is equal to zero if the area of the solid structure (i.e., pipe wall) is much smaller than the model's cross-sectional area.
Tables 3 and 4 summarize the physical properties of the pipe, which were obtained in part from the pipe's manufacturer.
Table 3
The physical properties of HDPE pipe
Normal stiffness, EA (kN/m)
4860
Flexural Rigidity, EI (kNm2/m)
0.01458
Equivalent thickness, deq, (m)
0.006
Weight, W (kN/m3)
0
Poisson's ratio, v
0.43
Table 4
Input parameters for fiberglass pipe, D = 150 mm
Parameters
Normal stiffness, EA (kN/m)
66,000
Flexural Rigidity, EI (kNm2/m)
0.198
Equivalent thickness, deq, (m)
0.006
Weight, W (kN/m2)
0
Poisson's ratio, v
0.29
The findings and discussion
The primary goal of this research is to identify the various factors that influence the behavior of embedded HDPE and fiberglass pipes in sandy soil. Surcharge stress, pipe type and thickness, and embedment ratio were all investigated factors. The effect of footing width was also investigated (Fig. 3).
Fig. 3
Numerical models with: a different embedment depths with footing widths of 1.67D and b different footing widths with embedment ratio H/D = 1
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The influence of embedment depth
Both experimental work and finite element methods are used to investigate the factor of embedment ratio against surcharge stress. The pipe's vertical crown deflection and stress were measured under various surface stresses. Figures 4 and 5 show an experimental test result of crown deflections and stress for both HDPE and fiberglass pipe versus surface stress at various embedding ratios (H/D). The experimental results show that the pipe behavior is primarily determined by the intensity of the surcharge surface stress. The results show that as the surcharge stress in sand increases, the crown deflection of the embedded pipe increases linearly.
Fig. 4
Influence of embedment ratio and intensity of surcharge load on a deflections and b stress of 150 mm diameter HDPE pipe with a thickness of (T = 6 mm)
Fig. 5
Influence of embedment ratio on a deflections and b stress of 150 mm diameter Fiberglass pipe with thickness of (T = 6 mm)
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The results also explain that pipe crown deflections and stress decrease as embedment ratios increase. It has been discovered that, for the same surface stress, decreasing the backfill increases both crown deflection and pipe stress. Because of the small backfill, the stress is directly transmitted to the pipe.
The influence of pipe rigidity
The effect of pipe rigidity is investigated in the study, and two materials are used to model the problem. The results show that pipe displacements decrease as pipe rigidity increases. Figure 6a shows that the displacements of fiberglass pipes are less than those of HDPE pipes. The effect of surface pressure on measured stress for both types of pipes is also depicted in Fig. 6b. Because fiberglass pipe is stiffer than HDPE pipe, it attracts more load than HDPE pipe. As a result, the crown stress value for the fiberglass pipe was found to be greater than that of the HDPE pipe. At any embedment depth, the behavior was the same.
Fig. 6
The effect of rigidity of pipe on a pipe deflection (σ = 200 kN/m2) b Crown stress (T = 6 mm, H/D = 1).
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Surface pressure effect
The analysis also looked at the impact of five different surface pressures on model response 40, 80, 120, 160, and 200 kN/m2. As shown in Fig. 7a, b, increasing surface pressure raises all parameters. All of the values under investigation are sensitive to changes in surface pressure variation. Increased surface pressure from 120 to 200 kN/m2 increases pipe deflection from 5.79 to 8.78 mm and earth pressure on the pipe crown from 64 to 92 kN/m2. For both pipe type and thickness, this typical behavior was observed in the pipe embedded at depths of 250 mm and 350 mm from the surface e of the sand backfills.
Fig. 7
Effect of surface pressure variation on: a pipe deflection b pipe crown stress at embedment ratio of (H/D = 1)
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The effect of cover depth and pipe material on the damage ratio
This analysis took three levels of the cover into account. Figure 8 shows the sensitivity of the embedment ratio (H/D) to the damage ratio or the percentage pipe vertical deflection to the 5% deflection criterion. According to the results, the shallower the pipe, the greater the predicted vertical pipe deflection and damage ratio. All analyses are performed under static loading conditions.
Fig. 8
Effect of embedment depth on damage ratio for HDPE and fiberglass pipes
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Because of the higher material stiffness, the predicted damage ratio decreased dramatically as the pipe material changed from HDPE to fiberglass. This finding is consistent with the findings of the laboratory tests conducted as part of this study.
Results comparison and discussion
The results of experimental tests and numerical simulations will be compared in this section, and the effect of burial depth and surface pressure on pipe deflection and stress variation will be discussed.
Models for predicting pipe stress
For buried pipe subjected to traffic loads, Spangler [6] developed the first pipe stress perdition equation. This equation is widely used in the pipeline industry during the design and condition assessment stages. The following equation calculates the circumferential bending stress at the pipe invert due to vertical load:
where Wvertical denotes the vertical load due to backfill and surface loads including an impact factor, E denotes the pipe modulus of elasticity, D denotes pipe diameter, t denotes pipe wall thickness, and p denotes internal pressure. Kb and Kz are bending moment and deflection parameters that are affected by the bedding angle, respectively. Moser and Folkman [4] contain the appropriate values for Kb and Kz.
However, the effect of soil lateral support on pipe stress is not taken into account in Eq. (1). Warman et al. [7] recently proposed a modified Spangler equation by combining the original Spangler formula and the Iowa formula, as shown in Eq. (4).
where E’ is the modulus of passive soil resistance and r is the radius of the pipe.
But the accuracy in predicting pipe stress is questionable for the following reasons: (1) the Boussinesq theory, which assumes that the loaded soil mass is homogeneous and ignores the presence of a stiff pipe within the soil; (2) the stress equations are based on an assumed and approximate distribution of soil stress around the pipe. (3) The slip between the pipe and the surrounding soil is not taken into account. Therefore, most of these limitations can be overcome by using a more comprehensive stress analysis method.
Formulation of a stress prediction equation
The magnitude and distribution of the external loads, to which the pipe is subject, as well as the soil condition and pipe material and geometric properties, all influence the stress in the pipe. The contribution of each of these factors must be determined and incorporated into the stress prediction models. To develop the pipe stress prediction equation in this study, the following variables are considered: traffic load (W), loading width (B), soil modulus (Es), soil density (γ), pipe diameter (D), pipe wall thickness (t), and burial depth (h). Finite element analyses with the results of the experiments were performed with varying levels of the variable and its combinations to develop the stress prediction equation. The functional relationship between maximum pipe stress and variable is as follows:
Table 5 shows the regression coefficients that were computed. In Eq. (5), the following units are used for the input variable: W, Ep, and Es are measured in kPa; t, B, h, and D are measured in m; and the output stress is measured in kPa (Fig. 9).
Table 5
Values of the regression coefficient
Parameter
Value
\({\alpha }_{1}\)
0.015
\({\alpha }_{2}\)
−0.1
\({\alpha }_{3}\)
6
\({\alpha }_{4}\)
−4.1*10–3
Fig. 9
Comparison between experimental tests and numerical simulations for HDPE pipe stress
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Figures 10 and 11 depict a comparison of simulated and predicted stress values.
Fig. 10
Comparison between proposed equation and experimental measurements for HDPE pipe crown stress with t = 6 mm at different buried depth
Fig. 11
Comparison between proposed equation and experimental measurements for fiberglass pipe crown stress with t = 6 mm at different buried depth
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Conclusions
To evaluate the crown stress and deflections of buried pipes in sandy soil, a series of experiments and numerical analysis were performed. Some parameters influencing crown stress and deflections of buried pipes were investigated.
On the current work's findings, the following conclusions can be drawn:
1.
Deeper burial reduces pressure on the pipe crown and pipe deflection.
2.
Increasing surface pressure also had a significant impact on increasing pipe deflection, soil surface settlement, and pipe pressure, as expected.
3.
The behavior of vertical total stress on pipe with applied surface stress from the PLAXIS analyses showed generally similar behavior with experimental work results. There is negligible deviation between the FEM and experimental results.
4.
The hardening soil (HS) model effectively depicts the response of backfill material above the pipe under footing loading.
5.
This research could be extended in the cyclic phase to provide a better understanding of the behavior of buried pipes in response to external cyclic loading.
6.
Furthermore, the current experimental section study was conducted only in the laboratory, and full-scale field verification is still required.
Declarations
Conflict of interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Informed consent
For this type of study formal consent is not required.
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