Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 6, No. 2, 2023 

 

146 

Comparative	Analysis	of	Buried	Pipe	Under	Heavy	Train	
Loads	
Rui Xie1, 2, Peng Yu3, *, Fei Luo4, Chaobin Du5 

1School of Intelligent Manufacturing, Sichuan Institute of Arts and Science, Dazhou 635000, China 
2Dazhou Industrial Technology Institute of Intelligent Manufacturing, Dazhou 635000, China 
3Meishan CRRC Brake Science & Technology Co., Ltd, Meishan 620010, China. 
4Pigprox Inspection Technology (Chengdu) Co., Ltd, Chengdu 610500, China 
5Better Petroleum Technology Co., Ltd, Chengdu 610066, China 
*The corresponding author 

 

Abstract: With rapid development of railway transportation and increasing demand of oil and gas in China, the heavy haul 
train load becomes an important factor that threaten the safe operation of pipe. The mechanical behavior of buried pipe subjected 
to heavy haul train load was investigated in this study. A finite element model was established to investigate the effect of train 
load. Finally, the multiple train loads were also discussed. Results show that the high stress area occurs under the train track. In 
the pipe segment below the track, the top of pipe is under compression and the bottom of pipe is under tension. The cross section 
of pipe is still circular. The maximum vertical and horizontal displacement are at the top and side of pipe. The maximum von 
Mises stress, axial strain, and displacement of pipe increase with the increase of train load. Under the multiple train loads, there 
are two high stress and high strain areas at the top and bottom of pipe. With the increase of multiple train loads, the maximum 
von Mises stress, axial strain, displacement and ovality increase. 

Keywords: Buried pipe, Heavy haul train load, Finite element method, Multiple train loads. 
 

1. Introduction 
In recent years, with the large-scale construction of rail 

transit and the increasing of underground pipeline in various 
cities, the underground space is becoming more and more 
crowded. It is more and more common for rail transit lines to 
be close or cross with buried pipes (Weng 2016). The loads of 
pipe at the intersection mainly include static loads such as 
gravity and soil pressure, and live loads such as vehicle traffic 
load, ground stacking load, temperature load and pipe internal 
pressure. In vehicle traffic load, train load is very important 
type that will affect the buried pipes. With the development 
of China's economy, railway transportation also reflects the 
characteristics of increased load and speed (Tian 2015), which 
leads to serious deformation effect of ground surface under 
the action of train load (Yao 2019). Although the train does 
not directly roll on the pipe, the transmission of rolling load 
through the ground and soil will eventually affect the safe 
operation of the pipes. Thus, conducting mechanical analysis 
of buried pipe subject to heavy haul train load is of great 
significance for engineering practice. 

A series of literatures are available for mechanical behavior 
analysis of buried pipes subjected to traffic load. Wang (2021) 
established a 2D FE model to simulate the polyethylene pipe 
performance with traffic loading, and some parameters on the 
effect of bending moment in the pipe were investigated. Fang 
(2018) investigated the bell and spigot concrete drainage pipe 
under various working conditions of traffic loads by using FE 
method, he also discussed the effect of load types, load 
locations and buried depth on the mechanical responses of 
pipe. Zha (2019) used numerical simulation to analyze the 
reliability of gas PE pipe under traffic load, and calculated the 
stress and stress distribution of buried pipe with single 
random variables of traffic load. Alzabeebee (2019) 
investigated the response of buried concrete pipes under the 

British Standard traffic load by using finite element model, 
the effect of the pipe diameter and backfill height on the 
bending moment in the pipe wall and soil pressure around the 
pipe were provided. 

Previous researches focused on the pipe under soil 
deformation. Zeng (2019) developed an analytical method of 
strain and deformation of pipeline, the equivalent spring is 
used in numerical model to study the effect of mechanical 
properties of pipeline. Kouretzis (2016) presented an 
analytical method to estimation of internal forces and strains 
of buried pipes subjected to permanent ground settlement and 
heave. Demirci (2018) setup a new experiment to study the 
effect of reverse faulting on buried pipeline, and the 
experiment results were compared with FE analysis result to 
verify the FE model.  

Although so many researches had been done, few of them 
focused on the mechanical behavior of buried pipe subjected 
to heavy haul train load, and strain analysis is important for 
buried pipe. Therefore, mechanical behavior of buried pipe 
subjected to heavy haul train load was investigated in this 
paper, the finite element model considered train load, train 
track, sleeper and pipe was established, the interaction 
between pipe and soil were considered accurately by contact 
algorithm. These results can provide a theoretical reference 
for the application of pipe in engineering practice. 

2. Materials and Methods  

2.1. Materials properties 
A linear isotropic strain hardening model had been used in 

steel pipe material, the numerical results were obtained for the 
X65 steel pipe in this study. The yield stress is 448.5MPa 
(Vazouras et al. 2010), the Young’s modulus is 210GPa, the 
Poisson`s ratio is 0.3, and the density is 7800kg/m3.  

The soil and ballast were described as the Mohr-Coulomb 



 

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model, characterized by the density r, the cohesion c, the 
friction angle f, the elastic modulus E, and Poisson’s ratio m, 
the dilation angle was assumed equal to zero for all cases 
considered in this paper (Vazouras et al. 2012). It was 
assumed that soil and ballast are isotropic material and do not 
contain gravel or pore. The train track and sleeper were 
described as linear elastic model (Huang 2019). Type 75 
heavy rail was used for the train track, and type Ⅲ reinforced 
concrete is used for sleeper, the parameters were given in 
Table 1 (Huang 2019; Ling 2020; Yang 2009). 

2.2. Finite element model and boundary 
conditions 

The load generated in the process of train operation mainly 
comes from the interaction between wheel and rail. In this 
study, the C80 coal heavy haul train with designed axle load 
of 300kN was considered, and the vertical load was adopted 

to analysis the mechanical performance of buried pipe. 
The finite element model was established by general 

nonlinear finite element program. The diameter and wall 
thickness of pipe were set to be true value which were used in 
engineering. The pipe diameter is 660mm, the pipe wall 
thickness is 8mm. The soil around the pipe is the same length 
with pipe, the whole soil model is set to be 16m×8m×5m. The 
distance between pipe center and ground is 1.5m. The cross 
section of train track was simplified as a rectangle, the width 
of cross section is 15cm, and the height is 15cm (Huang 2019). 
The standard gauge of 1.435m was adopted for rail gauge 
(Industry Standard of the People`s Republic of China 2017). 
The cross section of sleeper was simplified to a cuboid, the 
length is 2.5m, the width is 0.3m and the height is 0.23m. The 
longitudinal spacing of sleepers along the track is 0.6m 
(Huang 2019). Schematic diagram of geometric model is 
shown in Figure 1. 

 
Table 1. Material parameters 

 (kg/m3) E(MPa)   C(kPa) 
Soil 190 18 0.4 18 20 

Ballast 1950 190 0.25 34 80 
Train track 7810 210000 0.3 - - 

Sleeper 2400 35000 0.17 - - 
 

 
Figure 1. Schematic diagram of geometric model 

 
In the numerical model, the load imposed by the train 

corresponds to the train wheelset in space, and the 
concentrated force was applied on the wheel rail contact point 
to describe the interaction force between wheel and rail 
(Huang 2019). The moving load of the train was equivalented 
to the static load. The static wheel load was calculated from 
the axle load of the train in the code, and then multiplied by 
the coefficient, which is about 1.3 times of the maximum 
static load to simulate the train load (Ling 2020; Industry 
Standard of the People`s Republic of China 2017). Take the 
position of the joint of the train analysis, where the wheels 
and load were densely distributed, there were four sets of 
wheels, as shown in Figure 1. The distance between two 
adjacent wheels in the same train carriage is 1.8m, and the 
distance between two adjacent wheels in the different train 
carriage is 1.5m (Huang 20190; Industry Standard of the 
People`s Republic of China 2017). 

The whole model was calculated by 1/2 model considering 
the symmetry of load and geometry. In the numerical analysis, 
the x-y and y-z surfaces of the soil was restrained in z direction 
and x direction. The bottom surface (the underside x-z surface) 

of the soil was restrained in the xyz direction, the topside x-z 
surface was set to be free. Symmetry constraints were used 
for symmetry surfaces. The Dynamic/Explicit analysis was 
used to simulate the load process. The numerical analysis is 
conducted in three steps: the gravity loading step, the internal 
pressure step and the train load step. In the first gravity 
loading step, gravity load was applied on the whole model. In 
the internal pressure load step, internal pressure was applied 
on the inner surface of pipe. In the train load step, train load 
was applied on the train track in y direction. The finite 
element model is shown in Figure 2. 

Interaction between soil and pipe was simulated by using 
surface to surface contact algorithm, which allows separation 
of soil and pipe. The interface friction was described by 
friction coefficient, the value of coefficient is considered 
equal to 0.3.  

The soil, sleeper and train track were all simulated by eight-
node reduced integration elements (C3D8R), the pipe was 
simulated by four-node shell elements(S4R). The mesh 
method used in this study is as follows: In the circumferential 
direction of pipe, it was discretized into 40 equal sized 



 

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continuum elements. In the longitudinal direction of pipe, a 
fine mesh (40 equal sized elements) was used for 1.25m long 
pipe segment in axial direction of the pipe under the train 
track, while a coarse mesh was used for the pipe in the end. 

3. Single Train Load Analysis 
The load on the pipe induced by heavy haul train is random 

in true cases. In this section, mechanical behavior of buried 
pipe with different train load were investigated. Figure 2 

shows the von Mises stress distribution of pipe with different 
train loads. With the increase of train load, the high stress area 
extends along the axial direction of pipe, the maximum stress 
of inside and outside surface of pipe increase, and the change 
rate increases sightly. The stress of inside surface is larger, 
and the maximum stress located in the inside surface of top of 
pipe. When train load increases from 150kN to 350kN, the 
maximum stress increases about 60MPa. Therefore, the 
buried pipe may be dangerous when train load is larger. 

 

 
Figure 2. Von Mises stress distribution of pipe with different loads 

 

 
Figure 3. Axial strain distribution of pipe with different loads 

 
Figure 3 shows the axial strain distribution of pipe with 

different train loads. With the increase of train load, the 
maximum strain of top and bottom of pipe increase, and the 
change rate basically unchanged. In the middle of pipe, the 



 

149 

top of pipe still under compression and the bottom of pipe is 
under tension. Additionally, the axial strain of the end of pipe 
is very small when train load is 150kN, the pipe bending 
degree is too small. 

 

 
Figure 4. Displacement of pipe with different loads 

 
Figure 4 shows the displacement of pipe with different train 

loads. When train load increases from 150kN to 350kN, the 
maximum horizontal displacement increases a little, while the 
maximum vertical displacement increases obviously, which 
changes from 6.4mm to 11.5mm. The critical section of pipe 
trends to be slightly oval with the increase of train load. The 
vertical displacement of top of pipe is larger than the bottom 
of pipe, because the train load is mainly sustained by the top 
of pipe, the pipe deforms uniformly in the circumferential 
direction. Additionally, with the increase of train load, the 
vertical displacement of top of pipe increases obviously. 

4. Multiple Train Loads Analysis 
In practical engineering, train group is widely used, so that 

there are many groups of tracks with close distance on the 
ground. In this section, mechanical behavior of buried pipe 
with different multiple heavy haul train loads were 
investigated. Figure 5 shows the schematic diagram of buried 
pipe with multiple train load. The whole model was used, the 
distance between multiple loads is 4m, the buried depth of 
pipe is 1.5m, the diameter of pipe is 660mm, and the thickness 
of pipe is 8mm. Geometric and material parameters are 
declared in section 2. The two different train loads were 
described by Load-1 and Load-2, which ranging from 150kN 
to 350kN. 

 

 
Figure 5. Schematic diagram of buried pipe with multiple train 

load 

When the Load-1 equals to Load-2, and the load ranging 
from 150kN to 350kN, the stress-strain distribution of pipe is 
shown in Figure 20. In Figure 6(a), there are two high stress 
area at the top and bottom of pipe, each of high stress area is 
located under the train track. When load-1 and load-2 are 
larger, the high stress areas trend to merge together. But the 
high stress area is separated when load is small. The 
difference between the maximum stress of pipe with same 
multiple train loads and the maximum stress of pipe with 
single train load is very small. Therefore, multiple train loads 
will affect the stress area of pipe, but it has little effect on the 
maximum stress of pipe. In Figure 6(b), the axial strain 
distribution is similar with the stress distribution. Two high 
strain area at the top and bottom of pipe, the high strain area 
gradually separates when the train load decreases. 

Figure 7 shows the displacement of pipe with same 
multiple train loads. With the increase of multiple train load, 
the maximum vertical and horizontal displacement increase, 
and the trend is similar to the single train load. However, the 
maximum displacement of pipe with multiple train loads is 
larger than single train load. This is because deformation area 
of pipe with multiple train loads is larger than single train load, 
and the bending area of the pipe is larger. Additionally, the 
variation of vertical displacement is more obviously. And 
with the increase of multiple train loads, the ovality of the 
critical section of pipe increases. 

 

 
(a) Von Mises stress distribution of pipe 

 
(b) Axial strain distribution of pipe 

Figure 6. Stress-strain distribution of pipe with same multiple 
train loads 

 



 

150 

 
Figure 7. Displacement of pipe with same multiple train loads 

5. Conclusions 
Mechanical behavior of buried pipe subjected to heavy haul 

train load were investigated in this study. The main 
conclusions are as follows:  

(1) High stress area occurs under the train track, and the 
shape of high stress area is ellipse. In the pipe segment below 
the track, the top of pipe is under compression and the bottom 
of pipe is under tension. The strain of inside and outside 
surface of pipe is similar. The cross section of pipe can be kept 
circular. The maximum vertical and horizontal displacement 
are at the top and side of pipe respectively. The maximum von 
Mises stress, axial strain, and displacement of pipe increase 
with the increase of train load. 

(2) There are two high stress and high strain area at the top 
and bottom of pipe when pipe subjected to multiple train loads. 
When multiple loads are larger, the high stress and high strain 
areas trend to merge together. The difference between the pipe 
with same multiple train loads and the pipe with single train 
load is very small. With the increase of multiple train load, the 
maximum displacement and ovality increase, and the 
variation of vertical displacement is more obviously.  

Acknowledgment 
This work was supported by the Key Project of CRRC 

(2020CHA097), and Open fund of Dazhou Industrial 
Technology Institute of Intelligent Manufacturing 
(ZNZZ2215). 

Conflicts of Interest 
The authors declare that they have no known competing 

financial interests or personal relationships that could have 
appeared to influence the work reported in this paper. 

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