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Research Papers: Pipeline Systems

# Numerical Analysis of Mechanical Behavior of Buried Pipes in Subsidence Area Caused by Underground MiningPUBLIC ACCESS

[+] Author and Article Information
Jie Zhang

School of Mechatronic Engineering,
Southwest Petroleum University,
Chengdu 610500, China
e-mail: longmenshao@163.com

Rui Xie

School of Mechatronic Engineering,
Southwest Petroleum University,
Chengdu 610500, China

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received October 2, 2018; final manuscript received January 26, 2019; published online February 21, 2019. Assoc. Editor: Oreste S. Bursi.

J. Pressure Vessel Technol 141(2), 021703 (Feb 21, 2019) (8 pages) Paper No: PVT-18-1220; doi: 10.1115/1.4042711 History: Received October 02, 2018; Revised January 26, 2019

## Abstract

The buried pipe crossing the subsidence area is prone to failure. The mechanical behavior of buried pipe in subsidence area was investigated in this paper. Effects of subsidence displacement, pipe parameters and soil parameters on the mechanical behavior were investigated. The results show that high stress appears on the pipe's surface and exceeds the yield strength after the strata subsidence. As subsidence displacement increases, the ranges of high-stress area and displacement increase, and the pipe section changes from a circle to an ellipse. The maximum axial strain occurs on the pipe in no-subsidence area. The maximum plastic strain and ovality of the pipe increase with the increasing of subsidence displacement. The displacement, plastic strain, and ovality of the pipe increase with the increasing of diameter–thickness ratio and buried depth. Internal pressure and friction coefficient has a little effect on the pipe displacement. The ovality decreases as internal pressure increases. The plastic strain and ovality increase with the increasing of the friction coefficient. As the elastic modulus and cohesion of soil increase, the displacement, plastic strain, and ovality of the pipe increase. The effect of Poisson's ratio on the deformation of pipe is small.

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## Introduction

Buried pipes are the main method for oil and gas transportation. Long-distance oil and gas pipes crossing complex strata are prone to failure under various geological disasters [1]. Strata subsidence that caused by underground mining is one of the important factors threatening pipe safety. According to the investigation, there are 76 underground minings along the West–East gas pipe, and the length of the pipe crossing subsidence area is about 388 km. In the Yangcheng section of Shanxi, the maximum settlement of the pipe is 1.885 m, and the axial tensile stress exceeds the allowable value [2]. The area of the underground mining along the Hubei section of the Sichuan Natural Gas Pipe Project is about 2.4 km2; the maximum depth of the subsidence area reaches 15 m [3]. The strata subsidence is likely to cause large local deformation of the buried pipe, which may cause accidents such as squeeze and breakage. Therefore, mechanical behavior analysis of buried pipe in subsidence area is very important for safety evaluation.

Many scholars have conducted relevant research on this problem. Sarvanis [4] proposed an analytical methodology for pipe strain subjected to permanent ground-induced actions in geohazard areas. Wu [5] studied the mechanical characteristics of pipe in mining collapse areas according to the effects of mining areas and properties of pipe material. Zhang [6] suggested a continuous elastic method to evaluate the effect of underground excavation on existing pipes in multilayered, and the physical behavior of jointed pipes is also considered. Klar [7] studied the soil–pipe interaction based on elastic continuum solution and Winkler solution. Wang [8] used the probability function integration method to predict the three-dimensional deformation of the subsidence area considering the action between the pipe and soil, and the deformation coordination equation of the pipe is pushed to solve the axial stress and strain of the pipe. Jiang et al. [9] established a finite element model of buried pipe in mined-out subsidence area by using pipe–soil interaction element and combining with three-dimensional soil spring nonlinear model. In order to compare the effects of soil stratifications on the pipe behavior subject to soil movement, Zhang and Zhang [10] proposed a Galerkin solution and a layered transfer matrix solution for the soil–pipe interaction. Kratzsch [11] proposed some simplified methods of analyses of the mining subsidence effects on pipes. Liang [12] assessed the stress distribution of buried pipe based on elastic foundation beam theory.

Large deformation of the pipe occurs during the strata displacement. There are few studies that focus on the plastic deformation of pipes. In this paper, a mechanical model of buried pipe in subsidence area is established. Based on the pipe–soil interaction, the effects of strata subsidence, pipe parameters, and soil parameters on the mechanical behavior of buried pipe were investigated.

## Analytical Model

Under the strata subsidence, the buried pipe deformation appears for bending moment caused by subsidence displacement. Many estimate formulas of strain and displacement of the pipe under strata displacement have been proposed. Vazouras et al. [13] proposed a simple calculation method for solving the deformation of buried pipes under strata displacement. It is assumed that the pipe is horizontal in the subsidence area and the no-subsidence area, and the bending deformation only occurs in the transition subsidence area. As shown in Fig. 1, the deformed pipe is regarded as a smooth S-shaped curve. The cross section of the pipe is still circular; the pipe and soil are not separated. Then, the displacement equation of the pipe after the strata subsidence can be calculated by

Display Formula

(1)$y(x)=d2(1−cos πxL)$

where d is the subsidence displacement. L is the length of S-shape deformed pipe.

Then, the maximum bending curvature can be derived as follow: Display Formula

(2)$k=−(d2ydx2)max=d2(πL)2$

And, the corresponding bending strain can be derived as follow: Display Formula

(3)$εb=kD2=π2dD4L2$

where D is the outer diameter of pipe.

Then, the increase of pipe length at x = 0 and x = L is Display Formula

(4)$Δ=∫0x1+y′2dx−L$

where Δ is the pipe stretching of pipe length between x =0 and x = L.

So, the axial strain of pipe can be derived as follow: Display Formula

(5)$εm=ΔL=1L(∫0L1+y′2dx)−1$

Apply power series expansion Display Formula

(6)$1+y′2=1+12y′2+⋯+12(12−1)…(12−n+1)n!y′2$

And keeping only first two terms, the axial strain of pipe can be expressed Display Formula

(7)$εm=ΔL=12L(∫0Ly′2dx)=d2π216L2$

## Materials and Methods

###### Numerical Simulation Model.

Pipe is a thin shell structure, when the large deformation appears on the cross section of pipe, the principle of superposition cannot be used for pipe deformation. There may be residual stress and stress concentration on the surface of the pipe [14]. So, the mechanical behavior of buried pipe in subsidence area is examined numerically by using general finite element program [15]. The nonlinear material properties of the pipe and the soil, the interaction between the pipe and the soil, and the deformation of the pipe cross section are simulated strictly, which makes the evaluation of the pipe performance standard highly accurate.

Figure 2 shows the finite element model of buried pipe and soil. To save computation time, 1/2 model was established for the symmetry of the structure. The size of the whole model is 60 m × 10 m × 15 m, the diameter of pipe D =660 mm, the wall thickness t =8 mm, the buried depth of pipe H =2 m. Four-node reduced integration shell elements are employed to simulate the pipe, eight-node reduced-integration elements are employed to simulate the soil [16]. A total of 40 shell elements around the cylinder circumference of pipe, the size of shell elements in the axial direction of pipe is 0.125 m.

The whole analysis is divided into two steps: gravity loading and internal pressure of the pipe are applied first, and then the subsidence displacement is applied. The soil divides two parts: the subsidence area and no-subsidence area. The subsidence displacement w is applied on the subsidence area (y =0 m to y =30 m). The node on the bottom planes of the no-subsidence area (y =30 m to y =60 m) remain fixed in z-direction. The symmetry constraint is applied to the xz plane (y =0 m) and normal constraints to the rest planes.

An elastic-perfectly plastic Mohr–Coulomb constitutive model is used to describe the mechanical behavior of soil material; the density of soil is 1950 kg/m3; the elastic modulus is E =50 MPa; the Poisson's ratio is μ = 0.3; the cohesion is c =30 kPa; and the friction angle is 22.5 deg [17]. A large-strain plastic model with isotropic hardening is used for buried pipe. The numerical results are obtained for X65 steel pipe. The yield stress of pipe is 448.5 MPa; the elastic modulus is 210 GPa; the Poisson's ratio is 0.3; and the density is 7800 kg/m3 [18,19].

For pipe–soil interaction, the buried pipe is in contact with surrounding soil. The deformation of buried pipe is caused by the interaction of internal pressure and surrounding soil. The contact algorithm is used to simulate the interface between the outer surface of the pipe and the soil. The algorithm can simulate the separation state of pipe and soil considering the interface friction. Isotropic Coulomb friction is applied by a suitable, the friction coefficient equals to 0.3 [20].

###### Model Verification.

When the subsidence displacement w =6 m, the displacement curves of no pressure pipe are obtained by the analytical model and the numerical model are shown in Fig. 3. Through normalization, the displacement curves obtained from the numerical model and the analytical model are similar, and the overall trend is consistent. The axial strain of the pipe calculated by analytical model is 0.0287, whereas by numerical model is 0.0304, which is increased by 5.92% compared with the analytical calculation. Therefore, the finite element model established in this paper is reliable.

## Simulation Results and Discussion

In subsidence area, the subsidence pits are formed on the surface. The deformation of buried pipe and the strata occur together, but deformation coordination will occur due to the difference between the stiffness of the pipe and the soil. Figure 4 shows the deformation of the strata and the pipe after strata subsidence. During the subsidence process, the pipe and soil are separated; the separation of the pipe between the transition subsidence area and the subsidence area occurs below the pipe, and the separation is very obvious. This is because the stiffness of pipe is much larger than the soil stiffness. Under the action of soil subsidence, the pipe resists the soil deformation, which resulting in the separation. When the subsidence displacement is large, it is highly likely that the buried pipe will be suspended or broken.

When the subsidence displacement is 1 m, the local stress of the pipe reaches the yield strength. As the collapse amount increases, the high-stress area of the pipe gradually increases along the pipe axial direction. When the subsidence displacement is 4 m, the pipe stress reaches the yield strength in a large area. When the subsidence displacement is 8 m, the maximum stress of the pipe reaches 480 MPa, which is far exceeded the yield strength (Fig. 5).

Figure 6 shows the displacement and cross section of the pipe with different subsidence displacements. In Fig. 6(a), the pipe displacement increases as the subsidence displacement increases, and the deformation range also increases. Because of the cohesive effect in the soil and the deformation coordination of the pipe and the soil, the pipe displacement is smaller than the soil displacement. In Fig. 6(b), the dangerous section of the pipe occurs in the subsidence transition area. As the subsidence displacement increases, the pipe section gradually changes from a circle to an ellipse. Due to the large tensile deformation, the pipe has a tendency to be squashed.

Figure 7 shows the axial strain on the upper surface of the pipe under different subsidence displacements. There are two strain peaks on the pipe surface, and the maximum axial strain appears in the no-subsidence area. The axial strain increases with the increasing of subsidence displacements.

In order to describe the cross-sectional shape of pipe, ovality k is defined (k = (Dmax − Dmin)/D). Figure 8 shows the plastic strain and the ovality of most dangerous section with different subsidence displacements, and εp is the maximum plastic strain of the pipe. The plastic strain and ovality of the pipe increase with the increase of the subsidence displacement, but the change is nonlinear. In addition, the high-strain area of the pipe extends along the axial direction of pipe, and the edge of the high-strain area is wavy.

## Effect of Pipe Parameters

###### Diameter–Thickness Ratio Effect.

The diameter–thickness ratio of pipe (D/t) affects the pipe's stiffness, which affects the pipe bending deformation ability. According to the standard, when the outer diameter of the pipe is 660 mm, the wall thickness of the pipe is allowed to vary from 6.4 to 20.6 mm [21]. Otherwise, it is necessary to consider the local buckling of pipes, which is more prone to failure when the D/t ratio is large. Therefore, the diameter–thickness ratios are 33, 39, 47, 60, 83, 94, 110, and 132, respectively.

Figure 9 shows the displacement curves of pipe with different diameter–thickness ratios, when the subsidence displacement is 5 m. The degrees of separation between pipe and soil are different. When D/t =33, the separation degree between pipe and soil is the largest, and the resistance of pipe is the strongest. When D/t =132, the degree of separation between pipe and soil is the smallest, and the deformation range of pipe is also small. The pipe displacement locates far away from the subsidence interface in the subsidence area, and it does not change with the diameter–thickness ratio. In addition, the displacement curves of the pipe located in the no-subsidence area about 1 m from the subsidence interface is approximately at the same point.

Figure 10 shows the plastic strain curves of pipe with different diameter–thickness ratios. When D/t =132, the maximum plastic strain of the pipe appears in the no-subsidence area about 4 m away from the subsidence interface. As the diameter–thickness ratio increases, the position of the maximum plastic strain gradually moves away from the subsidence interface, and the edges of the high-strain zone are distributed in stripes.

Figure 11 shows the maximum plastic strain and ovality of pipe with different diameter–thickness ratios. As the diameter–thickness ratio increases, the cross section of the most dangerous part of pipe increases, and it is linearly when D/t <90, but the maximum plastic strain increases nonlinearly. When D/t <40, the plastic strain increases greatly, and then the growth rate is small.

###### Buried Depth Effect.

When D/t =83, w =5 m, the displacement curves of the pipe with different buried depths are shown in Fig. 12. With the increasing of the buried depth, the separation degrees between pipe and soil are different. When the buried depth is large, the pipe is most likely to be deformed, the deformation range is small, and the bending deformation is first completed under the stratum subsidence. This is because when the pipe is deformed, it needs to overcome the tensile and compressive stress of the adjacent part, and it also need to resist the sinking of the overlying soil, and the thickness of the overlying soil determines the resistance of the pipe.

Figure 13 shows the maximum plastic strain and ovality of the pipe with different buried depths. The maximum plastic strain of the pipe increases with the increase of the buried depth, and the growth rate is reduced. The plastic strain is distributed on the pipe surface in a stripe shape, and the stripe density increases in the axial direction as the buried depth increasing. As the buried depth increases, the ovality of the dangerous section of the pipe increases nonlinearly. When H <4 m, the pipe's ovality growth rate increases continuously, and when H >4 m, the pipe growth rate decreases.

###### Internal Pressure Effect.

When H =2.5 m, D/t =83, w =5 m, the displacement curves of the pipe with different internal pressures are shown in Fig. 14. In the range of the maximum internal pressure, no matter what the internal pressure is, the displacement of the pressure pipe is the same as the nonpressure pipe. It is indicated that the internal pressure is not sensitive to the deformation of the buried pipe under the action of stratum subsidence. The effect of the internal pressure of the pipe can be ignored when analyzing the pipe displacement.

Figure 15 shows the von Mises stress distribution of the pipe with different internal pressures. The high stress area of the pipe increases with the increasing of internal pressures. When P >1 MPa, the pipe will easily appear striped high-stress area. When the internal pressure increases, the high-stress area is no longer extended. This adds uncertainty to the safety of the pipe.

Figure 16 shows the maximum plastic strain and ovality of the pipe with different internal pressures. As the internal pressure increases, the plastic strain increases gradually, but the ovality of the pipe decreases. The plastic strain distribution expands along the pipe axial direction as the internal pressure increasing. The plastic strain area gradually increases, and there are intervals between two adjacent plastic strain areas. As the internal pressure increases, the change rate of ovality gradually decreases. The ovality of the pressure pipe is much smaller than the nonpressure pipe, when P =1 MPa, the ovality is reduced by 79.2%. Because the internal pressure can increase the pipe's relative stiffness, so the deformation of the pipe cross section decreases.

###### Friction Coefficient Effect.

During the subsidence process, when the pipe is axially deformed, the soil around the pipe will have some resistance to this relative motion. However, when the resistance exceeds the limit value, the soil around the pipe will partially yield, and the relative sliding will occur. Figure 17 shows the displacement curves of the pipe with different friction coefficients. With the increasing of the friction coefficient, the pipe displacement has hardly changed.

Figure 18 shows the maximum plastic strain and ovality of the pipe under different friction coefficients. As the friction coefficient increases, the maximum plastic strain and ovality of the pipe increase. When the friction coefficient is less than 0.4, the change rate of ovality is large. When the friction factor is greater than 0.4, the change rate is small. However, the variation of maximum plastic strain and ovality are small.

## Effect of Soil Parameters

###### Elastic Modulus Effect.

The elastic modulus reflects the ability of the material to resist deformation, and the elastic modulus of different soils has a great influence on the pipe–soil interaction. When the Poisson's ratio of soil is 0.3 and w =6 m, the displacement curves of pipe with different soil elastic moduli are shown in Fig. 19. The pipe displacement increases with the increasing of the soil elastic modulus, but the separation between pipe and soil decreases. The change of pipe's displacement is small.

Figure 20 shows the maximum plastic strain and ovality of the pipe with different soil elastic moduli. The maximum plastic strain and ovality increase with the increasing of the soil elastic modulus, and the rate of change does not change linearly.

###### Poisson's Ratio Effect.

Figure 21 shows the maximum plastic strain and ovality of pipe with different Poisson's ratios. The change of pipe ovality is less than 2%, the Poisson's ratio has a little effect on the pipe's cross section. The change of plastic strain is less than 1.3%, and the change rate is very small when μ > 0.3. It shows that the Poisson's ratio of soil has a little effect on the pipe deformation.

###### Cohesion Effect.

Cohesion indicates the attraction between adjacent parts of the same substance, and this attraction is the performance between the molecular forces of the same substance. When w =6 m, the displacement curves of the pipe with different soil's cohesions are shown in Fig. 22. As the soil cohesion increases, the pipe displacement increases continuously, and the displacement invariant point is close to the subsidence interface. In addition, the deformation range of the pipe is continuously reduced, and the separation of the pipe and soil is gradually reduced. Because the soil with a large cohesive is not easy be deformed, so that the pipe needs to withstand the deformation of the soil body. When the buried pipe is located in hard soil, it is more likely to failure.

Figure 23 shows the maximum plastic strain of the pipe with different cohesions. The maximum plastic strain increases with the increasing of soil's cohesion, and the change rate is nonlinear. However, the plastic strain changes with different subsidence displacement are different, and the change rate of plastic strain increases with the increasing of the subsidence displacement.

Figure 24 shows the ovality of pipe with different soil's cohesion. The pipe ovality increases with the increasing of soil cohesion. When the subsidence displacement is 4 m, the change rate is approximately linear. When subsidence displacement is more than 4 m, the change rate of the ovality increases continuously, and it increases rapidly when the soil cohesion is large. It indicates that the pipe's section is crushed very seriously at this time, the pipe has been seriously deformed. In actual engineering, it should be paid attention to the safety of buried pipes in hard strata.

## Conclusions

1. (1)In the strata subsidence area, the pipe and soil are separated, and high stress area appears on the pipe surface. As subsidence displacement increases, the range of high-stress area and pipe displacement gradually increases, and the pipe section changes from a circle to an ellipse. There are two strain peaks on the pipe surface, and the maximum axial strain of pipe is in no-subsidence area. The maximum plastic strain and pipe ovality increase with the increasing of subsidence displacement.
2. (2)The displacement, plastic strain, and ovality of the pipe increase with the increasing of diameter–thickness ratio and buried depth. Internal pressure and friction coefficient have a little effect on the pipe displacement. As internal pressure increases, the stress and plastic strain of the pipe increase, but pipe ovality decreases. The plastic strain and ovality increase as the increasing of the friction coefficient, but the effect is small.
3. (3)As the elastic modulus and cohesion of soil increase, the displacement, plastic strain, and ovality of pipe increase. The effect of soil Poisson's ratio on the deformation of pipe is small.

## Funding Data

• Scientific Research Starting Project of SWPU (No. 2017QHZ011; Funder ID: 501100002855/501100004753).

• State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining & Technology (No. SKLGDUEK1729; Funder ID: 10.13039/501100011362).

• Youth Research Innovation Training Team of SWPU (2018CXTD12; Funder ID: 10.13039/501100004753).

• Sichuan Science and Technology Project (19YYJC0824; Funder ID: 10.13039/501100004829).

• Nanchong Science and Technology Project (No. NC17SY4018; Funder ID: 10.13039/501100002855).

## References

Di, Y. , Shuai, J. , Wang, X. L. , and Shi, L. , 2013, “ Study on Methods for Classifying Oil & Gas Pipe Incidents,” China Saf. Sci. J., 23(7), pp. 109–115.
Li, L. , 2013, “ Impact of Mining Subsidence on Long-Distance Pipe Stress and Deformation,” M.S. thesis, Beijing Jiaotong University, Beijing, China (in Chinese).
Zhang, G. H. , 2007, “ Preliminary Discussion on Geological Hazards Along the Pipe Project for Transferring Gas From Sichuan Province to Eastern China,” Hydrogeol. Eng. Geol., 5, pp. 81–84.
Sarvanis, G. C. , and Karamanos, S. A. , 2017, “ Analytical Model for the Strain Analysis of Continuous Buried Pipes in Geohazard Areas,” Eng. Struct., 152, pp. 57–69.
Wu, Z. Z. , Hao, J. B. , Tan, D. J. , Sun, W. M. , Han, B. , Jing, H. Y. , and Liu, J. P. , 2010, “ Characteristics of Pipe-Soil Interaction in Mining Collapse Areas,” Chin. J. Geol. Hazard Control, 21, pp. 77–81.
Zhang, C. R. , Yu, J. , and Huang, M. S. , 2012, “ Effect of Tunneling on Existing Pipes in Layered Soils,” Comput. Geotech., 43, pp. 12–25.
Klar, A. , Vorster, T. E. B. , Soga, K. , and Mair, R. J. , 2005, “ Soil-Pipe Interaction Due to Tunnelling: Comparison Between Winkler and Elastic Continuum Solution,” Geotechnique, 55(6), pp. 461–466.
Wang, X. L. , Shuai, J. , and Zhang, J. Q. , 2011, “ Mechanical Response Analysis of Buried Pipe Crossing Mining Subsidence Area,” Rock Soil Mech., 32(11), pp. 3373–3386.
Jiang, H. Y. , Wang, H. , and Xu, T. L. , 2016, “ Analysis on Deformation and Stress of Buried Gas Pipe in Mined-Out Subsidence Area,” J. Saf. Sci. Technol., 12(2), pp. 45–51.
Zhang, Z. G. , and Zhang, M. X. , 2013, “ Mechanical Effects of Tunneling on Adjacent Pipes Based on Galerkin Solution and Layered Transfer Matrix Solution,” Soils Found., 53(4), pp. 557–568.
Kratzsch, H. , 1983, Mining Subsidence Engineering, Springer-Verlag, Berlin.
Liang, Z. , 1999, Some Mechanical Problems in Petroleum Engineering, Petroleum Industry Press, Beijing, China.
Vazouras, P. , Karamanos, S. A. , and Dakoulas, P. , 2010, “ Finite Element Analysis of Buried Steel Pipes Under Strike-Slip Fault Displacements,” Soil Dyn. Earthquake Eng., 30(11), pp. 1361–1376.
Zhang, J. , Xie, R. , and Zhang, H. , 2018, “ Mechanical Response Analysis of the Buried Pipeline Due to Adjacent Foundation Pit Excavation,” Tunnelling Underground Space Technol., 78, pp. 135–145.
Dassault Systèmes, 2014, “Abaqus 6.14 Documentation,” Abaqus Software Manual, Dassault Systèmes, Vélizy-Villacoublay, France.
Zhang, J. , Zhang, L. , and Liang, Z. , 2018, “ Buckling Failure of a Buried Pipeline Subjected to Ground Explosions,” Process Saf. Environ. Prot., 114, pp. 36–47.
Zhao, X. , 2015, “ Deformation and Stress Analysis of Buried Pipe Crossing Mining Subsidence Area and Remote Monitoring,” M. S. thesis, Southwest Petroleum University, Chengdu, China (in Chinese).
Zhang, J. , Xiao, Y. , and Liang, Z. , 2018, “ Mechanical Behaviors and Failure Mechanisms of Buried Polyethylene Pipes Crossing Active Strike-Slip Faults,” Compos. Part B, 154, pp. 449–466.
Zhang, J. , and Xie, J. , 2018, “ Investigation of Static and Dynamic Seal Performances of a Rubber O-Ring,” ASME J. Tribol., 140(4), p. 042202.
Vazouras, P. , Karamanos, S. A. , and Dakoulas, P. , 2012, “ Mechanical Behavior of Buried Steel Pipes Crossing Active Strike-Slip Faults,” Rock Dyn. Earthquake Eng., 41, pp. 164–180.
ASME, 2007, “ Gas Transmission and Distribution Pipe Systems,” American Society of Mechanical Engineers, New York, Standard No. ANSI/ASME B31.8.
Topics: Pipes , Soil , Displacement
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## References

Di, Y. , Shuai, J. , Wang, X. L. , and Shi, L. , 2013, “ Study on Methods for Classifying Oil & Gas Pipe Incidents,” China Saf. Sci. J., 23(7), pp. 109–115.
Li, L. , 2013, “ Impact of Mining Subsidence on Long-Distance Pipe Stress and Deformation,” M.S. thesis, Beijing Jiaotong University, Beijing, China (in Chinese).
Zhang, G. H. , 2007, “ Preliminary Discussion on Geological Hazards Along the Pipe Project for Transferring Gas From Sichuan Province to Eastern China,” Hydrogeol. Eng. Geol., 5, pp. 81–84.
Sarvanis, G. C. , and Karamanos, S. A. , 2017, “ Analytical Model for the Strain Analysis of Continuous Buried Pipes in Geohazard Areas,” Eng. Struct., 152, pp. 57–69.
Wu, Z. Z. , Hao, J. B. , Tan, D. J. , Sun, W. M. , Han, B. , Jing, H. Y. , and Liu, J. P. , 2010, “ Characteristics of Pipe-Soil Interaction in Mining Collapse Areas,” Chin. J. Geol. Hazard Control, 21, pp. 77–81.
Zhang, C. R. , Yu, J. , and Huang, M. S. , 2012, “ Effect of Tunneling on Existing Pipes in Layered Soils,” Comput. Geotech., 43, pp. 12–25.
Klar, A. , Vorster, T. E. B. , Soga, K. , and Mair, R. J. , 2005, “ Soil-Pipe Interaction Due to Tunnelling: Comparison Between Winkler and Elastic Continuum Solution,” Geotechnique, 55(6), pp. 461–466.
Wang, X. L. , Shuai, J. , and Zhang, J. Q. , 2011, “ Mechanical Response Analysis of Buried Pipe Crossing Mining Subsidence Area,” Rock Soil Mech., 32(11), pp. 3373–3386.
Jiang, H. Y. , Wang, H. , and Xu, T. L. , 2016, “ Analysis on Deformation and Stress of Buried Gas Pipe in Mined-Out Subsidence Area,” J. Saf. Sci. Technol., 12(2), pp. 45–51.
Zhang, Z. G. , and Zhang, M. X. , 2013, “ Mechanical Effects of Tunneling on Adjacent Pipes Based on Galerkin Solution and Layered Transfer Matrix Solution,” Soils Found., 53(4), pp. 557–568.
Kratzsch, H. , 1983, Mining Subsidence Engineering, Springer-Verlag, Berlin.
Liang, Z. , 1999, Some Mechanical Problems in Petroleum Engineering, Petroleum Industry Press, Beijing, China.
Vazouras, P. , Karamanos, S. A. , and Dakoulas, P. , 2010, “ Finite Element Analysis of Buried Steel Pipes Under Strike-Slip Fault Displacements,” Soil Dyn. Earthquake Eng., 30(11), pp. 1361–1376.
Zhang, J. , Xie, R. , and Zhang, H. , 2018, “ Mechanical Response Analysis of the Buried Pipeline Due to Adjacent Foundation Pit Excavation,” Tunnelling Underground Space Technol., 78, pp. 135–145.
Dassault Systèmes, 2014, “Abaqus 6.14 Documentation,” Abaqus Software Manual, Dassault Systèmes, Vélizy-Villacoublay, France.
Zhang, J. , Zhang, L. , and Liang, Z. , 2018, “ Buckling Failure of a Buried Pipeline Subjected to Ground Explosions,” Process Saf. Environ. Prot., 114, pp. 36–47.
Zhao, X. , 2015, “ Deformation and Stress Analysis of Buried Pipe Crossing Mining Subsidence Area and Remote Monitoring,” M. S. thesis, Southwest Petroleum University, Chengdu, China (in Chinese).
Zhang, J. , Xiao, Y. , and Liang, Z. , 2018, “ Mechanical Behaviors and Failure Mechanisms of Buried Polyethylene Pipes Crossing Active Strike-Slip Faults,” Compos. Part B, 154, pp. 449–466.
Zhang, J. , and Xie, J. , 2018, “ Investigation of Static and Dynamic Seal Performances of a Rubber O-Ring,” ASME J. Tribol., 140(4), p. 042202.
Vazouras, P. , Karamanos, S. A. , and Dakoulas, P. , 2012, “ Mechanical Behavior of Buried Steel Pipes Crossing Active Strike-Slip Faults,” Rock Dyn. Earthquake Eng., 41, pp. 164–180.
ASME, 2007, “ Gas Transmission and Distribution Pipe Systems,” American Society of Mechanical Engineers, New York, Standard No. ANSI/ASME B31.8.

## Figures

Fig. 1

Schematic diagram of the pipe in subsidence area

Fig. 2

Finite element model of buried pipe and soil

Fig. 3

Displacement curves of the pipe

Fig. 4

Deformation of strata and pipe after soil subsidence

Fig. 5

von Mises stress of pipe under different subsidence displacements

Fig. 6

Displacement and cross section of pipe under different subsidence displacements: (a) displacement of buried pipe and (b) cross section of most dangerous part of pipe

Fig. 7

Axial strain of pipe with different subsidence displacements

Fig. 8

Plastic strain and ovality of pipe with different subsidence displacements

Fig. 9

Displacement curves of pipe with different diameter–thickness ratios

Fig. 10

Plastic strain curves of pipe with different diameter–thickness ratios

Fig. 11

Maximum plastic strain and ovality of pipe with different diameter–thickness

Fig. 12

Displacement curves of pipe with different buried depths

Fig. 13

Maximum plastic strain and ovality of pipe with different buried depths

Fig. 14

Displacement curves of pipe with different internal pressures

Fig. 15

von Mises stress of pipe with different internal pressures

Fig. 16

Maximum plastic strain and ovality of pipe with different internal pressures

Fig. 17

Displacement curves of the pipe with different friction coefficients

Fig. 18

Maximum plastic strain and ovality of pipe with different friction coefficients

Fig. 19

Displacement curves of pipe with different soil elastic moduli

Fig. 20

Maximum plastic strain and ovality of pipe with different soil elastic moduli

Fig. 21

Maximum plastic strain and ovality of pipe with different soil Poisson's ratios

Fig. 22

Displacement curves of the pipe with different soil cohesions

Fig. 23

Maximum plastic strain of the pipe with different soil cohesions

Fig. 24

Ovality of the pipe with different cohesions

## Errata

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