# Numerical Simulation Study on the Performance of Buried Pipelines under the Action of Faults
## 4 Analysis of Parameters Affecting Pipeline Response under Fault Action
### Influence of Pipe Wall Thickness  
Here, to investigate the influence of wall thickness on the performance of pipes, four kinds of wall thicknesses are selected, 15.3 mm, 18.4 mm, 22.0 mm, and 26.4 mm, and the corresponding critical axial compressive strains are 0.0073, 0.0085, 0.01, and 0.0118, respectively (dashed line in Figure 12a). The variations in the axial strain and the von Mises stress of the pipeline under different pipe wall thickness are given in Figure 12.  
As can be seen from Figure 12a, the critical fault displacements necessary for the pipe to reach tensile damage and shell buckling damage differ greatly under the four kinds of thicknesses. The overall trend can be described as, the thinner the wall is, the earlier the damage occurs in the pipe. When the wall thickness of the pipe is 15.3 mm, the growth rate of the tensile strain is significantly higher than for other thicknesses, and tensile damage occurs first when the fault displacement is 1.6 m. As the fault displacement increases, the tensile strain of the other wall thicknesses does not reach the critical condition of tensile damage before the fault displacement of 2 m.  
Figure 11: Deformation of pipelines under different internal pressures: (**a**) Internal pressure is 0; (**b**) internal pressure is 12 MPa. The variation in the compressive strain between different wall thicknesses is even more obvious, and the pipeline with a wall thickness of 15.3 mm has already undergone shell buckling failure when the fault displacement is only 0.23 m. This shows that, when the wall thickness of the pipe is too small and there is a large pressure inside the pipe (12 MPa), the pipe may be in a very fragile state. The pipe will undergo shell buckling damage under a very small fault displacement, and the damage will develop very rapidly, making the pipeline experience large deformation. In Figure 12b, it can be seen that the initial von Mises stress is as high as 471 MPa under an internal pressure of 12 MPa and wall thickness of 15.3 mm. The von Mises stress rises rapidly with the increase in fault displacement, and the yield strength of the pipe has been reached when the fault displacement is 0.096 m. After the von Mises stress of the pipe exceeds the yield strength, the growth rate of the von Mises stress with the fault displacement decreases with the increase in the wall thickness. When the wall thickness increases to 26.4 mm, the von Mises stress hardly increases up to 0.8 m of fault displacement change. The deformation of pipelines also requires special attention. The deformation of the pipe with a wall thickness of 15.3 mm at fault displacements of 0.52 m, 0.62 m, and 0.72 m is shown in Figure 13. It can be seen that the pipe deformation changes considerably for every 0.1 m increase in fault displacement after shell buckling damage occurs in the pipe. The deformation of the pipe under four wall thicknesses is given in Figure 14, where the dashed line represents the location of the fault plane, and the length marked in the figure is the distance between the positions of the maximum axial compressive strain on both sides of the fault. It can be seen that, the smaller the wall thickness of the pipeline, the more obvious the deformation of the pipeline is under the same fault displacement, and the farther apart the maximum axial compressive strain on both sides of the fault is located. The main reason for this situation is that, during the fault displacement process,  
Figure 12: The response of pipeline under different wall thicknesses: (**a**) Axial strain; (**b**) von Mises stress. Figure 13: Development of pipe bulging as the displacement of faults increases. the soil stiffness is relatively small compared to the pipe material, and the soil on both sides is equivalent to applying a flexible compression shear effect on the pipe. The smaller the wall thickness of the pipeline, the easier it is to damage, so the location of the damage is closer to the \"shear plane\" of the fault displacement surface.