# Numerical Simulation Study on the Performance of Buried Pipelines under the Action of Faults
## 4 Analysis of Parameters Affecting Pipeline Response under Fault Action
### The Influence of Pipeline Internal Pressure  
The internal pressure during the operation of long-distance buried pipelines has a significant impact on the economy and safety of pipelines. With the progress of science and technology, the performance of the steel used in pipelines is constantly improving, and the operating internal pressure that pipelines can withstand is also constantly improving. Most gas pipelines were built between the internal pressure of 3 and 10 MPa, while some pipelines have a higher internal pressure, such as the Second West-East Gas Pipeline Project (China), for which the internal design pressure can reach up to 12 MPa [28]. In this section, the internal pressures are taken to be 0 MPa, 3 MPa, 6 MPa, 9 MPa, and 12 MPa, and the corresponding critical axial compressive strains are calculated to be 0.0065, 0.007, 0.0085, 0.01, and 0.01, respectively (dashed line in Figure 10a). The variation in the axial strain and the von Mises stress of the pipeline under different internal pressures are plotted in Figure 10.  
As the displacement of the fault increases, the maximum axial tensile strain and compressive strain of the pipeline also increase. The growth rate with internal pressure is as follows, 0 MPa < 3 MPa < 6 MPa < 9 MPa. For the maximum axial tensile strains, the variation between the different internal pressures is not obvious, and \(\varepsilon_{\text{tmax}}\) is less than \(\varepsilon_{\text{t}}^{\text{crit}}\) under the five internal pressures when the fault displacement reaches 2 m. For the maximum axial compressive strains, the growth rate is more significantly increased with the increase in the internal pressures. With the increase in the internal pressure, the growth rate of \(\varepsilon_{\text{tmax}}\) rises more significantly, and the maximum axial compressive strain of the pipeline under the five types of internal pressures has been up to the shell buckling damage condition before the fault displacement reaches 2 m, as seen in Figure 10a. From the comparative analysis of \(\varepsilon_{\text{tmax}}\) and \(\varepsilon_{\text{tmax}}\), it can be seen that the existence of internal pressure in pipelines can partly offset the tensile effect caused by fault displacement,  
Figure 10: The response of pipeline under different internal pressures: (**a**) Axial strain; (**b**) von Mises stress. and delays the growth of \(\varepsilon_{\text{tmax}}\). However, the compression effect caused by pipeline internal pressure and fault dislocation superimposed on each other accelerates the growth rate of \(\varepsilon_{\text{cmax}}\). From Figure 10b, it can be seen that the maximum von Mises stress of the pipeline increases gradually with the increase in the internal pressure. Before reaching the yield strength, the stresses under five types of internal pressures increase relatively fast. The initial maximum von Mises stress of the pipeline is significantly different due to the existence of the internal pressure. The initial maximum von Mises stress of the pipeline without internal pressure is almost 0, while, when the internal pressure is 12 MPa, the initial maximum von Mises stress is as high as 330 MPa, which is equivalent to the maximum von Mises stress of the pipe without internal pressure when the fault displacement is 0.33 m.  
Figure 11 depicts the deformation of the pipe for both cases, with and without internal pressure. When the internal pressure is 0 MPa, after the pipe is damaged by shell buckling, the location of the maximum axial compressive strain and the nearby wall will appear to be inwardly concave as the fault displacement continues to increase. In the presence of internal pressure, the pipe will eventually appear to be outwardly convex under the compressive effect after the pipe is damaged by shell buckling as the fault displacement increases. The maximum axial compressive displacement increases, the location of the strain and the nearby pipe wall in the compression will eventually appear to the outwardly convex.