# Numerical Simulation Study on the Performance of Buried Pipelines under the Action of Faults
## 3 Analysis of Pipeline Response under the Action of Strike-Slip Reverse Fault  
### Analysis of Vertical Displacement Response of Pipeline  
The vertical displacement of the pipe under a strike-slip reverse fault is studied to determine whether the damage of the pipeline can be categorized as beam-type buckling. In the model, the burial depth is taken as 1.5 m, the pipe outer diameter is 1.219 m, the wall thickness is 22 mm, the internal pressure is 12 MPa, and the fault angle is 60 degrees. By comparing the vertical displacement of the middle and end of the pipe, it is determined whether it has undergone beam-type buckling failure.  
The vertical displacement at the top of the pipe along the pipeline axis under the effect of fault displacement is shown in Figure 3. In Figure 3, \(\delta_{\text{max}}\) indicates the maximum value of vertical displacement of the pipe, and \(\delta_{40}\) indicates the value of vertical displacement at the end of the pipe on the side of the movable disk. The peak vertical displacement of pipe under different fault displacements is plotted in Table 3.  
As can be seen from Figure 3, the vertical displacement of the pipe under the action of the fault is basically consistent with the distribution trend along the pipeline axis. From the side of the fixed disk to the side of the movable disk, the response is smooth and unchanged, and then increases rapidly at 10 m away from the fault surface. The maximum displacement occurs at about 4 m away from the fault surface on the side of the movable disk.  
From Figure 3, it can be seen that \(\delta_{\text{max}}\) is slightly larger than \(\delta_{40}\), which indicates a certain upward bulge in the middle of the pipe. However, as can be seen from Table 3, the difference in vertical displacement of the pipe (\(\delta_{\text{max}}-\delta_{40}\)) is negligible compared to \(\delta_{40}\) and \(\delta_{\text{max}}\) (both less than 2%), which reflects that there is not a sudden change in vertical displacement along the pipeline axis. That is to say, the pipe in the case of this study does not undergo beam-type buckling damage.  
Figure 3: Variation in vertical displacement for different fault displacements.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Fault Displacement/m** & \(\delta_{\text{max}}\)/m & \(\delta_{40}\)/m & (\(\delta_{\text{max}}-\delta_{40}\))/m & (\(\delta_{\text{max}}-\delta_{40}\))/\(\delta_{\text{max}}\) \\ \hline
0.501 & 0.380 & 0.375 & 0.005 & 0.013 \\
1.054 & 0.797 & 0.789 & 0.008 & 0.010 \\
1.499 & 1.133 & 1.122 & 0.011 & 0.0097 \\
2.016 & 1.522 & 1.508 & 0.014 & 0.0092 \\
2.495 & 1.885 & 1.868 & 0.017 & 0.009 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Peak vertical displacement of pipelines for different fault displacements.  
[PERSON] et al. [29] pointed out that the minimum burial depth of the pipe between about 0.5 m and 1.0 m can avoid the occurrence of beam-type buckling damage. Considering both the above results and the relevant codes [24; 30; 31], the minimum burial depth of the pipe is 0.8 m. In the case of the selected pipe material and the buried depth of 1.5 m in this study, beam-type buckling failure will not occur, which is consistent with the above research conclusion.