# 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 Axial Compressive Strain of Pipe  
In this section, the axial compressive strain of the pipe is analyzed to determine whether the damage belongs to shell buckling damage or not. This study adopts the critical compressive strain corresponding to the occurrence of pipe-wall shell buckling damage given by CSA Z662-2007 [31] as the basis for judgment:  
\[\epsilon_{\mathrm{c}}^{\mathrm{crit}}=0.5\frac{t}{D}-0.0025+3000(\frac{ \sigma_{\mathrm{h}}}{E})^{2}, \tag{2}\]  
\[\sigma_{\mathrm{h}}=\left\{\begin{array}{cc}\frac{(P_{\mathrm{i}}-P_{ \mathrm{e}})D}{2t}&\frac{(P_{\mathrm{i}}-P_{\mathrm{e}})D}{2t\sigma_{\mathrm{ s}}}<0.4\\ 0.4\sigma_{\mathrm{s}}&\frac{(P_{\mathrm{i}}-P_{\mathrm{e}})D}{2t\sigma_{ \mathrm{s}}}\geq 0.4\end{array}\right. \tag{3}\]  
where \(\epsilon_{\mathrm{c}}\)cit is the critical compressive strain at which the pipe undergoes shell buckling damage, \(t\) is the thickness of the pipe wall, \(D\) is the outer diameter of the pipe, \(\sigma_{\mathrm{h}}\) is the hoop stress, \((P_{\mathrm{i}}-P_{\mathrm{e}})\) is the internal pressure, and \(\sigma_{\mathrm{s}}\) is the yield stress of the pipe.  
Here, \(D=1219\) mm, \(t=22\) mm, and \((P_{\mathrm{i}}-P_{\mathrm{e}})=12\) MPa is selected as the object of study. Calculated by the above equations, \(\epsilon_{\mathrm{c}}\)cit = 1% is taken as the critical compressive strain for the occurrence of shell buckling damage of the pipe. Taking the case that the pipe crosses a strike-slip reverse fault with an angle 60 degrees, the trend of the maximum compressive strain \(\epsilon_{\mathrm{c}}\)max of the pipeline with the displacement of the fault is depicted in Figure 4. The deformation behaviors of the pipe at different stages are shown in Figure 5.  
As can be seen from Figure 4, the maximum axial compressive strain increases with the fault displacement, and when the fault displacement is 0.82 m, the maximum axial compressive strain has reached the critical compressive strain of the pipe shell buckling damage. This indicates that the pipeline has started to undergo shell buckling failure at this time.  
Figure 4: Variation in maximum axial compressive strain under different fault displacements.  
Combined with Figure 5, it can be found that, when the fault displacement is less than 0.82 m (Figure 5a), the pipe wall has not experienced shell buckling damage, and the pipe is still in the elastic stage. As the displacement of the fault increases, small folding and compression deformation gradually begin to appear on the pipe wall. The peak position of axial compressive strain on the pipe wall changes with increasing fault displacement, and at this time, the pipeline does not experience local instability. When the fault displacement is 1.76-0.82 m (Figure 5b), the location of pipe wall has reached the critical compressive strain value. Multiple folds of the pipe wall compressive pattern are gradually concentrated in a certain point, and the maximum axial compressive strain of the pipe wall is also gradually stabilized in the same place. When the fault displacement is more than 1.76 m (Figure 5c), with the increase in the fault displacement, the compressive strain increases rapidly and, under the action of the larger fault displacement and the internal pressure, the pipe wall gradually shows local outward protrusion. At this time, the structural integrity and bearing capacity have been seriously damaged.