## 3 Results
### Simulation Analysis of Earthquake Damage of Oil and Gas Pipeline Structure
#### 3.1.2 Stress and Strain Analysis of Pipeline Structure  
In order to further elucidate the failure mechanism of pipe bridge systems during earthquakes, we obtained the strain at multiple maximum stress points in oil and gas pipeline structures. The resulting equivalent strain cloud map, depicting the maximum stress conditions under six different operational scenarios, is presented in Figure 4.  
The stress-strain conditions of the pipeline structure under various seismic waves were derived from the strain cloud map depicting the maximum stress in Figure 4, as presented in Table 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Working** & **Maximum Stress** & **Maximum Stress** & **Maximum Strain** & \\
**Conditions** & **Moment (s)** & **(MPa)** & **(10\({}^{-3}\))** & **Maximum Stress Position** \\ \hline \hline X & _27.6_ & 458.79 & 2.279 & Pipe inlet end, upper side \\ Y & 11.7 & 404.22 & 1.964 & Pipe inlet end, upper side \\ Z & 25.5 & 663.02 & 4.420 & Bottom sides of tower \\ X + Y & 27.6 & 462.09 & 2.244 & Pipe inlet end, upper side \\ X + Z & 25.2 & 516.36 & 3.442 & Bottom sides of tower \\ X + Y + Z & 27.6 & 467.84 & 2.731 & Pipe inlet end, upper side \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Strain at the maximum stress of the pipeline structure under various working conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Working Conditions** & **Maximum Deformation** & **Maximum Deformation** & **Maximum Deformation** \\  & **Time (s)** & **(m)** & **Characteristics** \\ \hline X & 11.94 & 1.901 & Right straddle mid–upper bend \\ Y & 11.66 & 0.659 & Bend the left and right midspan under \\ Z & 25.76 & 1.991 & Lateral side bend at the top of the tower \\ X + Y & 11.98 & 1.695 & Right straddle mid–upper bend \\ X + Z & 11.96 & 2.010 & Lateral side bend at the top of the tower \\ X + Y + Z & 11.96 & 1.779 & Lateral and vertical bending of the left- \\  & & & and right-side span, midspan \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Preview of the maximum deformation of the pipeline structure under different working conditions. Figure 4: _Cont._  
Figure 4: _Cont_. It can be observed from Figure 4 and Table 4 that, under the six operational conditions, the strain duration at the pipeline's maximum stress induced by seismic waves was concentrated around 27 s. By comparing and analyzing the strains at maximum stress caused by three unidirectional seismic waves on the pipeline, it became evident that vertical and horizontal seismic waves primarily generated maximum strains at the inlet and outlet  
Figure 4: Strain at the maximum stress of the pipeline structure under different working conditions. Maximum deformation of the pipeline structure under different working conditions. (**a**) Strain under the X-direction earthquake, (**b**) strain under the Y-direction earthquake, (**c**) strain under the Z-direction earthquake, (**d**) strain under the X + Y direction earthquake, (**e**) strain under the X + Z direction earthquake, and (**f**) strain under the X + Y + Z direction earthquake. of the pipeline. The maximum strain generated by vertical seismic waves was 1.4 times greater than that of horizontal seismic waves, resulting in a peak stress of 458.79 MPa on the pipeline, which exceeds its material yield limit, causing plastic deformation to occur. Additionally, under transverse seismic wave action, the structural system experienced its highest strain at both ends of the bridge tower's bottom section. Consequently, when subjected to these three directional seismic waves, buckling failure is prone to occur at both ends of the pipeline due to excessive stress and strain. Furthermore, due to excessive vertical displacement of the pipeline's left and right sides in the middle span, there was also a significant increase in stress at the lower end of the pipeline. Simultaneously, as the bridge tower underwent substantial displacement and deformation in both spans, there was a corresponding amplification of stress and strain at the upper end of the pipeline in the middle span.