# Safety Analysis and Condition Assessment of Corroded Energy Pipelines under Landslide Disasters
## 4 Results and Discussion
### Model Validation  
The model validation is divided into three parts: model size validation, mesh validation for landslide models without pipeline corrosion, and mesh validation for landslide models with pipeline corrosion. In the landslide region with a soil thickness of 3 m, a thickness impact analysis was performed to minimize potential computational biases. The axial equivalent stress distribution at the central area of the pipeline exposed to sliding is depicted in Figure 3a. To assess the influence of the non-landslide width on the distribution of equivalent stress in the pipeline, models with a non-landslide region width ranging from 15 to 30 m were established, and the axial stress distribution is illustrated in Figure 3b. The soil thickness shows minimal deviation between 5 m and 6 m. In other cases, the stress distribution and values of the pipeline are nearly identical, suggesting that a model with a thickness of 6 m can be used for subsequent research. For a non-landslide width of 15 m, the edge equivalent stress of the pipeline is notably high, attributed to the stress not being fully accounted for and not yet stabilized. At 20 m, the stress nears stability but varies from those observed at 25 m and 30 m. With almost identical stress distributions at 25 m and 30 m, selecting a 25 m width for the non-landslide area optimizes both the precision and computational efficiency. Mesh quality in the model directly impacts the accuracy of computational results. With the pipeline wall subjected to internal pressure, the number of layers in the thickness \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\rho\) (kg/m\({}^{3}\)) & \(E\) (MPa) & \(\mu\) & \(D\) (mm) & \(T\) (mm) & [\(\sigma\)] (MPa) & \(\sigma_{s}\) (MPa) \\ \hline
7850 & 207,000 & 0.3 & 1016 & 18.2 & 499 & 555 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material parameters of X80 pipeline. Figure 3: Model dimension verification: (**a**) soil thickness; and (**b**) width of non-landslide area. direction can influence the stress transmission within the pipeline. The wall thickness was meshed with 2-6 layers, and the axial stress distribution of the pipeline under various conditions is illustrated in Figure 4a. For the entire landslide-pipeline model, a 0.5 m mesh size was applied in the landslide area and a 0.75 m mesh size in the non-landslide area. Doubling the overall refinement serves as the refined model, with comparisons between the two shown in Figure 4b. The analysis reveals that while the stress distribution is consistent across layer counts, a distinct variance emerges between two and four layers, the stress patterns for three and four layers align closely, and the curves for five and six layers virtually match the four-layer curve. Hence, a four-layer mesh in the thickness direction is optimal. Additionally, the high overlap between the current and refined mesh stresses confirms the current mesh's robustness. For the mesh sensitivity analysis, a corrosion defect of 20 cm in length, 0.25\(t\) in depth, and 6\({}^{\circ}\) in width is considered. The defect is positioned at the midpoint in the axial direction of the pipeline and on the inner wall facing the landslide. The mesh layers in the pipeline thickness direction are set as two layers for the defect area and two layers for the non-defect area, totaling four layers in the thickness direction. The corrosion zone is meshed at intervals of 0.01 m in length and 0.5\({}^{\circ}\) in width, and based on this, the mesh refinement of the corrosion with the rest of the model dimensions follow the previous specifications. The axial equivalent stress at the pipeline defect is illustrated in Figure 5. The stress distribution curves largely overlap, with a mere 0.4 MPa difference at the central defect, indicating that the mesh precision for the defect meets the requirements. Hence, the corrosion length and width can be segmented at 0.01 m and 0.5\({}^{\circ}\), respectively.