# Safety Analysis and Condition Assessment of Corroded Energy Pipelines under Landslide Disasters
## 4 Results and Discussion
### Effect of Corrosion Dimension
The maximum equivalent stress in the slide-facing region is located at the corrosion site at 90\({}^{\circ}\), while the highest equivalent stress in the slide-backing area is positioned at 300\({}^{\circ}\). Between 15\({}^{\circ}\) and 90\({}^{\circ}\), the pipeline stress increases. A sudden increase in stress is evident at the corrosion point, followed by a decline with the circumferential angle. It then reaches another peak at 120\({}^{\circ}\), highlighting the significance of the landslide movement direction for the circumferential pipeline contact. With increasing displacement, the difference in the equivalent stress between the pipeline face directly exposed to the slide and the stress concentration at the defect is continuously decreasing. It is anticipated  
Figure 7: Stress distribution in the pipeline with a corrosion depth of 0.25\(\!\)f: (**a**) maximum equivalent stress distribution with varying landslide displacements; (**b**) axial stress distribution in the pipeline; and (**c**) circumferential stress distribution in the pipeline. that as the displacement reaches a certain level, the stress at the 120\({}^{\circ}\) front-facing slide surface will surpass that of the defect, making it the first area to yield. To comprehensively assess the influence of the corrosion length and depth on the axial and circumferential pipeline stress, the stress distribution is studied for a displacement load of 0.5 m, as shown in Figure 8. As the corrosion length and depth increase, the equivalent stresses for different lengths are 495 MPa, 507 MPa, 516 MPa, 522 MPa, and 526 MPa, and the maximum equivalent stresses or different depths are 453 MPa, 474 MPa, 503 MPa, 516 MPa, 545 MPa, 555 MPa, and 556 MPa. Notably, the increment is relatively modest, and the stress levels at other axial positions remain roughly consistent. As shown in Figure 8c, it is evident that at a depth of 0.25\(t\), circumferential stress curves for various lengths essentially overlap, except at the corrosion site. It is clear that stress concentration in the pipeline only occurs at the corrosion site when compared with the circumferential distribution for non-corroded pipelines. In the corresponding area of the non-corroded pipeline, the stress is much lower, while stress levels in other regions are nearly identical. This suggests that, given a certain landslide displacement, the variation in the corrosion size has a negligible impact on the stress distribution of the pipeline outside the corroded region. Define the limit displacement under landslide conditions as the displacement when reaching the allowable stress of the pipeline, and the extracted limit displacements for various corrosion dimensions are shown in Figure 9. At depths ranging from 0.15\(t\) to 0.40\(t\), it is evident that the limit landslide displacement decreases with the increase in the corrosion length. The maximum reduction rates in the limit displacement are 2.57%, 7.80%, 14.71%, 35.08%, 50.14%, and 84.95%, respectively, indicating that the rate of reduction grows with the increase in the corrosion depth. Interestingly, at a depth of 0.1\(t\), the landslide limit displacement for a corrosion length of 15 cm is 0.64 m, which is greater than the 0.62 m displacement for a 10 cm corrosion length. This contrasts with the previously observed pattern. In reality, at a depth of 0.1\(t\) with a corrosion length of 10 cm, the pipeline experiences stress concentration. The enlarged corroded area reduces the stress concentration when  
Figure 8: Stress distribution in the pipeline with a displacement of 0.5 m: (**a**) axial stress distribution with varying lengths; (**b**) axial stress distribution with varying depths; and (**c**) circumferential stress distribution. this length increases to 15 cm, resulting in a decrease in the maximum equivalent stress of the pipeline, which leads to an increase in the limit displacement. The corrosion depth significantly affects the limited landslide displacement.