## 6 Discussion
### Failure Analysis of the Pipeline  
Figure 16 depicts the failure mechanisms observed in the pipeline at three critical sections under mining-induced subsidence. At the edges of the subsidence area (X = 562 mm and X = 1921 mm), the pipeline exhibited irregular wave-shaped buckling failure. These failure points were located near the maximum curvature positions of surface subsidence. The large curvature significantly increased the bending moment experienced by the pipeline, resulting in considerable tensile stress at the top of the pipeline, which entered the plastic failure stage first. In contrast, the bottom of the pipeline remained relatively stable due to the presence of comparatively smaller compressive stress, leading to a relatively smooth failure surface observed in the bottom region. Additionally, an asymmetry was observed in the failure locations along the pipeline. Additionally, an asymmetry was observed in the failure locations along the pipeline. The distance between the left failure surface (X = 562 mm) and the model boundary was notably larger than that of the right failure surface (X = 1921 mm). This asymmetry can be attributed to the inclination angle of the left rock fracture line. The steeper angle with the horizontal plane on the left side, leading to the point of maximum curvature, is located closer to the model boundary. This difference emphasizes the role of overburden rock structure and fracture geometry in determining failure locations. Figure 15: Subsidence diagram. Figure 17 shows the strain response of the middle of the pipeline under different mining ratios, and presents the axial and circumferential strains measured at both the top and bottom of the pipeline using strain gauges and optical fiber sensors. As shown in Figure 17, the pipeline exhibits circumferential tensile strain, with the strain at the top of the pipeline being significantly larger, while the bottom circumferential strain remains negligible. Furthermore, the pipeline stress results from the combined effects of axial strain and circumferential strain, and its evolution corresponds closely to the disturbance stages of the overlying rock induced by mining activities. Mining-induced subsidence triggered the soil-arching effect, further contributing to stress concentration in the pipeline. In the middle section of the subsidence area (X = 1256 mm), the pipeline exhibited shear failure characterized by inclined cracks. The top of the pipeline was subjected to both axial and circumferential tensile stresses, while the bottom primarily experienced axial compressive stress. This formed an opposing stress pair between the top and bottom of the pipeline, which was a critical factor in the occurrence of shear failure. Based on the stress distribution within the mining area and the observed failure locations, it can be concluded that the maximum curvature points at the edges and the center of the subsidence area correspond to the locations of maximum additional stress, which are the most likely locations for pipeline yield or failure. Figure 16: Three failure cross-section of the pipeline. Figure 17: Strain of the pipeline at the center of the subsidence area. This study provides experimental insights into the failure mechanisms and deformation behaviors of pipelines under mining-induced subsidence. The findings are consistent with and expand upon previous research. The wave-shaped buckling and shear failures observed in this study align with findings by [PERSON] et al. [17], who identified similar failure patterns through their segmented elastic beam model under mining conditions. However, this study goes further by correlating failure locations with theoretical predictions of maximum surface curvature, highlighting the critical role of bending moments induced by surface deformations. Additionally, the stress evolution patterns in this study are consistent with [PERSON] et al. 's [18] numerical investigations into pipeline responses to reverse faulting, which also identified the amplification of tensile stress at critical points.