## 4 Application: A Real Case
### Computational Results  
When using the DEM to simulate the Songmugou landslide, since the distance between the 9# and 10# coal seams is relatively short and the thickness of the coal seams is relatively thin, we will excavate the 9# coal seam, 10# coal seam and the interlayer at one time. The total thickness is 20m. Then, the energy under gravity and the correlation coefficient are calculated corresponding to each iteration step, so as to draw a curve about the relationship between the correlation coefficient and the number of iterations; finally, the number of calculation steps is determined for termination by analyzing the convergence of the curve. After the simulated excavation of the 9# and 10# coal seams is completed, the Z-displacement diagram of the Songmugou landslide is shown in Figure 11.  
Figure 11 shows the overall \(Z\)-displacement diagram after the excavation is completed, and Figure 11 shows the \(Z\)-direction displacement of the cross-section after the excavation is completed. From Figure 11, we find that due to the excavation of the coal seams, the rock mass on the upper part of the coal seam moves downward and slides down along the joint. From Figure 11, we could see that the split level is approximately 15 m. In addition, the landslide also has a large displacement along the Y direction. As shown in Figure 12, we can see that the sliding displacement is large on the left boundary of the model and the top of the landslide. We compared the numerical simulation results with the on-site survey results and found that they are basically consistent with the actual landslide result, and they all showed basically the same sliding surface, as shown in Figure 13.  
In Figure 13, the Songmugou landslide is in the shape of a dustpan and could be roughly divided into three deformation zones. Zone I: Deformation stability zone. This part of the area does not slide with the main sliding body, but is caused by deformation after the main sliding body slides, and is adjacent to the east pine wood ditch. It is mainly silt and crushed stone that collapses and slides in the direction of the empty surface. Zone II: Intensive deformation zone. This part of the zone belongs to the most obvious deformation zone affected by landslide action. The upper part is a platform with a large slope. The trees on it were originally the top of the slope and slide together with the landslide. However, due to the sliding force, these trees have been bent and deformed, and due to the difference in the sliding speed of the upper sliding body and the lower sliding body, the lower sliding body is squeezed to produce a bulge and multiple fan-shaped cracks. Zone III: Unstable deformation development zone. Because the landslide slides slowly, the landslide does not quickly fall to the bottom of the valley, but slowly accumulates along the slope. If coal mining activities proceed further, torrential rain and other factors induce  
Figure 12: The Y-direction displacement after excavating 9# and 10# coal seams. (**a**) Overview, (**b**) cross-section. Figure 13: Actual landslide result. this part. The area may undergo large-scale deformation, and the deposits on the slope will slide into the valley. If the rainfall reaches more than 300 mm/h, it may induce a debris flow. Due to the mining of the coal seams, the rock mass above the coal seam produces different degrees of slipping. The main slipping is along the Y direction and the Z direction. Compared with the displacement in the Y direction, the displacement in the Z direction is larger and the sliding range is wider. The method proposed in this paper will be used to perform a statistical analysis of the landslide, and the statistical results are shown in Figure 14. Figure 14 shows that when the number of iterative steps reaches the 7000 th step, the curves in Figure 14a,b tend to converge. The CC value of the 8000 th step is approximately equal to the CC value of the 7000 th step. Therefore, when the calculation reaches the 8000 th step, the iterative calculation will be terminated.