# A Theory of Slope Shear Scouring and the Failure Mechanism of PFC3D on a Gangue Slope
## 3 Results
### Displacement Analysis  
The change in the displacement with the time of each monitoring point of the model is shown in Figure 15. The displacement curve can further elucidate the scouring and damage laws of the slope's bottom, middle, top, and tributary areas. From the change in the surface displacement (Figure 15a,c), the trends for the displacement curves of each point in the horizontal Y-direction and the vertical Z-direction are essentially consistent, indicating that the surface soil particles in the scouring area are subject to more hydraulic scouring when they follow the flow and the constraints between soil particles are lower, and when the movement direction is consistent with the slope direction. From the perspective of deep particles, the particles at the bottom of the slope and at the top of the slope show similar curve trends in the process of comparing the horizontal displacement curve with the vertical displacement curve; however, the particle displacement curve trends in the middle of the slope and in the tributary region are quite different. This shows that when the rainfall infiltration reaches the deep soil particles, the internal disturbance of the particles in the middle of the slope is greatest, which causes the water flow to change in the middle of the slope, thus forming a gully tributary. Figure 14: Comparison diagram of the final damage boundary. Figure 15: _Cont._According to the analysis of the failure mode, we deduced that the coal gangue slope model is divided into four stages (0-20 min, 20-40 min, 40-60 min, and 60-80 min) in the process of scouring failure. Within the period 0-20 min, the surface particle displacement (MP1, MP2) at the bottom and middle of the slope increases linearly, reaches the maximum value, and tends to be flat at 10 min. The maximum horizontal displacement of the surface particle MP1 at the bottom of the slope during this period is 12 m, and the maximum vertical displacement is 2 m; the horizontal peak displacement of surface particle MP2 in the middle of the slope is 40 m, and the vertical peak displacement is 13 m. During this period, there is no change in displacement at the top of the slope and at the tributaries, which indicates that the first stage of scouring damage impacts the slope bottom first, but the damage trend is obviously more violent in the middle of the slope. When reaching the second stage (20-40 min), there is still no displacement change at the slope bottom, the slope top, or the tributaries. The particle displacement of the surface soil in the middle of the slope increases slowly, but the displacement of its deep particles (Figure 14d) fluctuates, indicating that the erosion damage is concentrated in the middle of the slope at this time. The surface particles are washed with the water flow, and the deep particles are damaged by turbulence. When the scouring reaches the third stage (40-60 min), the surface particle displacement curve between the slope top and the tributary area begins to increase sharply. The maximum horizontal displacement of the slope top can reach 102 m, accounting for 41.76% of the overall horizontal displacement, and the maximum vertical displacement of the slope top can reach 42 m, accounting for 45.85% (see Figure 16). It can be seen from the displacement curve that the displacement at the top of the slope changes prior to the displacement of the tributaries. This shows that after the scouring and accumulation in the middle of the slope, the tributary gap is formed, which is also the reason for the formation of multiple gullies caused by scouring. However, at this time, the stress is not concentrated in the direction of the tributary, but at the top of the slope, so the direction of the gully is not completely changed at this time.