# A Theory of Slope Shear Scouring and the Failure Mechanism of PFC3D on a Gangue Slope
## 3 Results
### Scour Tracking and Accumulation  
During the numerical calculations, the positions of eight typical monitoring particles were selected, as shown in Figure 17, and the tracked particles were analyzed in combination with the results of the failure mode. At the bottom of the slope, MP1 is preferentially denuded by the thin-layer water flow, and MP6 is greatly affected by turbulence, but this effect is limited to the large particle resistance at the bottom of the slope; the movement tracks of the two are not obvious, and they are characterized by a slow creeping phenomenon, which is defined as a slow accumulation at the bottom of the slope. With the development of the main gully, particles MP2 and MP7 in the middle of the slope move along the main gully to the bottom of the slope under the scouring action, and then accumulate in the Y-direction along with the particles at the bottom of the slope. The mixing effect of the huge laminar flow and turbulent flow in the middle of the slope causes the development of tributaries. It can be seen that the MP5 and MP10 particles move from the side to the middle of the slope, then enter the mainstream gully and accumulate in the positive Y-direction at the bottom of the slope. We can clearly see that the particles at different depths in the tributary area have different stacking heights at the bottom of the slope, and the deep particles accumulate on the surface particles due to the later denudation sequence. Therefore, in the deposits at the bottom of the slope, the soil particles washed out from the deep layer cover the soil particles that originally accumulated on the surface layer. Finally, the two particles MP3 and MP4 are scoured at the top of the slope. They all move along the direction of the main gully from the top of the slope to the middle of the slope. However, due to the influence of height difference accumulation, when moving to the bottom of the slope, the two particles change their motion trajectory: the MP3 particles move diagonally  
Figure 16: Percentage of the peak displacement of the monitoring points. (**a**) Proportion of peak displacement in the Y-direction. (**b**) Proportion of peak displacement in the Z-direction. in the XY-direction, while the MP4 particles move in the positive Y-direction. Therefore, we know that MP6 and MP1 tracks belong to slow accumulation movement, MP7 and MP2 and MP3 and MP4 tracks belong to fast scouring movement, and MP5 and MP10 belong to DC steering movement. Depending on the scouring location, the resulting particle trajectories vary considerably. Figure 17: Movement trajectories of the monitoring particles. Interestingly, we combined several sets of motion trajectory curves and changed the perspective to obtain Figure 18. It can be seen from Figure 18a that there are two gullies in the whole scouring process, which are defined as the first and second gullies (i.e., tributary gullies and mainstream gullies) in order of completion. A further analysis shows that there are two modes of scouring pile integration, namely, the arc erosion accumulation mode (Figure 18b) and the fan erosion accumulation mode (Figure 18c). Arc erosion accumulation is mainly controlled by deep particles, namely, MP3, MP6, MP7, and MP10. Fan erosion accumulation is mainly affected by shallow particles, namely, MP1, MP2, MP4, and MP5. In the actual rainfall scouring process, the mainstream gullies rarely exist alone, and most of the slope erosion failure modes are characterized by the combination of multiple tributaries and the main stream, which is the effect of multiple gullies (only two gullies are considered in this model). The main stream gully mainly controls arc-shaped or linear erosion and accumulation. Due to their complex role in the slope, the interaction between laminar flow and turbulent flow is pronounced, which provides conditions for the development of tributaries and further forms the fan erosion and accumulation model.