# A Theory of Slope Shear Scouring and the Failure Mechanism of PFC3D on a Gangue Slope
## 5 Conclusions  
1. Based on the previously derived rainfall scouring shear failure theory, a scouring depth optimization theory was further developed by taking into account the two types of scouring intensity factors (c and \(\varphi\)) and combining the characteristics of the PFC time effect calculation. Verification shows that the curve trends of the PFC calculation, the optimization theory calculation, and the actual slope depth data are consistent. Figure 20: Peak stress and strain. (**a**) peak stress, (**b**) peak strain. The combination of these methods provides a valuable reference for early warnings of coal gangue slope engineering disasters and for the hydrodynamic theory. 2. The rain erosion failure of the coal gangue slope can be divided into four stages: (1) overall splash erosion and local schist erosion at the bottom of the slope; (2) erosion diversion and sheeting in the middle of the slope; (3) the tributary-slope crest extension and etching stage; and (4) the integral gully erosion and landslide stage. The scouring failure process has the characteristics of a discontinuous failure. Moreover, the failure sequence is as follows: slope bottom-slope middle-lateral tributary-slope top. The tributary gully in area A on the slope is determined by the water flow trend in the early catchment stage. The process of coal gangue scouring and destruction forms a three-stage ladder effect, which is concentrated at the top of the slope, the middle of the slope, and the bottom of the slope (0-25 m, 25-65 m, and 65-110 m). This step effect fully verifies the intermittent characteristics of the erosion failure of the coal gangue slope. 3. During the whole process, the maximum displacement is concentrated at the top of the slope, according to the following proportions: top of the slope > tributaries > middle of the slope > bottom of the slope. The peak displacement of the slope top in the horizontal Y-direction accounts for 41.76%, and that in the Z-direction accounts for 45.84%. In efforts to prevent and control rainfall-induced landslides, priority should be given to the protection of the sliding soil mass at the bottom of the slope, and the focus should be on reducing the soil mass in the middle of the slope to prevent the maximum energy fluctuation caused by scouring, so as to prevent extensive displacement damage at the top of the slope. The latter part of the second stage of scouring is the incubation period for the tributary gully. During the whole scouring process, the strain fluctuation caused by scouring in the middle of the slope is the largest; this is the hub area for the development of scouring damage. The peak stress is up to 8.9 MPa, the peak strain is up to 14.3, and the damage caused by scouring is the strongest. The larger peak stress and strain values of coal gangue slope scouring failure are distributed in the horizontal Y-direction of the middle of the slope, the horizontal X-direction for the tributary, and the vertical Z-direction for the slope bottom. The generation of the branch notch is mainly determined by the X-direction stress, and 8.6 MPa is the critical stress. 4. There are two modes of erosion accumulation integration, namely, the arc erosion accumulation mode and the fan erosion accumulation mode. Arc-shaped erosion and accumulation are mainly controlled by deep particles, and fan-shaped erosion and accumulation are mainly affected by shallow particles. In the actual process of rainfall erosion, most of the slope erosion and failure modes show the effect of multi-ditch collection. The main stream gully mainly controls arc-shaped or linear erosion and accumulation. Due to their complex roles in the slope, the interaction between laminar flow and turbulent flow is intense, providing conditions for the development of tributaries and further forming the fan erosion and accumulation model. This provides favorable conditions for a more effective study of the internal mechanisms of coal gangue scouring and accumulation. Conceptualization, Y.W. ; Software, H.L. ; Formal analysis, H.W. and H.Z.