# A Theory of Slope Shear Scouring and the Failure Mechanism of PFC3D on a Gangue Slope
## 3 Results
### Failure Mode
At the same time, due to the infiltration of the rainfall, the strength of the soil on the slope decreases, and the small erosion holes formed in the slope gradually deepen and widen towards the slope's top, forming headward erosion. The accumulation at the bottom of the slope also gradually diffuses; the shape of the gully is not limited to the strip gully, and the width of the gully gradually expands outward. At this time, the direction and structure of the mainstream and tributaries are formed, and the runoff channel gradually becomes visible. (3) Branch crest extension sheet erosion stage. With the continuous development of rill erosion, the main gully continues to widen under the action of hydraulic force. Up to 50 min, the displacement of the accumulated particles can reach 98.32 m. At this time, the main stream's erosion capacity is less than that of the tributaries. The upper part of the main stream gully is suspended from erosion, and the lower part is further accumulated downwards. The gully section is exposed (a fault phenomenon), forming a large erosion pit with a depth of about 8 m. At the same time, the denudation of the tributaries is ongoing, and the trend of the slope gully changes from two paths to one, forming a large closed Z-type gully. The flow path is diverted, so the scouring capacity is mainly concentrated in the direction of the branch in area A. Based on the tension between the hydraulic and particle forces, the tributary valleys extend and increase continuously. When the time point of 60 min is reached, the peak displacement of the accumulated particles reaches 122.23 m, the side valleys are penetrated, and the transverse particle tension is reduced. At this time, due to continuous rainfall, the force chain between particles near the section of the erosion pit in area B reaches the limit state. The direction of denudation changes from the branch direction in area A to the main direction in area B and continues to produce schistity upwards, forming headward erosion at the top of the slope. (4) Overall Gully Erosion and the Collapse Stage  
According to the phenomenon whereby two scouring diversions occurred in the previous stage, the effect of hydraulic pressure on particles reaches its peak at 70 min, and the scouring intensity is the most intense at this point. When the top erosion pit section is gradually destroyed and collapses, the energy at the top of the slope is gradually released, the particles begin to accelerate the erosion, and a large number of particles are washed to the bottom of the slope and accumulate outward. At this time, the maximum displacement of the accumulated particles is 122.24 m, which is similar to the displacement observed in the previous stage, indicating that the whole model is in a state of gradual convergence at this time. Finally, the model tends to converge at 80 min, and, at this time, the gully of the lateral tributary in Zone A also reaches the maximum depth. The particles on the slope top of Zone B are completely connected through the pipe, forming a complete and continuous multidirectional gully with a peak displacement of 149.72 m.  
In contrast to the failure mode, the process of the rain-erosion-induced failure of the coal gangue slope has the characteristics of discontinuous failure. Moreover, the failure sequence is bottom of the slope-middle of the slope-lateral tributary-top of the slope. The tributary gully in area A on the slope is determined by the water flow trend in the early catchment stage, and the whole gully trend is diverted in the middle and late stages of rainfall. However, the main stream's hydraulic action soon causes the secondary diversion in area B and completes the penetration damage at the top. This phenomenon provides a favorable reference for proving the shear erosion theory and a further detailed analysis in the later stage.