# A Theory of Slope Shear Scouring and the Failure Mechanism of PFC3D on a Gangue Slope
## 3 Results
### Stress-Strain Analysis  
Finally, in order to elucidate the internal failure mechanism of the model, the four representative measuring balls in the model were selected, their stress-strain data were extracted, and the real-time stress-strain curves of the PFC scouring model were obtained, as shown in Figure 19. At the beginning of the scouring process, due to the initial contact between rainwater and the coal gangue particles, the overall stress on the slope surface increased, with a maximum of 4.9 MPa located at the bottom of the slope. In the later part of the first stage of scouring, the stress change in each area is not obvious, but the strain in the slope changes sharply, fluctuating between 5 and 8. When reaching the second stage (20-40 min), there are large stress fluctuation values at the bottom and middle of the slope, and the stress increases sharply at 20 min. At this time, a large number of particles in the middle of the slope accumulate towards the bottom of the slope. The large accumulation causes the stress at the bottom of the slope to increase sharply, with a fluctuation value between 2 and 6.8 MPa. It is worth noting that the stress generated by accumulation is  
Figure 18: Gully distribution and accumulation mode. (**a**). Two gully directions; (**b**). Erosion trend-arc trend; (**c**). Erosion trend-alluvialfan trend. greater than the stress caused by erosion and denudation. At this time, the stress and strain in the tributary area also begin to increase slightly, with the stress reaching 1.7 MPa and the strain reaching 5.1, indicating that the later part of the second stage is the incubation period of the tributary gully. After that, in the third stage (40-60 min), the bottom of the slope continues to accumulate, and the stress continues to fluctuate. However, due to the dense particles at the bottom of the slope, the particles are denuded less, and there is no obvious strain. At this time, the stress of the tributary increases sharply to 3.8 MPa, the tributary notch begins to form, and the strain reaches six. Then, the stress concentration is transferred from the tributary to the top of the slope, the stress of the tributary decreases to 0.4 MPa, and the stress at the top of the slope increases to 4.4 MPa. The trend of the strain curve is similar: the maximum strain at the top of the slope reaches 7.5, and then decreases sharply. At the fourth stage (60-80 min), the stress in the tributary area increases again, reaching 3.9 MPa, and the final scouring damage is completed. An alternation can be seen in the change in stress and strain at the top of the slope and in the tributary after the second stage of scouring. During the whole scouring process, the stress generated by the accumulation at the bottom of the slope is always the largest, but the damage it causes is the smallest. The strain fluctuation caused by the scouring in the middle of the slope is the largest, and the damage it causes is the strongest. The peak values of the measurement ball data of the whole model were extracted, and the stress and strain were divided into the three directions of the XYZ data; the peak stress and strain curve is shown in Figure 20. It can be seen from the figure that the higher peak stress and strain values of the coal gangue slope scouring failure are distributed in the horizontal Y-direction of the middle of the slope, the horizontal X-direction of the tributary, and the vertical Z-direction of the slope bottom. From the peak data in the X-direction, it can be seen that the transverse peak stress increases from the top of the slope to the bottom of the slope, and the maximum value can reach 8.6 MPa in the tributary area. At this time, the peak strain also reaches the maximum value of 10.3 in the tributary region, and then decreases at the bottom of the slope (because the bottom of the slope is dense). This shows that the generation of the branch notch is mainly determined by the X-direction stress, and 8.6 MPa is the critical stress.