# Progressive Formation of Retrogressive Landslide and the Lateral Length of Instability
## 2 Numerical Simulation of Landslide Failure Process
### Analysis of Landslide Failure Mode  
The failure process is observed after the constraint wall is removed, gravity is added, and the model is run for 100,000 steps. At 37,500 time-steps, the slope begins to break, as shown in Figure 8. From the grouping of particles in the model, it can be seen that the planting soil part on the upper part of the slope and the strongly weathered calcium argillaceous sandstone began to slide along the sliding surface, and two obvious tension cracks appeared. One appeared in front of the slope, about 4.54 m away from the foot of the slope, which was the first part to crack. The other appeared in the middle of the slope, and gradually expanded from the foot of the slope. The overall displacement and velocity of the slope are small, which is due to the artificial removal of the foot of the slope to form a free surface. Under the action of gravity, the slope body undergoes shear creep in the direction of the free surface. PFC2D continues to run, resulting in Figure 9. At this point, damage occurs in the middle of the slope. With the increase of displacement, the middle part of the slope is pulled and cracked into several blocks, and five pull-crack cracks penetrate the front and middle part of the slope. The displacement of the slope gradually increases from top to bottom, and the maximum displacement of particles in the lower part of the slope reaches 12.57 m. At this time, the rock mass on the upper part of the slope has not slipped yet. It can be seen that the speed of particles in different parts is different, which is a ladder-shaped distribution. The front particles of the slope body have a fast speed, constantly dragging the rear particles, showing obvious displacement segmentation. This is because the lower part of the slope slides downward due to the failure of particle adhesion, causing the upper part of the particle to lose support and generate downward acceleration and kinetic energy, pushing the particles in the front of the slope to continue to slide forward. It can be seen that when the particle adhesion force is large, the rock mass will not fall completely apart when a landslide occurs, but rather slides down as a coherent block. Figure 7: Slope model. In later time steps the upper part of the slope begins to destabilize, as shown in Figure 10. At time-step 388 \(\times\) 10\({}^{3}\) the displacement is further increased, and the central rock mass was completely pulled off. At this time, a new crack appeared in the upper rock mass, but it has not yet been pulled into multiple blocks. At the top of the rock mass a longer crack appears along the sliding surface and increases in thickness. At this time, the maximum displacement of rock particles is 19.926 m, and the sliding zone has basically cut through with the overlying rock mass sliding along the underlying soft rock layer. Under the self-weight stress, it fills the empty surface and is continuously piled up at the foot of the slope. Figure 8: Displacement diagram in the early stage of slope collapse. Figure 9: Displacement diagram in the middle of the collapse. The numerical simulation of the slope was completed, and Figure 11 was obtained. The slope has completely collapsed. The displacement of the upper particles is the largest, and the displacement of the lower particles is relatively small. This is due to the sliding of the rock mass at the front edge of the slope; shear failure occurs in the middle of the slope, the rock mass at the rear edge loses its support and slides downward, and the stress on the upper particles of the slope is greater than that of the lower particles, resulting in a significant change in the displacement of the upper particles of the slope. At this time, the rock mass at the front edge of the slide slides forward through the retaining wall to the model highway. At this time, the maximum displacement of the rock particles reached 43.822 m.  
This research demonstrates that the particle flow method has good applicability to the simulation of the failure movement process of landslides.