## 4 Results  
### Influence of joints in Rock Strata on the Stability of Interbedded Anti-Dip Rock Slopes  
#### 4.1.1 Failure Characteristic of the Slopes with Joints  
The evolving characteristics of the crack distribution, displacement field, and force field during a landslide were analyzed, and the failure mechanisms of the interbedded anti-dip rock slope influenced by these randomly distributed rock joints were studied. We recorded the state of the slope at six moments (i.e., time steps = 100, 200, 1000, 5000, 10,000, and 30,000) to facilitate analysis. As depicted in Figure 3a, when the time step = 100, the cracks initially occurred around the joints in the brown shale strata. The excavation and unloading process resulted in noticeable displacements between adjacent particles near the joints, as the strength of a pre-existing joint is weaker compared to intact rock. Additionally, the shear strength of brown shale is smaller than that of mudstone, resulting in an earlier appearance of cracks in the brown shale layers. As the time step increased, the number of cracks gradually rose. When the time step was 200, more cracks formed around the slope surface (Figure 3b). When the time step reached 1000 (Figure 3c), the small cracks propagated and coalesced. New cracks were formed between the two different rock strata due to their weak contact strength. According to the distribution of the cracks at the 5000 time step (Figure 3d), the number of cracks around the joints continued to increase, mainly distributed along the directions of the joints. As the time step increased to 10,000 (Figure 3e), more cracks occurred inside the rock slope, and their location was far away from the rock slope surface. Additionally, these new cracks were almost perpendicular to the rock strata orientation. At the time step of 30,000 (Figure 3f), the crack density significantly increased, with a large number of small cracks gathering and connecting along the bedding direction and the slope sliding surface. The rock mass near the slope surface fragmented into small blocks and then slid along the sliding surface. An analysis of slope stability relies on the understanding of its deformation characteristics, which serve as crucial indicators of rock slope destruction and instability. The displacement field monitored during the calculation process provided more valuable information about the deformation characteristics of the whole slope. According to Figure 4a, the largest displacement occurred along the slope surface at the time step of 100, and the area in the vicinity of the joints also showed a larger displacement than the other areas. With the increasing time step, the overall displacement of the slope increased (Figure 4b). In contrast to the displacement at a time step of 100, the displacement of the area around the joints significantly decreased, indicating that the contact of the joint surfaces became tighter under gravity. For the 1000 time step (Figure 4c), the displacement increased as the distance to the slope surface increased. Furthermore, following the direction of the red arrow, the color gradient from light blue to dark blue became clear, and the color layering and transition were very obvious. Cracks were more likely to develop due to the change of the deformation. When the time step reached 5000 (Figure 4d), the rock mass of the slope top became fragmented, leading to a sharp decrease in the carrying capacity of the rock slope. Simultaneously, significant deformation occurred at the top of the slope, accompanied by the dropping of small fragments. Subsequently, the deformation extended further from the slope surface toward the interior of the slope, and the area of the dark blue decreased as the test proceeded (Figure 4e,f). From Figure 4f, the crack coalescence resulted in the downward sliding of rock blocks, ultimately leading to a larger deformation and overall damage to the rock slope. Figure 3: Crack progression for a slope with closed joints.