## 4 Results
### Influence of the Dip Angle of Rock Layers on the Stability of an Anti-Dip Interbedded Rock Slope
#### 4.2.2 Analysis of Failure  
(1) Fragmentation Characteristics  
The fragmentation patterns of the anti-dip interbedded rock slope with different dip angles are shown in Figure 12. The rock slope model with a 20\({}^{\circ}\) dip angle of rock layers produced a greater number of fragments compared with the slope model with a 70\({}^{\circ}\) dip angle. In addition, the size of the fragments showed different characteristics in the two slopes with different dip angles. There were larger fragments in the interbedded anti-dip rock slope with a 70\({}^{\circ}\) dip angle. Large rock fragments or blocks typically toppled over rather than sliding along the sliding surface. The varying numbers and sizes of the fragments also indicate the differences in the rock slopes with two kinds of dip angles. (2) Deformation characteristics  
As shown in Figure 13a, the deformation was small for locations that were far away from the slope surface when the dip angle of the rock stratum was 20\({}^{\circ}\). The rock mass on the sliding fracture zone surface was highly fragmented and primarily underwent shear deformation and movement along the slope surface, suggesting that shear-sliding instability occurred in the slope. Figure 13b shows the displacement field of the slope model at a 70\({}^{\circ}\) dip angle of rock strata. It can be observed that the deformation range of the sliding fracture zone increased. Furthermore, the upper part of the fragments experienced greater displacement than the lower part, indicating a tendency for downward rotation and toppling of these fragmented rock masses. The formation of these larger rock fragments primarily arose from the prominent shear dislocation phenomena within the middle rock mass caused by the different lithology of the brown shale and the mudstone, ultimately leading to bedding separation in the rock slope. In addition to its own gravity, the rock mass at a relatively low position of the slope bore the pressure from the overlying rock layers. This pressure facilitated crack formation and crack connection, resulting in the formation of a continuous sliding surface. Additionally, the upper rock mass was susceptible to shearing and downward movement due to the loss of support from the lower rock mass. Eventually, this progression transformed into a combined failure characterized by tilting and sliding during the later stage of the landslide. Figure 12: Fragmentation patterns of slopes with (**a**) 20\({}^{\circ}\) and (**b**) 70\({}^{\circ}\) dip angles when the time step was 30,000. (3) Stress distribution characteristics  
It can be observed that shear cracks mainly appeared perpendicular to the bedding plane in the thicker mudstone layer, while tensile cracks were more common in the brown shale layer in the thinner failure stage (Figures 10, 11 and 14). Additionally, the overlying rock stratum of the slope was subjected to compression, while the lower layer was subjected to tension due to the influence of the overlying load and its own gravity during the sliding process. The range of tensile contacts in Figure 14b was more concentrated between the sliding surface and the toppling surface. Therefore, it was more likely to overturn and collapse on the rock mass in this area. Generally, a small dip angle of the rock strata leads to long rock strata, which means a long lever arm. The minimum force moment that causes the rock layers to rotate is assumed to be a constant. For longer rock strata, the force causes the fragmented rock from the rock layers to be small. Consequently, folding and toppling of the rock blocks is difficult for an interbedded anti-dip slope with a small dip angle of rock strata. In contrast, it is easy to realize the toppling for a slope with a large dip angle. In conclusion, the failure mode of the anti-dip interlayer rock slope model is related to the dip angle of the strata. When the dip angle of the rock strata is small, the failure mode is shear-sliding.