## 3 Results and Discussion
### The Impact of the Dip Angle of Muddy Interlayers
In a comprehensive analysis of horizontal displacement (Figure 6) and grid deformation (Figure 7) of \(\beta=45^{\circ}\) slope, the slope deformation failure exhibited the following laws: (1) When \(\theta\) was \(0^{\circ}\) (horizontally bedding rock slope), the slope was compression-shear failure, i.e., under the action of its own gravity, the vertical pressure and horizontal pressure increased with depth, the compression-shear phenomenon became more obvious with increasing depth, and the shear-out displacement of the toe of the slope was the largest (Figure 7a); (2) \(\theta\) in the range of (\(0^{\circ}\), \(10^{\circ}\)), the slope was damaged by \"traction- sliding\", and the relative slip increased gradually from the shoulder to the toe of the slope, and the potential shear outlet location was the muddied interlayer through the toe of the slope (Figure 7b); (3) \(\theta\) in the (10\({}^{\circ}\), 45\({}^{\circ}\)) zone, the slope was damaged by \"traction-sliding-bending-shear\", with uplift-bending deformation of the underlying rock layer at the toe of the slope and simultaneous slip and uplift-bending deformation of the exposed rock layer on the slope surface, especially the rock layer near the toe of the slope (Figure 7c); (4) \(\theta\) in the range of [45\({}^{\circ}\), 80\({}^{\circ}\)), the slope rock layer mainly deformed in flexure, the shoulder of the slope dipped and deformed towards the back of the slope, while the toe of the slope rose towards the surface (Figure 7d). Similar to the principle of a cantilever beam, the length of the cataclastic rock layer near the toe of the slope was short and the dumping deformation toward the back of the slope was small, while the length of the cataclastic rock layer on the shoulder of the slope was long and the dumping deformation was large, so the rock layer on the slope was separated along the muddy interlayers due to uncoordinated deformation (Figure 7e), and a tension zone was formed in the interlayer; and (5) \(\theta\) was in the interval of [80\({}^{\circ}\), 90\({}^{\circ}\)], the slope was damaged by \"bending-buckling-collapse\", i.e., by the action of the slope thrust. When \(\theta\) was 80\({}^{\circ}\), the fractured rock layer at the toe of the slope was nearly upright, and the collapse may have occurred (Figure 7f), while when \(\theta\) was 90\({}^{\circ}\), the rock layer in the middle of the slope was deformed by bending, while the rock layer at the lower part (toe of the slope) was deformed by bending-buckling and collapsed to the prograde, and the tendency of the slope to collapse disaster was more obvious (Figure 7g). In a similar computational model by [PERSON] et al. [12], \(\theta\) increased from 0\({}^{\circ}\) to 90\({}^{\circ}\) and the slope damaged modes were compression-shear failure, sliding-tensioning failure, sliding-splitting failure, bending-buckling failure, and collapse failure, in that order. In contrast to their study, traction-sliding-bending-shear failure and flexural deformation also occurred in bedding cataclastic rock slope containing multi-muddy interlayers. The relationship between slope failure modes and dip angle \(\theta\) of the muddy interlayers in the rocky slopes is shown in Figure 8.  
For the slope with slope angle \(\beta=60^{\circ}\), when the dip angle \(\theta\) of the muddy interlayers was \(0^{\circ}\) (Figure 9a), the horizontal displacement of the slope was dominated by negative values, and the horizontal displacement had abrupt changes along the interlayer, indicating the relative slip of the rock layer. For each cataclastic rock layer, the horizontal displacement at the bottom of the layer was significantly larger than at the top of the layer, and the relative slip phenomenon became weaker and weaker from the toe to the shoulder of the slope and from the face to the inside of the slope.