## 3 Results and Discussion
### The Impact of the Dip Angle of Muddy Interlayers  
First of all, it should be noted that, when the model with slope angle \(\beta\) = 60\({}^{\circ}\) is calculated according to the material parameters in Table 1, when \(\theta\) is 30\({}^{\circ}\) or 40\({}^{\circ}\), the numerical calculation cannot be carried out and the most unsafe inclination angle cannot be determined because of the poor self-stabilization of the slope. Therefore, the shear strength values of both the cataclastic rock mass and the muddy interlayers were increased by 30% (Table 2), and then numerical calculations were performed. The grid deformation of the bedding cataclastic rock slope containing multi-muddy interlayers, with different dips of cis-fragmented rocky slopes at slope angle \(\beta\) = 30\({}^{\circ}\), showed that the slope deformation damage was mainly rock bending deformation, and there was no slippage. Figure 5 gives the grid deformation diagram of the slope when the dip angle \(\theta\) was \(0^{\circ},30^{\circ},60^{\circ}\), and 90\({}^{\circ}\). Figure 4: Relationship between safety factor, maximum horizontal displacement, and the number of exposed muddy interlayers on the slope. For the slope with slope angle \(\beta=45^{\circ}\), when the dip angle \(\theta\) of the muddy interlayers was \(0^{\circ}\) (Figure 6a), the horizontal displacement of the slope was mainly negative, and the horizontal displacement had abrupt changes along the interlayer, indicating the relative slip of the rock layer. For each cataclastic rock mass, 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. When the dip angle \(\theta\) of the muddied interlayer increased to \(10^{\circ}\) (Figure 6b), the overall characteristics of the horizontal displacement diagram of the slope were not significantly different from those at \(0^{\circ}\), excepted that the maximum value of the absolute value of horizontal displacement in the X-negative direction increased by 167%, indicating that the tendency of the slope to slide toward the prograde was enhanced. \(\theta\) increased from \(10^{\circ}\) to \(45^{\circ}\), the number of layers of muddy interlayers exposed on the slope surface gradually decreased, and the horizontal displacement diagram of the slope showed the following three characteristics: (1) The maximum value of the absolute value of the horizontal displacement increased first and then decreased, with a maximum value at \(25^{\circ}\); (2) The relative slip phenomenon between the layers was weak to strong and then decreased, with the most significant relative slip at \(25^{\circ}\), the slip at \(30^{\circ}\) occurring mainly in the muddy interlayers through the toe of the slope (Figure 6c), and basically no relative slip in the rock layers at \(45^{\circ}\) (Figure 6d); (3) The horizontal displacement of the underlying rock layer at the toe of the slope gradually increased, and the uplift of the foot of the slope gradually became obvious. \(\theta\) increased from \(45^{\circ}\) to \(80^{\circ}\), the dip angle of the rock layer became steeper and steeper, the self-stability of the fractured rock layer was poor, and the displacement in the X-positive direction started to appear on the shoulder of the slope, and it showed a change pattern of increasing and then decreasing. And the displacement of the toe of the slope to the X negative direction and the maximum value of its absolute value showed a trend of decreasing and then increasing (Figure 6d-f). \(\theta\) increased from \(80^{\circ}\) to \(90^{\circ}\), the displacement of side slope X in the positive direction decreased, the absolute value of displacement in the negative direction increased, the displacement contour was circular, and the sliding trend of the side slope toward the critical surface was more significant (Figure 6g).