## 3 Results and Discussion
### The Influence of the Internal Friction Angle of the Muddy Interlayers  
Similarly to the influence of the cohesion \(c\) of the muddy interlayers, the stress concentration phenomenon of maximum principal stress and maximum shear stress in the slope was weakened by increasing the angle of internal friction angle \(\varphi\), the stress contour became smoother and smoother, and the maximum shear strain gradually decreased. The horizontal displacement diagram of the slope (Figure 18) exhibited the following characteristics: (1) Horizontal displacement was mainly in the X negative direction, the angle of internal friction angle \(\varphi\) increased, the maximum value of the absolute value of horizontal displacement gradually decreased, and the maximum position was always in the second layer of the mezzanine; and (2) When \(\varphi\) decreased, the sudden change in displacement between the exposed rock layers on the slope surface and between the underlying rock layers on the slope body was not strong, but the sudden change in displacement between the exposed rock layers on the slope surface and the underlying rock layers on the slope body was strong. When \(\varphi\) increased, the displacement mutation between the exposed rock layers on the slope surface and between the underlying rock layers on the slope body was enhanced, but the displacement mutation between the exposed rock layers on the slope surface and the underlying rock layers on the slope body was weakened. There was no uniform law on the influence of \(\varphi\) on the slope deformation damage law, as shown in Figure 18. When \(\varphi\) was \(8^{\circ}\), the slope showed traction-slip damage (Figure 19a), when \(\varphi\) increased to \(14^{\circ}\), the slope showed traction-sliding-bending-shear failure (Figure 19b), when \(\varphi\) increased to \(20^{\circ}\), the slope was again traction-slip damage (Figure 19c), and when \(\varphi\) increased to \(24^{\circ}\), the slope again showed traction-sliding-bending-shear failure (Figure 19d). Figure 20 shows that the internal friction angle \(\varphi\) of the muddy interlayers increased from \(8^{\circ}\) to \(30^{\circ}\), and the maximum horizontal displacement first decreased rapidly, then decreased slowly and tended to 0. The slope safety factor increased linearly from 0.89 to 1.83, and the slope stability gradually improved. Figure 17: Relationship between slope safety factor, maximum horizontal displacement, and cohesion of muddy interlayers. For bedding rock slope containing a single soft interlayer, the analytical models of [PERSON] [14] and [PERSON] [15] were \(H=50\) m, \(\beta=60^{\circ}\), \(\theta=50^{\circ}\), \(c=0.046\) MPa, and \(\varphi=15^{\circ}\) to \(30^{\circ}\). The numerical model of [PERSON] et al. [17] was \(H=50\) m, \(\beta=45^{\circ}\), \(\theta=39^{\circ}\), \(c=0.025\) MPa, and \(\varphi=10^{\circ}\)-\(25^{\circ}\), and they argued that the displacement of the slope first decreased rapidly and then decreased slowly as \(\varphi\) increased, and the safety factor increased linearly, while, in the  
Figure 19: Grid deformation diagram of the computational model (Scheme 4). Figure 20: Relationship between slope safety factor, maximum horizontal displacement, and internal friction angle of muddy interlayers. calculation model of Lu [13], \(H\) = 50 m, \(\beta\) = 60\({}^{\circ}\), \(\theta\) = 45\({}^{\circ}\), \(c\) = 0.046 MPa, \(\varphi\) = 20\({}^{\circ}\)-35\({}^{\circ}\), they considered that \(\varphi\) increased, the slope displacement decreased first and then increased, and the safety factor increased first and then decreased. Differing from the results in the above literature, this paper argued that the internal friction angle of the soft interlayer increased the overall slope displacement when it exceeded the internal friction angle of the interbedded surrounding rock, which was not conducive to rock stability.