## 5 Influence of the Inclination Angle  
### Failure Modes  
The stability of the slope is significantly impacted by the rough joints (Figure 1d), owing to the presence of weak interlayers on the rock slope. Figure 9 illustrates the failure characteristics of rough slopes with joint inclination angles of \(0^{\circ},30^{\circ},45^{\circ},60^{\circ},\) and \(90^{\circ}\) after they are loaded. As shown in Figure 9a, it slides as a whole, and the surface collapses locally when there is a slope with a \(0^{\circ}\) joint inclination angle. Some visible cracks are mainly located at the bottom of the top step slope, and the plate of the bottom step is flat. A potential slip surface is formed inside the slope from the lower part of the top step to the upper part. The joints are weak interlayers that lie horizontally; however, the failure destination of the slip line stops at the joint. [PERSON] et al. (2020) used the north slope of an open-pit mine as a case study. Through finite element software modeling analysis, he concluded that the failure mode of the layered slope occurred primarily through sliding, with a weak layer being the main failure layer. Additionally, the occurrence of a multi-slide failure indicated that joints had a lower impact on the stability of the self-weight slope when they were not distributed in the upper slope. Figure 8: Vector distribution of slope slip displacement. (**i**) Sliding trend of linear slope under varied inclination angles; (**ii**) sliding trend of rough slope under varied inclination angles. (1—Tension fracture in green; 2—Slide plane in red). As shown in Figure 9b, with regards to the 30\({}^{\circ}\) joint inclination angle, the overall slip distance of the slope increases, and multiple tensile cracks appear on its surface after loading. The fractures are distributed mainly in the center and lower sections of the slope, especially in the central part, which traverses multiple joints within the slope. The stability is significantly affected by loading, and a complete slip surface forms within a depth range from the slope's top to its foot. The angle of the joint inclination is roughly parallel to the surface of the slope, which is considered to be a weak layer compound. In research by [PERSON] et al. [23], the composite slope of a substation site in a rich karst was examined using the strength reduction method and ABAQUS 2021 numerical simulation software. The study also revealed that the composite slope with multiple weak layers first produced a shear fracture and slipped along the weak layer, which may result in a potential fracture surface that is circular arc-shaped. Furthermore, it was found that the stability was mostly affected by the joint dip angle that was parallel to the side slope, which aligned with the numerical simulation results. The loading failure mode of the slope with a joint inclination angle of 45\({}^{\circ}\) (Figure 9c) is similar to that of a slope with a joint inclination angle of 0\({}^{\circ}\). The slope body exhibits the sliding phenomenon and local caving, and tiny cracks that connect the upper and lower parts are also observed. A sliding surface through the lower part of the slope's top step to the platform at the foot of the slope is also formed. The failure modes of slopes with joint inclination angles of 60\({}^{\circ}\) and 90\({}^{\circ}\) are also similar, as shown in Figure 9d.e. There are some cracks appearing at the partial top of the slope, and there are local sliding phenomena occurring. However, the starting points of the potential sliding surfaces inside the two slopes differ. The former forms exclusively in the middle of the slope and terminates at the top of the lower step, whereas the latter originates at the top of the slope and terminates at the top of the lower step. As the joint inclination angle increases, the fracture range of the slip surface formed after the internal loading of the slope initially increases, then decreases, and then increases again.