## 5 Influence of the Inclination Angle
### Failure Modes
At a joint inclination angle of 60\({}^{\circ}\), there is reduced internal fracturing of the slope. According to [24], which uses PFC2D to simulate a typical slope, joint distribution in only the upper part of the slope leads to substantial displacement of the upper rock while the lower part remains unaffected. This suggests that joint distribution has a significant influence on slope stability. [PERSON] et al. [25] presented a mechanical model and failure analysis for a bedding rock slope, along with a numerical simulation of the Shanyang landslide. Research has shown that the slope initially developed a shear-slip zone from the weak parallel structural plane. This zone continued to expand with time and ultimately  
Figure 9: Comparison of slope failure modes under varied inclination angles. 1—Tension fracture in yellow; 2—Slide plane in red; 3—Rock element; 4—Joint element. connected with the tension zone lower down the slope, resulting in slope instability. It has been observed that the shear strength in an unstable bedding slope decreases, owing to the parallel weak structural plane on the slope surface. This observation aligns with the failure state of the simulation slope, which had a joint dip angle of 30\({}^{\circ}\) (close to 37\({}^{\circ}\) slope angle). A weak joint initiates at the top of the slope and terminates at the slip surface, penetrating the platform beneath the slope. In engineering, the dip angles of 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\) degrees more accurately represent the distribution of joint fluctuation angles in the slope. Most of the dip angles appear as the slope in a composite form. In their study, [PERSON] et al. [26] proposed a generalization of the rock slope model having serrated structural planes with low, medium, and high undulations (with respective undulation angles being 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\)). They also established the cumulative damage evolution model of the slope through experiments. [PERSON] et al. [27] concluded that slope instability follows a specific process, starting from the initiation and development of micro-cracks, followed by expansion and penetration of cracks, and ending with the failure of a slope sliding. The experimental result is consistent with the simulation result, indicating that the difference in joint number has little effect on the final slope failure model. However, the difference in the final failure trace at different joint levels is notable. Landslide suggests that the slope is influenced by discontinuous stress concentration points during the landslide process. This is due to joints dividing the continuous rock, creating a landslide locking section that primarily consists of rock bridges and supporting arches [28]. The joint units on the slope surface become more severely deformed due to rock rolling and sliding as there are increases in the joint dip angle. The high-stress concentration areas between the joint units are also significantly damaged. This suggests that the slope's instability is notably influenced by the locking section as the joint inclination angle increases. The variation in the locking section's shape results in different slope slip lines corresponding to varying joint inclination angles. Figure 10 illustrates the progression of slope landslides on the engineering site. Several tensile fractures were identified at the measured position. The obtained failure result resembles the simulated slope failure mode, and a slip surface can be observed that formed in the upper part. It shows that the two-dimensional numerical simulation can match some landslide areas on the actual slope, and rock particles accumulate in the lower part after loading, validating the trustworthiness of analyzing the sliding instability of the rock slope structural plane using the PFC2D code.