## 4 Mechanism Responsible for Slope Failure under Seismic Action  
The mechanism that leads to the failure of an anti-dip bedding rock slope subject to earthquake activity can be investigated by monitoring the displacement of the slope in the \(Y\)-direction as a function of time. Figure 11 presents contour plots of displacement data calculated for a slope with \(\alpha=40^{\circ}\) and \(\beta=60^{\circ}\) by a cross parallel to the \(Y\)-axis through the center of the model. In the figure, the critical displacement value is taken to be 2 cm.  
According to Figure 11, failure begins to occur under the seismic action at the leading edge of the slope. Furthermore, the failure surface is step-like, showing that the failure process has the characteristics of flexure toppling on the whole. As time progresses, a free surface is generated after the flexure toppling of the front edge and thus the rear part of the slope starts to undergo flexure toppling failure. The failure surface is therefore continuously extended to the rear part of the slope body. After the 5 s seismic loading wave had ended, the slope was already in a destabilized state. However, the slope displacement continued to develop beyond this point until the slope was completely destroyed.  
These results should be compared with the results of shaking-table experiments conducted by previous authors [25]. In the current paper, it is found that the seismic wave induces the anti-dip bedding rock slope to start to fail at the bottom of the slope. In contrast, previous work has suggested that failure is due to the opening up of the structural planes at the top of the slope, which leads to the generation of tension cracks. It can thus be seen that the component of the seismic waves in the \(X\)-direction cannot be neglected. Furthermore, it is not just related to the stability of the anti-dip bedding rock slope, it also directly affects its failure mode.  
The influence of the spatial effect of the structural planes on the failure mode of the slope was also investigated. Figure 12 shows the displacement (again in the \(Y\)-direction) of a slope with \(\alpha=40^{\circ}\) and \(\beta=70^{\circ}\) for different angles \(\gamma\) between the joint and slope trends. This time, the slope is subjected to the action of sinusoidal waves. In these plots,the critical displacement value is once again taken to be 2 cm. When \(\gamma\) = 0 (Figure 12a), the failure surface has a regular step-like shape. However, when \(\gamma\
eq 0\), the failure surface becomes irregular.  
It is also noticeable that, on the whole, the depth of the failure surface increases as the value of \(\gamma\) increases. At the same time, the scope of the slope instability becomes wider. Consequently, the slope will be less stable when subjected to dynamic action. When \(\gamma\
eq 0\), the maximum displacement occurs around the upper shoulder of the slope, indicating that the most dangerous region of the slope (when it is subjected to dynamic action) is located in the upper part of the slope. Therefore, in areas of high seismic activity, it is essential that the statistics of the structural planes of an anti-dip bedding rock slope are thoroughly investigated before assessing the level of geological hazard present. This is because the spatial effects of the structural planes will directly affect the stability of the slope when it is subjected to seismic action.  
Figure 11: Contour plots of the displacement in the \(Y\)-direction of a slope (\(\alpha\) = 40\({}^{\circ}\) and \(\beta\) = 60\({}^{\circ}\)) subjected to a natural seismic wave. The plots show the displacements in the plane corresponding to \(x\) = 10 m at different times after the onset of the seismic disturbance: (**a**) 1 s, (**b**) 2 s, (**c**) 3 s, (**d**) 4 s, (**e**) 5 s, and (**f**) 6 s.