## 3 Dynamic Response of the Slope
### Analysis of the Amplification Effect
This coincides with the regularity of the results derived from shaking-table tests conducted by previous workers [26]. This phenomenon can also explain the large amount of horizontal throwing failure that occurred on the slopes during the Wenchuan earthquake. Figure 7d further shows that the high \(AAF\) values are concentrated on one side of the slope (point A20), i.e., they are not axisymmetric along the width direction of the slope (\(X\)-direction). Overall, the spatial distribution of the slope amplification effect in the case of three-directional dynamic loading is much less regular than that in the case of the planar problem (one- or two-directional dynamic loading). The \(AAF\)s in each direction also have larger increases compared to those in the planar problem. Intuitively, this is also a reflection of the complexity of the propagation and mutual superposition effects of the three-directional seismic waves within the rock mass of the slope. In order to investigate the effect that the regularity of the structural planes has on the slope amplification effect, the variation of the _AAFs_ in the upper part of slopes subjected to the action of sinusoidal waves was studied for different values of \(\gamma\) (angle between the joint and slope trends; the slope and joint angles were fixed at 40\({}^{\circ}\) and 70\({}^{\circ}\), respectively). The results are shown in Figure 8. It can be seen that the amplification effect is strong in the upper part of the slope (Figure 8b) when \(\gamma\) is small (\(-5^{\circ}\) to \(5^{\circ}\)). Then, as \(\gamma\) increases, the _AAF_ values tend to decrease and then increase again when a certain angle is reached (\(\sim\)15\({}^{\circ}\)). That is, there is a certain regularity in the _AAF_ values (showing an overall decrease at first and then increasing again). This phenomenon can also be used to visualize the direct relationship between energy dissipation and angle of incidence when a seismic wave is reflected/refracted. It also confirms that the spatial effect of the structural planes is an important factor that cannot be neglected when studying the dynamic response of an anti-dip bedding slope subjected to earthquake activity. The effect of slope geometry (i.e., slope angle \(\alpha\) and joint angle \(\beta\)) on the amplification effect was also investigated. The point A8 at the top of the slope was selected for this purpose. Figure 9 shows surface plots of the AAF results for slopes subjected to sinusoidal and natural seismic waves for different values of \(\alpha\) and \(\beta\). Overall, in both cases, the magnitudes of the components decrease in the order \(AAF_{z}>AAF_{y}>AAF_{x}\). In fact, the \(AAF_{x}\) component essentially remains constant and does not vary much as \(\alpha\) and \(\beta\) are changed. Thus, the geometry of the slope has a stronger influence on the diffraction and superposition of seismic waves in the \(YZ\)-plane (while it has almost no effect in the \(XY\)-plane). The trends in \(AAF_{y}\) and \(AAF_{z}\) are basically the same, i.e., they both increase and  
Figure 7: Variation of the acceleration amplification factors at different acceleration monitoring points due to the action of natural seismic and sinusoidal waves for points along profiles: (**a**) 1, (**b**) 2, (**c**) 3, and (**d**) 4.  
then decrease as the slope angle \(\alpha\) increases, and decrease and then increase as the joint angle \(\beta\) increases. The largest values of \(AAF_{y}\) and \(AAF_{z}\) occur when \(\alpha\) = 50\({}^{\circ}\) and \(\beta\) = 50\({}^{\circ}\) and 70\({}^{\circ}\), and the smallest values occur when \(\alpha\) = 50\({}^{\circ}\) and \(\beta\) = 60\({}^{\circ}\). It is not difficult to find that both the slope angle \(\alpha\) and the joint angle \(\beta\) have significant effects on both \(AAF_{y}\) and \(AAF_{z}\), because they directly determine the way seismic waves propagate within the rock and the intensity of diffraction, which is intuitively reflected in the magnitude of \(AAF\).