## 3 Results Analysis of Pseudo-Dynamic Method
### Dynamic Characteristics of Bedding Slope
#### 3.2.2 The Effects of Various Parameters on Safety Factor
Similarly, when \(k_{\rm v}>0\), it represents a vertical inertia force whose direction points to the outside of the slope, which means that the driving force of the rock mass will decrease. This is logical since a greater \(k_{\rm v}\) implies a weaker driving force to which a slope is subject, thereby improving slope safety. As shown in Figure 6b, the safety factor increases with an increase in \(k_{\rm v}\). For example, for \(\varphi=40^{\circ}\), when \(k_{\rm v}\) increases 0\(\sim\)0.4, the safety factor increases by 15.78% (from 1.9 to 2.2). As can be seen in Figure 6a, the effect of \(k_{\rm v}\) on the safety factor is lower than that of \(k_{\rm h}\), and less than half. In order to better understand the law of the safety factor with the \(k_{\rm h}\) and \(k_{\rm v}\), the spatial distribution of safety factors under the bidirectional seismic interaction is depicted in Figure 7. In Figure 7, the colors in different positions indicate the values of the safety factor under different horizontal and vertical seismic action, with red representing the high value and blue representing the low value. It can be seen that the influence efficiency of \(k_{\rm h}\) on the safety factor is significantly greater than \(k_{\rm v}\), so the horizontal inertia force plays a vitally important role in the instability of the bedding slope under seismic loads. And that, fundamentally, is why vertical seismic acceleration is often ignored in the simplified analysis process, and only horizontal seismic acceleration is considered. However, for some important slope engineering in the high-intensity seismic belt, it is necessary to consider the effects of vertical seismic action because the earthquake itself has multi-dimensional characteristics. Additionally, more and more, the destruction phenomena after earthquakes show that considering the effects of vertical seismic action in slope stability analysis is becoming increasingly important. Figure 6: Effect of seismic acceleration coefficients \(k_{\rm h}\) and \(k_{\rm v}\) on safety factor (\(t=0.1\) s, \(c=200\) kPa, \(f=1\)). (**a**) Result of \(k_{\rm h}\) on safety factor; (**b**) result of \(k_{\rm v}\) on safety factor. (4) The effects of amplification factor f on safety factor  
Figure 8 represents the effects of the amplification factor on the safety factor. It can be seen that the amplification factor also has an important influence on slope stability; as \(f\) increases, the difference in the results between the pseudo-dynamic method and the pseudo-static method also increases, especially for the higher values of \(f\). According to a comparative study of the two methods, the results of the pseudo-dynamic method are gradually increasing (\(k_{\rm v}\) = 0.1-0.3) or decreasing (\(k_{\rm h}\) = 0.1-0.3) with \(f\) increasing, whereas the results of the pseudo-static method are unchanged. Note that when the amplification factor changes, the degree of influence on the safety factor caused by seismic acceleration coefficients in the vertical direction is obviously larger than that in the horizontal direction. For example, when \(k_{\rm v}=0.3,f\) increases from 1.0 to 2.0 and the value of the safety factor increases by 218.49% (from 1.19 to 3.19). However, for \(k_{\rm h}\) = 0.3, the value of the safety factor decreases only by 21.78% (from 1.01 to 0.79). Thus, this shows that, when considering the background of the amplification factor, the vertical seismic acceleration coefficient still has a significant effect on slope stability. From the above analysis, based on the parameters of the seismic acceleration coefficient and amplification factor effects on the safety factor, it can be concluded that the pseudo-dynamic method is more reasonable for considering the seismic effect. 2. The effects ofgeometrical parameters of slope on safety factor  
The geometrical parameters of slope mainly include slope height \(H\) and slope angle \(\alpha\). Figure 9 illustrates the effects of the slope height and slope angle on the safety factor.