## 3 Results Analysis of Pseudo-Dynamic Method  
### Validation of the Present Method  
In order to verify the rationality of the pseudo-dynamic method, the safety factors of the two examples taken from the present method were compared with the results reported in [PERSON]'s [32] studies based on different methods. One example was a comparison of slope safety that did not consider the seismic inertia force. Another example was a comparison of seismic slope safety using the pseudo-static method, the minimum stability factor method, and the dynamic analysis method.  
**Example 1**.: _The slope has height \(H=60\ m\), slope angle is \(\alpha=60^{\circ}\), inclination of structural plane is \(\beta=30^{\circ}\). The rock mass parameters are as follows: \(\gamma=26.4\ kN\cdot m^{-3}\), \(c=750\ kPa\), \(\varphi=44.8^{\circ}\). The structural plane parameters are \(c=150\ kPa\), \(\varphi=28.8^{\circ}\). For Example 1, the stability of the slope is a static problem, without considering the seismic effect. Table 1 presents the safety factor calculated by different methods._  
As can be seen from Table 1, the pseudo-dynamic method derived in this study provides a safety factor \(F\) that is in close agreement with the values obtained from the strength reduction method and is marginally less than the results of the simplified Janbu method and imbalance thrust force method. The present analytical result is satisfactory with the relative error between the calculated value and the reported values not exceeding 6%. It can be noted that the present result is slightly higher than the value calculated by the finite element slip surface stress method, and this significant difference can be attributed to the definition of the constitutive relation of rock mass and the selection of material parameters in the finite element method. Hence, under the framework of the limit equilibrium theory, the present result is reasonable compared with the other results and shows a good agreement.  
**Example 2**.: _The slope angle is \(\alpha=45^{\circ}\), inclination of structural plane is \(\beta=27^{\circ}\), and height \(H=64~{}m\). The landslide translational slides along the structural plane, consisting of fluvial stone in the upper and petilite siltsitone and mudstone on the bottom. The landslide is located in the Sanjiang earthquake zone with the seismic region of VII degree fortification, and the horizontal seismic acceleration coefficient is \(k_{h}=0.127\). The fluvial stone parameters are as follows: \(\gamma=19~{}kN\cdot m^{-3}\), \(c=9~{}kPa\), \(\varphi=34^{\circ}\). The siltstone parameters are \(\gamma=23~{}kN\cdot m^{-3}\), \(c=245~{}kPa\), \(\varphi=47^{\circ}\)._  
If we only consider the effect of the seismic acceleration coefficient as a single factor on the slope stability, the present formulae may be reduced to the result of the pseudo-static method. It is observed from Table 2 that the present result and the value obtained from the pseudo-static method matched exactly. As mentioned previously, the pseudo-static method is only a simple method to calculate the seismic effects. In fact, the pseudo-dynamic method is more rational because of the consideration of the variation of time and space. By comparing it to the minimum stability factor method and the dynamic analysis method, the similarities can be found which are that the finite element technique is used to calculate the safety factor. The consideration of the influence of the material elastic-plastic deformation results in a low safety factor being calculated with the above two methods. It is obvious that the results presented in Tables 1 and 2 indicate that the present method is reasonable and effective.