## 5 Conclusions  
In the present study, the algorithm of FDEM is improved in depth: the vibration deterioration model of structural plane is added, the solution steps of the dynamic safety factor considering the vibration deterioration effect of structural plane are provided; by comparing and analyzing the existing bolt element model in FDEM, the combined one-dimensional and entity element model of anchor cable element is proposed, and the generalization model for the landslide-anchorage structure system during earthquake is established to discuss the dynamic response law and entire evolution process of the landslide-anchorage structural system. The main conclusions are as follows:  
1. Considering that the most significant inducement factor of earthquake-induced rock landslides is the gradual vibration deterioration on the structural plane, the present study proposes a dynamic strength reduction method for FDEM, which considers the effects of cumulative displacement, relative velocity, and shear cycle number. Based on this method, the entire damage process of earthquake-induced landslide can be reproduced, and its internal evolution mechanism can be deeply investigated; in addition, this method can give a quantitative evaluation index of dynamic safety with practical significance, and it can be promoted and applied in the field of seismic design of slopes. 2. The advantages of the combined one-dimensional and entity element model of the anchor cable in FDEM are as follows: (1) simplifying the modeling process and optimizing the mesh size distribution; (2) realizing the prestress application by the one-dimensional element model and simplifying the application process; and (3) optimizing the calculation process by simplifying the constitutive law of anchor cable. 3. Based on the generalized slope model, the entire process of dynamic evolution of landslide-anchorage structure system under seismic load is investigated: (1) the dynamic response of unreinforced and cable-reinforced slopes is inconsistent, but overall, the dynamic response of the cable-reinforced slope is obviously smaller than that of the unreinforced slope, which is due to the fact that the presence of prestressed anchor cable improves the integrity of slope body and the strength of joints on the one hand, while on the other hand, it reduces the slope's vibration acceleration; (2) the distribution of PGA amplification factor within the slope is nonlinear, and the reason for this is multifaceted and complex; the structural plane and the newly generated fracture surface have the effect of attenuating the stress wave, but the free face formed by them will have the effect of amplifying the stress wave. These two effects of attenuation and enhancement compete with each other within the slope, and the results show nonlinear characteristics in the macro sense; (3) with  
Figure 16: Comparison of crack initiation and penetration time, and crack number and kinetic energy at penetration time under different seismic intensities. the increase in seismic intensity, the axial force of the anchor cable also increases gradually; (4) the axial force at the structural plane and fracture surface is larger, and the PGA amplification factor has a correlation with the axial force of the anchor cable; therefore, according to the distribution characteristics of the axial force and the PGA amplification factor, the fracture of the slope can be preliminarily judged; (5) the crack initiation and penetration times advance with the increase in the seismic intensity, and the crack number and kinetic energy at the penetration time increase with the increase in the seismic intensity. Methodology, Validation, Formal analysis, and Writing, C.X. ; Conceptualization, Supervision, and Funding acquisition, Y.H. ; Writing, Review and Editing, G.L. ; Software, C.M. ; Investigation, M.L. All authors have read and agreed to the published version of the manuscript.