## 1 Introduction  
Landslide is a common natural disaster with high frequency and wide range in nature, and its occurrence is often accompanied by transportation disruption, river blockage, village and town burial, factory destruction, and tunnel collapse, being the second most hazardous to earthquakes [1, 2, 3]. The deformation and destruction process of landslides is not only controlled by internal factors (topography, geological structure, stratigraphic lithology, and hydrogeology, etc. ), but also facilitated by external factors (rainfall, fluctuation of reservoir level, earthquakes, and blasting by manual excavators, etc.) [4, 5, 6]. Landslides may be triggered in sensitive areas when the earthquake magnitude exceeds Mw 4.0, and many landslides can be induced simultaneously when the earthquake magnitude exceeds Mw 6.0 [7; 8; 9]. Larger earthquakes can trigger thousands of landslides over large areas. For example, the Wenchuan earthquake (Mw 8.0) triggered nearly 200,000 landslides, making it the largest, densest, most widespread, and most catastrophic earthquake-induced landslide event ever recorded for a single earthquake in China. Earthquake-induced landslides have caused serious loss of life and property, so studying them is of great practical significance [10]. As an in situ rock reinforcement technology, prestressed anchorage technology can effectively improve the destructive strength and integrity of geotechnical materials, and has the characteristics of sample operation, convenient construction, low cost, and high practicality [11; 12; 13]. Numerous studies have shown that compared with unreinforced slopes, the peak ground acceleration (PGA) amplification factor is smaller with reinforced slopes, while the rock acoustic wave velocity is larger [14; 15]. As a result, the deformation damage condition and the degree of fragmentation of the reinforced slopes have been significantly improved, indicating that the reinforced slope has better seismic performance and a certain practical engineering significance [16]. At present, there are relatively few studies on the seismic performance of slopes reinforced with prestressed anchor cable, and especially on the dynamic evolution process of the new system formed with anchorage body after slope anchoring, that is, the landslide-anchorage structural system [4]. The evolution mechanism of landslides is very complicated. Firstly, its generation and development process is a spatio-temporal evolution process. The development of the entire instability process is realized gradually with the increase in time, and it is a dynamic development in time and space. Secondly, the progressive failure of mesocracks in the rock mass (nucleation, expansion, and penetration) during the instability process of landslide will lead to the emergence of macroscopic sliding surfaces, which is not only a continuous to discontinuous progressive failure behavior but also a cross-scale mechanical behavior from mesoscopic to macroscopic. If the effects of dynamic loads and anchorage systems on the evolution process are considered, the analysis process will become more complicated. The above characteristics determine that the theoretical analytical and laboratory test methods have more significant difficulties in quantitatively describing the instability process of landslides and the mechanical behavior of rock failure, while numerical simulation methods provide a powerful means to solve this problem [17]. At present, a large number of numerical methods have been applied to dynamic stability analysis of the slope. However, there are still many shortcomings: continuum methods such as finite element method (FEM) and boundary element method (BEM) are all based on the continuity assumption, and their algorithms cannot take into account crack propagation in slopes under seismic load and large deformation after instability, so these methods cannot directly describe the entire dynamic evolution process of landslide progressive failure [18; 19; 20].