Using software UDEC to simulate the instability failure process of slope under seismic load, studing the dynamic response of slope failure, obtaining the deformation characteristics and displacement cloud map of slope, then analyzing the instability state of slope by using the theory of persistent homology, generates bar code map and extracts the topological characteristics of slope from bar code map. The topological characteristics corresponding to the critical state of slope instability are found, and the relationship between topological characteristics and instability evolution is established. Finally, it provides a topological research tool for slope failure prediction. The results show that the change of the longest Betti 1 bar code reflects the evolution process of the slope and the law of instability failure. Using discrete element method and persistent homology theory to study the failure characteristics of slope under external load can better understand the failure mechanism of slope, provide theoretical basis for engineering protection, and also provide a new mathematical method for slope safety design and disaster prediction research.
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