  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.
