Topological feature study of slope failure process via persistent homology-based machine learning

TL;DR

This paper combines persistent homology and machine learning to analyze slope failure processes, providing a novel topological approach for predicting slope instability and understanding failure mechanisms.

Contribution

It introduces a new topological analysis method using persistent homology to study slope failure, linking topological features to instability evolution.

Findings

Longest Betti 1 bar code reflects slope failure evolution

Topological characteristics correlate with critical instability states

Method enhances slope failure prediction accuracy

Abstract

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.