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.

中文翻译：

---

基于持久同源性的机器学习边坡破坏过程拓扑特征研究

利用UDEC软件模拟地震荷载作用下边坡失稳破坏过程，研究边坡破坏动力响应，得到边坡变形特征和位移云图，然后利用持久同调理论分析边坡失稳状态，生成条码图，并从条码图中提取斜率的拓扑特征。找到边坡失稳临界状态对应的拓扑特征，建立拓扑特征与失稳演化的关系。最后，为边坡失稳预测提供了拓扑研究工具。结果表明，最长Betti 1条码的变化反映了边坡的演化过程和失稳破坏规律。