基于持续同调的边坡土颗粒应力链失稳分析

Instability analysis of soil particle stress chain on slope based on persistent homology

采用颗粒离散元方法和持续同调理论,研究了内排土场堆叠至不同高度时的边坡稳定性。为便于研究,现采用一水平金属板向下施加压力,代替不同厚度土层的重力荷载,对边坡在竖向荷载作用下的失稳破坏过程进行了颗粒离散元模拟。研究了二维边坡土颗粒速度总矢量、边坡失稳破坏时滑移开裂面的角度以及边坡坡顶y方向的平均速度等宏观响应过程,并构建了自然堆积下边坡堆积体颗粒的法向力链无向网络模型。最后,用持续同调方法对边坡坡顶颗粒接触力链网络的拓扑特征进行分析,获得条码图,建立了岩体结构持续同调特征与失稳演化的关系。本文为研究边坡失稳拓扑识别提供了一种新方法,从而可以有效预测边坡的失稳破坏。

In this paper,the stability of inner dump slope at different heights is studied by the method of particle discrete element and the theory of persistent homology.In order to facilitate the study,a horizontal metal plate is used to apply downward pressure instead of gravity load to soil layers with different thickness to simulate the instability failure process of the slope under the vertical load.The macroscopic responses such as the total velocity vector of the two-dimensional slope deposit,the angle of the slip cracking surface when the slope is unstable,and the average velocity in the y-direction of the slope were studied.Then,the normal force chain undirected network model of the natural accumulation of slope stacking particles was constructed.Finally,the topological characteristics of the particle contact force chain network of the slope top were analyzed by the persistent homology method to obtain the barcode.Finally,the relationship between the instability evolution and the characteristics of persistent homology is established.This research provides a new method for the study of slope instability topology identification.Thus,the instability of slope destruction can be predicted effectively.