基于ICMP和图论算法的边坡稳定性分析

Slope Stability Analysis Based on ICMP and Graph Theory

ICMP(Independent Cover Meshless Particle)方法利用与分析区域任意几何形状无关的离散结点及其独立矩形影响域覆盖分析物体,采用一般多项式作为结点的无网格插值函数,较好地克服了传统无网格方法面临的一些困难.本文借助ICMP方法,计算得到边坡的应力场分布,并将边坡稳定性分析转化为图论问题,利用Bellman-Ford搜索算法快速稳定地寻找出边坡的安全系数和最危险滑裂面,发展了一种新的ICMP-图论边坡稳定性分析方法.该方法计算过程和数值实施简单,无需做过多假设及迭代计算,适合于复杂地层条件、几何形状的边坡稳定性分析,具有稳定和高效的算法特点.相关典型算例验证了本文方法的适用性和正确性.

A jointed rock slope stability analysis method was developed based on the independent cover meshless particle method（ICMP） and graph theory. In the ICMP method, the analysis model is described with the arbitrary discrete nodes, and a general polynomial is employed as the meshless interpolation function for each discrete node which results in a very simple formulation and numerical implementation. The complex rock joint, rock interface and supporting structure can be easily modeled and simulated in the ICMP. In this work, the ICMP is used to calculate the stress distributions of rock slope with joints, the slope stability analysis is converted to a graph problem. The Bellman-Ford algorithm is used to obtain the slip surface, and the safety factor is defined as the ratio of the resistant force over the slip force along the slip surface. The proposed method is easy to build complex 2 D/3 D geotechnical engineering numerical models, and removes the difficulties of the iterative calculations for the stability analysis of rock slope. Several typical numerical examples are presented to demonstrate the capability and robustness of the method in rock slope stability analysis.