一种边坡稳定性分析的三维极限平衡法及应用

将离散后的条柱间作用力等效成滑面正应力,依据整个滑体的平衡条件,提出一种适用一般空间形态滑面的边坡三维极限平衡法。首先通过类比经典土压力理论和Spencer的条间力假定,提出了条柱间作用力假设模型,由典型条柱的平衡条件得到滑面正应力的分布函数(含3个待定参数),再根据整个滑体的4个主要平衡条件建立平衡方程,采用数值方法和解析法求解平衡方程组获得三维安全系数。算例验证研究结果表明：该方法计算结果与已有方法相印证,其精度与严格三维极限平衡法相当,适用于任意空间滑面形态。最后,应用该方法初步评价金坪子II区边坡的整体稳定性,取得较理想的效果。该方法理论严谨,结果可靠,计算过程简单且易于编程,可在边坡工程设计及滑坡治理中推广应用。

3D limit equilibrium method for slope stability analysis and its application

By obtaining the normal stresses over slip surface and considering the equilibrium conditions of the whole sliding body, a three-dimensional slope stability analysis method is proposed, which satisfies four equilibrium conditions and accommodates to slip surfaces of any shape. The functions of inter-column force are assumed and the distribution function of the normal stress over slip surface containing three undetermined parameters is obtained based on the force equilibrium conditions of typical discretized column. Equilibrium equations are established considering the equilibrium conditions of the whole sliding body, and then 3D factor of safety is derived using the numerical and analytic methods. Some examples are given to verify the proposed method. The results show that the proposed method is more reliable compared with several other 3D slope stability analysis methods. Finally, this method has been successfully used in the stability analysis of slope on Jin Ping-zi Mountain. The present 3D slope stability analysis method can be widely used by geotechnical engineers in the design of slopes and treatment of landsides for its easy computing and programming.