中文摘要：

最大最小原理在边坡稳定性分析中的应用,不仅可以检验所建模型的准确性,还可以进一步获得改进计算模型的相关条件。本文利用三维简化Sarma法,分析了滑面剪切力方向采用不同的分布形式引起的稳定系数的变化,计算结果表明,不管采用何种分布形式,当它发生变化时,对应的稳定系数总是存在一个极大值,这就证明了边坡稳定性最大原理在三维边坡稳定分析中的适用性;同时,本文还在一种严格的二维临界滑面搜索算法的基础上,建立了三维临界滑面搜索的算法,利用ZhangXing算例详细分析了目标函数中各变量对稳定系数的影响,结果表明,二维上寻找临界滑面是切实可行的,这也证明最小原理在二维边坡稳定分析中是满足的,三维上则由于三维极限平衡法未考虑三维边坡的边界条件,导致基于三维极限平衡法的三维临界滑面理论上不存在,三维边坡稳定分析结果与最小原理的要求有一定的差异。

英文摘要：

The maximum and minimum principles in the slope stability analysis,can be used to test the accuracy of the stability analysis model,and obtain the related condition used in improving the model.This paper uses the Simplified Three-dimensional Sarma Method.It analyzes the variation of the stability factor caused by the direction of shearing force on the sliding surface.The results show that no matter what the distribution of the direction,when it changes,the corresponding stability factors has a great value.This just proves that the maximum principle in three-dimensional slope stability analysis is applicable.At the same time,on the base of a rigorous determining method for the two-dimensional potential sliding surface of slope,this paper builds an algorithm for determining the three-dimensional potential sliding surface,and analyzes the effect of the parameters in the object function on the stability factor through the case in ZhangXing＇s paper.The results show that two-dimensional determining method is feasible,and it also proves that the minimum principle in the two-dimensional slope stability analysis is met.But in the three-dimensional slope stability,the results have some difference with the demand of the minimum principle for the three-dimensional limit equilibrium method not taking into account the boundary conditions of three-dimensional slope.