粘性土坡稳定性的变分分析

The Variational Analysis of Soil slope Stability

本文将粘性土坡的稳定性问题等价于一个单参变量函数的待定边界的泛函的变分问题。利用变分法,推导了滑裂面所应满足的微分方程(欧拉方程)和横截性条件。本文方法可确定滑裂面形状函数和安全系数。作为特例,本文讨论了简单土坡所可能出现的滑裂面形状,以及临界状态时的土坡的各种参数所应满足的条件,从而可确定临界坡高或临界坡度。

In this paper,the problem of soil slope stability is equivalent to a variation problem of the funtional of one-variable function with a variable boundary.By applying the variational calculus,the differential equation(Euler's equation)and transversality conditions governing the critical sliding surface have been developed.The method given in the paper allows for the determination of the sliding surface shape and the safety factor.For example,the possible sliding surface shapes and the conditions satisfied by every parameter of the simple slope on critical state have been developed.Then,the critical height or critical angle of slope can be de- termined.