Generalized Three‐Dimensional Slope‐Stability Analysis

Abstract

A 3‐D slope‐stability‐analysis method, explicitly satisfying all limiting‐equilibrium equations, is presented. To make the problem statically determinate, the variational approach, rather than intuition in 3‐D, is used. In this approach, the normal stress over the user's specified slip surface, which satisfies global limiting equilibrium and produces the minimum factor of safety for the critical surface, is sought and obtained mathematically. A simple numerical scheme to attain the safety factor is detailed and all the algorithms needed to assemble a computer program are given. Upon discretization of the surface by n rectangular elements, n simultaneous linear equations are solved for n discrete normal stresses. It is also necessary to solve three nonlinear equations for the factor of safety, $F_s\text{,}$ and the coordinate of the center of rotation $x_c{z}_c\text{.}$ It was observed that for a selected potential slip surface there may be many possible combinations of $(n+2)$ roots, all giving essentially the same $F_s\text{.}$ The presented example problem demonstrates the importance of 3‐D back‐analysis if one is to configure in‐situ soil strength.