Three-Dimensional Finite Element Limit Equilibrium Method for Slope Stability Analysis Based on the Unique Sliding Direction

A three-dimensional finite element limit equilibrium method (3DFLEM) based on the concept of strength reduction and the unique sliding direction is presented. The definition and physical meaning of factor of safety (FOS) as well as the relationship of FOS and the unique sliding direction are clarified. On the basis of mean value theorem of integrals, the FOS corresponding to sliding body of an arbitrary shape is defined. The relationship of partial FOS and overall FOS can be demonstrated by the definition of factor of safety. The results of stability analysis obtained from the proposed approach, 3D rigid limit equilibrium method (3DLEM) and 3D shear strength reduction method (3DSSRM) are compared. It is shown that: 1) the factor of safety and critical sliding surface are generally in good agreement; 2) the element size of slope and sliding surface has certain effect on FOS by causing maximum difference of 2%. However, the effect of yield criterion used in the stress- strain analysis may be negligible.