Implementation of the Critical Unstable Condition in Extended Finite-Element Analysis to Calculate the Safety Factor of a Predefined Slip Surface

Abstract

This study incorporated the critical unstable condition into extended finite-element analysis to determine the safety factor of a slip surface that is regarded as a discontinuity embedded into the slope mesh. The displacement field and the safety factor can be obtained simultaneously by directly solving the final nonlinear equations. Moreover, the augmented Lagrange multiplier method and the vital vertex algorithm were used to improve the accuracy of the normal stress on the slip surface. Three examples were presented to demonstrate various aspects of the proposed method, including its efficiency in searching for the critical slip surface without remeshing and sensitivity to the finite-element mesh.