Comparison of Factors of Safety Using a 3D Failure Mechanism with Kinematic Approach

Abstract

In slope stability analysis, there are two commonly used methods for calculating the factors of safety (FS). The first is the strength reduction method (SRM), which defines the FS as the ratio of the real material shear strength to the critical shear strength in the limit equilibrium state. The second is the gravity increase method (GIM), which defines the FS as the ratio of the critical increased gravity to the actual gravity. On the basis of a kinematically admissible three-dimensional (3D) failure mechanism, this paper develops a framework to compare these two kinds of FS. Earthquake effects are included in the study by using the quasi-static representation. By means of the kinematic approach of limit analysis, the GIM can give an explicit function about the FS, while the SRM can only provide an implicit equation on the FS. The lowest solutions for both two kinds of FS are obtained by optimizing the variables from the 3D failure mechanism. Numerical results are calculated and presented in the forms of graphs to show the difference between these two kinds of FS. It is shown that the FS calculated by the SRM is equal to that calculated by the GIM when the slope is in the limit state (FS = 1.), that the FS by the SRM is greater than that by the GIM for an unstable slope (FS < 1.), and that the FS by the SRM is smaller than that by the GIM for a safe slope (FS > 1.). Finally, a power function is proposed to approximately express the relationship between these two kinds of FS.