General Slice Method Based on Rigorous Equilibrium to Solve the Factor of Safety

Abstract

For a general slice, force and moment equilibrium equations are developed, the recurrence equations of inter-slice force and inter-slice moment are derived, the general formulation based on rigorous equilibrium to solve the factor of safety is studied, hence, the theoretical framework of rigorous method of general slice is developed, rigorous method of vertical slice is a special case of it. Analyzing the applicability of Sarma’s method, two new inter-slice shear force equations are presented based on the compatible relationship among slice’s displacements by leading in the scaling parameter λ and inter-slice force function f(x),hey make the relationship between the inter-slice shear forces and slip surface geometry clear, and indicate that the reduction factor for shear strength along inter-slice boundaries varies from one boundary to the next depending on the geometry of the slices and the slip surface. The rigorous methods of general slice can be developed based on the modified inter-slice shear force equations, they think that the reduction factor for shear strength along inter-slice boundary is different from that for shear strength along slip surface. The example analysis indicates that the proposed new methods work better than Sarma’s method, the reasonable value of safety factor can be obtained by using them. Even if the shape of slice is varied, the proposed new methods can also give consistent values of safety factor and ensure that the iteration is stably convergent.