A Rigorous Limit Equilibrium Method for the Slope Stability Analysis

In the stability analysis of slopes based on limit equilibrium methods, rigorous methods that satisfy complete equilibrium conditions are more reliable and preferred. This study presents an alternative method, which is rigorous and applicable to slip surfaces of all shapes. On the analogy of the classical earth pressure theory and Spencer's assumption about inter-slice forces, the relational functions containing two unknowns are obtained between inter-slice forces and gravity of the slice. According to equilibrium equations of a typical slice, the function of normal stress distribution over the slip surface, containing two undetermined parameters, is derived. Considering the whole sliding body, instead of an individual slice, as the loaded object, all the equilibrium equations (horizontal and vertical forces equations and moment equation) are formulated. The mathematical elimination of these equations results in a single cubic equation in terms of the factor of safety, which can be explicitly solved. Example studies show that the proposed method yields a factor of safety in a reasonable agreement with other rigorous methods. This method enjoys merits of straightforward computation process without iteration, applicability to arbitrary shapes of slip surfaces and the solutions being within the context of rigorous limit equilibrium. The methodology developed herein can also make up the deficiency of theoretical basis for the previous normal stress assumption.