A novel displacement-based rigorous limit equilibrium method for three-dimensional landslide stability analysis

Conventional stability analysis of landslides is investigated using the factor of safety of the entire sliding body, which provides no information concerning displacements of the analyzed landslides. In this paper, a novel displacement-based rigorous limit equilibrium method is proposed to investigate the displacements and stabilities of three-dimensional landslides. The relationship between the shear stresses acting on the base of the columns and the shear displacements is established based on the hyperbolic soil model, which can be directly obtained from direct shear tests. According to the displacement compatibility among the columns, the shear displacements of all columns can be determined by the vertical and horizontal displacements at a key point. Combining the six equilibrium conditions of the discretized columns with the nonlinear constitutive relation between stress and displacement of soils, the vertical displacement at the key point can be determined. By introducing the strength reduction technique into the displacement-based rigorous limit equilibrium method, the relationship between the reduction factor and the vertical displacement can be obtained. The displacement and the safety factor of three-dimensional landslides can be defined. Moreover, two cases are given to verify the robustness and precision of the present method in detail.