Three-dimensional slope stability based on the finite element limit equilibrium method

A finite element limit equilibrium method was proposed based on finite element stress analysis combined with a limit equilibrium condition to analyze the slope stability. The local safety factor defined in the form of shear strength and shear stress ratio in a three-dimensional (3D) space does not consider the sliding direction influence on the calculation results. In this paper, a 3D finite element limit equilibrium method that considers the sliding direction was proposed. This method was different from the limit equilibrium and strength reduction methods and analyzed slope stability through the “true” stress state without reducing the material strength parameters. First, considering the sliding direction in the 3D space, the limit equilibrium condition of a point was proposed on the slip surface in the sliding direction. An equivalent relationship was proved of the slip surface was in the limit equilibrium state, and each point of the slip surface was in the limit equilibrium state in the sliding direction. Then, the main sliding direction and the sliding direction of each point on the slip surface were calculated assuming the rigid body limit equilibrium. Finally, the local safety factor was defined as the ratio of the shear strength to the shear stress projection in the sliding direction. Based on the equivalent relationship of the limit equilibrium state of the 3D slope, the local safety factor was transformed into a global safety factor by applying the integral median theorem. The method is simple to calculate, eliminates the limitation of the slip surface shape of the safety factor defined by the shear stress ratio form, and is reasonable and effective. The verification result of the calculation example shows that the sliding direction assumption of the method is reasonable, and the safety factor is consistent with the result of the strict 3D limit equilibrium method.