Analysis of stability of three-dimensional slopes using the rigorous limit equilibrium method

• The rigorous limit equilibrium method satisfies six equilibrium conditions.
• Inter-column forces are taken into account.
• The relationship between width of sliding body and factor of safety is determined.
• The factor of safety for 3D slopes can be obtained in arbitrary intervals.
• The present method is suitable for arbitrary slip surface.

Previously, quasi-rigorous limit equilibrium methods were applied to analyze the stability of three-dimensional slopes or landslides, which only satisfy three direction force equilibrium, and one or two direction moment equilibrium. In this paper, the rigorous limit equilibrium column method, in which inter-column forces are taken into account, is established based on six equilibrium conditions which include three direction force equilibrium conditions along coordinate axes and three direction moment equilibrium conditions around three coordinate axes. The relationship between the width of sliding body and factor of safety is determined using trust-region-reflective iterative algorithm. The value of the factor of safety is obtained using Levenberg–Marquardt least square method. Moreover, the present method can be applied to automatically search slip surface of three-dimensional landslides and to determine the factor of safety of three-dimensional landslides with the known arbitrary slip surface. Three examples are discussed to verify the robustness and precision of the present method in detail. Comparing with quasi-rigorous limit equilibrium methods which only considered four or five equilibrium conditions, the present method is more accurate and rigorous.