A three‐dimensional rigorous method for stability analysis of landslides

In the stability analysis of landslides based on limit equilibrium methods, the “rigorous” methods that satisfy complete equilibrium conditions are more reliable and are preferred. For two‐dimensional analyses, the rigorous methods of slices are becoming mature in both theory and practice. However, the attempts to realize their three‐dimensional rigorous counterparts have not yet been realized. Introducing the Morgenstern–Price (M‐P) assumption on the internal forces of the slip body, this study presents the three‐dimensional version of the M‐P method, which is rigorous and applicable to failure surfaces of complex shape. In the formulation, meanwhile, the volume integrals over the slip body are transformed into the boundary integrals, rendering column‐partitioning unnecessary. The methodology developed in this study can be utilized to extend those two‐dimensional rigorous methods of slices to their three‐dimensional rigorous versions.

► A 3D rigorous limit equilibrium method is proposed.
► A methodology for extending 2D rigorous methods to the 3D versions is developed.
► An example is analyzed, which can work as a benchmark for checking 3D LEMs.