A three-dimensional rigorous method for stability analysis and its application

Most traditional methods of three-dimensional (3D) limit equilibrium analysis of slopes have difficulties in satisfying all the equilibrium conditions and in encountering numerical problems in their applications. In this study, the traditional 3D column method is replaced by a new method, providing a better approach to obtain the 3D safety factor. By constructing the normal stresses over the slip surface and considering the equilibrium conditions of the whole sliding body, a 3D slope stability analysis method is proposed, which simultaneously satisfies all six equilibrium conditions and accommodates slip surfaces of any shape. Inter-column force functions are assumed and the distribution function of the normal stress over the slip surface, containing five undetermined parameters, is obtained based on force equilibrium conditions of a typical discretized column. All six equilibrium equations are established considering the whole sliding body in equilibrium, and then the 3D factor of safety is derived using an analytic method. A rigorous and explicit solution is realized and the numerical problems in the 3D analysis procedures of the columns, such as non-convergence and failure of the solution, are thoroughly overcome. Some examples are given to verify the present method. The results demonstrate that the present method is more reliable compared with several other 3D slope stability analysis methods. Finally, this method is successfully applied in stability analysis of the Jinpingzi instability slope. The present 3D slope stability analysis method is easy to implement in computer models and can be widely used by geotechnical engineers for slope design and treatment of landsides.