Eigenvalue Problem from the Stability Analysis of Slopes

Of the existing methods for the three-dimensional (3D) limit equilibrium analysis of slopes, none can simultaneously satisfy all six equilibrium equations. Except for Fellenius’ method that satisfies only one condition of moment equilibrium, all these methods could encounter numerical problems in their applications. Based on the global analysis procedure that considers the whole sliding body instead of individual columns as the loaded body, it is shown that the 3D limit equilibrium analysis of slopes simply reduces to the solution of a generalized eigenvalue problem in which the largest real eigenvalue is just the factor of safety (FOS). The proposed solution is rigorous and can accommodate any shape of slip surfaces. Under undrained conditions, the problem has a unique solution and the FOS has an explicit expression. In addition, through transforming the volume integrals over the sliding body into the boundary integrals, the proposed method does not need to partition the sliding body into columns.