Advanced continuation and iterative methods for slope stability analysis in 3D

This paper addresses the solution of slope stability problems in 3D using the finite element method and incremental procedures like the shear strength reduction or limit load methods. We build on Mohr–Coulomb plasticity, Davis’ modifications of the non-associated plastic flow rule and recent mathematical results, which relate the factor of safety (FoS) with convex optimization. A complex solution concept is presented in detail and completed with in-house developed, publicly available open-source MATLAB codes. The concept consists of a combination of indirect continuation techniques, inexact Newton-like solvers and deflated Krylov methods with preconditioners. Further, mesh adaptivity is used to reduce overestimation of FoS and determine failure zones more accurately. The solution concept is tested on slope stability benchmarks in 3D and its efficiency is demonstrated. Numerical results are validated against either literature or software COMSOL Multiphysics.