Optimization and variational principles for the shear strength reduction method

TL;DR

This paper introduces a new optimization-based shear strength reduction method for slope stability analysis that avoids elasto-plastic analysis, using duality principles, regularization, and finite element techniques, validated on real slope data.

Contribution

The paper develops a novel OPT-SSR method based on optimization principles, providing an efficient alternative to traditional shear strength reduction approaches.

Findings

The OPT-SSR method is well-defined and mathematically sound.

Numerical solutions are effectively obtained using regularization and finite element methods.

Application to real slope data demonstrates the method's practical utility.

Abstract

This paper is focused on the definition, analysis and numerical solution of a new optimization variant (OPT) of the shear strength reduction (SSR) problem with applications to slope stability problems. This new variant is derived on the basis of recent results by Tschuchnigg et al. 2015, where limit analysis and a modified Davis approach were used for approximation of the standard SSR method. The OPT-SSR method computes the factor of safety without performing an elasto-plastic analysis, similarly as in limit analysis. It is shown that this optimization problem is well-defined. Next, the duality between the static and kinematic principles of OPT-SSR is derived. For the numerical solution, a regularization method is introduced and analyzed. This method is combined with the finite element method, mesh adaptivity and a damped Newton method. In-house codes (Matlab) are used for the implementation of this solution concept. Finally, two slope stability problems are considered, one of which follows from analysis of a real slope. The softwares packages Plaxis and Comsol Multiphysics are used for comparison of the results.