Optimization and variational principles for the shear strength reduction method

Abstract

In this paper, a modified shear strength reduction method (MSSR) and its optimization variant (OPT‐MSSR) are suggested. The idea of MSSR is to approximate the standard shear strength reduction to be more stable and rigorous from the numerical point of view. The MSSR method consists of a simplified associated elasto‐plastic model completed by the strength reduction depending on the dilatancy angle. Three Davis' modifications suggested by Tschuchnigg et al. (2015) are interpreted as special cases of MSSR and their factors of safety are compared. The OPT‐MSSR method is derived from MSSR on the basis of rigid plastic assumption, similarly as in limit analysis. Using the variational approach, the duality between the static and kinematic principles of OPT‐MSSR is shown. The numerical solution of OPT‐MSRR is obtained by performing a regularization method in combination 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.

Zum Einfluss des Dilatanzwinkels auf die Sicherheit am Beispiel einer einfach verankerten Spundwand

“…Ein Materialmodell mit nicht assoziierter Fließregel kann aber trotzdem näherungsweise berücksichtigt werden, indem mit reduzierten Scherparametern nach Davis gerechnet wird, und damit eine assoziierte Fließregel ψ * ¼ φ * gilt, z.B. [17,[24][25][26].…”

Stability analysis of ultra-high and steep reinforced soil fills slopes based on strength reduction

“…Sysala et al proposed an improved shear strength reduction method (MSSR) and its optimized variant (OPT-MSSR). The feasibility of the method was verified through two slope stability problems [12]. Bouzid calculated the dynamic response of the Caofeidian submarine slope during a similar Tangshan earthquake, and quantitatively reflected the impact of the earthquake on the slope through displacement values [13].…”