Stability and Factor of Safety of Gravity-Retaining Structures Using the Strength Reduction Method

The stability of gravity-retaining structures has traditionally been checked within the limit equilibrium framework. However, limit equilibrium methods require that prior assumptions be made regarding the collapse mechanism of the wall–soil system. Using the strength reduction method (SRM) with finite-element analysis (FEA) to analyze the stability of a wall does not require the collapse mechanism of the wall–soil system or even its general form or location to be known a priori; instead, it results from the analysis automatically. This paper uses the results of SRM-based FEA simulations performed using a sophisticated two-surface-plasticity sand model to evaluate the stability and factor of safety of gravity-retaining walls. The SRM-based FEA simulations were performed via ABAQUS and Python scripting using novel strength reduction techniques for both the backfill soil and the gravity wall. The generalized bisection method was used as the search algorithm to find the minimum backfill relative density $D_{R,\min }$ or the minimum wall width $B_{\min }$ just prior to the instability and collapse of the wall–soil system. The stability of the wall–soil system was detected based on the convergence (or lack thereof) of the Newton–Raphson (N-R) iterative solution implemented in an implicit FE modeling scheme. The proposed approach does not rely on the assumption that a wall would independently achieve overturning, sliding, or bearing capacity limit states and is therefore more accurate in describing wall stability.