Effect of 2D spatial variability on slope reliability: A simplified FORM analysis

TLDR

The paper introduces a simplified HLRF iterative algorithm for first‑order reliability method (FORM) to meet the high demand for reliability‑based slope design. The algorithm is formulated directly in x‑space, requiring no transformation of correlated variables or optimization tools, and its solution can be refined by iteratively adjusting the step length; it was applied via direct perturbation analysis to a case study of earth slope reliability that fully considered soil uncertainty and spatial variability. The method is particularly useful for practicing engineers using standalone deterministic numerical packages, as shown by its successful application to an earth slope reliability case study that incorporated complete soil uncertainty and spatial variability.

Abstract

To meet the high demand for reliability based design of slopes, we present in this paper a simplified HLRF (Hasofer–Lind–Rackwitz–Fiessler) iterative algorithm for first-order reliability method (FORM). It is simply formulated in x-space and requires neither transformation of correlated random variables nor optimization tools. The solution can be easily improved by iteratively adjusting the step length. The algorithm is particularly useful to practicing engineers for geotechnical reliability analysis where standalone (deterministic) numerical packages are used. Based on the proposed algorithm and through direct perturbation analysis of random variables, we conducted a case study of earth slope reliability with complete consideration of soil uncertainty and spatial variability.