A Practical HLRF Algorithm for Slope Reliability Analysis

The first-order reliability method (FORM) can provide useful information such as reliability index and design point for a reliability based design of slopes. Thus practical FORM-based slope reliability analysis is in great demand for practicing engineers. One difficulty for FORM-based slope reliability analysis is that the slope problem can be very complicated and some standalone numerical packages which are not designed with probabilistic considerations have to be resorted to. Another difficulty lies in the dealing with correlated non-Gaussian random variables which usually involves mathematical transformation of the random variables to their independent standard normal counterparts (in u-space). In the literature, the first difficulty is usually resolved by the use of a surrogate model to estimate the complicated (usually implicit) limit state function (LSF), and the second is resolved by developing FORM algorithms that can be directly implemented in the original space of random variables (x-space, non-Gaussian type), for example, with the Low and Tang's constrained optimization approach. Then a question is can we have a practical FORM algorithm in x-space that can be easily integrated with standalone numerical packages with no surrogate models? To answer this question, this paper presents a simplified HLRF algorithm for FORM. Naturally, the new algorithm is simply formulated in x-space and requires neither transformation of correlated random variables nor optimization tools. The algorithm is particularly useful for reliability analysis involving correlated nonnormals subjected to implicit LSF. The convergence of the algorithm can be easily improved by adjusting the step length during the iteration. It is first verified using a simple example with closed-form solution. Through perturbation analysis in x-space, it is then illustrated for case studies of earth slope reliability with both limit equilibrium and finite element analyses.