Robust reliability-based design approach by inverse FORM with adaptive conjugate search algorithm

The concept of reliability-based design (RBD) of geotechnical works has seen great success in recent years, nevertheless, its application in real-world engineering practice is still limited. This phenomenon could be mainly attributed to two aspects: the engineer's unfamiliarity of reliability algorithms even in their simplest forms, and the lack of direct connection between reliability algorithms and deterministic design tools. To promote the geotechnical RBD application, this study proposes an inverse first-order reliability method (FORM) integrating adaptive conjugate direction search technique (RBD via conjugate FORM) to solve classical RBD problems where the number of (multiple) limit state functions is usually equal to the number of unknown design parameters. Notably, the RBD via conjugate FORM can readily back-calculate those unknown design parameters subject to prescribed reliability index or probability of failure, by means of iterative evaluation of the parametric sensitivities. The proposed algorithm is first verified by several well-documented examples. Comparative studies show that when the reliability problem to solve is highly nonlinear, the RBD results based on steepest descent search direction may fall in oscillation and non-convergence, while the proposed RBD via conjugate FORM algorithm performs robustly and efficiently. It is then illustrated in combination with standalone numerical codes to conduct risk-based optimization of unknown design parameters for two soil slope stability models. The first slope RBD model achieves designing the slope angle under specified reliability index, and the second slope RBD model is to optimize multiple design parameters of the stabilization pile, which can meet different slope reliability requirements under static and seismic loading conditions simultaneously.