Novel copula-based iHLRF-X algorithm for assessing reliability of geo-structures

This study presents a simple and explicit iterative formula (called copula-based iHLRF-X algorithm) to directly solve the copula-based first-order reliability method (FORM) in the original random variable space (X-space), i.e. the physical parameter space. Compared with those iterative algorithms developed in the independent standard normal space (U-space), the proposed method is more advantageous for geotechnical practitioners as it bypasses cumbersome variable transformations. First, a brief introduction to the copula-based method for modelling the joint probability distribution is provided. Second, the conventional iHLRF algorithm for the FORM in the U-space is reviewed. Third, a novel copula-based iHLRF-X algorithm and its implementation procedure are proposed. Finally, two representative geotechnical examples, namely a semi-gravity retaining wall and a multi-layered soil slope, are presented to verify the proposed algorithm. The results imply that the proposed algorithm exhibits high accuracy and computational efficiency in addressing geotechnical reliability problems involving explicit and implicit performance functions. The choice of copulas remarkably affects the reliability of geo-structures, particularly under a strong degree of correlation and a high reliability level. Furthermore, the Gaussian dependence structure implied in the Nataf distribution may overestimate the reliability of geo-structures, thereby rendering the geotechnical design unreliable.