A layer assigned probability space partition method for structural small failure probability problem

The Physical Synthesis Method (PSM) stands out as a robust framework for conducting structural reliability analyses due to its clear conceptual foundation. However, this approach often necessitates significant computational resources when addressing scenarios with small failure probabilities. In response to this challenge, this study introduces a layer assigned probability space partition method designed to identify pivotal points based on the ultimate bearing capacity failure criterion of structural components within the PSM framework. Drawing inspiration from Harbitz's β-sphere, this method effectively utilizes the minimum reliability index of components to discern essential representative points within the probability space, thus streamlining computations. The efficacy of this approach is showcased through two case studies: a simply supported beam and a six-story reinforced concrete frame. The outcomes demonstrate that the proposed method, when integrated with PSM, exhibits a substantial enhancement in efficiency compared to the conventional Monte Carlo method. Besides, under equivalent computational resources, it achieves superior computational accuracy compared to the importance sampling method, particularly in scenarios with small failure probabilities. Furthermore, by introducing the notion of a common safe domain, this method addresses challenges in structural reliability analyses involving multiple failure surfaces.