Efficient Residual Displacement‐Based Seismic Fragility Assessment Procedure for Nonlinear Systems Utilizing the Total Probability Theorem

ABSTRACT Nonlinear structural system inevitably experiences residual displacement (RD) following severe earthquake event, which compromises post‐earthquake functionality and increases structural fragility. Despite its importance, RD has received limited attention compared to maximum displacement (MD). This study proposes an innovative procedure to evaluate RD‐based seismic fragility using the total probability theorem with MD as an intermediate variable. The distribution of RD given MD is described by q‐Weibull distribution in this procedure, and RD‐based fragility is then determined through combining this distribution with the intensity measure (IM)‐MD relationship obtained from cloud method. This approach not only mitigates the limitations of conventional cloud method but also significantly reduces computational efforts compared with incremental dynamic analysis (IDA). Additionally, the procedure is extended for dual‐criteria seismic fragility assessment, incorporating both RD and MD. The effectiveness of the proposed q‐Weibull‐based model is validated against time history analysis results and is shown to outperform conventional bivariate lognormal models in capturing joint MD‐RD distributions. Finally, application to a prototype global bridge with laminated rubber bearings demonstrates the procedure's accuracy and practicality for complex practical structures.