Limit-State Capacity Sampling and Dependence Effects in Seismic Damage-State Distributions

Abstract In simulation-based seismic fragility assessment, multilimit-state (multiLS) capacities are often sampled under simplified dependence assumptions—such as independent sampling with ordering or fully correlated thresholds—to enforce their inherent ordering constraint. These practices are not unbiased approximations and can systematically distort damage-state (DS) distributions, with direct implications for fragility curves and risk metrics. This paper develops a unified probabilistic framework that interprets the ordering constraint as conditioning of a prior joint distribution and compares three capacity sampling models: independent sampling with rejection, a fully correlated (comonotonic) model, and a nondegenerate autoregressive AR (1) model implemented via a truncated multivariate normal (TMVN) process. A dual-metric system—Wasserstein distance and Jensen–Shannon (JSD) divergence—is used to quantify “shift” and “shape” differences in DS distributions across capacity uncertainty, heteroscedasticity, demand uncertainty, and correlation strength. Results show that the independent and fully correlated schemes can induce significant biases under moderate-to-high capacity uncertainty, whereas the TMVN-based model preserves the prescribed dependence structure without pathological DS distributions, providing guidance on when refined multiLS sampling is necessary in performance-based earthquake engineering (PBEE).