Probabilistic Seismic Demand Analysis of Structures Using Reliability Approaches
Mehdi Kia, Ali Amini, Mahmoud Bayat, Paul Ziehl
Abstract
The Probabilistic Seismic Demand Analysis (PSDA) which is frequently implemented in the first generation performance-based earthquake engineering quantifies seismic behavior of a structure by computing mean annual frequency of exceeding a specific value of a desired demand parameter given all anticipated earthquakes. This framework, based on the total probability integration formula, provides a technical basis on which aleatory uncertainties, uncertainties originated due to inherent randomness of the phenomena, are explicitly addressed. However, variability in the mean value of different model parameters, referred to as epistemic uncertainties and mainly due the finite-sample size of observations, is neglected. In this study, as an alternative to total probability integration, a reliability-based formulation tailored to effortlessly reflect both aleatory and epistemic uncertainties is put-forward to perform unified PSDA. Next, as an application of the proposed methodology, a reliability-based seismic demand curve of a 4-story example building is developed. Results demonstrate that the Second-Order Reliability Method (SORM) and important sampling method (ISM) along with multi-step Monte Carlo simulation (MSMCS) methods are appropriate candidates for computing reliability-based PSDA with differentiable and nondifferentiable performance functions, respectively.