When evaluating the probabilistic seismic performance of a structure in the context of Performance-Based Earthquake Engineering (PBEE) applications, only estimates of the true response are obtained due to the finite size of the group of records selected to represent the seismic scenario. The proposed study examines the variability of these estimates, in terms of fragility parameters and failure rates, by implementing a procedure that creates seismic scenario-consistent groups of records based on regrouping criteria applied to a larger set of records. The results are then compared to those obtained from a statistical approach based on the bootstrap resampling procedure, whose validity is disputed due to its incompatibility with common applications involving probabilistic seismic performance assessment. Given that bootstrap resampling assumes that each bootstrap sample is random, this condition is incompatible with requirements involving the need to match specific spectral statistics of the group of records with a target spectrum. Due to the increased computational cost of the procedure based on regrouping criteria, the effect of this incompatibility is analysed by examining the agreement between the two procedures for several case studies and the conditions under which bootstrap resampling leads to a reduced level of error. Further insights about the variability of the estimates are obtained by analysing scenarios with deterministic and probabilistic thresholds of the limit state capacity. Among other aspects, the results show that, for both capacity thresholds, bootstrap resampling can provide acceptable results as long as a sufficient number of ground motions and number of stripes are used.

Introduction

Practical guidelines provided by the Performance-Based Earthquake Engineering framework for the probabilistic assessment of the seismic performance of a building [1] draw attention to various sources of uncertainty. Common sources are those associated with the seismic input, usually expressed by the seismic hazard uncertainty [2] and the record-to-record variability [3], the structural modelling, such as the variability of geometric properties and material constitutive laws [1], and limit state definitions, like the capacity modelling errors [4]. These uncertainties can be accounted for during the structural analysis of the numerical model or in a subsequent post-processing stage of the analysis results. Depending on the stage of the analysis in which the different uncertainties are accounted for, their combination can be performed using Monte Carlo simulation-based techniques or alternative simplified methods, such as first-order second-moment techniques (e.g. see [5–۹]). Nevertheless, it is commonly agreed that accounting for uncertainties changes the seismic demand, the fragility function parameters [10], the associated seismic risk [11,12], as well as the expected losses [13].