Bayesian Updating of Fragilities with Application to RC Frames

Abstract

This paper presents a Bayesian statistical analysis method for updating earthquake ground motion versus damage relationships in the form of fragility curves and for estimating confidence bounds on these fragility curves. As building damage data from past earthquakes become increasingly available, these data need to be combined with analytical fragility curves to arrive at more robust fragility curves. The Bayesian method provides a technique for updating these relationships. The parameters of analytical fragility curves are used to estimate the prior distributions of damage in the Bayesian analysis. In an earlier paper, Singhal and Kiremidjian presented a general methodology for the development of analytical motion-damage relationships in terms of seismic fragility curves and damage probability matrices. Data on building damage are used to estimate the likelihood functions. The Bayesian method for fragility analysis is illustrated by using the damage data on reinforced concrete (RC) frame buildings from the January 17, 1994 Northridge, Calif. earthquake. The uncertainties in the fragility curves are represented by confidence bounds around the median fragility curves.