An Unbiased Estimation of Empirical Lognormal Fragility Functions with Uncertainties on the Ground Motion Intensity Measure

In an effort to incorporate building fragility into seismic risk assessment, simple formulations of fragility functions are developed, such as a cumulative lognormal distribution, which describe the probability of damage of a building experiencing a given ground motion. We show here that when a lognormal fragility function is empirically estimated from data with uncertainty on the intensity of ground motion experienced by buildings, the estimate is biased towards fragility functions with larger variances. We show that this bias, due to the uncertainty on the ground motion, can be semi-analytically determined and we devise a methodology to correct for it.