Assessing structural vulnerability against earthquakes using multi-dimensional fragility surfaces: A Bayesian framework

The present paper advocates a probabilistic framework for assessing structural vulnerability against earthquakes. This is justified by the significant randomness that characterizes not only the earthquake excitation (amplitude, frequency content, duration), but also the structural system itself (i.e. stochastic variations in the material properties). Performance predictions can readily be summarized in the form of fragility curves which express the probability of exceeding various damage levels (from minor to collapse) with respect to a metric of the earthquake intensity. In this paper, a Bayesian framework is proposed for the derivation of fragility curves which can produce estimates irrespective of the amount of data available. It is particularly flexible when combined with Markov Chain Monte Carlo (MCMC) techniques and can efficiently provide credible intervals for the estimates. Furthermore, a general procedure based on logistic regression is illustrated that can lead in a principled manner to the derivation of fragility surfaces which express the probability of exceeding a damage level with respect to several measures of the earthquake load and can thus produce more accurate predictions. The methodologies presented are illustrated using data generated from computational simulations for a structure on top of a saturated sand deposit which is susceptible to liquefaction.