Hierarchical Bayesian framework for uncertainty reduction in the seismic fragility analysis of concrete gravity dams

Concrete gravity dams are critical infrastructures for communities to meet the basic human needs as well as rising standards of living. Most of the existing concrete gravity dams in Italy were built before the introduction of seismic regulations. Although no concrete gravity dams have as yet suffered a catastrophic collapse during or after a seismic event, their preservation remains a key aspect for communities, also in view of that older dams may have deteriorated to a critical level. For these reasons, researchers and practitioners in dam engineering are working to improve seismic fragility, and ultimately seismic risk, assessment procedures. Since no case histories are available, numerical modelling plays an important role, even though many uncertainties can affect the models and then the estimation of the seismic fragility. This paper presents a robust hierarchical Bayesian framework for the calibration of dynamic parameters of dam numerical models based on ambient vibrations, which allows an analyst to reduce uncertainties in the seismic fragility derivation. A probabilistic predictive model of the dam modal behaviour based on the general Polynomial Chaos Expansion is adopted in order to reduce the computational burden and a numerical algorithm for the solution of the inverse problem based on Markov Chain Monte Carlo is also presented. The proposed approach is applied to an existing large concrete gravity dam in Italy, and the effect of epistemic uncertainty reduction is finally evaluated in terms of fragility curves.