Impact on loss/risk assessments of inter-model variability in vulnerability analysis

Fragility curves (FCs) constitute an emerging tool for the seismic risk assessment of all elements at risk. They express the probability of a structure being damaged beyond a specific damage state for a given seismic input motion parameter, incorporating the most important sources of uncertainties, that is, seismic demand, capacity and definition of damage states. Nevertheless, the implementation of FCs in loss/risk assessments introduces other important sources of uncertainty, related to the usually limited knowledge about the elements at risk (e.g., inventory, typology). In this paper, within a Bayesian framework, it is developed a general methodology to combine into a single model (Bayesian combined model, BCM) the information provided by multiple FC models, weighting them according to their credibility/applicability, and independent past data. This combination enables to efficiently capture inter-model variability (IMV) and to propagate it into risk/loss assessments, allowing the treatment of a large spectrum of vulnerability-related uncertainties, usually neglected. As case study, FCs for shallow tunnels in alluvial deposits, when subjected to transversal seismic loading, are developed with two conventional procedures, based on a quasi-static numerical approach. Noteworthy, loss/risk assessments resulting from such conventional methods show significant unexpected differences. Conventional fragilities are then combined in a Bayesian framework, in which also probability values are treated as random variables, characterized by their probability density functions. The results show that BCM efficiently projects the whole variability of input models into risk/loss estimations. This demonstrates that BCM is a suitable framework to treat IMV in vulnerability assessments, in a straightforward and explicit manner.