A multidimensional discrete sampling method for deriving regional level seismic fragility and losses of RC existing buildings

The paper presents a framework for deriving regional seismic fragility and direct economic losses for reinforced concrete buildings based on a multidimensional discrete sampling of the available exposure data. The main challenge posed by the paper consists of considering multimodality and multidimensionality of exposure data, which at regional level assume high relevance, especially when data derive from different sources. Usually, the exposure model constitutes a high dimensional space and the approximation to a multidimensional continuous space could sensibly affect the accuracy of results (e.g., loss of modes, variability not captured). To comply with data heterogeneity, the proposed methodology consists of sampling data from one or more multidimensional discrete spaces through an iterative method to generate a Markov chain converging towards an approximated high dimensional joint distribution. To ensure a robust comparison between target and empirical distributions and to determine the sub-optimal number of representative samples, the Kullback-Leibler divergence is employed. Sampled data are used to automatically generate numerical models to investigate through nonlinear time history analyses. The results are post-processed to obtain overall fragility and losses metrics, according to the frequency of each configuration in the sample space. The proposed approach was tested on the case of Puglia region, Southern Italy, providing specific fragility and loss parameters according to the actual distribution of the available data.