Abstract
This article presents a method for the development of vector-valued fragility functions, which are a function of more than one intensity measure (IM, also known as ground-motion parameters) for use within seismic risk evaluation of buildings. As an example, a simple unreinforced masonry structure is modelled using state-of-the-art software and hundreds of nonlinear time-history analyses are conducted to compute the response of this structure to earthquake loading. Dozens of different IMs (e.g. peak ground acceleration and velocity, response spectral accelerations at various periods, Arias intensity and various duration and number of cycle measures) are considered to characterize the earthquake shaking. It is demonstrated through various statistical techniques (including Receiver Operating Characteristic analysis) that the use of more than one IM leads to a better prediction of the damage state of the building than just a single IM, which is the current practice. In addition, it is shown that the assumption of the lognormal distribution for the derivation of fragility functions leads to more robust functions than logistic, log-logistic or kernel regression. Finally, actual fragility surfaces using two pairs of IMs (one pair are uncorrelated while the other are correlated) are derived and compared to scalar-based fragility curves using only a single IM and a significant reduction in the uncertainty of the predicted damage level is observed. This type of fragility surface would be a key component of future risk evaluations that take account of recent developments in seismic hazard assessment, such as vector-valued probabilistic seismic hazard assessments.
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Acknowledgments
The work presented in this article has been partially supported by the French Research National Agency (ANR) through the PGCU-2007 program (Project: A mechanical approach for evaluating seismic vulnerability of masonry structures, EVSIM, under grant number: ANR-07-PGCU-002), and the PERPETUATE (Performance-based approach to earthquake protection of cultural heritage in European and Mediterranean countries) project of the EC-Research Framework Programme FP7. In addition, we thank Guillaume Pousse, for his computer program to simulate ground motion, and Prof. Sergio Lagomarsino, for sharing with us the research and development version of TREMURI. Finally, we thank the two anonymous reviewers for their constructive comments on a previous version of this article.
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Gehl, P., Seyedi, D.M. & Douglas, J. Vector-valued fragility functions for seismic risk evaluation. Bull Earthquake Eng 11, 365–384 (2013). https://doi.org/10.1007/s10518-012-9402-7
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DOI: https://doi.org/10.1007/s10518-012-9402-7