# Fragility curves for risk-targeted seismic design maps

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## Abstract

Seismic design using maps based on “risk-targeting” would lead to an annual probability of attaining or exceeding a certain damage state that is uniform over an entire territory. These maps are based on convolving seismic hazard curves from a standard probabilistic analysis with the derivative of fragility curves expressing the chance for a code-designed structure to attain or exceed a certain damage state given a level of input motion, e.g. peak ground acceleration (PGA). There are few published fragility curves for structures respecting the Eurocodes (ECs, principally EC8 for seismic design) that can be used for the development of risk-targeted design maps for Europe. In this article a set of fragility curves for a regular three-storey reinforced-concrete building designed using EC2 and EC8 for medium ductility and increasing levels of design acceleration \((\hbox {a}_\mathrm{g})\) is developed. These curves show that structures designed using EC8 against PGAs up to about 1 m/s\(^{2}\) have similar fragilities to those that respect only EC2 (although this conclusion may not hold for irregular buildings, other geometries or materials). From these curves, the probability of yielding for a structure subjected to a PGA equal to \(\hbox {a}_\mathrm{g}\) varies between 0.14 (\(\hbox {a}_\mathrm{g}=0.7\) m/s\(^{2})\) and 0.85 (\(\hbox {a}_\mathrm{g}=3\) m/s\(^{2})\) whereas the probability of collapse for a structure subjected to a PGA equal to \(\hbox {a}_\mathrm{g}\) varies between 1.7 \(\times 10^{-7}\) (\(\hbox {a}_\mathrm{g}=0.7\) m/s\(^{2})\) and 1.0 \(\times 10^{-5}\) (\(\hbox {a}_\mathrm{g}=3\) m/s\(^{2})\).

## Keywords

Seismic risk Fragility curves Eurocode 8 (EC8) Risk-targeting Reinforced concrete Eurocode 2 (EC2)## Notes

### Acknowledgments

This article was supported by the internal BRGM research programme VULNERISK/MULTIRISK/MIR2 2012 and 2013. We thank Pierre Gehl for his help in conducting the analyses presented here and his comments on an earlier version of this article. Finally, we thank Helen Crowley and an anonymous reviewer for their constructive and detailed comments on a previous version of this article.

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