# The peak over the design threshold in strong earthquakes

## Abstract

In state-of-the-art seismic design, reference seismic actions are based on probabilistic seismic hazard assessment, which provides the ground-motion intensity corresponding to a reference return period of exceedance at the site. Exceedance of elastic actions, which is systematically observed in the epicentral areas of strong earthquakes, does not necessarily mean violation of the structural design limit-state; nevertheless, in such a case, the safety margins inherent to design are left to other factors beyond the elastic spectrum, which are, in general, not explicitly controlled. Therefore, it might be useful to quantify the expected (i.e., mean) amount of ground-motion intensity exceedance in earthquakes for which the design spectrum is not conservative. In fact, this study, with reference to Italy, provides and discusses the map of the expected value of acceleration, given the exceedance of the design spectra at any site in the country. It is shown, among other results, that: (1) the expected exceedance varies significantly from site-to-site across the country despite the same return period of the threshold is considered everywhere, (2) its pattern is opposite to that of the \(\varepsilon\) from disaggregation, and (3) the peak-over-the-threshold can be larger than 2.5 times than the corresponding ordinate of the design spectrum with 475 years return period. These results may be informative about what to expect for code-conforming structures in terms of seismic actions during strong earthquakes, that is, those able to cause exceedance of design elastic spectra.

## Keywords

Performance-based seismic design Building code Seismic structural safety## Notes

### Acknowledgements

This article was developed within the activities of the ReLUIS-DPC 2014–2018 research project, funded by *Presidenza del Consiglio dei Ministri* – *Dipartimento della Protezione Civile*. The conclusions and opinions expressed, does not necessarily correspond to those of the funding entity. The helpful comments by Simone Barani (*Università degli Studi di Genova*) and Laurentiu Danciu (*Swiss Seismological Service*) are also acknowledged.

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