Peak-over-threshold: Quantifying ground motion beyond design

In performance-based seismic design, as adopted by several building codes worldwide, the structural performance is verified against ground motions that have predetermined exceedance return periods at the site of interest. Such a return period is evaluated by means of probabilistic seismic hazard analysis (PSHA), and the corresponding ground motion is often represented by the uniform hazard spectrum (UHS). The structural performance for ground motions larger than those considered in this design approach is, typically, not explicitly controlled under the assumption that they are sufficiently rare. On one hand, this does not achieve uniform safety at sites characterized by different design ground motions corresponding to the same return period; on the other hand, exceedances of the design spectra are systematically observed over large areas, for example in Italy. The latter issue is because of the nature of UHS, the exceedance of which is likely-to-almost-certain when the construction site is in the epicentral area of moderate-to-high magnitude earthquakes (ie, the design spectrum may be not conservative at these locations), especially if PSHA is based on seismic source zones. The former is partially because of the systematic difference of ground motions for return periods larger than the design one at the different sites. Quantification of the expected ground motion given the exceedance of the design ground motions (ie, the recently introduced as the expected peak-over-threshold or POT) can be of help in quantitatively assessing these issues. In the study, a procedure to compute the POT distribution is derived first; second, POT spectra are introduced and used to help understanding why and how seismic structural reliability of code-conforming structures decreases as the seismic hazard of the site increases; third, expected and 95th percentile POT maps are shown for Italy to discuss how much high hazard sites are exposed to much larger peak-over-threshold with respect to mid-hazard and low-hazard sites; finally the POT is discussed with respect to the slope of the hazard curve (in log-log scale) at the threshold, a known proxy for ground motion beyond design. All data presented in the maps are made available for the interested reader as a supplemental archive.