The role of epsilon for the identification of groups of earthquake inputs of given hazard

Response spectra have been used in the years not only to obtain estimations of the seismic response for given dynamic system in response spectral analysis, but also as a useful reference for the identification of design time-history inputs (when time-history analysis are required). This second use is somehow improper. Indeed, uniform hazard response spectra are capable of providing information regarding the value of the spectral acceleration (characterized by a given probability of exceedance) for a given precise system period, but may prove to be misleading when the overall shape of the design response spectra is used to identify groups of time-history inputs. In this paper, a tool which can be used for the identification of groups of design time-history earthquake inputs for Performance-Based Seismic Design applications is developed.First, a peculiar Probabilistic Seismic Hazard Analysis, which allows to explicitly handle (exclude/include and numerically quantify) the epistemic uncertainty due to the error of the ground-motion prediction (attenuation) model and to clearly distinguish it from the space-time aleatory variability, is developed.Second, grounded on this Probabilistic Seismic Hazard Analysis, a relationship is obtained between a given hazard level and the statistical characteristics of the ensemble of response spectral ordinates, as computed at multiple periods. This allows to identify the characteristics that must be possessed by the groups of design earthquake inputs, by means of a newly introduced tool, herein defined as “spectral cloud”.