The “spectral cloud” for the identification of groups of earthquake inputs of given hazard

Within a Performance Based Seismic Design framework, in order to evaluate the seismic performance of a given structure in probabilistic terms, it is fundamental to associate a probability of occurrence/exceedance with a given structural response parameter, often referred to as “Engineering Demand Parameter” (EDP). This is carried out by means of numerical non-linear dynamic analyses which make use, as seismic input(s), of properly chosen groups of accelerograms characterised by given hazard. These groups have been referred in scientific literature to as “earthquake bins” and, for sake of clarity, will be herein referred to as “groups of uniform hazard time-histories”. The choice of the uniform hazard time-histories is deeply rooted upon their probabilistic identification. However, the hazard level cannot be directly associated to the time-histories, whilst it can be associated, by means of Probabilistic Seismic Hazard Analyses (PSHA), to earthquake “intensity measures” (IMs), which consist of scalar or vector-valued combinations of selected ground motion parameters (GMPs) associable to a given probability of exceedance. In recent years, many research works have focused on the identification of the optimal IM for the identification of groups of uniform hazard time-histories. Among all possible and commonly used IMs, the spectral acceleration, at a specified period, has been recently suggested as optimal. With reference to the spectral acceleration, the uniform hazard spectrum has been obtained and widely used for the identification of groups of uniform hazard time-histories. However, due to its intrinsic properties, such use of the uniform hazard spectrum presents limitations, which make it meaningless for structures sensitive to the response spectra over a period range rather than a single period (i.e. non-linear systems …). Therefore, new tools should be introduced in order to correctly face the problem of the identification of uniform hazard time-histories which can be used, in general, for both linear and non-linear systems.