Vector-valued ground-motion intensity measures (IMs) have been the focus of a significant deal of research recently. Proposed measures are mainly functions of spectral ordinates, which have been shown to be useful in the assessment of structural response. This is especially appropriate in the case of structures following modern earthquake-resistant design principles, in which structural damage is mainly caused by peak displacements experienced during nonlinear dynamics. On the other hand, there may be cases in which the cumulative damage potential of the earthquake is also of concern, even if it is generally believed that integral ground-motion IMs, associated with duration, are less important with respect to peak parameters of the record. For these IMs, it seems appropriate to develop conditional hazard maps, that is, maps of percentiles of a secondary IM (e.g., duration-related) given the occurrence or exceedance of a primary parameter (e.g., peak acceleration), for which a design hazard map is often already available. In this paper, this concept is illustrated, and conditional hazard is developed for a parameter, which may account for the cumulative damage potential of ground motion, the so-called Cosenza and Manfredi index (ID), given peak ground acceleration (PGA). To this aim, a ground-motion prediction relationship was derived for ID first. Subsequently, the residuals of PGA and ID were tested for correlation and for joint normality. Finally, the study obtained analytical distributions of ID conditional on PGA and on the corresponding design earthquake in terms of magnitude and distance from hazard disaggregation. As shown by the application to the Campania region (southern Italy), ID maps conditional on the code design values of PGA may be useful, for example, for a more refined ground-motion record selection as an input for nonlinear dynamic analysis of structures.

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