Prediction relationships for a vector-valued ground motion intensity measure accounting for cumulative damage potential

Vector-valued ground motion intensity measures have been extensively investigated recently. Proposed measures are mainly related to pairs of spectral ordinates because the spectral shape has been shown to be useful in the probabilistic assessment of structural and non-structural response of buildings. This is especially appropriate in the case of structures following modern earthquake resistant design principles, in which structural damage is mainly due to displacements experienced in non-linear behavior. Although it is generally believed that, under some hypotheses, integral ground motion parameters associated to duration are less important for structural demand assessment with respect to peak quantities of ground motion, there are cases in which the cumulative damage potential of the earthquake is also of concern. In this paper the joint distribution of peak ground acceleration (PGA) and a parameter which may account for the cumulative damage potential of ground motion, is investigated with respect to some engineering seismology issues. The chosen energy related measure is the so-called Cosenza and Manfredi index (ID). A ground motion prediction relationship has been retrieved for ID on the basis of an empirical dataset of Italian records already used for well known attenuation laws proposed in the past by other researchers. Subsequently, the residuals have been tested for correlation and for joint normality. The study allowed to obtain distributions of ID conditional on PGA and on the corresponding design earthquake, in terms of magnitude and distance, from hazard disaggregation.