Probability density function of the peak ground acceleration due to the seismic action

In order to evaluate the structural reliability of systems with respect to seismic risk it is necessary to know the statistic characteristics of both structural resistance and of the dynamic loading (i.e. probability distribution functions). The analysis here presented develops the probability distribution function (PDF) of the Peak Ground Acceleration (PGA), for a given site, over a given period of observation. This analysis was based on Cornell's methodology, specialized using the most recent scientific developments and specifically updated to take into account the latest contributions in geophysics developed for the Italian peninsula. The probability density function PDF (and the corresponding cumulative distribution function CDF) is given here for the earthquake induced Peak Ground Acceleration (PGA) at a given site due to the activity of a single Seismo-Genetic Zone ("Zona Sismogenetica") over a period of time, with the simultaneous treatment of the magnitude MS and the distance R of the site of interest from the epicenter, as random variables. It is also shown that the CDF of the PGA due to the seismic activity of all Seismo-Genetic Zones is given by the product of all CDFs relative to each single Seismo-Genetic Zone.