A procedure for the determination of reduced-variance equal-probability response spectra for Performance Based Seismic Design

This paper aims at illustrating a method for determining the probability functions (PDF and/or CDF) of the peak ground acceleration (PGA) and peak ground velocity (PGV) due to the seismic action at a specific site, over a given observation time, for Performance Based Seismic Design purposes. The method is based upon the Cornell widely upheld methodology (1968), specifically updated to take into account the latest contributions in geophysics developed for the Italian territory. This methodology assimilates the occurrence of seismic events to Poisson processes and characterises the magnitude return period of each seismogenetic area using the Gutenberg-Richter law (1954). At this regard, the authors propose the innovative use of the completeness analysis suggested by Mulargia, Tinti and Gasperini (1985) for the correct interpretation of the seismic catalogues. The method makes use of specific attenuation laws developed for the European territory for both PGA and PGV. The method treats the distance of the site from the epicenter as a random variable, by subdividing the territory in circular sectors, annuluses and annulus portions. This treatment allows an exact determination of the PDF and CDF of PGA and PGV at the site. The statistical characterisations of PGA and PGV thus obtained feature the same accuracy. This allows to use the couples PGA-PGV (characterised by given probabilities of occurrence) as a vectorial intensity measure IM (R. Bertero and V. Bertero 2002) for the determination of the correct “bin” of earthquake inputs (P. Giovenale et al. 2004) for probabilistic design approach in performance based seismic engineering. The paper presents an illustrative example (developed for the Italian territory) of how this joined use of PGA and PGV as IM allows to obtain earthquake bins characterised by response spectra with a reduced coefficient of variation.