Seismic hazard analysis for alternative measures of ground motion intensity employing stochastic simulation methods

The wide application of spectral acceleration as a ground motion intensity measure (IM) is in part due to the fact that various empirical (attenuation) relationships, that relate spectral acceleration to ground motion source and path parameters, are already available and tabulated. In the recent years, various scalar and vector IM’s have been proposed and shown to be more suitable than spectral acceleration; however, their wider use is hindered by limited availability of site-specific empirical attenuation relations for these variables. Subset Simulation is an advanced simulation method which is particularly efficient for calculating small failure probabilities. The (target) failure region in the Subset Simulation is regarded as the last in a sequence of nested intermediate failure regions in which, a Markov Chain Monte Carlo algorithm is used to sample from the original probability distribution conditioned on the previous intermediate failure region in the sequence. This study demonstrates that Subset Simulation, based on a stochastic model for ground motion, can be effectively employed in order to develop hazard curves for alternative scalar and vector IM’s. Two example applications are illustrated in which hazard curves are derived for a scalar structure-specific IM that includes the effect of both higher modes and inelastic response and a vector IM consisting of spectral acceleration and spectral shape for a California site. The algorithm is efficient and relatively straight-forward, however, some care should be taken in defining the sequence of nested failure regions which guide the simulation procedure into regions with small exceedance probabilities.