Testing PSHA Output via Precariously Balanced Rocks

Purvance (2005) has shown that the overturning responses of precariously balanced rocks (PBRs) depend on the PBR shapes, sizes, and the vector of ground motion intensity measures including PGA and either PGV, SA@1sec, or SA@2sec. This formulation allows one to quantify the overturning probability of an object that has been exposed to a ground motion time history with specified peak parameters (e.g. PGA and PGV). Vector-valued PSHA (VPSHA) provides a methodology to estimate the rate of occurrence of all ground motions. Combining the VPSHA output with the PBR fragility results in the rate of PBR overturning. In this way, one can compare the PBR age with the estimated failure date given the assumptions inherent in the VPSHA calculation. This study focuses on the variability of estimated failure dates of PBRs as a function of attenuation relations utilized in the VPSHA calculations. The following attenuation relations have been investigated: Abrahamson and Silva (1997), Boore et al. (1997), Abrahamson (2005), and Gregor et al. (2002). The Boore et al. (1997) and Abrahamson (2005) relations produce ground motion models that are more consistent with the PBRs in southern California than the Abrahamson and Silva (1997) and Gregor et al. (2002) relations. It is apparent that the addition of recent data (e.g. Chi-Chi, Izmit) in the development of the Abrahamson (2005) attenuation relation significantly affects the VPSHA output. These findings highlight the utility of this methodology to test alternate attenuation relations such as those produced by the NGA initiative. In addition, varying RELM models may be assessed for consistency with PBRs via the described methodology.