The overturning fragility of a freestanding block such as a precariously balanced rock (PBR) has been parameterized as a function of a vector of ground-motion intensity measures. Methodologies are outlined to estimate the failure probabilities of such objects given their residence times. For deterministic seismic hazard analyses (DSHAs), a PBR is exposed to the scenario earthquakes that occur during its exposure time providing an estimate of the probability that the PBR survives the ensemble of events. For probabilistic seismic hazard analyses (PSHAs), the PBR overturning fragility is multiplied by the ground-motion occurrence rate from a vector-valued probabilistic seismic hazard analysis (VPSHA), yielding the marginal overturning rate for each ground-motion bin. Summing the marginal rates over all ground-motion bins produces the total overturning rate. For time-independent Poisson-based PSHA estimates, the probability of block failure can be easily calculated as a function of exposure time. This latter method is used to test VPSHA estimates similar to the 2002 U.S. Geological Survey (USGS) National Seismic Hazard Maps via PBR residence times. PBR overturning fragilities are estimated at sites in southern California near the San Andreas fault, between the San Jacinto and Elsinore faults, and near the White Wolf fault. The resulting failure probabilities for several of the PBRs are very high, suggesting that they are inconsistent with the 2002 USGS ground motions. An investigation of the hazard calculated with zero aleatory variability in the ground-motion prediction equations (GMPEs) suggests that the median ground motions or the earthquake rupture rates are too high at certain PBR sites.

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