Hazard characterization for alternative intensity measures using the total probability theorem

Since their inception in the 1980s, simplified procedures for the analysis of liquefaction hazards have typically characterized seismic loading using a combination of peak ground acceleration and earthquake magnitude. However, more recent studies suggest that certain evolutionary intensity measures (IMs) such as Arias intensity or cumulative absolute velocity may be more efficient and sufficient predictors of liquefaction triggering and its consequences. Despite this advantage, widespread hazard characterizations for evolutionary IMs are not yet feasible due to a relatively incomplete representation of the ground motion models (GMMs) needed for probabilistic seismic hazard analysis (PSHA). Without widely available hazard curves for evolutionary IMs, current design codes often rely on spectral targets for ground motion selection and scaling, which are shown in this study to indirectly result in low precision of evolutionary IMs often associated with liquefaction hazards. This study presents a method to calculate hazard curves for arbitrary intensity measures, such as evolutionary IMs for liquefaction hazard analyses, without requiring an existing GMM. The method involves the conversion of a known IM hazard curve into an alternative IM hazard curve using the total probability theorem. The effectiveness of the method is illustrated by comparing hazard curves calculated using the total probability theorem to the results of a PSHA to demonstrate that the proposed method does not result in additional uncertainty under idealized conditions and provides a range of possible hazard values under most practical conditions. The total probability theorem method can be utilized by practitioners and researchers to select ground motion time series that target alternative IMs for liquefaction hazard analyses or other geotechnical applications. This method also allows researchers to investigate the efficiency, sufficiency, and predictability of new, alternative IMs without necessarily requiring GMMs.