Selecting the Optimal Factor of Safety or Probability of Liquefaction Triggering for Engineering Projects Based on Misprediction Costs

In deterministic evaluations, liquefaction triggering potential is assessed by comparing the computed factor-of-safety ($FS$) against liquefaction triggering to some minimal acceptable $FS$. While some guidelines are available for selecting the minimal acceptable $FS$, there is no standard value. Herein, Receiver Operating Characteristic (ROC) analyses are used to develop an approach for selecting the optimal minimal acceptable $FS$ (i.e., optimal $FS$) for a project based on the relative costs of mispredictions. Utilizing different liquefaction triggering models and their associated case-history databases, relationships are established between the optimal $FS$ and the ratio of the cost of a false-positive prediction to the cost of a false-negative prediction (i.e., cost ratio, $CR$). Also, by combining the $FS$ data from different models, a “generic” $FS\text{-}CR$ relationship is developed that “averages out” the degree of conservatism inherent to the individual triggering models. Similarly, relationships relating the optimal probability of liquefaction triggering ($PL$) to $CR$ are developed for the probabilistic variants of the triggering models, as well as a generic $PL\text{-}CR$ curve.