Liquefaction hazards are usually evaluated using deterministic procedures for a level of ground shaking that is probabilistically determined. The level of ground motion is specified in terms of a ground motion parameter, or intensity measure. This intensity measure is determined through the process of probabilistic seismic hazard analysis (PSHA), and represents the weighted average of a number of possible combinations of earthquake magnitude and source-to-site distance. In the commonly used simplified procedure, earthquake loading is a function of peak ground surface acceleration (amax) and magnitude. The fact that many different magnitudes contribute to the amax at a particular return period leads to some difficulty in selecting a representative magnitude for use in a liquefaction potential evaluation; mean magnitudes from deaggregation analyses are commonly used. Performance-based earthquake engineering provides a framework in which liquefaction hazards can be evaluated probabilistically. This paper describes the basic concepts of a performance-based liquefaction evaluation, and illustrates those concepts with an example. The manner in which uncertainties in both magnitude and amax can be accounted for, and the effects of various approximations frequently used in practice, are described. Finally, the hazard levels produced by conventional procedures for evaluation of liquefaction potential are determined.
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Kramer et al. (2005) studied this question.