Impact of representative ground motion level on seismic PSA with the boundary between overestimation and underestimation

One commonly used approach to seismic probabilistic safety assessment (PSA) is the discrete method, which follows the conventional PSA framework and can be applied to various different model types (e.g., multi-unit models). As it is performed using standard software, this method reduces computational costs. However, as intervals cannot be subdivided infinitely, the discrete method instead utilizes an approximation based on a finite number of subintervals. In practice, different numbers of subinterval are applied, and the representative ground motion level is selected based on expert judgment. When employing a smaller number of subintervals, care must be taken to prevent underestimation of risk. The present study analyzes the impact of representative ground motion level on seismic risk, confirming that underestimation can indeed occur with a small number of subintervals, depending on the representative ground motion level. Specifically, using the left endpoint underestimates, the right endpoint overestimates, and the midpoint may do either. It also proposes a method for determining the underestimation-overestimation boundary. This method is demonstrated via examples, affording a mathematical basis for the appropriate selection of representative ground motion levels. Avoiding underestimation helps prevent significant risk contributors from being overlooked and enhances the current understanding of seismic risk.