Abstract:
Probabilistic seismic hazard analysis (PSHA) is a regularly applied practice that
precedes the construction of important engineering structures. The Cornell-McGuire procedure is
the most frequently applied method of PSHA. This paper examines the fundamental assumption
of the Cornell-McGuire procedure for PSHA, namely, the log-normal distribution of the residuals
of the ground motion parameters. Although the assumption of log-normality is standard, it has
not been rigorously tested. Moreover, the application of the unbounded log-normal distribution
for the calculation of the hazard curves results in non-zero probabilities of the exceedance of
physically unrealistic amplitudes of ground motion parameters. In this study, the distribution of
the residuals of the logarithm of peak ground acceleration is investigated, using the database of
the Strong-motion Seismograph Networks of Japan and the ground motion prediction equation
of Zhao and co-authors. The distribution of residuals is modelled by a number of probability
distributions, and the one parametric law that approximates the distribution most precisely
is chosen by the statistical criteria. The results of the analysis show that the most accurate
approximation is achieved with the generalized extreme value distribution for a central part of a
distribution and the generalized Pareto distribution for its upper tail. The e ect of replacing a
log-normal distribution in the main equation of the Cornell-McGuire method is demonstrated by
the calculation of hazard curves for a simple hypothetical example. These hazard curves di er
signi cantly from one another, especially at low annual exceedance probabilities.
