A modified three-parameter lognormal distribution for seismic demand assessment considering collapse data

Abstract

Consideration of parameter uncertainty in structural seismic performance has become an important issue in the last decade. A common means of including such uncertainties is through the reliability theory. Seismic reliability assessment is concerned with calculation of probability of exceeding a certain structural limit state against a ground motion intensity measure. However, an important factor which affects the reliability index is the selection of probability distributions for structural demand. Usually a lognormal distribution is assumed by researchers but recent studies show that such simple assumption may result in misleading reliability measures. In this study, a three parameter lognormal distribution is proposed to be used to describe seismic behavior at relatively high intensity measures. This distribution is unique as it considers the missing or collapse data and at the same time incorporates a location parameter to disregard the less likely displacements at high spectral accelerations in Incremental Dynamic Analysis (IDA). It was shown by means of the Shannon’s entropy that uncertainty of calculating the reliability index using the proposed distribution is minimum compared to other available methods and therefore it is recommended to be used for reliability assessment of collapse prevention limit state.