Conditional Mean Spectrum: Tool for Ground-Motion Selection

A common goal of dynamic structural analysis is to predict the response of a structure subjected to ground motions having a specified spectral acceleration at a given period. This is important, for example, when coupling ground-motion hazard curves from probabilistic seismic hazard analysis (PSHA) with results from dynamic structural analysis. The prediction is often obtained by selecting ground motions that match a target response spectrum and using those ground motions as input to dynamic analysis. The commonly used uniform hazard spectrum (UHS) is shown here to be an unsuitable target for this purpose, as it conservatively implies that large-amplitude spectral values will occur at all periods within a single ground motion. An alternative, termed a conditional mean spectrum (CMS), is presented here. The CMS provides the expected (i.e., mean) response spectrum, conditioned on occurrence of a target spectral acceleration value at the period of interest. It is argued that this is the appropriate target response spectrum for the goal described above and is thus a useful tool for selecting ground motions as input to dynamic analysis. The CMS is described, its advantages relative to the UHS are explained, and practical guidelines for use in ground-motion selection are presented. Recent work illustrating the impact of this change in target spectrum on resulting structural response is briefly summarized.