Selecting three components of ground motions from Conditional Spectra for multiple stripe analyses

For complex structures where the seismic response depends appreciably on the vertical (V) component of ground motion (GM) (e.g., base-isolated buildings, long-span bridges, dams, nuclear power plants), incremental dynamic analysis (IDA) is commonly utilized to estimate seismic risk, where the V components of GM are selected and scaled based on the corresponding horizontal (H) components. The resulting seismic risk (e.g., fragility estimates, annual rates of failure) will likely be significantly biased when the scale factors in IDA are very large. As an alternative to IDA, multiple stripe analyses (MSA) with GMs for each stripe selected from the Conditional Spectrum (CS) can be used to estimate the seismic risk; however, the V components are still commonly selected and scaled based on the corresponding H components. Consequently, these V components may still be inconsistent relative to the corresponding target hazard, again yielding biased estimates of seismic risk. To improve the accuracy of seismic risk estimates, we extend the CS to include the V component of GM and present an approach to select multicomponent GMs that are hazard consistent with respect to all three components of GM. Using the target and the GM selection approach developed in this study, we then evaluate typical current practice for selecting and scaling V components of GM. We observe that the latter approach can yield hazard-inconsistent multicomponent GMs, but hazard consistency can be improved by including the V component in the selection process, constraining the scale factors, or widening the period range for selecting GMs.