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The conditional mean spectrum (CMS) and its generalized forms, like the generalized CMS (GCMS), and the CMS conditioned at the logarithm-average spectral acceleration over a period range (CMS-AvgSa), are anchored on a conditional period (or periods) with a target hazard level. This study evaluated the vector hazard of multiple spectral accelerations (Sa) at different periods for CMS, GCMS, and CMS-AvgSa. By invoking the invariance property of scalar disaggregation and Copula function, we developed the computational methods for three types of multivariate exceedance rate (MER): multivariate simultaneous exceedance rate (MER s ), multivariate arbitrary exceedance rate (MER a ), and Kendall-function-based MER (MER k ). Taking the cities of Xi’an and Kunming (China) as examples, scalar probabilistic seismic-hazard analysis (PSHA), and disaggregation were performed and CMS was built at different conditional periods ( T * = 0.05, 0.2, 1.0, and 2.0 s, respectively). The MER k  computation results lies between the other two extreme cases (MER a  and MER s ), which are either too strict or too tolerant compared with the anchored hazard level. It is found that when the earthquake disaggregation characteristics not differ markedly between  T * and other periods in CMS, the calculated MER k  results would be roughly consistent with the anchored hazard level at  Sa ( T *). The conclusion holds true when different  Sa ( T ) were considered in the calculation of MER k  . On the other hand, the calculated MER a  and MER s  would be significantly influenced by the choice of  Sa ( T ) and the results are not comparable with the anchored hazard level. We also evaluated the MER k  for GCMS and CMS-AvgSa, which were constructed using mean scenario earthquake from vector-valued PSHA and disaggregation. Comparing with the UHS, the MER k  of GCMS and CMS-AvgSa are more close to the anchored hazard level within a certain period range. Although no benchmark exists for vector hazard level, the MER k  is likely to be a promising approach for measuring the hazard over a vector of intensity measures in target spectrum.

Evaluation of Vector Hazard for Conditional Mean Spectrum with Different Definitions of Multivariate Exceedance Rate