ABSTRACT

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.