Vector GCIM and multivariate return period theory considering joint occurrence of horizontal and vertical ground motions and their application in joint selection of ground motions

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Abstract
In the seismic analysis of structures and structural safety assessment, the joint occurrence of horizontal and vertical ground motions should be considered. In this paper, based on the joint distribution of horizontal and vertical generalized intensity measures, the theory of vector generalized conditional intensity measure (VGCIM) are summarized, and the theories of simultaneous exceedance, arbitrary exceedance and Kendall-based multivariate return periods (MRPHV,K) are proposed, which are subsequently applied to a case study site analysis. For the case study site, the results show that when calculating the target IMHV multivariate return period using the conditions IM and GCIM, the return period calculated via the Kendall-based method most closely matches the target return period; The joint MRPHV,K of intensity measures in VGCIM is more closely matched to the target return period than the joint MRPHV,K of intensity measures in GCIM and GCIM-avg; The hazard of multiple intensity measures can be assessed using the joint MRPK value from two intensity measures; When comparing different ground motion selection methods, the target spectral generated using the VGCIM-based, GCIM-avg-based and Kendall multivariate return period selection methods would present a relatively moderate mean and standard deviation; Furthermore, the VGCIM-based, GCIM-avg-based and Kendall multivariate return period selection methods show lower sensitivity to the selection of conditional seismic motion models, which indicate these methods are more reasonable ground motion selection method.

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