Directionality Scaling of Scalar and Vector Ground Motion Intensity Measures

ABSTRACT The azimuthal directionality of earthquake ground‐motion intensity measures (IMs) is conventionally described by the ratios between the orientation‐independent maximum (RotD100) and median (RotD50) values over the horizontal plane. This study presents a refined characterization of the directionality of 31 IMs, including spectral accelerations (SAs) at 21 periods ranging from 0.01 to 10 s and ten other typical IMs, with respect to rotation angle ( θ ) against various reference axes (RAs). Based on more than 5300 ground‐motion records, directionality scaling factors (RotDSFs) are proposed to quantify the ratios of orientation‐specific IMs to their orientation‐independent counterparts (RotD50 or RotD100), yielding the following results: (1) Logarithmic means and standard deviations of RotDSFs are parametrized as a function of RA and θ ; (2) Full‐probability distributions of RotDSFs in individual orientations are modeled using either Johnson or Beta distributions; (3) Auto‐correlations among various orientations for each IM and cross‐correlations among multiple IMs in individual orientations are quantified. The results show that the directionality scaling differs considerably across different IMs, and the RotDSF values strongly depend on the selection of RA, underscoring the necessity for modeling orientation‐dependent vector‐valued IMs within a consistent rotational system. The engineering application of the presented results is demonstrated through an example that establishes target spectra in specific orientations, conditioned on the RotD100 of a single spectral ordinate. This work could advance the characterization of earthquake ground motions in arbitrary orientations.