Generation of synthetic spectrum-compatible bi-directional ground motions with specific directionality

Ground motions compatible with the maximum-direction response spectrum (RotD100) condition are emphasized in performance-based design and seismic risk assessment of civil structures in different regions. Due to the complex nature and uncertainty of earthquakes, the comprehensive inclusion of essential characteristics of ground motions is crucial. Recently, the directionality effect of horizontal bi-directional ground motions, representing the variation of the response spectral ordinate amplitude along various directions, on the seismic performance assessment of certain structures or key structural elements has received increasing attention in seismic analysis. However, from the seismic design perspective, there is still a lack of a method that can generate bi-directional ground motions comprehensively reflecting the directionality effect. This study focuses on the correction of ground motion directionality when generating synthetic bi-directional ground motions for a given target response spectrum. An efficient and integrated algorithm is proposed. To demonstrate the applicability of the proposed algorithm, three different target RotD100 response spectra are determined according to modern seismic design codes, and 20 pairs of bi-directional ground motions are generated using the proposed algorithm for each target spectrum. It is shown that with the proposed algorithm, the generated motions present a close match to the target RotD100 response spectrum and meet the specific directionality requirement. In addition, due to the iterative modification of the envelope function, the energy of the generated ground motion is also consistent with the scaled natural records.