An algorithm for spectrally matching bi-directional ground motions to a target RotD100 spectrum while maintaining the radial spectral acceleration pattern

Abstract

An integrated algorithm to spectrally match two seed-recorded horizontal bi-directional ground motion components to a maximum-direction response spectrum (RotD100) while maintaining the radial spectral acceleration pattern (RadSAP) at target natural periods is presented. The algorithm is based on the complex-discrete-Fourier-transform (CDFT) and iterative manipulation of the seed-recorded bi-directional ground motions. Initially, a population of candidate bi-directional ground motion pairs is generated, and the candidate resulting in the minimum error in RadSAP is picked. Subsequently, the CDFT coefficients of the picked bi-directional ground motion near the target natural periods are rotated to modify the orientation angle, which contributes to the modification of RadSAP. Then, a double iterative method is introduced to modify the bi-directional ground motion after CDFT coefficients rotation to be spectral and envelope shape compatible in the frequency and time domain. In order to show the effectiveness of the proposed algorithm, two target response spectra are determined following the current ASCE/SEI 7-16 and CJJ 166-2011 specifications, and 10 bi-directional ground motions are selected based on the resemblance in response spectrum for each target spectrum. It is shown that with the proposed algorithm, the RotD100 response spectra estimated from the modified bi-directional ground motions closely match the smooth target RotD100 response spectrum, and the RadSAPs at these target natural periods show an improved match with the seed-recorded bi-directional ground motions than the previous version method. Furthermore, the waveforms of the results obtained using the proposed method are similar to that of the scaled seed records in terms of acceleration, velocity, and displacement. Thus, the generated bi-directional ground motions can be used for future seismic risk assessment of buildings considering the directionality effects.