Modern seismic design codes require the simultaneous input of horizontal bi-directional ground motions for nonlinear time history analysis (NLTHA) in structural seismic assessments. This necessitates the generation of suitable bi-directional ground motions. By representing the two horizontal components as the real and imaginary parts of imaginary numbers, this study proposes a new algorithm to generate target maximum-direction spectrum (RotD100) and energy-compatible (SEC) bi-directional ground motions using the complex-valued continuous wavelet transform (CWT). This algorithm stands out from conventional spectral matching approaches for bi-directional ground motions, as it can generate ground motions that not only closely match the target RotD100 spectrum but also match the Arias intensity build-up process. The efficacy of the proposed algorithm is demonstrated by generating SEC bi-directional ground motions using 20 pairs of seed records. The compatibility between the SEC ground motions response spectra and the target RotD100 spectrum is discussed. In order to assess the accuracy of SEC bi-directional ground motions to produce accurate seismic estimates compared to amplitude-scaled records, extensive NLTHAs are performed on a series of elastoplastic oscillators. The analysis involves one suite of amplitude-scaled records and one suite of SEC ground motions, each consisting of 120 pairs of bi-directional ground motions. By analyzing the ratio of absolute peak horizontal acceleration (PHA) and relative displacement of the oscillators under the two suites of bi-directional ground motions, the study finds that the generated SEC bi-directional ground motions can provide accurate seismic response estimates.
 

Bi-directional ground motion; Spectral matching; RotD100; Complex-valued wavelet; Seismic assessment.