Comparison of the Spectral Representation Method to Simulate Spatially Variable Ground Motions |
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| Authors: | Yongxin Wu Dayong Li Tugen Feng Ali H Mahfouz |
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| Institution: | 1. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, China;2. Institute of Engineering Safety and Disaster Prevention, Hohai University, Nanjing, China;3. Department of Civil Engineering, Shandong University of Science and Technology, Qingdao, China;4. Geotechnical Research Institute, Hohai University, Nanjing, China;5. College of Engineering, Jazan University, Jazan, Saudi Arabia |
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| Abstract: | The spectral representation method (SRM) is widely used when simulating spatially variable ground motions. It has mainly two formulas, i.e., the random amplitudes and the random phases formulas. There exist three methods for decomposing the cross spectral density matrix: Cholesky decomposition, eigen decomposition, and root decomposition. Therefore, there are six forms with respect to the different combinations of the simulation formulas and the decomposition methods. To provide researchers and engineers with the guidance on choosing simulation method, the six forms are systematically investigated from five aspects: the power intensity, response spectra, and stochastic error of auto/cross spectral density, Fourier spectra, and difference indexes for Fourier amplitudes and phases. Finally, we give the following advice: the characteristics of the ground motions simulated by the random amplitudes formula are independent of the decomposition method, while the characteristics of the ground motions simulated by random phases formula are dependent of the decomposition method. Furthermore, the root decomposition is strongly recommended when utilizing the random phases formula. |
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| Keywords: | Spectral Representation Method Spatially Varying Ground Motions Power Intensity Response Spectra Stochastic Error Fourier Spectra Difference Index |
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