Normalized Response Spectrum of Ground Motion
Praveen K. MALHOTRA StrongMotions Inc. Praveen.Malhotra@StrongMotions.com www.StrongMotions.com Praveen K. Malhotra, Ph.D., P.E. is a Principal at StrongMotions Inc. in the Boston Area. He has more than 25 years of experience in practice and research of structural and geotechnical earthquake engineering, including teaching multiple short-courses throughout the United States and abroad. He specializes in transparent assessment and cost-effective mitigation of risk. He provides consulting services related to hazard analysis, risk analysis and performance-based engineering. He is often consulted to peer-review major projects.
Summary The peak ground acceleration PGA, peak ground velocity PGV and peak ground displacement PGD are the fundamental strong-motion parameters (intensity measures). The response spectrum of ground motion relative to PGA, PGV and PGD is known as the normalized response spectrum (NRS). In the past, the number of records has not been sufficient to conclusively establish the shape of the NRS and to study its sensitivity to various factors. In this study, the NRS is derived from 13,192 strong-motion records. It is shown that the shape of the NRS is sensitive only to the normalized velocity PGVn = PGV/(PGA•PGD)1/2. For the same PGVn, earthquake magnitude, distance and local soil conditions have insignificant effect on the NRS. For the same PGVn, the direction of motion (horizontal or vertical) has insignificant effect on the NRS. The shape of the NRS is rooted in structural dynamics; thus it should be preserved in predicting ground motions for future earthquakes. It is found that the latest empirical ground motion prediction equations do not always preserve the shape of the NRS. Therefore, it is recommended that ground motion prediction models should only be developed for PGA, PGV and PGD and that the response spectra for various damping ratios should be generated from PGA, PGV and PGD by using the NRS. The Bridge and Structural Engineer
Keywords: strong-motion, response spectrum, normalized response spectrum, ground motion prediction equations, damping.
Introduction The response spectrum provides valuable information regarding the ground motion. It allows an engineer to estimate forces and deformations in structures due to ground shaking. The spectral values at short-, intermediate- and long-periods correlate well with PGA, PGV and PGD, respectively. Numerous studies1-6 have shown that a smooth response spectrum of ground motion can be constructed from PGA, PGV and PGD. The response spectrum relative to PGA, PGV and PGD is known as the normalized response spectrum (NRS). The attractiveness of the NRS is that it reduces the number of intensity measures to just three: PGA, PGV and PGD. In the past, the ground motion records have not been sufficient to conclusively establish the shape of the NRS and to study its sensitivity to various factors. In this study 13,192 strong-motion records are used to establish the NRS and to examine its sensitivity to earthquake magnitude, distance, local soil conditions and the direction of motion. This study also examines the shape of the response spectra generated by latest ground motion prediction equations (GMPE). Volume 45 Number 1 March 2015
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