Physics-Based Planar Wavefront Model to Estimate Seismic Rocking Spectra Using Translational Spectra
Publication: Journal of Engineering Mechanics
Volume 145, Issue 4
Abstract
A new and simple planar wavefront model is presented for synthesizing the Fourier spectra of the seismic rocking ground motion (i.e., seismic ground rotation about a horizontal axis) at a station near the epicenter by using the corresponding translational motion data. As in the conventional models, the ground motion was assumed to result primarily from the incidence of planar wavefronts of body waves emitted by a point source buried in a homogeneous, elastic half-space. In contrast to the conventional models, however, the spatial variations of both the amplitudes and the incidence angles of the waves were considered. The spatial variation of the amplitudes was formulated by considering the far-field radiation patterns of body waves due to a kinematic shear dislocation point source. The proposed model can therefore accommodate information on the underlying focal mechanism and give the estimates of both in-plane and out-of-plane rocking spectra. It is shown through a numerical study that the proposed model leads to more accurate estimates of rocking spectra than the conventional models over a large range of frequencies, even when the input source information is unavailable.
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References
Achenbach, J. D. 1973. Wave propagation in elastic solids. Amsterdam, Netherlands: North Holland.
Acikgoz, S., and M. J. DeJong. 2016. “Analytical modelling of multi-mass flexible rocking structures.” Earthquake Eng. Struct. Dyn. 45 (13): 2103–2122. https://doi.org/10.1002/eqe.2735.
Aki, K., and P. G. Richards. 2002. Quantitative seismology. 2nd ed. Sausalito, CA: Univ. Science Books.
Basu, D., A. S. Whittaker, and M. C. Constantinou. 2012. “Estimating rotational components of ground motion using data recorded at a single station.” J. Eng. Mech. 138 (9): 1141–1156. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000408.
Bouchon, M., and K. Aki. 1977. “Discrete wave-number representation of seismic-source wave fields.” Bull. Seismol. Soc. Am. 67 (2): 259–277.
Burridge, R., and L. Knopoff. 1964. “Body force equivalents for seismic dislocations.” Bull. Seismol. Soc. Am. 54 (6): 1875–1888.
Castellani, A., and G. Boffi. 1986. “Rotational components of the surface ground motion during an earthquake.” Earthquake Eng. Struct. Dyn. 14 (5): 751–767. https://doi.org/10.1002/eqe.4290140506.
Castellani, A., and G. Boffi. 1989. “On the rotational components of seismic motion.” Earthquake Eng. Struct. Dyn. 18 (6): 785–797. https://doi.org/10.1002/eqe.4290180604.
Castellani, A., M. Stupazzini, and R. Guidotti. 2012. “Free-field rotations during earthquakes: Relevance on buildings.” Earthquake Eng. Struct. Dyn. 41 (5): 875–891. https://doi.org/10.1002/eqe.1163.
Chatzis, M. N., M. García Espinosa, C. Needham, and M. S. Williams. 2018. “Energy loss in systems of stacked rocking bodies.” J. Eng. Mech. 144 (7): 04018044. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001443.
Chiu, H. C., F. J. Wu, C. J. Lin, H. C. Huang, and C. C. Liu. 2012. “Effects of rotation motions on strong-motion data.” J. Seismol. 16 (4): 829–838. https://doi.org/10.1007/s10950-012-9301-z.
Cotton, F., and M. Campillo. 1995. “Frequency domain inversion of strong motions: Application to the 1992 Landers earthquake.” J. Geophys. Res. 100 (B3): 3961–3975. https://doi.org/10.1029/94JB02121.
Custódio, S., P. Liu, and R. J. Archuleta. 2005. “The 2004 Parkfield, California, earthquake: Inversion of near-source ground motion using multiple data sets.” Geophys. Res. Lett. 32 (23): 1–4. https://doi.org/10.1029/2005GL024417.
Gallovič, F., and J. Zahradník. 2012. “Complexity of the Mw 6.3 2009 L’Aquilla (Central Italy) earthquake. Part I: Multiple finite-extent source inversion.” J. Geophys. Res. 117 (B4): 1–14. https://doi.org/10.1029/2011JB008709.
Ghayamghamian, M. R., G. R. Nouri, H. Igel, and T. Tobita. 2009. “The effect of torsional ground motion on structural response: Code recommendation for accidental eccentricity.” Bull. Seismol. Soc. Am. 99 (2B): 1261–1270. https://doi.org/10.1785/0120080196.
Gupta, I. D., and M. D. Trifunac. 1987. “A note on contribution of torsional excitation to earthquake response of simple symmetric buildings.” Earthquake Eng. Eng. Vibr. 7 (3): 27–46.
Gupta, I. D., and M. D. Trifunac. 1988. “A note on computing the contribution of rocking excitation to earthquake response of simple buildings.” Bull. Indian Soc. Earthquake Technol. 25 (2): 73–89.
Gupta, V. K., and M. D. Trifunac. 1990. “Response of multistoried buildings to ground translational and torsion during earthquakes.” Eur. Earthquake Eng. IV (1): 34–42.
Gupta, V. K., and M. D. Trifunac. 1991. “Effects of ground rocking on dynamic response of multistoried buildings during earthquakes.” Struct. Eng./Earthquake Eng. 8 (2): 43–50.
Hartzell, S. H., and T. H. Heaton. 1983. “Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake.” Bull. Seismol. Soc. Am. 73 (6): 1553–1583.
Housner, G. W. 1963. “The behavior of inverted pendulum structures during earthquakes.” Bull. Seismol. Soc. Am. 53 (2): 403–417.
Ide, S., M. Takeo, and Y. Yoshida. 1996. “Source process of the 1995 Kobe earthquake: Determination of spatio-temporal slip distribution by Bayesian modeling.” Bull. Seismol. Soc. Am. 86 (3): 547–566.
Jalali, R. S., M. D. Trifunac, G. G. Amiri, and M. Zahedi. 2007. “Wave-passage effects on strength-reduction factors for design of structures near earthquake faults.” Soil Dyn. Earthquake Eng. 27 (8): 703–711. https://doi.org/10.1016/j.soildyn.2007.01.006.
Ji, C., D. J. Wald, and D. V. Helmberger. 2002. “Source description of the 1999 Hector Mine, California, earthquake. Part I: Wavelet domain inversion theory and resolution analysis.” Bull. Seismol. Soc. Am. 92 (4): 1192–1207. https://doi.org/10.1785/0120000916.
Kalkan, E., and V. M. Graizer. 2007a. “Coupled tilt and translational ground motion response spectra.” J. Struct. Eng. 133 (5): 609–619. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:5(609).
Kalkan, E., and V. M. Graizer. 2007b. “Multi-component ground motion response spectra for coupled horizontal, vertical, angular accelerations, and tilt.” ISET J. Earthquake Technol. 44 (1): 259–284.
Lee, V. W., and M. D. Trifunac. 1985. “Torsional accelerograms.” Soil Dyn. Earthquake Eng. 4 (3): 132–139. https://doi.org/10.1016/0261-7277(85)90007-5.
Lee, V. W., and M. D. Trifunac. 1987. “Rocking strong earthquake accelerations.” Soil Dyn. Earthquake Eng. 6 (2): 75–89. https://doi.org/10.1016/0267-7261(87)90017-0.
Li, H. N., L. Y. Sun, and S. Y. Wang. 2004. “Improved approach for obtaining rotational components of seismic motion.” Nucl. Eng. Des. 232 (2): 131–137. https://doi.org/10.1016/j.nucengdes.2004.05.002.
Liu, C. C., B. S. Huang, W. H. K. Lee, and C. J. Lin. 2009. “Observing rotational and translational ground motions at the HGSD station in Taiwan from 2007 to 2008.” Bull. Seismol. Soc. Am. 99 (2B): 1228–1236. https://doi.org/10.1785/0120080156.
Olson, A. H., and R. J. Apsel. 1982. “Finite faults and inverse theory with applications to the 1979 Imperial Valley earthquake.” Bull. Seismol. Soc. Am. 72 (6): 1969–2001.
Shakib, H., and R. Z. Tohidi. 2002. “Evaluation of accidental eccentricity in buildings due to rotational component of earthquake.” J. Earthquake Eng. 6 (4): 431–445. https://doi.org/10.1080/13632460209350424.
Singla, V. K., and V. K. Gupta. 2016. “On planar seismic wavefront modeling for estimating rotational ground motions: Case of 2-D SH line-source.” Soil Dyn. Earthquake Eng. 85: 62–77. https://doi.org/10.1016/j.soildyn.2016.03.002.
Singla, V. K., and V. K. Gupta. 2018. “Planar seismic wavefront modeling for estimating rotational ground motions: Case of 2D P-SV line-source.” J. Eng. Mech. 144 (7): 04018048. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001450.
Takeo, M. 1998. “Ground rotational motions recorded in near-source region of earthquakes.” Geophys. Res. Lett. 25 (6): 789–792. https://doi.org/10.1029/98GL00511.
Takeo, M. 2009. “Rotational motions observed during an earthquake swarm in April 1998 offshore Ito, Japan.” Bull. Seismol. Soc. Am. 99 (2B): 1457–1467. https://doi.org/10.1785/0120080173.
Trifunac, M. D. 1982. “A note on rotational components of earthquake motions on ground surface for incident body waves.” Soil Dyn. Earthquake Eng. 1 (1): 11–19. https://doi.org/10.1016/0261-7277(82)90009-2.
Trifunac, M. D. 2009. “The role of strong motion rotations in the response of structures near earthquake faults.” Soil Dyn. Earthquake Eng. 29 (2): 382–393. https://doi.org/10.1016/j.soildyn.2008.04.001.
Yin, J., R. L. Nigbor, Q. Chen, and J. Steidl. 2016. “Engineering analysis of measured rotational ground motions at GVDA.” Soil Dyn. Earthquake Eng. 87: 125–137. https://doi.org/10.1016/j.soildyn.2016.05.007.
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Published In
Journal of Engineering Mechanics
Volume 145 • Issue 4 • April 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Mar 7, 2018
Accepted: Sep 7, 2018
Published online: Jan 30, 2019
Published in print: Apr 1, 2019
Discussion open until: Jun 30, 2019
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