Abstract
A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum (EPS). Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average (ARMA) filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals’ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice.
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References
Bogdanoff JL, Goldberg JE and Bernard MC (1961), “Response of a Simple Structure to a Random Earthquake-type Disturbance,” Bulletin of the Seismological Society of America, 51(2): 293–310.
Bommer JJ and Martínez-Pereira A (1999), “The Effective Duration of Earthquake Strong Motion,” Journal of Earthquake Engineering, 3(2): 127–172.
Bommer JJ and Ruggeri C (2002), “The Specification of Acceleration Time-histories in Seismic Design Codes,” European Earthquake Engineering, 16(1): 3–16.
Boore DM (2003), “Simulation of Ground Motion Using the Stochastic Method,” Pure and Applied Geophysics, 160(3–4): 635–676.
Boore DM (2005), “On Pads and Filters: Processing Strong-motion Data,” Bulletin of the Seismological Society of America, 95(2): 745–750.
Boore DM and Akkar S (2003), “Effect of Causal and Acausal Filters on Elastic and Inelastic Response Spectra,” Earthquake Engineering and Structural Dynamics, 32(11): 1729–1748.
Boore DM and Bommer JJ (2005), “Processing of Strong-motion Accelerograms: Needs, Options and Consequences,” Soil Dynamics and Earthquake Engineering, 25(2): 93–115.
Carballo JE and Cornell CA (2000), “Probabilistic Seismic Demand Analysis: Spectrum Matching and Design,” Report RMS-41, Department of Civil and Environmental Engineering, Stanford University.
CEN (2004), Eurocode 8: Design of Structures for Earthquake Resistance — Part 1: General Rules, Seismic Actions and Rules for Buildings (EN 1998-1: 2004), Comité Européen de Normalisation, Brussels.
Chopra AK (2007), “Elastic Response Spectrum: A Historical Note,” Earthquake Engineering and Structural Dynamics, 36(1): 3–12.
Chopra AK and Lopez OA (1979), “Evaluation of Simulated Ground Motions for Predicting Elastic Response of Long Period Structures and Inelastic Response of Structures,” Earthquake Engineering and Structural Dynamics, 7(4): 383–402.
Clough RW and Penzien J (1993), Dynamics of Structures. 2nd ed, New York: Mc-Graw Hill.
Conte JP, Pister KS and Mahin SA (1992), “Nonstationary ARMA Modeling of Seismic Motions,” Soil Dynamics and Earthquake Engineering, 11(7): 411–426.
Converse AM and Brady AG (1992), “BAP: Basic Strong-motion Accelerogram Processing Software, Version 1.0,” Open File Report 92-296A, United States Department of the interior Geological Survey.
Crespi PG, Floris C and Paganini P (2002), “A Probabilistic Method for Generating Spectrum Compatible Earthquake Time Histories,” European Earthquake Engineering, 16(3): 3–17.
Das S and Gupta VK (2008), “Wavelet-based Simulation of Spectrum-compatible Aftershock Accelerograms,” Earthquake Engineering and Structural Dynamics, 37(11): 1333–1348.
Faccioli E, Paolucci R and Rey J (2004), “Displacement Spectra for Long Periods,” Earthquake Spectra, 20(2): 347–376.
Falsone G and Neri F (2000), “Stochastic Modeling of Earthquake Excitation Following the EC8: Power Spectrum and Filtering Equations,” European Earthquake Engineering, 14(1): 3–12.
GB 50011-2001 (2001), Code for Seismic Design of Buildings, National Standard of the People’s Republic of China, Beijing: China Building Industry Press. (in Chinese)
Giaralis A and Spanos PD (2009), “Wavelet-based Response Spectrum Compatible Synthesis of Accelerograms-Eurocode Application (EC8),” Soil Dynamics and Earthquake Engineering, 29(1): 219–235.
Gupta ID and Joshi RG (1993), “On Synthesizing Response Spectrum Compatible Accelerograms,” European Earthquake Engineering, 7(2): 25–33.
Hancock J and Bommer JJ (2006), “A State-of-Knowledge Review of the Influence of Strong-motion Duration on Structural Damage,” Earthquake Spectra, 22(3): 827–845.
Hancock J, Watson-Lamprey J, Abrahamson NA, Bommer JJ, Markatis A, McCoy E and Mendis R (2006), “An Improved Method of Matching Response Spectra of Recorded Earthquake Ground Motion Using Wavelets,” Journal of Earthquake Engineering 101): 67–89.
ICC (2006), International Building Code, International Code Council, USA.
Iervolino I, Manfredi G and Cosenza E (2006), “Ground Motion Duration Effects on Nonlinear Seismic Response,” Earthquake Engineering and Structural Dynamics, 35(1): 21–38.
Iyama J and Kuwamura H (1999), “Application of Wavelets to Analysis and Simulation of Earthquake Motions,” Earthquake Engineering and Structural Dynamics, 28(3): 255–272.
Jangid RS (2004), “Response of SDOF System to Non-stationary Earthquake Excitation,” Earthquake Engineering and Structural Dynamics, 33(15): 1417–1428.
Kanai K (1957), “Semi-empirical Formula for the Seismic Characteristics of the Ground,” Bulletin of Earthquake Research Institute, University of Tokyo, 35: 309–325.
Karabalis DL, Cokkinides GJ, Rizos DC and Mulliken JS (2000), “Simulation of Earthquake Ground Motions by a Deterministic Approach,” Advances in Engineering Software, 31(5): 329–338.
Kottke A and Rathje E (2008), “A Semi-automated Procedure for Selecting and Scaling Recorded Earthquake Motions for Dynamic Analysis,” Earthquake Spectra, 24(4): 911–932.
Kozin F (1989), “Autoregressive Moving Average Models of Earthquake Records,” Probabilistic Engineering Mechanics, 3(2): 58–63.
Lai SP (1982), “Statistical Characterization of Strong Ground Motions Using Power Spectral Density Function,” Bulletin of the Seismological Society of America, 72(1): 259–274.
Lam N, Wilson J and Hutchinson G (2000), “Generation of Synthetic Earthquake Accelerograms Using Seismological Modeling: A Review,” Journal of Earthquake Engineering, 4(3): 321–354v.
Lin C-CJ and Ghaboussi J (2001), “Generating Multiple Spectrum Compatible Accelerograms Using Stochastic Neural Networks,” Earthquake Engineering and Structural Dynamics, 30(7): 1021–1042.
Lutes LD and Lilhanand (1979), “Frequency Content in Earthquake Simulation,” Journal of the Engineering Mechanics Division, ASCE, 105(EM1): 143–158.
Marano GC, Trentadue F, Morrone E and Amara L (2008), “Sensitivity Analysis of Optimum Stochastic Nonstationary Response Spectra under Uncertain Soil Parameters,” Soil Dynamics and Earthquake Engineering, 28(12): 1078–1093.
Mason AB and Iwan WD (1983), “An Approach to the First Passage Problem in Random Vibration,” Journal of Applied Mechanics, ASME, 50(3): 641–646.
Michaelov G, Lutes LD and Sarkani S (2001), “Extreme Value of Response to Nonstationary Excitation,” Journal of Engineering Mechanics, 127(4): 352–363.
Morikawa H and Zerva A (2008), “Approximate Representation of the Statistics for Extreme Responses of Single Degree-of-freedom System Excited by Non-stationary Processes,” Probabilistic Engineering Mechanics, 23(3): 279–288.
Mukherjee S and Gupta VK (2002), “Wavelet-based Generation of Spectrum-compatible Time-histories,” Soil Dynamics and Earthquake Engineering, 22(9–12): 799–804.
Naeim F, Alimoradi A and Pezeshk S (2004), “Selection and Scaling of Ground Motion Time Histories for Structural Design Using Genetic Algorithms,” Earthquake Spectra, 20(2): 413–426.
Newland DE (1994), “Harmonic and Musical Wavelets,” Proceedings of the Royal Society of London. Series A, 444(1921): 605–620.
Newland DE (1998), “Time-frequency and Time-scale Signal Analysis by Harmonic Wavelets,” Procházka A, Uhlír J, Rayner PJW and Kingsbury NG, Signal analysis and prediction, Chapter 1, Boston: Birkhaüser.
Nocedal J and Wright SJ (1999), Numerical Optimization, New York: Springer-Verlag.
Ólafsson S, Remseth S and Sigbjornsson R (2001), “Stochastic Models for Simulation of Strong Ground Motion in Iceland,” Earthquake Engineering and Structural Dynamics, 30(9): 1305–1331.
Politis NP, Giaralis A and Spanos PD (2007), “Joint Time-frequency Representation of Simulated Earthquake Accelerograms via the Adaptive Chirplet Transform,” Deodatis G and Spanos PD, Computational Stochastic Mechanics-5, Rotterdam: Millpress.
Preumont A (1984), “The Generation of Spectrum Compatible Accelerograms for the Design of Nuclear Power Plants,” Earthquake Engineering and Structural Dynamics, 12(4): 481–497.
Priestley MB (1965), “Evolutionary Spectra and Non-Stationary Processes,” Journal of the Royal Statistical Society. Series B, 27(2): 204–237.
Quek S-T, Teo Y-P and Balendra T (1990), “Nonstationary Structural Response with Evolutionary Spectra Using Seismological Input Model,” Earthquake Engineering and Structural Dynamics, 19(2): 275–288.
Roberts JB and Spanos PD (2003), Random Vibration and Statistical Linearization, New York: Dover Publications.
Hu Shiping (1993), “Seismic Design of Buildings in China,” Earthquake Spectra, 9(4): 703–737.
Shrikhande M and Gupta VK (1996), “On Generating Ensemble of Design Spectrum-compatible Accelerograms,” European Earthquake Engineering, 10(3): 49–56.
Spanos PD (1983), “Digital Synthesis of Response-Design Spectrum Compatible Earthquake Records for Dynamic Analyses,” The Shock and Vibration Digest, 15(3): 21–30.
Spanos PD, Giaralis A, Politis NP and Roesset JM (2007), “Numerical Treatment of Seismic Accelerograms and of Inelastic Seismic Structural Responses Using Harmonic Wavelets,” Computer-Aided Civil and Infrastructure Engineering, 22(4): 254–264.
Spanos PD and Lutes LD (1980), “Probability of Response to Evolutionary Process,” Journal of the Engineering Mechanics Division, ASCE, 106(EM2): 213–224.
Spanos PD, Tezcan J and Tratskas P (2005), “Stochastic Processes Evolutionary Spectrum Estimation via Harmonic Wavelets,” Computer Methods in Applied Mechanics and Engineering, 194(12–16): 1367–1383.
Spanos PD and Vargas Loli LM (1985), “A Statistical Approach to Generation of Design Spectrum Compatible Earthquake Time Histories,” Soil Dynamics and Earthquake Engineering, 4(1): 2–8.
Spanos PD and Zeldin BA (1998), “Monte Carlo Treatment of Random Fields: A Broad Perspective,” Applied Mechanics Reviews, 51(3): 219–237.
Suárez LE and Montejo LA (2005), “Generation of Artificial Earthquakes via the Wavelet Transform,” International Journal of Solids and Structures, 42(21–22): 5905–5919.
Suárez LE and Montejo LA (2007), “Application of the Wavelet Transform in the Generation and Analysis of Spectrum-compatible Records,” Structural Engineering and Mechanics, 27(2): 173–197.
Trifunac MD and Brady AG (1975), “A Study on the Duration of Strong Earthquake Ground Motion,” Bulletin of the Seismological Society of America, 65(3): 581–626.
Vanmarcke EH (1976), “Structural Response to Earthquakes,” Lomnitz C and Rosenblueth E, Seismic Risk and Engineering Decisions, Chapter 8, Amsterdam: Elsevier.
Wang Yayong (2004), “Comaprison of Seismic Actions and Structural Design Requirements in Chinese Code GB 50011 and International Standard ISO 3010,” Earthquake Engineering and Engineering Vibrations 3(1): 1–9.
Wang Junjie, Fan Lichu, Qian Shie and Zhou Jing (2002), “Simulations of Non-stationary Frequency Content and Its Importance to Seismic Assessment of Structures,” Earthquake Engineering and Structural Dynamics, 31(4): 993–1005.
Wen YK and Gu Ping (2004), “Description and Simulation of Nonstationary Processes Based on Hilbert Spectra,” Journal of Engineering Mechanics, ASCE, 130(8): 942–951.
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Spanos, P.D., Giaralis, A. & Li, J. Synthesis of accelerograms compatible with the Chinese GB 50011-2001 design spectrum via harmonic wavelets: artificial and historic records. Earthq. Eng. Eng. Vib. 8, 189–206 (2009). https://doi.org/10.1007/s11803-009-9017-4
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DOI: https://doi.org/10.1007/s11803-009-9017-4