基于相位差谱的空间相关非平稳地震动场的模拟
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摘要
地震动的非平稳特性主要是由其相位差谱决定的,相位差谱与相位导数之间存在线性倍数关系。根据相位导数的显式计算公式,从能量的角度解释了相位导数的均值大致决定了时程峰值的发生时刻,相位导数的方差决定了强震段的持续时间。在相关地震动场模拟方法中,首次将相位差谱的统计模型引入空间相关非平稳地震动场的模拟方法之中,利用快速傅立叶变换技术生成地震动场。表示地震动随机特性的随机相位谱利用相位差谱的统计模型生成,生成的地震动场不仅具有空间相关性,而且在时域、频域内均具有非平稳特性。
The non-stationary characteristics of an earthquake ground motion are dependent on the phase difference spectrum,which is proportional to the phase derivatives.As viewed from the energy of acceleration time history,the time of PGA is related to the mean value of the phase derivatives while the duration of strong seismic ground motion is related to the variance of the phase derivatives.The empirical model of phase difference spectrum is introduced firstly into the simulation of spatial correlated and nonstationary ground motions.The simulated ground motions are expressed by the power spectra,coherence functions and random phase angles generated according to the empirical model of phase difference spectrum and are synthesized by discrete Fourier transform.
The non-stationary characteristics of an earthquake ground motion are dependent on the phase difference spectrum,which is proportional to the phase derivatives.As viewed from the energy of acceleration time history,the time of PGA is related to the mean value of the phase derivatives while the duration of strong seismic ground motion is related to the variance of the phase derivatives.The empirical model of phase difference spectrum is introduced firstly into the simulation of spatial correlated and nonstationary ground motions.The simulated ground motions are expressed by the power spectra,coherence functions and random phase angles generated according to the empirical model of phase difference spectrum and are synthesized by discrete Fourier transform.
引文
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[2]Ramadan O,Novak M.Simulation of spatially inco-herent random ground motions[J].Journal of Engi-neering Mechenics,1993,119:997-1016.
[3]Hao H,Oliveira C S,Penzien J.Multiple-station ground motion processing and simulation based on SMART-1array data[J].Nuclear Engng and De-sign,1989,111:293-310.
[4]Li Y,Kareem A.Simulation of multivariate nonsta-tionary random processes by FFT[J].Journal of En-gineering Mechenics,1991,117:1037-58.
[5]Deodatis G.Non-stationary stochastic vector proces-ses:seismic ground motion applications[J].Probabi-listic Engineering Mechenics,1996,11:149-168.
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[7]Ellis G W,Cakmak A S.Effect of spatial variability on ARMA modelling of ground motion[J].Structural Safety,1991,10(1-3):181-191.
[8]Conte J P,Pister K S,Mahin S A.Nonstationary ARMA modeling of seismic motions[J].Soil Dynam-ics and Earthquake Engineering,1992,11(7):411-426.
[9]Suarez L E,Montejo L A.Generation of artificial earthquakes via the wavelet transform[J].Interna-tional Journal of Solids and Structures,2005,42(21-22):5905-5919.
[10]Mukherjee S,Gupta V K.Wavelet-based character-ization of design ground motions[J].Earthquake En-gineering and Structural Dynamics,2002,31(5):1173-1190.
[11]Shrikhande M,Gupta V K.Synthesizing ensembles of spatially correlated accelerograms[J].Journal of Engineering Mechenics,1998,124(11):1185-1192.
[12]Vanmarcke E H,Heredia-Zavoni E,Fenton G A.Conditional simulation of spatially correlated earth-quake ground motion[J].Journal of Engineering Mechenics,1993,119(11):2333-2352.
[13]Yang Qing-shan,Jiang Hai-peng.Generation of re-sponse-spectrum-compatible ground motions based on phase-difference spectrum[J].Earthquake Engineer-ing and Engineering Vibration,2001,21(3):32-38.(in Chinese)
[14]Ohsaki Y.On the significance of phase content in earthquake ground motions[J].Earthquake Engi-neering and Structural Dynamics,1979,7:427-439.
[15]Nigam N C.Phase properties of a class of random processes[J].Earthquake Engineering and Structur-al Dynamics,1982,10:711-717.
[16]Boore D M.Phase derivatives and simulation of strong ground motions[J].Bulletin of the Seismo-logical Society of America,2003,93(3):1132-1143.
[17]Yang Qing-shan,Jiang Hai-peng,Chen Ying-jun.Generation of ground motion non-stationary both in time and frequency domains on phase difference spec-trum[J].Earthquake Engineering and Engineering Vibration,2001,1(2):167-180.(in Chinese)
[18]Shrikhande M,Gupta V K.On the characterisation of the phase spectrum for strong motion synthesis[J].Journal of Earthquake Engineering,2001,5(4):465-482.
[19]Thráinsson H,Kiremidjian A S.Simulation of dig-ital earthquake accelerograms using the inverse dis-crete Fourier transform[J].Earthquake Engineering and Structural Dynamics,2002,31:2023-2048.
[20]Sato T,Muro Y,Wang H B,et al.Design spectra and phase spectrum modeling to simulate design earthquake motions:a case study through design standerds of railway facilities in Japan[J].Journal of Natural Disaster Science,2001,23(2):89-100.
[21]Sato T,Muro Y,Wang H B,et al.Phase spectrum modeling to simulate design earthquake motion[J].Journal of Natural Disaster Science,2002,24(2):91-100.
[22]Kanai K.Semi-empirical formula for the seismic characteristics of the ground motion[J].Bulletin of the Earthquake Research Institute University of To-kyo,1957,35:309-25.
[23]Clough R,Penzien J.Dynamics of structures(M).New York:McGraw-Hill,Inc.,1993:673-675.
[24]Harichandran R S,Vanmarke E H.Stochastic varia-tion of earthquake ground motion in space and time[J].Journal of Engineering Mechanics,1986,112(2):108-129.
[25]Oliverra Carlos S,Hong H,Penzien J.Ground mo-tion modeling for multiple-input structural analysis[J].Structural Safety,1991,10:79-93.
[26]Abrahamson N A.Empirical spatial coherency func-tions for application to soil-structure interaction ana-lyses[J].Earthquake Spectra,1991,7:1-28.
[27]Yang Qing-shan,Chen Ying-jun.A practical coher-ency model for spatial varying ground motions[J].Structural Engineering and Mechanics,2000,9(2):141-152.
[2]Ramadan O,Novak M.Simulation of spatially inco-herent random ground motions[J].Journal of Engi-neering Mechenics,1993,119:997-1016.
[3]Hao H,Oliveira C S,Penzien J.Multiple-station ground motion processing and simulation based on SMART-1array data[J].Nuclear Engng and De-sign,1989,111:293-310.
[4]Li Y,Kareem A.Simulation of multivariate nonsta-tionary random processes by FFT[J].Journal of En-gineering Mechenics,1991,117:1037-58.
[5]Deodatis G.Non-stationary stochastic vector proces-ses:seismic ground motion applications[J].Probabi-listic Engineering Mechenics,1996,11:149-168.
[6]Heredia-Zavoni E,Santa-Cruz S.Conditional Simula-tion of a class of non-stationary space-time random fields[J].Journal of Engineering Mechenics,2000,126(4):398-404.
[7]Ellis G W,Cakmak A S.Effect of spatial variability on ARMA modelling of ground motion[J].Structural Safety,1991,10(1-3):181-191.
[8]Conte J P,Pister K S,Mahin S A.Nonstationary ARMA modeling of seismic motions[J].Soil Dynam-ics and Earthquake Engineering,1992,11(7):411-426.
[9]Suarez L E,Montejo L A.Generation of artificial earthquakes via the wavelet transform[J].Interna-tional Journal of Solids and Structures,2005,42(21-22):5905-5919.
[10]Mukherjee S,Gupta V K.Wavelet-based character-ization of design ground motions[J].Earthquake En-gineering and Structural Dynamics,2002,31(5):1173-1190.
[11]Shrikhande M,Gupta V K.Synthesizing ensembles of spatially correlated accelerograms[J].Journal of Engineering Mechenics,1998,124(11):1185-1192.
[12]Vanmarcke E H,Heredia-Zavoni E,Fenton G A.Conditional simulation of spatially correlated earth-quake ground motion[J].Journal of Engineering Mechenics,1993,119(11):2333-2352.
[13]Yang Qing-shan,Jiang Hai-peng.Generation of re-sponse-spectrum-compatible ground motions based on phase-difference spectrum[J].Earthquake Engineer-ing and Engineering Vibration,2001,21(3):32-38.(in Chinese)
[14]Ohsaki Y.On the significance of phase content in earthquake ground motions[J].Earthquake Engi-neering and Structural Dynamics,1979,7:427-439.
[15]Nigam N C.Phase properties of a class of random processes[J].Earthquake Engineering and Structur-al Dynamics,1982,10:711-717.
[16]Boore D M.Phase derivatives and simulation of strong ground motions[J].Bulletin of the Seismo-logical Society of America,2003,93(3):1132-1143.
[17]Yang Qing-shan,Jiang Hai-peng,Chen Ying-jun.Generation of ground motion non-stationary both in time and frequency domains on phase difference spec-trum[J].Earthquake Engineering and Engineering Vibration,2001,1(2):167-180.(in Chinese)
[18]Shrikhande M,Gupta V K.On the characterisation of the phase spectrum for strong motion synthesis[J].Journal of Earthquake Engineering,2001,5(4):465-482.
[19]Thráinsson H,Kiremidjian A S.Simulation of dig-ital earthquake accelerograms using the inverse dis-crete Fourier transform[J].Earthquake Engineering and Structural Dynamics,2002,31:2023-2048.
[20]Sato T,Muro Y,Wang H B,et al.Design spectra and phase spectrum modeling to simulate design earthquake motions:a case study through design standerds of railway facilities in Japan[J].Journal of Natural Disaster Science,2001,23(2):89-100.
[21]Sato T,Muro Y,Wang H B,et al.Phase spectrum modeling to simulate design earthquake motion[J].Journal of Natural Disaster Science,2002,24(2):91-100.
[22]Kanai K.Semi-empirical formula for the seismic characteristics of the ground motion[J].Bulletin of the Earthquake Research Institute University of To-kyo,1957,35:309-25.
[23]Clough R,Penzien J.Dynamics of structures(M).New York:McGraw-Hill,Inc.,1993:673-675.
[24]Harichandran R S,Vanmarke E H.Stochastic varia-tion of earthquake ground motion in space and time[J].Journal of Engineering Mechanics,1986,112(2):108-129.
[25]Oliverra Carlos S,Hong H,Penzien J.Ground mo-tion modeling for multiple-input structural analysis[J].Structural Safety,1991,10:79-93.
[26]Abrahamson N A.Empirical spatial coherency func-tions for application to soil-structure interaction ana-lyses[J].Earthquake Spectra,1991,7:1-28.
[27]Yang Qing-shan,Chen Ying-jun.A practical coher-ency model for spatial varying ground motions[J].Structural Engineering and Mechanics,2000,9(2):141-152.
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