平稳地震地面运动改进金井清谱的相关函数模型
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摘要
胡聿贤平稳地震地面运动谱模型是对Kanai-Tajimi模型的一种改进。通过数学推导证明胡聿贤谱是将基岩地震动模拟为过滤白谱过程,经具有某种特性的线性单自由度土层滤波后而形成的,从而在物理上解释了胡聿贤模型的合理性;研究了低频截止频率的作用,推导出胡聿贤模型的相关函数的表达式。本文所得结果可为结构随机地震反应时域分析提供基础。
A modified Kanai-Tajimi power spectral model of earthquake ground motion,called Hu spectral model,is analyzed in this paper.In the Hu model,the spectral density function of the Kanai-Tajimi model is modified only for the low frequency range and it is in good accordance with the Kanai-Tajimi spectrum for the moderate and high frequencies.According to the Hu spectrum,the singular point in zero frequency is eliminated so that the convergence problem of the displacement and velocity variance of the ground motion can be solved.It is proved that the earthquake-induced ground acceleration process with the Hu spectrum is essentially the filtered color noise process.In fact,the Hu spectrum is the result that a filtered Gaussian white noise process on the rock is filtered by the overlaying soil represented by a linear single degree-of-freedom system,namely it is a twice filtered white noise process.This shows that the Hu spectral density model is not only concise in the mathematic expression but also distinct in physical meaning and reasonable in practice.Furthermore,the frequency factor to restrain the low frequency content of earthquake ground motion is discussed.The function of the frequency factor is to cut down spectral amplitude during the frequency range from zero to the twice frequency factor.Finally,on the basis of physical meaning and filter equation of Hu spectrum,the state equation is established and the autocorrelation function of the stochastic model is deduced by correlation method in time domain.The result represented by equation(34) provides a basis for random response analysis and reliability assessment of the seismic structures.
A modified Kanai-Tajimi power spectral model of earthquake ground motion,called Hu spectral model,is analyzed in this paper.In the Hu model,the spectral density function of the Kanai-Tajimi model is modified only for the low frequency range and it is in good accordance with the Kanai-Tajimi spectrum for the moderate and high frequencies.According to the Hu spectrum,the singular point in zero frequency is eliminated so that the convergence problem of the displacement and velocity variance of the ground motion can be solved.It is proved that the earthquake-induced ground acceleration process with the Hu spectrum is essentially the filtered color noise process.In fact,the Hu spectrum is the result that a filtered Gaussian white noise process on the rock is filtered by the overlaying soil represented by a linear single degree-of-freedom system,namely it is a twice filtered white noise process.This shows that the Hu spectral density model is not only concise in the mathematic expression but also distinct in physical meaning and reasonable in practice.Furthermore,the frequency factor to restrain the low frequency content of earthquake ground motion is discussed.The function of the frequency factor is to cut down spectral amplitude during the frequency range from zero to the twice frequency factor.Finally,on the basis of physical meaning and filter equation of Hu spectrum,the state equation is established and the autocorrelation function of the stochastic model is deduced by correlation method in time domain.The result represented by equation(34) provides a basis for random response analysis and reliability assessment of the seismic structures.
引文
[1]Housner G.W.Characteristics of strong motion ofearthquakes[J].BSSA,1947,37(1):19-31
[2]Kanai K.Semi-empirical formula for the seismic char-acteristics of the ground motion[J].Bulletin of theEarthquake Research Institute,University of Tokyo,1957,35(2):308-325
[3]Tajimi H.A statistical method of determining themaximum response of a building structure during anearthquake[A].2nd WCEE[C].Tokyo,Japan,1960
[4]胡聿贤,周锡元.弹性体系在平稳和平稳化地面运动下的反应[A].中国科学院土木建筑研究所地震工程研究报告集(第一集)[C].北京:科学出版社,1962
[5]金家和,胡聿贤,周锡元.关于“弹性系统在平稳和平稳化地面运动下的反应”一文的讨论[A].中国科学院工程力学研究所地震工程研究报告集(第二集)[C].北京:科学出版社,1965
[6]Clough R W,Penzien J.Dynamics of structures[M].2nd edition,New York,McGraw-Hill,Inc.,1993
[7]欧进萍,牛荻涛,杜修力.设计用随机地震动的模型及其参数确定[J].地震工程与工程振动,1991,11(3):45-54Ou J P,Niu D T,Du X L.Random earthquakeground motion model and its parameter determinationused in aseismic design[J].Earthquake Engineeringand Engineering Vibration,1991,11(3):45-54
[8]杜修力,陈厚群.地震动随机模拟及其参数确定方法[J].地震工程与工程振动,1994,14(4):1-5Du X L,Chen H Q.Random simulation and its pa-rameter determination method of earthquake groundmotion[J].Earthquake Engineering and EngineeringVibration,1994,14(4):1-5
[9]赖明,叶天义,李英民.地震动的双重过滤白噪声模型[J].土木工程学报,1995,28(6):60-66Lai M,Ye T Y,Li Y M.Bi-filtered white noise mod-el of earthquake ground motion[J].China Civil Engi-neering Journal,1995,28(6):60-66
[10]李春祥,翟文杰.改进的Clough-Penzien地震地面运动模型[J].地震工程与工程振动,2003,23(5):53-56Li C X,Zhai W J.Modified Clough-Penzien earth-quake ground motion model[J].Earthquake Engi-neering and Engineering Vibration,2003,23(5):53-56
[11]洪峰,江近仁,李玉亭.地震地面运动的功率谱模型及其参数的确定[J].地震工程与工程振动,1994,14(2):46-52Hong F,Jiang J R,Li Y T.Power spectral models ofearthquake ground motions and evaluation of its pa-rameters[J].Earthquake Engineering and Engineer-ing Vibration,1994,14(2):46-52
[12]洪峰.基底隔震结构的随机地震反应分析和概率设计[D].哈尔滨:国家地震局工程力学研究所,1995Hong F.Stochastic earthquake response analysis andprobability design of base-isolated structures[D].Harbin:Institute of Engineering Mechanics,StateSeismological Bureau,1995
[13]王君杰,江近仁.关于地震动平稳自功率谱模型的注记[J].世界地震工程,1997,13(2):37-40Wang J J,Jiang J R.A note on stationary auto-powerspectrum models for earthquake ground motion[J].World Information on Earthquake Engineering,1997,13(2):37-40
[14]孙广俊,李鸿晶.平稳随机地震地面运动过程模型及其统计特征[J].地震工程与工程振动,2004,24(6):21-26Sun G J,Li H J.Stationary models of random earth-quake ground motion and their statistical properties[J].Earthquake Engineering and Engineering Vibra-tion,2004,24(6):21-26
[2]Kanai K.Semi-empirical formula for the seismic char-acteristics of the ground motion[J].Bulletin of theEarthquake Research Institute,University of Tokyo,1957,35(2):308-325
[3]Tajimi H.A statistical method of determining themaximum response of a building structure during anearthquake[A].2nd WCEE[C].Tokyo,Japan,1960
[4]胡聿贤,周锡元.弹性体系在平稳和平稳化地面运动下的反应[A].中国科学院土木建筑研究所地震工程研究报告集(第一集)[C].北京:科学出版社,1962
[5]金家和,胡聿贤,周锡元.关于“弹性系统在平稳和平稳化地面运动下的反应”一文的讨论[A].中国科学院工程力学研究所地震工程研究报告集(第二集)[C].北京:科学出版社,1965
[6]Clough R W,Penzien J.Dynamics of structures[M].2nd edition,New York,McGraw-Hill,Inc.,1993
[7]欧进萍,牛荻涛,杜修力.设计用随机地震动的模型及其参数确定[J].地震工程与工程振动,1991,11(3):45-54Ou J P,Niu D T,Du X L.Random earthquakeground motion model and its parameter determinationused in aseismic design[J].Earthquake Engineeringand Engineering Vibration,1991,11(3):45-54
[8]杜修力,陈厚群.地震动随机模拟及其参数确定方法[J].地震工程与工程振动,1994,14(4):1-5Du X L,Chen H Q.Random simulation and its pa-rameter determination method of earthquake groundmotion[J].Earthquake Engineering and EngineeringVibration,1994,14(4):1-5
[9]赖明,叶天义,李英民.地震动的双重过滤白噪声模型[J].土木工程学报,1995,28(6):60-66Lai M,Ye T Y,Li Y M.Bi-filtered white noise mod-el of earthquake ground motion[J].China Civil Engi-neering Journal,1995,28(6):60-66
[10]李春祥,翟文杰.改进的Clough-Penzien地震地面运动模型[J].地震工程与工程振动,2003,23(5):53-56Li C X,Zhai W J.Modified Clough-Penzien earth-quake ground motion model[J].Earthquake Engi-neering and Engineering Vibration,2003,23(5):53-56
[11]洪峰,江近仁,李玉亭.地震地面运动的功率谱模型及其参数的确定[J].地震工程与工程振动,1994,14(2):46-52Hong F,Jiang J R,Li Y T.Power spectral models ofearthquake ground motions and evaluation of its pa-rameters[J].Earthquake Engineering and Engineer-ing Vibration,1994,14(2):46-52
[12]洪峰.基底隔震结构的随机地震反应分析和概率设计[D].哈尔滨:国家地震局工程力学研究所,1995Hong F.Stochastic earthquake response analysis andprobability design of base-isolated structures[D].Harbin:Institute of Engineering Mechanics,StateSeismological Bureau,1995
[13]王君杰,江近仁.关于地震动平稳自功率谱模型的注记[J].世界地震工程,1997,13(2):37-40Wang J J,Jiang J R.A note on stationary auto-powerspectrum models for earthquake ground motion[J].World Information on Earthquake Engineering,1997,13(2):37-40
[14]孙广俊,李鸿晶.平稳随机地震地面运动过程模型及其统计特征[J].地震工程与工程振动,2004,24(6):21-26Sun G J,Li H J.Stationary models of random earth-quake ground motion and their statistical properties[J].Earthquake Engineering and Engineering Vibra-tion,2004,24(6):21-26
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