强震地面运动的超随机特性研究
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摘要
简述了几种常用的地震动平稳随机模型,这几种地震动平稳随机模型的功率谱是一组光滑的函数,相应的自相关函数基本上是指数衰减的振荡函数,且很快衰减到零;但是真实地震动的归一化自相关函数则有一较显著的随机噪声项,这个随机噪声的幅值为0. 15左右,这就是本文中所说的超随机特性。目前常用的地震动平稳随机模型没有考虑这个随机噪声项及其对结构反应的影响。本文将真实地震动的自相关函数分解为一确定性函数和一随机噪声的叠加,并对自相关函数中的噪声部分进行了分析,得出两条重要性质。本文的研究结果表明地震动加速度时程的平方和(SS)比峰值加速度(PGA)更好地量度了地震地面运动强度。由于归一化自相关函数的随机噪声部分所对应的功率谱的随机波动成分对频率的积分为零,即归一化自相关函数的噪声部分对地震动总功率或平方和的贡献为零,因此自相关函数的随机噪声项对地震动的幅值影响不大,但自相关函数的随机噪声项明显改变了地震动功率谱在频域上的分布特征,因此会对结构反应产生一定的影响。由于篇幅所限详细内容将在下一篇文章中作进一步探讨。
This paper reviews some common stationary random models of earthquake ground motion. These models’ power spectra are smooth functions, and the corresponding auto-correlations are oscillating functions which attenuate exponentially to zero quickly. But the normalized auto-correlation of real seismic acceleration record comprises an obviously random noise with amplitude value of 0.15 or so, that is so called super random content. Such kind of noise in seismic wave and its effect on the structure response is never included in the common random models of earthquake ground motion. The paper points out that the auto-correlation function of ground motion can be decomposed to two parts: one is a determinate function, and the other is a random noise. The paper analyzes the noise part of autocorrelation function, and put forward two important properties possessed by the noise part. It is indicated that the SS (sum of squares) or the total power of ground motion is more adaptable measurement of the ground motion severity rather than the peak ground acceleration (PGA) of ground motion while whose main phase can be regarded as a stationary random process. Since the zero contribution of the noise part of the normalized auto-correlation to the SS of acceleration which is the integral of power spectrum density over the entire frequencies, the effect of the noise part on the manmade seismic wave’s amplitude is insignificant. It is pointed out that the random noise part in normalized autocorrelation may greatly change the frequency contents of the power spectra and then yields certain effect on the structure response.
This paper reviews some common stationary random models of earthquake ground motion. These models’ power spectra are smooth functions, and the corresponding auto-correlations are oscillating functions which attenuate exponentially to zero quickly. But the normalized auto-correlation of real seismic acceleration record comprises an obviously random noise with amplitude value of 0.15 or so, that is so called super random content. Such kind of noise in seismic wave and its effect on the structure response is never included in the common random models of earthquake ground motion. The paper points out that the auto-correlation function of ground motion can be decomposed to two parts: one is a determinate function, and the other is a random noise. The paper analyzes the noise part of autocorrelation function, and put forward two important properties possessed by the noise part. It is indicated that the SS (sum of squares) or the total power of ground motion is more adaptable measurement of the ground motion severity rather than the peak ground acceleration (PGA) of ground motion while whose main phase can be regarded as a stationary random process. Since the zero contribution of the noise part of the normalized auto-correlation to the SS of acceleration which is the integral of power spectrum density over the entire frequencies, the effect of the noise part on the manmade seismic wave’s amplitude is insignificant. It is pointed out that the random noise part in normalized autocorrelation may greatly change the frequency contents of the power spectra and then yields certain effect on the structure response.
引文
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[13] KaulMK.Stochasticcharacterizationofearthquakethroughtheirresponsespectrum[J].EarthquakeEngineeringandStructuralDynamics,1978,6(5):497~509.
[2]KanaiK.Semi empiricalformulafortheseismicCharacteristicsofgroundmotion[J].东京大学地震研究所汇报,1957,35:306~325.
[3]BarsteinMF.ApplicationofprobabilitymethodsofdesigntheeffectofseismicforcesonengineeringStructure[A].Proc.2ndWorldConf. onEarthquakeEng.[C].Japan,1960.
[4]胡聿贤,周锡元.地震力统计理论评价[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]欧进萍,牛荻涛,杜修力.设计用随机地震动模型及其参数的确定[J].地震工程与工程振动,1991,11(3):45~54.
[6]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):1~5.
[7]杜修力,胡晓,陈厚群.强震地运动随机过程模拟[J].地震学报,1995,17(1):103~109.
[8]王国权.921台湾集集地震近断层地面运动特征[D].北京:中国地震局地质研究所,2001.
[9]王国权,周锡元.921台湾地震近断层强震地面运动加速度时程的随机特性[J].防灾减灾工程学报,2003,(4):10~19.
[10] WangGuoquan,ZhouXiyuan,MaZongjin, andZhangPeizhen.Apreliminarystudyontherandomnessofresponsespectraofthe1999ChiChi,TaiwanEarthquake[J].BulletinoftheSeismologicalSocietyofAmerica,2001,91(5):1358~1369.
[11] WangGQ,ZhouXY,ZhangP,IgelandH.Characteristicsofamplitudeanddurationfornearfaultstronggroundmotionfromthe1999ChiChi,Taiwanearthquake[J].SoilDynamicsandEarthquakeEngineering,2002,22(1):73~96.
[12] 沈聚敏,周锡元,高小旺,刘晶波.抗震工程学[M].北京:中国建筑工业出版社,2002.
[13] KaulMK.Stochasticcharacterizationofearthquakethroughtheirresponsespectrum[J].EarthquakeEngineeringandStructuralDynamics,1978,6(5):497~509.
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