平稳地震地面运动改进金井清谱的相关函数模型  

A Correlation Function Model of Earthquake-Induced Ground Motion Process with a Modified Kanai-Tajimi Spectrum

作　　者：李鸿晶[1] 孙广俊[2] 任永亮[1] 

机构地区：[1]南京工业大学土木工程学院,南京210009 [2]东南大学土木工程学院,南京210096

出　　处：《防灾减灾工程学报》2007年第3期251-257,共7页Journal of Disaster Prevention and Mitigation Engineering

基　　金：国家自然科学基金项目(50678084);江苏省自然科学基金项目(BK2005115)

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.

关 键 词：地震地面运动 随机过程 Kanai-Tajimi谱 胡聿贤谱 相关函数 

分 类 号：P315.9[天文地球—地震学]