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

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.