剪切模量是幂函数的成层土的地震随机反应

基于改进的一维剪切梁模型，对剪切模量是其深度的某一幂函数的成层非均质土层，得到其稳态动力响应的封闭型解析表达式。首次证明了这种土层振型函数的正交性，然后利用随机振动理论，并基于基岩输入地震加速度的功率谱密度函数：白噪声谱和过滤白噪声谱。研究了该土层对地震的随机动力响应问题。计算结果表明，1)在基岩输入地震加速度的功率谱为白噪声谱的情况下，土层的最大期望反应均有别于过滤白噪声谱时的相应值；2)平稳输入与输出过高地估计了土层的随机响应。

Seismic Random Response of Stratified Foundations with Power Function Shear Modulus

Based on a generalized non-homogeneous shear-beam model 1] ,for stratified foundations with power function shear modulus, closed-form analytical expressions are derived for steadystate response function.The orthogonality property of the modal displacements is proved. Then,dynamic response of the stratified foundations to earthquake is studied by the theory of random vibration.Two cases of power spectral intensity function for the earthquake acceleration imput at the base rock are considered:the white noise spectrum and filter white noise spectrum.The numerical calculation results show that 1)in the case that the power spectral density of the earthquake acceleration input at the base rock is the white noise spectrum,the maximum expected response of the soil layer is diffrent from that for the case of the filter white noise spectrum.2)both the earthquake acceleration input the base rock and the response of the soil layer are stationary random process,which is over-estimates the random response of the soil layer.