本文将水平土层简化为剪切型多自由度线性体系,根据对土层地震反应的振型迭加法所得结果的统计分析,确定体系的传递函数。参考概率理论中有关求极值的办法,给出与功率谱密度相应的反应谱。同时,根据振型均方根的办法,给出土层的加速度、相对位移、剪应变和剪应力的最大反应值沿深度的分布。分析结果表明,文中所提供的方法与精确法所得的结果有很好的吻合。 In this paper, the horizontal soil layer is reduced to a shear-type multi-degree-of-freedom linear system. Based on the statistical analysis of the results obtained from the superposition of the mode shapes of the seismic response of the soil layer, the transfer function of the system is determined. Referring to the method of finding the extreme value in probability theory, the response spectrum corresponding to the power spectral density is given. At the same time, according to the root mean square method of vibration mode, the distribution of the maximum response value of acceleration, relative displacement, shear strain and shear stress along the depth is given. The analysis results show that the method provided in this paper is in good agreement with the result obtained by the exact method.