研究了非均匀土层自由场地震动的二维简化模型. 取非均匀土层剪切模量沿深度按幂函数变化( G=G0ΖP ,其中G0 和P为常数) . 首先,利用弹性波动理论,得到土介质的二维波动方程;再采用分离变量法来求解该方程,根据波的衰减特性确定波沿水平方向衰减系数,得到水平分量的解析解;然后,将水平分量的解析解带入原二维波动方程组中,将原二维波动方程组转化为一维形式.再利用MATLAB计算软件计算出其数值解;最后,通过具体算例,分别对研究的二维简化模型与一维剪切梁模型进行比较.%In this paper the simplified 2-D model for determination of free field seismic motion of non-homogeneous soil stratum is studied. The variation of shear modulus of non-homogeneous soil along the depth is taken in a power function (G=G0ΖP, G0 and P for the constant). Firstly, the two-dimensional wave equation of the soil is obtained by using the theory of elastiodynamics. The variable separation method is used to solve the equation. According to the attenuation properties of wave propagation to infinity the wave attenuation coefficient along the horizontal direction is determined. And the analytical solution of horizontal component is obtained. Then the solution of horizontal component was substituted into the original two-dimensional motion equation and the two-dimensional motion equation is transformed into one-dimensional motion equation. The numerical solution is obtained by using MATLAB codes. Finally an numerical example is given to compare the 2-D model and 1-D model.
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