非饱和土半空间表面在垂直集中力作用下的Lamb问题

以多孔介质混合物理论为基础，同时引入土体双变量本构关系，得到了非饱和土中的一组动力控制方程。利用Hankel积分变换方法，直接对频域内的波动方程进行求解，得到了轴对称情况下土体骨架位移及应力分量在变换域内的解。在此基础上研究了非饱和土半空间体在垂直集中力作用下的动力响应，给出了Lamb问题积分形式解。当不计土中水、气的存在时，上述结果退化到单相弹性半空间中的经典Lamb解。通过数值计算分析，进一步研究了各物理参数对地基动力响应的影响规律。

Lamb's Problem for Unsaturated Soils Half-space by Vertical Surface Load

Based on the mixture theory of porous media, the dynamic governing equations for unsaturated soils are developed by introducing the di-variable constitutive relations. General solutions in frequency field for axisymmetric problem are obtained by using the method of Hankel transform. The integral solutions are then presented for unsaturated soils half-space due to a vertical surface load. In the absence of pore fluid, the result are reduced to known solutions of Lamb’s problem for a conventional one-phased elastic medium. Numerical analysis is performed to study the effects of some physical parameters to the displacement of surface soil.