垂直集中表面荷载作用下非饱和土半空间中的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,对频域内的轴对称问题进行了求解.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问题的积分形式解.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.数值计算结果表明:激振频率、渗透系数对地表位移影响显著,随激振频率的升高或渗透系数的降低,近场地表位移幅值减小,但当渗透系数低于一定值时,地表位移基本不再随其变化;饱和度对地表位移的直接影响是饱和度升高时,地表位移幅值略有减小.

Lamb's Problem for Unsaturated Soils Half-Space Under Vertical Concentrated Surface Load

Based on the mixture theory for porous medium, a group of dynamic governing equations for unsaturated soils is developed by introducing the bi-variable constitutive relations of soils. Then, with the help of Hankel integral transform, general solutions to axisymmetric problems are obtained in the frequency field, based on which the dynamic response of the unsaturated soils half-space subjected to a vertical concentrated surface load is investigated. Moreover, the integral solutions to Lamb's problem are obtained, which, in the absence of water and gas, degrade to the known conventional ones to Lamb's problem for one-phase elastic medium. Numerical results show that (1) both the excitation frequency and the permeability coefficient have significant effects on the displacement of ground surface;(2) the displacement decreases with the increase in excitation frequency and with the decrease in permeability coefficient, but remains unchanged when the permeability coefficient decreases to a certain low value;and (3) the direct influence of saturation on displacement lies in the facts that the latter slightly decreases with the increase of the former.