Abstract:

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.

Key words: unsaturated soil, Lamb＇s problem, mixture theory, dynamic response, integral transform