Research on the Lamb Problem in Semi-Infinite Space of Non-Uniform Unsaturated Soil

The porosity and shear modulus, permeability coefficient of pore water pressure and permeability coefficient of pore gas pressure of unsaturated foundation soil are considered to vary continuously and unevenly along the depth of soil layer. Couple these parameters with each other, Based on Biot’s theory of unsaturated porous media, by giving the trial function, Hankel transform is applied to transform the time-domain problem into the frequency-domain problem for solution, The analytical solutions of pore water pressure and pore gas pressure of dynamic response of semi-infinite non-uniform unsaturated space under concentrated load are given. The variation of porosity, shear modulus, permeability coefficient of pore water pressure and permeability coefficient of pore gas pressure along the depth of soil layer is analyzed. The influence of non-uniform gradient factor on the variation of pore water pressure and deformation with depth is revealed. The results show that: Within a certain depth, the greater the gradient factor, the greater the change rate of porosity with depth and the change rate of pore gas permeability coefficient with depth. The smaller the change rate of relative soil skeleton density with depth, relative fluid density with depth, relative gas density with depth, and pore fluid permeability coefficient with depth. The change rate of shear modulus with depth increases first and then decreases. The smaller the value of pore water pressure; The smaller the deformation of the non-uniform unsaturated soil layer is. The deeper the distance from the vibration source, the smaller the influence of gradient factor on the pore water pressure and deformation of the non-uniform unsaturated soil layer. After a certain depth from the vibration source, the non-uniform gradient factor does not have an impact, The parameters of unsaturated soil are equal to those of homogeneous unsaturated soil. The research results are of great significance to the theoretical study of the vibration of non-uniform unsaturated soil foundation.