Analytical solution for lateral dynamic response of pile foundation embedded in unsaturated soil

The lateral dynamic interaction of the soil and pile has been extensively studied, however, most of the existing studies simplified the soil medium as a one-phase (solid) or two phase (pore fluid, soil skeleton) medium, which is far from the true condition of the soil in nature. Based on the poroelastic continuum mechanics, a coupled dynamic unsaturated soil-pile interaction model is established in this paper. The potential function, operator decomposition method and variable separation method are introduced herein to obtain the lateral force of the unsaturated soil acting on the pile shaft. Afterwards, the analytical solution of the pile dynamic impedance in the frequency domain is derived by employing the soil-pile continuous deformation conditions and the boundary conditions of the pile. The reliability of the obtained solution is verified through the comparisons against classic simplified answers. The main conclusions found in this paper can be drawn as: (a) The increase in the saturation of the soil would decrease the soil strength, resulting in an increase in the displacements and internal force of the pile; (b) Both the increase in soil permeability and the decrease in soil saturation will lead to the decrease in the pore pressure at the side of the pile. And, the smaller the saturation is, the greater the matrix suction would be; (c) The natural frequency of the pile decreases with the increase of the soil saturation.