Analytical Solutions for Consolidation of Unsaturated Soil with Time-Dependent Boundary Conditions

Unsaturated soil is widely distributed in geotechnical projects, of which the consolidation and settlement are of great importance. Based on the consolidation theory of unsaturated soil, proposed by Fredlund and Hansan, this paper deals with one-dimensional consolidation of single-layer unsaturated soil with six types of boundary conditions, which can be denoted by arbitrary specified time-dependent functions. The analytical solutions in the time domain are provided directly, by homogenization of nonhomogeneous boundary conditions and the eigenfunction expansion method. Until then, the solutions for excess pore-water pressure and excess pore-air pressure in the single-layer unsaturated soil with all possible Dirichlet or Neumann boundary conditions are provided. Finally, the analytical solutions in this paper are validated against published results, and responses of excess pore-water pressure and excess pore-air pressure in the soil layer subjected to different time-dependent boundary conditions are investigated.