Semi-Analytical Solution to One-Dimensional Consolidation for Unsaturated Soils with Exponentially Time-Growing Drainage Boundary Conditions

This paper presents a semi-analytical solution to Fredlund and Hasan's one-dimensional consolidation for unsaturated soils subjected to exponentially time-growing drainage-boundary conditions. Two variables are introduced to transform the two coupled governing equations of pore-water and pore-air pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform method. Then, pore-water pressure, pore-air pressure, and soil settlement are obtained in the Laplace domain. Crump's method is adopted to perform the inverse Laplace transform to obtain semi-analytical solutions for the time domain. It is shown that the present solution is more general and applicable to various types of boundary conditions. Furthermore, several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with single, double, and mixed drainages. Finally, changes in pore-air and pore-water pressures and soil settlement with the time factor at different values of the boundary condition parameters are illustrated. In addition, parametric studies are conducted using different ratios of the air-water permeability coefficient to investigate the variations of pore-air and pore-water pressures.