Generalized analytical solution for the consolidation of unsaturated soil under partially permeable boundary conditions

Previous studies have usually idealized the boundary conditions of unsaturated soil as absolutely permeable or impermeable. However, this assumption is not sound for the majority of cases where the boundary is partially permeable. In this study, partially permeable conditions are described using exponential functions for the excess pore-air and pore-water pressures at the boundaries. A generalized analytical solution for the consolidation of unsaturated soil under these proposed boundary conditions and constant initial excess pore-air and pore-water pressure conditions were obtained. The results of the proposed solution agreed with an analytical solution available in the literature, which verifies the feasibility of this study. The proposed solutions were subsequently tested and compared to published experimental data. Furthermore, a new concept, degree of drainage, was developed to characterize the partial-drainage conditions at the boundaries. Finally, a parametric study was carried out to show the consolidation characteristics under different degrees of drainage and ratios of hydraulic conductivities of air and water phases. The excess pore-pressure dissipation processes at the boundaries and the average degrees of consolidation for both the air and water phases are presented and discussed.