Solutions for one-dimensional consolidation of unsaturated soil with general boundary conditions subjected to time-dependent load

Based on the governing equations proposed by Fredlund and Hasan, this paper firstly establishes a mathematical model for one-dimensional consolidation of single-layer unsaturated soil with general boundary conditions, arbitrary initial conditions and time-dependent external load. Then the eigenfunction expansion method is used to derive series solutions for excess pore water pressure and excess pore air pressure in time domain directly. It can be inferred that the series solutions in this paper for one-dimensional consolidation of unsaturated soil are more general compared with previous researches, due to the generality of boundary conditions and time-dependent load. They could be degenerated into solutions for one-dimensional consolidation of unsaturated soil in various conditions. Finally, comparisons with results from previous literatures are made to validate the general series solutions in this research. More examples are provided to illustrate the consolidation behaviors of unsaturated soil with different impeded drainages on air and water phases at the boundary, and different types of external load.