A general analytical solution to the one-dimensional consolidation problem for unsaturated soil under various loading conditions

A general analytical solution is developed for the one-dimensional consolidation problem of unsaturated soil under various time-dependent loading conditions based on a differential transformation method (DTM). In particular, analytical solutions are obtained for different relationships between the coefficients in the governing equations for unsaturated soil consolidation. The Fourier series expansion technique is adopted to account for both the continuous differentiable loading and the periodic piecewise loading. A comparison between the results of the current solution and the existing theoretical solution indicates that the proposed solution yields excellent results, while it is straightforward to obtain the analytical solution of the unsaturated consolidation problems. It was also found that the variations in the coefficients in the governing equations can significantly influence the dissipation of both the excess pore-air pressure and the excess pore-water pressure, though the magnitudes of their variations are different.