Finite Hankel Transform Method–Based Analysis of Axisymmetric Free-Strain Consolidation Theory for Unsaturated Soils

Abstract In this paper, the smear effect and the sand cushion that modifies the permeability of the top boundary are considered equivalently as semipermeable boundaries, to obtain an axisymmetric free-strain consolidation model for unsaturated soils capable of allowing for coupled radial–vertical flow under time-dependent loading. The semianalytical solution is then solved with finite Hankel transform and Laplace transform. This is also verified by comparison with two special cases of axisymmetric consolidation solutions in unsaturated soils. After analysis of the parameters, it is concluded that as the radial or vertical semipermeability factor increases, there is less impediment to the dissipation of excess pore pressures (EPPs); and when it takes values within 0.1–50, it can be used to simulate boundaries with arbitrary permeability from permeable to impermeable. The EPP distribution at different points and times reveals that the effect of the air- and water-phase semipermeability factor on the consolidation of unsaturated soil is different. Furthermore, the contour plots of EPP distribution under free-strain assumption provide a decent reflection of the smear effect and the alteration of the top boundary permeability due to the sand cushion.