Semi-analytical solution to one-dimensional consolidation of double-layered unsaturated ground

Combining the one-dimensional (1D) consolidation theory of unsaturated soils proposed by Fredlund and Hasan and the interfacial continuity conditions during the consolidation, the 1D consolidation model for a double-layered unsaturated ground is obtained in this study. The Laplace transformation is adopted to convert the partial differential equations into the ordinary ones, and the solutions to the excess pore pressures and settlements in the Laplace domain can be acquired. The semi-analytical solution to 1D consolidation of the double-layered unsaturated ground in the time domain is calculated after taking the inverse Laplace transformation by numerical Crump method. A comparison with the finite difference solution and the available analytical solution illustrates that the proposed solution is effective. Based on the proposed semi-analytical solution, the distribution of the excess pore pressures with ratio of various permeability coefficients in the two-layered unsaturated ground is studied, and the parametric studies are made to investigate the influences of the thickness ratio of the soil layer and the ratio of permeability coefficients on the settlement of the double-layered unsaturated ground.