2D Plane Strain Consolidation Process of Unsaturated Soil with Vertical Impeded Drainage Boundaries

The consolidation process of soil stratum is a common issue in geotechnical engineering. In this paper, the two-dimensional (2D) plane strain consolidation process of unsaturated soil was studied by incorporating vertical impeded drainage boundaries. The eigenfunction expansion and Laplace transform techniques were adopted to transform the partial differential equations for both the air and water phases into two ordinary equations, which can be easily solved. Then, the semi-analytical solutions for the excess pore-pressures and the soil layer settlement were derived in the Laplace domain. The final results in the time domain could be computed by performing the numerical inversion of Laplace transform. Furthermore, two comparisons were presented to verify the accuracy of the proposed semi-analytical solutions. It was found that the semi-analytical solution agreed well with the finite difference solution and the previous analytical solution from the literature. Finally, the 2D plane strain consolidation process of unsaturated soil under different drainage efficiencies of the vertical boundaries was illustrated, and the influences of the air-water permeability ratio, the anisotropic permeability ratio and the spacing-depth ratio were investigated.