Semi-analytical solutions to the two-dimensional plane strain consolidation for unsaturated soil with the lateral semi-permeable drainage boundary under time-dependent loading

Using Fourier sine series expansion and Laplace transform, semi-analytical solutions for the two-dimensional plane strain consolidation problem of unsaturated soils are presented subjected to time-dependent loading with the lateral semi-permeable drainage boundary (LSDB), which is the third boundary and can be used to consider the smear effect of the vertical drain. Then, degenerated and numerical solutions are provided to verify the validity of the proposed solutions. Finally, the consolidation property involving the LSDB and time-dependent loading is depicted and analyzed, and the consolidation behavior is shown to result from the application of the LSDB and loading.