A closed-form solution for 2D plane strain consolidation in unsaturated soils considering the lateral semipermeable drainage boundary

Abstract

This paper presents a closed-form solution for two-dimensional (2D) plane strain consolidation in unsaturated soils with the lateral semipermeable drainage boundary. The partial differential governing equations (PDEs) of the 2D plane strain consolidation were expanded into two ordinary differential equations (ODEs) about time t by the eigenfunctions determined from the lateral semipermeable drainage boundary conditions. Subsequently, the ODEs were solved by the Laplace transform and its inverse transform analytically. The closed-form solution is then verified against the finite element simulation and the existing semi-analytical. The results show that the normalized pore-water pressure and pore-air pressure calculated by the closed-form solution are in perfect agreement with both finite element simulations and the existing semi-analytical solution, which indicates the correctness of the analytical solution. Based on the presented closed-form solution, it can be concluded that the closed-form solution is found to be more straightforward, simpler, and computationally faster than the semi-analytical solution. Moreover, only when the soil size H/L is greater than 1, it is meaningful to discuss the effect of semipermeable boundary on the consolidation behavior.