An Analytical Solution for 2D Plane Strain Consolidation in Unsaturated Soils with Lateral and Vertical Semipermeable Drainage Boundaries under Time-Dependent Loading

This paper has proposed a closed-form solution for two-dimensional (2D) plane strain consolidation in unsaturated soils with lateral and vertical semipermeable drainage boundaries under time-dependent loading. By using the eigenfunction expansion technique, the governing equations are expanded into coupled ordinary differential equations, and the final solution of pore pressures is obtained by the integral transform method. The degraded proposed solution is then verified with the existing solution. The results show full agreement with the solutions, which indicates the proposed solution and program are completely correct. Meanwhile, the comparison between the analytical solutions and the finite-element simulations also demonstrates the correctness of the proposed solution. Subsequently, the effect of semipermeable parameters and loading parameters on the consolidation behavior has been investigated through the obtained analytical solution. And the distribution of consolidation profiles along two different directions has also been studied. It can be concluded that time-dependent loading changes the dissipation process obviously compared with constant loading.