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.

Automated summary

This study proposes a closed-form solution for two-dimensional plane strain consolidation in unsaturated soils under time-dependent loading, considering lateral and vertical semipermeable drainage boundaries. The solution is obtained using eigenfunction expansion and integral transform methods. The correctness of the solution is verified through comparison with existing solutions and finite-element simulations. The study also investigates the effects of semipermeable parameters and loading parameters on consolidation behavior, as well as the distribution of consolidation profiles along different directions.