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

Abstract

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. As the soil above the water table line is unsaturated, when constructing structures (e.g., houses and highways) on unsaturated soft soil, assessing the joint deformation of the structure and the foundation soil is essential to prevent excessive settlement and perhaps even cracking of the structures. When constructing on this soil, the foundations are often treated by some measures to avoid settlement and cracking. For example, vertical drains are used to accelerate the consolidation of the foundation soil. However, the presence of factors that impede drainages, such as the well resistance effect and the smear effect, brings some difficulties in calculating the coordinated deformation of the structure and the foundation soil. To integrate the effects of these factors, the research in this paper provides an analytical solution to evaluate the coordinated deformation of buildings and unsaturated soil. The analytical model can provide guidance for the construction of structures on such foundations by taking into account the unsaturated soil, the impeded drainage boundary, and the construction process.