Semi-analytical solutions for two-dimensional plane strain consolidation of layered unsaturated soil

In preloading ground improvement projects, vertical drains are frequently installed to accelerate the consolidation process of a soil stratum which is generally unsaturated and layered in natural. To address such issue, this study attempts to constitute a reliable two-dimensional (2D) plane strain consolidation system of layered unsaturated soil. A novel semi-analytical solution for this system is developed using the methods of Fourier expansion, Laplace transform and their inversions. In order to obtain the final solution, the proposed system is firstly converted into a set of ordinary differential systems using the methods of Fourier expansion and Laplace transform. By defining a set of new variable vectors, these ordinary differential systems are further changed into diagonal ones and solved. Then, the semi-analytical solutions for the pore-air and pore-water pressures and the soil settlement are formulated, and numerical inversion of Laplace transform is applied to obtain the final results in temporal domain. Through comparing against the existing solution and the finite difference solution, the validity and the accuracy of the proposed solutions are verified. Moreover, a worked example incorporating a step load is presented to illustrate the 2D plane strain consolidation behavior of layered unsaturated soil and the influence from the coefficient of horizontal permeability is investigated.

Automated summary

This study developed a novel semi-analytical solution for a two-dimensional plane strain consolidation system of layered unsaturated soil using Fourier expansion and Laplace transform methods. The system was converted into a set of ordinary differential systems and solved, resulting in semi-analytical solutions for pore-air and pore-water pressures as well as soil settlement, verified against existing and finite difference solutions. A worked example with a step load was used to illustrate consolidation behavior and investigate the influence of horizontal permeability coefficient.