Two‐Dimensional Analytical Solution for Transient Flow in Unsaturated Soils Considering Hydromechanical Coupling

This paper presents a two‐dimensional solution for unsaturated transient seepage flow in a trapezoidal region using analytical solutions for flow in a series of rectangular regions. The coupled formulation considers the interaction among fluid flow due to differences in head and displacement of soil particles. The solution in each rectangular region is derived using Laplace Transform and Discrete Fourier Series for two top boundary conditions: specified pressure head and specified flow rate. The accuracy of the proposed solution is verified by comparing the results against those attained from the finite difference method. The proposed solution is applied to two example problems, demonstrating its efficacy and accuracy. The findings show a significant difference in the coupled and uncoupled results for fine‐grained soils possessing a small Gardner's coefficient. Additionally, the uncoupled pressure heads advanced quicker to a steady state than the coupled ones for soils with a small Gardner's coefficient. The coupling effect becomes less prominent as Gardner's coefficient increases. This study is the first attempt in the literature to provide a solution for unsaturated flow in a trapezoidal or non‐rectangular domain using analytical solution techniques, which can better represent complex real‐world applications (e.g., slopes, embankments, dams).