Combined Effect of Non-Darcian Flow and Semipermeable Drainage Boundaries on One-Dimensional Consolidation of Unsaturated Soil

Abstract

The present article aims to understand the consolidation of unsaturated soil enclosed by semipermeable drainage boundaries and subjected to nonlinear water flow. The transient process of fluid flow is governed by the classical diffusion equations of air and water phases. The impeded drainage boundaries are modeled as a combination of the field variables and their gradient. The nonlinear water flow is dictated by an exponent and the threshold gradient-based non-Darcian model. The fluid phases are assumed to be continuous, inviscid, and flowing in the vertical direction. The deformation modulus of the air and water phases with respect to the net normal stress and matric suction are duly incorporated into the formulations. The numerical simulations are carried out by employing the Crank–Nicolson implicit scheme of the finite-difference technique. The nonlinear differential equations are linearized by evaluating the space gradient term within the exponent in the previous (known) time step. The results are presented and analyzed in the form of normalized isochrones, consolidation curves at specific spatial points, and in the global (average) scale. The flow rule impacts the dissipation process at the later stage of consolidation.