THEORETICAL ASPECTS OF THE FLOW OF WATER THROUGH ANISOTROPIC UNSATURATED SOILS

Open Access
Publisher Website
Google Scholar
Abstract
The description of flow of water through an unsaturated soil is governed by the same general laws that govern all kinds of fluid motion. The laws expressed in terms of mathematical equations are the continuity equation, the equation of state and the dynamical equation of motion. The flowing water has to satisfy the above three equations at any point of the considered soil and at any time. This leads to a non-linear partial differential equation in which the independent variables are the time and the position in space and the dependent variable is the pressure of the water or the volumetric water content. The equation is derived in cartesian and cylindrical coordinates by considering a cubical and a sector element of water conducting soil respectively. The governing equation is of such a nature that a solution exists for time t > 0 and is uniquely determined if two relationships are defined together with the specified state of the system at the initial time t = 0 and at the boundaries. The two required relations are these of pressure versus hydraulic conductivity and pressure versus volumetric water content. Because of the strong non-linearity in its terms, the equation can be solved for various initial and boundary conditions by approximating the differentials with finite differences at discrete points in the solution domain. Either a relaxation or an iteration procedure can be used.

This publication has 1 reference indexed in Scilit: