Flow in a vertical porous column drained at its bottom at constant flux

Abstract

A soil column, saturated at its lower portion and initially in condition of hydrostatical equilibrium is drained at a constant flux at its bottom. Due to the presence of the unsaturated zone above the water table, the motion of the saturation surface depends in a complex manner on time and on soil properties. After defining a characteristic length, the equation of unsaturated flow is solved numerically by a finite difference scheme for different values of drained flux, for two similar soils. Although moisture and head profiles are different for both soils, drawdown curves have been found to be in good agreement during a certain time interval which depends on the value of the drained flux. The same problem is solved analytically by a linearization procedure. A simple expression which predicts saturation surface drawdowns quite accurately for small values of the drained flux and for moderate time intervals, is derived. An effective porosity coefficient is defined and its variation with time is represented. The bearing of the results on flow in unconfined aquifers is discussed.