Water table fluctuation in soils overlying semi-confined aquifers in response to time-varying replenishment

Abstract

The water table height in drained agricultural land depends on time-varying replenishment that is due to the vertical downward recharge from irrigation or rainfall, and in some cases to the upward vertical leakage from a semi-confined aquifer. The downward recharge may be assumed to vary exponentially with time, whereas the upward leakage may be expressed as a function of the unknown water table height. Furthermore, the rising of the water level in the field drainage system, that may cause an inverse flow from the drains towards the soil, is introduced through a properly defined boundary condition. A non-homogeneous form of the Boussinesq equation, that is used to describe this particular drainage problem, is solved for three different initial conditions. The same drainage problems were solved numerically by using the finite element method. Comparison between analytical and numerical solutions shows satisfactory agreement. From the analytical solutions we obtain the non-dimensional water table height at the midpoint between the drains, and the non-dimensional discharge of the drains per unit drained area, as functions of non-dimensional time and constants describing the aforementioned drainage conditions. Variation of these functions has also been illustrated graphically in non-dimensional diagrams; these can be used to show the sensitivity to various sets of parameter values and to calculate easily the water table height and the drain discharge in practical problems.