A numerical model and semi-analytic equations for determining water table elevations and discharges in non-homogeneous subsurface drainage systems
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PublisherThe University of Arizona.
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AbstractA free water surface finite element model was developed. The method was implemented with the Galerkin approach to solve the Laplace equation in the saturated region. It was developed in the object oriented Visual C ++ computer language to permit easy update and drawing of the adaptive mesh. For each time step, the new water table position was calculated based on flux across the water table, a Brooks-Corey equation mass balance for the unsaturated region, and an equation that calculates water table position for the saturated region. An equation was developed to calculate a drainage transfer coefficient, alpha, based on percentage of perforated area in the drain tube wall. The drainage transfer coefficient was incorporated into the finite element model as a Fourier boundary condition. To validate the finite element model, its results were compared with the Kirkham equation results for steady state recharge of three subsurface drainage systems. The finite element model was used to calibrate a semi-analytical frozen stream tube model for subsurface drainage of heterogeneous soils. The first step in the calibration procedure is to run the finite element model for steady state recharge and calculate the water table height divided by recharge rate (the stream tube resistance to flow) as a function of distance between drains. Least squares regression is used to fit a polynomial logarithmic equation, called the resistance function, to the stream tube resistance to flow vs. distance from the drain curve. A differential equation based on the principle of conservation of mass and application of Darcy's law to the frozen stream tube was solved to obtain an equation that calculates stream tube flow rate and final water table elevation as a function of the resistance function and initial water table elevation. An example was developed for a non-homogeneous subsurface drainage system to illustrate the use of the semi-analytical model to predict water table fall and discharge.
Degree ProgramGraduate College
Agricultural and Biosystems Engineering