Unlined trench as a falling head permeameter: Analytic and HYDRUS2D modeling versus sandbox experiment

An isosceles triangle in a vertical cross-section of a trench is considered as a boundary from which free water in the trench seeps into a porous bed. A finite, initially impounded water volume vanishes from the channel and soil moisture moves in conjugation with surface water in a transient 2-D saturated-unsaturated regime. If capillarity is ignored and the subjacent soil is assumed to be dry before filling the channel, then a wetting front propagates as a sharp interface mated with drawdown of the channel free water. A Lembke method of consecutive steady states is used to model the interface as a rotating straight-line. A zone of Darcian seepage is a triangle, three sides of which (at each time instance) are a streamline, a constant piezometric head line and isobar. The instantaneous hinge point of the interface demarcates a zone of imbibition from a zone of drainage of this saturated triangle. Mathematically, a Green-Ampt type nonlinear first order ODE is obtained and explicitly integrated by separation of variables and the drawdown time t is explicitly expressed through the water depth H in the trench. In a sandbox with a dune sand, an experimental H(t) is measured in a trench having mild and steep bank slopes. When H(t) > 0 the drawdown rate increases that is attributed to an increase of the effect of capillarity. For this stage, Riesenkampf's analytical solution for steady 2D tension-saturated flow with a capillary fringe is used. The analytical and experimental results are compared with those obtained by HYDRUS-2D (numerical modeling), involving a reservoir boundary condition introduced for furrow irrigation applications. Model performance parameters including the root mean squared error (RMSE), mean absolute error (MAE), coefficient of determination (r²) and Nash-Sutcliffe efficiency (E) showed a good agreement between the measured and simulated values of drawdown time. Results of the t-test between the measured and simulated drawdown time showed insignificant differences at a 5% confidence interval for all the trenches (p > 0.05). HYDRUS simulations quantified the dynamics of a “sinking” saturated “bubble” under the trench: isobars, isotachs, streamlines and loci of the stagnation points are plotted. We illustrate how to use a drawdown curve H(t) for determination of saturated hydraulic conductivity and air-entrance pressure in the Vedernikov-Bouwer model.