Abstract 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.

中文翻译：

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无衬里沟槽作为落水头渗透计：分析和 HYDRUS2D 建模与沙盒实验

摘要 沟渠垂直截面上的等腰三角形被认为是沟渠中自由水渗入多孔床的边界。有限的初始蓄水量从通道中消失，土壤水分在瞬态二维饱和-不饱和状态下与地表水共轭移动。如果毛细作用被忽略，并且在填充通道之前假设下面的土壤是干燥的，那么湿润的前沿会作为一个尖锐的界面传播，与通道自由水的下降相配合。连续稳态的 Lembke 方法用于将界面建模为旋转直线。达西渗流区是一个三角形，其三边（在每个时间点）是流线、恒压头线和等压线。界面的瞬时铰接点从这个饱和三角形的排水区划分出一个吸水区。在数学上，通过分离变量获得并显式积分 Green-Ampt 型非线性一阶常微分方程，并且通过沟渠中的水深 H 显式表示下降时间 t。在具有沙丘的沙箱中，在具有温和和陡峭岸坡的沟渠中测量实验 H(t)。当 H(t) > 0 时，由于毛细作用效应的增加，压降率增加。对于此阶段，使用 Riesenkampf 的具有毛细管条纹的稳定 2D 张力饱和流的解析解。将分析和实验结果与 HYDRUS-2D（数值建模）获得的结果进行比较，涉及为沟灌应用引入的水库边界条件。模型性能参数包括均方根误差 (RMSE)、平均绝对误差 (MAE)、决定系数 (r2) 和 Nash-Sutcliffe 效率 (E)，表明压降时间的测量值和模拟值之间具有良好的一致性。测量的和模拟的回撤时间之间的 t 检验结果显示所有沟槽在 5% 置信区间内的差异不显着 (p > 0.05)。HYDRUS 模拟量化了海沟下“下沉”饱和“气泡”的动力学：绘制了等压线、等压线、流线和停滞点的轨迹。我们说明了如何使用下降曲线 H(t) 来确定 Vedernikov-Bouwer 模型中的饱和导水率和进气压力。