Steady, 2D Darcian seepage from a zero-depth reservoir into a homogeneous porous bank is studied analytically. Using the Green-Ampt assumption for hydraulic conductivity as a function of pressure and the Vedernikov model for the tension-saturated zone, a free boundary problem with the capillary fringe spread along the bank surface is solved. Accurate direct calculations are made for the extent of the capillary rise along a vertical and horizontal bank. Unsaturated flow from a vertical phreatic surface into a bank with either an impermeable or isobaric vertical soil slope is analyzed in terms of the Philip model. Explicit expressions for the Darcian velocity components, stream function, and/or Kirchhoff potential are presented. The flow topology and characteristics are shown to depend strongly on the boundary condition at the soil surface.
Abstract Accurate estimation of effective saturated hydraulic conductivity ( K sat ) of a vadose zone with an underlying shallow perched aquifer is challenging. Standard pumping tests and double‐ring infiltrometers are unsuitable for this purpose. Therefore, a bailout test (BOT) was conducted in nine soil pits to evaluate the hydraulic properties of the vadose zone and the subjacent shallow‐perched aquifer in a porous bed of a wadi in Oman. The analytical (Kirkham's type) and numerical (HYDRUS‐2D) models were also used. Upon instantaneous emptying, the water level rises in a pit, owing to seepage from the ambient shallow aquifer. The draw up was monitored and compared with modeling, which assumes a homogeneous or layered van Genuchten's soil. The soils of the excavated pits were characterized as sandy‐textured, gleyed, and containing calcareous and clay‐enriched layers. A good match between HYDRUS‐analytical results for layered soils and an idealized homogeneous one illustrates that BOT is a robust and quick technique for the estimating K sat = 2–3 cm/h in the coarse‐textured wadi bed vadose zone overlaying a transient water table. BOT is better than classical auger hole tests because they test a larger soil volume through induced seepage. BOT is also more suitable for drainage trenches and other excavations, allowing for easier observation, soil sampling from the banks, and rapid dewatering.
A complex‐variable method and series expansions are applied to optimal‐shape design problems for a channel bed. A dimensionless depth of a trapezoidal and rectangular channel is determined by minimizing the cost function constrained by specified hydraulic characteristics. The cost function includes seepage losses and the cost of lining. The hydraulic constraints are cross‐sectional area, the hydraulic radius, and the discharge. The problem of steady‐state two‐dimensional seepage involves determination of a phreatic surface with geometrical parameters as control functions. The extremes found are stable for minor perturbations of channel shape. The optimal criterion value for trapezoidal channels is close to Preissmann's for an arbitrary bed outline. The including of supplementary factors (the cost of evaporating water, of the channel land area, and so on) as criteria are discussed.
Abstract A tension-saturated water slug descends through a homogenous soil after a rainfall (irrigation) event and shrinks due to transpiration by a distributed root-sink and evaporation. The upper (drainage) and lower (imbibition) sharp fronts of the slug separate it from the superjacent and subjacent vadose zones, where water is immobile. In the slug, the hydraulic conductivity is constant according to the Green-Ampt model. The capillary pressures as well as effective porosities on the fronts are given (generally, different) constants that can be viewed as a kind of hysteresis. A volumetric sink models mild (no desaturation of the slug) soil water withdrawal by the plant roots. The sink intensity varies with the depth from the soil surface and with time. Mathematically, the hydraulic head is immediately expressed by double integration of a governing 1-D flow equation. The pressure and kinematic conditions on the fronts result in a Cauchy problem for a system of two ODEs, which is solved by computer algebra routines. Editor D. Koutsoyiannis Citation Kacimov, A. and Obnosov, U., 2013. Pseudo-hysteretic double-front hiatus-stage soil water parcels supplying a plant–root continuum: the Green-Ampt-Youngs model revisited. Hydrological Sciences Journal, 58 (1), 1–12.
