Soil slopes satisfying the condition of a constant exit gradient (constant Darcian velocity) and the seepage face (isobaricity) condition are found by complex analysis. For an empty drainage trench, soil is infinitely deep and the flow domain is bounded by two branches of a phreatic surface and the trench contour. The problem is solved by conformal mapping of the Zhukovskii domain (half-plane) onto the hodograph domain (lune). The ultimately stable seepage face and the inflow rate are determined as functions of a specified exit gradient. With decreasing of the gradient the trench flattens. If the gradient is 1, the depth-width aspect ratio of the trench reaches 0.21. Similar conformal mapping of a lune in the hodograph plane on a half-strip in the complex potential plane is used to solve the problem of a phreatic surface flow from a soil channel, whose equipotential contour satisfies the condition of constant "entrance" gradient. For a dam slope, the flow domain is underlain by an impermeable bottom and the hodograph is a circular triangle with a unit-gradient circle as the slope image. The Polubarinova-Kochina method of analytical differential equations is modified to reconstruct the complex coordinate and the complex potential as a function of an auxiliary variable. The resulting slope of unit exit gradient has a depth-width ratio of 1.22.
Abstract Macroscopically, a Darcian unsaturated moisture flow in the top soil is usually represented by an one-dimensional volume scale of evaporation from a static water table. On the microscale, simple pore-level models posit bundles of small-radius capillary tubes of a constant circular cross-section, fully occupied by mobile water moving in the Hagen–Poiseuille (HP) regime, while large-diameter pores are occupied by stagnant air. In our paper, cross-sections of cylindrical pores are polygonal. Steady, laminar, fully developed two-dimensional flows of Newtonian water in prismatic conduits, driven by a constant pressure gradient along a pore gradient, are more complex than the HP formula; this is based on the fact that the pores are only partially occupied by water and immobile air. The Poisson equation in a circular tetragon, with no-slip or mixed (no-shear-stress) boundary conditions on the two adjacent pore walls and two menisci, is solved by the methods of complex analysis. The velocity distribution is obtained via the Keldysh–Sedov type of singular integrals, and the flow rate is evaluated for several sets of meniscus radii by integrating the velocity over the corresponding tetragons.
Seepage through a triangular dam core is studied by the hodograph method. Core slope providing minimal seepage rate at prescribed head value and core cross-sectional area is found. A simple flow pattern involving seepage face, constant head, and non-flow boundaries is assumed. Seepage through a cake of low permeable sediments deposited along the bottom of a channel is treated analogously. © 1997 John Wiley & Sons, Ltd.
Seawater intrusion is a common problem in almost all coastal aquifers. However, the degree of intrusion may differ from one aquifer to another depending on many factors including, among others, geometric and geological conditions of the coastal aquifer, hydrological parameters, climatic conditions, pumping rates and recharge events. Proper assessment and mapping of the groundwater quality and transition zone in coastal aquifers are needed for any groundwater management in coastal aquifers. Geophysical methods represent a feasible tool for the monitoring and assessment of seawater water intrusion problems in coastal aquifers. This paper presents earth resistivity surveys that have been conducted in the coastal aquifer of Wadi Ham in United Arab Emirates. Existing monitoring wells were used to measure the horizontal and vertical variations in water salinity and thus improve the interpretation of earth resistivity imaging data. Results of 2D earth resistivity imaging surveys and chemical analyses of collected water samples were used to obtain an empirical relationship between the inferred earth resistivity and the amount of total dissolved solids. A three-dimensional mapping of the seawater intrusion transition zone was developed through the integration of two-dimensional vertical resistivity profiles. The paper demonstrates the feasibility and accuracy of geophysical methods in three-dimensional mapping of seawater intrusion problems.
Abstract Siltation of reservoir beds of recharge dams in arid climates seriously diminishes dams' storage capacity, lessens infiltration and deep percolation rates, increases water loss via evaporation, and ultimately lowers the recharge efficiency to the underlying unconfined aquifer. This study explores possibilities for enhancing the infiltration rate of a silt‐clogged recharge‐dam bed by cultivation of the Christ's thorn tree ( Ziziphus spina‐christ ), locally known as Sidr, as a hydro‐ecoengineering technique. We experimentally quantified the effect of this indigenous tree on the infiltration rates and moisture dynamics in soil tanks and pots. Descriptive statistics and a two‐way‐repeated‐measures analysis at p < .05 were used to compare the effects of the Christ's thorns' roots and plant growth over time on the infiltration rate of silty loam soils (sediments) in the pots and tanks. The Christ's thorn trees significantly increased the steady state infiltration rate of the sediments by 1.9–5.9 times and by 1.7–3.3 times compared to the control (bare soil) in the tank and pot experiments, respectively ( p < .05). This study demonstrates the possibility of applying hydro‐ecoengineering techniques for improving the infiltration rate and hence the recharge efficiency of recharge dams in arid areas.
By the methods of complex analysis media composed of double- periodic phases with different (arbitrary) conductivity are considered. Within each phase temperature is a harmonic function and along interfaces two conjugation conditions are rigorously satisfied (continuity of temperature and normal flux component) as well as periodicity conditions along the boundaries of elementary cells. For specific examples of composites (lensed structure and chequer-board) explicit analytic solutions are derived in terms of the thermogradients. The effective conductivities are calculated. For the chequer-board composite the hodograph of effective conductivity absolute value is shown to coincide exactly with an ellipse. As a limiting case of parquets developed surfaces are studied. In the class of semi-ellipsoidal spines two non-trivial local extrema of the total flux exist alongside two global ones. Both for two-dimensional and three-dimensional protrusions these extrema appear if the conductivity ratio exceeds some critical value.
