Computer algebraic routines are applied for determination of the phreatic surface from standard boundary-value problems for ordinary differential equations. The method does not require iterative steps as other methods do and therefore may be readily used by engineers. The problem of seepage from (into) an unconfined semiinfinite aquifer into (from) an adjacent reservoir that has a sudden change of water level is revised. Comparisons with the Polubarinova-Kochina series expansion are done. Superelevation of the water table in a wetting regime compared to a drainage regime is quantified by the value of sorptivity (desorptivity). The absolute values of sorptivity and desorptivity diverge as the amplitude of the reservoir level change increases. A problem of a steady flow into (from) a constant head well from (into) an unconfined leaky aquifer is also examined. The water table elevation, well rate, and volume of the cone of depression (injection) are calculated.
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.
Axisymmetric, steady-state, Darcian flows in homogeneous and isotropic aquifers towards a toroid or disk intake are analytically studied. Both unbounded (infinite) and bounded (by an equipotential soil surface or by an impermeable horizontal caprock-bedrock) aquifers are considered. The Gauss closed-form solution from astronomy for a gravitating circle having a uniform mass distribution and the Weber solution from electrostatics for an equipotential disk are utilized. The scalar/vector fields of piezometric head (potential)/specific discharge allow for reconstruction of stream lines, isobars, isochrones, and isotachs. An air-filled toroid drains much more water than equipotential, or – inversely – at a given flow rate, the size of an empty toroid is much smaller than that of a water-filled one. The hydraulic gradients in the vicinity of modelled wells/tunnels are very high, triggering colmation and suffusion. The functionals of dissipation and drawdown over a specified zone in the far field are evaluated.
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.
Steady two-dimensional gravity-driven seepage in homogeneous porous lumps is studied with the help of conformal mappings and boundary value problem technique. The Terzaghi flow pattern for a trapezoidal dam exposed to a heavy rainstorm is analysed. For a semi-circular massif, the influence of impervious bed inclination is studied. Recharge–discharge distributions, hinge points, gradients along the lump contour as well as the total flow rate exhibiting water–bearing capacity of the unit are found in explicit form. Generalizations for non-isobaric boundary conditions are discussed.
Steady two–dimensional groundwater flow in an aquifer of constant thickness discharging into an inclined sea bottom is studied by the methods of complex analysis. The shape of an abrupt interface between moving fresh water and stagnant saline water appearing at the bottom corner of the aquifer is determined in an explicit analytical form depending on the values of the incident flow, hydraulic conductivity of the aquifer, its thickness, slope angle and densities of the two waters. The hodograph domain in this problem is an infinite curvilinear triangle. Its conformal mapping on an auxiliary half–plane and the mappings of the physical domain and a priori unknown complex potential domain are obtained by the method of PolubarinovaKochina based on the analytic theory of ordinary differential equations. The solution shows that, at small values of the incident flow, sea water intrudes deeply landward into the aquifer. Comparisons with special cases of a horizontal bottom and vertical beach are presented.
