We consider solutions to two boundary values problems for the Poisson equation on plane domains. We prove several estimates for integrals of solutions using geometric characteristics of domains.
Summary An analytical solution is obtained for 2‐D steady Darcian flow under and through a cutoff wall partially obstructing a homogeneous isotropic foundation of a dam. The wall is leaky; that is, flow across it depends on the ratio of hydraulic conductivity of the wall and the wall thickness that results in the third‐type (Robin) boundary condition along the wall, as compared with the Terzaghi problem for an impermeable wall. The Laplace equation for the hydraulic head is meshlessly solved in a non‐standard flow tube. A Fredholm equation of the second kind is obtained for the intensity of leakage across the wall. The equation is tackled numerically, by adjusted successive iterations. Flow characteristics (total Darcian discharge and its components through the wall and the window between the wall top and horizontal bedrock, stream function, head distribution, and Darcian velocity along the wall and tailwater bed) are obtained for various conductivity ratios, head drops across the structure, thicknesses of the foundation, and the degree of its blockage by the wall. Comparisons with the Terzaghi limit of an impermeable wall show that for common wall materials and thicknesses, the leakage may constitute tens of percent of the discharge under the dam. The through‐flow hydraulic gradients on a vertical wall face (Robin's boundary condition) as well as the exit gradients along a horizontal tailwater boundary (Dirichlet's boundary condition) acting for decades have deleterious impacts on dam stability because of potential heaving, piping, and mechanical–chemical suffusion. Copyright © 2017 John Wiley & Sons, Ltd.
Experimental measurements of the volumetric moisture content and temperature in a composite soil were done during March-May in an open area subject to direct solar radiation in Muscat, Oman. The composite was made of a silt block and sand sheath adjacent to five faces of the block, with one face open to direct evaporation. For a two layered composite soil, an analytical solution is obtained for 1-D evaporation between two isobaric horizons. A composite of minimal water losses is found by varying the thickness of the upper coarse stratum. Convection in this composite was modeled for cyclostationary temperature variations at the soil surface.
Earth and Space Science Open Archive This preprint has been submitted to and is under consideration at Water Resources Research. ESSOAr is a venue for early communication or feedback before peer review. Data may be preliminary.Learn more about preprints preprintOpen AccessYou are viewing the latest version by default [v1]Saturated Water Storage in Shallow Perched Aquifer With Evapotranspiration From the Phreatic Surface and Unsaturated Lacunae: the Saint-Venant Theory RevisitedAuthorsFaritAvkhadievAnvar RKacimoviDSee all authors Farit Avkhadievobachevsky Institute of Mathematics and Mechanics, Kazan Federal Universityview email addressThe email was not providedcopy email addressAnvar R KacimoviDCorresponding Author• Submitting AuthorSultan Qaboos UniversityiDhttps://orcid.org/0000-0003-2543-3219view email addressThe email was not providedcopy email address
Abstract An analytical solution is obtained for steady 2‐D potential seepage flow from a nonclogged and nonlined soil channel into a highly permeable porous layer, with phreatic surfaces tapering toward a horizontal interface with a subjacent low‐permeable formation. Along this boundary, a vertical component of the Darcian velocity vector equals the formation saturated hydraulic conductivity. The image of the physical flow domain in the hodograph plane is a circular polygon, a triangle or digon in a limiting case of a “phreatic jet” impinging on the low‐permeable substratum. The polygon is mapped onto an auxiliary half plane, where the complex physical coordinate and complex potential are reconstructed by the Polubarinova‐Kochina method, i.e., by solution of a Riemann BVP. The seepage flow rate from the channel, free surfaces, and a saturated (water‐logged) area are found for different thicknesses of the top layer, channel widths, and conductivity ratios of the two strata. In particular, the earlier results of Brock, Kirkham, and Youngs, which are based on a numerical solution, Dupuit‐Forchheimer (DF) approximation, and approximate potential model, are confirmed in the full 2‐D models. Sufficiently far from the channel, the phreatic surface and interface make a wedge. For a sufficiently deep substratum, three zones are analytically distinguished: an almost vertical 1‐D descending flow, an almost wedge‐configured 1‐D flow, and an essentially 2‐D zone in between, where neither a standard infiltration theory nor DF analysis are valid.
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.
