Analytical Solution for Transient Water Table Heights and Outflows from Inclined Ditch-Drained Terrains
Publication: Journal of Irrigation and Drainage Engineering
Volume 128, Issue 6
Abstract
This paper presents two analytical solutions of the linearized Boussinesq equation for an inclined aquifer, drained by ditches, subjected to a constant recharge rate. These solutions are based on different initial conditions. First, the transient solution is obtained for an initially fully saturated aquifer. Then, an analytical expression is derived for the steady state solution by allowing time to approach infinity. As this solution represents the groundwater table shape more realistically, this water table profile is used as an initial condition in the derivation of the second analytical solution for the groundwater table height, and the in- and outflow into the ditches. The solutions allow the calculation of the transient behavior of the groundwater table, and its ouflow, due to changing percolation rates or water level heights in both ditches.
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References
Arfken, G. B., and Weber, H. J. (1995). Mathematical methods for physicists, Academic, New York.
Boussinesq, J.(1877). “Essai sur la théorie des eaux courantes.” Mem. Acad. Sci. Inst. France, 23(1), 252–260.
Brutsaert, W.(1994). “The unit response of groundwater outflow from a hillslope.” Water Resour. Res., 30(10), 2759–2763.
Brutsaert, W., and Nieber, J. L.(1977). “Regionalized drought flow hydrographs from a mature glaciated plateau.” Water Resour. Res., 13(3), 637–643.
Childs, E. C.(1971). “Drainage of groundwater resting on a sloping bed.” Water Resour. Res., 7(5), 1256–1263.
Dumm, L. D.(1954). “Drain spacing formula.” Agric. Eng., 35, 726–730.
Glover, R. (1974). Transient ground water hydraulics, Water Resources Publications, Colorado State University.
Hooghoudt, S. B.(1940). “Bijdragen tot de kennis van enige natuurkundige grootheden van de grond. Deel 7.” Versl. Landb. Onderzoek, 46(14), B:515–707. (in Dutch)
Kim, D.-J., and Ann, M.-J.(2001). “Analytical solutions of water table variation in a horizontal unconfined aquifer: Constant recharge and bounded by parallel streams.” Hydrolog. Process., 15, 2691–2699.
Kraijenhoff van de Leur, D.(1958). “A study of non-steady groundwater flow with special reference to a reservoir coefficient.” DeIngenieur, 70, B87–B94.
Maasland, M.(1959). “Water table fluctuations induced by intermittant recharge.” J. Geophys. Res., 64, 549–589.
Su, N.(1994). “A formula for computation of time-varying recharge of groundwater.” J. Hydrol., 160, 123–135.
van der Ploeg, R. R., Krikham, M. B., and Marquardt, M.(1999). “The Colding equation for soil drainage: its origin, evolution, and use.” Soil Sci. Soc. Am. J., 63(1), 33–39.
Verhoest, N. E. C., and Troch, P. A.(2000). “Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer.” Water Resour. Res., 36(3), 793–800.
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Published In
Journal of Irrigation and Drainage Engineering
Volume 128 • Issue 6 • December 2002
Pages: 358 - 364
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Apr 17, 2001
Accepted: Jan 2, 2002
Published online: Nov 15, 2002
Published in print: Dec 2002
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