Transient Canal Seepage to Sloping Aquifer
Publication: Journal of Irrigation and Drainage Engineering
Volume 120, Issue 1
Abstract
The problem of seepage from an unlined earthen canal is considered. The phreatic surface generated on the two sides of the canal is characterized by the nonlinear Boussinesq equation incorporating the slope element. A closed‐form analytical solution to the linearized Boussinesq equation was derived. A finite‐difference solution to the nonlinear Boussinesq equation was also obtained using the unconditionally stable Du Fort‐Frankel explicit method for the seepage problem in the semiinfinite flow problem. The numerical solution in general predicted a higher phreatic surface than the analytical solution.
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References
1.
Bouwer, H. (1965). “Theoretical aspects of seepage from open channels.” J. Hydr. Engrg. Div., ASCE, 91(3), 37–59.
2.
Boussinesq, J. (1904). “Recherches theoretiques sur ecoulement des nappes d'eau infiltrees dans le sol et sur le debit des sources.” J. Math. Pures et Appl., 10(5), 5–78.
3.
Chauhan, H. S., Schwab, G. O., and Hamdy, M. Y. (1968). “Analytical and computer solutions of transient water tables for drainage of sloping lands.” Water Resour. Res., 4(3), 573–579.
4.
Dumm, L. D. (1954). “Drain spacing formula.” Agric. Engrg., 35(10), 726–730.
5.
Douglas, J. (1958). “The application of stability analysis in the numerical solution of quasi‐linear parabolic differential equations.” Trans., American Mathematical Society, 89, 484–518.
6.
Du Fort, H. C., and Frankel, S. P. (1953). “Stability conditions in the numerical treatment of parabolic differential equations.” Math. Tables Aids Comput., 7, 135–152.
7.
Garg, S. P., and Chawla, A. S. (1970). “Seepage from trapezoidal channels.” J. Hydr. Div., 96(6), 1261–1282.
8.
Hunt, W. (1972). “Seepage from shallow open channel.” J. Hydr. Div., ASCE, 98(5), 779–785.
9.
Jaiswal, C. S., and Chauhan, H. S. (1975). “A Hele‐Shaw model study of steady state flow in an unconfined aquifer resting on a sloping bed.” Water Resour. Res., 11(4), 595–600.
10.
Karadi, G., Krizek, R. J., and Elnaggar, H. (1968). “Unsteady seepage flow between fully penetrating trenches.” J. Hydrol., 6, 417–430.
11.
Kochina, P. Ya. (1962). Theory of ground water movement. Translated from Russian by J. M. R. de Wiest, Princeton University Press, Princeton, N.J.
12.
Muskat, M. (1937). The flow of homogeneous fluids through porous media. McGraw‐Hill Book Co., Inc., New York, N.Y.
13.
Rosenberg, D. U. V. (1969). Methods for the solution of partial differential equations. John Wiley and Sons, Inc., New York, N.Y.
14.
Schmid, P., and Luthin, J. N. (1964). “The drainage of sloping lands.” J. Geophys. Res., 69(8), 1525–1529.
15.
Sewa Ram, and Chauhan, H. S. (1987). “Drainage of sloping lands with constant replenishment.” J. Irrig. and Drain. Engrg., ASCE 113(2), 212–223.
16.
Sharma, H. D., and Chawla, A. S. (1974). “Analysis of canal seepage to interceptor drains.” J. Irrig. and Drain. Div., ASCE, 100(1), 351–369.
17.
Shukla, K. N., Chauhan, H. S., and Srivastava, V. K. (1990). “Finite difference solution of Boussinesq unsteady state equation for highly sloping lands.” J. Irrig. and Drain. Engrg., ASCE, 116(1), 107–113.
18.
Singh, S. R., and Jacob, C. M. (1977). “Transient analysis of phreatic aquifer lying between two open channels.” Water Resour. Res., 13(2), 411–419.
19.
Todsen, M. (1971). “On solution of transient free surface flow problems in porous media by finite difference methods.” J. Hydro., 12(3), 177–210.
20.
van Schilfgaarde, J. (1963). “Design of tile drainage for falling water table.” J. Irrig. and Drain. Div., ASCE, 89(2), 1–11.
21.
Wachyan, E., and Rushton, K. R. (1987). “Water losses from irrigation canals.” J. Hydro., 92(3–4), 275–288.
22.
Young, E. G., and Al‐Najim, M. A. (1978). “Flow through unconfined aquifers containing interceptor drains.” J. Hydro., 37(3–4), 339–348.
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Copyright © 1994 American Society of Civil Engineers.
History
Received: Dec 11, 1990
Published online: Jan 1, 1994
Published in print: Jan 1994
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