Transient Drainage to Partially Penetrating Drains in Sloping Aquifers
Publication: Journal of Irrigation and Drainage Engineering
Volume 125, Issue 5
Abstract
The nonlinear Boussinesq unsteady-state differential equation used for evaluating drainage of sloping lands with drains lying at a distance above the impermeable layer was solved. A combination of explicit and implicit difference methods was used to obtain a finite-difference solution for a linearized system of equations of Graute-Nicolson type on two time levels, ensuring the stability of the solution. The maximum height of the water tables was obtained as a function of time for different slopes varying from 0 to 70%. Model results were compared with the available experimental solutions of Luthin and Guitjens and Chauhan et al. as well as the numerical solution of Moody and were found to be in reasonable agreement.
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References
1.
Boussinesq, J. (1904). “Rescherches theoretiques surl ecoulement des nappes d'eau infiltrees dans le sol et sur le de'bit des sources.” J. Math. Pures et Appl., 10(5), 5–78 (in French).
2.
Chapman, T. G. (1980). “Modeling groundwater flow over sloping beds.” Water Resour. Res., 16(6), 1114–1118.
3.
Chauhan, H. S., Schwab, G. O., and Hamdy, M. Y. (1968). “Analytical and computer solutions of transient water table of drainage of sloping land.” Water Resour. Res., 4(3), 573–579.
4.
Douglas, J. (1958). “The application of stability analysis in the numerical solution of quasi-linear parabolic differential equations.” Trans., Am. Math. Soc., 89, 484–518.
5.
Douglas, J., and Jones, D. F. (1963). “On predictor-corrector methods for non linear parabolic differential equations.” J. Soc. Indust. Appl. Math., 11, 195–204.
6.
Du Fort, E. C., and Frankel, S. P. (1953). “Stability conditions in the numerical treatment of parabolic differential equations.” Mathematical Tables and other Aids to Computation, 7, 135–152.
7.
Guitjens, J. C., and Luthin, J. N. (1965). “Viscous model study of drain spacing on sloping land and comparison with mathematical solution.” Water Resour. Res., 1(4), 523–530.
8.
Luthin, J. N., and Guitjens, J. C. (1967). “Transient solutions for drainage of sloping land.”J. Irrig. and Drain. Div., ASCE, 93(13), 43–51.
9.
Moody, W. T. (1966). “Non linear differential equation of drain spacing.”J. Irrig. and Drain. Div., ASCE, 92(2), 1–9.
10.
Rosenberg, D. U. V. (1969). Methods for the solution of partial differential equation. Wiley, New York.
11.
Schmid, P., and Luthin, J. N. (1964). “The drainage of sloping lands.” J. Geophys. Res., 69(8), 1525–1529.
12.
Shukla, K. N., and 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.
13.
Sewa Ram, and Chauhan, H. S. (1987a). “Subsurface drainage of a sloping lands with constant replenishment.”J. Irrig. and Drain. Engrg., ASCE, 113(2), 213–223.
14.
Sewa Ram, and Chauhan, H. S. (1987b). “Analytical and experimental solutions for drainage of sloping lands with time varying recharge.” Water Resour. Res., 23(6), 1090–1096.
15.
Yates, S. R., Warrick, A. W., and Lomen, D. O. (1985). “Hillside seepage: An analytical solution to a nonlinear Dupit-Forchheimer problem.” Water Resour. Res., 21(3), 331–336.
16.
Yussuff, S. M. H., Chauhan, H. S., Kumar, M., and Srivastava, V. K. (1994). “Transient canal seepage to sloping aquifer.”J. Irrig. and Drain. Engrg., ASCE, 120(1), 97–109.
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Received: Oct 28, 1997
Published online: Oct 1, 1999
Published in print: Oct 1999
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