TECHNICAL PAPERS
Oct 1, 1999

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.

Get full access to this article

View all available purchase options and get full access to this article.

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.

Information & Authors

Information

Published In

Go to Journal of Irrigation and Drainage Engineering
Journal of Irrigation and Drainage Engineering
Volume 125Issue 5October 1999
Pages: 246 - 253

History

Received: Oct 28, 1997
Published online: Oct 1, 1999
Published in print: Oct 1999

Permissions

Request permissions for this article.

Authors

Affiliations

Prof., Dept. of Irrig. and Drain. Engrg., Coll. of Technol., G. B. Pant Univ. of Agr. and Technol., Pantnagar, District Nainital, U.P. 263145, India.
Prof., Dept. of Irrig. and Drain. Engrg., Coll. of Technol., G. B. Pant Univ. of Agr. and Technol., Pantnagar, District Nainital, U.P. 263145, India.
Prof. and Head, Dept. of Mathematics, Statistics and Comp. Sci., C.B.S.H., G. B. Pant Univ. of Agr. and Technol., Pantnagar, District Nainital, U.P. 263145, India.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share