Theories of Ditch Drainage in Layered Anisotropic Soil
Publication: Journal of Irrigation and Drainage Engineering
Volume 122, Issue 6
Abstract
Approximate theoretical formulas are derived for predicting the water table position for steady rainfall or steady irrigation recharge into soil bounded by equally spaced ditch drains dug up to an impervious layer in single-, two-, and three-layered anisotropic soils. The ditch drainage problem is first solved for the single-layered case and subsequently, solutions are obtained to the twoand three-layered cases of the problem. All the solutions are based on exact mathematical procedures but utilize a physical assumption that the head loss in the arch-shaped region of the water table is negligible compared with the head loss for the remainder of the region. A correction, however, is provided to account for this head loss for all the solutions and the corrected formulas are found to be on the “safe side” for drainage design since the water table heights predicted by these formulas are higher than the actual ones. The accuracy of the proposed solution to the single-layered problem is tested by comparing it with independent solutions of Kirkham and Youngs to the same problems. A good agreement is obtained among the predicted results and the results obtained from the existing theories.
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References
1.
Barua, G., and Tiwari, K. N.(1995a). “Analytical solutions of seepage into ditches from ponded fields.”J. Irrig. and Drain. Engrg., 121(6), 396–404.
2.
Barua, G., and Tiwari, K. N.(1995b). “Theories of seepage into auger holes in homogeneous anisotropic soil.”J. Hydro., 167, 1–22.
3.
Bazaraa, A. S., et al. (1986). “Artesian and anisotropic effects on drain spacing. J. Irrig. and Drain. Engrg., 112(1), 55–64.
4.
Bear, J. (1975). Dynamics of fluids in porous media, 2nd Ed., American Elsevier Publishing Co., Inc., New York, N.Y.
5.
Childs, E. C.(1945). “The water table, equipotentials and streamlines in drained land, III.”Soil Sci., 59, 405–415.
6.
Childs, E. C.(1960). “A treatment of the capillary fringe in theory of drainage. II. Modifications due to an impermeable sub-stratum.”J. Soil Sci., 11, 293–304.
7.
Childs, E. C. (1969). An introduction to the physical basis of soil water phenomena . Wiley-Interscience, New York, N.Y.
8.
Childs, E. C., and Youngs, E. G.(1958). “The nature of the drain channel as a factor in the design of a land-drainage system.”J. Soil Sci., 9, 316–331.
9.
Dagan, G.(1964). “Spacings of drains by an approximate method.”J. Irrig. and Drain. Div., ASCE, 90(1), 41–46.
10.
Dagan, G.(1965). “Steady drainage of a two-layered soil.”J. Irrig. and Drain. Div., ASCE, 91(3), 51–64.
11.
Engelund, F.(1951). “Mathematical discussion of drainage problems.”Trans. Dan. Acad. Tech. Sci., 3, 1–64.
12.
Ernst, L. F.(1956). “Calculation of the steady flow of groundwater in vertical cross-section.”Netherlands J. Agric. Sci., 4, 126–131.
13.
Ernst, L. F. (1962). “Groundwater flow in the saturated zone and its calculation when parallel horizontal open conduits are present,” PhD thesis, Utrecht Univ., Utrecht, The Netherlands.
14.
Hammad, H. Y.(1962). “Depth and spacing of tile drain systems.”J. Irrig. and Drain. Div., ASCE, 83(1), 15–33.
15.
Herbert, R.(1970). “Modelling partially penetrating rivers on aquifer models.”Ground Water, 8, 29–36.
16.
Hinesly, T. D., and Kirkham, D.(1966). “Theory and flow nets for rain and artesian water seeping into soil drains.”Water Resour. Res., 2(3), 497–511.
17.
Kessler, J., and Oosterbaan, R. J. (1980). “Determining hydraulic conductivity of soils.”Drainage principles and applications, 2nd Ed., Publ. 16, (Edited from lecture notes of the international course on land drainage) Vol. III, Wageningen, The Netherlands, 254–296.
18.
Kirkham, D.(1958). “Seepage of steady rainfall through soil into drains.”Trans. Am. Geophys. Union, 39, 892–908.
19.
Kirkham, D.(1966). “Steady-state theories for land drainage.”J. Irrig. and Drain. Div., ASCE, 92(1), 19–39.
20.
Kirkham, D.(1967). “Explanation of paradoxes in Dupuit-Forchheimer seepage theory.”Water Resour. Res., 3, 609–622.
21.
Kirkham, D., and Powers, W. L. (1972). Advanced soil physics. Wiley-Interscience, Inc., New York, N.Y.
22.
Kirkham, D., et al. (1974). “Steady flow to drains and wells.”Drainage for Agriculture, Vol. 17, Am. Soc. of Agron., Madison, Wis., J. Van Schilfgaarde, Ed.
23.
List, E. J.(1964). “The steady flow of precipitation to an infinite series of tile drains above and impervious layer.”J. Geophys. Res., 69, 3371–3381.
24.
Lovell, C. J., and Youngs, E. G.(1984). “A comparison of steady-state land-drainage equations.”Agric. Water Mgmt., 11, 1–21.
25.
Maasland, M. (1957). “Soil anisotropy and land drainage.”Drainage of agricultural lands, Vol. 7, Am. Soc. of Agron., Madison, Wis., J. N. Luthin, Ed., 258–262.
26.
Miles, J. C., and Kitmitto, K.(1989). “New drain flow formula.”J. Irrig. and Drain. Engrg., 115(2), 215–230.
27.
Muskat, M. (1946). The flow of homogeneous fluids through porous media . J. W. Edwards Inc., Ann Arbor, Mich.
28.
Najamii, M.(1978). “Tube drainage in stratified soil above an aquifer.”J. Irrig. and Drain. Div., ASCE, 104(2), 209–228.
29.
Powers, W. L.(1967). “Seepage of steady rainfall through soil into ditches of unequal water level heights.”Soil Sci. Soc. Am. Proc., 31, 301–312.
30.
Schilfgaarde, J. V. (1957). “Theory of land drainage.”Drainage of agricultural lands, Vol. 7, Am. Soc. of Agron., Madison, Wis., J. N. Luthin, Ed.
31.
Sharma, H. C.(1991). “Ditch drainage in layered soils.”J. Irrig. and Drain. Engrg., 117(2), 184–200.
32.
Smedema, L. K.(1985). “Use of the Hooghoudt formula for drain spacing calculations in homogeneous-anisotropic soils.”Agric. Water Mgmt., 10, 283–291.
33.
Toksoz, S., and Kirkham, D. (1961). “Graphical solution and interpretation of a new drain spacing formula.”J. Geophys. Res., 66(2), 509–516.
34.
Toksoz, S., and Kirkham, D.(1971). “Steady drainage of layered soils. I: Theory.”J. Irrig. and Drain. Div., ASCE, 97(1), 1–18.
35.
Van Beers, W. F. J. (1976). “Computing drain spacing.”Bull. No. 15, Int. Inst. for Land Reclamation and Improvement, Wageningen, The Netherlands.
36.
Wesseling, J. (1979). “Subsurface flow into drains.”Drainage principles and applications, 2nd Ed., Publication 16, Vol. II, Int. Inst. for Land Reclamation and Improvement, Wageningen, The Netherlands.
37.
Wu, G., and Chieng, S. T.(1991). “A convenient drain spacing formula for layered soils.”Can. Agric. Engrg., 33, 239–243.
38.
Youngs, E. G.(1965). “Horizontal seepage through unconfined aquifers with hydraulic conductivity varying with depth.”J. Hydro., 3, 283–296.
39.
Youngs, E. G.(1975). “The effect of the depth of an impermeable barrier on water table heights in drained homogeneous soils.”J. Hydro., 24, 283–290.
40.
Youngs, E. G.(1986). “Water-table heights in drained anisotropic homogeneous soils.”Agric. Water Mgmt., 11, 1–11.
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Copyright © 1996 American Society of Civil Engineers.
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Published online: Nov 1, 1996
Published in print: Nov 1996
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