Steady Seepage in Trenches and Dams: Effect of Capillary Flow
Publication: Journal of Hydraulic Engineering
Volume 125, Issue 3
Abstract
Steady seepage from two-dimensional domains is investigated using a dimensionless formulation for variably saturated media that depends on three dimensionless parameters, M, n, and α. The parameter M is the product of the anisotropy ratio and the squared ratio of the vertical length scale to the horizontal length scale. The parameter n increases with the uniformity of the pore sizes, and α represents the ratio of the domain height to the height of the capillary fringe. Our modeling results show that the seepage face height in rectangular domains is always larger than the seepage face height computed from saturated flow models. The results also show that the seepage face height increases with increasing M, increasing n, and/or decreasing α. The outflows computed from the present model are always larger than the outflows computed by the Dupuit assumption. Nomographs for rectangular and trapezoidal domains simulating trenches and dams are presented.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Atkinson, K. E. ( 1978). An introduction to numerical analysis . Wiley, New York, 587.
2.
Basha, H. A. ( 1994). “Multidimensional steady infiltration with prescribed boundary conditions at the soil surface.” Water Resour. Res., 30, 2105–2118.
3.
Bear, J. ( 1972). Dynamics of fluids in porous media . Elsevier Science, New York.
4.
Boufadel, M. C. ( 1988). “Nutrient transport in beaches: Effect of tides, waves, and buoyancy,” PhD thesis, Dept. of Civ. and Envir. Engrg., University of Cincinnati, Cincinnati.
5.
Boufadel, M. C., Suidan, M. T., Venosa, A. D., Rauch, C. H., and Biswas, P. (1998). “2D variably saturated flows: Physical scaling and Bayesian estimation.”J. Hydrologic Engrg., ASCE, 3(4), 223–231.
6.
Broabridge, P., and White, I. ( 1988). “Constant rate rainfall infiltration, a versatile nonlinear model. Part 1: Analytical solution.” Water Resour. Res., 24, 145–154.
7.
Cedergren, H. R. ( 1967). Seepage, drainage, and flow nets . Wiley, New York, 489.
8.
Celia, M. A., Bouloutas, E. T., and Zarba, R. L. ( 1990). “A general mass-conservative numerical solution for the unsaturated flow equation.” Water Resour. Res., 26, 1483–1496.
9.
Charni, I. A. ( 1951). A rigorous derivation of Dupuit's formula for unconfined seepage with seepage surface, Doklady Akademii Nauk USSR, 6, 79 (in Russian). Cooley, R. L. (1983). “Some new procedures for numerical solution of variably saturated flow problems.” Water Resour. Res., 19, 1271–1285.
10.
Craig, A. W., and Wood, W. L. ( 1981). “Cost-efficiency study of various methods for solving the seepage through dam problem using variational inequalities.” Int. J. Numer. Methods in Engrg., 17, 1325–1333.
11.
Cryer, C. W. ( 1976). “A survey of steady-state porous flow free boundary problems.” MRC Tech. Sum. Rep. 1657, Madison Research Center, Madison, Wisconsin.
12.
Dean R. G., and Dalrymple, R. A. ( 1984). Water wave mechanics for engineers and scientists . Prentice-Hall, Englewood Cliffs, N.J., 353.
13.
Dupuit, J. ( 1863). Etudes theoriques et pratiques sur le mouvement des eaux dans les canaux decouverts et a travers les terrains permeables, 2nd Ed., Dunod, Paris, (in French).
14.
Freeze, R. A. ( 1971). “Three-dimensional, transient, saturated-unsaturated flow in a groundwater basin.” Water Resour. Res., 7(2), 347–366.
15.
Freeze, R. A., and Cherry, J. A. ( 1979). Groundwater . Prentice-Hall, Englewood Cliffs, N.J., 604.
16.
Gardner, W. R. ( 1958). “Some steady state solutions of the unsaturated moisture flow equation with application to evaporation from a water table.” Soil Sci., 4, 85, 228–232.
17.
Gureghian, A. B. ( 1983). “TRIPM: A two-dimensional finite-element model for the simultaneous transport of water and reacting solutes through saturated and unsaturated porous media.” Tech. Rep., Battele Memorial Institute, Columbus, Ohio.
18.
Hornung, U., and Krueger, T. ( 1985). “Evaluation of the Polubarinova-Kochina formula for the dam problem.” Water Resour. Res., 21, 395–398.
19.
Huyakorn, P. S., and Pinder, G. F. ( 1983). Computational methods in subsurface flow . Academic, New York, 473.
20.
Huyakorn, P. S., Springer, E. P., Guvanasen, V., and Wadsworth, T. D. ( 1986). “A three-dimensional finite element model for simulating water flow in variably saturated porous media.” Water Resour. Res., 22, 1790–1808.
21.
Istok, J. ( 1989). Groundwater modeling by the finite element method . American Geophysical Union, Washington, D.C.
22.
Li, L., Barry, D. A., Parlange, J.-Y., and Pattiaratchi, C. B. ( 1997). “Beach water table fluctuations due to wave run-up: Capillarity effects.” Water Resour. Res., 33(5), 935–945.
23.
Morell-Seytoux, H. J., Meyer, P. D., Nacache, M., Touma, J., van Genuchten, M. T., and Lenhard, R. J. ( 1996). “Parameter equivalence for the Brroks-Corey and van Genuchten soil characteristics: Preserving the effective capillary drive.” Water Resour. Res., 32(5), 1251–1258.
24.
Muskat, M. ( 1937). The flow of homogeneous fluids through porous media . McGraw-Hill, New York, 763.
25.
Najem, W. ( 1982). Introduction aux techniques du calcul numerique, Engrg. Facu., University of Saint Joseph, Beirut, Lebanon, 54 (in French).
26.
Neuman, S. P. (1973). “Saturated-unsaturated seepage by finite elements.”J. Hydr. Div., ASCE, (12), 2233–2250.
27.
Pinder, G. F., and Gray, W. G. ( 1977). Finite element simulation in surface and subsurface hydrology . Academic, New York, 294.
28.
Polubarinova-Kochina, P. Ya. ( 1963). Theory of ground water movement . Translated from Russian by J. M. R. De Wiest, Princeton University Press, Princeton, N.J., 613.
29.
Richards, L. A. ( 1931). “Capillary conduction of liquids through porous mediums.” Phys., 1, 318–333.
30.
Sanford, W. E., Parlange, J.-Y., and Steenhuis, T. S. ( 1993). “Hillslope drainage with sudden drawdown: Closed form solution and laboratory experiment.” Water Resour. Res., 29(7), 2313–2321.
31.
Shamsai, A., and Narasimhan, T. N. ( 1991). “A numerical investigation of free surface-seepage face relationship under steady state flow conditions.” Water Resour. Res., 27(3), 409–421.
32.
Spangler, M. G., and Handy, R. L. ( 1982). Soil engineering . Harper and Row, New York, 819.
33.
van Genuchten, M. Th. ( 1980). “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. Proc., 44, 892–898.
34.
Vauclin, M., Khanji, D., and Vachaud, G. ( 1979). “Experimental and numerical study of a transient, two-dimensional unsaturated-saturated water table recharge problem.” Water Resour. Res., 15(5), 1089–1101.
35.
Verma, R. D., and Brutsaert, W. (1970). “Unconfined aquifer seepage by capillary flow theory.”J. Hydr. Div., ASCE, 96(6), 1331–1344.
36.
Voss, C. I. ( 1984). “SUTRA, a finite-element model for saturated-unsaturated. Fluid-density-dependent groundwater flow with energy transport or chemically reactive single species solute transport.” Water Resour. Invest. Rep. 84-4369, U.S. Geological Survey.
37.
Warrick, A. W., Islas, A., and Lomen, D. O. ( 1991). “An analytical solution to Richard's equation for time varying infiltration.” Water Resour. Res., 27(5), 763–766.
38.
Wise, W. R., Clement, T. P., and Molz, F. J. ( 1994). “Variably saturated modeling of transient drainage: Sensitivity to soil properties.” J. Hydro., Amsterdam, 161, 91–108.
39.
Yeh, G. T. ( 1981). “On the computation of Darcian velocity and mass balance in the finite element modeling of groundwater flow.” Water Resour. Res., 17, 5, 1529–1534.
Information & Authors
Information
Published In
History
Received: Feb 3, 1997
Published online: Mar 1, 1999
Published in print: Mar 1999
Authors
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.