Exact and Approximate Solutions for Seepage through Semipermeable Cutoff Walls
Publication: International Journal of Geomechanics
Volume 15, Issue 6
Abstract
An explicit analytical solution is developed for the problem of steady, two-dimensional seepage in the vertical plane through a fully penetrating, semipermeable cutoff wall. The flow is driven by a head drop across an overlying dam, whose width is equal to the width of the wall. Results including the discharge beneath the dam, the differential head across the wall, the hydraulic efficiency of the wall, and the exit gradient along the bed of the downstream reservoir are presented as dimensionless charts. Rigorous comparisons are made with solutions obtained by approximate methods, which are applicable to more-general problems. The analytical solutions and approximate methods are used to estimate the discharge and the differential head at the Shikwamkwa Dam in Ontario, Canada, and to assess the need for more-detailed seepage modeling.
Get full access to this article
View all available purchase options and get full access to this article.
References
Ambraseys, N. N. (1963). “Cut-off efficiency of grout curtains and slurry trenches.” Proc., Symp. on Grouts and Drilling Muds in Engineering Practice, Butterworths, London, 43–46.
Anderson, E. I. (2000). “The method of images for leaky boundaries.” Adv. Water Resour., 23(5), 461–474.
Anderson, E. I. (2002). “Conformal mapping of groundwater flow fields with internal boundaries.” Adv. Water Resour., 25(3), 279–291.
Anderson, E. I. (2003a). “An approximation for leaky boundaries in groundwater flow.” J. Hydrol., 274(1–4), 160–175.
Anderson, E. I. (2003b). “The effective resistance to vertical flow in Dupuit models.” Adv. Water Resour., 26(5), 513–523.
Anderson, E. I. (2005). “Modeling groundwater–surface water interactions using the Dupuit approximation.” Adv. Water Resour., 28(4), 315–327.
Anderson, E. I. (2006). “Analytical solutions for flow to a well through a fault.” Adv. Water Resour., 29(12), 1790–1803.
Anderson, E. I., and Bakker, M. (2008). “Groundwater flow through anisotropic fault zones in multiaquifer systems.” Water Resour. Res., 44(11), W11433.
Bakker, M., and Anderson, E. I. (2003). “Steady flow to a well near a stream with a leaky bed.” Ground Water, 41(6), 833–840.
Bear, J., and Dagan, G. (1965). “The relationship between solutions of flow problems in isotropic and anisotropic soils.” J. Hydrol., 3(2), 88–96.
Bruce, D. A. Ressi di Cervia, A., Amos-Venti, J. (2006). “Seepage remediation by positive cut-off walls: A compendium and analysis of North American case histories.” Proc., Canadian Dam Association Conf., Canadian Dam Association, Toronto.
Casagrande, A. (1961). “Control of seepage through foundations and abutments of dams.” Géotechnique, 11(3), 161–182.
Donnelly, C. R., Rigbey, S. J., Rigby, C., and Clark, C. (2007). “The design and construction of the Shikwamka replacement dam.” Proc., 2007 Canadian Dam Association Annual Conf., Canadian Dam Association, Toronto.
Ernst, L. F. (1979). “Groundwater flow to a deep well near a rectilinear channel.” J. Hydrol., 42(1–2), 129–146.
Gautschi, W., and Cahill, W. F. (1972). “Exponential integral and related functions.” Handbook of mathematical functions with formulas, graphs, and mathematical tables, M. Abramowitz and I. A. Stegun, eds., Dover Publications, New York, 228–237.
Harr, M. E. (1962). Groundwater and Seepage, McGraw Hill, New York.
Kacimov, A. R., and Obnosov, Y. (2012). “Analytical solutions for seepage near material boundaries in dam cores: The Davison–Kalinin problems revisited.” Appl. Math. Modell., 36(3), 1286–1301.
Kacimov, A. R., and Obnosov, Y. V. (2001). “Semipermeable boundaries and heterogeneities: Modeling by singularities.” J. Hydrol. Eng., 217–224.
Kacimov, A. R., and Obnosov, Y. V. (2008). “Leaky-layer seepage: The Verigin function revisited.” J. Eng. Math., 62(4), 345–354.
Marsal, R. J., and Resendiz, D. (1971). “Effectiveness of cutoffs in earth foundations and abutments of dams.” Proc., 4th Panamerican Conf. on Soil Mechanics and Foundation Engineering, ASCE, Reston, VA, 237–312.
Muskat, M. (1937). The flow of homogeneous fluids through porous media, McGraw Hill, New York, 208–225.
Obdam, A. N. M., and Veling, E. J. M. (1987). “Elliptical inhomogeneities in groundwater flow—An analytical description.” J. Hydrol., 95(1–2), 87–96.
Obnosov, Y., Kasimova, R., Al-Maktoumi, A., and Kacimov, A. (2010). “Can heterogeneity of the near-wellbore rock cause extrema of the Darcian fluid inflow rate from the formation (the Polubarinova-Kochina problem revisited)?” Comput. Geosci., 36(10), 1252–1260.
Obnosov, Y. V. (2009). “A generalized Milne–Thomson theorem for the case of parabolic inclusion.” Appl. Math. Modell., 33(4), 1970–1981.
Obnosov, Y. V. (2013). “An R-linear conjugation problem for a plane two-component heterogeneous structure with an array of periodically distributed sinks/sources.” Appl. Math. Modell., 37(5), 2830–2837.
Obnosov, Y. V., Kasimova, R. G., and Kacimov, A. R. (2011). “A well in a ‘Target' stratum of a two-layered formation: The Muskat–Riesenkampf solution revisited.” Transp. Porous Media, 87(2), 437–457.
Polubarinova-Kochina, P. Y. (1962). Theory of ground water movement, Princeton University Press, Princeton, NJ.
Powell, R. D., and Morgenstern, N. R. (1985). “The use and performance of seepage reduction measures.” Proc., Seepage and Leakage from Dams and Impoundments, R. L. Volpe and W. E. Kelly, eds., ASCE, Reston, VA, 158–182.
Rice, J. D., and Duncan, J. M. (2010a). “Deformation and cracking of seepage barriers in dams due to changes in the pore pressure regime.” J. Geotech. Geoenviron. Eng., 16–25.
Rice, J. D., and Duncan, J. M. (2010b). “Findings of case histories on the long-term performance of seepage barriers in dams.” J. Geotech. Geoenviron. Eng., 2–15.
Strack, O. D. L. (1989). Groundwater mechanics, Prentice Hall, Englewood Cliffs, NJ.
Strack, O. D. L., Barnes, R. J., and Verruijt, A. (2006). “Vertically integrated flows, discharge potential, and the Dupuit-Forchheimer approximation.” Ground Water, 44(1), 72–75.
Tatone, B. S. A., Donnelly, C. R., Protulipac, D. G., and Clark, C. (2009). “Evaluation of the hydraulic efficiency of a newly constructed plastic concrete cut-off wall.” Proc., 2009 Canadian Dam Association Annual Conf., Canadian Dam Association, Toronto.
U.S. Army COE. (1986). “Seepage control in earth foundations.” Chapter 9, Engineer manual No. 1110-2-1901, Washington, DC.
Van Der Veer, P. (1978). “Exact solutions for two-dimensional groundwater flow problems involving a semi-pervious boundary.” J. Hydrol., 37(1–2), 159–168.
Veling, E. J. M. (2012). “About the porous media flow through circular and elliptical anisotropic inhomogeneities.” Transp. Porous Media, 91(2), 717–732.
Verigin, N. N. (1949). “On calculation of subsurface water uptake in conditions of 2d groundwater movement.” Dokl. Akad. Nauk, 64(2), 183–186 (in Russian).
Verruijt, A. (1982). Theory of groundwater flow, 2nd Ed., Macmillan, London.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 15 • Issue 6 • December 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Apr 29, 2014
Accepted: Jul 10, 2014
Published online: Aug 7, 2014
Published in print: Dec 1, 2015
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.