Technical Papers
Sep 14, 2012

Assessment of Potential for Seepage-Induced Unraveling Failure of Flow-Through Rockfill Dams

Publication: International Journal of Geomechanics
Volume 12, Issue 5

Abstract

A purely numerical parametric study of 24 flow-through rockfill dam geometries was conducted. The nonlinear nature of the p-LaPlacian–like partial differential equation was dealt with using a finite-difference scheme that directly incorporated the exponent of a power law that replaced Darcy’s law. Convergence, use of specialty nodes, nodal density, and boundary condition effects were quantitatively investigated. The flow-field angle of the toe was found to be a useful starting point in studying the potential for unraveling failure. Factors of safety (FS) against this type of failure are then presented for a range of downstream slopes, thus showing which combinations of slope and particle diameter are unsafe. It is shown that the FS tends to drop below unity under the seepage face primarily because of the strength of the exit gradient near the toe of the structure and secondarily because of the overflow velocity. It is hoped that the techniques and results presented will facilitate the design and assessment of flow-through rockfill structures.

Get full access to this article

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

References

Basak, P. (1977). “Non-Darcy flow and its implications to seepage problems.” J. Irrig. Drain. Div., 103(IR4), 459–473.
Budd, C. J., and Collins, G. J. (1998). “An invariant moving mesh scheme for the non-linear diffusion equation.” Appl. Numer. Math., 26(1–2), 23–39.
Canadian Dam Association (CDA). (2007). “Flow-through rockfill dams.” Technical Bull. on Dam Safety. Geotechnical Considerations, sub-section 8.5. Hydro Quebec, Quebec.
Cedergren, H. R. (1989). Seepage, drainage, and flow nets, 3rd Ed., Wiley, New York.
Curtis, R. P., and Lawson, J. D. (1967). “Flow over and through rockfill banks.” J. Hydraul. Div., 93(HY5), 1–21.
DeLillo, S., Lupo, G., and Sanchini, G. (2006). “A Cauchy problem in non-linear heat conduction.” J. Phys. Math. Gen., 39(23), 7299–7303.
Desai, C. S. (1972). “Seepage analysis of earth banks under drawdown.” J. Soil Mech. Found. Div., 98(SM11), 1143–1162.
Desai, C. S. (1973). “An approximate solution for unconfined seepage.” J. Irrig. Drain. Div., 99(IR1), 71–87.
Desai, C. S., and Sherman, W. C. (1971). “Unconfined transient seepage in sloping banks.” J. Soil Mech. Found. Div., 97(SM2), 357–373.
Esteban, J. R., Rodriguez, A., and Vazquez, J. L. (1988). “A non-linear heat equation with singular diffusivity.” Commun. Partial Differ. Equ., 13(8), 985–1039.
Freeze, R. A., and Cherry, J. A. (1979). Groundwater, Prentice Hall, Englewood Cliffs, NJ.
Gao, L., and Li, Z. (1996). “Non-linear thermal conductivity of granular composite medium.” Solid State Commun., 100(1), 53–56.
Garga, V. K., Hansen, D., and Townsend, R. D. (1995). “Mechanisms of massive failure for flowthrough rockfill embankments.” Can. Geotech. J., 32(6), 927–938.
George, G., and Hansen, D. (1992). “Conversion between quadratic and power law for non-Darcy flow.” J. Hydraul. Eng., 118(5), 792–797.
Gerodetti, M. (1981). “Model studies of an overtopped rockfill dam.” Water Power Dam Construct., 25–31.
Hansen, D. (1992). “The behavior of flowthrough rockfill dams.” Ph.D. thesis, Univ. of Ottawa, Dept. of Civil Engineering, Ottawa.
Hansen, D. (2003). “A review of terminology pertaining to Darcy's Law and flow through porous media.” J. Porous Media, 6(2), 83–97.
Hansen, D., Zhao, W. Z., and Han, S. Y. (2005). “Hydraulic performance and stability of coarse rockfill deposits. Proc. Inst. Civ. Eng. Water. Manage., 158(4), 163–175.
Jardin, S. C., Bateman, G., Hammett, G. W., and Ku, L. P. (2008). “On 1-D diffusion problems with a gradient-dependent diffusion coefficient.” J. Comput. Phys., 227(20), 8769–8775.
Kells, J. A. (1995). “The analysis of flow through and over a Gabion dam.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Saskatchewan, Saskatoon, Canada.
Kleiner, D. E. (1985). “Engineering with spreadsheets.” ASCE Civil Eng. Mag., Oct., 55–57.
Leps, T. M. (1973). “Flow through rockfill.” Embankment-dam engineering, R. C. Hirschfeld, ed., Wiley, New York, 87–107.
Munier, A., Burgan, J. R., Gutierrez, J., Fijalknow, E., and Feix, M. R. (1981). “Group transformations and the non-linear heat diffusion equation.” SIAM J. Appl. Math., 40(2), 191–207.
Olsthoorn, T. N. (1985). “Modelling without special programs.” Ground Water, 23(3), 381–390.
Özisik, M. N. (1993). Heat conduction, 2nd Ed., Wiley, New York.
Parkin, A. K. (1971). “Field solutions for turbulent seepage flow.” J. Soil Mech. Found. Div., 97(SM1), 209–218.
Parkin, A. K., Trollope, D. H., and Lawson, J. D. (1966). “Rockfill structures subject to water flow.” J. Soil Mech. Found. Div., 92(SM6), 135–151.
Polyanin, A. D., and Zaitsev, V. F. (2004). Handbook of non-linear partial differential equations, Chapman & Hall/CRC Press, Boca Raton, FL
Sharp, B. B., and James, J. P. (1963). “Spatially varied flow at the toe of a rock-fill slope.” Proc. 1st Australasian Conf. on Hydraulics and Fluid Mechanics, Perth, Australia.
Smith, G. D. (1978). Numerical solution of partial differential equations: Finite difference methods, 2nd Ed., Clarendon Press, Oxford, U.K.
Souplet, P., and Weissler, F. B. (2003). “Regular self-similar solutions of the non-linear heat equations with internal data above the singular steady state.” Ann. I. H. Poincare, 20(2), 213–235.
Southwell, R. V. (1946). Relaxation methods in theoretical physics, Oxford University Press, Oxford, U.K.
Stephenson, D. (1979). Rockfill in hydraulic engineering, Elsevier Scientific, Amsterdam, Netherlands.
Stevens, M. A., and Simons, D. B. (1971). “Stability analysis for coarse granular material on slopes.” Chapter 17, River mechanics, H. W. Shen, ed., Vol. I, Fort Collins, CO.
Tanigawa, Y., Akai, T., Kawamura, R., and Oka, N. (1996). “Transient heat conduction and thermal stress problems of a nonhomogeneous plate with temperature-dependent material properties.” J. Therm. Stresses, 19(1), 77–102.
Townsend, R. D., Garga, V. K., and Hansen, D. (1991). “Finite difference modelling of the variation in piezometric head within a rockfill embankment.” Can. J. Civ. Eng., 18(2), 254–263.
Vazquez, J. L. (2007). The porous medium equation: Mathematical theory, Oxford University Press, New York.
Volker, R. E. (1969). “Non-linear flow in porous media by finite elements.” J. Hydraul. Div., 95(HY6), 2093–2114.
Wilkins, J. K. (1956). “The flow of water through rockfill and its application to the design of dams.” Proc., 2nd Australia-New Zealand Conf. on Soil Mechanics and Foundation Engineering, Institution of Engineers, Technical Publications, Wellington, New Zealand, 141-149.
Wilkins, J. K. (1963). “The stability of overtopped rockfill dams.” Proc., 4th Australia-New Zealand Conf. on Soil Mechanics and Foundation Engineering, Institution of Engineers, Univ. of Adelaide, Adelaide, Australia, 1–7.

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 12Issue 5October 2012
Pages: 560 - 573

History

Received: Aug 3, 2010
Accepted: May 19, 2011
Published online: Sep 14, 2012
Published in print: Oct 1, 2012

Permissions

Request permissions for this article.

Authors

Affiliations

David Hansen [email protected]
Associate Professor, Dept. of Civil and Resource Engineering, Dalhousie Univ., Halifax, NS, Canada B3H 4R2 (corresponding author). E-mail: [email protected]
Ali Roshanfekr
Doctoral Candidate, Dept. of Civil and Resource Engineering, Dalhousie Univ., Halifax, NS, Canada B3H 4R2.

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