Seepage through earth dam with clay core and toe drain: the Casagrande–Numerov analytical legacy revisited

References

• Al-Saqri, S., Al-Maktoumi, A., Al-Ismaily, S., Kacimov, A., and Al-Busaidi, H. (2016). “Hydropedology and soil evolution in explaining the hydrological properties of recharge dams in arid zone environments.” Arabian. J. Geosci., 9(1), 1–12. doi:10.1007/s12517-015-2076-0.
   Web of Science ®Google Scholar
• Aravin, V.I., and Numerov, S.N. (1953). Theory of fluid flow in undeformable porous media, Gostekhizdat, Moscow (in Russian). English Translation: Israel Program for Scientific Translation, Jerusalem, 1965.
   Google Scholar
• Bardet, J.P., and Tobita, T. (2002). “A practical method for solving free-surface seepage problems.” Comput. Geotech., 29(6), 451–475. doi:10.1016/S0266-352X(02)00003-4.
   Web of Science ®Google Scholar
• Bazyar, M.H., and Graili, A. (2012). “A practical and efficient numerical scheme for the analysis of steady state unconfined seepage flows.” Int. J. Numer. Anal. Methods Geomech., 36(16), 1793–1812. doi:10.1002/nag.1075.
   Web of Science ®Google Scholar
• Borja, R.I., and Kishnani, S.S. (1991). “On the solution of elliptic free-boundary problems via Newton’s method.” Comput. Methods Appl. Mech. Eng., 88(3), 341–361. doi:10.1016/0045-7825(91)90094-M.
   Web of Science ®Google Scholar
• Caffarelli, L.A., and Friedman, A. (1978). “The dam problem with two layers.” Arch. Ration. Mech. Anal., 68(2), 125–154. doi:10.1007/BF00281407.
   Web of Science ®Google Scholar
• Casagrande, A. (1937). “Seepage through dams.” J. N. Engl. Water Works, 51, 295–336.
   Google Scholar
• Cedergren, H.R. (1989). Seepage, drainage and flow nets, Wiley, New York, USA.
   Google Scholar
• Chahar, B. (2004). “Determination of length of a horizontal drain in homogeneous earth dams.” J. Irrig. Drain. Eng., ASCE, 130(6), 530–536. doi:10.1061/(ASCE)0733-9437(2004)130:6(530).
   Web of Science ®Google Scholar
• Crank, J. (1984). Free and moving boundary problems, Clarendon Press, Oxford.
   Google Scholar
• Darbandi, M., Torabi, S.O., Saadat, M., Daghighi, Y., and Jarrahbashi, D. (2007). “A moving‐mesh finite‐volume method to solve free‐surface seepage problem in arbitrary geometries.” Int. J. Numer. Anal. Methods Geomech., 31(14), 1609–1629. doi:10.1002/nag.611.
   Web of Science ®Google Scholar
• Design of small dams. (1987). USBR-ISDI, Washington. https://www.usbr.gov/tsc/techreferences/mands/mands-pdfs/SmallDams.pdf
   Google Scholar
• FEMA (Federal Emergency Management Agency). (2011). Filters for Embankment Dams – Best Practices for Design and Construction.https://www.fema.gov/media-library/assets/documents/23795
   Google Scholar
• France, J.W., Alvi, I.A., Dickson, P.A., FAlvey, H.T., Rigbey, S.J., and Trojanowksi, J., 2018. Independent Forensic Team Report: Oroville Dam Spillway Incident. https://damsafety.org/sites/default/files/files/IndependentForensicTeamReportFinal01-05-18.pdf
   Google Scholar
• Friedman, A., Huang, S., and Yong, J. (1987). “Bang-bang optimal control for the dam problem.” Appl. Math. Optim., 15(1), 65–85. doi:10.1007/BF01442646.
   Web of Science ®Google Scholar
• Fukuchi, T. (2018). “New high-precision empirical methods for predicting the seepage discharges and free surface locations of earth dams validated by numerical analyses using the IFDM.” Soils Found., 58(2), 427–445. doi:10.1016/j.sandf.2018.02.011.
   Web of Science ®Google Scholar
• Gakhov, F.D. (1966). Boundary value problems, Pergamon Press, Oxford.
   Google Scholar
• Gol’dshte˘ın, R.V., and Entov, V.M. (1994). Qualitative methods in continuum mechanics, Longman, London.
   Google Scholar
• Gradstein, I.S., and Ryzhik, I.M. (1962). Tables of integrals, sums, series and products, Nauka, Moscow.
   Google Scholar
• Herreros, M.I., Mabssout, M., and Pastor, M. (2006). “Application of level-set approach to moving interfaces and free surface problems in flow through porous media.” Comput. Methods Appl. Mech. Eng., 195(1–3), 1–25. doi:10.1016/j.cma.2004.12.015.
   Web of Science ®Google Scholar
• ICOLD. (2013). Internal erosion of existing dams, levees and dikes, and their foundations. bulletin. Volume 1: Internal erosion processes and engineering assessment, ICOLD, Paris.
   Google Scholar
• Ilyinsky, N.B., and Kacimov, A.R. (1992). “The estimation of integral seepage characteristics of hydraulic structures in terms of the theory of inverse boundary-value problems.” Zeitschrift Fur Angewandte Mathematik Und Mechanik, 72(2), 103–112. doi:10.1002/zamm.19920720207.
   Web of Science ®Google Scholar
• Ilyinsky, N.B., Kacimov, A.R., and Yakimov, N.D. (1998). “Analytical solutions of seepage theory problems. Inverse methods, variational theorems, optimization and estimates (A review).” Fluid Dyn., 33(2), 157–168. doi:10.1007/BF02698697.
   Google Scholar
• The international levee handbook. (2013). CIRIA, London. http://webissimo.developpement-durable.gouv.fr/IMG/pdf/A_The_International_Levee_Handbook_C731__cle7f8a33.pdf
   Google Scholar
• Istomina, V.S. (1957). Soil stability against seepage, Gosstrojizdat, Moscow (in Russian).
   Google Scholar
• Jaafar, H.H. (2014). “Feasibility of groundwater recharge dam projects in arid environments.” J. Hydrol., 512, 16–26. doi:10.1016/j.jhydrol.2014.02.054.
   Web of Science ®Google Scholar
• Junghanns, P., and Oestreich, D. (1989). “Numerische Lösung des Staudammproblems mit Drainage.” Zeitschrift Für Angewandte Mathematik Und Mechanik, 69(2), 83–92. (in German). doi:10.1002/zamm.19890690213.
   Web of Science ®Google Scholar
• Kacimov, A.R., and Brown, G. (2015). “A transient phreatic surface mound, evidenced by a strip of vegetation on an earth dam.” Hydrol. Sci. J., 60(2), 361–378. doi:10.1080/02626667.2014.913793.
   Web of Science ®Google Scholar
• Kacimov, A.R., and Obnosov, Y.V. (2012). “Analytical solutions for seepage near material boundaries in dam cores: The Davison-Kalinin problems revisited.” Appl Math Model, 36, 1286–1301. doi:10.1016/j.apm.2011.07.088.
   Web of Science ®Google Scholar
• Kacimov, A.R., and Obnosov, Y.V. (2016). “Size and shape of steady sea water intrusion, sharp-interface wedge: The Polubarinova-Kochina analytical solution to the dam problem revisited.” J. Hydrol. Eng., ASCE, 21(8), 06016005-1-006016005-6. doi:10.1061/(ASCE)HE.1943-5584.0001385.
   Web of Science ®Google Scholar
• Kamble, R.K., Muralidhar, B., Hanumanthappa, M.S., Patil, A.V., and Edlabadkar, J.S. (2014). “Multiple approaches to analyse and control seepage in hydraulic structures.” ISH J. Hydraul. Eng., 20(1), 7–13. doi:10.1080/09715010.2013.821787.
   Google Scholar
• Lacy, S.J., and Prevost, J.H. (1987). “Flow through porous media: A procedure for locating the free surface.” Int. J. Numer. Anal. Methods Geomech., 11(6), 585–601. doi:10.1002/nag.1610110605.
   Web of Science ®Google Scholar
• Liggett, J.A., and Liu, P.L.-F. (1979). “Unsteady interzonal free surface flow in porous media.” Water Resour. Res., 15(2), 240–246. doi:10.1029/WR015i002p00240.
   Web of Science ®Google Scholar
• Martin, S., and Vázquez, C. (2013). “Homogenization of the layer-structured dam problem with isotropic permeability.” Nonlinear Anal., 14(6), 2133–2151. doi:10.1016/j.nonrwa.2013.04.002.
   Web of Science ®Google Scholar
• Mishra, G.C., and Parida, B.P. (2006). “Earth dam with toe drain on an impervious base.” Int. J. Geomech., ASCE, 6(6), 379–388. doi:10.1061/(ASCE)1532-3641(2006)6:6(379).
   Google Scholar
• Mishra, G.C., and Singh, A.K. (2005). “Seepage through a levee.” Int. J. Geomech., ASCE, 5(1), 74–79. doi:10.1061/(ASCE)1532-3641(2005)5:1(74).
   Google Scholar
• Moran, R., and Toledo, M.A. (2011). “Research into protection of rockfill dams from overtopping using rockfill downstream toes.” Can. J. Civ. Eng., 38, 1314–1326.
   Web of Science ®Google Scholar
• National Research Council. (2012). Dam and levee safety and community resilience: A vision for future practice, National Academies Press, Washington, DC.
   Google Scholar
• Nichiporovich, A.A. (1973). Dams of local materials, Strojizdat, Moscow (in Russian).
   Google Scholar
• Obnosov, Y.V., Kacimov, A.R., and Castro-Orgaz, O. (2015). “An exact analytical solution for steady phreatic flow disappearing/re-emerging towards/from a bedrock/caprock isobaric breach: The Polubarinova-Kochina-Numerov and Pavlovsky problems revisited.” Transp. Porous Media, 108(2), 337–358. doi:10.1007/s11242-015-0522-9.
   Web of Science ®Google Scholar
• Oden, J.T., and Kikuchi, N. (1980). “Theory of variational inequalities with applications to problems of flow through porous media.” Int. J. Eng. Sci., 18(10), 1173–1284. doi:10.1016/0020-7225(80)90111-1.
   Web of Science ®Google Scholar
• Ouria, A., and Toufigh, M.M. (2009). “Application of Nelder-Mead simplex method for unconfined seepage problems.” Appl Math Model, 33(9), 3589–3598. doi:10.1016/j.apm.2008.12.001.
   Web of Science ®Google Scholar
• Peter, P. (1982). Canal and river levees, Elsevier, Amsterdam.
   Google Scholar
• Polubarinova-Kochina, P.Y. (1962). Theory of ground water movement, Princeton University Press, Princeton. Second edition of the book in Russian is published in 1977, Nauka, Moscow.
   Google Scholar
• Rice, J.D., and Duncan, J.M. (2010). “Findings of case histories on the long-term performance of seepage barriers in dams.” J. Geotechnical Geoenviron.Eng., ASCE, 136(1), 2–15. doi:10.1061/(ASCE)GT.1943-5606.0000175.
   Web of Science ®Google Scholar
• Simcore Software. (2012). Processing modflow: An integrated modeling environment for the simulation of groundwater flow, transport and reactive processes.
   Google Scholar
• Strack, O.D.L. (2017). Analytical groundwater mechanics, Cambridge Univ. Press, Cambridge, UK.
   Google Scholar
• Sumi, T. (2008). “Designing and operating of flood retention dry dams in Japan and USA.” Adv. Hydro-Sci. Eng., 8, 1768–1777.
   Google Scholar
• Tanchev, L. (2014). Dams and appurtenant hydraulic structures, CRC Press, Boca Raton.
   Google Scholar
• Tayfur, G., Swiatek, D., Wita, A., and Singh, V. (2005). “Case study: Finite element method and artificial neural network models for flow through Jeziorsko earthfill dam in Poland.” J. Hydraulic Eng. ASCE, 131(6), 431–440. doi:10.1061/(ASCE)0733-9429(2005)131:6(431).
   Web of Science ®Google Scholar
• Wolff, T.F. (2002). Performance of levee under seepage controls: A critical review (Paper No. ERDC/GSL-TR-02-19). Vicksburg Lab.
   Google Scholar
• Wolfram, S. (1991). Mathematica. A system for doing mathematics by computer, Addison-Wesley, Redwood City.
   Google Scholar
• Wu, M.X., Yang, L.Z., and Yu, T. (2013). “Simulation procedure of unconfined seepage with an inner seepage face in a heterogeneous field.” Sci. China. Phys. Mech. Astron., 56(6), 1139–1147. doi:10.1007/s11433-013-5071-z.
   Web of Science ®Google Scholar
• Zhang, L.M., Peng, M., Chang, D., and Xu, Y. (2016). Dam failure mechanisms and risk assessment, Wiley, Singapore.
   Google Scholar
• Zhilenkov, V.N. (1968). Hydroisolation properties of soils making cores and liners in large dams, Energiya, Leningrad (in Russian).
   Google Scholar