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Hydraulic Conductivity of Coarse Rockfill used in Hydraulic Structures


Internal erosion is a major cause of embankment dam failure. Unravelling and instability of the downstream slope, initiated by internal erosion and leakage through the dam core, is one of the most likely breach mechanisms for large, zoned embankment dams. To be able to model this mechanism, the relationship between the hydraulic gradient and the flow velocity for the coarse rockfill material must be understood. Because most studies of this topic have focused on the flow parameters in gravel-size materials with Reynolds (Re) numbers lower than 25,000, permeability measurements are needed coarser rockfill material under heavily turbulent flow regimes prevailing in rockfill material under certain design flow scenarios. This paper presents the set-up and results of a series of field and laboratory experimental studies and the subsequent data interpretation, from which relevant hydraulic conductivity parameters, defined in applicable flow laws, were extracted. This study demonstrates that the exponent of a power flow law relating the hydraulic gradient and the flow velocity is Re number dependent for pore Re numbers \(<\)60,000. The power remains constant (Re number independent) above this Re number threshold for the fully developed turbulent regime. This validity threshold as well as the constant behaviour also applies if the flow law is written in a quadratic form. The aforementioned threshold lies beyond the ranges investigated experimentally by previous researchers. The experiments in this study examined Re numbers as large as 220,000 for grain-diameter distributions in the range 100–160 mm and as large as 320,000 in the range 160–240 mm.

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\(a\) :

Energy dissipation index (–)

\(A_{\mathrm{vs}}\) :

Volume-specific surface area (\(\hbox {m}^{2}\))

\(b\) :

Coefficient depending on the fluid and porous medium properties (\(\hbox {m}^{1-\mathrm{a}}\,\hbox { s}^{\mathrm{a}-1}\))

\(\acute{b}=b/n^{a}\) :

Permeability parameter used for field test ODE (\(\hbox {m}^{1-\mathrm{a}}\,\hbox { s}^{\mathrm{a}-1}\))

\(c_{\mathrm{q}}\) :

Medium’s constants for the quadratic flow law (–)

\(c_{\mathrm{p}}\) :

Medium’s constants for the power flow law (–)

\(C_{\mathrm{E}}\) :

Ergun’s constant (\(\hbox {m}^{-1}\,\hbox {s}^{2}\))

\(d\) :

Characteristic length parameter of the medium (m)

\(d_{i}\) :

Grain diameter at i % passing (m)

\(d_{\mathrm{H}}\) :

Harmonic mean particle diameter (m)

\(Fr\) :

Froude number (–)

\(\mathop {F}\limits ^{\rightharpoonup }\) :

Body forces due to the friction force per unit volume of medium (\(\hbox {Nm}^{-3}\))

\(\mathop {g}\limits ^{\rightharpoonup }\) :

Acceleration vector due to gravity (\(\hbox {ms}^{-2}\))

\(g\) :

Standard gravity (\(\hbox {ms}^{-2}\))

\(h\) :

Piezometric head (m)

\(h_{0}\) :

Piezometric head at the well’s radius (m)

\(h_{\mathrm{L}}\) :

Piezometric head in the laminar flow region (m)

\(h_{\mathrm{T}}\) :

Piezometric head in the turbulent flow region (m)

\(H\) :

Hydraulic head (m)

\(\mathop {\iota }\limits ^{\rightharpoonup }\) :

Gradient vector of hydraulic head (–)

\(J_{\mathrm{rock}}\) :

Shape (geometry) coefficient (–)

\(K\) :

Intrinsic permeability (\(\hbox {m}^{2}\))

\(k\) :

Hydraulic conductivity (\(\hbox {ms}^{-1}\))

\(L\) :

A characteristic length of the porous medium channel size (m)

\(n\) :

Porosity of the medium (–)

\(p\) :

Pressure (Pa)

\(Q\) :

Discharge (\(\hbox {m}^{3}\,\hbox {s}^{-1}\))

\(q\) :

Flux (\(\hbox {ms}^{-1}\))

\(R_{\mathrm{h}}\) :

Mean hydraulic radius (m)

\(r\) :

Radius (m)

\(r_{\mathrm{c}}\) :

Critical radius (m)

\(r_{\mathrm{well}}\) :

Radius of the well (m)

\(Re\) :

Reynolds number (–)

\(Re_{\mathrm{c}}\) :

Critical Reynolds number (–)

\(T\) :

Time (s)

\(\mathop {U}\limits ^{\rightharpoonup }\) :

Velocity vector (\(\hbox {ms}^{-1}\))

\(\mathop {V}\limits ^{\rightharpoonup }=\mathop {U}\limits ^{\rightharpoonup }/n\) :

Pore velocity (\(\hbox {ms}^{-1}\))

\(W\) :

Wilkin’s parameter representing the medium’s property (\(\hbox {s}^{\mathrm{a}}\,\hbox { m}^{-0.5\mathrm{a}}\))

\(z\) :

Vertical elevation (m)

\(\alpha \) :

Forchheimer viscous term coefficient (\(\hbox {s\,m}^{-1}\))

\(\alpha _0\) :

Engelund equation constant (–)

\(\beta \) :

Forchheimer dynamic term coefficient (\(\hbox {s}^{2}\,\hbox { m}^{-2}\))

\(\beta _0 \) :

Engelund equation constant (–)

\(\rho \) :

Fluid’s density (\(\hbox {kg\,m}^{-3}\))

\(\mu \) :

Dynamic viscosity of the fluid (Pa s)

\(\nu \) :

Fluid kinematic viscosity (\(\hbox {m}^{2}\,\hbox {s}^{-1}\))

\(\nabla \) :

Nabla operator (\(\hbox {m}^{-1}\))

\(| \,|\) :

Symbol for the magnitude (norm) of a vector (–)


  • Åberg, B.: A theory for calculation of the void ratio of non-cohesive soils and similar materials. Hydraulic engineering studies dedicated to Prof. Erling Reinius, Bulletin No. TRITA-VBI-97, Hydr. Lab., Royal Inst. of Tech., Stockholm, Sweden, pp. 25–46 (1978)

  • Ahmed, N., Sunada, D.K.: Nonlinear flow in porous media. J. Hydraul. Div. ASCE 95(HY6), 1–12 (1969)

    Google Scholar 

  • Allen, P.: Modelling flow over and through overtopped rockfill embankments. M. Eng. Thesis, Department of Civil Engineering, University of Queensland, Brisbane, Australia (1984)

  • ASTM method D4043–96: Standard guide for Selection of Aquifer Test Method in Determining Hydraulic Properties by Well Techniques. Conshohocken, Pennsylvania (2004)

  • ASTM method D2434: Standard Test Method for Permeability of Granular Soils (Constant Head). Conshohocken, Pennsylvania (2006)

  • Blake, F.C.: The resistance of packing to fluid flow. Trans. Am. Inst. Chem. Eng. 14, 415–421 (1922)

    Google Scholar 

  • Burke, S.P., Plummer, W.B.: Gas flow through packed columns. Ind. Eng. Chem. 20(11), 1196–1200 (1928)

    Article  Google Scholar 

  • Bonelli, S.: Erosion in Geomechanics Applied to Dams and Levees. Wiley, Hoboken (2013)

    Book  Google Scholar 

  • Centre for Civil Engineering, CUR/RWS.: The Rock Manual, The use of rock in hydraulic engineering. CUR report 169, Gouda, Netherlands (1995)

  • Dudgeon, C.R.: Flow of water through coarse granular materials. M. Eng. thesis, Water Research Laboratory, Univ. of New South Wales, Manly Vale, New South Wales, Australia (1964)

  • Dudgeon, C.R.: An experimental study of flow through coarse granular materials. La Houille Blanche 7, 785–801 (1966a)

    Article  Google Scholar 

  • Dudgeon, C.R.: Wall effects in permeameters. J. Hydraul. Div. ASCE 93(HY5), 137–148 (1966b)

    Google Scholar 

  • Ergun, S., Orning, A.: Fluid flow through randomly packed columns and fluidized bed. Ind. Eng. Chem. 41(6), 1179–1184 (1949)

    Article  Google Scholar 

  • Ergun, S.: Fluid flow through packed columns. Chem. Eng. Prog. 48, 89–94 (1952)

    Google Scholar 

  • Ergun, S.: Determination of Size Distribution of Macropores in Porous Materials. Carnegie Institute of Technology, Pittsburgh (1953)

    Google Scholar 

  • Engelund, F.: On the laminar and turbulent flows of ground water through homogeneous sand. Akademiet for de tekniske videnskaber 3(4), 1–105 (1953)

    Google Scholar 

  • Ferdos, F., Yang, J., Wörman, A.: Characterization of hydraulic behaviours of coarse rock materials in a large permeameter. J Geosci. Environ. Prot. 1(3), 1–6 (2013)

    Google Scholar 

  • Forchheimer, P.: Wasserbewegung durch boden. Z. Ver. Deutsch. Ing. 45, 1788 (1901)

    Google Scholar 

  • Foster, M., Fell, R., Spannagle, M.: Analysis of embankment dam incidents. UNICEF Report R374, UNSW (1998)

  • Foster, M., Fell, R., Spannagle, M.: The statistics of embankment dam failures and accidents. Can. Geotech. J. 37(5), 1000–1024 (2000a)

    Article  Google Scholar 

  • Foster, M., Fell, R., Spannagle, M.: A method of assessing the relative likelihood of failure of embankment dams by piping. Can. Geotech. J. 37(5), 1025–1061 (2000b)

    Article  Google Scholar 

  • Fell, R., Fry, J.-J.: The state of the art of assessing the likelihood of internal erosion of embankment dams, water retaining structures and their foundations. In: Fell, R., Fry, J.-J. (eds.) Internal Erosion of Dams and their Foundations, pp. 1–24. Taylor and Francis, London (2007)

    Google Scholar 

  • Fell, R., Foster, M., Davidson, R., Cyganiewicz, J., Sills, G., Vroman, N.: A unified method for estimating probabilities of failure of embankment dams by internal erosion and piping. UNICIV Report R 446, The School of Civil and Environmental Engineering, University of New South Wales, Sydney, Australia, 2052 (2008)

  • Hansen, D., Garga, V., Townsend, R.: Considerations on the design of flowthrough rockfill drains. In: Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC (1990)

  • Hansen, D., Garga, V., Townsend, R.: Selection and application of a one-dimensional non-Darcy flow equation for two-dimensional flow-through rockfill embankments. Can. Geotech. J. 32(2), 223–232 (1995)

    Article  Google Scholar 

  • Hansen, D., Zhao, W.Z., Han, S.Y.: Hydraulic performance and stability of coarse rockfill deposits. Inst. Civil Eng. Water Manage. 158(4), 163–175 (2005)

    Article  Google Scholar 

  • Hansen, D., Roshanfekr, A.: Use of index gradients and default tailwater depth as aids to hydraulic modeling of flow-through rockfill dam. ASCE J. Hydraul. Eng. 138(8), 726–735 (2012)

    Article  Google Scholar 

  • ICOLD: Lessons from Dam Incidents. International Commission on Large Dams, Paris (1974)

  • ICOLD: Deterioration of Dams and Reservoirs. International Commission on Large Dams, Paris (1983)

  • ICOLD: Dam Failures Statistical Analysis. Bulletin 99, International Commission on Large Dams, Paris (1995)

  • Kovacs, G.: Relationship between seepage velocity and hydraulic gradient in the zone of high velocity. In: Proceedings of Thirteenth Congress of IAHR, 4. MAGI, Kyoto, Japan (1969)

  • Kozeny, J.: Uber Kapillare Leitung Des Wassers in Boden. Sitzungsber Akad.Wiss. Wien Math. Naturwiss. KI., Abt. 2a, 136, 271–306 (1927) (In German)

  • Lawson, J.D.: Protection of rockfill dams and cofferdams against overflow and throughflow. The Australianexperience. Civil Eng. Trans. Instit. Eng. Aust. CE 29(3), 138–147 (1987)

    Google Scholar 

  • Martins, R.: Turbulent seepage flow-through rockfill structures. Int. Water Power Dam Constr. 42(3), 41–42 (1990)

    Google Scholar 

  • McCorquodale, J.A., Hannoura, A.A., Nasser, M.S.: Hydraulic conductivity of rockfill. J. Hydraul. Res. 16(2), 123–137 (1978)

    Article  Google Scholar 

  • Missbach, A.: Non-linear flow through porous materials. In: Stark, K.P., Volker, R.E. (eds.) Res. Bull., No.1. Dept. Civil Engineering, University College, Townville, Australia (1967)

    Google Scholar 

  • Mott, R.A., Fric, F.: The laws of motion of particles in fluids and their application to the resistance of beds of solids to the passage of fluid. Inst. of Physics, Conf, Proc., Leamington, Spa, England, Edward Arnold and Co., London (1950)

  • Privat, N.C.: Evaluating design methods for rockfill dams. M.Sc. thesis, Univ. of Manitoba, Winnipeg, MB, Canada (2007)

  • Rose, H.E.: Fluid flow through beds of granular material. Inst. of Physics, Conf, Proc., Leamington, Spa, England, Edward Arnold and Co., London (1950)

  • Scheidegger, A.E.: The Physics of Flow through Porous Media. The University of Toronto Press, Toronto (1963)

    Google Scholar 

  • Sedghi-Asl, M., Rahimi, H.: Adoption of Manning’s equation to 1D non-Darcy flow problems. J. Hydraul. Res. 49(6), 814–817 (2011)

    Article  Google Scholar 

  • Siddiqua, S., Blatz, J., Privat, N.: Evaluating turbulent flow in large rockfill. J. Hydraul. Eng. 137(11), 1462–1469 (2011)

    Article  Google Scholar 

  • Siddiqua, S., Blatz, J., Privat, N.: Evaluating the behaviour of instrumented prototype rockfill dams. Can. Geotech. J. 50, 298–310 (2013)

    Article  Google Scholar 

  • Sunada, D.K.: Laminar and turbulent flow of water through homogeneous porous media. PhD thesis presented to the University of California, Berkeley, CA (1965)

  • Teng, H., Zhao, T.S.: An extension of Darcy’s law to non-Stokes flow in porous media. Chem. Eng. Sci. 55(14), 2727–2735 (2000)

    Article  Google Scholar 

  • Ward, J.C.: Turbulent flow in porous media. J. Hydraul. Div. ASCE 90(HY5), 110–121 (1964)

    Google Scholar 

  • Ward, J.C.: Closure to ‘Turbulent flow in porous media’. J. Hydraul. Div. ASCE 92(HY4), 110–121 (1966)

    Google Scholar 

  • Wilkins, J.K.: Flow of water through rockfill and its application to design of dams. N. Z. Eng. 1(11), 382–387 (1955)

    Google Scholar 

  • Wilkins, J.K.: The flow of water through rockfill and its application to the design of dams. In: Proc. 2nd Australia-New Zealand Conference on Soil Mechanics and Foundation Engineering, pp. 141–149 (1956)

  • Wilkins, J.K.:The stability of overtopped rockfill dams. Proc. Fourth Australian Conf. on Soil Mech. Found. Engrg., Adelaide, Australia, pp. 1–7 (1963)

  • Whitaker, S.: The Forchheimer equation: a theoretical development. Transp. Porous Media 25(1), 27–61 (1996)

    Article  Google Scholar 

  • Wörman, A., Olafsdottir, H.: Erosion in a granular medium interface. J. Hydraul. Res. 30(5), 639–655 (1992)

    Article  Google Scholar 

  • Zingg, T.: Bietrage zur schotteranalyse. Schweiz Miner. Petrogr. 15, 39–140 (1935)

    Google Scholar 

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This study was conducted as part of a Ph.D. programme financed by the Swedish Hydropower Centre (SvensktVattenkraftcentrum, SVC), Stockholm. SVC was established by the Swedish Energy Agency, Elforsk and SvenskaKraftnät, together with Luleå University of Technology (LTU), the Royal Institute of Technology (KTH), Chalmers University of Technology and Uppsala University. Data for field test analysis were provided by SWECO consulting company from their field tests conducted at the Trängslet embankment dam in Sweden.

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Correspondence to Farzad Ferdos.

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Ferdos, F., Wörman, A. & Ekström, I. Hydraulic Conductivity of Coarse Rockfill used in Hydraulic Structures. Transp Porous Med 108, 367–391 (2015).

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  • Embankment dam failure due to internal erosion
  • Hydraulic conductivity
  • Coarse rockfill
  • Nonlinear flow law