KSCE Journal of Civil Engineering

, Volume 12, Issue 1, pp 45–60 | Cite as

Sediment threshold under stream flow: A state-of-the-art review

Water Engineering


The doctoral research of Albert Frank Shields on sediment movement conducted in Technischen Hochshcule Berlin becomes a legend that is most often referred by many authors and has initiated a sizable number of researches over last seven decades. The Shields diagram is famous due to its application in ascertaining the threshold of sediment motion that is an essential prerequisite for the estimation of sediment transport in an alluvial stream. Since his pioneering work, numerous attempts have so far been made to study the sediment threshold both experimentally and theoretically. This paper presents a comprehensive state-of-the-art review of the important laboratory experimental and theoretical investigations on sediment threshold under steady stream flow highlighting the empirical concepts, hydrodynamic background and the mathematical treatment of the problem. The role of the turbulent bursting on sediment threshold is also discussed.


sediment transport sediment threshold fluvial hydraulics open channel flow stream flow 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aksoy, S. (1973). “Fluid forces acting on a sphere near a solid boundary.” Proc. 15th IAHR Congr., Istanbul, Turkey, Vol. 1, pp. 217–224.Google Scholar
  2. Allen, J.R.L. (1982). “Simple models for the shape and symmetry of tidal sand wave: (1) statistically stable equilibrium forms.” Mar. Geol., Vol. 48, pp. 31–49.CrossRefGoogle Scholar
  3. Apperley, L.W. (1968). “Effect of turbulence on sediment entrainment.” PhD thesis, University of Auckland, New Zealand.Google Scholar
  4. Bagnold, R.A. (1974). “Fluid forces on a body in shear flow; experimental use of stationary flow.” Proc. R. Soc. London A, Vol. 340, pp. 147–171.Google Scholar
  5. Brayshaw, A.C., Frostick, L.E., and Reid, I. (1983). “The hydrodynamics of particle clusters and sediment entrainment in course alluvial channels.” Sedimentology, Vol. 30, pp. 137–143.CrossRefGoogle Scholar
  6. Buffington, J.M. (1999). “The legend of A. F. Shields.” J. Hydraul. Eng., Vol. 125, No. 4, pp. 376–387.CrossRefGoogle Scholar
  7. Buffington, J.M. and Montgomery, D.R. (1997). “A systematic analysis of eight decades of incipient motion studies, with special reference to gravel-bedded rivers.” Wat. Resour. Res., Vol. 33, No. 8, pp. 1993–2029.CrossRefGoogle Scholar
  8. Carstens, M.R. (1966). “An analytical and experimental study of bed ripples under water waves.” Quart. Rep. 8 and 9, Georgia Institute of Technology, School of Civil Engineering, Atlanta, USA.Google Scholar
  9. Casey, H.J. (1935). “Über die geschiebebewegung.” PhD thesis, Teknikal Hochschule-Scharlottenburg, Berlin, Germany.Google Scholar
  10. Chepil, W.S. (1958). “The use of evenly spaced hemispheres to evaluate aerodynamic force on a soil surface.” Trans. Am. Geophys. Union, Vol. 39, No. 3, pp. 397–404.Google Scholar
  11. Chepil, W.S. (1961). “The use of spheres to measure lift and drag on wind-eroded soil grains.” Proc. Soil Sci. Soc. Am., Vol. 25, No. 5, pp. 343–345.CrossRefGoogle Scholar
  12. Chiew, Y.M. and Parker, G. (1994a). “Basic data on incipient sediment motion on non-horizontal slopes in closed-conduit flow.” Tech. Memo. No. 234, St. Anthony Falls Hydraulics Laboratory, University of Minnesota.Google Scholar
  13. Chiew, Y.M. and Parker, G. (1994b). “Incipient sediment motion on non-horizontal slopes.” J. Hydraul. Res., Vol. 32, No. 5, pp. 649–660.CrossRefGoogle Scholar
  14. Church, M. (1978). “Palaeohydraulic reconstructions from a Holocene valley fill in.” Miall, A. D. (ed.) Fluvial Sedimentology, Canadian Society of Petroleum Geologists, Alberta, Canada, pp. 743–772.Google Scholar
  15. Clifford, N.J., McClatchey, J., and French, J.R. (1991). “Measurements of turbulence in the benthic boundary layer over a gravel bed and comparison between acoustic measurements and predictions of the bedload transport of marine gravels.” Sedimentology, Vol. 38, pp. 161–171.CrossRefGoogle Scholar
  16. Coleman, N.L. (1967). “A theoretical and experimental study of drag and lift forces acting on a sphere resting on a hypothetical stream bed.” Proc. 12th IAHR Congr., Fort Collins, Colorado, Vol. 3, pp. 185–192.Google Scholar
  17. Corino, E.R. and Brodkey, R.S. (1969). “A visual investigation of the wall region in turbulent flow.” J. Fluid Mech., Vol. 37, pp. 1–30.CrossRefGoogle Scholar
  18. Damgaard, J.S., Whitehouse, R.J.S., and Wallingford, H.R. (1966). “Gravity effects in bed-load sediment transport.” Progress Rep. HR Wallingford MAFF Contract CSA 3051, Ministry of Agriculture, Fisheries and Food, London, UK.Google Scholar
  19. Dancy, C.L., Diplas, P., Papanicolaou, A., and Bala, M. (2002). “Probability of individual grain movement and threshold condition.” J. Hydraul. Eng., Vol. 128, No. 12, pp. 1069–1075.CrossRefGoogle Scholar
  20. Davies, T.R.H. and Samad, M.F.A. (1978). “Fluid dynamic lift on a bed particle.” J. Hydraul. Div., Vol. 104, No. 8, pp. 1171–1182.Google Scholar
  21. Dey, S. (1999). “Sediment threshold.” Appl. Math. Modelling, Vol. 23, No. 5, pp. 399–417.MATHMathSciNetCrossRefGoogle Scholar
  22. Dey, S. (2001). “Bank profile of threshold channels: a simplified approach.” J. Irrig. and Drain. Eng., Vol. 127, No. 3, pp. 184–187.CrossRefGoogle Scholar
  23. Dey, S. (2003). “Threshold of sediment motion on combined transverse and longitudinal sloping beds.” J. Hydraul. Res., Vol. 41, No. 4, pp. 405–415.CrossRefGoogle Scholar
  24. Dey, S. (2004). “Critical bed shear for initial movement of sediments on a combined lateral and longitudinal slope.” Nordic Hydrol., Vol. 35, No. 2, pp. 153–164.Google Scholar
  25. Dey, S. and Debnath, K. (2000). “Influence of stream-wise bed slope on sediment threshold under stream flow.” J. Irrig. and Drain. Eng., Vol. 126, No. 4, pp. 255–263.CrossRefGoogle Scholar
  26. Dey, S., Dey Sarker, H.K., and Debnath, K. (1999). “Sediment threshold under stream flow on horizontal and sloping beds.” J. Eng. Mech., Vol. 125, No. 5, pp. 545–553.CrossRefGoogle Scholar
  27. Dey, S. and Raikar, R.V. (2007). “Characteristics of loose rough boundary streams at near-threshold.” J. Hydraul. Eng., Vol. 133, No. 3, pp. 288–304.CrossRefGoogle Scholar
  28. Dey, S. and Zanke, U.C.E. (2004). “Sediment threshold with upward seepage.” J. Eng. Mech., Vol. 130, No. 9, pp. 1118–1123.CrossRefGoogle Scholar
  29. Dyer, K.R. (1986). Coastal and estuarine sediment dynamics. John Wiley and Sons Limited, London, UK.Google Scholar
  30. Egiazaroff, J.V. (1965). “Calculation of non-uniform sediment concentrations.” J. Hydraul. Div., Vol. 91, No. 4, pp. 225–247.Google Scholar
  31. Einstein, H.A. (1950). “The bed-load function for sediment transportation in open channel flows.” Tech. Bulletin No. 1026, US Department of Agriculture.Google Scholar
  32. Einstein, H.A. and El-Samni, E.A. (1949). “Hydrodynamic forces on rough wall.” Rev. Modern Phys., Vol. 21, No. 3, pp. 520–524.CrossRefGoogle Scholar
  33. Fan, C.H. (1947). “A study of stable channel cross section.” J. Hydraul. Eng., Chinese Society of Hydraulic Engineers, Vol. 15, No. 1, pp. 71–79 (in Chinese).Google Scholar
  34. Fenton, J.D. and Abbott, J.E. (1977). “Initial movement of grains on a stream bed: the effect of relative protrusion.” Proc. R. Soc. London A, Vol. 352, pp. 523–537.Google Scholar
  35. Forchheimer, P. (1924). Hydraulik. Teubner Verlagsgesellschaft, Berlin, Germany (in German).MATHGoogle Scholar
  36. Gessler, J. (1966). “Geschiebetrieb bei mischungen untersucht an naturlichen, abpflasterungserscheinungen in kanalen.” Nr. 69, Mitteilungen der Versuchsanstalt für Wasserbau und Erdbau, ETH Zurich, Germany.Google Scholar
  37. Gessler, J. (1970). “Self-stabilizing tendencies of alluvial channels.” J. Waterways Harbors Div., Vol. 96, No. 2, pp. 235–249.Google Scholar
  38. Glover, R.E. and Florey, Q.L. (1951). “Stable channel profiles.” Hydraul. Lab. Rep. Hyd-325, US Bureau of Reclamation.Google Scholar
  39. Gilbert, G.K. (1914). “Transportation of debris by running water.” Prof. Paper No. 86, United States Geological Survey, Washington DC, USA.Google Scholar
  40. Goncharov, V.N. (1964). Dynamics of channel flow. Israel Programme for Scientific Translation, Moscow, Russia.Google Scholar
  41. Grass, A.J. (1970). “Initial instability of fine bed sand.” J. Hydraul. Div., Vol. 96, No. 3, pp. 619–632.Google Scholar
  42. Grass, A.J. (1971). “Structural features of turbulent flow over smooth and rough boundaries.” J. Fluid Mech., Vol. 50, 233–255.CrossRefGoogle Scholar
  43. Howard, A.D. (1977). “Effect of slope on the threshold of motion and its application to orientation of wind ripples.” Bull. Geol. Soc. Am., Vol. 88, pp. 853–856.CrossRefGoogle Scholar
  44. Ikeda, S. (1982). “Incipient motion of sand particles on side slopes.” J. Hydraul. Div., Vol. 108, No. 1, pp. 95–114.Google Scholar
  45. Ippen, A.T. and Eagleson, P.S. (1955). “A study of sediment sorting by waves shoaling on a plane beach.” Tech. Memo. No. 63, US Army Corps Engineers, Beach Erosion Board.Google Scholar
  46. Iversen, J.D. and Rasmussen, K.R. (1994). “The effect of surface slope on saltation threshold.” Sedimentation, Vol. 41, pp. 721–728.Google Scholar
  47. Iwagaki, Y. (1956). “Fundamental study on critical tractive force.” Trans. Jap. Soc. Civ. Eng., Vol. 41, pp. 1–21.Google Scholar
  48. James, C. (1990). “Prediction of entrainment conditions for nonuniform, noncohesive sediments.” J. Hydraul. Res., Vol. 28, No. 1, pp. 25–41.CrossRefGoogle Scholar
  49. Jeffreys, H. (1929). “On the transport of sediments in stream.” Proc. Camb. Phil. Soc., Vol. 25, pp. 272.CrossRefMATHGoogle Scholar
  50. Julien, P.Y. (1998). Erosion and sedimentation. Cambridge University Press, Cambridge, UK.Google Scholar
  51. Karahan, E. (1975). “Initiation of motion for uniform and non-uniform materials.” PhD thesis, Technical University, Istanbul, Turkey.Google Scholar
  52. Kennedy, J.F. (1995). “The Albert Shields story.” J. Hydraul. Eng., Vol. 121, No. 11, pp. 766–772.CrossRefGoogle Scholar
  53. Keshavarzy, A. and Ball, J.E. (1996). “Characteristics of turbulent shear stress applied to bed particles in an open channel flow.” Proc. 7th IAHR Int. Symp. Stochastic Hydr. 96, pp. 451–458.Google Scholar
  54. Kline, S.J., Reynolds, W.C., Straub, F.A., and Runstadler, P.W. (1967). “The structure of turbulent boundary layers.” J. Fluid Mech., Vol. 30, pp. 741–773.CrossRefGoogle Scholar
  55. Krogstad, P.A., Antonia, R.A., and Browne, L.W.B. (1992). “Comparison between rough and smooth wall turbulent boundary layers.” J. Fluid Mech., Vol. 245, pp. 599–617.CrossRefGoogle Scholar
  56. Kramer, H. (1935). “Sand mixtures and sand movement in fluvial levels.” Trans. Am. Soc. Civ. Eng., Vol. 100, pp. 798–838.Google Scholar
  57. Kurihara, M. (1948). “On the critical tractive force.” Rep. No. 3, Vol. 4, Research Institute for Hydraulic Engineering.Google Scholar
  58. Lane, E.W. (1955). “Design of stable channels.” Trans. ASCE, Vol. 120, pp. 1234–1260.Google Scholar
  59. Lane, E.W. and Kalinske, A.A. (1939). “The relation of suspended to bed materials in river.” Trans. Am. Geophys. Union, Vol. 20, pp. 637.Google Scholar
  60. Lavelle, J.W. and Mofjeld, H.O. (1987). “Bibliography on sediment threshold velocity.” J. Hydraul. Eng., Vol. 113, No. 3, pp. 389–393.Google Scholar
  61. Leliavsky, S. (1966). An introduction to fluvial hydraulics. Dover, New York.Google Scholar
  62. Li, R., Simons, D.B., and Stevens, M.A. (1976). “Morphology of cobble streams in small watersheds.” J. Hydraul. Div., Vol. 102, No. 8, pp. 1101–1117.Google Scholar
  63. Ling, C.H. (1995). “Criteria for incipient motion of spherical sediment particles.” J. Hydraul. Eng., Vol. 121, No. 6, pp. 472–478.CrossRefGoogle Scholar
  64. Lu, S.S. and Willmarth, W.W. (1973). “Measurements of the structures of the Reynolds stress in a turbulent boundary layer.” J. Fluid Mech., Vol. 60, pp. 481–571.CrossRefGoogle Scholar
  65. Luque, R.F. and van Beek, R. (1976). “Erosion and transport of bed-load sediment.” J. Hydraul. Res., Vol. 14, No. 2, pp. 127–144.CrossRefGoogle Scholar
  66. Mantz, P.A. (1977). “Incipient transport of fine grains and flanks by fluids-extended Shields diagram.” J. Hydraul. Div., Vol. 103, No. 6, pp. 601–615.Google Scholar
  67. McEwan, I. and Heald, J. (2001). “Discrete particle modeling of entrainment from flat uniformly sized sediment beds.” J. Hydraul. Eng., Vol. 127, No. 7, pp. 588–597.CrossRefGoogle Scholar
  68. Meyer-Peter, E. and Müller, R. (1948). “Formulas for bed-load transport.” Proc. 2nd IAHR Congr., Stockholm, Sweden, pp. 39–64.Google Scholar
  69. Miller, M.C., McCave, I.N., and Komar, P.D. (1977). “Threshold of sediment motion under unidirectional currents.” Sedimentology, Vol. 24, pp. 507–527.CrossRefGoogle Scholar
  70. Mingmin, H. and Qiwei, H. (1982). “Stochastic model of incipient sediment motion.” J. Hydraul. Div., Vol. 108, No. 2, pp. 211–224.Google Scholar
  71. Morsi, S.A. and Alexander, A.J. (1972). “An investigation of particle trajectories in two-phase flow systems.” J. Fluid Mech., Vol. 55, pp. 193–208.MATHCrossRefGoogle Scholar
  72. Neill, C.R. (1967). “Mean velocity criterion for scour of course uniform bed material.” Proc. 12th IAHR Congr., Fort Collins, Colorado, USA, Vol. 3, pp. 46–54.Google Scholar
  73. Neill, C.R. (1968). “Note on initial movement of coarse uniform bed-material.” J. Hydraul. Res., Vol. 6, No. 2, pp. 173–176.CrossRefGoogle Scholar
  74. Nelson, J., Shreve, R.L., McLean, S.R., and Drake, T.G. (1995). “Role of near-bed turbulence structure in bed load transport and bed form mechanics.” Wat. Resour. Res., Vol. 31, No. 8, pp. 2071–2086.CrossRefGoogle Scholar
  75. Nezu, I. and Nakagawa, H. (1993). Turbulence in open-channel flows. Balkema, Rotterdam, Netherlands.Google Scholar
  76. Papanicolaou, A., Diplas, P., Dancey, C., and Balakrishnan, M. (2001). “Surface roughness effects in near-bed turbulence: implications to sediment entrainment.” J. Eng. Mech., Vol. 127, No. 3, pp. 211–218.CrossRefGoogle Scholar
  77. Papanicolaou, A.N., Diplas, P., Evaggelopoulos, N., and Fotopoulos, S. (2002). “Stochastic incipient motion criterion for spheres under various bed packing conditions.” J. Hydraul. Eng., Vol. 128, No. 4, pp. 369–380.CrossRefGoogle Scholar
  78. Paphitis, D. (2001). “Sediment movement under unidirectional flows: an assessment of empirical threshold curves.” Coastal Eng., Vol. 43, pp. 227–245.CrossRefGoogle Scholar
  79. Parker, G. (1978). “Self-formed straight rivers with equilibrium banks and mobile bed. Part 2. The gravel river.” J. Fluid Mech., Vol. 89, pp. 127–146.MATHCrossRefGoogle Scholar
  80. Raupach, M.R. (1981). “Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers.” J. Fluid Mech., Vol. 108, pp. 363–382.MATHCrossRefGoogle Scholar
  81. Reichardt, H. (1951). “Vollstandige darstellung der turbulenten geschwindig-keitsverteilung in glatten leitungen.” Z. Angew. Math. Mech., Vol. 31, No. 7, pp. 208–219.MATHCrossRefGoogle Scholar
  82. Reitz, W. (1936). “Uber geschiebebewegung.” Wasserwirtsch. und Tech., pp. 28–30.Google Scholar
  83. Rubinow, S. I. and Keller, J.B. (1961). “The transverse force on a spinning sphere moving in a viscous fluid.” J. Fluid Mech., Vol. 11, pp. 447–459.MATHMathSciNetCrossRefGoogle Scholar
  84. Saffman, P.G. (1965). “The lift on a small sphere in a slow shear flow.” J. Fluid Mech., Vol. 22, pp. 385–400.MATHCrossRefGoogle Scholar
  85. Saffman, P.G. (1968). “Corrigendum, the lift on a small sphere in a slow shear flow.” J. Fluid Mech., Vol. 31, pp. 624.Google Scholar
  86. Sarre, R.D. (1987). “Aeolian sand transport.” Progr. Phys. Geogr., Vol. 11, pp. 157–182.Google Scholar
  87. Schlichting, H. (1960). Boundary layer theory. McGraw-Hill Book Companies, New York, USA.MATHGoogle Scholar
  88. Shields, A.F. (1936). “Application of similarity principles and turbulence research to bed-load movement.” Mitteilungen der Preussischen Versuchsanstalt für Wasserbau und Schiffbau, Berlin, Germany, Vol. 26, pp. 5–24.Google Scholar
  89. Soulsby, R.L. and Whitehouse, R.J.S. (1997). “Threshold of sediment motion in coastal Environments.” Proc. Combined Australasian Coastal Eng. and Port Conf., Christchurch, New Zealand, pp. 149–154.Google Scholar
  90. Stevens, M.A., Simons, D.B., and Lewis, G.L. (1976). “Safety factor for riprap protection.” J. Hydraul. Engrg., Vol. 102, No. 5, pp. 637–655.Google Scholar
  91. Task Committee. (1966). “Sediment transportation mechanics: Initiation of motion.” J. Hydraul. Div., Vol. 92, No. 2, pp. 291–314.Google Scholar
  92. USWES. (1936). “Flume tests made to develop a synthetic sand which will not form ripples when used in movable bed models.” Tech. Memo. 99-1, United States Waterways Experiment Station, Vieksburg, Mississippi, USA.Google Scholar
  93. Vanoni, V.A. (1946). “Transport of suspended sediment by water.” Trans. Am. Soc. Civ. Eng., Vol. 111, pp. 67–102.Google Scholar
  94. Vanoni, V.A. (1964). “Measurements of critical shear stress.” Rep. No. KH-R-7, California Institute of Technology, USA.Google Scholar
  95. van Rijn, L.C. (1984). “Sediment transport, part I: bed-load transport.” J. Hydraul. Eng., Vol. 110, No. 10, pp. 1431–1456.Google Scholar
  96. van Rijn, L.C. (1993). Principles of sediment transport in rivers, estuaries and coastal seas. Aqua Publications, The Netherlands.Google Scholar
  97. Velikanov, M.A. (1955). Dynamics of alluvial stream. Vol. 2, State Publishing House of Theoretical and Technical Literature, Russia (in Russian).Google Scholar
  98. Watters, G.Z. and Rao, M.V.P. (1971). “Hydrodynamic effects of seepage on bed particles.” J. Hydraul. Div., Vol. 97, No. 3, pp. 421–439.Google Scholar
  99. White, C. M. (1940). “The equilibrium of grains on the bed of a stream.” Phil. Trans. Royal Soc., Vol. 174A, pp. 322–338.Google Scholar
  100. White, S.J. (1970). “Plane bed thresholds of fine grained sediments.” Nature, Vol. 228, No. October, pp. 152–153.CrossRefGoogle Scholar
  101. Whitehouse, R.J.S. and Hardisty, J. (1988). “Experimental assessment of two theories for the effect of bed slope on the threshold of bedload transport.” Mar. Geol., Vol. 79, pp. 135–139.CrossRefGoogle Scholar
  102. Wiberg, P.L. and Smith, J.D. (1987). “Calculations of the critical shear stress for motion of uniform and heterogeneous sediments.” Wat. Resour. Res., Vol. 23, No. 8, 1471–1480.Google Scholar
  103. Wu, F.C. and Chou, Y.J. (2003). “Rolling and lifting probabilities for sediment entrainment.” J. Hydraul. Eng., Vol. 129, No. 2, pp. 110–119.CrossRefGoogle Scholar
  104. Yalin, M.S. (1963). “An expression of bed-load transportation.” J. Hydraul. Div., Vol. 89, No. 3, pp. 221–250.Google Scholar
  105. Yalin, M.S. (1977). Mechanics of sediment transport. Pergamon Press, Braunschweig, Germany.Google Scholar
  106. Yalin, M.S. and Karahan, E. (1979). “Inception of sediment transport.” J. Hydraul. Div., Vol. 105, No. 11, pp. 1433–1443.Google Scholar
  107. Yang, C.T. (1973). “Incipient motion and sediment transport.” J. Hydraul. Div., Vol. 99, No. 10, pp. 1679–1704.Google Scholar
  108. Zanke, U.C.E. (1977). “Neuer Ansatz zur Berechnung des Transportbeginns von Sedimenten unter Stromungseinfluss.” Mitt. Des Franzius-Institut, Technical University Hannover, Germany, Heft 46.Google Scholar
  109. Zanke, U.C.E. (2003). “On the influence of turbulence on the initiation of sediment motion.” Int. J. Sediment Res., Vol. 18, No. 1, pp. 17–31.Google Scholar

Copyright information

© Korean Society of Civil Engineers 2008

Authors and Affiliations

  1. 1.Department of Civil EngineeringIndian Institute of TechnologyKharagpurIndia
  2. 2.IIHR-Hydroscience and EngineeringThe University of IowaIowa CityUSA

Personalised recommendations