Critical Bed Shear Stress for Unisize Sediment
Publication: Journal of Hydraulic Engineering
Volume 132, Issue 2
Abstract
The overall, spatially averaged, mean magnitude of local, spatially averaged (over a small area enclosing the particles’ projected area), instantaneous, critical Shields shear-stress parameters required for incipient motion of uniform-sized sand grains, independent of the bed shear-velocity particle Reynolds number, equal to 0.16, is obtained from calibration of a theory for bed load sediment transport, by minimizing the sum of the squares of the deviations between theoretical and experimental bed load rates. Additionally, optimized expressions for a proposed probability density distribution of the bed shear stresses, for its standard deviation, for finite, maximum, and minimum bed shear stresses, and a bed load rate are obtained. In terms of the mean fluid shear stress, a dimensionless, critical, shear-stress parameter equal to 0.0513 is obtained. Investigation of the probability density distribution of the spatially varying, critical shear stresses would allow a more accurate formulation for the case of low transport rates.
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References
Ackers, P. (1993). “Sediment transport in open channels: Ackers and White update.” Proc., Institution of Civil Engineers, Water, Maritime and Energy, 101(4), 247–249.
Blinco, P. H., and Partheniades, E. (1971). “Turbulence characteristics in free surface flows over smooth and rough boundaries.” J. Hydraul. Res., 9(1), 43–71.
Blinco, P. H., and Simons, D. B. (1974). “Characteristics of turbulent boundary shear stress.” J. Eng. Mech. Div., Am. Soc. Civ. Eng., 100(2), 203–220.
Brownlie, W. R. (1981). “Compilation of alluvial channel data: Laboratory and field.” Rep. No. KH-R-43 B, W. M. Keck Laboratory, California Institute of Technology, Pasadena, Calif.
Buffington, J. M. (1999). “The legend of A. F. Shields.” J. Hydraul. Eng., 125(4), 376–387.
Buffington, J. M., and Montgomery, D. V. (1997). “A systematic analysis of eight decades of incipient motion studies, with special reference to gravel-bedded rivers.” Water Resour. Res., 33(8), 1993–2029.
Cao, Z. (1997). “Turbulent bursting-based sediment entrainment function.” J. Hydraul. Eng., 123(3), 233–236.
Cheng, D. H., and Clyde, G. (1972). “Instantaneous hydrodynamic lift and drag forces on large roughness elements in turbulent open channel flow.” Sedimentation, H. W. Shen, Fort Collins, Colo, 3–1 and 3–20.
Cheng, N. S., and Law, A. W. (2003). “Fluctuations of turbulent bed shear stress.” J. Eng. Mech., 129(1), 126–130.
Chin, C. O., and Chiew, Y. M. (1993). “Effect of bed surface structure on spherical particle stability.” J. Waterw., Port, Coastal, Ocean Eng., 119(3), 231–242.
Dancey, C. L., Diplas, P., Papanicolaou, A., and Bala, M. (2002). “Probability of individual grain movement and threshold condition.” J. Hydraul. Eng., 128(12), 1069–1075.
Einstein, H. A. (1950). “The bed-load function for sediment transportation in open channel flows.” Technical Bull. No. 1026, U.S. Dept. of Agriculturer, Soil Conservation Service, Washington, D.C.
Engelund, F., and Fredsøe, J. (1982). “Hydraulic theory of alluvial rivers.” Advances in hydroscience, Academic, New York, 13, 187–215.
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, Ser. A, 352, 523–537.
Fernandez, L., and Van Beek, R. (1976). “Erosion and transport of bed-load sediment.” J. Hydraul. Res., Delft, The Netherlands, 14(2), 127–143.
Grass, A. (1970). “Initial instability of fine bed sand.” J. Hydraul. Div., Am. Soc. Civ. Eng., 96(3), 619–632.
Gessler, J. (1967). “The beginning of bed load movement of mixtures investigated as natural armoring in channels.” Translation T-5 by E. Prych, W. M. Keck Laboratory, California Institute of Technology, Pasadena, Calif.
Hinze, J. O. (1959). “Measurements of mean-velocity distribution.” Turbulence, McGraw–Hill, New York, 476–479.
Jain, S. C. (1992). “Note on lag in bed load discharge.” J. Hydraul. Eng., 118(6), 904–917.
Kalinske, A. A. (1947). “Movement of sediment as bed-load in rivers.” Trans., Am. Geophys. Union, 28(4), 615–620.
Karim, M. F., and Kennedy, J. F. (1981). “Computer-based predictions for sediment discharges and friction factors of alluvial streams.” Rep. No. 242, Iowa Institute of Hydraulic Research, The Univ. of Iowa, Iowa City, Iowa.
Kennedy, J. F. (1995). “The Albert Shields story.” J. Hydraul. Eng., 121(11), 766–772.
Kirchner, J. W., Dietrich, W. E., Iseya, F., and Ikeda, H. (1990). “The variability of critical shear stress, friction angle, and grain protrusion in water-worked sediments.” Sedimentology, 37(4), 647–672.
Lavelle, J. W., and Mofjeld, H. O. (1987). “Do critical stresses for incipient motion and erosion really exist?” J. Hydraul. Eng., 113(3), 370–387.
Mehta, A. J., and Christensen, B. A. (1976). “Incipient sediment motion in entrances with shell beds.” Proc., Coastal Engineering, Hawaii, II, 960–977.
Meyer-Peter, E., and Muller, R. (1948). “Formula for bed load transport.” Proc., 2nd Conf., IAHR, Stockholm, 2, 39–64.
Paintal, A. S. (1971). “A stochastic model of bed load transport.” J. Hydraul. Res., 9(4), 527–554.
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., 128(4), 369–380.
Paphitis, D. (2001). “Sediment movement under unidirectional flows: An assessment of empirical threshold curves.” Coastal Eng., 43(3-4), 227–245.
Raudkivi, A. J. (1998). “Turbulence and initiation of motion, sediment transport.” Loose boundary hydraulics, A. A. Balkema, Rotterdam, The Netherlands, 42–43, 135.
Shields, A. (1936). “Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung.” Mitteilungen der Preussiischen Versuchsanstalt für Wasserbau und Schiffhau, Heft 26, Berlin, Germany (in German), (English translation by W. P. Ott and J. C. van Uchelen, available as Hydrodynamics Laboratory Publication No. 167, Hydrodynamics Lab., California Institute of Technology, Pasadena, Calif.).
Sumer, B. M., Chua, L. H., Cheng, N. S., and Fredsøe, J. (2003). “Influence of turbulence on bed load sediment transport.” J. Hydraul. Eng., 129(8), 585–596.
Sun, Z., and Donahue, Y. M. (2000). “Statistically derived bed load formula for any fraction of nonuniform sediment.” J. Hydraul. Eng., 126(2), 105–111.
Sutherland, A. J. (1966). “Entrainment of fine sediment by turbulent flows.” Rep. No. KH-R-13, W. M. Keck Laboratory, California Institute of Technology, Pasadena, Calif.
Sutherland, A. J. (1967). “Proposed mechanism for sediment entrainment by turbulent flows.” J. Geophys. Res., 72(24), 6183–6194.
Van Rijn, L. C. (1984). “Sediment transport, Part I: Bed load transport.” J. Hydraul. Eng., 110(10), 1431–1456.
Van Rijn, L. C. (1987). “Mathematical modeling of morphological processes in the case of suspended sediment transport.” PhD dissertation, Delft Univ. of Technology, Delft, The Netherlands.
Vanoni, V. A. (1964). “Measurements of critical shear stress for entraining fine sediment in a boundary layer.” Rep. No. KH-R-7, W. M. Keck Laboratory, California Institute of Technology, Pasadena, Calif.
Vanoni, V. A. (1975). “Side-wall correction procedure.” Sedimentation Eng., ASCE M&R, 54, 152–154.
White, C. M. (1940). “The equilibrium of grains on the bed of a stream.” Proc. R. Soc. London, Ser. A, 174(958), 322–338.
Wu, F. C., and Chou, Y. J. (2003). “Rolling and lifting probabilities for sediment entrainment.” J. Hydraul. Eng., 129(2), 110–119.
Wu, F. C., and Lin, Y. C. (2002). “Pickup probability for sediment under log-normal velocity distribution.” J. Hydraul. Eng., 128(4), 438–442.
Yalin, M. S. (1977). “The beginning of sediment transport.” Mechanics of sediment transport, 2nd Ed., Pergamon, Oxford, U.K., 76.
Yang, C. T., and Huang, C. (2001). “Applicability of sediment transport formulas.” International Journal of Sediment Research, 16(3), 335–353.
Zanke, U. C. E. (2003). “On the influence of turbulence on the initiation of sediment motion.” International Journal of Sediment Research, 18(1), 17–31.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 132 • Issue 2 • February 2006
Pages: 172 - 179
Copyright
© 2006 ASCE.
History
Received: Mar 28, 2003
Accepted: Aug 5, 2004
Published online: Feb 1, 2006
Published in print: Feb 2006
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