Water Science and Engineering 2014, 7(2) 183-193 DOI:   10.3882/j.issn.1674-2370.2014.02.006  ISSN: 1674-2370 CN: 32-1785/TV

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incipient motion
sediment transport
Shields diagram
critical shear stress
critical shear velocity
movability number
Article by Francisco,J.S

Shear velocity criterion for incipient motion of sediment

Francisco J. M. SIMÕES*

U.S. Geological Survey, Geomorphology and Sediment Transport Laboratory, Golden, CO 80403, USA


The prediction of incipient motion has had great importance to the theory of sediment transport. The most commonly used methods are based on the concept of critical shear stress and employ an approach similar, or identical, to the Shields diagram. An alternative method that uses the movability number, defined as the ratio of the shear velocity to the particle’s settling velocity, was employed in this study. A large amount of experimental data were used to develop an empirical incipient motion criterion based on the movability number. It is shown that this approach can provide a simple and accurate method of computing the threshold condition for sediment motion.

Keywords incipient motion   sediment transport   Shields diagram   critical shear stress   critical shear velocity   movability number  
Received 2012-11-20 Revised 2013-06-16 Online: 2014-04-25 
DOI: 10.3882/j.issn.1674-2370.2014.02.006
Corresponding Authors: Francisco J. M. SIM?ES
Email: frsimoes@usgs.gov
About author:


Ashworth, P. J., Ferguson, R. I., Ashmore, P. E., Paola, C., Powell, D. M., and Prestegaard, K. L. 1992. Measurements in a braided river chute and lobe, 2: Sorting of bed load during entrainment, transport, and deposition. Water Resoures Research, 28(7), 1887-1896. [doi:10.1029/92WR00702]

Bathurst, J. C., Graf, W. H. and Cao, H. H. 1987. Bed load discharge equations for steep mountain rivers. Thorne, C. R., et al. eds., Sediment Transport in Gravelbed Rivers, 453-491. New York: John Wiley & Sons.

Beheshti, A. A., and Ataie-Ashtiani, B. 2008. Analysis of threshold and incipient conditions for sediment movement. Coastal Engineering, 55(5), 423-430. [doi:10.1016/j.coastaleng.2008.01.003]

Carling, P. A. 1983. Threshold of coarse sediment transport in broad and narrow natural streams. Earth Surface Processes and Landforms, 8(1), 1-18. [doi:10.1002/esp.3290080102]

Casey, H. J. 1935a. About Bedload Movement. Ph. D. Dissertation. Berlin: Technischen Hochschule.       (In German)

Casey, H. J. 1935b. About Bedload Movement. Berlin: Communications of the Prussian Laboratory of Hydraulics and shipbuilding. (In German)

Collins, M. B., and Rigler, J. K. 1982. The use of settling velocity in defining the initiation of motion of heavy mineral grains, under unidirectional flow. Sedimentology, 29(3), 419-426.

Dey, S., and Debnath, K. 2000. Influence of streamwise bed slope on sediment threshold under stream flow. Journal of Irrigation and Drainage Engngineering, 126(4), 255-263. [doi:10.1061/(ASCE)0733-9437 (2000)126:4(255)]

Dey, S., and Raju, U. V. 2002. Incipient motion of gravel and coal beds. Sadhana-Academy Proceedings in Engineering Sciences, 27(5), 559-568.

Dietrich, W. E. 1982. Settling velocity of natural particles. Water Resources Research, 18(6), 1615-1626. [doi:10.1029/WR018i006p01615]

Everts, C. H. 1973. Particle overpassing on flat granular boundaries. Journal of the Waterways, Harbors and Coastal Engineering Division, 99(4), 425-438.

Ferguson, R. I., Prestegaard, K. L., and Ashworth, P. J. 1989. Influence of sand on hydraulics and gravel transport in a braided gravel bed river. Water Resources Research, 25(4), 635-643. [doi:10.1029/ WR025i004p00635]

Ferguson, R. I. 1994. Critical discharge for entrainment of poorly sorted gravel. Earth Surface Processes and Landforms, 19(2), 179-186. [doi:10.1002/esp.3290190208]

Gilbert, G. K. 1914. The Transportation of Debris by Running Water. Washington: U.S. Government   Printing Office.

Grass, A. J. 1970. Initial instability of fine bed sand. Journal of the Hydraulics Division, 96(3), 619-632.

Hammond, F., Heathershaw, A., and Langhorne, D. 1984. A comparison between Shields’ threshold criterion and the movement of loosely packed gravel in a tidal channel. Sedimentology, 31(1), 51-62.

Komar, P. D., and Clemens, K. E. 1986. The relationship between a grain’s settling velocity and threshold of motion under unidirectional currents. Journal of Sedimentary Research, 56(2), 258-266.

Komar, P. D., and Carling, P. A. 1991. Grain sorting in gravel-bed streams and the choice of particle sizes for flow-competence evaluations. Sedimentology, 38(3), 489-502.

Kramer, H. 1932. Modellgeschiebe und schleppkraft. Ph. D. Dissertation. Dresden: Technischen Hochschule. (In German)

Kramer, H. 1935. Sand mixtures and sand movement in fluvial models. Transactions of the American Society of Civil Engineers, 100(1), 798-878.

Liu, T. Y. 1935. Transportation of the Bottom Load in an Open Channel. M. S. Dissertation. Iowa: University of Iowa.

Liu, H. K. 1957. Mechanics of sediment ripple formation. Journal of the Hydraulics Division, 83(2), 1-23.

Liu, H. K. 1958. Closure: Mechanics of sediment ripple formation. Journal of the Hydraulics Division, 84(5), 5-31.

Luque, R. F., and van Beek, R. 1976. Erosion and transport of bed-load sediment. Journal of Hydraulic Research, 14(2), 127-143.

Mantz, P. A. 1975. Low Transport Stages by Water Streams of Fine, Cohesionless Granular and Flaky Sediments. Ph. D. Dissertation. London: University of London.

Meyer-Peter, E., and Müller, R. 1948. Formulas for bed-load transport. Proceedings of the 2nd Meeting of the International Association for Hydraulic Structures Research, 39-64. Delft: IAHR.

Milhous, R. T. 1973. Sediment Transport in a Gravel-bottomed Stream. Ph. D. Dissertation. Corvallis: Oregon State University.

Misri, R. L., Garde, R. J., and Ranga Raju, K.G. 1984. Bed load transport of coarse nonuniform sediment. Journal of Hydraulic Engineering, 110(3), 312-328.

Mizuyama, T. 1977. Bedload Transport in Steep Channels. Ph. D. Dissertation. Kyoto: Kyoto University.

Neill, C. R. 1967. Mean-velocity criterion for scour of coarse uniform bedmaterial. Proceedings of the 12th Congress of the International Association of Hydraulics Research, vol. 3, 46-54. Delft: IAHR.

Paphitis, D. 2001. Sediment movement under unidirectional flows: an assessment of empirical threshold curves. Coastal Engineering, 43(3-4), 227-245. [doi:10.1016/S0378-3839(01)00015-1]

Petit, F. 1994. Dimensionless critical shear stress evaluation from flume experiments using different gravel beds. Earth Surface Processes and Landforms, 19(6), 565-576. [doi:10.1002/esp.3290190608]

Pilotti, M., and Menduni, G. 2001. Beginning of sediment transport of incoherent grains in shallow shear flows. Journal of Hydraulic Research, 39(2), 115-124.

Powell, D. M., and Ashworth, P. J. 1995. Spatial pattern of flow competence and bed load transport in a divided gravel bed river. Water Resources Research, 31(3), 741-752. [doi:10.1029/94WR02273]

Rao, A. R., and Sitaram, N. 1999. Stability and mobility of sand-bed channels affected by seepage. Journal of Irrigation and Drainage Engineering, 125(16), 370-379. [doi:10.1061/(ASCE)0733-9437(1999) 125:6(370)]

Shields, A. 1936. Application of Similarity Principles and Turbulence Research to Bedload Movement. Berlin: Wasserbau Schiffbau. (English translation by Ott, W. P., and van Uchelen, J. C., Hydraulics Laboratory, California Institute of Technology)

Talapatra, S. C., and Ghosh, S. N. 1983. Incipient motion criteria for flow over a mobile bed sill. Proceedings of the 2nd International Symposium on River Sedimentation, 459-471. Nanjing: Water Resources and Electric Power Press.

U.S. Waterways Experiment Station (USWES). 1935. Study of River Bed Material and Their Movement: With Special Reference to the Lower Mississippi River. Vicksburg: U.S. Waterways Experiment Station.

Vollmer, S., and Kleinhans, M. G. 2007. Predicting incipient motion, including the effect of turbulent pressure fluctuations in the bed. Water Resources Research, 43(5), W05410. [doi:10.1029/2006WR004919]

Ward, B. D. 1968. Surface Shear at Incipient Motion of Uniform Sands. Ph. D. Dissertation. Tucson: University of Arizona.

Wathen, S. J., Ferguson, R. I., Hoey, T. B., and Werritty, H. A. 1995. Unequal mobility of gravel and sand in weakly bimodal river sediments. Water Resources Research, 31(8), 2087-2096. [doi:10.1029/ 95WR01229]

White, S. J. 1970. Plane bed thresholds of fine grained sediments. Nature, 228, 152-153. [doi:10.1038/ 228152a0]

Wilcock, P. R. 1987. Bed-load Transport of Mixed-size Sediment. Ph. D. Dissertation. Cambridge: Massachusetts Institute of Technology.

Yalin, M. S. 1972. Mechanics of Sediment Transport. New York: Pergamon Press.

Yalin, M. S., and Karahan, E. 1979. Inception of sediment transport. Journal of the Hydraulics Division, 105(11), 1433-1443.

Yalin, M. S., and da Silva, A. M. F. 2001. Fluvial Processes. Delft: International Association of Hydraulic Research.

Zanke, U. C. E. 2003. On the influence of turbulence on the initiation of motion. International Journal of Sediment Research, 18(1), 17-31.

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