A New Theoretical Framework to Model Incipient Motion of Sediment Grains and Implications for the Use of Modern Experimental Techniques

  • Andrea Marion
  • Matteo Tregnaghi
Part of the GeoPlanet: Earth and Planetary Sciences book series (GEPS)


The entrainment of sediments in rivers is recognized to exhibit an intermittent nature, hence incipient motion is inherently a random process that requires an appropriate stochastic description. The effect of near-bed turbulence on grain entrainment and the variation in stability of randomly configured bed particles due to local surface heterogeneity are included into a probabilistic framework based on a concept first proposed by Grass. Bedload transport tests were carried out in a flume where sediment movement was monitored using a three-camera 3D PIV system. Simultaneous grain motion and flow velocity measurements were made on a plane located slightly above and parallel to the sediment bed. Detailed statistical velocity information was acquired to model the velocity distribution at the bed level accounting for the probabilistic distribution of particle exposures. This was combined with the probabilistic distribution of grain resistance to motion, which was obtained from discrete particle modeling (DPM) simulations. The analysis provides detailed insight, in terms of grain dynamics, into the physical aspects that determine the initiation of movement, and the stochastic equations of incipient motion are derived. The key feature of the proposed analysis is the potential of including into the model as much statistical information as one can obtain from experimental observations based on state-of-the-art flow measurement techniques and from the use of numerical simulations performed with discrete particle models.


Particle Imaging Velocimetry Sediment Transport Streamwise Velocity Fluid Shear Stress Critical Shear Stress 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Modeling and data analysis was carried out within the Project “PARTS: Probabilistic Assessment of the Retention and Transport of Sediments and Associated Pollutants in Rivers”, funded by the EU Research Executive Agency via an Intra-European Fellowship to Dr Tregnaghi under a Marie Curie action funding scheme.


  1. Bridge JS, Bennet JW (1992) A model for the entrainment and transport of sediment grains of mixed sizes, shapes, and densities. Water Resour Res 28(2):337–363. doi: 10.1029/91WR02570 CrossRefGoogle Scholar
  2. Battin TJ, Kaplan LA, Newbold JD, Hansen CME (2003) Contributions of microbial biofilms to ecosystem processes in stream mesocosms. Nature 426:439–441. doi: 10.1038/nature02152 CrossRefGoogle Scholar
  3. Bottacin-Busolin A, Singer G, Zaramella M, Battin TJ, Marion A (2009) Effects of streambed morphology and biofilm growth on the transient storage of solutes. Environ Sci Technol 43:7337–7342. doi: 10.1021/es900852w CrossRefGoogle Scholar
  4. Bottacin-Busolin A, Tait SJ, Marion A, Chegini A, Tregnaghi M (2008) Probabilistic description of grain resistance from simultaneous flow field and grain motion measurements. Water Resour Res 44:W09419. doi: 10.1029/2007WR006224 CrossRefGoogle Scholar
  5. Buffington JR, Montgomery DR (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. doi: 10.1029/96WR03190 CrossRefGoogle Scholar
  6. Buffington JM, Montgomery DR (1999) Effects of sediment supply on surface textures of gravel-bed rivers. Water Resour Res 35:3523–3530. doi: 1029/1999WR900138 CrossRefGoogle Scholar
  7. Cheng NS, Chiew YN (1998) Pickup probability for sediment entrainment. J Hydraul Eng 124(2):232–235. doi: 10.1061/(ASCE)0733-9399(1998)124:2(232) CrossRefGoogle Scholar
  8. Cheng NS, Law AWK, Lim SY (2003) Probability distribution of bed particle instability. Advances in Water Resources 26(4):427–433. doi:  10.1016/S0309-1708(02)00184-7.
  9. Dancey CL, Diplas P, Papanicolaou AN, Bala M (2002) Probability of individual grain movement and threshold condition. J Hydraul Eng 128(12):1069–1075. doi: 10.1061/(ASCE)0733-9429(2002)128:12(1069) CrossRefGoogle Scholar
  10. Drake TG, Shreve RL, Dietrich WE, Whiting PJ, Leopold L (1988) Bedload transport of fine gravel observed by motion picture. J Fluid Mech 192:2193–2217. doi: 10.1017/S0022112088001831 CrossRefGoogle Scholar
  11. Einstein HA (1942) Formulas for the transportation of bed load. Trans ASCE 107:561–597Google Scholar
  12. Grass AJ (1970) Initial instability of fine sand. J Hydraul Div ASCE 96(3):619–632Google Scholar
  13. Jimenez J (1998) Turbulent velocity fluctuations need not be gaussian. J Fluid Mech 376:139–147. doi: 10.1017/S0022112098002432 CrossRefGoogle Scholar
  14. Kirchner JW, Dietricht WE, Iseya F, Ikeda H (1990) The variability of critical shear stress, friction angle, and grain protrusion in water-worked sediments. Sedimentology 37:647–672. doi: 10.1111/j.1365-3091.1990.tb00627.x CrossRefGoogle Scholar
  15. Lopez F, Garcia MH (2001) Risk of sediment erosion and suspension in turbulent flows. J Hydraul Eng 127(3):231–235. doi: 10.1061/(ASCE)0733-9429(2001)127:3(231) CrossRefGoogle Scholar
  16. McEwan IK, Heald JGC (2001) Discrete particle modelling of entrainment from flat uniformly sized sediment beds. J Hydraul Eng 127(7):588–597. doi: 10.1061/(ASCE)0733-9429(2001)127:7(588) CrossRefGoogle Scholar
  17. McEwan IK, Soressen M, Heald JGC, Tait SJ, Cunningham G, Goring D, Willetts BB (2004) Probabilistic modelling of bed-load composition. J Hydraul Eng 130(2):129–140. doi: 10.1061/(ASCE)0733-9429(2004)130:2(129) CrossRefGoogle Scholar
  18. Nelson JM, Shreve RL, McLean SR, Drake TG (1995) Role of near bed turbulence structure in bed load transport and bed mechanics. Water Resour Res 31(8):2071–2086. doi: 10.1029/95WR00976 CrossRefGoogle Scholar
  19. Nikora V, Goring DK, Biggs BJF (1998) On gravel-bed roughness characterization. Water Resour Res 34(3):515–527. doi: 0043-1397/98/98WR-02886 CrossRefGoogle Scholar
  20. Paintal AS (1971) A stochastic model of bed-load transport. J. Hydraul Res 9(4):527–554. doi: 10.1080/00221687109500371 CrossRefGoogle Scholar
  21. Papanicolaou AN, Diplas P, Balakrishnan M, Dancey CL (1999) Computer vision techniques for tracking bedload movement. J Comput Civil Eng 13(2):71–80. doi: 10.1061/(ASCE)0887-3801(1999)13:2(71) CrossRefGoogle Scholar
  22. Papanicolaou A, Diplas P, Dancey C, Balakrishnan M (2001) Surface roughness effects in near-bed turbulence: implications to sediment transport. J Eng Mech 127(3):211–218. doi: 10.1061/(ASCE)0733-9399(2001)127:3(211) CrossRefGoogle Scholar
  23. Papanicolaou A, Diplas P, Evaggelopoulos N, Fotopoulos S (2002) Stochastic incipient motion criterion for spheres under various bed packing conditions. J Hydraul Eng 128(4):369–380. doi: 10.1061/(ASCE)0733-9429(2002)128:4(369) CrossRefGoogle Scholar
  24. Schmeeckle MW, Nelson JM, Shreve RL (2007) Forces on stationary particles in near-bed turbulent flows. J Geophys Res 112:F02003. doi: 10.1029/2006JF000536 CrossRefGoogle Scholar
  25. Shields A (1936) Application of the similarity principles and turbulence research to bedload movement, Report 167. California Institute of Technology, Pasadena, (translated from German)Google Scholar
  26. Tregnaghi M, Busolin-Bottacin A, Tait S.J, Marion A (2010) 3D near-bed flow field measurements at low sediment transport rates. Paper presented at river flow 2010, International conference on fluvial hydraulics, Braunschweig, Germany, 8–10 SeptGoogle Scholar
  27. Wu FC, Chou YJ (2003) Rolling and lifting probabilities for sediment entrainment. J Hydraul Eng 129(2):110–119. doi: 10.1061/(ASCE)0733-9429(2003)129:2(110) CrossRefGoogle Scholar
  28. Wu FC, Yang KH (2004) A stochastic partial transport model for mixed-size sediment. Application to assessment of fractional mobility. Water Resour Res 40:W04501. doi: 10.1029/2003WR00225 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Industrial EngineeringUniversity of PaduaPaduaItaly

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