River, Coastal and Estuarine Morphodynamics: RCEM 2007 Dohmen-Janssen & Hulscher (eds) 2008 Taylor & Francis Group, London, ISBN 978-0-415-45363-9Effects of particle exposure, near-bed velocity and pressure fluctuationson incipient motion of particle-size mixturesStefan VollmerFederal Institute of Hydrology, Department River Morphology, Koblenz, GermanyMaarten G. KleinhansUniversiteit Utrecht, Fac. Geosciences, Dept. Physical Geography, Utrecht, The NetherlandsABSTRACT: For the prediction of river bed destabilisation and fractional sediment transport of mixtures, weaim to solve two problems that are poorly understood. First, the flow and pressure fluctuations surrounding boththe embedded and exposed particles must be parameterised for hydraulically smooth to rough flow. Second, anadequate relation between particle size and particle exposure should be based on the particle size distribution andthe (water-worked) bed structure. We use a recently developed force balance model for the threshold of motionofuniformsedimentsincorporatingtheeffectsofparticleexposure,pressurefluctuationsintothebed,veryshallow flow and bed slope. The flow module is extended to non-uniform roughness of sediment mixtures. Ourextended model predicts the critical Shields values of arbitrary mixtures directly as function of exposure and nolonger needs empirical hiding-exposure relations. Several empirical and geometrical relations between particlesize and exposure were tested. The results are compared to extensive datasets from the literature of incipientfractionaltransportrates. Themodelledhiding-exposurerelationsareverysensitivetotherelationbetweenparticle size and exposure, which differ for unimodal, skewed and bimodal mixtures. This is explained by thepore structure of these sediments. The existing relations fail particularly for the smaller particles in bimodal andskewed distributions. These small particles percolate through the pores so their exposure or embedding stronglydepends on the fractional content and pore structure, in agreement with empirical data. We are working on auniversal relation for exposure containing particle size distribution, pore structure and water-working. The modelreproduces data of uniform sediments well for the entire physically possible range of particle exposures and forhydraulically rough to nearly smooth conditions. Trends in existing data for mixtures are also reproduced butdepend strongly on exposures that were not measured.1 INTRODUCTIONTheaimofthispaperistodevelopamodelfortheprediction of the threshold of motion of particle-sizemixtures. Prediction of incipient motion of sedimentmixturesispresentlylimitedtoempiricallyderivedequations. First wereviewtherelevant parametersto predict incipient motion of uniform sediments byphysics-based modelling. Then we review the currentempirical knowledgeofincipient motionofnaturalmixtures of various particle sizes. We then extend arecently developed force balance model for the thresh-old of motion of uniform sediments to sediment mix-tures. Our extended model predicts the critical Shieldsvaluesof arbitrarymixturesdirectlyasfunctionofexposure and no longer needs empirical relations. Thediscussion is used to validate and verify the model todemonstrate where current knowledge of the relevantparameters is limited, after whichconclusions aredrawn.2 REVIEWThe classical empirical study by A.F. Shields demon-strated that incipient motion of sands and gravels ofall densities occurs in a narrow range of a nondimen-sional ratio of the sediment entraining and detrainingforces:where c=critical shear stress, s and are the densi-ties of the sediment and water, g =gravitational accel-erationandD=particlesize. Thiscritical Shields54110210 110010110210210 1grain size D (mm)Shields number *cr Soulsby Zanke WibergSmiththis paperdata10 210 210 1*cr data*cr modelFigure1. A.ComparisonbetweentheSoulsby(1997)fitand the models by Zanke (2003), Wiberg and Smith (1987)and Vollmer and Kleinhans (2007) models. The dataset wascompiled by Buffington and Montgomery (1997). The low-est points are by Coleman (1967, in vollmer and Kleinhans2007) for maximum grain, exposure. B. Model predictionscompared to data for individual data points including slopeand depth effects. The lines are perfect agreement and a factorof 1.5 deviation.number has a value of about 0.057 for fine sand andgravel, a somewhat smaller value for mediumsand andan increasing value for finer sediment (Fig. 1).Wiberg and Smith (1987) reduced the Shields curvepartlytophysicsofflowaroundsphericalparticles.Theelementsoftheirmodel arepivotinganglesofnaturallypackedparticles, dragandlift forceswithindependentlyderivedcoefficients, andauniversalvelocity profile for the entire range of hydraulicallysmoothtoroughflow. ThedipintheShieldscurvecoincides withthe transitionbetweensmoothandrough 3.5