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Journal ArticleDOI

Initial Instability of Fine Bed Sand

01 Mar 1970-Journal of Hydraulic Engineering (ASCE)-Vol. 96, Iss: 3, pp 619-632
TL;DR: In this paper, the initial entrainment characteristics of fine bed sand are objectively defined in terms of the measured distributions of critical instantaneous bed shear stress associated with the observed movement of individual surface grains.
Abstract: The initial entrainment characteristics of fine bed sand are objectively defined in terms of the measured distributions of critical instantaneous bed shear stress associated with the observed movement of individual surface grains. Critical flow conditions are then predicted by equating the lower extremes in these characteristic critical shear stress distributions to the upper extremes in the distribution of instantaneous bed shear stress produced by the particular type of background flow under consideration. The method is applied to the case of two-dimensional channel flow over a flat bed and yields sufficiently consistent results to suggest an extension to Shields' curve for small grain Reynolds numbers. The detailed experimental observations clearly illustrate the important role played by bed region turbulence in the interaction process between the fluid and the mobile bed grains constituting the deformable boundary.
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Journal ArticleDOI
TL;DR: In this paper, a modified Shields-type threshold diagram is presented for sediment movement under unidirectional flow conditions, which extends the limits of the original diagram by three orders of magnitude in the grain-Reynolds number.
Abstract: Carefully selected data for the threshold of sediment movement under unidirectional flow conditions have been utilized to re-examine the various empirical curves that are commonly employed to predict this threshold. After a review of the existing data, we employed only that data obtained from open channel flumes with parallel sidewalls where flows were uniform and steady over flattened beds of unigranular, rounded sediments. Without these restrictions, an unmanageable amount of scatter is introduced. This selected data is used to develop a modified Shields-type threshold diagram that extends the limits of the original diagram by three orders of magnitude in the grain-Reynolds number. The equally general but more easily employed Yalin diagram for sediment threshold is also examined. Although the Shields and Yalin diagrams are general in that they apply to a wide range of different liquids, in both cases somewhat different curves are obtained for threshold under air than for the liquids. The often used empirical curves of the friction velocity u,, the velocity 100 cm above the bed ul,,,,, the bottom stress T, and Shields’ relative stress Bt, all versus the grain diameter D, are limited in their ranges of application to certain combinations of grain density, fluid density, fluid viscosity and gravity. These conditions must be selected before the curves are generated from either the more general Shields or Yalin curves. For example, on the basis of the data selected for use in this paper, empirical threshold relationships for quartz density material in water are uloo = 122.6 Do.2B for D 0.2 crn where the velocity uloo measured 100 cm above the sediment bed is given in cmjsec and the grain diameter D is in cm. The limitations on any of the threshold relationships are severe. These limitations should be properly understood so that the empirical curves and relationships are not improperly employed.

982 citations

Journal ArticleDOI
TL;DR: In this article, the authors used data compiled from eight decades of incipient motion studies to calculate dimensionless critical shear stress values of the median grain size, t* c 50.
Abstract: Data compiled from eight decades of incipient motion studies were used to calculate dimensionless critical shear stress values of the median grain size, t* c 50 . Calculated t* c 50 values were stratified by initial motion definition, median grain size type (surface, subsurface, or laboratory mixture), relative roughness, and flow regime. A traditional Shields plot constructed from data that represent initial motion of the bed surface material reveals systematic methodological biases of incipient motion definition; t* c 50 values determined from reference bed load transport rates and from visual observation of grain motion define subparallel Shields curves, with the latter generally underlying the former; values derived from competence functions define a separate but poorly developed field, while theoretical values predict a wide range of generally higher stresses that likely represent instantaneous, rather than time-averaged, critical shear stresses. The available data indicate that for high critical boundary Reynolds numbers and low relative roughnesses typical of gravel-bedded rivers, reference-based and visually based studies have t* c50 ranges of 0.052-0.086 and 0.030-0.073, respectively. The apparent lack of a universal t*50 for gravel-bedded rivers warrants great care in choosing defendable t* c50 values for particular applications.

919 citations


Cites methods from "Initial Instability of Fine Bed San..."

  • ...Reported data are derived from Grass' [1970] averages of instantaneous shear stresses and are assumed equivalent to time-averaged values; instantaneous equivalents are shown in parentheses for comparison. Grass' [1970] direct shear stress measures implicitly account for sidewall effects....

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  • ...Reported data are derived from Grass' [1970] averages of instantaneous shear stresses and are assumed equivalent to time-averaged values; instantaneous equivalents are shown in parentheses for comparison....

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Journal ArticleDOI
TL;DR: In this article, an expression for the critical shear stress of noncohesive sediment is derived from the balance of forces on individual particles at the surface of a bed, where the initial motion problem for mixed grain sizes additionally depends on the relative protrusion of the grains into the flow and the particle angle of repose.
Abstract: An expression for the critical shear stress noncohesive sediment is derived from the balance of forces on individual particles at the surface of a bed. The resulting equation, for a given grain size and density, depends on the near-bed drag force, lift force to drag force ratio, and particle angle of repose. Calculated values of the critical shear stress for uniformly sized sediment correspond closely to those determined from Shields' diagram. The initial motion problem for mixed grain sizes additionally depends on the relative protrusion of the grains into the flow and the particle angle of repose. The latter decreases when the diameter of a moving grain, D, is larger than the length scale of the bed roughness, ks (D/ks > 1), and increases when D/ks < 1, producing a corresponding decrease or increase in critical shear stress. Using the Miller and Byrne experimental relationship between D/ks and particle angle of repose, which is consistent with Shields' definition of initial motion, we obtain results that are in good agreement with the available experimental critical shear stress data for heterogeneous beds.

578 citations

Journal ArticleDOI
TL;DR: In this article, a general derivation is given of the macro-equations of mass and linear-momentum balance that govern the mo'mentum transfer from a Newtonian fluid to rigid particles in a fluid-solid mixture.
Abstract: In this thesis first a general derivation is given of the 'macro'-equations of mass- and linear-momentum balance that govern the mo'mentum transfer from a Newtonian fluid to rigid particles in a fluid-solid mixture. In particular, attention is paid to a) the attenuation of viscous-momentum transfer from the boundary to the interior of a granular bed subject to a surface flow, b) the drag and lift forces exerted by a turbulent shear flow on particles of the bed surface, and, c) the balance of forces acting on a bed load under uniform-flow conditions. It is shown that filter flow driven by shearing along the boundary of a granular sediment bed exerts a drag force on a layer of only two or three particle diameters within the bed. A drag force on the bulk mass of sediment is only exerted by a pore-pressure gradient. Stability conditions are formulated for a loose granular bed subject to erosive flow, at SHIELDS' grain-movement condition and dUring bed-load transport. 'Macro'-stresses acting along 'wavy' surfaces parallel to the bed are defined for that purpose, and an attenuation factor is introduced for the transmission of turbulent fluid shear from the surface towards the interior of the bed. It is shown that SHIELDS' dimensionless expression for the critical bed shear stress at the threshold of continuous sediment motion, 1/Phi , must reach a constant value for low-shear Reynolds' numbers (Re* < O. 5), as long as there is no cohesion between the particles. It is concluded that the bed load, consisting of particles rolling and saltating over the bed, must reduce the maximum turbulent fluid shear at the bed surface, at sufficiently high bed shear stress, to the critical threshold drag that would lead to the initiation of non-ceasing scour.

553 citations

Journal ArticleDOI
TL;DR: In this paper, all available data on the resistance of topsoils to concentrated flow erosion in terms of channel erodibility (Kc) and critical shear stress (τcr) has been collected together with all soil and environmental properties reported in literature to affect the soil erosion resistance.

457 citations