Calculations of the critical shear stress for motion of uniform and heterogeneous sediments

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.

On the suspension of graded sediment by waves above ripples: Inferences of convective and diffusive processes

“…This dependence might seem counterintuitive in a study focussing on the independent behaviour of individual grain fractions, but it arises from the role of d50b in determining the bed shear stress, which connects with the remarks of Wiberg and Smith (1987) noted following Eq. (12).…”

“…This increases the critical stress for finer particles and decreases it for more exposed coarser particles (Wiberg and Smith, 1987;Van Rijn, 1993;Wallbridge et al, 1999;Hassan 2003). In a multi-fraction approach Van Rijn (2007b) included an additional correction to the shear stress itself due to Day (1980).…”

“…(4), and vi) the number of analysed grain fractions available for each test from the pumped sampling. Wiberg and Smith (1987) noted that, for mixed sediment beds, there are two length scales of importance: the diameter of the grain fraction of interest, and the local roughness scale of the surrounding bed which contributes to Eq. (12) through ks=2.5d50b.…”

Erodibility of aquaculture waste from different bottom substrates

“…fluid drag) and upward (i.e. fluid lift) forces overcome the forces keeping a particle in contact with the bed (Wiberg & Smith 1987). The stress on the bed required to induce motion is the critical erosion shear stress, which is denoted τ crit (Einstein 1950, Partheniades 1962, Amos et al 1992, Tolhurst et al 1999).…”

Catchment‐scale mapping of surface grain size in gravel bed rivers using airborne digital imagery

“…[2] Grain size measurements of fluvial gravels are a fundamental descriptor for many fields of geomorphological research, including sediment transport [e.g., Middleton and Southard, 1984;Wiberg and Smith, 1987] and the study of flow resistance and the prediction of flow velocities in open channel flow [e.g., Bray, 1982;Clifford et al, 1992]. Furthermore, grain size has also been demonstrated to be an important variable for the habitat preferences of salmonids [e.g., Rimmer et al, 1983;Cunjak, 1988;Heggenes, 1996].…”