Calculations of the Critical Shear Stress for Motion of Uniform and Heterogeneous Sediments

TLDR: 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.