Threshold of Grain Motion 1. Definition - “general sediment movement” beyond occasional motion a. more or less continuous b. includes grains on all surfaces c. causes bed deformation. 2. What factors of the fluid and sediment are important? (Assume: steady, uniform flow; nearly spherical grains; moderately well-sorted) 1st Order:

2nd Order: Hjulstrom (30s) worked with the very first order variables: ū and D Hjulstrom diagram, mean flow velocity required to initiate movement on a flat, uniform bed. Flow velocity required to sustain movement is less (lower curve)

Sundborg (1956) - added more detail, and dealt with consolidation in fine-grained end.

In more physical detail - Force balance on particle under incipient motion. FLFL FdFd FgFg F g - total gravitational force. F g = (  s -  )gV F L - lift force caused by pressure differences around the particle due to velocity shear across the grain diameter F L = f (velocity profile very near the bed)

F d - Drag force depends on the undisturbed flow velocity in the vicinity of the grain (so also a function of the very nearbed velocity profile). Moment Balance: r (F g - F L ) sin  = r F d cos  After significant manipulation (see Harris notes):

Non-dimensionalize the shear stress: Therefore, the critical shear stress for transport depends on: the drag coefficient, the vertical velocity profile near the bed, the ratio of lift to drag, and the shape and angle of repose of the sediment or the Shield’s parameter, 

Now that we know our key variables, we can form a relationship for  as a function of: Roughness Reynolds number, R * controls very nearbed velocity profile & lift and drag coefficients Constants of the sediment: shape, angle of repose Shields Diagram

Miller, McCave & Komar, Sedimentology, 1977

Others have non-dimensionalized the axes, Miller, McCave & Komar, Sedimentology, 1977

And made more assumptions to simplify further..

Effects of grain sorting on threshold of grain motion: If there is a range of sizes: Or… Effects of organic factors: density differences binding at surface bioturbation