Threshold of Grain Motion

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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
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2nd Order Hjulstrom (30s) worked with the very
first order variables u 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)
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Sundborg (1956) - added more detail, and dealt
with consolidation in fine-grained end.
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In more physical detail - Force balance on
particle under incipient motion.
FL
Fd
Fg
Fg - total gravitational force. Fg (?s - ?)gV
FL - lift force caused by pressure differences
around the particle due to velocity shear across
the grain diameter FL f (velocity profile very
near the bed)
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Fd - 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 (Fg - FL) sin? r
Fd cos ? After significant manipulation (see
Harris notes)
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• 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 Shields parameter, ?
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• 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
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Miller, McCave Komar, Sedimentology, 1977
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Others have non-dimensionalized the axes,
Miller, McCave Komar, Sedimentology, 1977
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And made more assumptions to simplify further..
Miller, McCave Komar, Sedimentology, 1977
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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