Transcript Lec 7

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
(Assume: steady, uniform flow; nearly spherical
grains; moderately well-sorted)
1st Order:
2nd Order:
Hjulstrom (30s) worked with the very first order
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.
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)
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):
tan 
2 D
 cr 
(  s   ) gD f ( )
zo 1  FL tan 
Non-dimensionalize the shear stress:
* 
 s   gD
or the Shield’s parameter, 
Therefore, the critical shear stress for transport depends
• 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
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..
Miller, McCave & Komar,
Sedimentology, 1977
Effects of grain sorting on threshold of grain motion:
If there is a range of sizes:
Effects of organic factors:
density differences
binding at surface