Suspended Load
 threshold 

U z   b   critical 
 of motion 
Bed Load
1. Bedload Transport
• transport rate of sediment moving near or in
contact with bed
• particles roll or hop (saltate), with grain-to-grain
contact
2. Suspended-Sediment Transport
• fluid conditions suspending particles
• particles supported by turbulence
Bedload Transport
Definition:
1. Bagnold - the particles which are supported by
inter-granular collisions as opposed to fluid drag.
2. The particles moving in a band up to some height
above the bed.
3. Pragmatic - those particles that can be caught in a
bedload sampler.
Major early body of work done by:
H.A. Einstein (1950s)
Meyer-Peter and Muller (1948)
Bagnold (1940 - 1950s)
As with initiation of motion, bedload transport can be
treated:
• Empirically
• Balance of forces
• Dimensional arguments incorporating both physics
and empirical findings.
Bagnold - Concept of bedload sediment transport is
related to the rate of transfer of energy (work) done by
the fluid on the moving grains.
Work = transfer of energy across a system boundary
(e.g., from a shaft to a fluid)
Power = rate at which energy transfer is done, or
Work/Time
On the seabed, Work can be defined in terms of the
shear stress.
Transfer of energy from bottom boundary layer
fluid to seabed particles  b
Rate of transfer (Power)  ū b
In terms of u*,
Power  ū b = ( u*2) (f (u* ) )
Power   u*3
Note: very small changes in velocity, or bed roughness, can
have significant effects on the rate of bedload transport.
Not all energy gets transferred to bedload grains,
need an “efficiency factor”
Bedload transport rate = K · Power
Bagnold’s Relationship for bedload transport rate:
 s   

 g  j  Power
 s 
 s   

 g  j  K u*3
 s 
Need to experimentally evaluate K
First work focused on: K = f ( D, relative roughness)
Inman, Coastal dunes: K  C D 250
where C = 1.5 in uniform sand, 1.8 in naturally
sorted sand, and 2.5 in poorly sorted sand
D is diameter in m
Need to consider Flow as well as seabed parameters.
- Marine Environment - Sternberg & Kachel, 1971.
Sternberg & Kachel, 1971
Measured ripple migration rates with stereo-cameras
in Puget Sound.
Evaluated K as a function of: D & flow conditions
Found:
  b  c 

K  0.005 exp  0.7
c 

for D  250m
 D
  b   c 
K  0.005 exp 
 1.5 


  c 
 140
for D  300m
Applicable for: D between 0.2 and 2 mm
steady to accelerating flow
limited amounts of suspended sediment
1. Given flow
conditions, find u*
and then b
2. Given D and u*
use a threshold curve
to find cr
3. Find K
graphically, or
through the curve-fit
equations.
4. Calculate j
Sternberg and Kachel, 1971
Tidal Bedload Transport Example:
The changes in tidal
current velocity measured
at 1 m above the bed
during a complete tidal
cycle in the North Sea.
As a result of the u 3
relationship, appreciable
differences occur
between the amounts of
sediment that can be
transported in each tidal
direction
Open University, 1989