Sediment Transport Concepts - Sediment Transport in Irrigation Canals: A New Approach - page 123

Yalin (1977) expressed this process by:

No motion τ<τ cr (5.67)

τ cr ≤ τ ≤ τ cr Bed load transport (5.68)

τ cr

Bed and suspended load transport τ ≥ (5.69)

where:
τ = bottom shear stress

τ cr = critical shear stress for initiation of motion

τ cr =

critical shear stress for initiation of suspension.
In reality, there is not one critical value at which the motion and sus-
pension suddenly begins, but it fluctuates around an average value. The
movement of the particles is highly unsteady and depends on the turbu-
lence of the flow. It is not possible to give a single value that presents
zero movement and for that reason it is easier to define the condition
for initiation of motion as the one below a certain value for which the
sediment transport rate has no practical meaning (Paintal, 1971).
Several authors have developed theories to explain the initiation of
motion. Most of these are based either on a critical depth-averaged velocity
or on a critical bed shear stress. The theories based on the critical velocity
require water depths that completely satisfy the flow condition at which
the initiation of motion occurs, whereas the theories based on critical shear
stress describe the flow condition for the initiation of motion by using a
single critical value for the shear stress. ASCE (1966) recommends that
data on critical shear stress should be used wherever possible. Among the
theories based on critical shear stress, the Shields' diagram is the most
widely accepted criterion to describe the conditions for initiation of motion
of uniform and non-cohesive sediment on a horizontal bed.
The Shields' diagram (see Figure 5.16) gives the relation between the
critical mobility Shields' parameter ( θ cr ) and the dimensionless particle
Reynold's number (Re ∗ ). The particle Reynold's number represents the
hydraulic condition on the bed and is based on the grain size and the shear
velocity. The initiation of motion will occur when the mobility Shields'
parameter ( θ ) is greater than the critical mobility Shields' parameter ( θ cr ).
These parameters are expressed by:

u 2
∗ cr

τ cr

θ cr =

1) gd 50 =

(5.70)

− −

( s ( s 1) ρgd 50