Geoscience Reference
In-Depth Information
Figure 3.9
Comparison of measured and calculated critical shear stresses (Wu
et al
., 2000b).
shown in Fig. 3.9. Themeasured critical shear stresses in Fig. 3.9were determined using
Eq. (3.26) as the reference transport threshold. The agreement between measurements
and predictions is generally good.
3.2.5 Incipient motion of sediment particles
on slopes
For a sediment particle on a sloped bed or bank, its incipient motion is affected not
only by the drag and lift forces, but also by the component of gravity along the slope.
Brooks (1963) suggested the following method to determine the critical shear stress
τ
for the incipient motion of sediment on a sloped bed:
c
ϕ
sin
2
τ
sin
ϕ
sin
θ
ϕ
cos
2
θ
c
ϕ
s
s
c
=−
+
cos
2
ϕ
−
(3.46)
τ
tan
φ
tan
2
φ
r
r
ϕ
θ
s
is the angle
where
is the slope angle with positive values for downslope beds,
between the flow direction and the horizontal line of the slope, and
φ
r
is the repose
angle.
Van Rijn (1989) also suggested a method to determine
τ
c
ϕ
:
τ
ϕ
=
k
1
k
2
τ
(3.47)
c
c
where
k
1
is the correction factor for the streamwise-sloped bed (in the flow direc-
tion), determined by
k
1
r
; and
k
2
is the correction factor for
the side
ward-sloped bed (
normal to the flow direction), determined by
k
2
=
sin
(φ
−
ϕ
)/
sin
φ
r
L
=
T
1
tan
2
tan
2
cos
ϕ
−
ϕ
/
φ
r
. Here,
ϕ
L
and
ϕ
T
are the slope angles in the flow and
T
sideward directions, respectively.
