Geoscience Reference
In-Depth Information
incipient motion of non-uniform sediment particles on gravel beds:
q
b
∗
k
(ρ
s
/ρ
−
1
)
W
k
=
2
hS
f
=
0.002
(3.26)
p
bk
(
ghS
f
)
1
/
where
W
k
is a dimensionless bed-load transport rate,
q
b
∗
k
is the volumetric transport
rate per unit width for the
k
th size class of bed load,
p
bk
is the fraction by weight of
the
k
th size class in bed material,
h
is the flow depth, and
S
f
is the energy slope.
3.2.3 Incipient motion of uniform sediment particles
Critical average velocity
Using Eq. (3.25) and the power-law distribution of velocity
z
h
1
/
m
+
m
1
u
=
U
(3.27)
m
yields the critical average velocity for sediment incipient motion:
K
ρ
gd
1
/
2
h
d
1
/
m
−
ρ
ρ
s
U
c
=
(3.28)
s
−
1
),
and
K
is the coefficient determined by experiments. For example, Shamov (1959; see
Zhang and Xie, 1993) used
m
·
where
U
c
is the critical velocity averaged over the cross-section or flow depth (m
=
6 and
K
=
1.14, while Zhang (1961) used
m
=
7
=
and
K
1.34.
The similarity between Eqs. (3.3) and (3.28) yields the following formula for the
critical average velocity (Yang, 1973):
0.66
U
c
ω
+
2.5
/
[
log
(
U
∗
d
/ν)
−
0.06
]
1.2
<
U
∗
d
/ν <
70
s
=
(3.29)
2.05
U
d
/ν
≥
70
∗
where
U
∗
is the bed shear velocity.
Critical shear stress
Using Eq. (3.25) and the logarithmic distribution of velocity
5.75
U
∗
log
30.2
z
χ
s
k
s
=
u
(3.30)
yields
τ
2
k
1
a
1
k
2
a
2
C
D
+
1
c
d
=
(3.31)
5.75 log
)
2
(γ
−
γ)
k
3
a
3
C
L
(
30.2
z
d
χ
/
k
s
s
s
