Geoscience Reference
In-Depth Information
1.0,
M
>
0.38
C
m
=
0.7092 log
M
+
1.293, 0.05
<
M
≤
0.38
τ
c
is the critical shear stress for the
where
M
is the Kramer uniformity coefficient, and
arithmetic mean size
d
m
.
Wu et al. formula
Wu
et al
. (2000b) related the bed-load transport rate to the non-dimensional excess
grain shear stress
T
k
=
τ
b
/τ
ck
−
τ
b
determined using Eqs. (3.45) and
(3.51), respectively. The established relation for the fractional transport rate of non-
uniform bed load is graphically shown in Fig. 3.17 and expressed as
1, with
τ
ck
and
0.0053
n
n
1
2.2
3
/
2
τ
b
τ
ck
−
bk
=
(3.80)
p
bk
gd
k
]
where
bk
=
q
b
∗
k
/
[
(γ
/γ
−
1
)
,
q
b
∗
k
is by volume per unit time and width
s
d
1
/
6
50
(m
2
s
−
1
),
n
20, and
n
is the Manning roughness coefficient of channel bed.
Note that the hiding and exposure effect in non-unifrom bed material is accounted for
through
=
/
ck
determined using Eq. (3.45).
Eq. (3.80) was verified by using laboratory data for non-uniform bed load mea-
sured by Samaga
et al
. (1986a), Liu (1986), Kuhnle (1993), and Wilcock and
McArdell (1993), as well as field data from five natural rivers: the Susitna, Chulitna,
τ
Figure 3.17
Relation of fractional bed-load transport rate (Wu
et al
., 2000b).
