Geoscience Reference
In-Depth Information
case of low sediment transport, because they adopt different criteria for incipient
motion.
Karim formula
Karim (1998) related the availability of sediment to the areal fraction of bed material,
and established the following formula for the fractional transport rate of bed-
material load:
0.00139
2.97
U
∗
ω
sk
1.47
q
t
∗
k
U
=
p
ak
η
k
(γ
/γ
−
1
)
gd
k
gd
k
(γ
/γ
−
1
)
s
s
(3.118)
where
q
t
∗
k
is inm
2
s
−
1
;
p
ak
is the areal fraction of bedmaterial, related to the volumetric
fraction of bed material,
p
bk
,by
⎛
⎝
⎞
N
p
bk
d
k
p
bk
d
k
⎠
p
ak
=
(3.119)
k
=
1
and
η
k
is the hiding and exposure correction factor:
C
1
d
k
d
50
C
2
η
k
=
(3.120)
where
d
50
is the median size of bed material; and
C
1
and
C
2
are coefficients:
C
1
=
1.15
ω
/
U
(3.121)
s
50
∗
C
2
=
0.60
ω
/
U
∗
(3.122)
s
50
with
s
50
being the settling velocity for
d
50
.
Eqs. (3.121) and (3.122) show that
C
1
and
C
2
increase as
ω
U
∗
increases. This
suggests that the coarser the sediment mixture, the stronger the hiding and exposure
effect. This is physically reasonable. However, the correction factor in Eq. (3.121) is
not equal to 1 for uniform sediment, so that Eq. (3.118) may be significantly different
from the original uniform sediment transport formula.
ω
/
s
50
3.6.3 Comparison of bed-material load formulas
Many investigators — e.g., Vanoni (1975), Alonso (1980), Brownlie (1981), Shen
and Hung (1983), van Rijn (1984b), Nakato (1990), and Woo and Yoo (1991) —
have compared the existing formulas for the total and fractional transport rates of
bed-material load using extensive flume and field data. Several examples are briefly
introduced below. More details can be found in relevant publications.
