Geoscience Reference
In-Depth Information
m
−
1
s
−
1
),
U
c
is the critical average
velocity for sediment particles to cease motion, and
K
0
is an empirical coefficient with
a value of 0.01 for sand.
Eq. (3.67) can also be used to determine bed-material load, for which
K
0
where
q
b
∗
is by mass per unit time and width (kg
·
=
0.1 as
calibrated using Gilbert's data.
Yalin formula
Yalin (1972) analyzed the bed-load velocity and weight and then established the
following bed-load formula:
0.635
s
1
q
b
∗
1
as
ln
=
−
(
1
+
as
)
(3.68)
γ
s
dU
∗
m
−
1
s
−
1
),
s
where
q
b
∗
is by weight per unit time and width (N
·
=
(
−
)/
c
,
a
=
2.45
√
c
0.4
, and
(γ/γ
)
is the Shields number
τ
b
/
[
(γ
−
γ)
d
]
.
c
s
s
Engelund-Fredsøe formula
Engelund and Fredsøe (1976) related the bed-load transport rate to the bed-load
velocity and the probability for bed material to start moving, and obtained
√
c
0.7
b
=
11.6
(
−
)
−
(3.69)
c
s
(γ
where
b
=
q
b
∗
/
[
γ
/γ
−
1
)
gd
3
]
, and
q
b
∗
is by weight per unit time and width
s
m
−
1
s
−
1
).
(N
·
Van Rijn formula
Van Rijn (1984a) determined bed load as
0.053
ρ
g
0.5
d
1.5
50
T
2.1
D
0.3
∗
−
ρ
ρ
s
q
b
∗
=
(3.70)
where
q
b
∗
is by volume per unit time and width (m
2
s
−
1
),
D
∗
is the particle parameter
defined in Eq. (3.16), and
T
is the transport stage number defined in Eq. (3.57).
Eq. (3.70) was calibrated using data with a size range of 0.2-2 mm.
In addition, several bed-material load formulas, such as those of Ackers and White
(1973) and Engelund and Hansen (1967), can be used to calculate the bed-load trans-
port rate for coarse sediments. Yang (1984) modified his 1973 bed-material load
formula for gravel transport, which is primarily in bed load.
Note that the bed-load formulas introduced above calculate the transport rate of
uniform bed load or the total transport rate of non-uniform bed load as a single size
class. Thus, they may be used for narrowly graded sediment mixtures.
