Geoscience Reference
In-Depth Information
sediment, is a function of flow conditions and sediment properties. A variety of such
functions for bed load, suspended load, and bed-material load have been established
in the literature. Some of them are introduced in Sections 3.4-3.6.
3.4.1 Total transport rate of bed load
Many investigators — e.g., Duboys (1879), Schoklitsch (1930), Meyer-Peter and
Mueller (1948), Bagnold (1966, 1973), Dou (1964), Graf (1971), Yalin (1972),
Engelund and Fredsøe (1976), and van Rijn (1984a) — established formulas to cal-
culate the total transport rate of bed load. The following formulas are presented as
examples.
Meyer-Peter-Mueller formula
Meyer-Peter and Mueller (1948) related the bed-load transport rate to the excess grain
shear stress:
8
0.047
3
/
2
k
)
3
/
2
(
k
/
γ
RS
f
q
b
∗
s
(γ
gd
m
=
d
m
−
(3.65)
(γ
−
γ)
γ
/γ
−
1
)
s
s
m
−
1
s
−
1
);
d
m
is the arithmetic mean diameter of the bed sediment mixture (m);
k
is the reciprocal
of the Manning roughness coefficient
n
of channel bed;
k
is the reciprocal of the
Manning coefficient
n
due to grain roughness, calculated by
k
=
where
q
b
∗
is the bed-load transport rate byweight per unit time andwidth (N
·
d
1
/
6
90
26
/
; and
R
is
the hydraulic radius of the channel (m).
Bagnold formula
Bagnold (1966, 1973) related the sediment transport rate to the stream power
τ
b
U
and derived a bed-load transport formula:
log
0.37
h
nd
⎛
⎞
5.75
U
+
ω
ρ
b
U
tan
τ
U
∗
−
U
∗
c
U
∗
∗
s
s
ρ
s
−
ρ
⎝
1
⎠
q
b
∗
=
−
(3.66)
α
U
m
−
1
s
−
1
),
m
−
2
, tan
where
q
b
∗
is
the friction coefficient of about 0.63,
nd
is the average height of acting force during a
saltation,
d
is the sediment size (m), and
n
is by weight per unit time and width (N
·
τ
b
is in N
·
α
0.6
.
=
1.4
(
U
∗
/
U
∗
c
)
Dou formula
Dou (1964) also established an empirical formula for bed-load transport rate based
on the stream power concept:
K
0
ρ
U
g
s
U
c
)
q
b
∗
=
−
ρ
τ
b
(
U
−
(3.67)
ρ
ω
s
s