Geoscience Reference
In-Depth Information
p
s
1
3
d
0.7
c
g
=
0.03
G
∗
−
(3.123)
(ρ
/ρ
−
1
)
s
where
p
s
is the pickup rate, defined as the probability density per unit time for a
sediment particle to be dislodged from the bed; and
G
∗
and
are coefficients:
sin
(β
d
+
δ
d
)
+
k
L
µ
s
G
∗
=
(3.124)
1
+
k
L
µ
s
=
µ
s
cos
θ
−
sin
θ
n
cos
β
d
n
(3.125)
µ
s
G
∗
where
s
is the static friction factor, with a value of about 0.7;
k
L
is the drag and
lift force ratio, which is about 0.85;
µ
δ
d
represents the
deflection angle of the flow velocity vector from the longitudinal direction; and
θ
n
is the transverse slope angle;
β
d
is the angle of the sediment movement (resultant force) direction measured from the
p
-axis defined along the wetted perimeter.
Damgaard et al. formula
Damgaard
et al
. (1997) modified the Meyer-Peter-Mueller (1948) bed-load formula
(3.65) to consider the effect of gravity in longitudinal slopes. The modified formula is
written as
3
/
2
f
slope
b
=
(
−
c
ϕ
)
8
(3.126)
s
gd
50
]
where
b
=
q
b
∗
/
[
γ
(γ
/γ
−
1
)
,
is the Shields number
τ
b
/
[
(γ
−
γ)
d
50
]
, and
s
s
is the critical Shields number on sloped beds determined by
c
ϕ
sin
(φ
−
ϕ)
c
ϕ
r
c
=
(3.127)
sin
φ
r
where
φ
r
is the repose angle;
ϕ
is the bed slope angle, with positive values for downslope
beds; and
c
is the critical Shields number on the horizontal bed, calculated using the
following algebraic representation of the Shields curve suggested by Soulsby (1996):
0.24
D
∗
e
−
D
∗
/
50
=
+
0.055
(
1
−
)
(3.128)
c
3
.
The parameter
f
slope
is a correction factor, determined by
2
1
/
with
D
∗
=
d
50
[
(ρ
/ρ
−
1
)
g
/ν
]
s
1
−
φ
<ϕ
≤
0
r
f
slope
=
(3.129)
0.2
1.5
+
/
c
+
(
c
/)
(
−
c
ϕ
/
c
)
<ϕ<φ
r
1
0.8
1
0
