Geoscience Reference
In-Depth Information
The near-bed concentration c b is related to the average concentration C by c b = α
c C ,
as described in Section 2.5.1. Following Cao et al . (2004),
α
c is determined by
p m )/
α
=
min
[ α
0 ,
(
1
C
]
(9.64)
c
where
α 0 is given a value of 2.0. Note that Eq. (9.64) limits c b up to a maximum value
equal to 1
p m .
The 1-D bed-load transport equation is
Q b
U b
+
Q b
1
L (
=
Q b
Q b )
(9.65)
t
x
where Q b
is the equilibrium (capacity) bed-load transport rate; U b is the bed-load
velocity, which can be evaluated using the van Rijn (1984a) formula (3.136) or
Fig. (3.27) but is set to be the flow velocity here for simplicity; and L is the adaptation
length of sediment, determined using Eq. (2.155).
The bed change can be determined by
p m )
A b
1
L (
(
1
=
B
(
D b
E b ) +
Q b
Q b )
(9.66)
t
Empirical formulas
To close the aforementioned sediment transport model, additional empirical formulas
are required to determine the equilibrium bed-load transport rate Q b
and suspended-
load near-bed concentration c b
. The van Rijn (1984a & b) formulas (3.70) and (3.95)
herein are used. However, these formulas, which were calibrated in the lower flow
regime, should be modified for extension to the situation of dam-break flow.
According to the observation of Fraccarollo and Capart (2002), the sediment
concentration in the lower layer near the bed under dam-break flow conditions is very
high (nearly the same as that of bed material). Therefore, Wu and Wang (2007) intro-
duced a correction factor for the transport stage number in the van Rijn (1984a & b)
formulas by replacing the water density with the mixture density near the bed:
U 2
U 2
τ
b
b
b
c =
gd =
k t
(9.67)
τ
θ
mb
1
)
θ
f
1
)
gd
c
s
c
s
where
c is the critical Shields number for sediment incipient motion, determined using
the Shields diagram;
θ
ρ mb is the density of the water and sediment mixture near the
bed; and k t is the correction factor, expressed as k t
, with c a
being a concentration of sediment near the bed. In principle, c a can be related to the
average sediment concentration in the bed-load layer or the depth-averaged suspended-
load concentration, but this usually requires iteration in the sediment module. On the
other hand, the dynamic pressure in the dam-break wave front might affect sediment
entrainment and transport significantly, but it is very difficult to consider this effect
=
1
+
c a
ρ
/ [ (
1
c a
f ]
s
 
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