Geoscience Reference
In-Depth Information
where
Q
tk
and
Q
t
∗
k
are the actual and equilibrium (capacity) transport rates of the
k
th
size class of bed-material load, respectively;
L
t
is the adaptation length of bed-material
load;
q
tlk
is the side discharge of bed-material load per unit channel length; and
β
tk
is
the correction factor, which is determined in analogy to Eq. (2.92) but may be set to
1 in the simulation of long-term sedimentation processes.
The sediment transport capacity can be written in the general form:
p
bk
Q
tk
Q
t
∗
k
=
(5.35)
where
Q
tk
is the potential equilibrium transport rate for the
k
th size class of bed-
material load.
Extending Eq. (2.149) to the 1-D model yields the following equation for the
fractional change in bed area:
∂
k
=
A
b
∂
1
L
t
(
p
m
)
(
1
−
Q
tk
−
Q
t
∗
k
)
(5.36)
t
The total change in bed area is calculated using Eq. (5.31), while the bed material
sorting is determined using Eqs. (5.32) and (5.33).
Eqs. (5.31)-(5.36) constitute the governing equations of the total-load transport
model that directly computes bed-material load. This model has
N
less transport
equations than the previous bed-load and suspended-load transport model. Not only
can those aforementioned reliable bed-material load transport capacity formulas be
used, but also many bed-load and suspended-load transport capacity formulas, such
as the Wu
et al
. (2000b) formulas, can be applied jointly in this approach. However,
it does not provide the ratio of bed load and suspended load.
Note that if
L
, the bed-load and suspended-load model
and the bed-material load model give the same results for total sediment discharge, bed
change, and bed-material gradation. This explains why
L
is found to be approximately
equal to
L
t
, as stated in Section 2.6.2. Because normally
L
s
=
L
t
and
α
=
Uh
/(
L
t
ω
)
s
≥
L
b
, the condition
α
=
can usually be satisfied using Eqs. (2.154) and (2.155). For very coarse
sediments, this condition may be violated, but because such sediments move mainly
in bed load, the difference between the two models is small and the bed-material load
model is preferable.
In addition, both models can simulate the transport of wash load by setting the
adaptation coefficient
Uh
/(
L
t
ω
)
s
in Eq. (5.27) to zero and the adaptation lengths in Eqs. (5.28)
and (5.34) to be infinitely large. The wash-load size range can be defined using the
bed-material diameter
d
10
or the Rouse number
α
0.06, as discussed in
Section 3.5.1. The latter method is more convenient for numerical modeling.
Both models can also simulate sediment transport over non-erodible channel beds.
This is often called the hard-bottom problem. On the non-erodible cross-sections,
the sediment transport capacity
Q
t
∗
k
in Eqs.
ω
sk
/(κ
U
∗
)<
(5.34) and (5.36) is replaced by
(
Q
t
∗
k
,
Q
tk
)
min
, or the sediment transport capacities
Q
b
∗
k
and
C
∗
k
in Eqs. (5.27),
(5.28), and (5.30) are replaced by min
, respectively. This
method allows only deposition on the hard-bottom points. It can be easily extended
to 2-D and 3-D models.
(
Q
b
∗
k
,
Q
bk
)
and min
(
C
k
,
C
k
)
∗
