Geoscience Reference
In-Depth Information
bed-material load and wash load, as shown in Fig. 2.3, two total-load modeling
approaches are usually adopted. One is to simulate bed load and suspended load sepa-
rately, while the other is to compute bed-material (total) load directly. Both approaches
have advantages and disadvantages.
1-D bed-load and suspended-load transport model
As described in Section 2.7.1, the non-uniform sediment mixture is divided into a
suitable number of size classes (
N
). In the case of low sediment concentration, interac-
tions among different size classes are usually ignored and, thus, the transport of each
size class is simulated separately. For each size class, the moving sediment is further
divided into suspended load and bed load. Introducing Eq. (2.132) into Eq. (2.108) and
considering the lateral exchange with banks and tributaries yields the 1-D transport
equation of the
k
th size class of suspended load:
AC
k
β
sk
∂
∂
+
∂(
AUC
k
)
∂
=
αω
sk
B
(
C
−
C
k
)
+
q
slk
(
k
=
1, 2,
...
,
N
)
∗
k
t
x
(5.27)
where
C
k
and
C
k
are the actual and equilibrium (capacity) average concentrations
of the
k
th size class of suspended load, respectively;
∗
is the adaptation coefficient of
suspended load;
q
slk
is the suspended-load side discharge per unit channel length due
to the lateral exchange with banks and tributaries; and
α
β
sk
is the correction coefficient,
which is determined using Eq. (3.135) in general, but may be set to 1 in the simulation
of long-term sedimentation processes.
In analogy to Eq. (2.158), the 1-D bed-load transport equation is
Q
bk
U
bk
∂
∂
+
∂
Q
bk
∂
1
L
(
=
Q
b
∗
k
−
Q
bk
)
+
q
blk
(5.28)
t
x
where
Q
bk
and
Q
b
∗
k
are the actual and equilibrium (capacity) transport rates of the
k
th size class of bed load, respectively;
L
is the adaptation length of sediment, defined
in Section 2.6.2; and
q
blk
is the bed-load side discharge per unit channel length.
The bed-load velocity
U
bk
needs to be determined using one of the empirical formu-
las described in Section 3.8. However, the storage term, the first term on the left-hand
side of Eq. (5.28),
is often ignored in the simulation of long-term sedimentation
processes.
The equilibrium suspended-load concentration and bed-load transport rate can
be determined using the existing formulas described in Sections 3.4 and 3.5. For
convenience, these formulas are written in general forms:
p
bk
C
k
,
Q
b
∗
k
=
p
bk
Q
bk
C
∗
k
=
(5.29)
where
p
bk
is the sediment availability factor, usually set as the fraction of size class
k
in the mixing layer of bed material;
C
k
is the potential equilibrium concentration for
the
k
th size class of suspended load; and
Q
bk
is the potential equilibrium transport
rate for the
k
th size class of bed load.
C
k
and
Q
bk
can be interpreted as the equilibrium
