Geoscience Reference
In-Depth Information
the channel width, thus yielding
0
h
r
+
1
dy
0
h
(
3
r
−
1
)
m
dy
B
0
h
(
3
r
−
1
)
m
+
r
+
1
dy
α
1
d
α
=
λ
α
=
(2.144)
where
λ
α
is considered as a correction factor to account for the influence of cross-
sectional shape. Normally,
λ
α
is in the range of 0.25-1.0.
Effects of other factors
The settling velocity
s
in Eqs. (2.72) and (2.132) is often set as that of a single
particle in quiescent, distilled water. This is valid if the sediment concentration is very
low, but in general the effect of sediment concentration on
ω
ω
s
should be considered.
Moreover,
s
considers only the actions of drag force and submerged weight in still
water. In reality, sediment particles also experience other forces exerted by moving
water (Li, 1993; Wu and Wang, 2000). In particular, the Saffman (1965) lift force,
which might be important near the bed where the velocity gradient is high, may reduce
the settling velocity. These effects should be lumped in the adaptation coefficient
ω
,
if no corrections are made to the settling velocity. This usually leads to reduction in
α
α
values.
In addition, the above analyses of
consider only the flat bed without bed forms.
Bed forms often exist in natural rivers and affect the sediment exchange near the bed
and, in turn, the values of
α
. However, this effect is little understood. The bed-load
layer may become thicker because of bed forms, so that reduction in
α
α
values may be
expected based on Eq. (2.129) or (2.135).
Therefore, the adaptation coefficient
lumps the effects of many factors on sediment
transport. Tests inmany rivers and reservoirs conducted by Han (1980) andWu (1991)
suggest that
α
α
is about 1 for strong erosion, 0.5 for mild erosion and deposition, and
0.25 for strong deposition in 1-D models. These values differ from those (larger than
1) predicted by Eqs. (2.129), (2.130), (2.135), and (2.136), but they are qualitatively
reasonable if these corrections due to the effects of cross-sectional shape, sediment
concentration, Saffman lift force, and bed forms are considered. However, these values
are given for reference only, and calibrating
α
using measurement data is preferable
for a specific case study.
2.6 EQUILIBRIUM AND NON-EQUILIBRIUM SEDIMENT
TRANSPORT MODELS
2.6.1 Formulation of equilibrium transport model
Each of the 1-D, 2-D, and 3-D sediment transport models described in Section 2.4
has only two governing equations, namely the suspended-load transport equation and
the bed-load mass balance equation, but there are three unknowns: suspended-load
concentration, bed-load transport rate, and bed change rate. Thus, one more equation
is required to close each model. Most of the first sediment transport models adopt the
assumption of local (instantaneous) equilibrium for bed-load transport, which assumes
