Geology Reference
In-Depth Information
re-entrainment of sediment from this complete
layer is equal to the oppositely directed rate of
sediment deposition caused by gravity. This
maximum equilibrium concentration is identi-
fied with what Foster (1982) called the 'transport
limit', here written as
c
t
.
The rate of deposition,
d
, is written as:
ing an approximate estimate based on a determi-
nation of sediment size distribution and use of
an empirical equation relating settling velocity
to size (reviewed by Fentie
et al
., 2004a), such
as that of Cheng (1997). The Griffith University
Depositability Program (called GUDPRO; Lisle
et al
., 1995) allows analysis of data from a variety
of sources to yield
f
.
Determination of the fundamental erodibility
parameter
J
requires sediment concentration to
be measured as a function of time, which is so
difficult to measure in field experiments that it is
hardly attempted. Also, as seen earlier, since sedi-
ment concentration can fluctuate between source
and transport limits (Rose
et al
., 1990), some
overall average measure of erodibility is required.
Such problems have been overcome in GUEST
by introducing an empirical erodibility parameter
b
, defined by:
dvc
--
21
=S
(kg m
s )
(11.7)
ii
where sediment is characterized by a distribution
of settling velocities (
v
i
, m s
−1
) with sediment
concentration
c
i
.
The transport limit is conceived as the steady-
state sediment concentration achieved in over-
land flow when the rate of re-entrainment of
recently deposited sediment is equal to the rate of
deposition. If this recently deposited sediment is
assumed to have negligible strength, then the rate
of energy expenditure in re-entrainment is that
required to lift an upward flux of sediment against
its immersed weight, where the flux rate is equal
to
d
given in Equation (11.7). The stream power
(Equation (11.6) ) supplies this rate of energy
expenditure. The immersed weight of sediment is
(
b
-
3
cc
=
(kg m
)
(11.9)
t
Figure 11.1 illustrates that the form of the relation-
ship between
c
and
for any particular value of
J
can be closely approximated by
c
b
, where
b
Ω
1.
Whilst
c
and
c
t
in Equation (11.9) are instanta-
neous values, and although GUEST allows such
calculations of
c
if
b
is known, such measure-
ments are not usually made (for reasons men-
tioned earlier), with only the flow-weighted
average concentration on an event basis (
−
) being
available. Instantaneous values when summed
for the event as a whole, so that Equation (11.9)
also holds for event average quantities, allow
−
to
be calculated by summation which can be
expressed as:
≤
sr
s
-
)
multiplied by its un-immersed weight.
e
Then, as shown by Rose and Hairsine (1988) and
Hairsine and Rose (1992a) (and in simplified form
by Rose, 2004), it follows that, neglecting
Ω
0
in
comparison to
Ω
,
c
t
is given by:
æ
ö
F
rs
fsr
-
3
c
=
e
SV
(kg m
)
ç
÷
(11.8)
t
-
è
ø
e
where
f
is the average settling velocity of all
classes (m s
−1
),
s
is the sediment density (kg m
−3
),
and
S
is the land slope.
The value of the soil depositability,
f
, depends
upon the distribution of the values of the settling
velocity
v
i
across the size range of particles and
aggregates which engage in settling during ero-
sion. Perhaps the most relevant method of meas-
uring this distribution is the modified bottom
withdrawal tube method, for which the theory
and practice is given by Lovell and Rose (1988a,b).
However, there is a variety of methods which can
be used to obtain sediment depositability, includ-
T
ò
Q dt
c
t
=
0
(11.10)
c
t
T
ò
Q dt
0
and then:
ln
ln
c
b
=
(11.11)
c
t
