SEDIMENT TRANSPORT AND EROSION 1073
in which
I Ky yIKyAAz(^1) ee
1
2
1
∫∫(); 11 ();/d 11 y y /lnd
K
0.216
AAeZ′′^1 /( (^1) e) ;Z A e 2d D ; P e 2.3 log 30.2 d d 65 ;
Z ′ v s ( bU * ); ( X see Bed Load Formulae ).
The total sediment load per unit width in a stream q T is
q T q TB q w , (31)
where q w wash load (fines) which must be obtained inde-
pendently, e.g. by direct measurement. The Einstein method
requires a knowledge of: grain size distribution in the bed;
the grain density; the energy slope, S e ; and the water temper-
ature, in order to compute both bed material load and water
discharge for a given depth and width of flow.
Colby and Hembree 9,36 modified Einstein’s method in
order to compute total sediment load ( q T ). Their procedure
utilizes: the sampled suspended load Q s ; measured discharge;
measured depths and sampler depths, the extent of the sam-
pled zone; and all the data used by the Einstein procedure
except S e. Their main modifications are:
- The finer portion of the total suspended load, Q s ,
is based on extrapolation of the actual sampled
load Q′s (using Eqs. (25) and (26)). - The coarser part of the total load (including the
bed load) is computed from a simplified Einstein
procedure (using a modification of Eq. (30)). - Einstein’s grain shear velocity U′∗ is replaced
by an equivalent shear velocity U m based on the
Keulegan equations and the measured discharge. - Einstein’s flow intensity function (^) * , is replaced
by the larger of
C m 1.65 gd 35 ( U m )^2 or C m 0.66 gd ( U m )^2 (32) - The modified term m is used to enter Einstein’s
Eq. (9) to obtain a bed transport function ; the
modified bed transport function is
* 2. (33)
The value of m is used to compute the bed load associated
with a size range d, i.e.
i B q B ; 1200 d^3 ^2 i B m lbsecft. (34) - Using the computed bed load for a certain size
range, i B Q B , the measured suspended load in the
same size range, IsQ′s, and Einstein’s Eq. (30) one
can obtain a value for Z ′ in Eq. (25) which should
be better than a Z ′ based on an estimated v s.
Bishop, Simons, and Richardson^6 simplified the Einstein
procedure for determining total bed material load. They
introduced a single sediment transport function T which
includes both suspended bed material and bed load. Their
flow intensity term is
yTs
e
S
d
RS
=−
′
(). 1 35 (35)
The experimental relationship shown in Figure 11 were estab-
lished for actual river sediments of various median sizes. Using
T from Figure 11 the total bed material load per unit width, is
qTB = Trs(gd)3/2(Ss–1)1/2. (36)
The wash load must be added to q TB to obtain the total
sediment load.
Colby^37 analysed extension laboratory and field data to
establish the empirical relationship, shown in Figure 12, for
the determination of sand discharge. Figure 12 is valid for a
water temperature of 60°F and a flow to moderate wash load
(c^<10,000 ppm). Colby provides adjustment coefficients for
water temperature and wash load. For example, at a flow
depth of 10 feet a 20°F change in temperature would result
in about 25% change in the sand discharge and an increase
in the concentration of fines from 0 to 100,000 ppm could
cause up to 10 fold increase in the sand load.
The reader is referred to Graf,^16 Shen,^15 and Chang et al. ,^27
for other contributions to the determination of total bed
material load.
The Annual Sediment Transport
In general it is not practical to continuously sample the sedi-
ment in a stream; instead, representative samples are taken
for various flow conditions and a sediment load versus water
discharge or sediment rating curve is established. A typical
sediment rating curve is shown in Figure 13. A number of
factors contribute to the scatter of data points in Figure 13.
The sediment load is out of phase with the discharge hydro-
graph as illustrated by Figure 14. The sediment load depends
on the season of the year.
Using the available stream flows and the sediment
rating curve an average annual sediment transport can be
estimated.
Often the bed load is not included in the sediment rating
curve; if this is the case, the bed load may be computed as
discussed under Bed Load Formulae and added to the annual
sediment transport.
THE RESPONSE OF A CHANNEL TO CHANGES IN
ITS SEDIMENT CHARACTERISTICS
Lane’s Model
Lane^39 proposed the relationship
(sediment load) (sediment size) (stream slope)
(stream flow)
or
( Q s d ) ( S Q ) (37)
to describe qualitatively to behavior of a stream carrying
sediment.
Lane used the following terms in referring to streams:
(1) “grade equilibrium or regime slope; (2) “aggrad-
ing” rising of the stream bed due to deposition;
(3) “degrading” losing of the stream bed due to scouring
C019_001_r03.indd 1073C019_001_r03.indd 1073 11/18/2005 11:06:01 AM11/18/2005 11:06:01 AM