Morris & Fan. Reservoir Sedimentation Handbook
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HYDRAULICS OF SEDIMENT TRANSPORT 9.34
angle of the stable slope will also increase. Flow curvature will increase localized forces
at channel bends.
9.9 BED MATERIAL TRANSPORT
Bed material load consists of coarse material in the streambed which is mobilized by
flowing water, and may be transported either in suspension or as bed load. Bed material
transport for selected grain sizes may be supply limited when transport energy exceeds
the supply of material of a transportable size. A shortage of transportable material may
occur in a channel in rock which contains a thin bed of sand or gravel, or in a gravel-bed
river prior to mobilization of the armor layer, for example. However, when there is an
ample supply of transportable material on the streambed, the rate of sediment movement
is transport-limited and is determined by the available hydraulic energy in the stream.
Equations describing the capacity of flowing water to transport bed material may be
divided into two broad groups. Bed load equations describe the amount of material
transported as bed load, while total load equations actually describe the "total bed
material load," which includes bed material transported in suspension plus the bed load.
The total bed material load is normally the measure of interest in stream transport studies.
Wash load concentration and transport rate cannot be predicted from hydraulic conditions
in the stream, but depend on the rate of erosion in source areas and delivery rate of fine
sediment to stream channels.
Many bed material transport equations have been developed: Alonso (1980) listed 31
equations developed through 1973; the HEC-6 model offers the user a choice of 12
different equations or equation combinations, Yang (1996) includes a program listing and
diskette that can be used to compute sediment transport using 13 different "commonly
used" equations. Unlike hydraulic equations (e.g., Chezy, Manning, Darcy-Weisbach)
which give approximately equivalent results, the application of different sediment
transport equations to the same dataset can generate estimates of transport rates ranging
over more than 2 orders of magnitude, as illustrated in Fig. 9.15. Results of an analysis
can be heavily influenced by the choice of transport equation.
Most river and reservoir sediment transport problems involve the selection and use of
transport equations in the context of mathematical modeling. Criteria for selecting a bed
material transport equation are discussed in Chap. 11. The remainder of this section
briefly presents three transport equations which have been found to be generally reliable
when tested against a variety of datasets (Alonso, 1980; Brownlie, 1981; ASCE, 1983). A
more detailed description and comparison of these and other transport equations is
provided by Yang (1996) and Simons and Senturk (1992).
9.9.1 Ackers and White
Ackers and White related the weight concentration of bed material load C
s
to the mobility
function F
g
by the following equation:
C
s
cG
s
d
R
V
U
n
F
g
a
1
m
(9.33)
where G
s
= specific gravity of sediment and n, c, a, and m are coefficients. The mobility
number F
g
is computed as
HYDRAULICS OF SEDIMENT TRANSPORT 9.35
FIGURE 9.15 Measured total sediment discharge in Colorado River at Taylor's Ferry
and comparison with several transport equations (after Vanoni et al., 1960).
F
g
U
n
[gd(G
s
1)]
1/2
V
(32)
1/2
log(10R /d)
1n
(9.34)
Sediment size is expressed by a dimensionless grain diameter, d
previously given in Eq.
(9.23). The coefficient values were developed based laboratory data for sediment
diameters greater than 0.04 mm and a Froude number less than 0.8.
HYDRAULICS OF SEDIMENT TRANSPORT 9.36
9.9.2 Engelund and Hansen
The equation developed by Engelund and Hansen may be expressed in the following
form (Vanoni, 1975):
2/3
2/1
50
2
50
-
S
0
1/
05.0
d
S
g
d
Vq
ss
(9.35)
This equation is dimensionally homogeneous and can be solved using any set of
homogeneous units. In SI units the transport rate q
s
will be given in newtons per meter of
width, and it must be divided by the gravitational constant of 9.8 m/s
2
to express the
results in mass units of kg/(s•m).
9.9.3 Yang's Equation for Sand Transport
Yang (1983) observed that most sediment transport equations for bed load or total bed
material load are based on correlating sediment transport to a single hydraulic variable
using one of the following basic forms (Yang, 1996):
q
s
= A(Q - Q
cr
)
B
q
s
= A(V - V
cr
)
B
q
s
= A(S - S
cr
)
B
q
s
= A( -
cr
)
B
q
s
= A(τV -
cr
V
cr
)
B
q
s
= A(VS - V
cr
S
cr
)
B
where q
s
= sediment discharge per unit width of channel
Q = water discharge
V = mean velocity
S = energy or water surface slope
Τ = bed shear stress
V = stream power per unit bed area
V = unit stream power
A and B = parameters related to hydraulic and sediment conditions and
having different values in each equation
Some researchers have also used an empirical regression analysis to correlate sediment
transport to hydraulic parameters.
Yang (1983) plotted sediment discharge as a function of each hydraulic parameter
using laboratory flume data with 0.93-mm sand (Fig. 9.16). It was observed that more
than one sediment discharge rate can occur at a single value of water discharge or water
surface slope, making these two parameters poor predictors of transport rate. A single-
value relationship exists between sediment discharge and both velocity and shear stress.
However, the resulting curves are quite steep, which makes the independent variable a
poor predictor. The best correlations were achieved by using stream power. Unit stream
power, computed as the product of flow velocity and slope, was the best predictor.
A transport relation was developed based on the rate of energy expenditure per unit
weight of water, which is defined as the unit stream power and is computed as the
product of velocity and slope, VS. (See Appendix J.) The equation has the basic form
HYDRAULICS OF SEDIMENT TRANSPORT 9.37
FIGURE 9.16 Relationship between sediment discharge and selected hydraulic parameters fo
r
0.93-mm sand in a 2.4-m-wide flume (Yang, 1983).
HYDRAULICS OF SEDIMENT TRANSPORT 9.38
logC
ppm
I J log
VS
V
cr
S
(9.36)
where C
ppm
= bed material sediment concentration, excluding wash load (in ppm), and I,
J = dimensionless parameters related to flow and sediment characteristics. The
coefficient values were determined by regression analysis of 463 sets of laboratory data,
producing the following equation for sand transport [Yang (1973)]:
logC
ppm
5.435 0.286log
d
v
0.457log
U
1.799 0.409log
d
v
0.314 log
U
log
VS
V
cr
S
(9.37)
where C
ppm
= total sand concentration (ppm by weight), = sediment fall velocity, v =
kinematic viscosity, U
= shear velocity, d = median particle diameter, V
cr
S
= critical unit
stream power at incipient motion computed using Yang's method [Eq. (9.24) or (9.25)].
When the sediment concentration is more than about 100 ppm by weight, the incipient
motion criteria can be eliminated without affecting the accuracy of the equation, resulting
in the following relation (Yang, 1979):
logC
ppm
5.165 0.153log
d
v
0.297log
U
1.780 0.360log
d
v
0.480log
U
log
VS
(9.38)
These equations may be solved with either SI or fps units to determine sediment
concentration in ppm by weight, which is dimensionless.
9.9.4 Yang's Equation for Gravel
A gravel transport equation using the same form as Eq. (9.37) but different parameter
values is given as (Yang, 1984):
logC
ppm
6.681 0.633log
d
v
4.816log
U
2.784 0.305log
d
v
0.282log
U
log
VS
V
cr
S
(9.39)
where C
ppm
= total gravel concentration (ppm by weight).
9.9.5 Yang's Modification for Water-Sediment Mixtures
The foregoing equations were derived for sediment transport in essentially clear water.
The equations must be modified for use with other fluids, or for conditions in which there
is an extremely high sediment concentration in the water which requires that the
following parameter values be modified: fall velocity, kinematic viscosity, and relative
specific weight. Extremely high suspended-sediment concentrations and hyperconcen-
trated flows can occur in some river systems, such as China's Yellow River, and can also
occur during reservoir flushing. This section presents, as an example, an application
HYDRAULICS OF SEDIMENT TRANSPORT 9.39
specific to the Yellow River. Modification should be expected for use on another system
having a different grain size distribution.
Yang (1996) outlined the modification of the sand transport equation given in Eq.
(9.38) to include the characteristics of the water-sediment mixture, using the Yellow
River as an example. The effect of sediment concentration on fall velocity of fine sands
in the Yellow River may be estimated by
m
= (1 — C
v
)
M
(9.40)
where C
v
= sediment concentration by volume, including wash load, ω
m
and ω = sedi-
ment fall velocity in the mixture and in clear water respectively, and exponent M = 7.
The kinematic viscosity is a function of temperature, sediment concentration, and size
distribution. The expression for the kinematic viscosity of water-sediment mixtures for
the grain size distribution encountered in the Yellow River can be expressed by
v
m
m
e
5.06Cv
(9.41)
where and
m
= densities of clear water and the water-sediment mixture, respectively,
and ν
m
= kinematic viscosity of the mixture. The density of the mixture is given by
m
= + (
s
— )C
v
(9.42)
When revised to incorporate these effects, Yang's equation for sand transport given in Eq.
(9.38) is revised to the following form:
logC
ppm
5.165 0.153log
m
d
v
m
0.297log
U
m
1.780 0.360log
m
d
v
m
0.480log
U
m
log
m
s
m
VS
m
(9.43)
Note that the parameter coefficients are unchanged.
9.10 HYPERCONCENTRATED FLOW
Hyperconcentrated flows are sediment-water mixtures having a sediment concentration
high enough that the particles interact with one another to create a structural lattice within
the fluid of sufficient strength to affect characteristics such as velocity distribution within
the flow and particle settling rates. The behavior of the mixture departs significantly from
that of clear water, a Newtonian fluid, and is usually described based on the
characteristics of a Bingham fluid. High concentrations of cohesive sediments can
significantly affect the behavior of the sediment-water mixture as it flows in rivers and
enters or exits reservoirs. A comprehensive overview of both practical and theoretical
aspects of hyperconcentrated flow has been presented by Wan and Wang (1994).
Hyperconcentrated flow occurs naturally in China's Yellow River and its tributaries.
In this river system 300 g/L is the approximate threshold concentration for hyperconcen-
trated flow to occur, and peak suspended sediment concentrations exceeding 1000 g/L
have been reported at some gage stations. Because the hyperconcentration threshold
depends on factors including grain size distribution and mineralogy, the threshold
concentration will not necessarily be the same in other river systems. Hyperconcentrated
HYDRAULICS OF SEDIMENT TRANSPORT 9.40
flows are not limited to China, and may be generated during reservoir flushing in river
systems that otherwise never experience hyperconcentration. For instance, Ake Sundborg
observed hyperconcentrated flows during flushing at Cachi Reservoir, Costa Rica (Chap.
19).
High concentration flows can produce extremely rapid and large changes in the
configuration of erodible channels in rivers and reservoirs. Hyperconcentrated floods
cause the cross section to become narrower and deeper with the creation of lateral berms.
Because of the high sediment concentration they can also cause rapid channel
aggradation. The role of hyperconcentrated flows in some Chinese reservoirs has been
mentioned in the Sanmenxia and Heisonglin case studies, where they are important in the
formation of turbidity currents.
Whether produced naturally or by the erosion of upstream sediment deposits in a
reservoir, under favorable conditions hyperconcentrated flows can be passed through a
reservoir as a turbidity current with little sedimentation. The high concentrations
associated with hyperconcentrated flow produce high-velocity turbidity currents and can
transport coarse sediment to the dam, aided by the reduced settling velocity of the coarse
sediment within the hyperconcentrated fluid. Once the flow reaches the dam to form a
muddy lake, sedimentation within the muddy lake is hindered by hyperconcentration,
allowing the fluid to be vented through the dam over a period of several days under
favorable conditions. Due to settling and compaction within the submerged muddy lake,
the discharge from the muddy lake may have a higher concentration than the inflow.
9.11 COHESIVE SEDIMENTS
9.11.1 Importance of Cohesive Sediments
Reservoir sediments often contain a high percentage of clays, and their mechanical
behavior is strongly influenced by the interparticle cohesion caused by electrostatic and
related surface forces. These forces, which may be several orders of magnitude larger
than gravitational forces, give clay its "stickiness" and influence important phenomena
such as flocculation, the rate of sedimentation and compaction, the angle of repose, and
erosion resistance.
For coarse noncohesive sediments, characteristics such as settling velocity, condition
of incipient sediment motion, and erosion rate are determined by gravitational forces,
which can be represented by the grain diameter. However, in fine-grain sediments
(smaller than 0.01 mm) surface forces predominate, and the behavior of cohesive
sediments cannot be determined based on grain size alone. Colliding fine particles stick
together to form agglomerates having settling velocities orders of magnitude larger than
those of the individual particles. Thus, the floc rather than the individual particle becomes
the settling unit. These same physico-chemical surface forces provide the main resistance
to erosion of cohesive sediment deposits (Partheniades, 1986). While grain size
influences the surface forces through the relationship between surface area per unit of
mass and particle diameter, the strength of cohesive surface forces are also strongly
influenced by mineralogy and water chemistry parameters, such as ionic strength.
In 1935 Hjulstrom developed a graphical relationship between mean velocity and
grain size which illustrates the areas of sediment erosion, transportation, and deposition
(Fig. 9.12). Notice that the line of incipient motion, which separates erosion from
transportation, has a minimum value for a grain size around 0.1 mm, and increases for
both larger and smaller grains. The increased resistance to erosion for the larger sediment
particles is due to gravitational forces, whereas the increased resistance to erosion for fine
particles is primarily due to cohesive forces. Also note that for fine sediment there is a
HYDRAULICS OF SEDIMENT TRANSPORT 9.41
large difference between the thresholds for erosion and deposition. Once a fine particle is
eroded, it will not be redeposited unless flow velocity decreases substantially.
For practical applications in reservoirs, the characterization of cohesive sediment
properties is complicated by the nonuniform nature of the deposits. Different inflow
events will produce deposits having different thicknesses and grain size, and mineralogy
can vary as a function of the sediment source area for different inflow events. Differences
will also be caused by the fraction of coarse sediments or organics. Variations will occur
along the length of the reservoir due to the differential settling rates of the inflowing
sediment and other factors. Sediments will become compacted by consolidation and
dewatering over time, and deposits which are exposed to the air will experience
accelerated compaction and desiccation. As cohesive sediments compact, they become
more difficult to erode (Fig. 9.17).
The modeling of erosion processes in cohesive sediments at small French reservoirs
upstream of barrages was reported by Bouchard et al. (1989) and Bouchard (1993, 1995).
Following extensive sampling of continuously submerged cohesive sediment, the
mechanical properties were found to have wide variation both laterally and vertically
within the deposits. The mechanical characteristics of the cohesive bed material could be
represented in only a very approximate and aggregated fashion. At the very small (200 m
long) Kembs reservoir on the Rhine it was impossible to identify a clear succession of
FIGURE 9.17 Flow velocity required to initiate erosion of cohesive sediments from various
sites, as a function of dry bulk density of the sediment deposit (after Migniot, 1977), also
showing the muds from Kembs Reservoir reported by Bouchard (1993).
m
ud layers with a constant composition which could be followed from one bore hole to
another. The deposit structure consisted of a set of lenses with little continuity. More
uniform conditions may occur at larger reservoirs.
HYDRAULICS OF SEDIMENT TRANSPORT 9.42
Cohesive sediments in reservoirs may also be characterized by two different grain
sizes. At the Kembs reservoir the deposits were characterized by a mixture of clay
(d =
0.002 mm) and fine sand (d = 0.08 mm), and the variation in the mean d
50
diameter of any
sample primarily reflected the variation in the proportion of these two components. Thus,
mud characteristics were determined based on sediment concentration and the percentage
of dry matter having a diameter greater than 0.04 mm, thereby separating the cohesive
and noncohesive sediment fractions (Bouchard, 1995).
9.11.2 Settling and Compaction of Cohesive Sediment
The settling velocity of discrete clay particles is given by Stokes's law. As the
concentration of clay particles increases, the flocculation produces particle aggregates
having much larger effective diameters than discrete clay platelets. Consequently, the
settling rate of clay will initially increase as a function of concentration. However, at
some higher concentration the flocs begin to contact one another, creating a structural
lattice which greatly hinders fall velocity. Metha et al. (1989) indicate that settling rates
begin to be hindered when the flocculant suspension exceeds about 5 to 10 g/L in
concentration.
Particles settle as a group during the hindered settling process, which is characterized
by a sharp interface between the overlying clear water and a slowly compacting
flocculant mass that is settling uniformly. Coarser particles may be trapped within the
flocculant mass and settle together with it. As the flocculant mass compacts, clear water
is squeezed out of the structural lattice and makes its way to the interface through vertical
channels or small "drainage wells" which conduct water to the surface of the flocculant
material, and also along sidewalls when this phenomena is observed in a clear
sedimentation column. Pore water trapped within the flocculant mass must migrate
upward to the surface for settling to continue. This settling process is conceptually
illustrated in Fig. 9.18, where C
v
= concentration by volume.
Primary consolidation ends when the excess pore water pressure has completely
dissipated. Secondary consolidation, which is the result of plastic deformation of the
structural lattice due to overburden, begins during primary consolidation and may
continue long after primary consolidation ends (Mehta et al., 1989). The behavioral
characteristics of the sediment will change as it compacts, and the nomenclature used to
describe cohesive sediment varies based on the bulk density (Yang and Wang, 1996):
fluid mud density less than 1.2 g/cm
3
mud density between 1.2 and 1.6 g/cm
3
consolidated mud or clay density exceeds 1.6 g/cm
3
Consolidation rates vary widely from one site to another (Fig. 9.19), and in general the
concentration in the consolidating mass varies as a logarithmic function of time. There is
no general expression for the rate of hindered settling and consolidation of cohesive
sediment. It is necessary to determine the settling rate using laboratory settling columns.
Several characteristics of cohesive sediments must be specifically considered in the
evaluation of reservoir sedimentation. Flocculation may cause suspended sediment to
settle much faster than predicted based on the size of the individual grains, as
demonstrated at the Peligre Reservoir in Haiti by Frenette and Julien (1986).
HYDRAULICS OF SEDIMENT TRANSPORT 9.43
FIGURE 9.18 Settling processes for cohesive sediment (adapted from Migniot, 1968).
In many reservoirs it is observed that the rate of storage loss is initially high and then
declines (Murthy, 1977). This phenomena may be explained by the gradual compaction
of cohesive sediment: the volume occupied by cohesive sediment during the first year
after deposition is greater than the volume it will occupy after many years of compaction.
This compaction effect must be taken into account in short-interval volume
measurements (see Sec. 10.9.4).
In reservoirs where new sediment layers are being continuously deposited, the upward
migration and release of pore water may be retarded by the continued deposition of
additional fine sediment layers. Sediment deposition will also cause overburden to
increase with time. Because of these factors and others such as variation in the inflowing
grain size and surface drying during drawdown, the bulk density of reservoir deposits
often do not increase regularly with depth, and sediment density may actually be lower in
deeper layers, as illustrated in Fig. 10.17.