This article provides a brief introduction to the subjects of soil erosion, transport of detritus by streams and the response of a stream channel to changes in its sediment characteristi
Trang 1S
SEDIMENT TRANSPORT AND EROSION
INTRODUCTION
The literature on the subject of erosion and sediment transport
is vast and is treated in the publication of such disciplines as
civil engineering, soil science, agriculture, geography and
geol-ogy This article provides a brief introduction to the subjects of
soil erosion, transport of detritus by streams and the response
of a stream channel to changes in its sediment characteristics
The agriculturalist is concerned with the loss of fertile
land through erosion Sheet, gully and other erosion
mecha-nisms result in the annual movement of about five billion
tons of sediment in the United States. 1 By this process, plant
nutrients and humus are washed away and conveyed to the
streams, reservoirs, and lakes
The sediment characteristics of a stream also affect its
aquatic life Changes in the character of the sediment load
will normally tend to change the balance of aquatic life Fine
sediment, derived from sheet erosion, causes turbidity in the
waterways This turbidity may interfere with photosynthesis
and with the feeding habits of certain fish, thus favoring the
less susceptible (often less desirable) varieties of fish The
resulting mud deposits may have similar selective results on
spawning The plant nutrients (phosphates and nitrates) that
accompany erosion from farmlands may contribute to the
eutrophocation of the receiving waters
Turbidity also makes waters less desirable for municipal
and industrial use Mud deposits may ruin sand beaches for
recreational use
From the engineer’s point of view an understanding of
sed-iment transport processes is essential for proper design of most
hydraulic works For example, the construction of dam on a
stream is almost always accompanied by, a reservoir siltation
or aggradation problem and a degradation problem A
reason-able prediction of the rate of reservoir siltation is necessary in
order to establish the probable useful life and thus the
econom-ics of a proposed reservoir The degradation or erosion of the
downstream channel and the consequent lowering of the river
level may, unless properly accounted for, endanger the dam
and other downstream structures (due to under-cutting) After
construction of the Hoover Dam the bed of the Colorado River
downstream from the dam started to degrade In 12 years the bed level dropped about 14 feet (Brown 1 )
In addition the downstream channel may change its regime (i.e its dominant stable geometry) For example, a wide braided channel or delta area may become a much nar-rower and deeper meandering channel thus affecting the prior uses of the stream This appears to have happened as a result
of the Bennett Dam on the Peace River in British Columbia. 2
CLASSIFICATION OF STREAMBORNE SEDIMENTS
Terminology
The materials transported by a stream may be grouped under the following type of load:
1) dissolved load, 2) bed load, 3) suspended load
The dissolved load, although a significant portion of total stream load, is generally not considered in sediment trans-port processes According to Leopold, Wolman and Miller, 3
the dissolved load in US streams increases with increas-ing annual runoff, reachincreas-ing a maximum of about 125 tons sq.mileyear for runoffs of 10 inchesyear or more
Bed load consists of granular particles, derived from the stream bed, which are transported by rolling, skipping or slid-ing near the stream bed Einstein 4,5 defines the bed load as the sediment discharge within the bed layer which he assumes to have an extent of two sediment grain diameters from the bed
Suspended sediment load is that part of the sediment load which is transported within the main body flow, i.e above the bed layer in Einstein’s terminology Turbulent diffusion is the primary mechanisms of maintaining the sediment particles in suspension The suspended load may be subdivided into:
1) Wash load which consists of fine sediments mainly derived from overland erosion and not found in
Trang 2significant quantities in alluvial beds; often wash load is arbitrarily taken to be sediments finer than 0.062 mm, i.e silts and clays
2) Suspended bed material load which is the portion
of the suspended load derived primarily from the channel bed; generally the bed material is assumed
to be the sediment coarser than 0.062 mm, i.e
sands and gravels
Table 1 indicates the terminology used by the American
Geophysical Union in describing various sizes of sediment
Properties of Sediments
An excellent review of the properties of sediments is presented
by Brown. 1 He discussed the determination and significance
of the following:
a) properties of the individual particle,
b) particle size distribution and
c) bulk properties of sediments
Properties of the Particle Neglecting interaction effects, the
behavior of an individual particle in a stream depends on its
size, specific weight, shape, and the hydraulics of the stream
Two commonly used methods of determining particle
size are: (1) mechanical sieve analysis and (2) the fall velocity
method The sieve analysis method differentiates particle size
on the basis of whether or not the particle will pass through
a certain standard square opening in a sieve or mesh This
method is applicable for sands or coarser particles Except in
the case of spheres, “sieve size” will only be an
approxima-tion to the true equivalent diameter of the particle since the
results depend to some extent on the particle shape
The fall velocity method of determining the effective sedi-ment size is gaining popularity in sedisedi-ment transport research
On the basis of the particle’s terminal velocity, in a specified fluid (water) at a specified temperature, the particle is assigned
a fall or sedimentation diameter equal to the diameter of the quartz sphere which has the same terminal velocity in the same fluid at the same temperature. 1 This particle size inte-grates the effects of grain size, specific weight and shape into
a single meaningful parameter for sediment transport studies
Researchers at Colorado State University have developed a Visual Accumulation Tube to aid in the determination of the fall diameter distributions for sediment samples
Particle Size Distribution On the basis of a sieve analysis
of fall diameter analysis, of a sediment sample, a cumulative frequency curve for the particle size can be drawn Figure 1 shows typical particle size frequency curves for a sample taken from a sandy stream bed and for a sample of suspended load over the same bed. 6 The frequency curves are usually plotted
on logarithmic-probability paper
TABLE 1 Sediment grade scale Group Particle size range, mm
Boulders 4096–256 Cobbles 256–64 Gravel 64–2 Sand 2–0.062 Silt 0.62–0.004 Clay 0.004–0.00024
FIGURE 1 Typical particle size frequencies curves for stream sediments (after Bishop et al.).
IN TRANSPORT (by dunes)
PERCENT FINER (by weight)
ON THE BED
1.0
.10 08
.20 30 40 50 60 80
Trang 3Some important descriptors of the frequency distribution
are: (1) the median size or d 50 , that is, the size for which 50%
by weight of the sample has smaller particles; (2) the scatter of
particle size as indicated, for example, by the standard
devia-tion or perhaps the geometric deviadevia-tion; (3) the characteristic
grain roughness which has been associated with the d 65 ; 5,7,8
(4) the d 35 has also been used as characteristic sediment size. 9
Bulk Properties The determination of bulk, in place
specific weights of sediments is discussed under Reservoir
Sedimentation
EROSION
Most of the sediment in streams is produced by the following
processes: 1
1) Sheet erosion,
2) Gully erosion,
3) Stream channel erosion,
4) Mass movements of soil (e.g landslides and soil
creep), 5) Erosion to construction works,
6) Solids wastes from municipal, industrial,
agricul-tural and mining activities
Morisawa, 10 using a system diagram, similar to Figure 2,
sum-marizes the inter-relation of climatic and geologic factors that
influence soil erosion and runoff Figure 2 also shows man’s
influence on the system
Langbein and Schumm 3,17 proposed the correlation
shown in Figure 3between annual sediment yield and
tive annual precipitation for the United States The
effec-tive precipitation is the adjusted precipitation which would
have produced the observed runoff for an annual mean
temperature of 50°F
A recent paper by Saxton et al 11 relates total runoff, surface
runoff and land use practices to the sediment yield from loessial
watersheds in Iowa This paper compares erosion and surface runoff from contoured-corn watersheds and from pastured-grass and level-terraced areas In a 6-year study the contoured-corn areas yielded, annually, about 19,000 tonssq mile of sheet erosion plus 3000 tonssq mile of gully erosion while the level terraced and grassed watersheds yielded about 600 tons
sq mile Similarly the surface runoff from the contoured-corn areas was approximately 5 inches compared with 1.5 inches for the level-terraced and grassed areas The experimental watersheds were of the order of 100 square miles
Other land use factors are discussed in a paper by Dawdy 12
who presents sediment yields for the state of Maryland The annual sediment yield from heavily wooded areas is about
15 tonssq mile compared with 200 to 900 for crop land
The annual sediment yields from urban development areas (usually only a few acres) varied from about 1000 to 140,000 tonssq mile
Curtis 13 obtained annual sediment yields of 390 and 290 for two watersheds (264 and 651 square miles) in the Miami Conservancy District, Ohio
A number of empirical formulae have been devel-oped 1,14,15 to permit estimation of rates of overland erosion
The US Department of Agriculture developed the universal soil-loss equation (for upland areas),
where E soil lossunit area; R rainfall runoff factor;
K soil erodibility factor; L slope length factor; S slope steepness factor; C 1 crop management factor; and P 1 erosion control practice factor Details for estimating the above factors are given by Meyer. 15
MEASUREMENT OF SEDIMENT DISCHARGE Samplers have been developed to measure both suspended and bed load in streams However bed-load samplers are not
temp, rain rock type topography
excavations fills reservoirs
CLIMATE GEOLOGY
SOIL CHARACTER
SOIL EROSION (RUNOFF)
RAINFALL
VEGETATION MAN
farming lumbering
amount intensity duration
MAN eg.
eg.
FIGURE 2 The relationship of climate and geology to soil erosion (adapted from Morisawa).
Trang 4widely used because of their doubtful accuracy Generally, only
suspended load samples are collected in samplers of the type
shown schematically in Figure 4.This sampler is designed so
that the intake velocity is nearly the same as the local stream
velocity The extent of the suspended sampled zone is limited
by the size of the sampler Methods or extrapolating these measurements and estimating bed load are discussed in the next section
For more details of sediment measurement techniques and equipment, the reader is referred to Nordin and Richardson, 15
200 400 600 800 1000
EFFECTIVE PRECIPITATION (inches/year)
T = 50°F
FIGURE 3 Sediment yield in the United States (after Langbein and Schumm).
FLOW
AIR
INTAKE
SAMPLE BOTTLE SPRING
EXHAUST VENT
FIGURE 4 Sketch of a suspended load sampler.
Trang 5Shen, 15 Karaki, 15 Graf, 16 Brown, 1 Simons, and Senturk and
the ASCE Sedimentation Engineering Manual
In some instances 15 turbulence flumes (a concrete lined
reach with baffles to create severe turbulence) have been
con-structed across a stream channel in order to suspend the bed
load and thus to sample it by suspended load techniques
THE MECHANICS OF SEDIMENT TRANSPORT
IN A STREAM
General
The nature of sediment transport in a stream depends on the
shear intensity of the flow and the type of bed material The
diagram in Figure 5shows the sequence of bed forms (waves)
associated with increasing levels of shear on a fine granular
bed material. 3 This figure also shows, schematically, the
typi-cal changes in the Darcy friction factor and the sediment
con-centration with increasing flow velocity The primary mode
of transport of particles, in the case of ripples, 17 is discrete
steps along the bed; however with increasing shear more of
the bed material becomes suspended until the particle motion
is nearly continuous for anti-dunes
Dunes and ripples are triangular in shape with relative
flat upstream slopes and sleep downstream slopes The
water surface waves are out of phase with the dune
forma-tion while ripple formaforma-tions appear to be independent of the
free surface
Dune wave lengths, d , are related to the depth of flow
and in general,
whereas ripple wave lengths r are shorter,
Dune heights, H d , are related to the depth of flow, with the
limiting height approaching the average flow depth The ratio of dune length to height is given by 17
8 l 15
The maximum ripple height is about 0.1 feet
Both ripples and dunes progress downstream The tran-sition from dunes to anti-dunes occurs at a Froude number close to 1.0
Anti-dunes, as indicated by Figure 5, are in phase with the surface wave The may be stationary or move upstream
The maximum height of an anti-dune is approximately equal
to the flow depth at the trough of the surface wave
Simons, 17,18 on the basis of experimental data, developed the relationship shown in Figure 6 between stream power and bedform for varying fall diameters Simons and Richardson 19
also studied the variation of Chézy’s C with bed form Their
results are summarized in Table 2
V feet/sec.
Friction Factor f
0.02 0.04 0.06 0.08 0.1
1 10 100 1,000 10,000 100,000
Concentration of Bed Material
C ppm.
Flat
C f
FIGURE 5 The behavior of a mobile stream bed (adapted from Leopold, Wolman, and Miller).
Trang 6Initial Motion
White, in 1940, 20,21 using an analytical approach, showed
that, for sufficiently turbulent flow over a granular bed, the
critical shear or shear to initiate grain movement is
t c k c g f ( S s –1) d, (5)
in which k c ; 0.06; g f fluid specific weight; S s specific
gravity of sediment grain; d grain diameter
Shields, 21 using an experimental approach, obtained the more general equation
t c g f ( S s –1) d f ( R * ), (6)
in which R * U * d n; U * friction velocity; n kinematic viscosity; and f ( R * ) is defined in Figure 7
Permissible or allowable tractive stresses for use in chan-nel designs with granular or cohesive boundaries are given
by Chow. 7
Bed Load Formulae
When the bed shear, t o , due to the flowing stream exceeds the
critical shear, t c , a part of the bed material starts to move in a
layer of the stream near the bed, i.e the bed layer Experimental
0.2 0.4 0.6 0.8 1.0 1.2 0
Median Fall Diameter in mm.
0.001 0.002 0.004 0.006 0.008 0.01 0.02
0.04 0.06 0.08 0.1
0.1
0.2 0.4 0.6 0.8 1.0
1.0
10
4.0
2.0
Upper Region
Transition
Dunes
Ripples
Plane
FIGURE 6 Relation of stream power and median fall diameter to bed form (after
Simons).
TABLE 2
Chézy C in sand channels
Regime Bed Form Cl √ g (where C is Chézy C)
Lower regime
ripples d50 0.6 mm 7.8 to 12.4 dunes 7.0 to 13.2 transition 7.0 to 20 Upper regime plane bed 16.3 to 20
anti-dune {standing wave 15.1 to 20 {breaking wavechutes and
pools“slug” flow
10.8 to 16.3 9.4 to 10.7
—
Trang 7studies 3 indicate that this sediment discharge, known as the
bed load, q B , is a function of the excess of t o above t c or
q B fcn ( t o — t c ) (7)
Figure 8 illustrates a typical experimental relationship
between q B and ( t o — t c )
DuBoys in 1879 22 treated the bed material, involved
in the bed load, as it if consisted of sliding layers which
respond to and distribute the applied stress t o He proposed
the relation
q B C s t
o ( t o – t c ) (8)
Both C s and t c depend on particle size as indicated in Table 3
Chang, 1 Schoklitsch, 1,16 MacDougall, 1 and Shields 1 have presented bed load formulae similar to Eq (8)
The theoretical bed load model developed by Einstein 4,5,8,24
has formed the basis for a number of researches in sediment transport. 6,15,24,36 Einstein utilized: (1) the statistical nature of turbulent flow; (2) the fact that in steady uniform flow there
is an equilibrium between the processes of erosion and depo-sition, that is, (probability of erosion) (the probability of deposition); (3) the fact that grains near the bed are more in quick “steps” interrupted by “rest” periods; (4) a separate
hydraulic radius, R ′, associated with grain roughness and
another hydraulic radius, R ′′, associated with the bed form
Einstein obtained the erosion probability function by assuming that the lift force, on a grain, consists of an
aver-age component [related to ( U * ) 2 ] and a normally distributed random component Einstein thus obtained the “bed load”
equation
A
B o o
−
∗ ∗
∗ ∗
∫
1
1
1 1
d
( / )
( / )
(9)
in which
∗
i q
B B
b g s 3( s 1)
(10)
is Einstein’s bed transport function; A * 43.5; B * 0.143;
h o 12;
c∗ j
⎧
⎨
⎪
⎩
⎪
⎫
⎬
⎪
⎭
⎪
Y
d
S R
s
log log .
10.6
2
in the Einstein flow intensity function; i B fraction of q B in the
size range associated with d; d geometric mean of particle
1.0 0.01 0.1 1.0
Rs=Usf n
f(Rs)
Laminar flow of bed
Turbient flow of bed
FIGURE 7 Shields’ critical shear function (adapted from
Henderson).
0.001 0.003 0.005 0.007 0.009 0.011 0.013 0.0
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15
0.01
T0 (gm/cm 2 )
T0
FIGURE 8 Typical relation of shear and sediment load
(adapted from Leopold, Wolman and Miller).
TABLE 3
Typical values of Cs and tc (after Straub 22,23 )
8
1 4
1 2
2
16
0.81 0.48 0.29 0.17 0.10 0.06
t c
lb
ft 2
0.016 0.017 0.022 0.032 0.051 0.09
Trang 8size range being considered; S e energy slope; i b fraction
of bed sediment in specified range; j hiding factor; Y lift
correction factor; d 65 X; X correction factor for
hydrau-lically smooth flow; d 11.6 n U * ;
X 0.770 if d 1.80; X 1.39 d if d 1.80
Schen 15 gives an up-to-date review of the modern
stochas-tic approaches to the bed material transport problem
The Suspended Load
Equations of Motion of the Fluid The flow in natural streams
is almost always turbulent and may be assumed to be
incom-pressible; consequently the applicable equations of motion
for the fluid are the Reynolds 25 equations
∂
∂
∂
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
∂
∂
U
U
i j i
ji i
in which U _ i ensemble mean point velocity in the direction i;
s
ji mD _ ji i u j} average pressure;
d ji Kronecker delta; m dynamic viscosity; D _ ji
deforma-tion tensor; i u j turbulence or Reynolds Stresses; r
fluid density ; u i random component of velocity in the i
direction; F _ body force in the i direction The first term in
the stress tensor represents the normal stresses due to the
aver-age pressure at a point; the second term represents the viscous
shear forces; the last term or Reynolds stress has both normal
and tangential components A common method of
simplify-ing equations involves the introduction of an eddy viscosity,
m such that
r m D ji r u u i j j i(≠). (14)
The requirement that ( i j ) in Eq (14) eliminates the normal
stresses due to turbulence; in order to account for these
normal stresses an average turbulence pressure P _ i is added to
P _ thus yielding the simplified stress tensor
s ji t(P P )d D ji m i ji(m r ) (15)
The fluid continuity equation is
∂
∂
U x
i i
0 (16)
Equations (13), (15), and (16) may be solved in a few
cases by methods developed to solve the Navier-Stokes
equations
Transport of a Scalar Quantity in Turbulent Flow In an
incompressible turbulent fluid the conservation of a scalar
quantity requires that the rate of change of a scalar (say c _ plus the rate of generation of c _ at the point or
Dc
c
x u c F
i i
i c
∂
∂
∂
∂
⎛
⎝⎜
⎞
in which c c_ c ; c_ ensemble average of c; c random component of c; D Dt substantial derivative; F_c_ is the
gen-eration term; h molecular diffusion coefficient It is usual
to introduce, into Eq (17), an “eddy” transport coefficient
j , such that
x
i c
i
∂
Since in most practical problems c h, then Eq (17) can
be reduced to
Dc
c
i c i
c
∂
∂
∂
⎛
⎝⎜
⎞
Equations (3) and (19) are valid for low sediment concentrations A review paper by Vasiliev 26 discusses the governing equation which account for various levels of sedi-ment concentrations For example a first order correction to the Reynolds equations is
r DU s
i i
ji t
The volume continuity equation is the same as Eq (16) while the mass continuity equation becomes
Dc
Dt x cu v
c x
i
∂
∂
∂
∂
⎧
⎨
⎩
⎫
⎬
⎭
( )
3
(21)
in which r ( S s —1); c_ average ensemble concentration
at a point (massmass); n s settling viscosity; x 3 vertical
coordinate (opposite to the direction of n s )
The Vertical Concentration Profile There is no general
solu-tion for Eqs (3), (16), and (19) or (18), (20), and (21); however
a few special cases, of practical interest, have been solved
Using the simplifications which result for steady, uni-form flow in two dimensions (as shown in Figures 9 and 10),
it is possible to obtain a solution for the vertical velocity, and concentration profiles The following assumptions are typi-cal of those required to solve Eqs (13), (14), and (21):
a) c_ 1;
b) c m where b ; 1;
c) F _
x ; grs 0 ;
Trang 9d) ∂
∂
;
x
t
e) to rgSoDand t rgSo (D y);
Chang et al , used the above assumptions to obtain: (a) the
vertical velocity profile,
1 3
1 2
*
/
k 1n⎛
⎝⎜
⎞
⎠⎟
⎧
⎨
⎪
⎩⎪
⎫
⎬
⎪
and (b) the vertical concentration profile
c y c a y
a
D D a
D D y
z
⎝⎜ ⎞⎠⎟
−
−
⎧
⎨
⎩⎪
⎫
⎬
⎭⎪
(23)
in which U * friction velocity gDs0; fcn ( U * d v ) 0.4;
Z v s ( bU * k ) Using the Keulegan velocity distributions
v
x 5 75 log10⎛9 05. ∗
⎝⎜ ⎞⎠⎟ (for smooth boundaries) (24a)
d
x 5 75 10 30 2
65
⎝⎜
⎞
⎠⎟
(for smooth boundaries) (24b)
Einstein and others 5,1 have obtained a slightly different
equa-tion for c ( y ), i.e
c y c a a D y
y D a
z
−
⎡
⎣
⎤
The Suspended Sediment Load The suspended sediment dis-charge q s (weightunit timeunit width) above a reference
level y a is given by
D
where U – and c – are given by Eqs (22) and (23) or (24) and (25)
Longitudinal Dispersion Another problem which has
received some attention is that of longitudinal diffusion and dispersion in natural streams and estuaries Several research-ers 16,33,34,35 have sought analytical and numerical solutions for the longitudinal variation in the mean concentration in the
vertical, c – Considering two dimensional longitudinal dispersion,
Eq (17) can be approximated by 16
∂
∂
∂
∂
∂
∂
c
t U
c
c x
in which E L ; coefficient of longitudinal diffusion A typical 16
value for E L is
E L 5 9 U D∗
The solution of Eq (27) for an initial step change, M o , in
concentration, is
E t e
o L
x U t x E t L
4
2 4
Other treatments of the dispersion problem may be found in the works of Holley 28 Householder et al , 29 Chiu et al , 30 Conover
et al , 31 Sooky, 32 Fischer, 33 Harleman et al , 34 and Sayre. 35
The Total Sediment Load
Einstein 5 developed a unified total bed material formulae by
converting his computed bed load, q B to a reference
concen-tration at y a 2 d Inserting into Eqs (25) and (26) he
obtained an estimate of q sB the suspended bed material load
Hence the total bed material load per unit width, q TB is
q TB q B q sB
i B q B (1 P e I 1 I 2 ) (30)
S0 FLOW
T0=gDS0
g(D–y)S0
1 y
y D
T
FIGURE 9 Defining sketch for uniform flow.
D
Ux
Ux
C σ
C y
S0
σ
FIGURE 10 Defining sketch for velocity
and concentration profiles.
Trang 10in whichI K y z y I K y
1 1
2
1
∫ ( / ) d ; / (∫ )ln dy y;
K 0.216 A e Z A
e Z
1
/( ) ; 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:
1) 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))
2) The coarser part of the total load (including the
bed load) is computed from a simplified Einstein procedure (using a modification of Eq (30))
3) Einstein’s grain shear velocity U′∗ is replaced
by an equivalent shear velocity U m based on the
Keulegan equations and the measured discharge
4) 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)
5) The modified term m is used to enter Einstein’s
Eq (9) to obtain a bed transport function * ; the modified bed transport function is
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 mlbsecft (34)
6) Using the computed bed load for a certain size
range, i B Q B , the measured suspended load in the
same size range, I s Q′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
y T s
e
R S
= −
′
( 1) 35
(35)
The experimental relationship shown in Figure 11were estab-lished for actual river sediments of various median sizes Using
T from Figure 11 the total bed material load per unit width, is
q TB = Trs (gd)3/2(S s–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
... gives an up-to-date review of the modernstochas-tic approaches to the bed material transport problem
The Suspended Load
Equations of Motion of the Fluid 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. .. 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