1.2_Properties of Sediments

7/30/2019 1.2_Properties of Sediments

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1.2. Prop ert ies of Sedim ent s1.2. Prop ert ies of Sedim ent s

Sedimentat ion processes (erosion, entrainment,t ranspor t , and subsequent depos i t ion o f sed iment )depend on

proper t ies o f the sed iment character ist ics of t he f lo w involved

Those proper t ies o f most impor tant in thesedimentat ion processes can be div ided intoproper t ies o f

part ic les

sed iment as a wh ole

Size and shape of grains making up a sediment vary

over a w ide range

Size and Shap e o f Sedim ent Part ic les

meaningless to consider in detai l the propert ies of

an indiv idual part ic le

necessary t o d eterm ine average or stat is t ical values

Sediments are grouped into di f ferent s ize c lasses orgrades

Natural sedimen t p art ic les are of i r regular shape

Any single length or diameter that is to character izethe s ize of a group of grains must be chosen ei therarb i t rar i ly or accord ing to som e convenient m ethod ofmeasurement

Sediment particles are classif ied, based on their size,into six general categories: Clay, Silt, Sand, Gravel,Cobbles, andBoulders

Size and Shap e o f Sedim ent Part icles Sed im ent Grade Scale

Sieve diameter is the length of the s ide of a squaresieve opening through which the given part ic le wi l lju st p ass

Sedimentat ion d iameter is the diameter of a sphereof the same spec i f i c weight and the same term ina lset t l ing veloci ty as the given part ic le in the samesedimentat ion f lu id

sieving is convenient t o det erm ine t he s ize of sands

size of si l ts and clay is generally expressed assedimentat ion d iameter

Size and Shap e o f Sedim ent Part icles

Those character ist ics that seem most important to

engineers concerned wi th sediment t ransport areshapean d roundness

descr ibes the form of t he par t i c le w i tho ut re ferenceto the sharpness of i ts edges

has been expressed in ter ms of t rue sphericity

Shape

Nomina l d iameter i s the d iameter o f a sphere of t hesame vo lum e as the given p art ic le

Size and Shap e o f Sedim ent Part icles


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depends on the sharpness or radius of curvature ofth e edges

def ined as the rat io o f the average radius of curvatureof indiv idual edges to the radius of the largest c i rc lethat can be inscr ibed w i th in e i ther the pro jected areaor a cross sect ion o f th e grain

Roundness

sphericityhas been def ined as the rat io o f th e surfacearea o f the sphere w i th the same vo lum e as the grainto t he surface area of the part ic le

Size and Shap e o f Sedim ent Part ic les

i n w h ich

= length of th e longest perpendicular axis

= l ength o f th e in term edia te perpendicu lar ax is

= length of th e sho rtest perpend icular axis

In studying t he fal l veloci ty, the shapes of th e part ic leshave been expressed by shape factor, , given b y

Shap e of Sedim ent Part ic les

=

Al l sedim ents have their or igin in rock mater ial , and al lconst i tuents of the parent mater ial can usual ly befound in the sed iment

Speci f ic Weight of Sedim ent Part ic les

As the mater ia ls become f iner du e to w eather ing andabrasion, the less stable minerals tend to weatherfaster and be carr ied away as f ine part ic les or inso lu t ion, leaving beh ind m ore s tab le com ponent s

Al tho ugh quart z, because of i ts great stabi l i ty, is by farthe comm onest minera l found in sed iments mo ved by

water and w ind, numerous o ther minera ls a lso arepresent

A l though other mater ia ls bes ides quar tz may bepresent in ap preciable quant i t ies, the average speci f icgravi ty of sand is very c lose to t hat of q uart z, i .e., 2.65,and this value is used of ten in calculat ions andanalysis

Speci f ic Weight of Sedim ent Part ic les

Important for processes such as sedimentat ion andsuspension

A constant veloci ty of a vert ical ly fal l ing part ic le in st i l lwa te r

Direct ly character ize its react ion t o f low

Reflects the integrated result of size, shape, surfaceroughn ess, speci f ic gravi ty and viscosi ty o f t he f luid

I ts magni tude ref lects a balance between thedow nw ard act ing force due to the submerged par t i c leweight and opposing forces due to v iscous f luidresistan ce and iner tia effects (drag forces)

Fall (Sett l ing) Velocit y of Part icles Fal l Velocit y of Part icles

For part ic les coarser t han 2 m m encount er resistancefrom the in ert ia of th e wat er as they fal l , and v iscosi tyis un imp or tant

Wh en Reynolds number = / is less th an 0.1 fo rsmall particles in the si l t-clay range viscous resistancedom inates and inert ia is negligible

For a sphere of diameter , the fal l velocity, , fo rvalues of Reynolds number = / less thanapp rox 0.1 is given by Stokes law


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Fal l Velocit y o f Sph eres

i n wh ich

= kinem at ic v iscosity of the f lu id

= speci f ic w eight of the f lu id

= speci f ic weight of t he sphere

= accelerat ion of gravi ty

= specif ic gravity

Fal l veloci ty over t he ent i re range of Reynolds nu m bers,in term s of th e drag coeff ic ient , , is given b y

Drag coefficien t in t he sto kes range (R < 0.1) is given by

For larger Reyno lds num bers is st i l l a funct ion of bu t i t has been determined exper imenta l l y

Fal l Velocity of Sph eres

=4

3

=2 4

Fall velocity of q uart z sph eres in air and w ater

Shape effect is largest for relatively large particles( > 3 0 0 ) wh ich dev ia te more f rom a sphere thana smal l part ic le

Fal l veloci ty of non -spher ical sedim ent part ic les can b edeterm ined f rom the fo l low ing form ulae:

for 1 < d 100 m

for 100 < d 1000 m

Fall Velocit y o f N on -Sph erical Part icles

=

+ . ( )

.

=( )

fo r d 1000 m

i n wh ich = sieve diamet er

= specif ic gravity ( = 2 .6 5 )

= kinem atic v iscosi ty coeff ic ient

Fall Velocit y o f N on -Sph erical Part icles Fall velocities for d < 100 m accord ing to Stokes


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Fall velocit ies for par ticle sizes larger t han 1 00 maccordin g to US Inter-Agency Com m it tee (1957 )

Fal l veloci ty of a s ingle part ic le is modi f ied by thepresence o f o ther par t i c les due to the mutua l

interference of the part ic lesi f on ly a few closely spaced part ic les are in a f lu id,th ey wi l l fa l l in a group w i th a veloci ty that is higherth an that o f a part ic le fal l ing alone

i f part ic les are dispersed throughout the f lu id, theinterference between neighbouring part ic les wi l ltend to reduce thei r fa l l veloci ty referred to ashindered sett l ing

Effect of Sedim ent Con centrat io n on Fal l

Velocity

i n wh ich

ws,m = par ticle fal l velocity in a suspension

ws = part ic le fal l veloci ty in a clear f lu idc = vo lumet r i c sed iment concent ra t ion

Accordin g to Richardson and Zaki , the fal l veloci ty in af luid-sedimen t suspension can be determ ined as


Velocity

hindered sett l ing is largely caused by the f lu idre turn f low induced by th e set t l i ng ve loc i t ies

Oliver form ula read as

which y ields good resul ts over the ful l range ofconcent ra t ions

= coeff ic ient (var ies f rom 4.6 to 2.3 for Rincreasing from 10 -1 t o 10 3 ;

= 4 for par t i cles in the range of 50 to 500 m )


Velocity

In f luence of sediment con cent rat ion onfal l velocit y (Rsmall)

Spher ical part ic les wo uld sett le mo re slow ly in a f luidosci l lat ing in t he vert ical di rect ion th en in o ne at rest

Reduct ion in fal l veloci ty resul ted from the nonl inearre la t ion between drag on the par t i c le and the i rvelocity relat ive to th e f luid

Another mechanism may be in tens ive eddyproduct ion c lose to the bed inducing vert ical lyupward mot ions which may reduce the fa l l ve loc i tyunt i l the ed dies dissolve at h igher levels

Effect of Tur bu lence o n Fal l Velocit y


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Presence of bursting processes characterized by l i f t-up o f low-momentum f lu id (burs ts ) and a down-rushof h igh-mo ment um f lu id to the bed (sweeps)

Effect of Tur bu lence o n Fal l Velocit y

Asymmetr i c f lu id mot ion in ver t i ca l d i rec t ion w i thre la t i ve ly h igh (shor t dura t ion) downward ve loc i t iesm ay resul t in a s l ight in crease of th e fal l veloci ty

Grains pi le up on each other have an equi l ibr iumslope w hich is cal led the an gle of natural repose (n)

appears to be a funct ion of s ize, shape andporos i ty

increases wi th decreasing rou ndn ess

sand s izes f rom 0.001 to 0.01 m show values inthe range o f 30 o t o 40 o

Angle of Natu ral Repose

Referred to as the angle of internal f r ic t ion is relatedto the part ic le stabi l i ty on a hor izontal or s loppingb ed

Angle of Repo se ()

Usual ly determined f rom the in i t ia t ion o f mot ionexper iment

Because natural sediments are made up of grains wi thw ide ranges of s ize, shape, and o ther character ist ics, i tis natural to resort to stat ist ical methods to descr ibethese characteristics

Process of ob taining s ize distr ibut io n by separat ion ofa sample into a number of s ize c lasses is known asm echanical analysis

Results of such analyses of sediment are usuallypresented as cum ulat ive s ize-frequency curves, wh erethe f rac t ion or percentage by weight o f a sed imentthat is smal ler or larger than a given s ize is plot tedagainst th e size

Size-Frequency Distribution

Size-Freq uen cy Dist rib ut ion

Normal s ize-Frequency distribut ion

curve

Cum ulat i ve f requency of norm al

d is t r ibut ion i .e % f iner- than curve

median particle size which is the size at

w hich 50% by weight is f iner or coarser

mean particle size = () / w i t h = percentage by w eight of each grain s ize f ract ion

Frequen cy distr ibut ion is character ized by

standard deviation = / or

= .( + ) which is ameasure b ased on graphic values

Size-Freq uen cy Dist rib ut ion


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geometric standard deviation = . ..

Skewness

Kurtosis

geometric mean = ( ..). , in which

. an d . are th e grain sizes for w hich 84.1%and 15.9% by weight , respect ively of the sediment

is f iner

Size-Frequency Distribution 1.3. Character ist ic param eters1.3. Character ist ic param eters

Part icle Diameter, D*Reflects the influence of gravity, density and viscosityand read as:

in wh ich:

d50 = median par t i c le d iameter o f bed mater ia l

s = specif ic gravity (= s/ )

= kinematic viscosity coeff icientg = accelerat ion of gravity

is the rat io of the hydrodynamic f lu id (drag and l i f t )forces and the subm erged part ic le weight

in which: = overal l t im e-averaged b ed-shear stress

Fluid force is prop ort ional to and the

submerged par t i c le weight i s propor t iona l to

, yielding a rat io of :

Plane b ed

Part ic le M obi l i t y Param eter,

= specif ic gravity ( = /)

= f l ow dep th

= energy gradient

When bed forms are present , the gra in- re la ted oreffective bed-shear stress (

) instead of the overal l

bed-shear stress ( ) should be used to calculate thepar t i c le m obi l i t y parameter

Bed form s

= overal l bed shear veloci ty (b = u*2)

Part icle M obi l i t y Param eter,

The excess bed-shear stress param eter, , is def ined as:

in which:

, = cr i t ical t ime-averaged bed-shear stress

accordin g to Shields

Excess Bed-Shear Stress Parameter, T

=

,

,

Z ref lects the rat io of the downward gravi ty forcesand the upward f luid forces act ing on a suspendedsedim ent p art ic le in a current and read as:

in which:

ws = part ic le fal l veloci ty in c lear f lu id

u* = overal l bed-shear velocity

= Von Karm an constant = rat io of sedimen t and f luid mixing coeff ic ient

Suspen sion param eter, Z


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Dimensionless t ranspor t usual ly represented as:

in wh ich:

qt = vo lumet r i c to ta l t ranspor t ra te (m2/ s)

d50 = m edian part ic le size of bed m ater ial (m)

Anot her dim ensionless expression is:

g = accelerat ion of gravi ty (m/ s2)

Transpo rt Rate,

i n wh ich:

= part ic le fal l velocity o f bed m ater ial ( /)

= specif ic density (/)

Vo lum et r i c sed iment t ranspor t ra te can also be

made dimensionless wi th the speci f ic f low discharge( ) , yielding the discharge-weighted concent rat ion

q = specif ic f lo w d ischarge (m 2/ s)

qt = vo lumet r i c to ta l t ranspor t ra te (m2/ s)

Transpo rt Rate,

=

1.2_Properties of Sediments

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