SoilMechanicsICE222CE 222

WaterinSoil:Permeability

1

Flowofwaterthroughsoils 2

Thestructureofthesolidparticlesinanysoilwillalwayshavevoids.Thesevoidsprovidethewaterandairwithcontinuouspaths of flowpathsofflow.

Theflowwillaffectboththestructureandstabilityofthesoilmass. For example, the flow of water through an earth dammass.Forexample,theflowofwaterthroughanearthdamwilleventuallycreatelargerandlargerpaths,muchlikepipes,thatcouldeventuallyleadtothecollapseoftheentirestructurestructure. Loosesoil Densesoil

water

Flowofwaterthroughsoils 3

Th t d f th b h i f th fl f t d Thestudyofthebehavioroftheflowofwaterandairthroughsoilsisofgreatimportanceinthefieldofsoil and rock mechanicssoilandrockmechanics.

Ingeneral,therearetwogeneralconditionsofflow: Steadystate,and Transientflow.

Steadyandunsteadyflow 4

Thetermsteadystateconditionmeansasystemhasreachedequilibrium.

In groundwater analyses it means the flow pattern has been established Ingroundwateranalyses,itmeanstheflowpatternhasbeenestablishedandisnotinprocessofchanging.Thisconditioniscalledsteadyfloworsteadystateflow.

Theunsteadycondition(ortransientcondition)existswhensomethingisinprocessofchanging.

During unsteady flow pore water pressure groundwater table location Duringunsteadyflow,porewaterpressure,groundwatertablelocation,flowratearechanging.

Steadyandunsteadyflow 5

Formsofwaterinsoils 6

Adsorbedwaterinclays

Vapormoisture

Flowing ground waterFlowinggroundwater Permeability

Seepage studies Seepagestudies

Capillarymoisture

Hydrologicalcycle 7

Hydrologyisthestudyofwatermovementsacrosstheearth.Itincludesassessmentsofrainfallintensities,streamflows,andlakewaterlevels,knownassurfacewaterhydrology,aswellasstudiesofgroundwater,knownasgroundwaterh d l h i f d ll d h d l i lhydrology.Thevariousmovementsarepartofgrandprocesscalledhydrologiccycle.

Groundwater 8

Subsurfacewatermaybedividedintotwosections:

Theportionbelowthegroundwatertableiscalledthephreaticzone.Thiswaterissubjectedtopositivepressureasaresultoftheweightoftheoverlyingwater.Mostg y gsubsurfacewaterisinthephreaticzone.

The portion above the groundwater table is called theTheportionabovethegroundwatertableiscalledthevadosezone.Thiswaterhasanegativepressure,andisheldinplacebycapillaryactionandotherforcespresenttin the soilinthesoil.

Aquifersandaquicludes 9

Sandandgravelscantransmitlargequantitiesofgroundwater,knownasaquifers.Claystransmitwaterveryslowly,knownasaquicludes.Intermediatesoils(suchassiltysand)passwaterataslowtomoderateratearecalledaquitards.

Artesianandsurficial springs 10

Artesiansprings/wellsarewellsthatflowundertheirownpressure.Theserequireaslopingpermeablelayerofrock(Aquifer)witharecharge zone higher than the wellrechargezonehigherthanthewell.

Confinedaquifer 11

Confinedaquifer: Awaterbearinglayer,overlainandunderlain by far less permeable soils

Waterlevelinaquifer standpipe

underlainbyfarlesspermeablesoils.

Clay,silt

x

BernoullisEquation 12

Zvuh2

++= Zg

hw

2

++PressureTotal Velocity ElevationPressurehead,hp

Totalhead,h

Velocityhead,hv

Elevationhead,hz

BernoullisequationwasnamedaftertheSwissmathematicianDanial Bernoulli(1700 1782).

BernoullisEquationApplicationtosoilandrock

13

Theenergyofafluidismade of:madeof:

Kineticenergy duetofluidparticle

velocity

Strain energy due toZ

Strainenergyduetopressure

P t ti l dDatum

Potentialenergyduetoelevationwithrespect to datumrespecttodatum

14BernoullisEquationApplicationtosoilandrock

Expressingenergyinunitoflength:

Velocityheadfluidparticle

Total head =

+

PressureheadZ

Totalhead+

Elevation headDatum

Elevationhead

15BernoullisEquationApplicationtosoilandrock

Forflowthroughsoils,velocity(andthusvelocityhead)isverysmall.Th fTherefore,

Velocityheadfluidparticle0

Total head =

+

PressureheadZ

Totalhead+

Elevation headDatum

Elevationhead

Totalhead=Pressurehead+Elevationhead

Fieldinstrumentation 16

Anopenstandpipepiezometer consistspiezometerconsistsofaperforatedpipeinstalledinaboring

17Hydraulicgradient

Atanypointwithintheflowregime: Pressurehead=porewaterpressure/wp p /w Elevationhead=heightabovetheselecteddatum

H dra lic gradient i bet een A and B is the total Hydraulicgradient,i betweenAandBisthetotalheadlossperunitlength.

AB

BA

lTHTHi = water

ABl

A BlengthAB,alongthestreamline

Hydraulicgradient 18

Pi t iPiezometricheads

Hydraulicgradient,i

A

B

Effectofhydraulicgradientonvelocity 19

Inmostsoils,theflowofwaterthroughthevoidspacescanbeconsideredlaminar,thusv i

Darcyslaw 20

In1856,Darcypublishedasimpleequationforthedischargevelocityofwaterthroughsaturatedsoils,whichmaybeexpressed asexpressedas

kiv =where v = dischargevelocity,whichisquantityofwaterflowing

inunittimethroughaunitgrosscrosssectionalareaof soil at right angle angles to the direction of flow.ofsoilatrightangleanglestothedirectionofflow.

k = hydraulicconductivity(alsocalledcoefficientofpermeability)pe eab ty)

Theactualvelocityofwater(i.e.seepagevelocityvs)throughthevoidspacesisgreaterthandischargevelocityv(seenextslidep g g y (fordetails).

Dischargevel.v&seepagevel.vs relation21

svvAAvq == sv AAA +=( ) AAA + l( ) svsv vAvAAq =+=( ) ( ) ( ) V

VvVVvLAAvAA s

v

svsvsv

++++ 1

vs:seepagevel.

( ) ( ) ( ) vVVV

vVVLA

vA

vv

s

v

s

v

sv

v

sv

v

svs

====ve + 11 Vs nvv

nv

eevs =

=

+= 11

nvvs =

ExampleExample Waterflowsthroughthesandfilterasshownbelowbelow

The cross sectional area & length of the soil mass Thecrosssectionalarea&lengthofthesoilmassare0.250m2 &2.00m

The hydraulic head difference is 0.160 mThe hydraulic head difference is 0.160 m The coefficient of permeability is 6.90x10-4

m/sm/s Determine the flow rate of water through

the soilthe soil

S l tiSolution

From previous equation= kiq

0800.0m002m160.0 ===

Lhi

q

)m250.0)(0800.0)(m/s1090.6(m00.2

24=qL

/sm1038.1 35=

E lExample

In a soil test, it took 16.0 min for 1508 cm3of water to flow through a sand sample

The cross-sectional area was 50.3 cm2 The void ratio of the soil sample was 0.68.p Determine The velocity of water through the soilThe velocity of water through the soil

(apparent velocity)Actual velocity/ Seepage velocity

S l tiSolutionol me / time * area

/03120i/8741

v = volume / time * areav = 1508 / 16.0 * 50.3

)1(cm/s0312.0mincm/8741

+===

evv

.

/07710)68.01)(cm/s0312.0( +=actual ev

cm/s0771.068.0

))(( ==actualv

Hydraulicconductivity 27

Thehydraulicconductivity,k,inDarcysLawdescribestheeasewithwhichacertainliquidflowsthroughacertainsoil.Itd d l f l ddependsonseveralfactorsincluding:

Soilproperties: Voidsize(dependsonparticlesize,gradation,voidratio,andother

factors)

Soilstructure Voidcontinuity Particleshapeandsurfaceroughness

Degree of soil saturation Degreeofsoilsaturation

Liquidproperties:Density Density

viscosity

Typicalvaluesofhydraulicconductivity 28

Importanceofpermeability 29

Thefollowingapplicationsillustratetheimportanceofpermeabilityingeotechnicaldesign:p y g g

Permeabilityinfluencestherateofsettlementofsaturatedsoils under load.soilsunderload.

Thedesignofearthdamsisverymuchbaseduponthepermeability of soils usedpermeabilityofsoilsused.

Thestabilityofslopesandretainingstructurescanbegreatl affected b the permeabilit of the soils in ol edgreatlyaffectedbythepermeabilityofthesoilsinvolved.

Filtersmadeofsoilsaredesignedbasedupontheirb lpermeability.

Useofpermeability 30

Knowledgeofpermeabilitypropertiesofsoilsisnecessaryfor:y

Estimatingthequantityofundergroundseepage;

Solvingproblemsinvolvingpumpingseepagewaterfromconstructionexcavation;

Stabilityanalysesofearthstructureandearthretainingwallssubjectedtoseepageforces.

Lab.DeterminationofHydraulicconductivity 31

Twostandardlaboratorytestsareusedtodeterminethehydraulicconductivityofsoil:y y

Theconstantheadtest(suitableforgranularsoils)

Thefallingheadtest(suitableforclayeysoils)

Constantheadtest 32

( ) tkiAAvtQ ==Thetotalvolumeofwatercollectedis

( )QQ =volumeofwatercollectedA =xsecareaofsoilspeciment d ti f t ll tit =durationofwatercollection

hi = thkAQ =L tLkQ

QLk =Aht

Fallingheadtest 33

thkAQ Flowrate,qisdefinedasQ/t

== hkAQqtL

kAQ === LkAtq

dhaq =Also dtaq =Also

Fromaboveeqs.dhahkA =

qdtL

q =flowrate(flowperunittime)a = xsec area of standpipea =xsecareaofstandpipeA =xsecareaofsoilspecimen

dhaL

=hdh

AkaLdtRearranging

Fallingheadtest 34

=hdh

AkaLdt

Lettheheadish1 att=0,andh2 att=t

Integratingleftsidewithlimitsfrom0totandtherightsidewithlimitsfromh1 toh2

2

1loghh

AkaLt e=

Re arranging 1loghaLk =Rearranging2

loghAt

k e=

Empiricalrelationsforhydraulicconductivity 35

Forfairlyuniformsand(i.e.,sandwithasmalluniformitycoefficientcu),Hazen(1930)proposedanempiricalrelationshipforhydraulicconductivity in the formconductivityintheform

( ) 210cm/sec cDk =wherec=aconstantthatvariesfrom1.0to1.5,andD10 =theeffective size, in mm.effectivesize,inmm.

AboveequationisbasedonHazensobservationsofloose,clean,filter sandsfiltersands.

Equivalenthydraulicconductivityinstratifiedsoils

36

FromDarcyslaw Totalflowissumofflowsthrueachlayer

37Equivalenthydraulicconductivityinstratifiedsoils

Thevelocityofflowthrualllayersissame

Totalheadloss,h,isequaltosumofheadlossesinalllayers

FromDarcyslaw

38Equivalenthydraulicconductivityinstratifiedsoils

(i)

Above equation can be written asAboveequationcanbewrittenas

(ii)

SolvingEq.(i)and(ii)

Varved soil 39

Varved soil 40

Varve depositsattributedto GlacialLakeMissoula, Montana,USA.

Hydraulicconductivityofcompactedclayeysoils 41

Followingobservationsaremadefromtestresults:

Forsimilarcompactioneffortandmoldingmoisturecontent,th it d f k dthemagnitudeofkdecreaseswiththedecreaseinclodsize.

Foragivencompactioneffort,kdecreaseswithincreaseinmoldingmoisturecontent.g

Hydraulicconductivityofcompactedclayeysoils 42

Forsimilarcompactionpeffortanddryunitweight,asoilwillhavea lower hydraulicalowerhydraulicconductivitywhenitiscompactedonthewetd f hsideoftheoptimum

moisturecontent.

Fieldcompactionconsiderations 43

Patternofflowthroughacompactedclaywithimproperbondingbetweenlifts

Fieldpermeabilitytest:wellpumpingtest 44

Wellpumpingtest 45

tLhkAQ

=

==LhkA

tQqFlowrate,qisdefinedasQ/t

The e pression for the flow rate of groundwater into the ell hich isTheexpressionfortheflowrateofgroundwaterintothewell,whichisequaltotherateofdischargefrompumping,canbewrittenas

dh ( ) dh

=drdhkAq ( )

=

drdhkrhq 2

22 2 hr kd

=

2

1

2

1

2h

h

r

r

dhhqk

rdr

Integrating

1logrrq e

( )2221 2hhr

k =

Wellpumpingtest confinedaquifer 46

WaterenteringintowellWaterenteringintowell

Wellpumpingtest confinedaquifer 47

BecausewatercanenterthetestwellonlyfromtheaquiferofthicknessH,thesteadystateofdischargeis

( ) = dhkrHq 2( ) = drkrHq 2 22 2 rr kHd

=

2

1

2

1

2r

r

r

r

dhqkH

rdr

1logrrq e

( )212

2 hhHr

k =