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 =
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