Permeability of Soil

This presentation includes Definition of Permeability, measurement of Permeability, Validity of Darcy's law, Darcy's Law, Methods of Finding Permeability, factors affecting permeability, Permeability of Stratified Soil

1. PERMEABILITY
OF
SOIL
Prepared By:
Arbaz Kazi
B.E, M.E[Civil Engg.]

2. Freewater(bulkwater):Ithastheusualpropertiesofliquidwater.It
movesalwaysundertheinfluenceofgravity,orbecauseofa
differenceinhydrostaticpressurehead.Itisclassifiedintotwotypes.
Freesurfacewater.Freesurfacewatermaybefromprecipitation,
run-off,floodwater,meltingsnow,waterfromcertainhydraulic
operations.
Groundwater.Groundwateristhatwaterwhichfillsupthevoids
inthesoiluptothegroundwatertableandtranslocatesthrough
them.Itfillscoherentlyandcompletelyallvoids.Insuchacase,
thesoilissaidtobesaturated.
TYPES OF WATER

3. Capillarywater.Waterwhichisinasuspendedcondition,heldby
theforcesofsurfacetensionwithintheintersticesandporesof
capillarysizeinthesoil,iscalled‘capillarywater’.
HeldWater:
‘Heldwater’isthatwaterwhichisheldinsoilporesorvoidspaces
becauseofcertainforcesofattraction.Itcanbefurtherclassifiedas
(a)Structuralwaterand(b)Absorbedwater
a)Structuralwater.Waterthatischemicallycombinedasapartof
thecrystalstructureofthemineralofthesoilgrainsiscalled
‘Structuralwater’.
TYPES OF WATER

4. a)Adsorbedwater.Thiscomprises,(i)hygroscopicmoistureand
(ii)filmmoisture.
Hygroscopicmoisture.Soilswhichappearquitedrycontain,
nevertheless,verythinfilmsofmoisturearoundthemineralgrains,
called‘hygroscopicmoisture’,whichisalsotermed‘contact
moisture’or‘surfaceboundmoisture’.
Filmmoisture.Filmmoistureformsonthesoilgrainsbecauseof
thecondensationofaqueousvapour;thisisattachedtothesurfaceof
thesoilparticleasafilmuponthelayerofthehygroscopicmoisture
film.
TYPES OF WATER

5. Source:
https://www.vedantu.com/question-sets/b5ec9a6b-5a8d-4376-825a-d292ebb372492497045867512866004.png

6. WHAT IS PERMEABILITY?
•Permeabilityisdefinedasthepropertyofaporousmaterialwhich
permitsthepassageorseepageofwaterthroughitsinterconnecting
voids.
•Ameasureofhoweasilyafluid(e.g.,water)canpassthrougha
porousmedium(e.g.,soils)
•ItisaveryimportantEngineeringproperty
gravels highlypermeable
stiffclay leastpermeable

8. Permeability through soil is important for the following
engineering problems:
•Calculationofupliftpressureunderhydraulicstructureand
theirsafetyagainstpiping
•Groundwaterflowtowardswellsanddrainageofsoil
•Calculationofseepagethroughthebodyofearthdamsand
stabilityofslopes
•Determinationofrateofsettlementofasaturatedcompressible
soillayer

9. Phenomenon of piping action

10. Failed slope surface

11. How permeability is measured?
•Permeabilityismeasuredintermsofrate
offlowofwaterthroughthesoilina
givenperiodoftime.
•Itisexpressedincm/dayorcm/houror
m/sec.

12. Flowofwaterthroughsoilsmayeitherbealaminarflowora
turbulentflow
Each fluid particle travel
along a definite path
which never crosses the
path of any other
particle
Paths are irregular and
twisting, crossing at
random
Flow of water through Soils

13. Henry Darcy(1803-1858), Hydraulic Engineer.
His law is a foundation stone for several fields of
study
Assumptions of Darcy’s law :-
•ThefollowingassumptionsaremadeinDarcy’slaw.
Thesoilissaturated.
Theflowthroughsoilislaminar.
Theflowiscontinuousandsteady.
Thetotalcrosssectionalareaofsoilmassisconsidered.
Thetemperatureatthetimeoftestingis27
0
C.

14. Darcy’sLaw:Darcydemonstratedexperimentallythatfor
laminarflowconditionsinasaturatedsoil,therateoffloworthe
dischargeperunittimeisproportionaltothehydraulicgradientvAq kiv kiAq
Validity of Darcy’s law -When flow is laminar
Henry Darcy(1803-1858), Hydraulic Engineer.
His law is a foundation stone for several fields of
study

15. Darcy’s Law
Darcy’s Experiment.

16. VALIDITY OF DARCY’S LAW
1)Darcy’slawisvalidiftheflowthroughsoilsislaminar:
Theflowofwaterthroughsoilsdependsuponthedimensionof
particles.Infinegrainedsoilsthedimensionsoftheinterstices
(voids)areverysmallandflowisnecessarilylaminar.
Incourse-grainedsoil,theflowisalsolaminar.However,invery
coarse-grainedsoils,suchasgravels,theflowmaybeturbulent.
Forflowthroughsoils,theflowislaminariftheReynolds
numberislessthanunity.

17. 2)AsperAllenHazen,themaximumdiameteroftheparticleforthe
flowtobelaminarisabout0.50mm.
3)Itisvalidforflowinclays,slitsandfinesands.Incoarsesands,
gravelsandboulders,theflowmaybeturbulent,andDarcy’slaw
maynotbeapplicable.
4)ForDarcy’slawtobevalid,therelationshipbetweenvelocity(v)
andhydraulicgradient(i)shouldbelinear.
5)Inextremelyfine-grainedsoils,suchascolloidalclay,the
intersticesareverysmall.Thevelocityisthereforeverysmall.In
suchsoils,theDarcy’slawisnotvalid.
VALIDITY OF DARCY’S LAW

18. Relation between Discharge Velocity and Seepage
Velocity:
From Continuity equation we have, q = v.A= k.i.A
But, A = total area including voids and solids
Butinactualpracticeflowofwaterthroughsoiltakesplacethrough
voidsonly,theactualvelocitywillbemorethandischargevelocity.
Thisactualvelocityiscalledasseepagevelocity(vs),andisdefined
asrateofdischargeofpercolatingwaterperunitcross-sectionalarea
ofvoidsperpendiculartothedirectionofflow.
L

19. Relation between Discharge Velocity and Seepage
Velocity:
Therefore,
q = v.A= vs.Av
vs = v x A/Av
But, A/Av = V/Vv= 1/n
vs= v x 1/n
from definition we have, n = e /1+e
vs= v x (1 + e/e)
Hence from above equation it is clear that seepage velocity >
discharge velocity.

20. Factors affecting Permeability of soil
Inabove equation, the factor k depends on:
ThereisanequationknownasPoiseuille'sequation,whichwhen
comparedwiththeDarcy'slawgivesthevalueofcoefficientof
permeability,
k=
??????
�
n
∗Ds
2
∗
e
3
(1+e)
�??????
1.GrainSize:AllenHazenfoundthattheco-efficientof
permeabilitycanbeexpressedas
k(incm)=CxD
10
2
where,D
10=effectivediameter(cm),C=constant,approximatelyequalto100.
Fromtheaboverelationisclearthatgreaterthegrainsizeofsoil
greaterwillbethepermeabilityandvice-versa

21. Factors affecting Permeability of soil
2.Propertiesofporefluid:Viscosityofthefluidaffectstheflow,
moretheviscositylessisthefluidity,soitisinversely
proportionaltotheviscosity.
k
1/k
2= n
2/n
1
3.Voidratio:Basedonthemeanhydraulicradiusitcanbewritten
that,
k
1/k
2= (e
1/e
2)^2
Fromtheaboverelationitisclearthatco-efficientofpermeability
isdirectlyproportionaltovoidratio.So,greaterthevoidratio
greaterwillbethepermeabilityofsoilandvice-versa.

22. Factors affecting Permeability of soil
4.Structuralarrangements:Dependinguponthemethodof
compactionandconditionexistingduringdeposition,thestructural
arrangementofsoilmassmayvaryatthesamevoidratioand
consequentlypermeabilityalsovaries.itisdefinedbythefactorCis
theaboveequation.Forstratifieddepositstheflowisdifferentfor
flowparallelandperpendicularorstratification.
5.Degreeofsaturationandotherforeignmatter:
Thepermeabilityisaffectedbythepartialsaturationofthesoil,when
ithasentrappedtheairinside.Otherforeignmatterhasthegeneral
tendencytoflowtowardsthecriticalflowchannelandthuschoking
it.

23. 6.Adsorbedwater:Theadsorbedwaterheldonthesurfaceof
colloidalparticlesarehighlycohesiveandisimmobiletonormal
hydrodynamicforces.Becauseofthistheareaofeffectivevoid
spaceisreducedandthuspermeabilityisreduced.
Factors affecting Permeability of soil

24. Absolute permeability
Independentofthepropertiesofwater
Itdependsonlyonthecharacteristicsofsoil
Theabsolutepermeabilityonlydependsonthegeometryofthe
pore-channelsystem.
Relative permeability
Itistheratioofeffectivepermeabilityofaparticularfluidtoits
absolutepermeability.

25. Methods of Determination of co-efficient of
Permeability:

26. Constant Head Permeability Test
•Quantityofwaterthatflowsundera
givenhydraulicgradientthroughasoil
sampleofknownlength&cross
sectionalareainagiventime
•Waterisallowedtoflowthroughthe
cylindricalsampleofsoilundera
constanthead
•Fortestingofpervious,coarsegrained
soils
K = Coefficient of permeability
Q = total quantity of water
t = time, L = Length of the coarse soilAht
QL
k
Setup for Constant Head Test

27. TestProcedure:-
1.Measureinternaldimensionsofthemould.Applyalittlegreaseon
theinsidetothemould.
2.Takeabout2.5kgofthesoil,fromathoroughlymixedwetsoil,in
themould.Compactthesoilattherequireddrydensityusinga
suitablecompactingdevice.
3.Removethecollarandbaseplate.Trimtheexcesssoillevelwith
thetopofthemould.
4.Cleantheoutsideofthemould.Findthemassofthesoilinthe
mould.Takeasmallspecimenofthesoilincontainerforthewater.
Constant Head Permeability Test

28. 6.Placetheporousstone(disc)onthedrainagebaseandkeepafilter
paperontheporousstone.Placeafilterpaperandaporousstone
onthetopofspecimen.
7.Connecttheconstantheadtanktothedrainagecapinlet.
8.Openthestopcock,andallowthewaterdownwardsothatallthe
airisremoved,thenclosethestopcock.
9.Now,againopenthestopcockandatthesametimestartthe
stopwatch.Collectthewaterflowingoutofthebaseina
measuringflaskforsomeconvenienttimeinterval.
10.Measurethedifferenceofhead(h)inlevelsbetweentheconstant
headtankandtheoutletinthebase.
Constant Head Permeability Test

29. •Relativelyforlesspermeablesoils
•Waterflowsthroughthesamplefroma
standpipeattachedtothetopofthe
cylinder.
•Theheadofwater(h)changeswith
timeasflowoccursthroughthesoil.
Atdifferenttimestheheadofwateris
recorded.
t = time
L = Length of the fine soil
A = cross section area of soil
a = cross section area of tube
K = Coefficient of permeability 2
1
10log
30.2
h
h
At
aL
k
Falling Head Permeability Test
Setup for Falling Head Test

30. Test Procedure:-
Falling Head Permeability Test
1.Preparetheremouldedsoilspecimeninthepermeameterand
saturateit.
2.Keepthepermeametermouldinthebottomtankandfillthe
bottomtankwithwateruptoitsoutlet.
3.Connectthewaterinletnozzleofthemouldtothestandpipe
filledwithwater.
4.Permitwatertoflowforsometimetillsteadystateofflowis
reached.
5.Nowopenthevalveofstandpipeandrecordthetime(t)tofall
theheadfromh
1toh
2.Repeatthisstepatleasttwice.

31. By Indirect Method
Constants, a = 1.365
b = 5.15
c = value b/w 100 & 150
T= Tortuosity
S = surface area2
10
cDk
Allen hazen’sformulabnakS )(log
2
10 Loudon’s formulae
e
TSC
g
k
s
w


1)(
3
22


Kozenycarman equationvwv
mCk Consolidation test data

32. REFERENCES
•K.R.Arora“SoilMechanics&FoundationEngineering”
•GopalRanjan&A.S.R.Rao“Basic&AppliedSoil
Mechanics”
•B.C.Punmia“SoilMechanics&Foundation”
•T.WilliamLambe(1969)“soilmechanics”
•ErnstandSohn(2002)“GeotechnicalEngineeringHand
Book”

33. Permeability in Stratified Soils
Flow parallel to the plane of stratification
Letℎ
1,ℎ
2,ℎ
3...ℎ??????bethethicknessesofeachof
thenlayerswhichconstitutethedeposit,oftotal
thicknessh.Let??????
1,??????
2,??????
3...??????
??????betheDarcy
coefficientsofpermeabilityoftheselayers
respectively.
Let????????????=averagepermeabilityofsoildeposit
paralleltobeddingplane.
Totaldischargethroughthesoildeposit=sumofdischargethroughindividuallayers
??????=??????
1+??????
2+⋯??????
??????
??????
??????.??????.ℎ=??????
1.??????.ℎ
1+??????
2.??????.ℎ
2+⋯??????
??????.??????.ℎ
??????
??????
??????=
??????
1.ℎ
1+??????
2.ℎ
2+⋯??????
??????.ℎ
??????
ℎ

34. Permeability in Stratified Soils
Flow normal to the plane of stratification
Leth
1,h
2,h
3...h
nbethethicknessesofeachofthen
layerswhichconstitutethedeposit,oftotalthicknessh.
Letk
1,k
2,k
3...k
nbetheDarcycoefficientsof
permeabilityoftheselayersrespectively.
Letk
z=averagepermeabilityofsoildeposit
perpendiculartobeddingplane.
Inthiscase,h=h1+h2+…h
n
Buth
1=i
1*h
1,h
2=i
2*h
2,Similarlyh
n=i
n*h
n
Weknow,v=i*kz,Henceh=v*hkz
Therefore,v*hkz=v*h
1k
1+v*h
2k
2+……v*h
nk
n
kz=hh
1k
1+h
2k
2+…h
nk
n
??????
??????=
ℎ
ℎ
1
??????
1
+
ℎ
2
??????
2
+⋯
ℎ
??????
??????
??????