Consolidation of Soil

This presentation is all about consolidation of soil and it's importance in Civil Engineering, co-efficients of consolidation, methods of determining co-efficient of consolidation, Terzaghi's Spring Analogy, Terzaghi's Theory

1. CONSOLIDATION
OF SOIL
Preparedby:
ArbazM.Kazi
Asst.Professor,
VCET,Vasai(W)

2. Contents:
1.ImportantTerminologies
2.DifferencebetweenCompaction&Consolidation
3.Importanceofconsolidationtheory
4.Terzaghi’sSpringAnalogy
5.OneDimensionalConsolidationTest
6.ImportantDefinitions
7.Normally,Under&OverConsolidatedSoil
8.DeterminationofPre-consolidationPressure
9.Terzaghi’sOneDimensionalConsolidationTheory
10.Solutionto1-DConsolidation.
11.DeterminationofCo-efficientofConsolidation
12.ComputationofConsolidationSettlement

3. Compression:
Thechangeinthevolumeofasoilmassunderstressis
knownascompression.
Compressibility:
Thepropertyofsoilmasspertainingtoitssusceptibilityto
decreaseinvolumeunderpressureiscalledcompressibility.
Consolidation:
AccordingtoTerzaghi“everyprocessinvolvingadecrease
inwatercontentofasaturatedsoilwithoutreplacementofwaterbyair
iscalledconsolidation”
Swelling:
Theprocessofincreaseinwatercontentduetoincreaseinvolume
ofvoidsiscalledasswelling.
IMPORTANT TERMINOLOGIES

4. Sr.
No
COMPACTION CONSOLIDATION
1 Expulsion of pore air Expulsion of pore water
2Soil involved is partially saturated Fully saturated soil
3
Applies to cohesive as well as
cohesionless soils
Applies to cohesive soils only
4
Brought about by artificial or
human agency
Brought about by application of load
or by natural agencies
5
Dynamic loading is commonly
applied
Static loading is commonly applied
6 Relatively quick process Relatively slow process
7
Relatively complex phenomenon
involving expulsion, compression,
and dissolution of pore air-in water
Relatively simple phenomenon
8
Useful primarily in embankments
and earth dams
Useful as a means of improving the
properties of foundation soil
DIFFERENCE BETWEEN COMPACTION &
CONSOLIDATION

5. IMPORTANCE OF CONSOLIDATION STUDY
Thestudyofconsolidationhelpstoprovideanswers
for:
1.Totalsettlement(volumechange).
2.Timerequiredforthesettlementofcompressible
layer.Thetotalsettlementconsistsofthree
components.

6. ElasticSettlementorImmediateSettlement
Thissettlementoccursimmediatelyaftertheloadisapplied.Thisisduetodistortion
(changeinshape)ofsoilmass.Thereisnegligibleflowofwaterinlesspervioussoils.
Incaseofpervioussoils,theflowofwaterisquickatconstantvolume.Thisis
determinedbyelastictheory(E&μareused).
PrimaryConsolidationSettlement
Itoccursduetoexpulsionofporewaterfromthevoidsofasaturatedsoil.Incaseof
saturatedfine-grainedsoils,thedeformationisduetosqueezingofwaterfromthe
poresleadingtorearrangementofsoilparticles.Themovementofporewaterdepends
onthepermeabilityanddissipationofporewaterpressure.
SecondaryConsolidationSettlement
ThisisalsocalledSecondarycompression(Creep).“Itisthechangeinvolumeofa
fine-grainedsoilduetorearrangementofsoilparticles(fabric)atconstanteffective
stress”.Therateofsecondaryconsolidationisveryslowwhencomparedwithprimary
consolidation.
Types of Settlement

7. Terzaghi’s Spring Analogy

8. Fig.ashowspistonandspringarrangementwherepistonisof10units
andlengthofspringisZo.
Fig.bshowscompressionofthespringduetoadditionof2units
surchargeabovepistonwhichcompresseslengthofspringtoZ1.
Moreloadapplicationwillcausespringtofurtherdecreaseinlengthand
withinelasticlimittheloaddeflectioncurvemaybeassumedtobe
straight.
Fig.cshowspistonandspringarrangementkeptinacylinderinwhich
waterisfilledtillbottomofpistonandvalveiskeptopen.
Fig.dshowssurchargeof2unitsaddedabovepistonandvalveiskept
closed,butadditionalloaddoesn’tcausesspringtocompress(thisisso
becausewaterisincompressiblehenceentire2unitsloadisbeing
bornebywateraloneonly).

9. Fig.eshowsvalveispartiallyopenandwaterisallowedtoescape,the
pistonmovesdown,thereslightexchangeofpressurefromwaterto
spring.
Fig.fshowsvalvebeingcompletelyopen,hencewaterescapedoutthe
cylinderandlengthofspringcompressedtoZ1thisisbecauseentire
transferofpressurefromwatertospring.
Hencewecansaywhenthereispressureincrementitisfirstbornebythe
water.Aswaterescapesthesystem,loadtransfertakesplacefromwater
tospringuntilfullcompressionofspringtakesplace.
Thisanalogycanalsobeappliedtotheconsolidationprocessofsoilmass
comprisingofsoil-watersysteminwhichspringrepresentsgrain
structure,cylinderrepresentsvoidsfilledwithwaterandvalveopening
representspermeabilityofasoilsample.

10. One Dimensional Consolidation Test
•Thistestisalsocalledas‘OedometerTest”
•Thistestisperformedtodeterminethemagnitudeandrateofvolume
decreasethatalaterallyconfinedsoilspecimenundergoeswhen
subjectedtodifferentverticalpressures.
•Fromthemeasureddata,theconsolidationcurve(pressure-voidratio
relationship)canbeplotted.
•ThisdataisusefulindeterminingthecompressionindexCc,the
recompressionindexCrandthePreconsolidationpressure(or
maximumpastpressure)ofthesoil.
•Inaddition,thedataobtainedcanalsobeusedtodeterminethe
coefficientofconsolidationCvandthecoefficientofsecondary
compressionmvofthesoil.

11. Equipment:
Consolidationdevice(includingring,porousstones,waterreservoir,andload
plate).
Dialgauge(0.001mm=1.0ondial).
Sampletrimmingdevice,glassplate,Metalstraightedge,Clock,Moisturecan,
Filterpaper.
TestProcedure:
•Weighingtheemptyconsolidation
ringtogetherwithglassplate.
•Measuringtheheight(h)ofthering
anditsinsidediameter(d).
•Extrudingthesoilsamplefromthe
sampler,generallythin-walledShelby
tube.

12. •Cuttingapproximatelyathree-inchlongsample.Beingcarefulthroughout
thetrimmingprocesstoinsurethatthereisnovoidspacebetweenthe
sampleandthering.
•Turningtheringovercarefullyandremovingtheportionofthesoil
protrudingabovethering.Usingthemetalstraightedge,cuttingthesoil
surfaceflushwiththesurfaceofthering.
•PlacethepreviouslyweighedSaran-coveredglassplateonthefreshlycut
surface,turntheringoveragain,andcarefullycuttheotherendinasimilar
manner.
•Weighthespecimenplusringplusglassplate.
•Adjustthedialgaugetoazeroreadingsetthepressuregaugedial(based
oncalibrationcurve)toresultinanappliedpressureof0.2kg/sq.m
•Recordtheconsolidationdialreadingsattheelapsedtimesgivenonthe
datasheetetc.

15. •After24hrsincreasethe
appliedpressureto0.5kg/sq.m
andcontinuethistillapplied
pressureof8kg/sq.minatime
intervalof24hrs.
•Afterfinalsettlementis
observednoteitdownandstart
unloadingtheweights.
•Removeweightonebyone
•Tabulatethereadingsas
shown.

19. Thestraight-lineportionofvirgincompressivecurveisexpressedbytheequation
givenbyTerzaghi.
�=�
0−??????
�.�??????�
10
??????′
??????
0′
Where,e
0=initialvoidratiocoresspondingtoinitialpressureσ
0′
e=voidratiocoresspondingtoincreasedpressureσ′
C
c=compressionindex
Hencetheaboveequationcanberewrittenas
??????
�=
�
0−�
�??????�
10
??????′
??????
0′
=
∆
�
�??????�
10∆
??????′
IMPORTANT DEFINITIONS
1. Compression Index:

20. Theexpansioncurveisalsoastraightlineandisexpressedby;
�
0=�+??????
??????.�??????�
10
??????′
??????
0′
Where,C
s=swellingindex
Differentequationgivenforcompressionindexbydifferentresearchersare:
C
c=0.007(�
??????−10%)
C
c=0.009(�
??????−10%)
C
c=0.3(�
0−0.27)
2. Swelling Index:

21. 3.Co-efficientofcompressibility(�
??????):Itisdefinedasthedecreaseinthevoid
ratioperunitincreaseinpressure.
�
??????=
−∆�
∆??????′
=
�
0−�
??????
′
−??????
0′
4.Co-efficient of volume change(�
??????): It is defined as change in volume of a
soil per unit initial volume due to given unit increase in pressure.
�
??????=
∆�
1+�
0
.
1
∆??????′
=
�
??????
1+�
0
Whensoilislaterallyconfinedthechangeinvolumeisproportionalto
changeinthickness(ΔH)andinitialvolumeisproportionaltoinitial
thickness(??????
0)
�
??????=
−∆??????
??????
0
.
1
∆??????′
=
�
??????
1+�
0
Therefore,ΔH=−�
??????.??????
0.∆??????′

22. NormallyConsolidatedSoils
Itisasoildepositthathasneversubjectedtoaverticaleffectivestressgreater
thanthepresentverticalstress.
UnderConsolidatedSoils
Asoildepositthathasnotconsolidatedunderthepresentoverburdenpressure
(effectivestress)iscalledUnderConsolidatedSoil.Thesesoilsare
susceptibletolargerdeformationandcausedistressinbuildingsbuiltonthese
deposits.
OverConsolidatedSoils
Itisasoildepositthathasbeensubjectedtoverticaleffectivestressgreater
thanthepresentverticaleffectivestress.

23. DeterminationofPreconsolidationPressure:
Theearliestandthemostwidelyused
methodwastheoneproposedby
Casagrande(1936).Themethodinvolves
locatingthepointofmaximum
curvature,onthelaboratorye-logp
curveofanundisturbedsampleasshown
inFig.BelowFromB,atangentis
drawntothecurveandahorizontalline
isalsoconstructed.Theanglebetween
thesetwolinesisthenbisected.The
abscissaofthepointofintersectionof
thisbisectorwiththeupwardextension
oftheinclinedstraightpartcorresponds
tothepreconsolidationpressure.

24. Assumptions:
Thefollowingaretheassumptionsofone-dimensionalconsolidationtheory;
a)Thesoilishomogeneousandfullysaturated.
b)Soilparticlesandwaterareincompressible.
c)Darcy’slawforthevelocityofflowofwaterthroughsoilisperfectly
valid.
d)Coefficientofpermeability(k)isconstantduringtheprocess.
e)Soilislaterallyconfinedsothatthecompressionisonedimensional.
f)Excessporewaterdrainsoutonlyinaverticaldirection.
g)Linearrelationshipbetweeneffectivepressureandvoidratioexistare
constantforeverystageofconsolidation.
h)Thetimelogofconsolidationisdueentirelytothelowpermeabilityof
soil,andthusthesecondaryconsolidationisdisregarded.
Terzaghi’s1DConsolidationTheory:

25. t
V
dxdyvdxdydz
z
v
v
z
z
z










 t
V
dxdydz
z
v
z




 rate of water outflow] -[rate of water inflow] = [rate of change of volume]

26. Darcy's law gives z
u
k
z
h
kkiv
z





 since hu
w

combining gives t
V
dxdydzz
uk
w 






1
2
2

during settlement 
t
e
e
dxdydz
t
eVV
t
V
t
V
o
SSv












1 , since 0


t
V
S and oo
S
e
dxdydz
e
V
V




11
t
e
ez
uk
ow 







1
1
2
2 assume that the decrease in void ratio is proportional to the increase in effective stress (or the
decrease in pore pressure) uae
v

,

27. Where, �
� = coefficient of compressibility
Also, coefficient. of volume compressibility is, o
v
v
e
a
m


1
t
u
m
z
uk
v
w 






2
2

But coefficient. of consolidationvw
v
m
k
c

 t
u
c
z
u
v





2
2 ,
The above basic differential equation of consolidation which relates the rate of change of
excess hydrostatic pressure to the rate of expulsion of excess pore water from a unit volume of
soil during same interval. Solution of 1D Consolidation:
The solution of variation of excess pore water pressure with depth and time can be obtained for
various initial conditions.
Uniform excess pore water pressure with depth
1. Single Drainage (Drainage at top and bottom impervious)
2. Double Drainage (Drainage at top and bottom)

28. Single Drainage (drainage at top and bottom impervious)

Double Drainage

29. Boundary Conditions are
i) At t = 0 Δu = Δσ and Δσ’ = 0
ii) At the top z = 0 Δu =0 Δσ = Δσ’
iii) At the bottom z = 2Hdr Δu =0 Δσ = Δσ’
A solution of equation (1) for the above boundary conditions using Fourier seriesis given by
∆
�
(??????,�)
=
2∆
�0
??????
∞
�=0
.sin
??????�
??????
��
.�
−??????
2
.��
??????=
�
2
.(2�+1)
�
�=
??????
� .�
??????
��
2
Solution of 1D Consolidation:

30. Degree of Consolidation (U):

(a) Section of clay layer, (b) Excess pore pressure distribution
The degree of consolidation at any depth is given by
�
??????=1−
2
??????
∞
�=0
.sin
??????�
??????
.�
−??????
2
.�� Where, Uz = degree of consoildation.

31. Average Degree of Consolidation (U):

The average degree of consolidation for the whole soil deposit at any time isgiven by
U=
Area of the diagram of excess pore water pressure dissipated at any time
Area of the diagram of initial excess pore water pressure

U=
Area shaded
Area of abcd

As per Taylor (1948) solution, the following approximation is possible
when U ≤ 60 %�
�=
�
4
.�
2

when U ≥ 60 %�
�=1.781−0.933.log⁡(100−�%)
U = 50% Tv = 0.197
U = 60% Tv = 0.287
U = 90% Tv = 0.848

Typical values of Tv

32. Determinationofcoefficientofconsolidation(Cv)fromlaboratorydata
Thecoefficientoftwographicalprocedureareused
1.Logarithmoftimemethod
2.Squarerootoftimemethod
Log–timecurvefittingmethod
Thebasisforthismethodisthetheoretical
(Uz)versuslogTvcurveand
experimentaldialgaugereadingandlogt
curvesaresimilar.
Steps
I.Plotthedialreadingofcompressionforagivenpressureincrementversustimetolog
scaleasshowninfigure.
II.PlottwopointsBandContheupperportionoftheconsolidationcurve(say
compressionline)correspondingtotimet
1andt
2suchthatt
2=4.t
1

33. III.LetxbethedifferenceindialreadingbetweenBandC.locateDatavertical
distancexabovepointB
IV.DrawahorizontallineDEthedialreadingcorrespondingtothislineisd
0which
correspondswith0%consolidation.
V.Projectthestraight-lineportionofprimaryandsecondaryconsolidationto
intersectatpointA.ThedialreadingcorrespondingtoAisd
100andthis
correspondsto100%consolidation.
VI.DeterminethepointFontheconsolidationcurvewhichcorrespondstothedial
readingof
�0+�100
2
=�
50.ThetimecorrespondingtopointFist
50i.e.timefor
50%consolidation.
VII.DetermineC
vfrom
??????
??????=
�
??????.??????
2
�
=
0.197.??????
2
�
ForU
z=50%,T
v=0.197

34. Square-root–timecurvefittingmethod:
Steps:
I.Plotthedialreadingandsquarerootoftime
i.e.�forapressureincrementasshowninfig.
II.DrawatangentABtotheinitialportionoftheplot
asshowninfig.
III.DrawalineACsuchthatOB=1.15*OC.
IV.TheintersectionofthelineACwiththesecond
portionofthecurvei.e.pointDismarked.
V.ThetimecorrespondingtopointSrepresent�
90
(Squarerootoftimefor90%consolidation).
??????
??????=
�
??????.??????
2
�
=
0.848.??????
2
�
ForU
z>60%,�
??????=1.781−0.933.log(100−

35. Computation of Consolidation Settlement:
Consolidation settlement can e computed by two methods:
a. Using Co-efficient of Volume change(�
�)
The consolidation settlement (ρf) when the soil stratum of thickness H has fully consolidated
under a pressure increment Δσ’ is given by equation;
�
�= �
� .H .Δσ’
b. Using void ratio.
The final settlement can be computed using following relation;
�
�=∆H=
�
0−�
1+ �
0
.H
For normally consolidated clay:
�
�=H .
??????
�
1+ �
0
.�??????�
10
??????′
??????
0′

For Preconsolidated soil:
�
�=H .
??????
�
1+ �
0
.�??????�
10
??????′
??????
0′