Chapter 3 compaction and consolidation

Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 1 of 16
Compaction
Q: Differentiate betweencompactionand consolidation
Sr. Compaction Consolidation
1 Mechanical process carried outto reduce
the volume of sub-soil below the structure
It isunwanted processof reductioninvolume
of sub-soil below the structure
2 Compactioniscarriedout before
construction of structure.
Consolidationstarts afterconstruction of
structure
3 Soil experiences dynamicloadingforvolume
reduction
Soil experiences staticloading(self weightof
structure) forvolume reduction
4 It isvery fast process It isvery slow process
5 Expulsionof air voids,causesreductionin
volume
Expulsionof water voids,causesreductionin
volume
6 For propercompactionprocesswater
contentshouldbe at OMC level.
For consolidationprocesssoil shouldbe
saturated.
7 It doesnotgo indefinitely It goeson indefinitely
8 Reducessettlementof structure Responsible forsettlementof structure
Q: Explain dry densityand water contentrelationshipfor soil
Q: Explain compaction processand compaction curve.
 Mechanical process carried out to reduce the volume of sub-soil through expulsion of air voids
belowthe structure inorderto increase the drydensityof soil.
 The increase indry densityensuresthe increase inresistance (bearingcapacity) of soil.
 Compactioniscarriedout before constructionof structure.
dry density and water content relationship-compaction curve
OMC- optimummoisture contentatwhichdrydensityis maximumforsoil,
MDD – maximumdrydensity
ZERO AIR VOIDS LINE
MODIFIED
PROCTOR TEST
STANDARD
PROCTOR TEST
MDD-1
MDD-2
OMC-1 OMC-2
Water Content (%)
DryDensity

 Explanation ofgraph:
o Optimum Moisture Content (OMC) is the moisture content at which the maximum
possible dry density is achieved for a particular compaction energy or compaction
method.
o The correspondingdrydensityiscalledMaximumDryDensity(MDD).
o Water is added to lubricate the contact surfaces of soil particles and improve the
compressibilityof the soil matrix.
o It should be noted that increase in water content increases the dry density inmost soils
up to one stage (Dry side).
o Water acts as lubrication.
o Beyond this level, any further increase in water (Wet side)will only add more void space,
there byreducingthe dry density.
o Hence OMC indicatesthe boundarybetweenthe dryside andwetside.
o Hence the compaction curve as shown in figure indicates the initial upward trend up to
OMC and the downward trend.
 Effect of Compaction process: 1) Increases density 2) Increases strength characteristics 3)
Increases load-bearing capacity 4) Decreases undesirable settlement 5) Increases stability of
slopes and embankments 6) Decreases permeability 7) Reduces water seepage 8) Reduces
Swelling & Shrinkage 9) Reduces frost damage 10) Reduces erosion damage 11) Develops high
negative pore pressures(suctions) increasingeffective stress
Q: Explain Standard Proctor test/ ModifiedProctor test.
Q: differentiate between StandardProctor test& ModifiedProctor test.
Sr. Standard Proctor Test ModifiedProctor Test
1 Mouldcapacity 1000 cc or 2250 cc Mouldcapacity 1000 cc or 2250 cc
2 Rammerused- 2.6 kg
Drop height=31cm
Rammerused- 4.89 kg
Drop height= 45cm
3 Three layersforsoil compaction Five layersforsoil compaction
4 Numberof blows:
If 1000cc mouldused= 25 for eachlayer
Numberof blows:
5 MDD islowcomparedto Modifiedtest
OMC is highcomparedto Modified test
MDD ishighcomparedto Standardtest
OMC is low comparedto Standardtest
Procedure:
1. About3 kg of dry soil,passingthrough4.75 mm sieve.
2. Addapprox.5-8%of waterfor the firsttrial.(Less -Corse grained&more -Fine grainedsoil)
3. Finddimensionsandweightof mould.Note itdownseparately.
4. The innersurfacesof mould,base plate andcollarare greased.

5. Soil isplacedinmouldandcompactedin 3 uniformlayers forSPT/5 layersforMPT , with25
blowsineachlayerof standardrammer(Rammerused- 2.6 kg wt.& dropheight=31cm for
SPT/4.89 kg wt. & drop height=45cm for SPT forMPT)
6. Afterfinal layerremove excesssoil/trimtopsurface
7. Weighthe mouldandsoil.Take some sample of soil fordeterminationof watercontent.
8. The procedure isrepeatedwithincreasingwatercontent.
9. The numberof trialsshall be at least6 witha few afterthe decreasingtrendof bulkdensity.
10. Plotthe graph of dry densityvswatercontent.
Q: Explain compaction methodsand its suitability
 Rammers:
o Rammers are used for compacting small areas by providing impact load to the soil. This
equipmentislightandcanbe hand or machine operated.
o For machine operatedrammers,the usual weightvariesfrom30kgto 10 tonnes.
o These hammers with 2- 3 tonnes weights are allowed to free fall from a height of 1m to
2m on the soil for the compactionof rock fragments.
o Rammersare suitable forcompacting cohesive soilsaswell asothersoils.
o Thismachine usedinareaswithdifficultyinaccess.
 VibratingPlate Compactors:
o Vibratingplate compactorsare usedforcompactionof coarse soils
o These equipmentsare usedforsmall areas.
 Vibro Tampers:
o Vibrotampersisusedforcompactionof small areas inconfinedspace.
o Thismachine issuitable forcompactionof all typesof soil by
 Smooth WheeledRollers:
o Smooth wheeled rollers are of two types: Static smooth wheeled rollers & Vibrating
smoothwheeledrollers
o The most suitable soils for these roller type are well graded sand, gravel, crushed rock,
asphaltetc.where crushingisrequired.
o These are usedon soilswhichdoesnotrequire greatpressure forcompaction.
ZERO AIR VOIDS LINE
MODIFIED
PROCTOR TEST
STANDARD
PROCTOR TEST
MDD-1
MDD-2
OMC-1 OMC-2
Water Content (%)
DryDensity

o These rollersare generallyusedforfinishingthe uppersurface of the soil.
o These rollerare notusedfor compactionof uniformsands.
o The performance of smooth wheeled rollers depend on load per cm width it transfers to
the soil and diameterof the drum.
o The smooth wheeled rollers consists of one large steel drum in front and two steel
drumson the rear. The gross weightof these rollers isinthe range of 8-10 tonnes.
o The other type of smooth wheel roller is called Tandem Roller, which weighs between 6-
8 tonne.
o The performance of these rollers can be increased by increasing the increasing the
weightof the drumby ballastingthe insideof drumswithwetsandor water.
o In case of vibrating smoothwheeled rollers, the drums are made to vibrate by employing
rotatingor reciprocatingmass.
o These rollers are helpful from several considerations like:- (i) Higher compaction level
can be achieved with maximum work (ii) Compaction can be done up to greater depths
(iii) Outputismanytimesmore thanconventional rollers
o Although these rollers are expensive but in the long term the cost becomes economical
due to theirhigheroutputsandimprovedperformance.
o The latest work specifications for excavation recommends the use of vibratory rollers
due to theiradvantage overstaticsmoothwheeledrollers.
 SheepsfootrollerRoller:
o Sheepsfoot rollers are used for compacting fine grained soils such as heavy clays and
siltyclays.
o Sheepsfoot rollers are used for compaction of soils in dams, embankments, subgrade
layersin pavementsandrail roadconstructionprojects.
o Sheepsfootrollersare of staticandvibratorytypes.
o Vibratory types rollers are used for compaction of all fine grained soils and also soil with
sand-gravel mixes.
o Generallythisrollerisusedforcompactionof subgrade layersinroadand rail projects.
o The weight of drums can be increased as in the case of smooth wheeled rollers by
ballastingwithwater,wetsandorbymountingsteel sections.
o The efficiency of sheepsfoot rollers compaction can be achieved when lugs are gradual
walkout of the roller lugs with successive coverage. The efficiency is affected by the
pressure on the foot and coverage of ground obtained per pass. For required pressure
and coverage of ground, the parameters such as gross weight of the roller, the area of
each foot, the number of lugs in contact with the ground at any time and total number
of feetperdrumare considered.
o The compaction of soil is mainly due to foots penetrating and exerting pressure on the
soil.The pressure ismaximumwhenafootisvertical.
 PneumaticTyred Rollers:
o Pneumatictyredrollersare alsocalledasrubbertyredrollers.
o These rollersare usedforcompactionof coarse grainedsoilswithsome fines.
o These rollersare leastsuitableforuniformcoarse soilsandrocks.
o Generally pneumatic tyred rollers are used in pavement subgrade works both earthwork
and bituminousworks.

o Pneumatic rollers have wheels on both axles. These wheels are staggered for
compactionof soil layerswithuniformpressurethroughout the widthof the roller.
o The factor which affects the degree of compaction is tyre inflation pressure and the area
of the contact.
 GridRollers:
o Grid rollersare usedforcompactionof weatheredrocks,well gradedcoarse soils.
o These rollersare notsuitable forclayeysoils,siltyclaysanduniformsoils.
o The main use of these rollersare insubgrade andsub-base inroadconstructions.
o As the name suggests, these rollers have a cylindrical heavy steel surface consisting of a
networkof steel barsformingagrid withsquire holes.
o The weightof thisrollercan be increasedbyballastingwithconcrete blocks.
o Typical weightsvarybetween5.5tonnesnetand 15 tonnesballasted.
o Grid rollers provide high contact pressure but little kneading action and are suitable for
compactingmostcoarse grainedsoils.
 Pad Foot / Tamping Rollers:
o These rollers are similar to sheep foot rollers with lugs of larger area than sheep foot
rollers.
o The static pad foot rollers also called tamping rollers have static weights in the range of
15 to 40 tonnesand theirstaticlineardrumloadsare between30and 80 kg/cm.
o These rollers are more preferable than sheep foot roller due to their high production
capacity,and theyare replacing sheepfootrollers.
o The degree of compactionachievedismore than sheepfootrollers.
o The densityof soil achievedaftercompactionwiththisrollerismore uniform.
o These rollersoperate athighspeeds,andare capable tobreakinglarge lumps.
o These rollersalsoconsistsof levelingbladestospreadthe material.
o Pad footor tampingrollersare bestsuitable forcompactingcohesive soils.
Q: Explain compaction Fieldcontrol of compaction methodsand its suitability
Q: Explain fieldcompactioncontrol
Objective ofFieldCompactionControl:
The followingare the importantobjectivesof fieldcompactioncontrol:
1. To determine the in-situdrydensityandwatercontentimmediatelyafterthe compaction
2. To check and ensure that the soils from the prescribed borrow area, having the desired
properties,are usedforcompaction.
3. To check and ensure that the required compaction energy is used in compacting the soil. This
consists of ensuring that the required type of roller suitable to the soils being compacted is used
as well asthat the rollerisof requiredcapacity.
4. Certainminimumnumberof testsare to be done inthe fieldwhenthe compactionisinprogress
Determination of In-SituDensity:
The determinationof relative compaction requiresthe followingfinding:
 In-situbulk density.
 Field moisture content.
The in-situ density can be computed by following methods:
 Core cutter method.
 Sand replacementmethod.

 Rubberballoon method.
Determination of watercontentof compacted soilcan bedoneby following methods:
 Calciumcarbide method
 Proctor’s Needle Method:
 NuclearMethod
Proctor Needle Test
Principle: The basic principle of Proctor’s needle method is to determine the water content of
compacted soil indirectly without drying the sample based on the resistance offered by the
compactedsoil tothe penetration of Proctor’s needle.
About Test:
 The Proctor’s needle consists of a needle attached to a spring-
loaded plunger.
 The needle consists of a needle point attached to the bottom of a
needle shank, asshown inFig.
 The needle can be pushed into the compacted soil by pressing the
loadingplunger.
 The needle shank has graduations to read the penetration of the
needle intothe compactedsoil.
 The stem of the loading plunger has graduations to show the
resistance offered by the compacted soil to the penetration of the
needle.
 The loading plunger is calibrated to indicate the penetration
resistance of the compacted soil based on the deformation of the
spring, whichdepends onthe loadappliedandthe springconstant.
 Needle points of different cross-sectional areas are supplied along
with the equipment such as 0.25, 0.5, 1.0, and 2.5 cm2
to use in
compacted soilsof increasingpenetration resistance.
Determinationof In-SituMoisture Contentand Dry Density:
 The soil used for compaction in the field, mixed with placement water content, is compacted into
the compaction mouldusingthe same compaction energy.
 The Proctor’s needle with the same needle point as used for preparation of calibration chart is
forced intothe compactedsoil inthe mouldand the penetration resistance isdetermined.
 The water content and dry density of the compacted soil are then read from the calibration chart
correspondingtothe penetration resistance.

Consolidation
Q: Explain Terzaghi’sspring-massanalogy
Q: Explain Terzaghi’sconsolidationtheory
 Consolidation is process of reduction in volume due to expulsion of water particle with the
application of static load for long duration
Terzaghi’sSpring Mass Analogy
Assumptions:
 The soil mediumiscompletelysaturated
 The soil mediumisisotropicandhomogeneous
 Darcy’s lawisvalidforflowof water
 Flowisone dimensionalinthe vertical direction
 The coefficientof permeabilityisconstant
 The coefficientof volumecompressibilityisconstant
 The increase instresson the compressiblesoil depositisconstant(∆σ´= constant)
 Soil particlesandwaterare incompressible
One dimensional theoryisbasedonthe followinghypothesis
1. The change in volume of soil isequal tovolume of pore waterexpelled.
2. The volume of pore waterexpelledisequal tochange involume of voids.
3. Since compressionisinone directionthe change involume isequal tochange inheight.
 T=0
 σ = u and σ´=0
 Soil=Spring
 Water= Water Void
 After application of load -
primaryconsolidationStart
 No reductioninvolume
 0<T<∞
 σ = u + σ´
 All loadisresistedbywater
 flow is upward
 reductioninvolume
 spring& watershare load
 T = ∞
 All the load is resisted by
spring
 Water doesn’tcarry any load
 Soil solids carry external
pressure
 Excess pore water pressure is
zero
 End of primary consolidation

Theory
 Terzaghi’smodel consistsof avessel withapistonattachedtospringas shown.
 The space below piston is filled with water. The piston has outlet to allow for passage of
water.
 Piezometerscanbe insertedtomeasure the excesspore water pressure.
 Terzaghi has correlated the spring mass compression process with the consolidation of
saturatedclaysubjectedtoexternal loadσ.
 The springs and the surroundingwaterrepresentthe saturatedsoil.
 The springs represent the soil skeleton networks of soil grains and water in the vessels
representsthe waterinthe voids.
 In this arrangement the compression is one dimensional and flow will be in the vertical
direction.
 Whenpressure σis appliedthiswill be borne bywatersurroundingthe spring
σ = u and σ´=0 at time t =0
where,uiscalledexcesshydrostaticpressure andthere willbe novolume change.
 Aftersometime ‘t’there will be flow of waterthrough outlet.
 Since the flowisinupwarddirection/segmentthere will be reductioninvolume.
 Due to thisspringget compressedandbeingtocarry a portionof the applied load.
 Thissignifiesareduction inexcesspore waterpressure andincrease ineffectivestress.
σ = u + σ´ load shared by both water and spring
 At time t = ∞ when no more pore water flows out the excess hydrostatic pressure will be
and the entire loadiscarriedbyspring.
σ = σ’ and u=0 at time t =∞
Q: Explain laboratory consolidationtest
The test isconductedto determinethe settlementdue toprimaryconsolidation.Todetermine:
 Rate of consolidationundernormal load.
 Degree of consolidationatanytime.
 Pressure-voidratiorelationship.
 Coefficientof consolidationatvariouspressures.
 Compressionindex.
From the above information it will be possible for us to predict the time rate and extent of
settlement of structuresfounded on fine-grained soils. It is also helpful in analyzing the stress history
of soil. Since the settlement analysis of the foundation depends mainly on the values determined by
the test,thistestis veryimportantforfoundationdesign.
Principal Involved

When a compressive load is applied to soil mass, a decrease in its volume takes place, the
decrease in volume of soil mass under stress is known as compression and the property of soil mass
pertaining to its tendency to decrease in volume under pressure is known as compressibility. In a
saturated soil mass having its void filled with incompressible water, decrease in volume or
compression can take place when water is expelled out of the voids. Such a compression resulting
froma longtime staticloadand the consequentescape of pore wateristermedasconsolidation.
Procedure
1] Saturate two porous stones by keeping them submerged in the distilled water for 4 to 8 hrs.
Wipe awayexcesswater.
2] Assemble the consolidometer, with the soil specimen and porous stones at top and bottom of
specimen, providing a filter paper between the soil specimen and porous stone. Position the
pressure padcentrallyonthe topporous stone.
3] Mount the mould assembly on the loading frame, and center it such that the load applied is
axial.
4] Position the dial gauge to measure the vertical compression of the specimen. The dial gauge
holder should be set so that the dial gauge is in the begging of its releases run, allowing
sufficientmarginforthe swellingof the soil,if any.
5] Connect the mould assembly to the water reservoir and the sample is allowed to saturate. The
level of the waterinthe reservoirshouldbe ataboutthe same level asthe soil specimen.
6] Apply an initial load to the assembly. The magnitude of this load should be chosen by trial, such
that there isno swelling.
7] The load should be allowed to stand until there is no change in dial gauge readings for two
consecutive hoursorfora maximumof 24 hours.
8] Note the final dial reading under the initial load. Apply first load of intensity 0.1 kg/cm2 start the
stop watch simultaneously. Record the dial gauge readings at various time intervals. The dial
gauge readings are taken until 90% consolidation is reached. Primary consolidation is gradually
reachedwithin24 hrs.
9] At the end of the period, specified above take the dial reading and time reading. Double the load
intensity and take the dial readings at various time intervals. Repeat this procedure for
successive loadincrements.The usual loadingintensityare asfollows:
a. 0.1, 0.2, 0.5, 1, 2, 4 and 8 kg/cm2.
10] After the last loadingis completed, reduce the load to half of the value of the last load and allow
it to stand for 24 hrs. Reduce the load further in steps of half the previous intensity till an
intensityof 0.1kg/cm2 is reached.Take the final reading of the dial gauge.
11] Reduce the load to the initial load, keep it for 24 hrs and note the final readings of the dial
gauge.
12] Quickly dismantle the specimen assembly and remove the excess water on the soil specimen in
oven,note the dryweightof it.
Analysis:
(1) Calculate the initial watercontentandspecificgravityof the soil.
(2) For each pressure increment, construct a semi-log plot of the consolidation dial readings versus
the log time (inminutes). Determine the coefficientof consolidation (cv).
(3) Calculate the void ratio at the end of primary consolidation for each pressure increment. Plotlog
pressure versus void ratio. Based on this plot, calculate compression index, recompression index
and preconsolidation pressure (maximumpastpressure).

Q: Explain Log – time curve fittingmethod to findcoefficientofconsolidation(Cv)
The basis for this method is the theoretical (Uz ) versus log Tv curve and experimental dial
gauge readingandlog(t) curvesare similar.
Steps
i. Plot the dial reading of compression for a given pressure increment versus time to log scale as
showninfigure.
ii. Plot two points P and Q on the upper portion of the consolidation curve (say compression line)
correspondingtotime t1 and t2 suchthat t2 =4t 1
iii. Let x be the difference in dial reading between P and Q. locate R at a vertical distance x above
pointP
iv. Draw a horizontal line RS the dial reading corresponding to this line is d 0 which corresponds
with0% consolidation.
v. Project the straight line portion of primary and secondary consolidation to intersect at point T.
The dial readingcorrespondingtoT isd 100 andthiscorrespondsto 100% consolidation.
vi. Determine the pointV onthe consolidationcurve whichcorrespondstothe dial readingof
d50 = (d0 +d100)/2. The time correspondingtopointV ist 50 i.e time for50% consolidation.
Log – time curve fitting method

Q: Explain Square root of time method to findcoefficientofconsolidation(Cv)
i. Plotthe dial readingandthe correspondingsquare-root-of-time 𝑡asshownin Figure
ii. Draw the tangentPQ to the earlyportionof the plot.
iii. Draw a line PRsuch that OR = (1.15)(OQ).
iv. The abscissaof the pointS (i.e.,the intersectionof PRand the consolidationcurve) will give
√𝑡90 ( i.e.,the square-root-of-timefor90% consolidation).
v. The value of 𝑇 𝑣 for Uav = 90% 𝑖𝑠 0.848. so,
Square root of time method
Q: Explain soil compressibilitycharacteristics
Q: Explain normallyconsolidated,over and under consolidatedsoil
 A laboratory soil specimen of dia 60mm and height 20mm is extracted from the undisturbed soil
sample obtainedfromthe field.
 Thissample issubjectedto1D consolidationinthe ladundervariouspressureincrements.
 Each pressure increment is maintained for 24 hrs and equilibrium void ratio is recorded before
the applicationof the nextpressure increment.
 Thena plotof voidratioversuseffectivestressismade asshowninFig.
 When the sample is recompressed from point D it follows DE and beyond C it merges along BCF
and itcompressesasit movesalongBCF
 During the initial stages (at low effective stress) sample follows recompression path (portion AB)
and undergoeslesscompression.
 Beyond this is the virgin compression line (portion BC) also called the normal compression line
and the sample undergoeslarge compression.
1. BC – Virgincompressioncurve alsocalled normal consolidationline

2. From ‘C’ when the sample is unloaded, sample expands and traces path CD (expansion curve
unloading)
3. Sample undergoes Permanent strain due to irreversible soil structure and there is a small elastic
recovery.
4. The deformationrecoveredisdue to elasticrebound
5. When the sample is reloaded-reloading curve lies above the rebound curve and makes an
hysteresisloopbetweenexpansionandreloadingcurves.
6. The reloadedsoilsshowslesscompression.
7. Loading beyond ‘C’ makes the curve to merge smoothly into portion EF as if the soil is not
unloaded.
Soil Compressibility

It is the maximum effective stress experienced by a soil in its stress history (past existence)
 For the soil loaded along the recompression curve AB the effective stress close to point B will
be the preconsolidationpressure.
 If the soil is compressed along BC and unloaded along CD and then reloaded along DC the
effectivestressclose topointCwill be the new preconsolidationpressure.
Effectof Stress History
It isbasedon the stresshistory(preconsolidationpressure)soilsare classifiedas
1. NormallyConsolidatedSoils
2. Over ConsolidatedSoils
3. Under ConsolidatedSoils
Normally Consolidated Soils It is a soil deposit that has never subjected to a vertical effective stress
greaterthan the presentvertical stress.
Under Consolidated Soils A soil deposit that has not consolidated under the present overburden
pressure (effective stress) is called Under Consolidated Soil. These soils are susceptible to larger
deformationandcause distressinbuildingsbuiltonthese deposits.

Over Consolidated Soils Itis a soil deposit that has been subjected to vertical effective stress greater
than the presentvertical effective stress.
Q: how to determine pre-consolidationpressure ?
Determinationof PreconsolidationPressure (YieldStress)
Step1. Conductan oedometertestonthe undisturbedsoil sampleobtainedfromthe field.
Step2. Plot e - log σ´ plot as shown. The equilibrium void ratio at the end of each of the pressure
incrementsare usedinobtaininge - logσ´ plot.
Step3. Selectthe pointof maximumcurvature (PointA) onthe e - log σ´ curve
Step4. Draw a tangentat the pointof maximum curvature (PointA)
Step5. Draw a horizontal line AC
Step6. Draw the bisectorline ADbetweenthe tangentandhorizontal line
Step7. Extendthe normallyconsolidatedline tointersectthe bisectorlineat ‘O’
Step8. The vertical effective stress corresponding to point of intersection (O) is the
preconsolidationpressure (σ´pc)
Q: Explain compressibilitycharacteristicsmv, av,Cc
Compressibility Characteristics
The compressibility of soils under one-dimensional compression can be described from the decrease
in the volume of voids with the increase of effective stress. This relation of void ratio and effective
stresscan be depictedeitherasan arithmetic plotor a semi-logplot.
It can be said that the compressibility of a soil decreases as the effective stress increases.
This can be represented by the slope of the void ratio – effective stress relation, which is called the
coefficientofcompressibility,av.
𝑎 𝑣 =
𝑒1 − 𝑒2
𝜎2
′
− 𝜎1
′
O

Co-efficient of volume compressibility (mv) It is the ratio of change in volume of a soil per unitinitial
volume due tounitincrease ineffective stressandisgivenby 𝑚 𝑣 =
𝑎 𝑣
1+ 𝑒 𝑜
Coefficient of compression/compression index (Cc):It is the slope of the normal consolidationline in
a plotof voidratio-logarithmof effectivestress(e - logσ´).Itisgivenby
Empirical correlations
Cc = 0.009 (LL-10) Undisturbedclays
Cc = 0.007 (LL-10) Remouldedsoil sample
Cc = 1.15 (e0-0.30) Upperboundvalues
Cc = 0.30 (e0-0.27) Lowerboundvalues
The value of Cc is constant for a given soil. The compression index is used to determine primary
consolidation settlement of normally consolidated soils. A high value of Cc indicates high
compressibilityandhigherconsolidationsettlement.

Formulae in Consolidation chapter:
 Compressionindex
 It isa slope of pressure-voidsratiocurve whenplottedonlogarithmicgraph
 𝑐 𝑐 =
𝑒0− 𝑒
log10( 𝜎′
𝜎0
′
)
 Coefficientofcompressibility
 It isa slope of pressure-voidsratiocurve whenplottedonnatural graph
 𝑎 𝑣 =
𝑒0− 𝑒
𝜎′− 𝜎0
′
 Coefficientofvolume change
 𝑚 𝑣 =
𝑎 𝑣
1 + 𝑒0
 Where,e0 isinitial voidsratioswhenpressure = 𝜎0
′, e is voidsratiowhenpressure
change to 𝜎′
 Consolidationsettlement
 𝜌𝑓 = 𝑚 𝑣 𝐻 ∆𝜎′
 H = soil thickness, ∆𝜎′=pressure increment
 CoefficientofConsolidation
 𝑐 𝑣 =
𝑘
𝑚 𝑣 𝛾 𝑤
 Where,kis coefficientof permeability
 From consolidationtestdata
o 𝑐 𝑣 =
𝑇𝑣
𝑡
𝑑2
o 𝑇𝑣 =
𝜋
4
(
𝑈
100
)
2
….whendegree of consolidation=U < 60%
o 𝑇𝑣 = −0.9332 log10 (1 −
𝑈
100
) − 0.0851….whendegree of consolidation=U > 60%
o Where,Tv is time factor, t is time requiredforconsolidation,disdrainage path
o d = soil thicknesswhensoil hassingledrainage
o d = (soil thickness/2) whensoil hasdouble drainage

Chapter 3 compaction and consolidation

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