Lecture 12

Consolidation of ClaysConsolidation of Clays

What is Consolidation?What is Consolidation?

When a saturated clay is loaded externally,

GL

saturated clay

the water is squeezed out of the clay over a long time (due to low permeability of the clay).(due to low permeability of the clay).

Consolidation DefinitionConsolidation - Definition

C lid i f h i• Consolidation refers to the compression or settlement that soils undergo as a response of

l i l d h dplacing loads onto the ground • These loads produce corresponding increases

in the vertical effective stress, v’

SignificanceSignificance

• The amount of soil volume change that will occur is often one of the governing design criteria of a project

• If the settlement is not kept to tolerable limit, the desire use of the structure may be impaired and the design life of the structure may be reduced

• Consolidation is a time-dependent process, in some soils it may take long time (100 y g (years ?) to achieve complete settlement

• It is therefore important to have a mean of predicting the amount of soil compression p ed c g e ou o so co p ess oor consolidation

• It is also important to know the rate of• It is also important to know the rate of consolidation as well as the total consolidation to be expectedconsolidation to be expected

Consolidation - Case StudyConsolidation Case Study

Palacio de las Bellas, Artes, Mexico City

Total settlement = 9ftThe Leaning Tower of Pisa

Consolidation IntroductionConsolidation - Introduction

Th i i d b• The compression is caused by:– Deformation of soil particles– Relocations of soil particles– Expulsion of water or air from void spaces

• Most of the settlement of a structure on clay is mainly due to volumetric changes and y grarely due to shear strain.

Consolidation vs CompactionConsolidation vs. Compaction

During consolidationDuring consolidation…

Due to a surcharge q applied at the GL,

the stresses and pore pressures are increased at A

q kPa

the stresses and pore pressures are increased at A.

and they varyGL

A

u

..and, they vary with time.

saturated clay

A’

During consolidationDuring consolidation…

remains the same (=q) during consolidation.u decreases (due to drainage)

f h l d f h lwhile ’ increases,

q kPa

u

transferring the load from water to the soil.

GL

A

u

u

’

saturated clay

A’

q

One Dimensional ConsolidationOne Dimensional Consolidation

~ drainage and deformations are vertical (none laterally)~ a simplification for solving consolidation problems

GL

q kPa

saturated clayreasonable

simplification if the

water squeezed out

saturated clay psurcharge is of

large lateral extent

In granular soilsIn granular soils…

Granular soils are freely drained, and thus the settlement is instantaneous.

men

tse

ttle

m

time

What is Consolidation?What is Consolidation?

This leads to settlements occurring over a long time,tle

men

t

time

sett

which could be several years.

time

The consolidation process

P tPore water(incompressible) Voids

Skeletal MaterialSkeletal Material(incompressible) Solid

Initial State


P t

Pore water

(incompressible) Voids Voids

Skeletal MaterialSkeletal Material(incompressible) Solid Solid

Water

+

Initial State Deformed State

Water

Consolidation (cont )z

′z0′

}

Consolidation (cont.)

H

c

z

z0′

z }z f′

′′

VoidsVv = eVs

ez

′z0z0

′ }z f′

Voids

Solids

v s

Vs

Vv = (e - e)Vs

Vs Solids

Before After


Deformation of saturated soil occurs by reduction of pore space & the squeezing out of pore water. The water can only escape through the pores which for fine-grained soilsonly escape through the pores which for fine grained soils are very small

Consolidation (cont )Consolidation (cont.)

D i lid ti t th t i th• During consolidation, pore water or the water in the voids of saturated clay gets squeezed out –reducing the volume of the clay – hence causingreducing the volume of the clay – hence causing settlement called as consolidation settlement

The spring analogy to

lid iconsolidation.


Deformation of saturated soil occurs by reduction of pore space & the squeezing out of pore water. The water can only escape through the pores which for fine-grained soilsonly escape through the pores which for fine grained soils are very small

water squeezed out

waterEffective soil skeleton “spring”

water


water

Instantaneously no water can flow, and hence there can be no change in volume.


water


For 1-D conditions this means

zz = v = = 0 (1)

e

eC

eF I

1 1log ( / )

e e1 1


water


For 1-D conditions this means

zz = v = = 0 (1)

e

eC

eF I

1 1log ( / )

and hence ´ = 0 instantaneously

e e1 1


water

From the principle of effective stress we have

´ + u (2)

and thus instantaneously we must have

u u


Region of highexcess water

Region of lowexcess waterFlow

pressure pressure

The consolidation process is the process of the dissipation of the excess pore pressures that occur on load application because water cannot freely drain from the void space.


TotalStress

Time


TotalStress

Time

ExcessPorePressure

Time


EffectiveStress

Time


EffectiveStress

Time

Settlement

Time

Types of ConsolidationTypes of Consolidation

• There are three types of consolidation:– Immediate consolidation; caused by elastic

deformation of dry soil or moist and saturated soil without change in moisture contentPrimary consolidation; caused as a result of– Primary consolidation; caused as a result of volume change in saturated cohesive soils due to exclusion of water occupied the void spaces p p

– Secondary consolidation; occurs in saturated cohesive soils as a result of the plastic adjustment of soil fabrics

Types of Consolidation (cont )Types of Consolidation (cont.)

• Clayey soils undergo consolidation settlement not only under the action of “external” loads (surcharge loads) but also under its own weight or(surcharge loads) but also under its own weight or weight of soils that exist above the clay (geostatic loads).)

• Clayey soils also undergo settlement when dewatered (e.g., ground water pumping) – because th ff ti t th l ithe effective stress on the clay increases

• Coarse-grained soils DO NOT undergo consolidation settlement due to relatively yhigh hydraulic conductivity compared to clayey soils. Instead, coarse-grained soils y y , gundergo IMMEDIATE settlement.

1 D Consolidation Test1- D Consolidation Test

• The main purpose of consolidation tests is to obtain soil data which is used in predicting the rate and amount of settlement of structures founded onand amount of settlement of structures founded on clay.

Consolidation TestConsolidation Test

~ simulation of 1-D field consolidation in lab.

GL

di t b d il

porous stone

undisturbed soil specimen

Dia = 50-75 mm

H i ht 20 30

metal ring(oedometer)

fi ld l b

Height = 20-30 mm

field lab

• The fo r most important soil properties• The four most important soil properties determined by a consolidation test are:– The pre-consolidation stress, p’, This is the maximum

h h il h “f l ” i hp

stress that the soil has “felt” in the past.– The compression index, Cc , which indicates the

compressibility of a normally-consolidated soil.– The recompression index, Cr , which indicates the

compressibility of an over-consolidated soil.– The coefficient of consolidation, cv , which indicates

h f i d l d ithe rate of compression under a load increment.

Test ResultsTest ResultsRecompression

I d

B

CrIndex

CompressionIndex

Cc

p

Pre-Consolidation Stress


• Two types of consolidometers (oedometers) commonly used:y– Floating-ring– Fixed ringFixed ring

• This lab uses the fixed-ring consolidometerASTM D 2435• ASTM D 2435

Laboratory Consolidation TestLaboratory Consolidation Test

http://www.uic.edu/classes/cemm/cemmlab/Experiment%2011-Consolidation.pdf#search='consolidation%20test'


Measurement of soil properties

Th dThe oedometer apparatus

Load Displacement measuring device

Cell

g

Loading cap

wateSoil sample

water

Porous disks

Laboratory Consolidation TestLaboratory Consolidation Testv 1 Place sample in ringv p g

2 Apply load3 Measure height change4 Repeat for new load4 Repeat for new loadConfining

stress

v VoidsVoids

Vv Vv

V

Solids Solids

Voids

Vs

Vv

Vs

Before After

ProcedureProcedure

• Measure the inner diameter and height of the consolidation cutter/ring and record its massP il i f th t t b t i i d• Prepare a soil specimen for the test by trimming and placing the soil in the ring

• Determine the mass of ring + soilg• Collect some excess soil for moisture content • Assume Gs = 2.7

• Place the specimen and ring and place the upper stone/disk pp

• Saturate the lower (larger) porous stone on the base of the consolidometerthe base of the consolidometer

• Place 1.5 kg (1st day), 3kg (2nd day), 6kg (3rd

day) 12kg (4th day)day), 12kg (4 day)

H -e RelationH -e Relation

average vertical strain =oH

H

GL

q kPa

q kPaH

GL

Ho

saturated clay saturated claye = eo e = eo - e

Time = 0+ Time =


Consider an element where Vs = 1 initially.

eeo

1

Time = 0+ Time =

eaverage vertical strain =

oee

1


E i h i fEquating the two expressions for average vertical strain,

l d change in void ratio

e

Hconsolidation settlement

change in void ratio

oe1oH

initial thickness of initial void ratioinitial thickness of clay layer

Calculation SampleCalculation Sample

Eq 17.2

1(in) - Hs

Hv = Hi - HsHie = Hv / Hs

(1.0 + 0.9917) / 2 (0.848 x 0.99592)/(4 x 302)

t90

( ) ( ) ( )

More to come…

Compression and recompression indicesp p

o 1Cr

void

rat

io

Cc ~ compression index1

1

Cc

Cr ~ recompression index(or swelling index)(or swelling index)

1Cr

log v’

Preconsolidation pressurep

is the maximumtio

is the maximum vertical effective stress the soil

void

rat element has

ever been subjected tosubjected to

log v’p’preconsolidation pressure

• Preconsolidation stress (pressure)Terminology

Preconsolidation stress (pressure)The maximum effective stress which has been applied to an element of soilan element of soil

• Over - consolidated A soil is called over-consolidated (OC) if:

• Normally consolidated

Current Effective Stress Preconsolidation Stress<Normally consolidated

A soil is called normally consolidated (NC) if:

C t Eff ti St P lid tiCurrent Effective Stress Preconsolidation Stress=

Terminology

It is not possible for

Current Effective StressP lid ti StPreconsolidation Stress>

Virgin Consolidation Lineg

virgin consolidation lineeo

original state

atio

void

ra

eo, vo’

log v’p’vo’

Estimating the preconsolidation pressure

e

A

B

log (’)

Casagrande’s method


e

A C

B

log (’)


D


D

e

A C

B

log (’)


D


D

e

A C

F

BE

log (’)


D


D

e

A C

F

BE

pc log (’)


Overconsolidation ratio (OCR)( )

virgin consolidation lineeo

original state

atio

void

ra

vo’''pOCR

'vo

log v’p’vo’Field

Overconsolidation ratio (OCR)( )

OCR=1~current state

VCL

atio

OCR=2

OCR=13 Normally consolidated

clayvo

id r

a OCR=2

OCR=13

Heavily OCR=2

Slightly

ea yoverconsolidated clay

log v’overconsolidated clay

Calculations and Graphs - v vs w(time)

Plot of Vertical Displacement vs. Time(P = 1000 psf)

0.4235

0.4225

0.423

0.4215

0.422

Dis

plac

emen

t (in

)

0.4205

0.421

0.420.00 5.00 10.00 15.00 20.00 25.00

Time (min 0.5)

vs wtime Graph – Find t90v vs wtime Graph Find t90

Plot of Vertical Displacement vs. Time(P = 1000 psf)(P = 1000 psf)

0.423

0.4235

d0 A

0.422

0.4225

men

t (in

)

t90 = 2.5 min0.5

0.421

0.4215

Dis

plac

em

1 4

5

0.42

0.42052 3

t90

B DC

CD = 1.15 BC

0.00 5.00 10.00 15.00 20.00 25.00

Time (min 0.5)

Calculation and Graph – v vs log(time)

Logarithm of time curve fitting

0.423

0.4235

0.422

0.4225

acem

ent (

in)

0.421

0.4215

Verti

cal D

ispl

ac

0.42

0.4205

0.1 1 10 100 1000 10000

Time (min) - log Scale

v vs log(time) Graph – Find t50v g( ) p 50Logarithm of time curve fitting

0.4235

0.423 t 1

t 2= 4t 14 X 6

X7

d0 = 0.423058

d0

0.422

0.4225

acem

ent (

in)

5

d50 9

0.421

0.4215

Vertic

al D

ispl

a

1

d50=0.5(d0+d100)=0.42185

10

0 42

0.4205

d100 = 0.420652

A3d100

t50 = 10.2 min

0.420.1 1 10 100 1000 10000

Time (min) - log Scale

CalculationCalculation

• Determine the heights

s

GD

WH

2• Determine the height

of solids (Hs) of the specimen in the mold

wsGD

4

sftv HHH )(specimen in the mold• Determine the change

in height (H) Hg ( )• Determine the final

specimen height, Ht(f)

s

v

HHe

g t(f)

• Determine the height of voids (Hv)

• Determine the final void ratio

Calculation (cont )Calculation (cont.)• Calculate the

coefficient of tcconsolidation (cv) from t90

290

HtcT v

v

• Calculate the coefficient of

lid ti ( ) f250

HtcT v

v

consolidation (cv) from t50

• Plot e log p curve and• Plot e-log p curve and find:

, C , Cc, Cc, Cr

• Plot cv – log p curves

Coefficient of volume compressibility

~ denoted by mv

h l l l~ is the volumetric strain in a clay element per unit increase in stress

no units

volumeoriginal volumein change

V

V

Vmv

i.e.,

kPa or MPakPa-1 or MPa-1

e – log v’ plotg v p- from the above data

o loading

void

rat

io loading

v’ increases &

e decreasesunloading

v’ decreases &

e increases (swelling)

log v’

Settlement computationsSettlement computations

Two different ways to estimate the consolidation settlement:

q kPa(a) using mv

settlement m H=q

H

(b) i l ’ l t

settlement = mv H

eo, vo’, Cc,

(b) using e-log v’ plot

enext slide

eo, vo , Cc,Cr, p’, mv-oedometer

test

Heesettlement

o

1

Settlement computationsSettlement computations~ computing e using e-log v’ plot

If the clay is normally consolidated,

the entire loading path is along the VCL

i iti l

the entire loading path is along the VCL.

''log voCe

initialeo

e

'log

vocCe

vo’vo’+


If the clay is overconsolidated, and remains so by the end of consolidation,

'''log vo

rCe

voinitial

eo

e

VCL

note the use of Cr

vo’ vo’+


If an overconsolidated clay becomes normally consolidated by the end of consolidation,

'''log

''

log voc

pr CCe

'

g'

gp

cvo

r initial

eo

VCL

e

vo’ vo’+

VCL

p’

Engineering

Lecture 12