Slide 1

Consolidation of Clays
N. Sivakugan
Duration: 17 minutes

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Slide 2

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).

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Slide 3

What is Consolidation?

settlement

This leads to settlements occurring over a long time,

time

which could be several years.

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Slide 4

In granular soils…

settlement

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

time

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Slide 5

During consolidation…
Due to a surcharge q applied at the GL,
the stresses and pore pressures are increased at A.
q kPa


A

GL

..and, they vary
with time.

u

’
saturated clay

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Slide 6

During consolidation…
 remains the same (=q) during consolidation.
u decreases (due to drainage) while ’ increases,
transferring the load from water to the soil.


q kPa

u


A

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’

u

’
saturated clay

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GL

q

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Slide 7

One Dimensional Consolidation
~ drainage and deformations are vertical (none laterally)
~ a simplification for solving consolidation problems
q kPa
GL

water squeezed out

saturated clay

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reasonable
simplification if the
surcharge is of
large lateral extent

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Slide 8

H -e Relation
average vertical strain =

H
Ho

q kPa

GL

saturated clay
e = eo

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Time = 0+
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H

q kPa
GL

Ho

saturated clay
e = eo - e
Time = 

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Slide 9

H -e Relation
Consider an element where Vs = 1 initially.
e

eo

1

Time = 0+

Time = 

average vertical strain =

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e
1  eo

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Slide 10

H -e Relation
Equating the two expressions for average
vertical strain,
consolidation
settlement

change in void ratio

H
Ho

initial thickness of
clay layer

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

e
1  eo
initial void ratio

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Slide 11

Coefficient of volume compressibility
~ denoted by mv
~ is the volumetric strain in a clay element per
unit increase in stress
no units


change in volume
original

V

volume

i.e.,

mv 

kPa-1 or MPa-1

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V

kPa or MPa
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Slide 12

Consolidation Test
~ simulation of 1-D field consolidation in lab.
GL

porous stone
undisturbed soil
specimen

metal ring

Dia = 50-75 mm

(oedometer)

Height = 20-30 mm

field

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lab
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Slide 13

Consolidation Test
loading in increments
allowing full consolidation before next increment
q1

q2

H1

eo- e1

H o eo

 e1 

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H 1
Ho

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(1  e o )

 e2 

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Slide 14

Consolidation Test
unloading

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Slide 15

e – log v’ plot
- from the above data

void ratio

loading
v’ increases &
unloading

e decreases

v’ decreases &
e increases (swelling)

log v’

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Slide 16

Compression and recompression indices

Cr

void ratio

1

Cc ~ compression index
Cc

Cr ~ recompression index
(or swelling index)
Cr

1

1

log v’

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Slide 17

Preconsolidation pressure

void ratio

is the maximum
vertical effective
stress the soil
element has
ever been
subjected to

pressure
SIVA preconsolidation
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p’

log v’


Slide 18

Virgin Consolidation Line
original
state

void ratio

eo

virgin consolidation line

eo, vo’

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vo’

p’

log v’
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Slide 19

Overconsolidation ratio (OCR)
original
state

virgin consolidation line

vo’

Field

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void ratio

eo

OCR 

vo’

 p'
 vo '
p’

log v’


Slide 20

Overconsolidation ratio (OCR)
VCL
OCR=1

~current state

void ratio

OCR=13

Normally
consolidated
clay
OCR=2

OCR=13
Heavily
overconsolidated clay

OCR=2
Slightly
overconsolidated clay

log v’

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Slide 21

More to come…

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Slide 22

Settlement computations
Two different ways to estimate the
consolidation settlement:
q kPa

(a) using mv
settlement = mv  H

H

=q

(b) using e-log v’ plot
next slide

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eo, vo’, Cc,
Cr, p’, mv
-oedometer
test
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settlement



e
1  eo

H


Slide 23

Settlement computations
~ computing e using e-log v’ plot
If the clay is normally consolidated,
the entire loading path is along the VCL.
initial

eo
e

 e  C c log
vo’

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vo’+ 

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 vo '    '
 vo '


Slide 24

Settlement computations
~ computing e using e-log v’ plot
If the clay is overconsolidated, and remains so by
the end of consolidation,

 e  C r log
eo

initial

e

note the use of Cr
VCL
vo’

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 vo '    '

vo’+ 

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 vo '


Slide 25

Settlement computations
~ computing e using e-log v’ plot
If an overconsolidated clay becomes normally
consolidated by the end of consolidation,

 e  C r log
eo

initial

e

VCL
vo’

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p’

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vo’+ 

 p'
 vo '

 C c log

 vo '    '
 p'


Slide 26

Preloading

Preloading at West Kowloon Expressway, Hong Kong.
(5-10 m embankments for 2-5 months)

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Slide 27

Preloading
Piezometers measure pore pressures and thus
indicate when the consolidation is over.

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Slide 28

Preloading

Cross section of PVD

Installation
Prefabricated Vertical Drains to Accelerate Consolidation

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Slide 29

Prefabricated Vertical Drains

Installation of PVDs

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