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Consolidation of Clays N. Sivakugan Duration: 17 minutes
1
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).
SIVA
Copyright©2001
2
What is Consolidation?
settlement
This leads to settlements occurring over a long time,
time
which could be several years.
SIVA
Copyright©2001
3
In granular soils…
settlement
Granular soils are freely drained, and thus the settlement is instantaneous.
time
SIVA
Copyright©2001
4
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
SIVA
Copyright©2001
5
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
Copyright©2001
’
u
’ saturated clay
SIVA
GL
q
6
One Dimensional Consolidation ~ drainage and deformations are vertical (none laterally) ~ a simplification for solving consolidation problems q kPa GL
water squeezed out
saturated clay
SIVA
Copyright©2001
reasonable simplification if the surcharge is of large lateral extent
7
H -e Relation H average vertical strain = Ho q kPa
GL
saturated clay e = eo
SIVA
Time = 0+ Copyright©2001
H
q kPa GL
Ho
saturated clay e = eo - e Time =
8
H -e Relation Consider an element where Vs = 1 initially. e
eo
1
Time = 0+
Time =
average vertical strain =
SIVA
Copyright©2001
e 1 eo
9
H -e Relation Equating the two expressions for average vertical strain, consolidation settlement
initial thickness of clay layer
SIVA
Copyright©2001
change in void ratio
H e 1 eo Ho initial void ratio
10
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 volume
i.e.,
mv
kPa-1 or MPa-1
SIVA
Copyright©2001
V
V
kPa or MPa 11
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
SIVA
Copyright©2001
lab 12
Consolidation Test loading in increments allowing full consolidation before next increment q1
q2
H1
eo- e1
H o eo
H1 e1 (1 eo ) Ho
SIVA
Copyright©2001
e2
13
Consolidation Test unloading
SIVA
Copyright©2001
14
e – log v’ plot - from the above data
void ratio
loading v’ increases & unloading
e decreases
v’ decreases & e increases (swelling)
log v’
SIVA
Copyright©2001
15
Compression and recompression indices
Cr
void ratio
1
Cc ~ compression index Cc
Cr ~ recompression index (or swelling index) Cr
1
1
log v’
SIVA
Copyright©2001
16
Preconsolidation pressure
void ratio
is the maximum vertical effective stress the soil element has ever been subjected to
pressure SIVA preconsolidation Copyright©2001
p’
log v’
Virgin Consolidation Line original state
void ratio
eo
virgin consolidation line
eo, vo’
SIVA
Copyright©2001
vo’
p’
log v’ 18
Overconsolidation ratio (OCR) original state
vo’
Field
SIVA
Copyright©2001
void ratio
eo
virgin consolidation line
p' OCR vo ' vo’
p’
log v’
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’
SIVA
Copyright©2001
More to come…
SIVA
Copyright©2001
21
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
SIVA
eo, vo’, Cc, Cr, p’, mv -oedometer test Copyright©2001
e settlement H 1 eo
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
vo ' ' e Cc log vo '
e
vo’
SIVA
vo’+
Copyright©2001
Settlement computations ~ computing e using e-log v’ plot If the clay is overconsolidated, and remains so by the end of consolidation,
eo
vo ' ' e Cr log vo '
initial
e
note the use of Cr VCL vo’
SIVA
vo’+
Copyright©2001
Settlement computations ~ computing e using e-log v’ plot If an overconsolidated clay becomes normally consolidated by the end of consolidation,
eo
p' vo ' ' e Cr log Cc log vo ' p'
initial
e
VCL vo’
SIVA
p’
Copyright©2001
vo’+
Preloading
Preloading at West Kowloon Expressway, Hong Kong. (5-10 m embankments for 2-5 months)
SIVA
Copyright©2001
26
Preloading Piezometers measure pore pressures and thus indicate when the consolidation is over.
SIVA
Copyright©2001
27
Preloading
Cross section of PVD
Installation Prefabricated Vertical Drains to Accelerate Consolidation
SIVA
Copyright©2001
28
Prefabricated Vertical Drains
Installation of PVDs
SIVA
Copyright©2001
29
1
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).
SIVA
Copyright©2001
2
What is Consolidation?
settlement
This leads to settlements occurring over a long time,
time
which could be several years.
SIVA
Copyright©2001
3
In granular soils…
settlement
Granular soils are freely drained, and thus the settlement is instantaneous.
time
SIVA
Copyright©2001
4
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
SIVA
Copyright©2001
5
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
Copyright©2001
’
u
’ saturated clay
SIVA
GL
q
6
One Dimensional Consolidation ~ drainage and deformations are vertical (none laterally) ~ a simplification for solving consolidation problems q kPa GL
water squeezed out
saturated clay
SIVA
Copyright©2001
reasonable simplification if the surcharge is of large lateral extent
7
H -e Relation H average vertical strain = Ho q kPa
GL
saturated clay e = eo
SIVA
Time = 0+ Copyright©2001
H
q kPa GL
Ho
saturated clay e = eo - e Time =
8
H -e Relation Consider an element where Vs = 1 initially. e
eo
1
Time = 0+
Time =
average vertical strain =
SIVA
Copyright©2001
e 1 eo
9
H -e Relation Equating the two expressions for average vertical strain, consolidation settlement
initial thickness of clay layer
SIVA
Copyright©2001
change in void ratio
H e 1 eo Ho initial void ratio
10
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 volume
i.e.,
mv
kPa-1 or MPa-1
SIVA
Copyright©2001
V
V
kPa or MPa 11
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
SIVA
Copyright©2001
lab 12
Consolidation Test loading in increments allowing full consolidation before next increment q1
q2
H1
eo- e1
H o eo
H1 e1 (1 eo ) Ho
SIVA
Copyright©2001
e2
13
Consolidation Test unloading
SIVA
Copyright©2001
14
e – log v’ plot - from the above data
void ratio
loading v’ increases & unloading
e decreases
v’ decreases & e increases (swelling)
log v’
SIVA
Copyright©2001
15
Compression and recompression indices
Cr
void ratio
1
Cc ~ compression index Cc
Cr ~ recompression index (or swelling index) Cr
1
1
log v’
SIVA
Copyright©2001
16
Preconsolidation pressure
void ratio
is the maximum vertical effective stress the soil element has ever been subjected to
pressure SIVA preconsolidation Copyright©2001
p’
log v’
Virgin Consolidation Line original state
void ratio
eo
virgin consolidation line
eo, vo’
SIVA
Copyright©2001
vo’
p’
log v’ 18
Overconsolidation ratio (OCR) original state
vo’
Field
SIVA
Copyright©2001
void ratio
eo
virgin consolidation line
p' OCR vo ' vo’
p’
log v’
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’
SIVA
Copyright©2001
More to come…
SIVA
Copyright©2001
21
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
SIVA
eo, vo’, Cc, Cr, p’, mv -oedometer test Copyright©2001
e settlement H 1 eo
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
vo ' ' e Cc log vo '
e
vo’
SIVA
vo’+
Copyright©2001
Settlement computations ~ computing e using e-log v’ plot If the clay is overconsolidated, and remains so by the end of consolidation,
eo
vo ' ' e Cr log vo '
initial
e
note the use of Cr VCL vo’
SIVA
vo’+
Copyright©2001
Settlement computations ~ computing e using e-log v’ plot If an overconsolidated clay becomes normally consolidated by the end of consolidation,
eo
p' vo ' ' e Cr log Cc log vo ' p'
initial
e
VCL vo’
SIVA
p’
Copyright©2001
vo’+
Preloading
Preloading at West Kowloon Expressway, Hong Kong. (5-10 m embankments for 2-5 months)
SIVA
Copyright©2001
26
Preloading Piezometers measure pore pressures and thus indicate when the consolidation is over.
SIVA
Copyright©2001
27
Preloading
Cross section of PVD
Installation Prefabricated Vertical Drains to Accelerate Consolidation
SIVA
Copyright©2001
28
Prefabricated Vertical Drains
Installation of PVDs
SIVA
Copyright©2001
29
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