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Consolidation of Clays
N. Sivakugan
Duration: 17 minutes
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What is Consolidation?
When a saturated clay is loaded externally,
saturated clay
GL
the water is squeezed out of the clay over a long time (due to low permeability of the clay).
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What is Consolidation?
This leads to settlements occurring over a long time,
which could be several years.
time
settl
emen
t
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In granular soils…
Granular soils are freely drained, and thus the settlement is instantaneous.
time
settl
emen
t
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During consolidation…
Due to a surcharge q applied at the GL,
GL
saturated clay
q kPa
A
the stresses and pore pressures are increased at A.
∆σ
∆u
∆σ ’
..and, they vary with time.
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During consolidation…
∆σ remains the same (=q) during consolidation.
GL
saturated clay
q kPa
A
∆σ
∆u
∆σ ’
∆u decreases (due to drainage)
∆σ
∆u
∆σ’
q
transferring the load from water to the soil. while ∆σ’ increases,
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One Dimensional Consolidation
~ drainage and deformations are vertical (none laterally)
saturated clay
GL
q kPa
~ a simplification for solving consolidation problems
reasonable simplification if the
surcharge is of large lateral extent
water squeezed out
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∆H -∆e Relation
saturated clay
GL
q kPa
saturated clay
GLq kPa
Ho
Time = 0+
e = eo
∆H
Time = ∝
e = eo - ∆e
average vertical strain = oH
H∆
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∆H -∆e Relation
Consider an element where Vs = 1 initially.
∆e
1
eo
Time = 0+ Time = ∞
∴average vertical strain =oe
e
+∆
1
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∆H -∆e Relation
Equating the two expressions for average vertical strain,
oe
e
+∆
1=∆
oH
H
consolidation settlement
initial thickness of clay layer
initial void ratio
change in void ratio
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Coefficient of volume compressibility
~ denoted by mv
~ is the volumetric strain in a clay element per unit increase in stress
volumeoriginal
volumein change=
σ∆
∆= VV
mvi.e.,
no units
kPa or MPakPa -1 or MPa -1
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Consolidation Test
~ simulation of 1-D field consolidation in lab.
field
GL
lab
undisturbed soil specimen
Dia = 50-75 mm
Height = 20-30 mm
metal ring(oedometer)
porous stone
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Consolidation Test
∆H1
∆q1
eo- ∆e1
)1(11 o
o
eH
He +∆=∆
eoHo
∆q2
loading in increments
=∆ 2e
allowing full consolidation before next increment
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Consolidation Test
unloading
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e – log σv’ plot
log σv’
void
ratio
loading
σv’ increases &
e decreasesunloading
σv’ decreases &
e increases (swelling)
- from the above data
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Compression and recompression indices
log σv’
void
ratio
1
Cc
Cc ~ compression index
Cr ~ recompression index (or swelling index)
1C r
1Cr
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Preconsolidation pressure
log σv’
void
ratio
σp’preconsolidation pressure
is the maximum vertical effective stress the soil element has ever been
subjected to
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Virgin Consolidation Line
log σv’
void
ratio
virgin consolidation line
σp’σvo’
eo
eo, σvo’
original state
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Overconsolidation ratio (OCR)
log σv’
void
ratio
virgin consolidation line
σp’σvo’
eo
original state
Field
σvo’'
'
vo
pOCRσσ
=
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Overconsolidation ratio (OCR)
log σv’
void
ratio
OCR=1
OCR=2
OCR=2
OCR=13
OCR=13
~current state
VCL
Normally consolidated
clay
Slightly overconsolidated clay
Heavily overconsolidated clay
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More to come…
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Settlement computations
eo, σvo’ , Cc, C r, σp’ , mv
-oedometer test
∆σ=q
q kPa
H
Two different ways to estimate the consolidation settlement:
(a) using mv
(b) using e-log σv’ plot
settlement = mv ∆σ H
He
esettlement
o+∆=1
next slide
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Settlement computations~ computing ∆e using e-log σv’ plot
'
''log
vo
vocCe
σσσ ∆+=∆
initial
σvo’
eo
σvo’+ ∆σ
∆e
If the clay is normally consolidated,
the entire loading path is along the VCL.
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Settlement computations~ computing ∆e using e-log σv’ plot
'
''log
vo
vorCe
σσσ ∆+=∆
σvo’
initialeo
σvo’+ ∆σ
If the clay is overconsolidated, and remains so by the end of consolidation,
∆e
VCL
note the use of Cr
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Settlement computations~ computing ∆e using e-log σv’ plot
'
''log
'
'log
p
voc
vo
pr CCe
σσσ
σσ ∆++=∆
σvo’
initialeo
σvo’+ ∆σ
If an overconsolidated clay becomes normally consolidated by the end of consolidation,
VCL
σp’
∆e
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Preloading
Preloading at West Kowloon Expressway, Hong Kong.(5-10 m embankments for 2-5 months)
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PreloadingPiezometers measure pore pressures and thus indicate when the consolidation is over.
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Preloading
Prefabricated Vertical Drains to Accelerate Consolidation
Installation
Cross section of PVD
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Prefabricated Vertical Drains
Installation of PVDs