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1
Compressibility of Soil
ChihChih--Ping LinPing LinNational National ChiaoChiao TungTung [email protected]@mail.nctu.edu.tw
Soil Mechanics −
2
Outline
IntroductionIntroduction
Immediate SettlementImmediate Settlement
Primary Consolidation SettlementPrimary Consolidation SettlementConsolidation SettlementConsolidation Settlement
Consolidation RateConsolidation Rate
Secondary Consolidation SettlementSecondary Consolidation Settlement
3
δ versus δD
(a)Leaning Tower, Pisa
(b) Palacio de las BellasArtes, Mexico City
(The Palace of Fine Arts)
Introduction
4
Types of Settlements
Immediate (elastic) settlement (Immediate (elastic) settlement (SSee))
TimeTime--dependentdependentPrimary consolidation (Primary consolidation (SScc) ) transient pore transient pore pressurepressure
Secondary consolidation (Secondary consolidation (SSss) ) creepcreep
Total settlement STotal settlement STT==SScc+S+Sss+S+See
For soft soils (i.e., clays): SFor soft soils (i.e., clays): Scc>>S>>See>S>Ss s (Usually)(Usually)
Introduction
5
Contact Pressure and Settlement Profile
Immediate Settlement
Clay Sand
6
Theory of Elasticity
Immediate Settlement
Δσ
Es,μs
B
ps
se I
EBS
21 μσ
−Δ=
Influence Factor
(shape, position, foundation rigidity)
7
Improved Relationship for Se
EFGs
ee IIIE
BS0
21 μσ
−Δ= Foundation embedment
Foundation rigidity
Equivalent diameter
Immediate Settlement
8
©20
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Immediate Settlement
9
©20
01 B
rook
s/C
ole,
a d
ivis
ion
of T
hom
son
Lea
rnin
g, I
nc.
Tho
mso
n L
earn
ing ™
is a
trad
emar
k us
ed h
erei
n un
der
licen
se.
Immediate Settlement
10
©20
01 B
rook
s/C
ole,
a d
ivis
ion
of T
hom
son
Lea
rnin
g, I
nc.
Tho
mso
n L
earn
ing ™
is a
trad
emar
k us
ed h
erei
n un
der
licen
se.
Immediate Settlement
11
Fundamentals of ConsolidationConsolidation Settlement
Δu =Δσ
Δσ’=0
Δu =0
Δσ’= Δσ
12
Consolidation Settlement
13
Consolidation Settlement
14
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).
Consolidation Settlement
15
What is Consolidation?
This leads to settlements occurring over a long time,
which could be several years.
time
sett
lem
ent
Consolidation Settlement
16
In granular soils…
Granular soils are freely drained, and thus the settlement is instantaneous.
time
sett
lem
ent
Consolidation Settlement
17
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.
Δσ
Δu
Δσ’
..and, they vary with time.
Consolidation Settlement
18
During consolidation…
Δσ remains the same (=q) during consolidation.
GL
saturated clay
q kPa
A
Δσ
Δu
Δσ’
Δu decreases (due to drainage)
Δσ
Δu
Δσ’
q
transferring the load from water to the soil.while Δσ’ increases,
Consolidation Settlement
19
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
Consolidation Settlement
20
ΔH -Δe Relation
saturated clay
GL
q kPa
Ho
Time = 0+
e = eo
ΔH
saturated clay
GL
q kPa
Time = ∝
e = eo - Δe
average vertical strain = oH
HΔ
Consolidation Settlement
21
ΔH -Δe Relation
Consider an element where Vs = 1 initially.
Δe
1
eo
Time = 0+ Time = ∞
∴average vertical strain =oe
e
+Δ
1
Consolidation Settlement
22
ΔH -Δe Relation
Equating the two expressions for average vertical strain,
oe
e
+Δ
1=
Δ
oH
H
consolidation settlement
initial thickness of clay layer
initial void ratio
change in void ratio
Consolidation Settlement
23
Coefficient of volume compressibility
~ denoted by mv
~ is the volumetric strain in a clay element per unit increase in stress
volumeoriginal
volumein change=
σΔ
Δ= V
Vmv
i.e.,
no units
kPa or MPakPa-1 or MPa-1
Consolidation Settlement
Coefficient of compressibility
~ denoted by av = Δe/Δσ
24
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
Consolidation Settlement
25
Consolidation Test
ΔH1
Δq1
eo- Δe1
)1(11 o
o
eH
He +
Δ=Δ
eoHo
Δq2
loading in increments
=Δ 2e
allowing full consolidation before next increment
Consolidation Settlement
26
Consolidation Test
unloading
Consolidation Settlement
27
e – log σv’ plot
log σv’
void
rat
io loading
σv’ increases &
e decreasesunloading
σv’ decreases &
e increases (swelling)
- from the above data
Consolidation Settlement
28
Compression and recompression indices
log σv’
void
rat
io
1
Cc
Cc ~ compression index
Cr ~ recompression index(or swelling index)
1Cr
1Cr
Consolidation Settlement
Preconsolidation pressure
log σv’
void
rat
io
σp’preconsolidation pressure
is the maximum vertical effective stress the soil
element has everbeen subjected
to
Consolidation Settlement
30
Virgin Consolidation Line
log σv’
void
rat
io
virgin consolidation line
σp’σvo’
eo
eo, σvo’
original state
Consolidation Settlement
Overconsolidation ratio (OCR)
log σv’
void
rat
io
virgin consolidation line
σp’σvo’
eo
original state
Field
σvo’
'
'
vo
pOCRσσ
=
Consolidation Settlement
32
Consolidation Settlement
δ-logt or e-logt plot for each loading step
33
e-logσ’ plot for all loading steps
Consolidation Settlement
34
Determining Cc, Cr, Preconsolidation Pressure
Casagrande’s Method
Consolidation Settlement
35
Effect of Disturbance
Normally consolidatedClay of low to mediumplasticity
Consolidation Settlement
36
Effect of Disturbance
Over-consolidatedClay of low to mediumplasticity
Consolidation Settlement
37
Calculating Consolidation Settlement
Consolidation Settlement
Settlement computations
eo, σvo’, Cc, Cr, σp’, mv-oedometer
test
Δσ=q
q kPa
H
Two different ways to estimate the consolidation settlement:
(a) using mv
(b) using e-log σv’ plot
settlement = mv Δσ H
He
esettlement
o+Δ
=1
next slide
Consolidation Settlement
Settlement computations
~ computing Δe using e-log σv’ plot
'
''log
vo
vocCe
σσσ Δ+
=Δ
initial
σvo’
eo
σvo’+ Δσ
Δe
If the clay is normally consolidated,
the entire loading path is along the VCL.
Consolidation Settlement
Settlement computations
~ computing Δe using e-log σv’ plot
'
''log
vo
vorCe
σσσ Δ+
=Δ
σvo’
initialeo
σvo’+ Δσ
If the clay is overconsolidated, and remains so by the end of consolidation,
Δe
VCL
note the use of Cr
Consolidation Settlement
Settlement computations
~ computing Δe using e-log σv’ plot
'
''log
'
'log
p
voc
vo
pr CCe
σσσ
σσ Δ+
+=Δ
σvo’
initialeo
σvo’+ Δσ
If an overconsolidated clay becomes normally consolidated by the end of consolidation,
VCL
σp’
Δe
Consolidation Settlement
42
Calculation of Consolidation Settlement under a Foudation
Consolidation Settlement
43
More to come…
44
Time Rate of Consolidation
Consolidation Rate
45
Governing Eqn
Consolidation Rate
46
Consolidation Rate
47
Solution of Consolidation Equation
Consolidation Rate
48
Consolidation Rate
49
Consolidation Rate
50
Consolidation Rate
51
Consolidation Rate
52
Determining Cv (logarithmic method)
Consolidation Rate
53
Determining Cv (square root method)
Consolidation Rate
54
Secondary consolidation
Secondary Consolidation Settlement
55