Soil Mechanics − Outline

Transcription

Soil Mechanics −
Compressibility of Soil
Chih-Ping Lin
National Chiao Tung Univ.
[email protected]
1
Outline
Introduction
Immediate Settlement
Primary Consolidation Settlement

Consolidation Settlement
Consolidation Rate

Secondary Consolidation Settlement
2
Introduction
δ versus δD
(a)Leaning Tower, Pisa
(b) Palacio de las Bellas
Artes, Mexico City
(The Palace of Fine Arts)
3
Introduction
Types of Settlements
Immediate (elastic) settlement (Se)
Time-dependent

Primary consolidation (Sc) Å transient pore
pressure
Secondary consolidation (Ss) Å creep
Total settlement ST=Sc+Ss+Se
For soft soils (i.e., clays): Sc>>Se>Ss (Usually)

4
Contact Pressure and Settlement Profile
Sand
Clay
5
Theory of Elasticity
B
Δσ
1 − μ s2
S e = ΔσB
Ip
Es
Es,μs
Influence Factor
(shape, position, foundation rigidity)
6
Improved Relationship for Se
Equivalent diameter
Foundation embedment
Foundation rigidity
7
©2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
1 − μ s2
S e = ΔσBe
IG I F I E
E0
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9
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Fundamentals of Consolidation
Δu =Δσ
Δσ’=0
Δu =0
Δσ’= Δσ
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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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What is Consolidation?
settlement
This leads to settlements occurring over a long time,
time
which could be several years.
15
In granular soils…
settlement
Granular soils are freely drained, and thus the
settlement is instantaneous.
time
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During consolidation…
Due to a surcharge q applied at the GL,
the stresses and pore pressures are increased at A.
q kPa
Δσ
A
..and, they vary
with time.
GL
Δu
Δσ’
saturated clay
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During consolidation…
Δσ remains the same (=q) during consolidation.
Δu decreases (due to drainage) while Δσ’ increases,
transferring the load from water to the soil.
Δσ
q kPa
Δσ
A
GL
Δu
Δσ’
Δu
Δσ’
saturated clay
q
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One Dimensional Consolidation
~ drainage and deformations are vertical (none laterally)
~ a simplification for solving consolidation problems
q kPa
GL
water squeezed out
reasonable
simplification if the
surcharge is of
large lateral extent
saturated clay
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ΔH -Δe Relation
average vertical strain =
ΔH
Ho
q kPa
GL
saturated clay
e = eo
Time = 0+
ΔH
q kPa
GL
Ho
saturated clay
e = eo - Δe
Time = ∝
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ΔH -Δe Relation
Consider an element where Vs = 1 initially.
Δe
eo
1
Time = 0+
Time = ∞
∴average vertical strain =
Δe
1 + eo
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ΔH -Δe Relation
Equating the two expressions for average
vertical strain,
consolidation
settlement
initial thickness of
clay layer
change in void ratio
ΔH
Δe
=
Ho
1 + eo
initial void ratio
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Coefficient of compressibility
~ denoted by av = Δe/Δσ
Coefficient of volume compressibility
~ denoted by mv
~ is the volumetric strain in a clay element per
no units
unit increase in stress
=
change in volume
original volume
i.e.,
mv =
ΔV
V
Δσ
kPa-1 or MPa-1
kPa or MPa
23
Consolidation Test
~ simulation of 1-D field consolidation in lab.
GL
porous stone
undisturbed soil
specimen
metal ring
(oedometer)
Dia = 50-75 mm
Height = 20-30 mm
field
lab
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Consolidation Test
loading in increments
allowing full consolidation before next increment
Δq1
Δq2
ΔH1
eo- Δe1
Ho eo
Δe1 =
ΔH 1
(1 + eo )
Ho
Δe2 =
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Consolidation Test
unloading
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e – log σv’ plot
- from the above data
void ratio
loading
σv’ increases &
e decreases
unloading
σv’ decreases &
e increases (swelling)
log σv’
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Compression and recompression indices
Cr
void ratio
1
Cc ~ compression index
Cc
Cr ~ recompression index
1
(or swelling index)
Cr
1
log σv’
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Preconsolidation pressure
void ratio
is the maximum
vertical effective
stress the soil
element has ever
been subjected
to
preconsolidation pressure
σp’
log σv’
Virgin Consolidation Line
original
state
void ratio
eo
virgin consolidation line
eo, σvo’
σvo’
σp’
log σv’
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Overconsolidation ratio (OCR)
original
state
σvo’
Field
void ratio
eo
virgin consolidation line
σ p'
OCR =
σ vo '
σvo’
σp’
log σv’
δ-logt or e-logt plot for each loading step
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e-logσ’ plot for all loading steps
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Determining Cc, Cr, Preconsolidation Pressure
Casagrande’s Method
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Effect of Disturbance
Normally consolidated
Clay of low to medium
plasticity
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Effect of Disturbance
Over-consolidated
Clay of low to medium
plasticity
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Calculating Consolidation Settlement
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Settlement computations
Two different ways to estimate the
consolidation settlement:
q kPa
(a) using mv
settlement = mv Δσ H
H
Δσ=q
(b) using e-log σv’ plot
next slide
eo, σvo’, Cc,
Cr, σp’, mv
-oedometer
test
settlement =
Δe
H
1 + eo
~ computing Δe using e-log σv’ plot
If the clay is normally consolidated,
the entire loading path is along the VCL.
initial
eo
σ vo '+ Δσ '
Δe = Cc log
σ vo '
Δe
σvo’
σvo’+ Δσ
If the clay is overconsolidated, and remains so by
the end of consolidation,
eo
σ vo '+ Δσ '
Δe = Cr log
σ vo '
initial
Δe
note the use of Cr
VCL
σvo’
σvo’+ Δσ
If an overconsolidated clay becomes normally
consolidated by the end of consolidation,
eo
σ p'
σ vo '+ Δσ '
Δe = Cr log
+ Cc log
σ vo '
σ p'
initial
Δe
VCL
σvo’
σp ’
σvo’+ Δσ
Calculation of Consolidation Settlement
under a Foudation
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More to come…
43
Consolidation Rate
Time Rate of Consolidation
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Consolidation Rate
Governing Eqn
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Consolidation Rate
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Consolidation Rate
Solution of Consolidation Equation
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Consolidation Rate
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Consolidation Rate
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Consolidation Rate
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Consolidation Rate
51
Consolidation Rate
Determining Cv (logarithmic method)
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Consolidation Rate
Determining Cv (square root method)
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Secondary Consolidation Settlement
Secondary consolidation
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Soil Mechanics − Outline

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