Soil Mechanics − Outline

1

Compressibility of Soil

ChihChih--Ping LinPing LinNational National ChiaoChiao TungTung Univ.Univ.cplin@mail.nctu.edu.twcplin@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

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Immediate Settlement

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Immediate Settlement

10

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Immediate Settlement

11

Fundamentals of ConsolidationConsolidation Settlement

Δu =Δσ

Δσ’=0

Δu =0

Δσ’= Δσ

12

Consolidation Settlement

13

Consolidation Settlement

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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).

Consolidation Settlement

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What is Consolidation?

This leads to settlements occurring over a long time,

which could be several years.

time

sett

lem

ent

Consolidation Settlement

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In granular soils…

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

time

sett

lem

ent

Consolidation Settlement

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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.

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

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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=

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

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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

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Consolidation Test

unloading

Consolidation Settlement

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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

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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

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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

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e-logσ’ plot for all loading steps

Consolidation Settlement

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Determining Cc, Cr, Preconsolidation Pressure

Casagrande’s Method

Consolidation Settlement

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Effect of Disturbance

Normally consolidatedClay of low to mediumplasticity

Consolidation Settlement

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Effect of Disturbance

Over-consolidatedClay of low to mediumplasticity

Consolidation Settlement

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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

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More to come…

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Time Rate of Consolidation

Consolidation Rate

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Governing Eqn

Consolidation Rate

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Consolidation Rate

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Solution of Consolidation Equation

Consolidation Rate

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Consolidation Rate

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Consolidation Rate

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Consolidation Rate

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Consolidation Rate

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Determining Cv (logarithmic method)

Consolidation Rate

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Determining Cv (square root method)

Consolidation Rate

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Secondary consolidation

Secondary Consolidation Settlement

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