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Go back to BasicAssessment of Soil Stiffness

byIr. Chua Chai Guan

IEM Evening Talk on 18 Oct 2012


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Presentation Outlines

1. Definition of soil stiffness

2. Assessment of basic soil properties

3. Assessment of soil stiffness from laboratory testing

4. Non-linear soil stiffness

5. Conclusions


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Definition of Soil Stiffness


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Definition of Stress & Strain

Normal Stress

Shear Stress

Volumetric Strain

Shear Strain


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Definition of Stiffness Stress-Strain Behaviour

Hookes Law ofIsotropic Elasticity


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Typical Stress-Strain Curve For Soil & Definition ofTangent and Secant Modulus

During loading in soils, both shear and normal stresses are

likely to change simultaneously so there will be shearing

and volumetric straining together. The behaviour of stress-strain for soil is largely non-linear stiffness.


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Basic of Partial Safety Factor Limit Strain for AMobilized Strength

(after Bolton, 1993)


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Grading Curve for Particle Size Distribution


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Classification of Coarse and Fine Soils(BS5950:1981)

% of clay & silts < 35%

% of clay & silts >= 35%

Coarse Soils

Fine Soils


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1st Question to Audiences:

% of clay & silts < 35%

% of clay & silts >= 35%

Coarse Soils

Fine Soils

Is 35% (after omitting boulder and

cobbles) of boundary used to

divide coarse and fine soils

appropriate?


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Differentiate SILT and CLAY using PI Chart

PI = 0.73(LL-20)


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Water Content and Unit Weight

- The most convenient measureable parameters are water content

(w) and unit weight ()

- e = wGs for saturated soils and Gs is specific gravity (~2.65 for quartz

sand)

= (Gs+e)/(1+e)w for saturated soils

- Important mechanical properties to tell-tale the soil compressibility


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Differences of Coarse-Grained and Fine-Grained Soils

- The specific surface of clays is minimum 50,000 time more

than sands

- Fine-grained soils show significant volume changes as the

loading and water content changes

- Effects of surface forces are relatively important for fine-

rained soils

Activity=

PI/(% by weight of

clay)

Self-weight force

Inter-particleforce on contact

area


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Packing of Coarse-Grained Soils

Cubic Array

n =0.47

Densest array

n =0.25

- Specific volume (v)= V/Vs

where V = the volume of a sample containing a volume Vs of soil grains

- Void ratio (e) where e =Vw/Vs for saturated soil, v= 1+e

- Porosity = Vw/V for saturated soil

Coarse-grained soils

consistency

Dr e n kN/m

3

v.loose 0.2 1.13 0.53 17.7

loose 0.4 0.93 0.48 18.5

m.dense 0.6 0.73 0.42 19.5

dense 0.8 0.53 0.35 20.8

v.dense >0.8


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Type of soils specific vol void ratio porosity unit weight

v e n

kN/m3

montmorillonite 10 9 0.9 11.7

Kaolin 3 2 0.7 15.5

Range of Specific Volume for Fine-Grained Soils

Under large loads, the specific volume of clay soils may be reduced to as little as v=

1.2 as the flat clay plate become nearly parallel


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Atterberg Limits Basic Behaviour of Fine-GrainedSoil

Liquid limit determines thewater content at which the soil

has weakened so much it starts

to flow like a liquid

Plastic limit determines the

water content at which the soil

has become so brittle that it

crumbles


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Limits of Consistency for Soils


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Generalized Stress-Strain Response for VariousStates of a Soil

LI < 0

Brittle Solid or

Semi Solid

0 < LI < 1

Plastic Solid

LI > 0

Liquid


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Consistency of Fine-Grained Soils

Consistency Identification UndrainedStrength

cu, kPa

SPT N, blowcounts/30cm

Very soft Extrudes between fingers < 20 0 2

Soft Easily moulded in fingers 20 40 2- 4

Firm Moulded by strong finger

pressure

40-75 4- 8

Stiff Cannot be moulded in

fingers

75-100 8-15

Very Stiff Brittle and very tough > 150 15 - 30

w LL & LI = 1, cu ~ 1.5kPa and

w PL & LI = 0, cu ~ 150kPa


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Example of Good Presentation of Subsoil Profile

(After Lehane 2003)

35%


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Ground Water Table from Water Stand Pipe

Monitor the Fluctuation of Water Table


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Summary of Basic Information Required ForAssessment of Soil Stiffness

Information Required Basic Properties

Soil Types Fine-grained & coarse-grained

Particle Size Distribution Dominant grain size/Soil origin

Unit Weight & Specific Gravity Stress Profile and Void Ratio & SoilConsistency

Moisture Content Void Ratio and Soil States

Atterberg Limit LL, PL and PI, LI & Soil Consistency

Ground Water Table Stress Profile & Max Stress


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Assessment of Soil Stiffness from Laboratory


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Constrained Modulus Eoed from Oedometer


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(After Janbu 1963)

Typical Range of Eoed for Primary Loading of NC Soils

m = 0.5 for SAND

= 0.75 for SILT

= 1 for CLAY


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Eoed for Primary Loading from Porosity of NC Soils

eo ~ wGs where w = natural moisture content

Gs= specific gravity = 2.65~2.7

n = e/(1+e)


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Eoed for Primary Loading of Coarse-Grained Soils

(After Von Sooss 2002)

Eoedref = 60IDMPa

emax = 1.3

emin =0.3


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Eoed for Primary Loading from Liquid Limit (Fine-Grained Soil)

(After Engel 2001)

cc = 0.9(wL-0.1) by Terzaghi & Peck 1967

Eoedref = 230(1+eo)/cc

1+eo ~ 2.0


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(After Kulhawy and Mayne 1990)

Compression Index (cc and cr) vs PI

cc =(PIxGs)/200 ~ PI/74(after Atkinson,1993)

cs ~ 5cc

Eoedur ~ 5Eoed


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Modulus E50 from Drained Triaxial Test


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Modulus E50 using Janbu Formula

E50 =E50ref

m = 0.5 for SAND

= 0.75 for SILT

= 1 for CLAY


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Relationship Between E50ref and Eoedref

E50 =E50ref

Eoed =Eoedref

=

1

1 1 2

50

1

1 21

1

SAND m= 0.5

v ((1-v)/v)^0.5 (1-v)/((1-2v)(1+v)) Eref

50/Eref

oed

0.2 2.00 1.11 1.80

0.25 1.73 1.20 1.44

0.3 1.53 1.35 1.13

0.33 1.41 1.50 0.94

0.35 1.36 1.60 0.85

0.4 1.22 2.14 0.57

0.45 1.11 3.79 0.29

0.49 1.02 17.11 0.06

SILT m=0.75

v ((1-v)/v)^0.75 (1-v)/((1-2v)(1+v)) Eref

50/Eref

oed

0.2 2.83 1.11 2.55

0.25 2.28 1.20 1.90

0.3 1.89 1.35 1.40

0.33 1.68 1.50 1.12

0.35 1.59 1.60 0.99

0.4 1.36 2.14 0.63

0.45 1.16 3.79 0.31

0.49 1.03 17.11 0.06

CLAY m =1

v ((1-v)/v) (1-v)/((1-2v)(1+v)) Eref

50/Eref

oed

0.2 4.00 1.11 3.60

0.25 3.00 1.20 2.50

0.3 2.33 1.35 1.73

0.33 2.00 1.50 1.33

0.35 1.86 1.60 1.16

0.4 1.50 2.14 0.700.45 1.22 3.79 0.32

0.49 1.04 17.11 0.06


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Modulus E50u from Undrained Triaxial Test

Eu

50= 3G

50

E50u

E50u =200cu ifvf= 1%


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Modulus E50u from Cu and Plasticity Index

Eu50

=15000Cu

Ip%

For NC Clays


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Eu50

=15000Cu

Ip%

For NC Clays

2nd Question to Audiences:

Is Eu50 a stress-dependent parameter ?


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Summary for Soil Stiffness Assessment fromLaboratory Test

- Always be coupled with the knowledge of basic soil

properties, particularly on moisture content &stress level & plasticity index (for fine-grained soil)

- Loading and unloading steps are equally important

- Cross-check using different tests e.g. Oedometerand Drained Triaxial Test or Undrained Triaxial Test

- Cross- reference with typical range of soil stiffnessfor various soil types


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Non-Linear Soil Stiffness


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Soil Stiffness Non-linear Stress-Strain Behaviour

(after Atkinson, 2000)

Soils are packed withcollection of grainswith grading,mineralogy, shape andtexture.


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Soil Stiffness Yielding and Plastic Straining

e p

p related to y by hardening law



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Soil Stiffness Rigidity and Non-linearity


-Rigidity = Eo/qf =1/ r

-Non-linearity = f/ r

- r is a reference strain

Soil stiffness is principally related topeak strength and both of themincrease with effective stress andoverconsolidation


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Rigidity and Non-linearity for some commonmaterials


Rigidity Non-linearity


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Characteristic Stiffness-Strain Behaviour


(after Atkinson & Sallfors, 1991 and Mair , 1993)

very small strain

small strain

large strain


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Variation of Stiffness with Strain, Stress & OCR

(after Atkinson 1993)

(State parameters A, n, m varies for different soils


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Variation of Stiffness with State Parameters forReconstituted Kaolin Clay

(after Viggiani & Atkinson 1995)

n = 0.65

A=2000

m=0.2


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Variation of Stiffness with State Parameters forCarbonate Sand

(after Jovi i & Coop, 1997)

n = 0.58

A=4000


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Material Parameters for Go

(after Viggiani & Atkinson 1995)

All these parameters A, n& mare related to plasticity index


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Typical Values of Strength and Stiffness of Soils

(after Tatsuoko & Shibuya, 1992)

All these parameters A, n& mare related to plasticity index

80MPa

600MPa

80kPa 400kPa


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Variation of rigidity with state and plasticity index



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Variation of Failure Strain with State



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Non-linear Stress-Strain Expression for Soils

(after Georgiannou et al. 1991, Coop et al. 1997, Cuccovillo & Coop 1997 &

Atkinson 2000)

1

1

o = 0.0005% for low plasticity silts

o = 0.005% for high plasticity clays

o = 0.0001% for unbonded coarse grained soils

o = 0.02% for bonded soils and soft rocks

r = 0.1 to 0.5

o = 0.001%

= 0.1%

Es/Eo = 0.2

Es/Eo = 0.5


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Variation of Es/Eowith rigidity and non-linearity

(after Atkinson 2000)

= 0.1%

Es/Eo = 0.5

Es/Eo = 0.2


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Application of Non-Linear Stiffness for Design


(Settlement of model foundation onsands and clay)

(Stiffness-strain curve from triaxial)


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Summary for Non-linear Soil Stiffness

- Soil stress-strain behaviour is highly non-linear

- Non-linear behaviour can be characterized byrigidity and degree of non-linearity

- Very small strain-stiffness is measurable from fieldshear wave velocity or bender element test

- Peak strength and failure strain measurable fromroutine laboratory test

- Stiffness is related to its composition and to its

current state


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Conclusions

- The objectives of assessment for soil stiffness should be clear

particularly for the range of strain level for the targetedapplication (dynamic or static, small strain or large deformation)

- Basic information e.g. particle composition, unit weight, moisturecontent, Atterberg limits and fluctuation of ground water tableshould be gathered for the assessment of soil stiffness

- Always cross-check the measured soil stiffness using differenttests or correlation to basic soil properties


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Thank You for Your Attention

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