Context From reality to laboratory From laboratory to numerical modelling Conclusion

Cyclic behaviour of cohesionless soils under seismicloading

Cerfontaine Benjamin - Boursier FRIA

University of Liege - GEO3

February 2012

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Don’t forget the soil !

Outline

1 ContextDon’t forget the soil !

2 From reality to laboratoryEquivalence in-situ/triaxial testMonotonic behaviour charaterizationCyclic behaviour characterization

3 From laboratory to numerical modellingSummaryPrevost’s model

4 Conclusion

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Don’t forget the soil !

Nigata, 1964

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Don’t forget the soil !

Kobe, 1995

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Don’t forget the soil !

San Fernando dam, 1971

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Don’t forget the soil !

Soil-structure interaction

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Equivalence in-situ/triaxial test

Outline

1 ContextDon’t forget the soil !

2 From reality to laboratoryEquivalence in-situ/triaxial testMonotonic behaviour charaterizationCyclic behaviour characterization

3 From laboratory to numerical modellingSummaryPrevost’s model

4 Conclusion

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Equivalence in-situ/triaxial test

Stress state in the soil

Ground

Ground Water Table

σ'=σv

K0σv

before earthquake

σ3

shea

r s

tres

s

normal stress

K0=1

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Equivalence in-situ/triaxial test

Stress state in the soil

Ground

Ground Water Table

σ'=σv

K0σv

σ'=σv

K0σv

τhσ'=σv

K0σv

τh

during earthquakebefore earthquake

σ3σv

R

τh

-τh

K0=1

shea

r s

tres

s

shea

r s

tres

s

normal stress

normal stress

K0=1

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Equivalence in-situ/triaxial test

Stress state in laboratory

Essai triaxial :

• compresssion/extension

• monotonic/cyclic

• drained/undrained

And also :

• simple shear

• torsional shear test

σ1

σ3

σ2=σ3

σ1-σ3

σ3 u

u

u

NT

u

torque

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Equivalence in-situ/triaxial test

Stress state in laboratory

Essai triaxial :

• compresssion/extension

• monotonic/cyclic

• drained/undrained

And also :

• simple shear

• torsional shear test

σ1

σ3

σ2=σ3

σ1-σ3

σ3 u

u

u

NT

u

torque

9/26

Context From reality to laboratory From laboratory to numerical modelling Conclusion

Equivalence in-situ/triaxial test

Stress state in laboratory

Essai triaxial :

• compresssion/extension

• monotonic/cyclic

• drained/undrained

And also :

• simple shear

• torsional shear test

σ1

σ3

σ2=σ3

σ1-σ3

σ3 u

u

u

NT

u

torque

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Equivalence in-situ/triaxial test

Stress state in a triaxial test

σ'=σv

K0σv

τhσ'=σv

K0σv

τh

during earthquake

σv

R

τh

-τh

K0=1

shea

r s

tres

s

normal stress

X Y

45° 45°

σ3+1/2σd

σ3 σ3σ3-1/2σd

1/2σd 1/2σd

σ3+1/2σd

σ3-1/2σd

R45°

X

XY

Y

XX

+1/2σd

YY

-1/2σd

σ3

shea

r s

tres

s

normal stress

45° 45°

σ3-1/2σd

σ3 σ3σ3+1/2σd

1/2σd 1/2σd

σ3+1/2σd

σ3-1/2σd R45°

X

XY

YXX

+1/2σd

YY

-1/2σd

σ3

shea

r s

tres

s

normal stress

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Monotonic behaviour charaterization

Outline

1 ContextDon’t forget the soil !

2 From reality to laboratoryEquivalence in-situ/triaxial testMonotonic behaviour charaterizationCyclic behaviour characterization

3 From laboratory to numerical modellingSummaryPrevost’s model

4 Conclusion

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Monotonic behaviour charaterization

Monotonic undrained test

Steady State :

• continuous deformation

• constant p’

• constant q

• constant velocity

Contractancy : ∆V < 0under shearing

(a) (b)

Dev

iato

ric s

tres

s q

Effective mean stress p'

Dev

iato

ric s

tres

s q

Axial strain εa

PT line

Steady StateSSS

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Monotonic behaviour charaterization

Monotonic undrained test

Quasi Steady State :

• transient state

• p’ minimum

• q minimum

Contractancy : ∆V < 0under shearing

(a) (b)

Effective mean stress p' Axial strain εa

Dev

iato

ric s

tres

s q

Effective mean stress p'

Dev

iato

ric s

tres

s q

Axial strain εa

PT line

Steady State

Quasi Steady StateSQSS

SSS

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Monotonic behaviour charaterization

Monotonic undrained test

Dilative state

• strain hardening

• no instability

Dilatancy : ∆V > 0under shearing

(a) (b)

Dev

iato

ric s

tres

s q

Effective mean stress p'

Dev

iato

ric s

tres

s q

Axial strain εa

PT line

Steady State

Quasi Steady StateSQSS

SSS

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Monotonic behaviour charaterization

Triaxial undrained test examples (1)

Deformation controlled triaxial undrained tests : Toyoura sand[Verdugo and Ishihara, 1996]Dr = 18.5%

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Monotonic behaviour charaterization

Triaxial undrained test examples (1)

Deformation controlled triaxial undrained tests : Toyoura sand[Verdugo and Ishihara, 1996]

Dr = 18.5% Dr = 37.9%

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Monotonic behaviour charaterization

Triaxial undrained test examples (1)

Deformation controlled triaxial undrained tests : Toyoura sand[Verdugo and Ishihara, 1996]

Dr = 18.5% Dr = 37.9% Dr = 63.7%

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Monotonic behaviour charaterization

Triaxial undrained test examples (2)

Loose Toyoura sand [Hyodo and al., 1994]

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Cyclic behaviour characterization

Outline

1 ContextDon’t forget the soil !

2 From reality to laboratoryEquivalence in-situ/triaxial testMonotonic behaviour charaterizationCyclic behaviour characterization

3 From laboratory to numerical modellingSummaryPrevost’s model

4 Conclusion

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Cyclic behaviour characterization

The cyclic triaxial test

load/deformationcontrolled

drained/undrained

until failure : liquefactionor not

q

t

qs

qcycl

qsqcycl

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Cyclic behaviour characterization

The cyclic triaxial test

load/deformationcontrolled

drained/undrained

until failure : liquefactionor not

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Cyclic behaviour characterization

The cyclic triaxial test

load/deformationcontrolled

drained/undrained

until failure : liquefactionor not

Liquefaction failure (general term)

Liquefaction and liquefaction failures encompass all phenomenainvolving excessive deformations of saturated cohesionless soils.

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Cyclic behaviour characterization

Cyclic behaviour

after [Hyodo and al. 1994]q

p'

q

εa

q

εa

q

p'

Dr=50%Dr=70%Dr=50%Dr=50%

Initial liquefaction

Transient state when the soil sample is submitted to zero meaneffective stress (u = pconf ) and zero deviatoric stress for the firsttime. This phenomenon involves very large deformations.

Liquefaction (specific term)

True liquefaction occurs when the soil reaches the steady state anddeforms continuously.

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Cyclic behaviour characterization

Cyclic behaviour

after [Hyodo and al. 1994]q

εa

q q

p' p'

Dr=50%Dr=70%Dr=50%Dr=50%

Cyclic mobility

The cyclic mobility denotes the undrained cyclic soil responsewhere the soil undergoes strain softening which is mainly aconsequence of the build up of pore water pressure.

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Cyclic behaviour characterization

Cyclic behaviour

after [Hyodo and al. 1994]

flowq

p'

FL

FL

flow

Δu

time

flow

εa

time

loose sand

εaq

p'

qs

0flow

flow

flowΔu

timetime

loose sand

Flow deformation

Flow deformation is an instability characterized by a quickdevelopment of strain and pore pressure. If after this phenomenon,the strain increases slowly again, this behaviour is called limiteddeformation.

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Cyclic behaviour characterization

Flow deformation

Structural collapse

In a loose sand in undrained conditions, the structural collapse isthe specific response of the loose structure which is exhibited asvigorous pore pressure generation.

Arc

grosse

(a)

cavité

Metastable structure

1

3

X

E

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Cyclic behaviour characterization

Flow deformation

Structural collapse

In a loose sand in undrained conditions, the structural collapse isthe specific response of the loose structure which is exhibited asvigorous pore pressure generation.

Arc

grosse

(a) (b)

cavité

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Cyclic behaviour characterization

Flow deformation

Structural collapse

In a loose sand in undrained conditions, the structural collapse isthe specific response of the loose structure which is exhibited asvigorous pore pressure generation.

Arc

grosse

(a) (b) (c)

cavité

V=cste

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Cyclic behaviour characterization

Flow deformation

Structural collapse

In a loose sand in undrained conditions, the structural collapse isthe specific response of the loose structure which is exhibited asvigorous pore pressure generation.

FL PT

FL PT

qcycl

qs

SPT

SPT

q=σa-σr

p'=(σ'a+2σ'r)/3

FL PT

FL PT

qcycl

qsSPT

SPT

q=σa-σr

p'=(σ'a+2σ'r)/3

(a) (b)

after [Hyodo and al., 1994]18/26

Context From reality to laboratory From laboratory to numerical modelling Conclusion

Cyclic behaviour characterization

Flow deformation examples

[Vaid and al., 2001]

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Summary

Outline

1 ContextDon’t forget the soil !

2 From reality to laboratoryEquivalence in-situ/triaxial testMonotonic behaviour charaterizationCyclic behaviour characterization

3 From laboratory to numerical modellingSummaryPrevost’s model

4 Conclusion

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Summary

The model has to take intoaccount :

the contractive/dilativetransition and softening ;

the pore pressure buildup ;

the different modes offailure ;

the failure anisotropy ;

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Summary

The model has to take intoaccount :

the contractive/dilativetransition and softening ;

the pore pressure buildup ;

the different modes offailure ;

the failure anisotropy ;

[Alarcon-Guzman and al.,1988]

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Summary

The model has to take intoaccount :

the contractive/dilativetransition and softening ;

the pore pressure buildup ;

the different modes offailure ;

the failure anisotropy ;

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Summary

The model has to take intoaccount :

the contractive/dilativetransition and softening ;

the pore pressure buildup ;

the different modes offailure ;

the failure anisotropy ;

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Prevost’s model

Outline

1 ContextDon’t forget the soil !

2 From reality to laboratoryEquivalence in-situ/triaxial testMonotonic behaviour charaterizationCyclic behaviour characterization

3 From laboratory to numerical modellingSummaryPrevost’s model

4 Conclusion

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Prevost’s model

Characterization

N nested conical yield surfaces associated with H’, M, α ;Kinematic hardening in the stress-space ;Calibration using monotonic triaxial tests ;Non-associative volumic plastic potentialSophistication : p’ dependency, Lode angle dependency, ...

σ'1

σ'1σ'3

p'00 0

p'

(p'+p')α

σ'132

σ'232

σ'332

after [Yang ,Elgamal and Parra, 2003]23/26

Context From reality to laboratory From laboratory to numerical modelling Conclusion

Prevost’s model

Characterization

N nested conical yield surfaces associated with H’, M, α ;Kinematic hardening in the stress-space ;Calibration using monotonic triaxial tests ;Non-associative volumic plastic potentialSophistication : p’ dependency, Lode angle dependency, ...

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Prevost’s model

Characterization

N nested conical yield surfaces associated with H’, M, α ;Kinematic hardening in the stress-space ;Calibration using monotonic triaxial tests ;Non-associative volumic plastic potentialSophistication : p’ dependency, Lode angle dependency, ...

M1

M2

M

M

αp'

q

εy p'

qq

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Prevost’s model

Characterization

N nested conical yield surfaces associated with H’, M, α ;Kinematic hardening in the stress-space ;Calibration using monotonic triaxial tests ;Non-associative volumic plastic potentialSophistication : p’ dependency, Lode angle dependency, ...

P” =

1 −(η

η

)2

1 +

(η

η

)2

η =q

p′

p'

q

contractive

Dilative

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Prevost’s model

Characterization

N nested conical yield surfaces associated with H’, M, α ;Kinematic hardening in the stress-space ;Calibration using monotonic triaxial tests ;Non-associative volumic plastic potentialSophistication : p’ dependency, Lode angle dependency, ...

H ′ = H ′0 ·

(p′

pref

)n

, K = K0 ·(

p′

pref

)n

,

G = G0 ·(

p′

pref

)n

1σ

2σ

3σ

321 σσσ ==

after [Yang and Elgamal, 2008]

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Prevost’s model

Numerical examples

0 20 40 60 80 100 120 140 160 180 200-100

-50

0

50

100

150

200

250

p [kPa]

q [k

Pa]

Influence de p'init

(kPa)

90706040PT

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Prevost’s model

Numerical examples

0 10 20 30 40 50 60 70 80 90 100-40

-20

0

20

40

60

80

p [kPa]

q [k

Pa]

Influence de p'init

(kPa)

90706040PT

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Prevost’s model

Numerical examples

100 150 200 250 300 350 400 450-200

-100

0

100

200

300

400

500

600

700

p [kPa]

q [k

Pa]

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Prevost’s model

Numerical examples

-25 -20 -15 -10 -5 0 5 10 15 20 25-200

-150

-100

-50

0

50

100

150

200

250Essais Drainés p'=cst

εy

[%]

q [k

Pa]

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Prevost’s model

Numerical examples

-25 -20 -15 -10 -5 0 5 10 15 20 25-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1Essais Drainés p'=cst

εy

[%]

ε v[%

]

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Prevost’s model

Numerical examples

0 50 100 150 200 250 300 350 400-400

-300

-200

-100

0

100

200

300

400

500Essais Non Drainés

p [kPa]

q [k

Pa]

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Prevost’s model

Numerical examples

-5 -4 -3 -2 -1 0 1 2 3 4 5-400

-300

-200

-100

0

100

200

300

400

500Essais Non Drainés

εy

[%]

q [k

Pa]

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

Prevost’s model

Numerical examples

-10 0 10 20 30 40 50 60 70 80 90-20

-10

0

10

20

30

40

50

60

70

p' [kPa]

q [k

Pa]

Essai cyclique non drainé

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

To conclude

1 Very complex actual behaviour

• pore pressure buildup• different modes of failure• contractive/dilative transition• instability

2 Prevost model : qualitatively OK...BUT has to be modified quantitatively

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Context From reality to laboratory From laboratory to numerical modelling Conclusion

(en)Fin

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