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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
1/26
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
2/26
Context From reality to laboratory From laboratory to numerical modelling Conclusion
Don’t forget the soil !
Nigata, 1964
3/26
Context From reality to laboratory From laboratory to numerical modelling Conclusion
Don’t forget the soil !
Kobe, 1995
4/26
Context From reality to laboratory From laboratory to numerical modelling Conclusion
Don’t forget the soil !
San Fernando dam, 1971
5/26
Context From reality to laboratory From laboratory to numerical modelling Conclusion
Don’t forget the soil !
Soil-structure interaction
6/26
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
7/26
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
8/26
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
8/26
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
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
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
9/26
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
10/26
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
11/26
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
12/26
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
12/26
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
12/26
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%
13/26
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%
13/26
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%
13/26
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]
14/26
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
15/26
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
16/26
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
16/26
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.
16/26
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.
17/26
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.
17/26
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.
17/26
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
18/26
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
18/26
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
18/26
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]
19/26
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
20/26
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 ;
21/26
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]
21/26
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 ;
21/26
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 ;
21/26
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
22/26
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, ...
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, ...
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, ...
M1
M2
M
M
αp'
q
εy p'
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, ...
P” =
1 −(η
η
)2
1 +
(η
η
)2
η =q
p′
p'
q
contractive
Dilative
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, ...
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]
23/26
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
24/26
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
24/26
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]
24/26
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]
24/26
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[%
]
24/26
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]
24/26
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]
24/26
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
24/26
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
25/26
Context From reality to laboratory From laboratory to numerical modelling Conclusion
(en)Fin
26/26
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