Soil Constitutive Modeling
SANISAND and SANICLAY Models
Yannis F. Dafalias, Ph.D.
Department of Mechanics, National Technical University of Athens
Department of Civil and Environmental Engineering, University of California, Davis
Mahdi Taiebat, Ph.D., P.Eng.
Department of Civil Engineering, The University of British Columbia
1
Acknowledgements
•
NSF grant No. CMS-0201231
-
•
Shell Exploration and Production Company (USA)
-
•
Dr. Ralf Peek (Shell International Exploration and Production, B.V., The
Netherlands)
Norwegian Geotechnical Institute
-
•
Program directed by Dr. Richard Fragaszy.
Dr. Amir M. Kaynia
EUROPEAN RESEARCH COUNCIL (ERC) Project FP7_ IDEAS # 290963: SOMEF
2
COLLABORATORS
Prof. Majid Manzari,
George Washington University, USA
Prof. Xiang Song Li,
Hong Kong Univ. Sci. and Technology, China
Prof. Achilleas Papadimitriou,
University of Thessaly, Greece
Prof. Mahdi Taiebat,
University of British Columbia, Canada
.
3
Scope of this Presentation
•
Yield Surfaces and Rotational Hardening
•
SANISAND
•
SANICLAY (classical and structured)
4
Plasticity in One Page!
stress rate (
•
)
?
strain rate (
)
Yield surface
: internal variables
•
Additive decomposition
•
Rate equations
flow rule
plastic potential
hardening rule
•
Consistency
loading index
plastic modulus
5
Yield Surfaces and Rotational Hardening
Dafalias, Y. F., and Taiebat, M., “Rotational hardening in anisotropic soil plasticity”, Presented in the Inaugural
International Conference of the Engineering Mechanics Institute (EM08), Minneapolis, MN, 2008.
6
Why do we need Rotational Hardening (RH)?
•
Earliest proposition for RH
-
•
Sekiguchi and Ohta (1977); mentioned also in Hashiguchi (1977)
Many other contributors to RH
-
•
Figures from Wheeler et al. (2003)
Wroth, Banerjee and Stipho, Anandarajah and Dafalias, etc.
Elliptical Yield Surface (used in figures above)
-
Dafalias (1986)
7
Dafalias (1986)
•
Plastic work equality
-
•
The above equality provides a differential
equation for the plastic potential (and the yield
surface in case of associative flow rule) which
upon integration yields the expression:
Yield surface/Plastic potential
-
-
-
The peak q stress on the YS is always at the
critical stress-ratio M (related to the friction
angle at failure) for any degree of rotation.
There are two internal variables, the p0
(isotropic hardening) and the α (rotational
hardening).
For α=0 one obtains the Cam-Clay model.
Observe the necessity for non-associativity!
8
SANICLAY – Simple ANIsotropic CLAY model
•
Yield Surface:
•
Plastic potential:
9
More on the SANICLAY model
Yield surface fitting with N different than M
After Lin and collaborators
10
Dafalias (1986) YS Expression Fitted to Various Clay Experimental Data
11
Rotated/Distorted Yield Surface – Sands or Clays ?
Ellipse
Distorted Lemniscate
Eight Curve
Dafalias (1986)
Pestana & Whittle (1999)
Taiebat & Dafalias (2007)
neutral loading
12
SANISAND
Dafalias, Manzari, Papadimitriou, Li, Taiebat
Taiebat, M. and Dafalias, Y. F., “SANISAND: simple anisotropic sand plasticity model”, International Journal for
Numerical and Analytical Methods in Geomechanics, vol. 32, no. 8, pp. 915–948, 2008.
13
SANISAND Family of Models
General framework of the model
(stress-ratio)
-
Mean effective stress, p
Dependence on state parameter,
Void ratio, e
•
Yield surface
Deviatoric stress, q
•
How about constant stress-ratio loading?
CSL
Mean effective stress, p
14
Experimental Observations
Constant Stress-Ratio Tests
Deviatoric stress, q
•
Silica Sand
Mean effective stress, p
Data: McDowell, et al (2002)
Data: Miura, et al (1984)
Toyoura Sand
SilicaSand
Sand
Silica
15
Choice of the Yield Surface
•
Closed Yield surface
-
Avoid the sharp corners
Narrow enough to capture the plasticity under changes of h
Modified Eight-curve function:
Taiebat, M. and Dafalias, Y. F., “Simple Yield Surface Expressions Appropriate For Soil Plasticity”, Submitted to
the International Journal of Geomechanics, 2008.
16
Choice of the Yield Surface
•
Wedge (Manzari and Dafalias, 1997)
-
Internal variable: a
•
8-Curve (Taiebat and Dafalias, 2008)
-
Internal variables: a , p0
n=20 (default)
17
Appropriate Mechanism for the Plastic Strain
Limiting Compression Curve (Pestana & Whittle 1995)
First loading
Void ratio, e (log scale)
•
Limiting Compression Curve
(LCC)
Current state (e,p)
Unloading
Mean effective stress, p (log scale)
18
Flow Rule
•
First contribution
- Due to slipping and rolling
- Mainly with change of η
(stress point away from the tip of the YS)
•
Second contribution
- From asperities fracture and particle crushing
- Mainly under constant η
(stress point at the tip of the YS)
19
Hardening Rules
Kinematic hardening ( )
-
Depends on the bounding distance ( b-  )
-
Attractor: Drags a toward h
•
Isotropic hardening (po)
-
Only from the second contribution of plastic
strain
LCC
e (log scale)
•
(e,p)
p (log scale)
20
Generalization to Multiaxial Stress Space
•
SANISAND
Dafalias, Manzari, Li, Papadimitriou, Taiebat
21
SANISAND - Generalization
22
Constitutive Model Validation
Undrained triaxial compression tests (CIUC) - Toyoura Sand
•
Drained triaxial compression tests (CIDC) - Toyoura Sand
Data: Verdugo & Ishihara (1996)
•
Data: Verdugo & Ishihara (1996)
23
Constitutive Model Validation
Drained triaxial compression tests (CIDC) - Sacramento River Sand
•
Isotropic compression tests - Sacramento River Sand
Data: Lee & Seed (1967)
•
Data: Lee & Seed (1967), Lade (1987)
24
Constitutive Model Validation
Isotropic compression tests (constant stress-ratio) - Toyoura Sand
•
Constant stress-ratio compression tests - Silica Sand
Data: Miura, et al (1979, 1984)
•
Data: McDowell (2000)
25
Fully Coupled u−p−U Finite Element
•
•
Formulation: Zienkiewicz and Shiomi (1984), Argyris and Mlejnek (1991)
Unknowns:
u – displacement of solid skeleton (ux,uy,uz)
- p – pore pressure in the fluid
- U – displacement of fluid (Ux,Uy,Uz)
-
•
•
Equations:
-
Mixture Equilibrium Equation:
-
Fluid Equilibrium Equation:
-
Flow Conservation Equation:
Features:
Takes into account the physical velocity proportional damping
- Takes into account acceleration of fluid:
Important for Soil-Foundation-Structure-Interaction (SFSI)
Inertial forces of fluid allow more rigorous liquefaction modeling
- Is stable for nearly incompressible pore fluid
-
26
Liquefaction-Induced Isolation of Shear Waves
10m soil column – level ground
Permeability=10-4 m/s
Finite element model
Free drainage from surface
Medium Dense
(e=0.80)
Analysis:
Medium Dense
(e=0.80)
Self-weight & Shaking the base
Loose
(e=0.95)
27
Shear Stress vs. Vertical Stress
28
Shear Stress vs. Shear Strain
29
Acceleration vs. Time
30
Contours of Excess Pore Pressure & Excess Pore Pressure Ratio
Excess Pore Pressure
31
SANICLAY
Dafalias, Manzari, Papadimitriou
Dafalias, Y. F., Manzari, M. T., and Papadimitriou, A. G., “SANICLAY: simple anisotropic clay plasticity model”
International Journal for Numerical and Analytical Methods in Geomechanics, vol. 30, pp. 1231-1257, 2006.
32
SANICLAY – Simple ANIsotropic CLAY model
•
Yield Surface:
•
Plastic potential:
33
Generalization to Multiaxial Stress Space
•
SANICLAY
Dafalias, Manzari, Papadimitriou, Taiebat
34
Rotational Hardening
•
Wheeler et al (2003)
•
Dafalias et al (1986, 2006)
Hook type response
in clays?!
35
Calibration of SANICLAY
•
Three parameters in addition to the modified Cam-clay model: N, x, C
MCC
36
SANICLAY - Simulations
•
Undrained triaxial tests on
anisotropically consolidated
samples of LCT
•
Plane strain compression
tests on K0 consolidated
samples of LCT
37
SANICLAY with Destructuration
Taiebat, Dafalias, Peek
Taiebat, M., Dafalias, Y. F., and Peek, R., “A destructuartion theory and its application to SANICLAY model”
International Journal for Numerical and Analytical Methods in Geomechanics, 2009 (DOI: 10.1002/nag).
38
Numerical Simulation of Response in Clays
•
Safe burial depth for pipelines in the Beaufort Sea
•
Results: very sensitive to the constitutive model used for the soil
•
Advanced geotechnical design in natural soft clays:
-
Isotropic hardening
-
Anisotropic hardening
-
Destructuration mechanism
Shell International Exploration &
Production (SIEP)
39
Structured clays
40
Soft Marin Clays - Constitutive Modeling
SANICLAY: Simple ANIsotropic CLAY plasticity model
Dafalias, Manzari, Papadimitriou, Taiebat, Peek (1986-2009)
•
Based on MCC
•
Rotational hardening
•
Non-associative flow rule
•
Destructuration
41
SANICLAY with Destructuration
•
Destructuration mechanisms
-
Isotropic
Frictional
Si : isotropic structuration factor, Si > 1
Sf : frictional structuration factor, Sf > 1
M*
N*
N
(p,q)
p0
p0*
42
SANICLAY with Destructuration
•
Determination of
and
•
Si and Sf : internal variables affecting plastic modulus via consistency condition
43
SANICLAY with Destructuration
•
Effect of the frictional destructuration of rotational hardening
•
From consistency condition (
):
44
Calibration
45
Calibration
46
Calibration
47
The SANICLAY model with destructuration
Schematic illustration of the effect of isotropic and frictional de-structuration mechanisms for in
undrained triaxial compression and extension following a K0 consolidated state.
48
Calibration
49
Calibration
50
Calibration
51
Model parameters
52
Model Validation – Bothkennar clay
Undrained triaxial compression and extension following the
• in-situ state (point A), and consolidation at points B
• (oedometrically consolidated), C (isotropically consolidated)
• D (passively consolidated).
Data: Smith et al. (1992)
K0 consolidation on unstructured (reconstituted) and
structured (undisturbed) samples.
53
Model Validation – Bothkennar clay
54
Model Validation – Bothkennar clay
55
Conclusion
•
Experimental results show the necessity of use of rotational hardening.
•
Constitutive Ingredients:
The concept of attractor for constant stress-ratio loading (Sands and Clays)
- An upper bound for Rotational Hardening (Sands and Clays)
- Dependence of Rotational Hardening rate on plastic volumetric strain rate avoids hook-type
response (Clays) but results in non unique CSL – Dependence on both plastic volumetric and
deviatoric strain rates induces hook-type of response but it yields a unique CSL.
-
•
Attractors: the rotational hardening variables are attracted to and converge with specific
stress-ratio tensor points in stress space under constant stress-ratio loading.
•
Use of classical bounding surface techniques restricts the rotation to within appropriate
bounds. SANISAND can now address constant stress-ratio loading maintaining its ability
to capture variable stress ratio loading.
•
SANICLAY can now address destructuration in natural sensitive clays.
•
High fidelity mechanics-based simulations are inevitable step for transition toward
performance-based design in geotechnical engineering.
56