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Soil Constitutive ModelingSANISAND 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

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Acknowledgements

• NSF grant No. CMS-0201231 - Program directed by Dr. Richard Fragaszy.

• Shell Exploration and Production Company (USA)- Dr. Ralf Peek (Shell International Exploration and Production, B.V., The

Netherlands)

• Norwegian Geotechnical Institute- Dr. Amir M. Kaynia

• EUROPEAN RESEARCH COUNCIL (ERC) Project FP7_ IDEAS # 290963: SOMEF

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COLLABORATORS

Prof. Majid Manzari, George Washington University, USAProf. Xiang Song Li, Hong Kong Univ. Sci. and Technology, ChinaProf. Achilleas Papadimitriou, University of Thessaly, GreeceProf. Mahdi Taiebat, University of British Columbia, Canada

.

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Scope of this Presentation

• Yield Surfaces and Rotational Hardening

• SANISAND

• SANICLAY (classical and structured)

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stress rate ( ) strain rate ( )

• Yield surface

• Additive decomposition

• Rate equations

• Consistency

Plasticity in One Page!

?

loading index

plastic modulus

plastic potential

flow rule

hardening rule

: internal variables

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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.

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• Earliest proposition for RH- Sekiguchi and Ohta (1977); mentioned also in Hashiguchi (1977)

• Many other contributors to RH - Wroth, Banerjee and Stipho, Anandarajah and Dafalias, etc.

• Elliptical Yield Surface (used in figures above)- Dafalias (1986)

Why do we need Rotational Hardening (RH)?

Figures from Wheeler et al. (2003)

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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!

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SANICLAY – Simple ANIsotropic CLAY model

• Yield Surface:

• Plastic potential:

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Yield surface fitting with N different than M

More on the SANICLAY model

After Lin and collaborators

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Dafalias (1986) YS Expression Fitted to Various Clay Experimental Data

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Distorted Lemniscate Pestana & Whittle (1999)

EllipseDafalias (1986)

Eight CurveTaiebat & Dafalias (2007)

Rotated/Distorted Yield Surface – Sands or Clays ?

neutral loading

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SANISANDDafalias, 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.

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SANISAND Family of Models

• General framework of the model

- Yield surface

• Dependence on state parameter,

Mean effective stress, p

Vo

id r

ati

o,

e

Mean effective stress, p

De

via

tori

c s

tre

ss

, q

CSLHow about constant stress-ratio loading?

(stress-ratio)

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Data: M

cDowell, et al (2002)

Silica Sand

Experimental Observations

• Constant Stress-Ratio Tests

Toyoura Sand

Mean effective stress, p

Dev

iato

ric

stre

ss,

q

Data: M

iura, et al (1984)

Silica Sand

Data: M

cDowell, et al (2002)

Silica Sand

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Choice of the Yield Surface• Closed Yield surface

- Avoid the sharp corners- Narrow enough to capture the plasticity under changes of h

Taiebat, M. and Dafalias, Y. F., “Simple Yield Surface Expressions Appropriate For Soil Plasticity”, Submitted to the International Journal of Geomechanics, 2008.

Modified Eight-curve function:

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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)

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• Limiting Compression Curve (Pestana & Whittle 1995)

Appropriate Mechanism for the Plastic Strain

Mean effective stress, p (log scale)

Void

ratio

, e (l

og s

cale

) Current state (e,p)

First loading

Unloading

Limiting Compression Curve (LCC)

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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)

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Hardening Rules

• Kinematic hardening (α)- Depends on the bounding distance (αb- α)- Attractor: Drags a toward h

• Isotropic hardening (po)- Only from the second contribution of plastic

strain

p (log scale)

e (

log

sca

le)

(e,p)

LCC

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• SANISANDDafalias, Manzari, Li, Papadimitriou, Taiebat

Generalization to Multiaxial Stress Space

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SANISAND - Generalization

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Data: Verdugo &

Ishihara (1996)

Constitutive Model Validation

• Undrained triaxial compression tests (CIUC) - Toyoura Sand

• Drained triaxial compression tests (CIDC) - Toyoura Sand

Data: Verdugo &

Ishihara (1996)

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• Drained triaxial compression tests (CIDC) - Sacramento River Sand

• Isotropic compression tests - Sacramento River Sand

Constitutive Model Validation

Data: Lee &

Seed (1967)D

ata: Lee & Seed (1967), Lade (1987)

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Constitutive Model Validation

• Isotropic compression tests (constant stress-ratio) - Toyoura Sand

• Constant stress-ratio compression tests - Silica Sand

Data: M

iura, et al (1979, 1984)

Data: M

cDow

ell (2000)

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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

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Liquefaction-Induced Isolation of Shear Waves

10m soil column – level ground

Permeability=10-4 m/s

Finite element modelFree drainage from surface

Analysis:

Self-weight & Shaking the base

Medium Dense (e=0.80)

Loose (e=0.95)

Medium Dense (e=0.80)

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Shear Stress vs. Vertical Stress

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Shear Stress vs. Shear Strain

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Acceleration vs. Time

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Contours of Excess Pore Pressure & Excess Pore Pressure Ratio

Excess Pore Pressure

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SANICLAYDafalias, 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.

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SANICLAY – Simple ANIsotropic CLAY model

• Yield Surface:

• Plastic potential:

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Generalization to Multiaxial Stress Space

• SANICLAY Dafalias, Manzari, Papadimitriou, Taiebat

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• Wheeler et al (2003)

Rotational Hardening

• Dafalias et al (1986, 2006)

Hook type response in clays?!

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Calibration of SANICLAY

• Three parameters in addition to the modified Cam-clay model: N, x, C

MCC

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SANICLAY - Simulations

• Undrained triaxial tests on anisotropically consolidated samples of LCT

• Plane strain compression tests on K0 consolidated samples of LCT

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SANICLAY with DestructurationTaiebat, 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).

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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)

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Structured clays

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Soft Marin Clays - Constitutive Modeling

• Based on MCC

• Rotational hardening

• Non-associative flow rule

• Destructuration

SANICLAY: Simple ANIsotropic CLAY plasticity modelDafalias, Manzari, Papadimitriou, Taiebat, Peek (1986-2009)

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SANICLAY with Destructuration

• Destructuration mechanisms- Isotropic- Frictional

Si : isotropic structuration factor, Si > 1

Sf : frictional structuration factor, Sf > 1

(p,q)

N

N*M*

p0*p0

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SANICLAY with Destructuration

• Determination of and

• Si and Sf : internal variables affecting plastic modulus via consistency condition

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SANICLAY with Destructuration

• Effect of the frictional destructuration of rotational hardening

• From consistency condition ( ):

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Calibration

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Calibration

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Calibration

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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.

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Calibration

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Calibration

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Calibration

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Model parameters

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Model Validation – Bothkennar clay

K0 consolidation on unstructured (reconstituted) and structured (undisturbed) samples.

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: Sm

ith et al. (1992)

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Model Validation – Bothkennar clay

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Model Validation – Bothkennar clay

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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.