1. 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

2. Acknowledgements Program directed by Dr. Richard Fragaszy.
NSF grant No. CMS
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 # : SOMEF

3. 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 .

4. Scope of this Presentation
Yield Surfaces and Rotational Hardening
SANISAND
SANICLAY (classical and structured)

5. stress rate ( ) strain rate ( )
Plasticity in One Page! ?
stress rate ( ) strain rate ( )
Yield surface
Additive decomposition
Rate equations
Consistency
: internal variables
flow rule
plastic potential
hardening rule
Change of structure, orientation, density beside stress state
loading index
plastic modulus

6. 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.

7. 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
Wroth, Banerjee and Stipho, Anandarajah and Dafalias, etc.
Elliptical Yield Surface (used in figures above)
Dafalias (1986)
Figures from Wheeler et al. (2003)
Show some experimental data
(i) for the plastic potential from papers of Weeeler (?) which indicate the rotated shape.
(ii) for the yield surface show undrained loading in compression and extension for samples which have been consolidated first isotropically and second under Ko. With the comment that undrained stress paths DO follow the YS, we can indicate the need for rotation of the YS as well.
(iii) Anything else you might think

8. Observe the necessity for non-associativity!
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!
Mention earlier works of suggesting rotational hardening (careful to put the Japanese who appear to do it first – see SANICLAY) and then show the work equation of Dafalias 1986) and a plot of the rotated and distorted ellipse. Mention it is the PP. In case the PP is also used for YS, on the same plot show an undrained path in loading AND unloading, and show the straight line down of the path inside the YS in extension. Also show at the po point the normal to the YS which is NOT parallel to p-axis, in order to justify the necessity for non associativity.

9. SANICLAY – Simple ANIsotropic CLAY model
Yield Surface:
Plastic potential:
Show the SANICLAY shape of the YS and PP in one slide and below show their equations AND the two equations of evolution for b_dot and a_dot. Next to each equation show the saturation value of b and a under constant eta loading (find a way to mention the word “attractor”). From the equations will be clear that there are two CSL since the rates = 0, and also that there is a bound on the rotation. Comment on the rotational hardening occurring ONLY when one has volumetric plastic strain rate. Comment on the possibility to have infinitely fast rotation had it not been for the bound. 9

10. More on the SANICLAY model
Yield surface fitting with N different than M
After Lin and collaborators 10

11. Dafalias (1986) YS Expression Fitted to Various Clay Experimental Data11

12. Rotated/Distorted Yield Surface – Sands or Clays ?
Ellipse
Dafalias (1986)
Distorted Lemniscate
Pestana & Whittle (1999)
Eight Curve
Taiebat & Dafalias (2007)
neutral loading
Show the SANICALY, SANISAND and Pestana and Wittle YS AND PP (whenever applicable), one below the other. All these are in triaxial (and will be in triaxial unless I state otherwise). For the SANISAND show the slow rotational evolution as one loads under constant eta loading.

13. 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.

14. SANISAND Family of Models
General framework of the model
Yield surface
Dependence on state parameter,
(stress-ratio)
CSL
Deviatoric stress, q
Mean effective stress, p
Void ratio, e
How about constant stress-ratio loading?
Mean effective stress, p

15. Experimental Observations
Constant Stress-Ratio Tests
Silica Sand
Data: McDowell, et al (2002)
Deviatoric stress, q
Mean effective stress, p
Toyoura Sand
Data: McDowell, et al (2002)
Silica Sand
Data: Miura, et al (1984)

16. 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:
A closed yield surface should be introduced
Taiebat, M. and Dafalias, Y. F., “Simple Yield Surface Expressions Appropriate For Soil Plasticity”, Submitted to the International Journal of Geomechanics, 2008.

17. 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)

18. Appropriate Mechanism for the Plastic Strain
Limiting Compression Curve (Pestana & Whittle 1995)
Mean effective stress, p (log scale)
Void ratio, e (log scale)
Current state (e,p)
First loading
Unloading
Limiting Compression Curve (LCC)

19. 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)

20. Hardening Rules Isotropic hardening (po) Kinematic hardening (α)
Only from the second contribution of plastic strain
Kinematic hardening (α)
Depends on the bounding distance (αb- α)
Attractor: Drags a toward h
LCC
(e,p)
e (log scale)
p (log scale)

21. Generalization to Multiaxial Stress Space
SANISAND
Dafalias, Manzari, Li, Papadimitriou, Taiebat
Show generalization to multiaxial stress space. Show the π-plane figure for SANISAND or SANICALY ( I forgot, are they the same ?) so I can discuss the issue of attractors in multiaxial space. Show below the slide also the equations of the YS and the rate (preferable to have the SANICALY it is simpler). 21

22. SANISAND - Generalization

23. 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)

24. 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)

25. 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)

26. 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

27. Liquefaction-Induced Isolation of Shear Waves
Medium Dense (e=0.80)
10m soil column – level ground
Permeability=10-4 m/s
Finite element model
Free drainage from surface
Analysis:
Self-weight & Shaking the base
Medium Dense (e=0.80)
Loose
(e=0.95)
upU element
SANISAND material model – Toyoura

28. Shear Stress vs. Vertical Stress

29. Shear Stress vs. Shear Strain

30. Acceleration vs. Time

31. Contours of Excess Pore Pressure & Excess Pore Pressure Ratio

32. 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 , 2006.

33. SANICLAY – Simple ANIsotropic CLAY model
Yield Surface:
Plastic potential:
Show the SANICLAY shape of the YS and PP in one slide and below show their equations AND the two equations of evolution for b_dot and a_dot. Next to each equation show the saturation value of b and a under constant eta loading (find a way to mention the word “attractor”). From the equations will be clear that there are two CSL since the rates = 0, and also that there is a bound on the rotation. Comment on the rotational hardening occurring ONLY when one has volumetric plastic strain rate. Comment on the possibility to have infinitely fast rotation had it not been for the bound. 33

34. Generalization to Multiaxial Stress Space
SANICLAY
Dafalias, Manzari, Papadimitriou, Taiebat
Show generalization to multiaxial stress space. Show the π-plane figure for SANISAND or SANICALY ( I forgot, are they the same ?) so I can discuss the issue of attractors in multiaxial space. Show below the slide also the equations of the YS and the rate (preferable to have the SANICALY it is simpler). 34

35. Hook type response in clays?!
Rotational Hardening
Wheeler et al (2003)
Dafalias et al (1986, 2006)
Show what would happen had we introduced the rotational hardening of Wheeler etc in which case the hardening occurs also when plastic deviatoric strain occurs. In fact show a rotated ellipse (Wheeler uses exactly the Dafalias 1986 model) AND the equation for the rate of rotation of Wheeler and Karstunen etc and then show the undrained stress paths with the hook-type response we do NOT have in clays. Show in contrast what would be predicted by our model.
Hook type response in clays?!

36. Calibration of SANICLAY
Three parameters in addition to the modified Cam-clay model: N, x, C
Show relevant material for calibration of constants for SANICALY only. Show the closed form expression for the x and the initial value of a and b after Ko consolidation. Show the importance of C in rotation in extension by showing its effect (a couple of undrained stress paths in extension with different C’s). Show a Table with all relevant constants for the SANICLAY only (no need to get into extensive discussion for the SANISAND plethora of consttants since the emphasis is on the rotational part only).
MCC

37. SANICLAY - Simulations
Undrained triaxial tests on anisotropically consolidated samples of LCT
Plane strain compression tests on K0 consolidated samples of LCT
Show simulations where emphasis should be placed on the undrained stress paths but also the stress strain curves. Use this slide for clay. Perhaps throw in a slide with destructuration just to show off? (Only slide, not equations - we keep them for a next conference)

38. 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: /nag).

39. Numerical Simulation of Response in Clays
Shell International Exploration & Production (SIEP)
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
In order to determine a safe burial depth for piplines in the Beaufort Sea, SIEP is performing simulations of ice keels gouging the seafloor under which a pipeline is buried.
Preliminary simulations performed by C-Core for SIEP have shown that the results are sensitive to the constitutive model used for the soil.
Deep ice keels can penetrate into the bottom and create gouges and subgouge
deformations in the seabed. The study of the gouging is necessary for the determining of
pipeline foundation depth and methods of pipeline protection from the influence of ice keels.

40. Structured clays
Developed system, that is closely following the physics (mechanics) of the problem, allows for investigation of energy dissipation mechanisms during seismic events.

41. Soft Marin Clays - Constitutive Modeling
SANICLAY: Simple ANIsotropic CLAY plasticity model
Dafalias, Manzari, Papadimitriou, Taiebat, Peek ( )
Based on MCC
Rotational hardening
Non-associative flow rule
Destructuration

42. 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*
In order to determine a safe burial depth for piplines in the Beaufort Sea, SIEP is performing simulations of ice keels gouging the seafloor under which a pipeline is buried.
Preliminary simulations performed by C-Core for SIEP have shown that the results are sensitive to the constitutive model used for the soil.
Deep ice keels can penetrate into the bottom and create gouges and subgouge
deformations in the seabed. The study of the gouging is necessary for the determining of
pipeline foundation depth and methods of pipeline protection from the influence of ice keels.

43. SANICLAY with Destructuration
Determination of and
Si and Sf : internal variables affecting plastic modulus via consistency condition
In order to determine a safe burial depth for piplines in the Beaufort Sea, SIEP is performing simulations of ice keels gouging the seafloor under which a pipeline is buried.
Preliminary simulations performed by C-Core for SIEP have shown that the results are sensitive to the constitutive model used for the soil.
Deep ice keels can penetrate into the bottom and create gouges and subgouge
deformations in the seabed. The study of the gouging is necessary for the determining of
pipeline foundation depth and methods of pipeline protection from the influence of ice keels.

44. SANICLAY with Destructuration
Effect of the frictional destructuration of rotational hardening
From consistency condition ( ):
In order to determine a safe burial depth for piplines in the Beaufort Sea, SIEP is performing simulations of ice keels gouging the seafloor under which a pipeline is buried.
Preliminary simulations performed by C-Core for SIEP have shown that the results are sensitive to the constitutive model used for the soil.
Deep ice keels can penetrate into the bottom and create gouges and subgouge
deformations in the seabed. The study of the gouging is necessary for the determining of
pipeline foundation depth and methods of pipeline protection from the influence of ice keels.

45. Calibration
Developed system, that is closely following the physics (mechanics) of the problem, allows for investigation of energy dissipation mechanisms during seismic events.

46. Calibration
Developed system, that is closely following the physics (mechanics) of the problem, allows for investigation of energy dissipation mechanisms during seismic events.

47. Calibration
Developed system, that is closely following the physics (mechanics) of the problem, allows for investigation of energy dissipation mechanisms during seismic events.

48. 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.

49. Calibration
Developed system, that is closely following the physics (mechanics) of the problem, allows for investigation of energy dissipation mechanisms during seismic events.

50. Calibration
Developed system, that is closely following the physics (mechanics) of the problem, allows for investigation of energy dissipation mechanisms during seismic events.

51. Calibration
Developed system, that is closely following the physics (mechanics) of the problem, allows for investigation of energy dissipation mechanisms during seismic events.

52. Model parameters
Developed system, that is closely following the physics (mechanics) of the problem, allows for investigation of energy dissipation mechanisms during seismic events.

53. Model Validation – Bothkennar clay
K0 consolidation on unstructured (reconstituted) and structured (undisturbed) samples.
Data: Smith et al. (1992)
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).

54. Model Validation – Bothkennar clay

55. Model Validation – Bothkennar clay

56. 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.