Soil Constitutive Modeling SANISAND and SANICLAY Models

1. Soil Constitutive ModelingSANISAND and SANICLAY Models Yannis F. Dafalias, Ph.D. Department of Mechanics, National Technical University of AthensDepartment 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 • 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

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. Plasticity in One Page! ? stress rate ( ) strain rate ( ) • Yield surface • Additive decomposition • Rate equations • Consistency : internal variables flow rule plastic potential hardening rule 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)

8. 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!

9. SANICLAY – Simple ANIsotropic CLAY model Yield Surface: Plastic potential:

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

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

12. Rotated/Distorted Yield Surface – Sands or Clays ? Ellipse Dafalias (1986) Distorted Lemniscate Pestana & Whittle (1999) Eight Curve Taiebat & Dafalias (2007) neutral loading

13. 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.

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

15. Data: McDowell, et al (2002) Silica Sand Data: McDowell, et al (2002) Silica Sand Silica Sand Toyoura Sand Experimental Observations • Constant Stress-Ratio Tests Deviatoric stress, q Mean effective stress, p 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: 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. Limiting Compression Curve (LCC) First loading Current state (e,p) Void ratio, e (log scale) Unloading Mean effective stress, p (log scale) Appropriate Mechanism for the Plastic Strain • Limiting Compression Curve (Pestana & Whittle 1995)

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) • 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. SANISAND Dafalias, Manzari, Li, Papadimitriou, Taiebat Generalization to Multiaxial Stress Space

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

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 Excess Pore Pressure

32. 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.

33. SANICLAY – Simple ANIsotropic CLAY model • Yield Surface: • Plastic potential:

34. Generalization to Multiaxial Stress Space • SANICLAY Dafalias, Manzari, Papadimitriou, Taiebat

35. Wheeler et al (2003) Rotational Hardening Dafalias et al (1986, 2006) Hook type response in clays?!

36. Calibration of SANICLAY • Three parameters in addition to the modified Cam-clay model: N, x, C MCC

37. SANICLAY - Simulations • Undrained triaxial tests on anisotropically consolidated samples of LCT • Plane strain compression tests on K0 consolidated samples of LCT

38. 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).

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

40. Structured clays

41. Soft Marin Clays - Constitutive Modeling • Based on MCC • Rotational hardening • Non-associative flow rule • Destructuration SANICLAY: Simple ANIsotropic CLAY plasticity model Dafalias, Manzari, Papadimitriou, Taiebat, Peek (1986-2009)

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*

43. SANICLAY with Destructuration • Determination of and • Si and Sf : internal variables affecting plastic modulus via consistency condition

44. SANICLAY with Destructuration • Effect of the frictional destructuration of rotational hardening • From consistency condition ( ):

45. Calibration

46. Calibration

47. Calibration

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

50. Calibration