Report

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