1. ATTRIBUTES OF ROTATIONAL HARDENING RULES IN CLAY PLASTICITY Yannis F. Dafalias 1 and Mahdi Taiebat 2 1 Department of Mechanics, National Technical University of Athens, Hellas Department of Civil and Environmental Engineering, University of California, Davis, CA, USA, and 2 Department of Civil Engineering, The University of British Columbia, Vancouver, BC, Canada 8th NUMGE Conference Numerical Methods in Geotechnical Engineering Delft, The Netherlands, 18-20 June 2014 ACKNOWLEDGEMENT: EUROPEAN RESEARCH COUNCIL (ERC) Project FP7_ IDEAS # 290963: SOMEF

2. Most Relevant Publications Dafalias, Y.F. (1986). "An anisotropic critical state soil plasticity model," Mechanics Research Communications, Vol. 13, pp. 341-347. Wheeler, S.J., Naatanen, A., Karstunen, M., and Lojander, M. (2003). “An anisotropic elastoplastic model for soft clasy”, Can. Geotech. J., Vol. 40(2), pp.403- 418 Dafalias, Y.F., and Taiebat, M. (2013). “Anatomy of rotational hardening in clay plasticity”, Geotechnique, Vol. 63, pp. 1406-1418. Dafalias, Y.F., and Taiebat, M. (2014). “Rotational hardening with and without anisotropic fabric at critical state”, Geotechnique, doi.org/10.1680/geot.13.T.035.

3. Anisotropic MCC (AMCC) (Dafalias, 1986) Isotropic MCC (Burland, 1965) Isotropic and Anisotropic Modified Cam-Clay Models

4. SANICLAY: Plastic Potential Surface (PPS) and Yield Surface (YS) Dafalias (1986), Dafalias et al (2006), Jiang et al (2012) Modification

5. Fitting YS of AMCC to data with N=M (Wheeler et al., 2003)

6. Fitting YS of AMCC to data with N>M, N=M, N<M (Jiang and Ling, 2010)

7. Forms of Rotational Hardening (RH) Generic form: Loading index (plastic multiplier): Bounding attractor : with which converges under fixed Dafalias (1986) : Dafalias and Taiebat (2013): Dafalias and Taiebat (2014): Non generic form: (Wheeler et al, 2003)

8. Variation of bounding attractor under fixed

9. Requirements for RH Unique Critical State Line (CSL) in e – p space Must be able to simulate loading for calibration Not excessive rotation (e.g. ) Must have in order to avoid

10. RH and Uniqueness of Critical State Line (CSL)

11. Specification of Unique CSL by Various RH Rules

12. Comparison of RH Rule of Dafalias (1986) with and without. Non-Unique CSL Unique CSL

13. Comparison of Wheeler et al. (2003) and Dafalias and Taiebat (2013) RH Rules RH of Wheeler et al (2003) -> Unique CS <- RH of Dafalias and Taiebat (2013)

14. Softening when fabric at CS is small or zero RH by Dafalias and Taiebat (2014)

15. Value of RH variable α under Ko Loading

16. Calibration of RH parameters under Ko loading

17. Drained Loading Simulation for Otaniemi clay Wheeler et al (2003) RH & Dafalias and Taiebat (2013) RH

18. Undrained Simulation LCT Clay (Dafalias and Taiebat, 2013) Undrained Simulation LCT Clay (Wheeler et al, 2003) N=MN<MN=MN<M

19. Undrained Simulation LCT Clay (Dafalias and Taiebat, 2013) Undrained Simulation LCT Clay (Wheeler et al, 2003) N=MN<MN=MN<M

20. Undrained Loading Simulation of LCT Clay with N<M (Dafalias and Taiebat, 2014)

21. Undrained Loading Simulation of LCT Clay with the Simplest RH (Dafalias, 1986)

22. CONCLUSION: Basic Attributes of RH Rules RH Rule Unique CSL Restricted Rotation Ko simulation/calibration Dafalias (1986) Yes No Yes (modified) Wheeler et al (2003) Yes No Yes Dafalias/Taiebat (2013) Yes Yes Yes Dafalias/Taiebat (2014) Yes Yes Yes NOTE 1: With the exception of Dafalias/Taiebat (2014), all other RH rules provide necessarily non-zero anisotropic fabric at Critical State NOTE 2: The NO’s can be corrected