1. The role of microstructure in the incremental behavior of granular materials V. Magnanimo, N. Kumar and S. Luding MSM - University of Twente (NL)

2. We observe the (often disastrous) MACROSCOPIC behavior and we want to model it …. ….how is this related with the MICROSCOPIC structure?

3. Evolution of microstructure [Behringer (Duke)] Evolution of the microstructure

4. Inhomogeneity & anisotropy, instabilities & structures, rotations [Luding (UT)] Evolution of microstructure

6. Material idealization

7. Experimental background

9. Yang, Li and Yang (2008) Geotechnique 58(4) 237-248 Triaxial compression samples prepared with: dry deposition moist tamping

10. ISOTROPIC SYSTEM

11. Numerical protocol

12. Coordination number: HISTORY of the sample Magnanimo et al. (2008) EPL 81 34006

13. Elastic moduli We apply (  = inf) an incremental strain  ij and measure the variation in stress  ij after relaxation Calvetti et al. (2003) Rivista Italiana di Geotecnica 3 Magnanimo et al. (2008) EPL 81 34006 Sibille et al. (2009) EJECE 13(2) 187-201

14. Amplitude of the increment

15. Elastic moduli dependence on microstructure G/B Magnanimo et al. (2008) EPL 81 34006

16. Theoretical model with anisotropy

21. Luding and Perdahcioglu CIT (2011), Magnanimo and Luding, Granular Matter (2011) Simple constitutive model

22. ANISOTROPIC SYSTEM undrained biaxial test

23. O.I. Imole et al. KONA (2013), Kumar et al. Acta Mechanica (under review) Shear Stress Evolution of stress and fabric Deviatoric fabric  dev =√3 J 2  F dev =√3 J 2 Fc definition of fabric

24. We apply purely deviatoric perturbations along the path Elastic moduli

25. Incremental elastic behavior

26. Small enough before any local rearrangement happens How small is small?

27. Bulk modulus

28. Anisotropy modulus

29. Shear modulus

30. Theoretical prediction undrained cyclic biaxial test

31. Incremental elastic behavior

32. F dev =√3 J 2 Fc

33. Luding and Perdahcioglu CIT (2011), Magnanimo and Luding, Granular Matter (2011) Simple constitutive model

34. Initial state: isotropic volume fraction 0.711 Shear Stress Deviatoric Fabric Undrained biaxial test: calibration

35. Undrained CYCLIC biaxial test: prediction Initial state: isotropic volume fraction 0.711 Shear Stress Deviatoric Fabric

36. Isobaric compression

41. Conclusions We analyzed the incremental behavior of isotropic granular samples and we linked is with the coordination number We analyzed the incremental behavior of anisotropic granular samples and we linked is with volumetric and deviatoric fabric When a simple constitutive model with evolution equation for fabric is introduced and calibrated with the moduli cyclic shear can be predicted

42. Thank you