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

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

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

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

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Material idealization

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Experimental background

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

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ISOTROPIC SYSTEM

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Numerical protocol

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

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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 Sibille et al. (2009) EJECE 13(2)

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Amplitude of the increment

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

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Theoretical model with anisotropy

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

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ANISOTROPIC SYSTEM undrained biaxial test

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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

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We apply purely deviatoric perturbations along the path Elastic moduli

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Incremental elastic behavior

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

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Bulk modulus

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Anisotropy modulus

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Shear modulus

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Theoretical prediction undrained cyclic biaxial test

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Incremental elastic behavior

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F dev =√3 J 2 Fc

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

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

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

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Isobaric compression

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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

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Thank you

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