The role of microstructure in the incremental behavior of granular materials

The role of microstructure in the incremental behavior

of granular materials

V. Magnanimo, N. Kumar and S. LudingMSM - University of Twente (NL)

We observe the (often disastrous) MACROSCOPIC behaviorand we want to model it ….

….how is this related with the MICROSCOPIC structure?

Evolution of microstructure

[Behringer (Duke)]

Evolution of the microstructure

Inhomogeneity & anisotropy, instabilities & structures, rotations

[Luding (UT)]

Evolution of microstructure

Experimental background

Experimental background

Experimental background

Yang, Li and Yang (2008) Geotechnique 58(4) 237-248

Triaxial compression samples prepared with:

• dry deposition• moist tamping

ISOTROPIC SYSTEM

Coordination number: HISTORY of the sample

Magnanimo et al. (2008) EPL 81 34006

Elastic moduliWe apply (m = inf) an incremental strain eij and measure the variation instress sij after relaxation

Calvetti et al. (2003) Rivista Italiana di Geotecnica 3Magnanimo et al. (2008) EPL 81 34006 Sibille et al. (2009) EJECE 13(2) 187-201

Amplitude of the increment

Elastic moduli dependence on microstructure

G/B

Magnanimo et al. (2008) EPL 81 34006

ANISOTROPIC SYSTEMundrained biaxial test

O.I. Imole et al. KONA (2013), Kumar et al. Acta Mechanica (under review)

Shear Stress

Evolution of stress and fabricDeviatoric fabric

s dev

=√3

J 2s

F dev=

√3 J 2Fc

definition of fabric

We apply purely deviatoric perturbations along the path

Elastic moduli

Incremental elastic behavior

Small enough before any local rearrangement happens

How small is small?

Bulk modulus

Anisotropy modulus

Shear modulus

Theoretical predictionundrained cyclic biaxial test

Incremental elastic behavior

F dev=

√3 J 2Fc

Luding and Perdahcioglu CIT (2011), Magnanimo and Luding, Granular Matter (2011)

Simple constitutive model

Initial state: isotropic volume fraction 0.711

Shear Stress Deviatoric Fabric

Undrained biaxial test: calibration

Undrained CYCLIC biaxial test: prediction

Initial state: isotropic volume fraction 0.711

Shear Stress Deviatoric Fabric

Isobaric compression