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A novel experimental device for investigating the multiscale behavior of granular materials under shear

Abstract

In this paper, we report a set of experiments performed on a novel mechanical device that allows a specimen composed of a two-dimensional opaque granular assembly to be subjected to quasi-static shear conditions. A complete description of the grain-scale quantities that control the mechanical behavior of granular materials is extracted throughout the shear deformation. Geometrical arrangement, or fabric, is quantified by means of image processing, grain kinematics are obtained using Digital Image Correlation and contact forces are inferred using the Granular Element Method. Aiming to bridge the micro-macro divide, macroscopic average stresses for the granular assembly are calculated based on grain-scale fabric parameters and contact forces. The experimental procedure is detailed and validated using a simple uniaxial compression test. Macroscopic results of shear stress and volumetric strain exhibit typical features of the shear response of dense granular materials and indicate that critical state is achieved at large deformations. At the grain scale, attention is given to the evolution of fabric and contact forces as the granular assembly is sheared. The results show that shear deformation induces geometrical (fabric) and mechanical (force) anisotropy and that principal stresses and force orientation rotate simultaneously. At critical state, stress, force and fabric orientation reach the same value. By seamlessly connecting grain-scale information to continuum scale experiments, we shed light into the multiscale mechanical behavior of granular assemblies under shear loading.

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Acknowledgements

This work was supported in part by the Defense Threat Reduction Agency (DTRA) under award number HDTRA1-12-1-0041. This support is gratefully acknowledged.

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Correspondence to José E. Andrade.

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No potential conflict of interest is reported by the authors. None of the material presented in the paper is submitted or published elsewhere, and the paper does not contain any information with restricted access or proprietary content.

Appendix: The granular element method

Appendix: The granular element method

In this appendix, we describe the GEM algorithm in a pseudo-code format. Let \(i_p\) and \(i_\alpha \) denote the storage indices for, respectively, the p-th particle and the \(\alpha \)-th contact, for \(\alpha \in \{1,\ldots ,N_c\}\) and \(p \in \{1,\ldots ,N_p\}\). \(N_p\) is the total number of grains and \(N_c\) is the total number of contact. For more details on the mathematical framework of GEM, see [33,34,35].

Inputs: Position of contact points \(\varvec{x} = [\varvec{x}^1,\varvec{x}^2,\ldots ,\varvec{x}^{_{N_c}}]^T\) where \(\varvec{x}^{\alpha } = \{ x^{\alpha },y^{\alpha } \}\)
  Average grain stress \(\bar{\varvec{\sigma }} = [\bar{\varvec{\sigma }}^1,\bar{\varvec{\sigma }}^2,\ldots ,\bar{\varvec{\sigma }}^{_{N_p}}]^T\) where \(\bar{\varvec{\sigma }}^{p} = \{\bar{\sigma }^p_{xx}, \bar{\sigma }^p_{yy}, \bar{\sigma }^p_{xy} \}\)
  Surface of grains \(\Omega = [\Omega _1,\Omega _2,\ldots ,\Omega _{_{N_p}}]^T\)
  Normal unit contact vector \(\varvec{e} = [\varvec{e}^1,\varvec{e}^2,\ldots ,\varvec{e}^{_{N_c}}]^T\) where \(\varvec{e}^{\alpha } = \{ e_x^{\alpha },e_y^{\alpha } \}\)
  Tangential unit contact vector \(\varvec{t} = [\varvec{t}^1,\varvec{t}^2,\ldots ,\varvec{t}^{_{N_c}}]^T\) where \(\varvec{t}^{\alpha } = \{ t_x^{\alpha },t_y^{\alpha } \}\)
  Inter-particle friction coefficient \(\mu \)
  Boundary of granular assembly \(\Gamma \)
Output: Force vector \(\varvec{f} = [\varvec{f}^1,\varvec{f}^2,\ldots ,\varvec{f}^{_{N_c}}]^T\) where \(\varvec{f}^{\alpha } = \{ f_x^{\alpha },f_y^{\alpha } \}\)
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Marteau, E., Andrade, J.E. A novel experimental device for investigating the multiscale behavior of granular materials under shear. Granular Matter 19, 77 (2017). https://doi.org/10.1007/s10035-017-0766-x

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Keywords

  • Granular materials
  • Contact forces
  • Fabric
  • Multiscale
  • Critical state