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Strain tensor determination of compressed individual silica sand particles using high-energy synchrotron diffraction

Abstract

The three-dimensional X-ray diffraction (3DXRD) nondestructive technique was used to measure lattice strains within individual sand particles subjected to compressive loading. Three experiments were conducted on similar single columns of silica sand particles with particle sizes between 0.595 and 0.841 mm. In each experiment, three sand particles were placed inside an acrylic mold with an inner diameter of 1 mm. Multiple in situ 3DXRD scans were acquired for each sand column as compressive load was increased. The volume-averaged lattice strain tensor was calculated for each sand particle. In addition, particle orientation and volumetric strain were calculated for individual sand particles. The axial normal strain \(\upvarepsilon _\mathrm{zz}\) exhibited a linear response in the range of 0 to \(10^{-3}\) when the applied compressive axial load (F) increased from 0 to \(\sim \)30 N when one particle in the sand column fractured. Stress tensor of individual particles was calculated from the acquired lattice strain measurements and elastic constants of silica sand that were reported in the literature. To the best of our knowledge, there have been no reported experimental measurements of the lattice strain tensor measurements within individual silica sand particles. The quantitative measurements reported in this paper at the particle level are very valuable for developing, validating or calibrating micromechanics-based finite element and discrete element models to predict the constitutive behavior of granular materials. 3DXRD represents an exciting new non-destructive technique to directly measure constitutive behavior at the scale of individual particles.

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Acknowledgments

This material is based upon work supported by the National Science Foundation (NSF) under Grant No. (CMMI-1156436). The 3DXRD data were collected using the X-ray Operations and Research Beamline 1-ID and SMT scans were collected using the X-ray Operations and Research Beamline Station 13-BMD at the Advanced Photon Source (APS), Argonne National Laboratory (ANL). We thank Dr. Mark Rivers of (APS) for help in performing the SMT scans. We also acknowledge the support of GeoSoilEnviroCARS (Sector 13), which is supported by the National Science Foundation—Earth Sciences (EAR-1128799), and the Department of Energy, Geosciences (DE-FG02-94ER14466). Use of the Advanced Photon Source, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract No. DE-AC02-06CH11357.

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Correspondence to Khalid Alshibli.

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Alshibli, K., Cil, M.B., Kenesei, P. et al. Strain tensor determination of compressed individual silica sand particles using high-energy synchrotron diffraction. Granular Matter 15, 517–530 (2013). https://doi.org/10.1007/s10035-013-0424-x

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  • DOI: https://doi.org/10.1007/s10035-013-0424-x

Keywords

  • Silica sand
  • Lattice strain
  • 3D X-ray diffraction
  • Granular materials
  • Synchrotron