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Constitutive Behavior and strain localization in granular materials

Discrete Particle Translation Gradient Concept to Expose Strain Localization in Sheared Granular Materials

Granular materials are composed of discrete particles that translate and rotate against neighboring particles when they are subjected to global stresses applied at the soil mass boundaries. Particle level kinematics (translation and rotation) affect the behavior of sheared granular materials. Shear strains concentrate in zones of intensive shearing, known as shear bands. Experimental quantification of 3D particle kinematics can be used to calibrate and validate micromechanics based constitutive models that account for the effects of strain localization (shear bands) on the behavior of granular materials.

We use 3D measurements of individual particle kinematics for axisymmetric triaxial experiments to track the onset of strain localization within uniform silica sand, utilizing images that were acquired using synchrotron micro-computed tomography (SMT). A new experimental discrete approach is proposed to calculate the translation vectors of individual particles relative to translation vectors of neighboring particles using the second order norm, or Euclidian length difference, which gives the particle’s discrete relative translation.

Conventional particle kinematic techniques (e.g., Figs. 1 & 2) can be used to analyze and quantify failure shearing behavior of granular material; however, they cannot expose many intricacies and lesser intermittent localized strains (micro shear bands, MSB) during hardening that lead to failure, especially if a specimen fails through bulging. Intricate zones of localized shear strain within a specimen that are not exposed by particle kinematics can be mined from the data by comparing a particle translation vector with that of all of its neighboring particles. The concept of relative particle translation branches from kinematic displacements and relates a particle translation vector to that of all neighboring particles in contact with that particle.

Incremental relative translation of individual particles was calculated from the SMT images where the previous SMT image was taken as the reference for relative translation of particles in the current SMT image. Relative translation values are normalized by the global axial compression imposed by the top end plate. Figure 3 displays the incremental relative translation for the experiment.

The proposed relative translation concept shows much more intricate detail of particle behavior during the hardening than conventional particle kinematic or continuum approaches. The onset of multiple MSB in several directions is exposed using relative translations that are not apparent when quantifying particle translations or rotations, or from continuum based strain measurements. The MSB merge and contribute to the development of the final shear band in a very complex shear evolution process, which is not captured based on calculating particle translations or rotations. The final shear band is well defined and delineated with high relative translations, while conventional particle translation calculations and rotations do not expose delineation with as much detail.

Acknowledgments

This material is partially funded by the US National Science Foundation (NSF) under Grant No. CMMI-1266230 and Office of Naval Research (ONR) grant No. N00014-11-1-0691. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF or ONR. The SMT images were collected using the X-Ray Operations and Research Beamline Station 13-BMD at Argonne Photon Source (APS), a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. We 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). We thank Dr. Mark Rivers of APS for help in performing the SMT scans.

Behavior of sand under plane strain condition

Related Publications:

  1. Amirrahmat, S., Druckrey, A., Alshibli, K. A., and Al-Raoush, R. I. (2019). “Micro Shear Bands: Precursor for Strain Localization in Sheared Granular Materials”, ASCE Journal of Geotechnical & Geoenvironmental Engineering, Vol. 145, No. 2,
  2. Druckrey, A., Alshibli, K.A., Al-Raoush, R. (2018). “Discrete Particle Translation Gradient Concept to Expose Strain Localization in Sheared Granular Materials using 3D Experimental Kinematic Measurements”, Geotechnique, Vol 68, No. 2, 162-170,DOI:
  3. Amirrahmat, S., Alshibli, K. A., Jarrar, M. F., Zhang, B., and Regueiro, R. (2018). “Equivalent Continuum Strain Calculations based on 3D Particle Kinematic Measurements of Sand”, International Journal for Numerical and Analytical Methods in Geomechanics, 42: 999-1015, published online on March 6, 2018,
  4. Alshibli, K. A., Cil, B. (2018) “Influence of Particle Morphology on the Friction and Dilatancy of Sand”, ASCE Journal of Geotechnical & Geoenvironmental Engineering, Vol. 144, No. 3, published online Dec. 16, 2017, DOI: , “”
  5. Alshibli, K. A., Jarrar, M., Druckrey, A., Al-Raoush, R (2016). “Influence of Particle Morphology on 3D Kinematic Behavior and Strain Localization of Sheared Sand”, ASCE Journal of Geotechnical & Geoenvironmental Engineering, DOI 10.1061/(ASCE)GT.1943-5606.0001601, ,””
  6. Cil, M. B. and Alshibli, K. A. (2014) “3D Analysis of Kinematic Behavior of Granular Materials in Triaxial Testing Using DEM with Flexible Membrane Boundary”, Acta Geotechnica, Vol. 9, No. 2, pp. 287-298,
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  8. Hasan, A. and Alshibli, K. A. (2010) “Experimental Assessment of 3D Particle-to-Particle Interaction within Sheared Sand using Synchrotron Microtomography”, Geotechnique, Vol. 60, No. 5, pp. 369-379.
  9. Alshibli, K. A. and Akbas, I. S. (2007) “Strain Localization in Clay: Plane Strain versus Triaxial Loading Conditions”, Geotechnical and Geological Engineering, Vol. 25, No. 1, pp. 45-55, DOI:
  10. Alshibli, K. A., Alsaleh, M. I., and Voyiadjis, G. Z. (2006) “Modeling Strain Localization in Granular Materials Using Micropolar Theory: Numerical Implementation and Verification”, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 30, No. 15, pp. 1525-1544, DOI:
  11. Alsaleh, M. I., Voyiadjis, G. Z., and Alshibli, K. A. (2006) “Modeling Strain Localization in Granular Materials Using Micropolar Theory: Mathematical Formulations”, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 30, No. 15, pp. 1501-1524, DOI:
  12. Alshibli, K. A. and Roussel, L. (2006) “Experimental investigation of slip-stick behavior in granular materials”, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 30, No. 14, pp. 1391-1407, DOI:
  13. Alsaleh, M. I., Alshibli, K.A., and Voyiadjis, G. Z. (2006) “Influence of Micro-Material Heterogeneity on Strain Localization in Granular Materials”, ASCE: International Journal of Geomechanics, Vol. 6, No. 4, pp. 248-259, DOI:
  14. Voyiadjis, G. Z., Alsaleh, M. I., and Alshibli, K.A. (2005) “Evolving Internal Length Scales in Plastic Strain Localization for Granular Materials”, International Journal of Plasticity, Vol. 21, No. 10, pp. 2000-2024, DOI:
  15. Alshibli, K. A., Batiste, S. N., and Sture, S. (2003) “Strain Localization in Sand: Plane Strain Versus Triaxial Compression”, ASCE, Journal of Geotechnical & Geoenvironmental Engineering, Vol. 129, No. 6, pp. 483-499, DOI:
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  17. Alshibli, K. A., and El-Saidany, H. A. (2001) “Quantifying Void Ratio in Granular Materials Using Voronoi Tessellation”, ASCE, Journal of Computing in Civil Engineering Vol. 15, No. 3, pp. 232-238, DOI:
  18. Alshibli, K. A., and Sture, S. (2000) “Shear Band Formation in Plane Strain Experiments of Sand”, ASCE, Journal of Geotechnical & Geoenvironmental Engineering, Vol. 126, No. 6, pp. 495-503, DOI:
  19. Alshibli, K. A., and Sture, S. (2000) “Shear Band Formation in Plane Strain Experiments of Sand”, ASCE, Journal of Geotechnical & Geoenvironmental Engineering, Vol. 126, No. 6, pp. 495-503, DOI:
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