A Network of Fractal Force Chains and Their Effect in Granular Materials under Compression

  • Luis E. Vallejo
  • Sebastian Lobo-Guerrero
  • Zamri Chik

Summary

Granular materials forming part of civil engineering structures such as rockfill dams and the granular base in pavement systems are subjected to large compressive stresses resulting from gravity and traffic loads respectively. As a result of these compressive stresses, the granular materials break into pieces of different sizes. The size distribution of the broken granular material has been found to be fractal in nature. However, there is no explanation to date about the mechanisms that cause the granular materials to develop a fractal size distribution. In the present study, a compression test designed to crush granular materials is presented. The tests used 5 mm glass beads and a plexiglass cylinder having an internal diameter equal to 5 cm. As a result of compression in the cylinder, the glass beads broke into pieces that had a fractal size distribution. The compression test was numerically simulated using the Discrete Element Method (DEM). The DEM simulation indicated that the particles developed a network of force chains in order to resist the compressive stress. These force chains did not have a uniform intensity but was found to vary widely through out the sample. Also, the distribution of the force chains in the sample did not involve all the grains but only a selective number of them. Thus, the force chains did not cover the whole sample. Using the box method, it was determined that the distribution of the force chains in the sample was fractal in nature. Also, the intensity of the force chains in the sample was found to be fractal in nature. Thus, the fractal nature of the intensity of the force chains and their distribution were found to be the main reason why granular material develop fractal fragments as a result of compression.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lee, K.L., and Farhoomand, J. (1967). “Compressibility and crushing of granular soils in anisotropic triaxial compression”. Canadian Geotechnical J., Vol. 4, No. 1, pp. 68–86.CrossRefGoogle Scholar
  2. 2.
    Lade, P.V., Yamamuro, J.A., and Bopp, P.A. (1996). “Significance of particle crushing in granular materials”. J. of Geotechnical Eng., ASCE, Vol. 122, No. 4, pp. 309–316.CrossRefGoogle Scholar
  3. 3.
    Coop, M.R. (1999). “The influence of particle breakage and state on the behavior of sand”. Proceedings of the Int. Worshop on Soil Crushability, Yamaguchi, Japan, pp. 19–57.Google Scholar
  4. 4.
    Bolton, M.D. (1999). “The role of micro-mechanics in soil mechanics”. Proceedings of the Int. Workshop on Soil Crushability, Yamaguchi, Japan, pp. 58–82.Google Scholar
  5. 5.
    Cundall, P.A., and Strack, O.D.L. (1979). “A discrete numerical model for granular Assemblies”. Geotechnique, Vol. 29, No. 1, pp. 47–65.CrossRefGoogle Scholar
  6. 6.
    Radjai, F. (1995). “Dynamique des Rotations et Frottement Collectif dans les Sys-temes Granulaires”. Ph.D. Thesis, Universite de Paris-Sud XI, Orsay.Google Scholar
  7. 7.
    Liu, C.H., Nagel, D., Shecter, D., Coppersmith, S.N., Majumdar, S., Narayan, O., and Witten, T.A. (1995). “Force fluctuations in bead packs”. Science, Vol. 269, pp. 513–515.Google Scholar
  8. 8.
    Coppersmith, S.N., Liu, C.H., Majumdar, S., Narayan, O., and Witten, T.A. (1996). “Model for force fluctiations in bead packs”. Physical Review E, Vol. 53, No. 5, pp. 4673–4685.CrossRefGoogle Scholar
  9. 9.
    Howell, D.W., Behringer, R.P. (1999). “Fluctuations in granular media”. Chaos, Vo. 9, No. 3, pp. 559–572.CrossRefMATHGoogle Scholar
  10. 10.
    Cruz Hidalgo, R., Grosse, C.U., Kun, F., Reinhardt, H.W., and Herrmann, H.S. (2002). “Evolution of percolating force chains in compressed granular media”. Physical Review Letters, Vol. 89, No. 20, pp. 205501-1–205501-4.Google Scholar
  11. 11.
    McDowell, G.R., Bolton, M.D., and Robertson, D. (1996). “The fractal crushing of granular materials”. Int. J. of Mechanics and Physics of Solids, Vol. 44, No. 12, pp. 2079–2102.CrossRefGoogle Scholar
  12. 12.
    Tyler, S.W., and Wheatcraft, S.W. (1992). “Fractal scaling of soil particle-size distribution analysis and limitations”. Soil Science Society of America Journal, Vol. 56, No. 2, pp. 47–67.CrossRefGoogle Scholar
  13. 13.
    Hyslip, J.P., and Vallejo, L.E. (1997). “Fractal analysis of the roughness and size distribution of granular materials”. Engineering Geology, Vol. 48, No. 3–4, pp. 231–244.CrossRefGoogle Scholar
  14. 14.
    Itasca Consulting Group (2002). “Particle Flow Code in Two Dimensions, PFC2D”, Version 3.0. Minneapolis, Minnesota.Google Scholar
  15. 15.
    Watanabe, K., and Takahashi, H. (1995). “Fractal geometry characterization of geothermal reservoir fracture networks”. Journal of Geophysical Research, Vo. 100, No. B1, pp. 521–528.CrossRefGoogle Scholar
  16. 16.
    Acuna, J., and Yortsos, Y.C. (1997). “Application of fractal geometry to the study of networks of fractures and their pressure transient”. Water Resources Research, Vol. 31, No. 3, pp. 527–540.CrossRefGoogle Scholar
  17. 17.
    Strogatz, S. (2003). “Sinc: The Emerging Science of Spontaneous Order”. Theia-Hyperion Press, New York, pp.338.Google Scholar

Copyright information

© Springer-Verlag London Limited 2005

Authors and Affiliations

  • Luis E. Vallejo
    • 1
  • Sebastian Lobo-Guerrero
    • 1
  • Zamri Chik
    • 1
  1. 1.Department of Civil and Environmental EngineeringUniversity of PittsburghPittsburghUSA

Personalised recommendations