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Acta Geotechnica

, Volume 8, Issue 5, pp 547–560 | Cite as

Transmission of kinematic information in dense granular systems: local and nonlocal network sensing

  • David M. Walker
  • Antoinette TordesillasEmail author
  • Amy L. Rechenmacher
Research Paper

Abstract

We study how kinematic information propagates in plane strain compression tests for two granular samples, one comprising glass beads and the other is sand. Of interest are the structures of directed networks constructed from static linear relationships among grain-scale kinematical measurements obtained using digital image correlation. The exact form and kinematical information used in each linear relationship is selected using a data modelling algorithm that appeals to the information theory description length philosophy encapsulated by the principle of Occam’s Razor. For both tests, we find that the observation sites with the most complicated relationships (i.e., those which require the x- and y-coordinates of the displacements of both neighboring and distant sites to best represent their own kinematics) are located in that region where the persistent shear band develops. The static linear relationships for these sites involve a length scale that is around 7–15 times the mean particle diameter, consistent with the observed thickness of the shear band in each sample. Our findings corroborate earlier evidence from the extant literature that the kinematics inside shear bands are necessarily nonlocal and further highlights the crucial importance of incorporating shear band kinematics in constitutive modelling. We shed new insights not only for constitutive modelling but also in the use of sensors to detect motion in deforming granular systems: that sensors with local sensing and monitoring capabilities are sufficient for distilling information on kinematic transmission—except in the shear band where nonlocal information, or information from spatially distant sensors, is a necessity.

Keywords

Digital image correlation Directed networks Granular media Kinematics Sensor networks 

Notes

Acknowledgments

We thank Dr. John Peters for valuable insights and useful comments. This work was partially supported by the US Army Research Office (W911NF-11-1-0175), the Australian Research Council (DP0986876 and DP120104759), and the Melbourne Energy Institute (AT, DMW). ALR is supported by USA National Science Foundation (NSF) Grant CMMI-0748284.

References

  1. 1.
    Abedi S, Rechenmacher AL, Orlando AD (2012) Vortex formation and dissolution in sheared sands. Granul Matter 14:695–705CrossRefGoogle Scholar
  2. 2.
    Alonso-Marroquin F, Vardoulakis I, Herrmann HJ, Weatherley D, Mora P (2006) Effect of rolling on dissipation in fault gouges. Phys Rev E 74:031,306CrossRefGoogle Scholar
  3. 3.
    Andò E, Hall SA, Viggiani G, Desrues J, Bésuelle P (2012) Grain scale experimental investigation of localised deformation in sand: a discrete particle tracking approach. Acta Geotechnica 7(1):1–13CrossRefGoogle Scholar
  4. 4.
    Bardet JP, Proubet J (1991) A numerical investigation of the structure of persistent shear bands in granular media. Géotechnique 41:599–613CrossRefGoogle Scholar
  5. 5.
    Bathurst RJ, Rothenburg L (1988) Micromechanical aspects of isotropic granular assemblies with linear contact interactions. J Appl Mech 55:17–23CrossRefGoogle Scholar
  6. 6.
    Bernstein J, Miller R, Kelley W, Ward P (1999) Low-noise MEMS vibration sensor for geophysical applications. J Microelectromech Syst 8:433–438CrossRefGoogle Scholar
  7. 7.
    Chupin O, Rechenmacher AL, Abedi S (2012) Finite strain analysis of non-uniform deformations in shear bands in sand. Int J Numer Anal Methods Geomech 36:1651–1666CrossRefGoogle Scholar
  8. 8.
    Clauset A, Shalizi CR, Newman MEJ (2009) Power-law distributions in empirical data. SIAM Rev 51:661–703, companion toolbox http://www.santafe.edu/aaronc/powerlaws/ Google Scholar
  9. 9.
    Cundall P (1989) Numerical experiments on localization in frictional materials. Ingenieur Archiv 59(2):148–159CrossRefGoogle Scholar
  10. 10.
    Desrues J, Viggiani G (2004) Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int J Numer Anal Methods Geomech 28:279–321CrossRefGoogle Scholar
  11. 11.
    Ellenbroek WG, Zeravcic Z, van Saarloos W, van Hecke M (2009) Non-affine response: jammed packings vs. spring networks. Europhys Lett 87:34,004CrossRefGoogle Scholar
  12. 12.
    Elliot RJ, Aggoun L, Moore JB (2010) Hidden Markov Models: Estimation and Control, Springer, New YorkGoogle Scholar
  13. 13.
    Griffa M, Daub EG, Guyer RA, Johnson PA, Marone C, Carmeliet J (2011) Vibration-induced slip in sheared granular layers and the micromechanics of dynamics earthquake triggering. Europhy Lett 96:14,001CrossRefGoogle Scholar
  14. 14.
    Judd K, Mees A (1995) On selecting nonlinear models for nonlinear time series. Phys D 82:426–444CrossRefzbMATHGoogle Scholar
  15. 15.
    Liu J, Zhao F, Cheung P, Guibas L (2004) Apply geometric duality to energy-efficient non-local phenomenon awareness using sensor networks. IEEE Wirel Commun 11:62–68Google Scholar
  16. 16.
    Muthuswamy M, Tordesillas A (2006) How do interparticle contact friction, packing density and degree of polydispersity affect force propagation in particulate assemblies? J Stat Mech Theory Exp 06:P09,003Google Scholar
  17. 17.
    Nakamura T, Tanizawa T (2012) Networks with time structure from time series. Phys A 391:4704–4710CrossRefGoogle Scholar
  18. 18.
    Nakamura T, Judd K, Mees AI, Small M (2006) A comparative study of information criteria for model selection. Int J Bifurcat Chaos 16:2153–2175MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Oda M, Iwashita K (2000) Study on couple stress and shear band development in granular media based on numerical simulation analyses. Int J Eng Sci 38:1713–1740CrossRefGoogle Scholar
  20. 20.
    Oda M, Kazama H (1998) Microstructure of shear bands and its relation to the mechanisms of dilatancy and failure of dense granular soils. Géotechnique 48:465–481CrossRefGoogle Scholar
  21. 21.
    Peters JF, Walizer LE (2012) Patterned non-affine motion in granular media. Tech. Rep. ERDC/GSL TR-12-28, geotechnical and sturctures laboratory, US Army Corps of EngineersGoogle Scholar
  22. 22.
    Ramesh MV (2009) Real-time wireless sensor network for landslide detection. In: Third international conference on sensor technologies and applications, 2009. SENSORCOMM’09., IEEE Conference Publications, pp 405–409Google Scholar
  23. 23.
    Rechenmacher A, Abedi S, Chupin O (2010) Evolution of force chains in shear bands in sands. Géotechnique 60(5):343CrossRefGoogle Scholar
  24. 24.
    Rechenmacher AL, Abedi S (2011) Length scales for nonaffine deformation in localized, granular shear. In: Bonelli S, Dascalu C, Nicot F (eds) Advances in bifurcation and degradation in geomaterials, Springer series in geomechanics and geoengineering, vol 11. Springer, pp 59–65Google Scholar
  25. 25.
    Rechenmacher AL, Abedi S, Chupin O (2011) Characterization of mesoscale instabilities in localized granular shear using digital image correlation. Acta Geotechnica 6:205–217CrossRefGoogle Scholar
  26. 26.
    Rissanen J (1989) Stochastic complexity in statistical inquiry. World Scientific, SingaporezbMATHGoogle Scholar
  27. 27.
    Small M (2005) Applied nonlinear time series analysis: applications in physics, physiology and finance. Nonlinear science series A. vol 52. World Scientific, SingaporeGoogle Scholar
  28. 28.
    Small M, Judd K (1999) Detecting periodicity in experimental data using linear modeling techniques. Phys Rev E 59(2):1379–1385CrossRefGoogle Scholar
  29. 29.
    Suiker ASJ, Chang CS (2004) Modeling failure and deformation of an assembly of spheres with frictional contacts. J Eng Mech 130:283–293CrossRefGoogle Scholar
  30. 30.
    Sutton MA, Orteau JJ, Schreier HW (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer, New YorkGoogle Scholar
  31. 31.
    Tanizawa T, Nakamura T (2011) Complex network from time series. In: 2011 International symposium on nonlinear theory and its applications, NOLTA2011, Kobe pp 690–692Google Scholar
  32. 32.
    Tordesillas A (2007) Force chain buckling, unjamming transitions and shear banding in dense granular assemblies. Philos Mag 87:4987–5016CrossRefGoogle Scholar
  33. 33.
    Tordesillas A, Muthuswamy M (2009) On the modelling of confined buckling of force chains. J Mech Phys Solids 57:706–727MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Tordesillas A, Muthuswamy M, Walsh SDC (2008) Mesoscale measures of nonaffine deformation in dense granular assemblies. J Eng Mech ASCE 134:1095–1113CrossRefGoogle Scholar
  35. 35.
    Tordesillas A, Zhang J, Behringer RP (2009) Buckling force chains in dense granular assemblies: physical and numerical experiments. Geomech Geoeng 4:3–16CrossRefGoogle Scholar
  36. 36.
    Tordesillas A, Walker DM, Lin Q (2010) Force cycles and force chains. Phys Rev E 81:011,302CrossRefGoogle Scholar
  37. 37.
    Tordesillas A, Shi J, Peters JF (2012) Isostaticity in cosserat continuum. Granul Matter 14:295–231CrossRefGoogle Scholar
  38. 38.
    Utter B, Behringer RP (2008) Experimental measures of affin and nonaffine deformation in granular shear. Phys Rev Lett 100:208,302CrossRefGoogle Scholar
  39. 39.
    Walker DM, Tordesillas A (2012) Taxonomy of granular rheology from grain property networks. Phys Rev E 85:011,304CrossRefGoogle Scholar
  40. 40.
    Walker DM, Tordesillas A, Nakamura T, Tanizawa T (2013) Directed network topology from grain stress dynamics. Phys Rev E 87:032,203CrossRefGoogle Scholar
  41. 41.
    Werner-Allen G, Lorincz K, Ruiz M, Marcillo O, Johnson J, Lees J, Welsh M (2006) Deploying a wireless sensor network on an active volcano. Int Comput IEEE 10:18–25CrossRefGoogle Scholar
  42. 42.
    Whittle P (1971) Optimization under constraints. Wiley, ChichesterzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • David M. Walker
    • 1
  • Antoinette Tordesillas
    • 1
    Email author
  • Amy L. Rechenmacher
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of MelbourneParkvilleAustralia
  2. 2.Department of Civil and Environmental EngineeringUniversity of Southern CaliforniaLos AngelesUSA

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