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

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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.

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References

  1. Abedi S, Rechenmacher AL, Orlando AD (2012) Vortex formation and dissolution in sheared sands. Granul Matter 14:695–705

    Article  Google Scholar 

  2. Alonso-Marroquin F, Vardoulakis I, Herrmann HJ, Weatherley D, Mora P (2006) Effect of rolling on dissipation in fault gouges. Phys Rev E 74:031,306

    Article  Google Scholar 

  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):1–13

    Article  Google Scholar 

  4. Bardet JP, Proubet J (1991) A numerical investigation of the structure of persistent shear bands in granular media. Géotechnique 41:599–613

    Article  Google Scholar 

  5. Bathurst RJ, Rothenburg L (1988) Micromechanical aspects of isotropic granular assemblies with linear contact interactions. J Appl Mech 55:17–23

    Article  Google Scholar 

  6. Bernstein J, Miller R, Kelley W, Ward P (1999) Low-noise MEMS vibration sensor for geophysical applications. J Microelectromech Syst 8:433–438

    Article  Google Scholar 

  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 36:1651–1666

    Article  Google Scholar 

  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. Cundall P (1989) Numerical experiments on localization in frictional materials. Ingenieur Archiv 59(2):148–159

    Article  Google Scholar 

  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 28:279–321

    Article  Google Scholar 

  11. Ellenbroek WG, Zeravcic Z, van Saarloos W, van Hecke M (2009) Non-affine response: jammed packings vs. spring networks. Europhys Lett 87:34,004

    Article  Google Scholar 

  12. Elliot RJ, Aggoun L, Moore JB (2010) Hidden Markov Models: Estimation and Control, Springer, New York

  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 96:14,001

    Article  Google Scholar 

  14. Judd K, Mees A (1995) On selecting nonlinear models for nonlinear time series. Phys D 82:426–444

    Article  MATH  Google Scholar 

  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 11:62–68

    Google Scholar 

  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:P09,003

    Google Scholar 

  17. Nakamura T, Tanizawa T (2012) Networks with time structure from time series. Phys A 391:4704–4710

    Article  Google Scholar 

  18. Nakamura T, Judd K, Mees AI, Small M (2006) A comparative study of information criteria for model selection. Int J Bifurcat Chaos 16:2153–2175

    Article  MathSciNet  MATH  Google Scholar 

  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 38:1713–1740

    Article  Google Scholar 

  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 48:465–481

    Article  Google Scholar 

  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 Engineers

  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 405–409

  23. Rechenmacher A, Abedi S, Chupin O (2010) Evolution of force chains in shear bands in sands. Géotechnique 60(5):343

    Article  Google Scholar 

  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 59–65

  25. Rechenmacher AL, Abedi S, Chupin O (2011) Characterization of mesoscale instabilities in localized granular shear using digital image correlation. Acta Geotechnica 6:205–217

    Article  Google Scholar 

  26. Rissanen J (1989) Stochastic complexity in statistical inquiry. World Scientific, Singapore

    MATH  Google Scholar 

  27. Small M (2005) Applied nonlinear time series analysis: applications in physics, physiology and finance. Nonlinear science series A. vol 52. World Scientific, Singapore

    Google Scholar 

  28. Small M, Judd K (1999) Detecting periodicity in experimental data using linear modeling techniques. Phys Rev E 59(2):1379–1385

    Article  Google Scholar 

  29. Suiker ASJ, Chang CS (2004) Modeling failure and deformation of an assembly of spheres with frictional contacts. J Eng Mech 130:283–293

    Article  Google Scholar 

  30. Sutton MA, Orteau JJ, Schreier HW (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer, New York

    Google Scholar 

  31. Tanizawa T, Nakamura T (2011) Complex network from time series. In: 2011 International symposium on nonlinear theory and its applications, NOLTA2011, Kobe pp 690–692

  32. Tordesillas A (2007) Force chain buckling, unjamming transitions and shear banding in dense granular assemblies. Philos Mag 87:4987–5016

    Article  Google Scholar 

  33. Tordesillas A, Muthuswamy M (2009) On the modelling of confined buckling of force chains. J Mech Phys Solids 57:706–727

    Article  MathSciNet  MATH  Google Scholar 

  34. Tordesillas A, Muthuswamy M, Walsh SDC (2008) Mesoscale measures of nonaffine deformation in dense granular assemblies. J Eng Mech ASCE 134:1095–1113

    Article  Google Scholar 

  35. Tordesillas A, Zhang J, Behringer RP (2009) Buckling force chains in dense granular assemblies: physical and numerical experiments. Geomech Geoeng 4:3–16

    Article  Google Scholar 

  36. Tordesillas A, Walker DM, Lin Q (2010) Force cycles and force chains. Phys Rev E 81:011,302

    Article  Google Scholar 

  37. Tordesillas A, Shi J, Peters JF (2012) Isostaticity in cosserat continuum. Granul Matter 14:295–231

    Article  Google Scholar 

  38. Utter B, Behringer RP (2008) Experimental measures of affin and nonaffine deformation in granular shear. Phys Rev Lett 100:208,302

    Article  Google Scholar 

  39. Walker DM, Tordesillas A (2012) Taxonomy of granular rheology from grain property networks. Phys Rev E 85:011,304

    Article  Google Scholar 

  40. Walker DM, Tordesillas A, Nakamura T, Tanizawa T (2013) Directed network topology from grain stress dynamics. Phys Rev E 87:032,203

    Article  Google Scholar 

  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 10:18–25

    Article  Google Scholar 

  42. Whittle P (1971) Optimization under constraints. Wiley, Chichester

    MATH  Google Scholar 

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Melbourne, Parkville, VIC, 3010, Australia

    David M. Walker & Antoinette Tordesillas

  2. Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, CA, 90089-2531, USA

    Amy L. Rechenmacher

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  1. David M. Walker
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  2. Antoinette Tordesillas
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  3. Amy L. Rechenmacher
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Correspondence to Antoinette Tordesillas.

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Walker, D.M., Tordesillas, A. & Rechenmacher, A.L. Transmission of kinematic information in dense granular systems: local and nonlocal network sensing. Acta Geotech. 8, 547–560 (2013). https://doi.org/10.1007/s11440-013-0266-z

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  • DOI: https://doi.org/10.1007/s11440-013-0266-z

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