Pure and Applied Geophysics

, Volume 168, Issue 12, pp 2239–2257 | Cite as

Granular Controls on Periodicity of Stick-Slip Events: Kinematics and Force-Chains in an Experimental Fault

  • Nicholas W. Hayman
  • Lucie Ducloué
  • Kate L. Foco
  • Karen E. Daniels


It is a long-standing question whether granular fault material such as gouge plays a major role in controlling fault dynamics such as seismicity and slip-periodicity. In both natural and experimental faults, granular materials resist shear and accommodate strain via interparticle friction, fracture toughness, fluid pressure, dilation, and interparticle rearrangements. Here, we isolate the effects of particle rearrangements on granular deformation through laboratory experiments. Within a sheared photoelastic granular aggregate at constant volume, we simultaneously visualize both particle-scale kinematics and interparticle forces, the latter taking the form of force-chains. We observe stick-slip deformation and associated force drops during an overall strengthening of the shear zone. This strengthening regime provides insight into granular rheology and conditions of stick-slip periodicity, and may be qualitatively analogous to slip that accompanies longer term interseismic strengthening of natural faults. Of particular note is the observation that increasing the packing density increases the stiffness of the granular aggregate and decreases the damping (increases time-scales) during slip events. At relatively loose packing density, the slip displacements during the events follow an approximately power-law distribution, as opposed to an exponential distribution at higher packing density. The system exhibits switching between quasi-periodic and aperiodic slip behavior at all packing densities. Higher packing densities favor quasi-periodic behavior, with a longer time interval between aperiodic events than between quasi-periodic events. This difference in the time-scale of aperiodic stick-slip deformation is reflected in both the kinematics of interparticle slip and the force-chain dynamics: all major force-chain reorganizations are associated with aperiodic events. Our experiments conceptually link observations of natural fault dynamics with current models for granular stick-slip dynamics. We find that the stick-slip dynamics are consistent with a driven harmonic oscillator model with damping provided by an effective viscosity, and that shear-transformation-zone, jamming, and crackling noise theories provide insight into the effective stiffness and patterns of shear localization during deformation.


Granular Material Packing Density Local Failure Natural Fault Boundary Failure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We are grateful to Karin Dahmen and Luc Lavier for sharing key modeling results, and to Stefanos Papanikolaou and James Sethna for sharing the Wiener filtering technique. Three anonymous reviewers contributed to the revision of the manuscript. KLF and KED have been supported by a North Carolina State University FRPD and NSF CAREER award DMR-0766743. LD and NWH have been supported by the University of Texas Institute for Geophysics (UTIG) under an Innovation and Opportunity grant; this is UTIG contribution #2315.


  1. Abe S, Mair K. Effects of gouge fragment shape on fault friction: New 3D modeling results. Geophysical Research Letters 36:L23302, 2009.Google Scholar
  2. Aharonov E, Sparks D. Rigidity phase transition in granular packings. Physical Review E 60:6890–6896, Dec 1999.Google Scholar
  3. Alonso-Marroquin F, Vardoulakis I, Herrmann HJ, Weatherley D, Mora P. Effect of rolling on dissipation in fault gouges. Physical Review E 74(3):031306, 2006.Google Scholar
  4. Anthony JL, Marone C. Influence of particle characteristics on granular friction. Journal Of Geophysical Research–Solid Earth, 110(B8):B08409, Aug 19 2005.Google Scholar
  5. Ben-Zion Y. Collective behavior of earthquakes and faults: Continuum-discrete transitions, progressive evolutionary changes, and different dynamic regimes. Rev. Geophys 46:–, December 2008.Google Scholar
  6. Ben-Zion Y, Dahmen KA, Uhl JT. A unifying phase diagram for the dynamics of sheared solids and granular materials. 2010. Submitted to Pure and Applied Geophysics.Google Scholar
  7. Beroza GC, Ide S (2009) Deep tremors and slow quakes. Science, 324(5930):1025–1026.Google Scholar
  8. Blair D, Dufresne E. Matlab particle tracking code repository. Particle-tracking code available at
  9. Bretz M, Zaretzki R, Field SB, Mitarai N, Nori F. Broad distribution of stick-slip events in slowly sheared granular media: table-top production of a Gutenberg-Richter-like distribution. Europhysics Letters 74(6):1116–1122, 2006.Google Scholar
  10. Briscoe C, Song C, Wang P, Makse HA. Entropy of jammed matter. Physical Review Letters, 101(18):188001, 2008.Google Scholar
  11. Brodsky EE, Mori J. Creep events slip less than ordinary earthquakes. Geophysical Research Letters 34(16):5, 2007.Google Scholar
  12. Brudzinski MR, Allen RM. Segmentation in episodic tremor and slip all along Cascadia. Geology 35(10):907–910, 2007.Google Scholar
  13. Carlson JM. Two-dimensional model of a fault. Physical Review A 44(10):6226–6232, 1991.Google Scholar
  14. Cates ME, Wittmer JP, Bouchaud JP, Claudin P. Jamming, force chains, and fragile matter. Physical Review Letters 81:1841–1844, 1998.Google Scholar
  15. Chen KH, Nadeau RM, Rau RJ. Towards a universal rule on the recurrence interval scaling of repeating earthquakes?. Geophysical Research Letters 34(16):5, 2007.Google Scholar
  16. Dahmen K, Ertas D, Ben-Zion Y. Gutenberg-richter and characteristic earthquake behavior in simple mean-field models of heterogeneous faults. Physical Review E 58(2):1494–1501, 1998.Google Scholar
  17. Dahmen KA, Ben-Zion Y, Uhl JT. Micromechanical model for deformation in solids with universal predictions for stress-strain curves and slip avalanches. Physical Review Letters 102(17):175501, 2009a.Google Scholar
  18. Dahmen KA, Ben-Zion Y, Uhl JT. A simple analytic theory for the statistics of avalanches in sheared granular materials, with connections to plasticity and earthquakes. Submitted., 2009b.Google Scholar
  19. Daniels KE, Hayman NW. Force chains in seismogenic faults visualized with photoelastic granular shear experiments. Journal of Geophysical Research, 113:B11411, 2008. Movies available at
  20. Dantu P. Utilisation de reseaux pour l’étude experimentale des phenomenes elastiques et plastiques. Comptes Rendus Hebdomadaires Des Seances De L Academie Des Sciences 239(25):1769–1771, 1954.Google Scholar
  21. Daub EG, Carlson JM. Stick-slip instabilities and shear strain localization in amorphous materials. Physical Review E 80(6):066113, Dec 2009.Google Scholar
  22. Daub EG, Carlson JM. Friction, fracture, and earthquakes. Annual Review of Condensed Matter Physics, 1, 2010.Google Scholar
  23. Daub EG, Manning ML, Carlson JM. Pulse-like, crack-like, and supershear earthquake ruptures with shear strain localization. Journal Of Geophysical Research-solid Earth 115:B05311, May 18 2010.Google Scholar
  24. Drescher A, de Josselin de Jong G. Photoelastic verification of a mechanical model for flow of a granular material. Journal Of The Mechanics And Physics Of Solids, 20:337-&, 1972.Google Scholar
  25. Edwards SF, Oakeshott RBS. Theory of powders. Physica A 157:1080–1090, 1989.Google Scholar
  26. Eichhubl P, Hooker JH, Laubach SE. Pure and shear-enhanced compaction bands in Aztec Sandstone. Journal of Structural Geology 32:1873–1886, 2010.Google Scholar
  27. Falk ML, Langer JS. From simulation to theory in the physics of deformation and fracture. MRS Bulletin 25:40–45, May 2000.Google Scholar
  28. Fenistein D, van Hecke M. Kinematics - wide shear zones in granular bulk flow. Nature 425:256, Sep 18 2003Google Scholar
  29. Forterre Y, Pouliquen O. Flows of dense granular media. Annual Review Of Fluid Mechanics 40:1–24, 2008.Google Scholar
  30. Goldfinger C, Nelson CH, Johnson JE. Holocene earthquake records from the Cascadia subduction zone and northern San Andreas Fault based on precise dating of offshore turbidites. Annual Review of Earth and Planetary Sciences 31:555–577, 2003.Google Scholar
  31. Howell D, Behringer RP, Veje C. Stress fluctuations in a 2d granular Couette experiment: A continuous transition. Physical Review Letters 82:5241–5244, Jun 28 1999.Google Scholar
  32. Ide S, Beroza GC, Shelly DR, Uchide T. A scaling law for slow earthquakes. Nature 447(7140):76–79, May 3 2007.Google Scholar
  33. Jop P, Forterre Y, Pouliquen O. A constitutive law for dense granular flows. Nature 441:727–730, 8 June 2006.Google Scholar
  34. Kohlstedt DL, Evans B, Mackwell SJ. Strength of the lithosphere–constraints imposed by laboratory experiments. Journal of Geophysical Research-Solid Earth 100(B9):17587–17602, 1995.Google Scholar
  35. Luc L. Lavier and Richard A. Bennett. A model for ductile shear initiated by shear fracture: Application to slow slip events. 2010. Submitted.Google Scholar
  36. Luc L. Lavier and Richard A. Bennett. A model for ductile shear initiated by shear fracture: Application to slow slip events. EOS Trans. AGU, Fall meeting suppl., Abstract T51F-06, 2010.Google Scholar
  37. Liu AJ, Nagel SR. The jamming transition and the marginally jammed solid. Annual Review of Condensed Matter Physics, 2010.Google Scholar
  38. Liu CH, Nagel SR, Schecter DA, Coppersmith SN, Majumdar S, Narayan O, Witten TA. Force fluctuations in bead packs. Science 269(5223):513–515, Jul 28 1995.Google Scholar
  39. Mair K, Hazzard JF. Nature of stress accommodation in sheared granular material: Insights from 3d numerical modeling. Earth And Planetary Science Letters 259(3-4):469–485, Jul 30 2007.Google Scholar
  40. Marone C. Laboratory-derived friction laws and their application to seismic faulting. Annual Review Of Earth And Planetary Sciences 26:643–696, 1998.Google Scholar
  41. Miller B, O’Hern C, Behringer RP. Stress fluctuations for continuously sheared granular materials. Physical Review Letters 77:3110–3113, Oct 7 1996.Google Scholar
  42. Miller MM, Melbourne T, Johnson DJ, Sumner WQ. Periodic slow earthquakes from the Cascadia subduction zone. Science 295(5564):2423–2423, 2002.Google Scholar
  43. Mogi K. Recent earthquake prediction research in Japan. Science 233(4761):324–330, 1986.Google Scholar
  44. Moore DE, Rymer MJ. Talc-bearing serpentinite and the creeping section of the San Andreas fault. Nature 448:795–797, 2007Google Scholar
  45. Morgan JK. Particle dynamics simulations of rate- and state-dependent frictional sliding of granular fault gouge. Pure And Applied Geophysics 161(9-10):1877–1891, Oct 2004.Google Scholar
  46. Murray J, Segall P. Testing time-predictable earthquake recurrence by direct measurement of strain accumulation and release. Nature 419(6904):287–291, 2002.Google Scholar
  47. Nasuno S, Kudrolli A, Gollub JP. Friction in granular layers: Hysteresis and precursors. Physical Review Letters 79:949–952, Aug 4 1997.Google Scholar
  48. Nasuno S, Kudrolli A, Bak A, Gollub JP. Time-resolved studies of stick-slip friction in sheared granular layers. Physical Review E 58:2161–2171, Aug 1998Google Scholar
  49. O’Hern CS, Langer SA, Liu AJ, Nagel SR. Random packings of frictionless particles. Physical Review Letters 88:075507, Feb 18 2002.Google Scholar
  50. O’Hern CS, Silbert LE, Liu AJ, Nagel SR. Jamming at zero temperature and zero applied stress: The epitome of disorder. Physical Review E 68:011306, Jul 2003.Google Scholar
  51. Onoda GY, Liniger EG. Random loose packings of uniform spheres and the dilatancy onset. Phys. Rev. Lett 64(22):2727–2730, May 1990.Google Scholar
  52. Papanikolaou S, Bohn F, Sommer RL, Durin G, Zapperi S, Sethna JP. Beyond power laws: Universality in the average avalanche shape. 2010. doi: 10.1038/nphys1884.
  53. Peng T. Detect circles with various radii in grayscale image via Hough Transform. Particle-tracking code available at
  54. Pica Ciamarra M, Lippiello E, Godano C, de Arcangelis L. Unjamming dynamics: The micromechanics of a seismic fault model. Phys. Rev. Lett 104(23):238001, Jun 2010.Google Scholar
  55. Pouliquen O, Forterre Y. A non-local rheology for dense granular flows. Philosophical Transactions of the Royal Society A 367(1909):5091–5107, 2009.Google Scholar
  56. Puckett JG, Lechenault F, Daniels KE. Local origins of volume fraction fluctuations in dense granular materials. 2010. Submitted to Physical Review E: arXiv/1006.3790Google Scholar
  57. Rogers G, Dragert H. Episodic tremor and slip on the Cascadia subduction zone: the chatter of silent slip. Science 300(5627):1942–1943, 2003.Google Scholar
  58. Saffer DM, Marone C. Comparison of smectite- and illite-rich gouge frictional properties: application to the updip limit of the seismogenic zone along subduction megathrusts. Earth and Planetary Science Letters 215(1-2):219–235, 2003.Google Scholar
  59. Sammis CG, King GCP. Mechanical origin of power law scaling in fault zone rock. Geophysical Research Letters 34(4):L04312, Feb 28 2007.Google Scholar
  60. Scharer KM, Biasi GP, Weldon RJ, Fumal TE. Quasi-periodic recurrence of large earthquakes on the southern San Andreas fault. Geology 38(6):555–558, 2010.Google Scholar
  61. Schleicher AM, van der Pluijm BA, Warr LN. Nanocoatings of clay and creep of the San Andreas fault at Parkfield, California. Geology 38:667–670, 2010.Google Scholar
  62. Scholz CH. The frequency-magnitude relation of microfracturing in rock and its relation to earthquakes. Bulletin of the Seismological Society of America 58:399–415, 1968.Google Scholar
  63. Scholz CH. Earthquakes and friction laws. Nature 391(6662):37–42, 1998.Google Scholar
  64. Schwartz DP, Coppersmith KJ. Fault behvaior and characteristic earthquakes–examples from the Wasatch and San-Andreas fault zones. Journal of Geophysical Research 89(NB7):5681–5698, 1984.Google Scholar
  65. Scott GD, Kilgour DM. Density of random close packing of spheres. Journal Of Physics D-applied Physics 2(6):863–&, 1969.Google Scholar
  66. Segall P, Rice JR. Dilatancy, compation, and slip instability of a fluid-infiltrated fault. Journal of Geophysical Research-Solid Earth 100(B11):22155–22171, 1995.Google Scholar
  67. Segall P, Rubin AM, Bradley AM, Rice JR. Dilatant strengthening as a mechanism for slow slip events. Journal of Geophysical Research-Solid Earth. 2011. doi: 10.1029/2010JB007449.
  68. Sethna JP, Dahmen KA, Myers CR. Crackling noise. Nature 410(6825):242–250, Mar 8 2001.Google Scholar
  69. Silbert LE. Jamming of frictional spheres and random loose packing. Soft Matter 6:2918–2924, 2010.Google Scholar
  70. Smith SAF, Faulkner DR. Laboratory measurements of the frictional properties of the Zuccale low-angle normal fault, Elba Island, Italy. Journal of Geophysical Research-Solid Earth 115:17, 2010.Google Scholar
  71. Stein RS, King GCP, Lin J. Stress triggering of the 1994 M=6.7 Northridge, California, earthquake by its predecessors. Science 265(5177):1432–1435, 1994.Google Scholar
  72. Tordesillas A. Force chain buckling, unjamming transitions and shear banding in dense granular assemblies. Philosophical Magazine 87(32):4987–5016, 2007.Google Scholar
  73. Tordesillas A, Muthuswamy M. On the modeling of confined buckling of force chains. Journal of the Mechanics and Physics of Solids 57(4):706–727, April 2009.Google Scholar
  74. Torquato S, Truskett TM, Debenedetti PG. Is random close packing of spheres well defined? Physical Review Letters 84(10):2064–2067, Mar 2000.Google Scholar
  75. van Hecke M. Granular matter - a tale of tails. Nature 435:1041–1042, Jun 23 2005.Google Scholar
  76. van Hecke M. Jamming of soft particles: Geometry, mechanics, scaling and isostaticity. Journal of Physics: Condensed Matter 22:033101, 2010.Google Scholar
  77. Wintsch RP, Christoffersen R, Kronenberg AK. Fluid-rock reaction weakening of fault zones. Journal of Geophysical Research-Solid Earth, 100(B7):13021–13032, 1995.Google Scholar
  78. Wyart M. On the rigidity of amorphous solids. Annales De Physique 30(3):1,May-jun 2005.Google Scholar
  79. Yu P. Stick-slip in a 2D granular medium. PhD thesis, Duke University, 2008.Google Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Nicholas W. Hayman
    • 1
  • Lucie Ducloué
    • 1
    • 2
  • Kate L. Foco
    • 3
  • Karen E. Daniels
    • 3
  1. 1.Institute for Geophysics, University of TexasAustinUSA
  2. 2.Département de PhysiqueÉcole Normale SupérieureParisFrance
  3. 3.Department of PhysicsNorth Carolina State UniversityRaleighUSA

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