Potential Energy as Metric for Understanding Stick–Slip Dynamics in Sheared Granular Fault Gouge: A Coupled CFD–DEM Study

Original Paper


We study the stick–slip behavior in a sheared granular fault gouge using a coupled discrete element method and computational fluid dynamics. We compare characteristics of slip events in dry and fluid-saturated granular fault gouge in drained conditions. The granular layer is confined under constant normal load and sheared with a velocity-controlled mechanism. Potential energy is stored through overlaps between particles. We show that the potential energy builds up during the stick phase and drops during slip instability. Our observations show that on average 8% of the drop in potential energy is converted into particle kinetic energy, while the rest dissipates. Our simulations show that drop in potential energy is a good measure of slip size showing a strong correlation with the drop in macroscopic friction coefficient. Our simulations show that in fluid-saturated granular fault gouge, the potential energy drop is higher leading to a higher drop in friction coefficient and in a higher kinetic energy of particles during slip event.


Energy budget Stick–slip Granular materials CFD–DEM Fault gouge Friction 



The authors thank ETH Zurich for funding this study and Empa for infrastructural supports. We also thank Robert Guyer, Paul Johnson and Chris Marone for fruitful discussions and two anonymous reviewers that helped to improve the manuscript.


  1. Abe S, Mair K (2009) Effects of gouge fragment shape on fault friction: new 3D modelling results. Geophys Res Lett.  https://doi.org/10.1029/2009gl040684 Google Scholar
  2. Agnolin I, Roux JN (2007) Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks. Phys Rev E.  https://doi.org/10.1103/PhysRevE.76.061302 Google Scholar
  3. Aharonov E, Sparks D (2004) Stick–slip motion in simulated granular layers. J Geophys Res.  https://doi.org/10.1029/2003jb002597 Google Scholar
  4. Anderson JD, Wendt J (1995) Computational fluid dynamics, vol 206. Springer, BerlinGoogle Scholar
  5. Anthony JL, Marone C (2005) Influence of particle characteristics on granular friction. J Geophys Res.  https://doi.org/10.1029/2004jb003399 Google Scholar
  6. Bar-Sinai Y, Spatschek R, Brener EA, Bouchbinder E (2015) Velocity-strengthening friction significantly affects interfacial dynamics, strength and dissipation. Sci Rep 5:7841.  https://doi.org/10.1038/srep07841 CrossRefGoogle Scholar
  7. Brace WF, Byerlee JD (1966) Stick–slip as a mechanism for earthquakes. Science 153(3739):990–992.  https://doi.org/10.1126/science.153.3739.990 CrossRefGoogle Scholar
  8. Cooke ML, Madden EH (2014) Is the earth lazy? A review of work minimization in fault evolution. J Struct Geol 66(Supplement C):334–346.  https://doi.org/10.1016/j.jsg.2014.05.004 CrossRefGoogle Scholar
  9. Cooke ML, Murphy S (2004) Assessing the work budget and efficiency of fault systems using mechanical models. J Geophys Res.  https://doi.org/10.1029/2004jb002968 Google Scholar
  10. Cundall PA, Strack OD (1979) A discrete numerical model for granular assemblies. Géotechnique 29(1):47–65CrossRefGoogle Scholar
  11. De Paola N, Hirose T, Mitchell T, Di Toro G, Viti C, Shimamoto T (2011) Fault lubrication and earthquake propagation in thermally unstable rocks. Geology 39(1):35–38.  https://doi.org/10.1130/G31398.1 CrossRefGoogle Scholar
  12. Del Castello M, Cooke ML (2007) Underthrusting-accretion cycle: work budget as revealed by the boundary element method. J Geophys Res.  https://doi.org/10.1029/2007jb004997 Google Scholar
  13. Dempsey D, Ellis S, Archer R, Rowland J (2012) Energetics of normal earthquakes on dip-slip faults. Geology 40(3):279–282.  https://doi.org/10.1130/G32643.1 CrossRefGoogle Scholar
  14. Di Renzo A, Di Maio FP (2004) Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes. Chem Eng Sci 59(3):525–541.  https://doi.org/10.1016/j.ces.2003.09.037 CrossRefGoogle Scholar
  15. Doglioni C, Barba S, Carminati E, Riguzzi F (2015) Fault on-off versus strain rate and earthquakes energy. Geosci Front 6(2):265–276.  https://doi.org/10.1016/j.gsf.2013.12.007 CrossRefGoogle Scholar
  16. Dorostkar O, Guyer RA, Johnson PA, Marone C, Carmeliet J (2017a) On the micromechanics of slip events in sheared, fluid saturated fault gouge. Geophys Res Lett.  https://doi.org/10.1002/2017GL073768 Google Scholar
  17. Dorostkar O, Guyer RA, Johnson PA, Marone C, Carmeliet J (2017b) On the role of fluids in stick–slip dynamics of saturated granular fault gouge using a coupled computational fluid dynamics–discrete element approach. J Geophys Res.  https://doi.org/10.1002/2017JB014099 Google Scholar
  18. Dorostkar O, Johnson P, Guyer R, Marone C, Carmeliet J (2017c) Do fluids modify the stick–slip behavior of sheared granular media? In: Poromechanics VI: proceedings of the sixth biot conference on poromechanics, 2017, pp 158–163.  https://doi.org/10.1061/9780784480779.019
  19. Dorostkar O, Guyer RA, Johnson PA, Marone C, Carmeliet J (2018) Cohesion-induced stabilization in stick-slip dynamics of weakly wet, sheared granular fault gouge. J Geophys Res Solid Earth.  https://doi.org/10.1002/2017JB015171 Google Scholar
  20. Elbanna AE, Carlson JM (2014) A two-scale model for sheared fault gouge: competition between macroscopic disorder and local viscoplasticity. J Geophys Res 119(6):4841–4859.  https://doi.org/10.1002/2014JB011001 CrossRefGoogle Scholar
  21. Engelder JT (1974) Cataclasis and the generation of fault gouge. GSA Bull 85(10):1515–1522.  https://doi.org/10.1130/0016-7606(1974)85<1515:CATGOF>2.0.CO;2 CrossRefGoogle Scholar
  22. Ferdowsi B (2014) Discrete element modeling of triggered slip in faults with granular gouge: application to dynamic earthquake triggering. PhD dissertation, ETH ZurichGoogle Scholar
  23. Ferdowsi B, Griffa M, Guyer RA, Johnson PA, Marone C, Carmeliet J (2014) Three-dimensional discrete element modeling of triggered slip in sheared granular media. Phys Rev E.  https://doi.org/10.1103/PhysRevE.89.042204 Google Scholar
  24. Fulton PM, Rathbun AP (2011) Experimental constraints on energy partitioning during stick–slip and stable sliding within analog fault gouge. Earth Planet Sci Lett 308(1–2):185–192.  https://doi.org/10.1016/j.epsl.2011.05.051 CrossRefGoogle Scholar
  25. Goniva C, Kloss C, Deen NG, Kuipers JAM, Pirker S (2012) Influence of rolling friction on single spout fluidized bed simulation. Particuology 10(5):582–591.  https://doi.org/10.1016/j.partic.2012.05.002 CrossRefGoogle Scholar
  26. Goren L, Aharonov E, Sparks D, Toussaint R (2010) Pore pressure evolution in deforming granular material: a general formulation and the infinitely stiff approximation. J Geophys Res.  https://doi.org/10.1029/2009jb007191 Google Scholar
  27. Griffa M, Ferdowsi B, Guyer RA, Daub EG, Johnson PA, Marone C, Carmeliet J (2013) Influence of vibration amplitude on dynamic triggering of slip in sheared granular layers. Phys Rev E.  https://doi.org/10.1103/PhysRevE.87.012205 Google Scholar
  28. Hertz H (1882) Ueber die berührung fester elastischer körper. Journal für die reine und angewandte Mathematik 92:156–171Google Scholar
  29. Ikari MJ, Marone C, Saffer DM, Kopf AJ (2013) Slip weakening as a mechanism for slow earthquakes. Nat Geosci 6(6):468–472.  https://doi.org/10.1038/ngeo1818 CrossRefGoogle Scholar
  30. Johnson PA, Jia X (2005) Nonlinear dynamics, granular media and dynamic earthquake triggering. Nature 437(7060):871–874.  https://doi.org/10.1038/nature04015 CrossRefGoogle Scholar
  31. Johnson T, Wu FT, Scholz CH (1973) Source parameters for stick–slip and for earthquakes. Science 179(4070):278–280.  https://doi.org/10.1126/science.179.4070.278 CrossRefGoogle Scholar
  32. Johnson PA, Savage H, Knuth M, Gomberg J, Marone C (2008) Effects of acoustic waves on stick–slip in granular media and implications for earthquakes. Nature 451(7174):57-U55.  https://doi.org/10.1038/nature06440 CrossRefGoogle Scholar
  33. Johnson PA, Carpenter B, Knuth M, Kaproth BM, Le Bas PY, Daub EG, Marone C (2012) Nonlinear dynamical triggering of slow slip on simulated earthquake faults with implications to earth. J Geophys Res 117(B4):B04310.  https://doi.org/10.1029/2011jb008594 CrossRefGoogle Scholar
  34. Kanamori H, Rivera L (2013) Energy partitioning during an earthquake. In: Abercrombie R, McGarr A, Di Toro G , Kanamori H (eds) Earthquakes: radiated energy and the physics of faulting.  https://doi.org/10.1029/170GM03
  35. Kaproth BM, Kacewicz M, Muhuri S, Marone C (2016) Permeability and frictional properties of halite-clay-quartz faults in marine-sediment: the role of compaction and shear. Mar Pet Geol 78:222–235.  https://doi.org/10.1016/j.marpetgeo.2016.09.011 CrossRefGoogle Scholar
  36. Kloss C, Goniva C, Hager A, Amberger S, Pirker S (2012) Models, algorithms and validation for opensource DEM and CFD–DEM. Prog Comput Fluid Dyn 12(2–3):140–152CrossRefGoogle Scholar
  37. Koch DL, Hill RJ (2001) Inertial effects in suspension and porous-media flows. Annu Rev Fluid Mech 33:619–647.  https://doi.org/10.1146/annurev.fluid.33.1.619 CrossRefGoogle Scholar
  38. Koch DL, Sangani AS (1999) Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. J Fluid Mech 400:229–263.  https://doi.org/10.1017/s0022112099006485 CrossRefGoogle Scholar
  39. Kocharyan GG, Novikov VA, Ostapchuk AA, Pavlov DV (2017) A study of different fault slip modes governed by the gouge material composition in laboratory experiments. Geophys J Int 208(1):521–528.  https://doi.org/10.1093/gji/ggw409 CrossRefGoogle Scholar
  40. Lachenbruch AH, Sass JH (1980) Heat flow and energetics of the San andreas fault zone. J Geophys Res 85(B11):6185–6222.  https://doi.org/10.1029/JB085iB11p06185 CrossRefGoogle Scholar
  41. Lockner DA, Okubo PG (1983) Measurements of frictional heating in granite. J Geophys Res 88(B5):4313–4320.  https://doi.org/10.1029/JB088iB05p04313 CrossRefGoogle Scholar
  42. Madden EH, Cooke ML, McBeck J (2017) Energy budget and propagation of faults via shearing and opening using work optimization. J Geophys Res 122(8):6757–6772.  https://doi.org/10.1002/2017JB014237 CrossRefGoogle Scholar
  43. Mahabadi OK, Cottrell BE, Grasselli G (2010) An example of realistic modelling of rock dynamics problems: FEM/DEM simulation of dynamic Brazilian test on barre granite. Rock Mech Rock Eng 43(6):707–716.  https://doi.org/10.1007/s00603-010-0092-7 CrossRefGoogle Scholar
  44. Mair K, Hazzard JF (2007) Nature of stress accommodation in sheared granular material: insights from 3D numerical modeling. Earth Planet Sci Lett 259(3–4):469–485.  https://doi.org/10.1016/j.epsl.2007.05.006 CrossRefGoogle Scholar
  45. Mair K, Frye KM, Marone C (2002) Influence of grain characteristics on the friction of granular shear zones. J Geophys Res.  https://doi.org/10.1029/2001jb000516 Google Scholar
  46. Marone C (1998a) The effect of loading rate on static friction and the rate of fault healing during the earthquake cycle. Nature 391(6662):69–72.  https://doi.org/10.1038/34157 CrossRefGoogle Scholar
  47. Marone C (1998b) Laboratory-derived friction laws and their application to seismic faulting. Annu Rev Earth Planet Sci 26:643–696.  https://doi.org/10.1146/annurev.earth.26.1.643 CrossRefGoogle Scholar
  48. Marone C, Raleigh CB, Scholz CH (1990) Frictional behavior and constitutive modeling of simulated fault gouge. J Geophys Res 95(B5):7007–7025.  https://doi.org/10.1029/JB095iB05p07007 CrossRefGoogle Scholar
  49. McGarr A (1999) On relating apparent stress to the stress causing earthquake fault slip. J Geophys Res 104(B2):3003–3011.  https://doi.org/10.1029/1998JB900083 CrossRefGoogle Scholar
  50. McGarr A (2012) Relating stick–slip friction experiments to earthquake source parameters. Geophys Res Lett.  https://doi.org/10.1029/2011gl050327 Google Scholar
  51. MiDi GDR (2004) On dense granular flows. Eur Phys J E 14(4):341–365.  https://doi.org/10.1140/epje/i2003-10153-0 CrossRefGoogle Scholar
  52. Mitchell TM, Faulkner DR (2012) Towards quantifying the matrix permeability of fault damage zones in low porosity rocks. Earth Planet Sci Lett 339:24–31.  https://doi.org/10.1016/j.epsl.2012.05.014 CrossRefGoogle Scholar
  53. Nasuno S, Kudrolli A, Bak A, Gollub JP (1998) Time-resolved studies of stick–slip friction in sheared granular layers. Phys Rev E 58(2):2161–2171.  https://doi.org/10.1103/PhysRevE.58.2161 CrossRefGoogle Scholar
  54. Newman PJ, Griffith WA (2014) The work budget of rough faults. Tectonophysics 636:100–110.  https://doi.org/10.1016/j.tecto.2014.08.007 CrossRefGoogle Scholar
  55. Niemeijer A, Marone C, Elsworth D (2010) Frictional strength and strain weakening in simulated fault gouge: competition between geometrical weakening and chemical strengthening. J Geophys Res.  https://doi.org/10.1029/2009jb000838 Google Scholar
  56. Proctor B, Hirth G (2015) Role of pore fluid pressure on transient strength changes and fabric development during serpentine dehydration at mantle conditions: Implications for subduction-zone seismicity. Earth Planet Sci Lett 421:1–12.  https://doi.org/10.1016/j.epsl.2015.03.040 CrossRefGoogle Scholar
  57. Samuelson J, Elsworth D, Marone C (2009) Shear-induced dilatancy of fluid-saturated faults: experiment and theory. J Geophys Res.  https://doi.org/10.1029/2008jb006273 Google Scholar
  58. Scholz C, Molnar P, Johnson T (1972) Detailed studies of frictional sliding of granite and implications for the earthquake mechanism. J Geophys Res 77(32):6392–6406CrossRefGoogle Scholar
  59. Scuderi MM, Collettini C (2016) The role of fluid pressure in induced vs. triggered seismicity: insights from rock deformation experiments on carbonates. Sci Rep.  https://doi.org/10.1038/srep24852 Google Scholar
  60. Scuderi MM, Carpenter BM, Johnson PA, Marone C (2015) Poromechanics of stick–slip frictional sliding and strength recovery on tectonic faults. J Geophys Res 120(10):6895–6912.  https://doi.org/10.1002/2015jb011983 CrossRefGoogle Scholar
  61. Sheng Y, Lawrence CJ, Briscoe BJ, Thornton C (2004) Numerical studies of uniaxial powder compaction process by 3D DEM. Eng Comput 21(2–4):304–317.  https://doi.org/10.1108/02644400410519802 CrossRefGoogle Scholar
  62. Shimamoto T (1979) Experimental studies of simulated gouge and their application to studies of natural fault zones. Paper presented at the conference VIII: analysis of actual fault zones in Bedrock, National Earthquake Hazards Reduction Program, Menlo Park, CAGoogle Scholar
  63. Sibson RH (1996) Structural permeability of fluid-driven fault-fracture meshes. J Struct Geol 18(8):1031–1042.  https://doi.org/10.1016/0191-8141(96)00032-6 CrossRefGoogle Scholar
  64. Sleep NH (1997) Application of a unified rate and state friction theory to the mechanics of fault zones with strain localization. J Geophys Res 102(B2):2875–2895.  https://doi.org/10.1029/96JB03410 CrossRefGoogle Scholar
  65. Stukowski A (2010) Visualization and analysis of atomistic simulation data with OVITO—the open visualization tool. Model Simul Mater Sci Eng.  https://doi.org/10.1088/0965-0393/18/1/015012 Google Scholar
  66. Townend J, Zoback MD (2000) How faulting keeps the crust strong. Geology 28(5):399–402.  https://doi.org/10.1130/0091-7613(2000)28<399:HFKTCS>2.0.CO;2 CrossRefGoogle Scholar
  67. Weller HG, Tabor G, Jasak H, Fureby C (1998) A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput Phys 12(6):620–631.  https://doi.org/10.1063/1.168744 CrossRefGoogle Scholar
  68. White FM (2003) Fluid mechanics, 5th edn. McGraw-Hill Series in Mechanical Engineering, 866 pGoogle Scholar
  69. Young DF, Munson BR, Okiishi TH, Huebsch WW (2010) A brief introduction to fluid mechanics, 5th edn. Wiley, New YorkGoogle Scholar
  70. Zhao T, Utili S, Crosta GB (2016) Rockslide and impulse wave modelling in the vajont reservoir by DEM–CFD analyses. Rock Mech Rock Eng 49(6):2437–2456.  https://doi.org/10.1007/s00603-015-0731-0 CrossRefGoogle Scholar
  71. Zhou ZY, Kuang SB, Chu KW, Yu AB (2010) Discrete particle simulation of particle–fluid flow: model formulations and their applicability. J Fluid Mech 661:482–510.  https://doi.org/10.1017/s002211201000306x CrossRefGoogle Scholar

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© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chair of Building Physics, Department of Mechanical and Process EngineeringSwiss Federal Institute of Technology Zurich (ETH Zurich)ZurichSwitzerland
  2. 2.Laboratory for Multiscale Studies in Building PhysicsSwiss Federal Laboratories for Materials Science and Technology (Empa)DubendorfSwitzerland
  3. 3.Department of Civil, Environmental and Geomatic EngineeringSwiss Federal Institute of Technology Zurich (ETH Zurich)ZurichSwitzerland

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