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pure and applied geophysics

, Volume 143, Issue 1–3, pp 359–385 | Cite as

Scaling of rock friction constitutive parameters: The effects of surface roughness and cumulative offset on friction of gabbro

  • Chris Marone
  • S. J. D. Cox
Rock Friction and Shear Zone Mechanics: Laboratory Studies

Abstract

We describe experiments in which large (14×40 cm nominal contact area) blocks of gabbro were sheared in a direct shear apparatus at room temperature, 5 MPa normal stress, and slip velocities from 0.1 to 10 μm/s. The apparatus was servocontrolled using a displacement feedback measurement made directly between the gabbro blocks. Two surface roughnesses were studied (rough, produced by sandblasting, and smooth, produced by lapping with #60 grit) and accumulated displacements reached 60 mm. Measurements of surface topography were used to characterize roughness and asperity dimensions. Step changes in loading velocity were used to interrogate friction constitutive properties. Both rough and smooth surfaces showed appreciable displacement hardening. The coefficient of friction μ for rough surfaces was about 0.45 for initial slip and 0.7 after sliding 50 mm. Smooth surfaces exhibited higher μ and a greater tendency for unstable slip. The velocity dependence of frictiona−b and the characteristic friction distanceD c show systematic variations with accumulated displacement. For rough surfacesa−b started out positive and became negative after about 50 mm displacement andD c increased from 1 to 4 μm over the same interval. For smooth surfaces,a−b began negative and decreased slightly with displacement andD c was about 2 μm, independent of displacement. For displacements <30 mm, rough surfaces exhibit a second state variable with characteristic distance about 20 μm. The decrease ina−b with displacement is associated with disappearance of the second state variable. Our data indicate thatD c is controlled by surface roughness in a complex way, including but not limited to the effect of roughness on contact junction dimensions for bare rock surfaces. The data show that simple descriptions of roughness, such as rms and peak-to-trough, are not sufficient to inferD c . Our observations are consistent with a model in whichD c scales with gouge thickness.

Key words

Rock friction constitutive laws scaling characteristic friction distance 

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References

  1. Archard, J. F. (1957),Elastic Deformation and the Laws of Friction, Proc. R. Soc. London, Ser. A243, 190–205.Google Scholar
  2. Aki, K. (1957),Magnitude-frequency Relation for Small Earthquakes: A Clue to the Origin of f max of Large Earthquakes, J. Geophys. Res.92, 1349–1355.Google Scholar
  3. Biegel, R. L., Sammis, C. G., andDieterich, J. H. (1989),The Frictional Properties of a Simulated Gouge Having a Fractal Particle Distribution, J. Struc Geology11, 827–846.Google Scholar
  4. Beeler, N. M., Tullis, T. E., andWeeks, J. D. (1993),The Contribution of Simulated Gouge to the Velocity Dependence of Experimental Granite Faults, EOS, Trans. Amer. Geophys. Un.74, 296.Google Scholar
  5. Blanpied, M. L., andTullis, T. E. (1986),The Stability and Behavior of a Frictional System with a Two State Variable Constitutive Law, Pure and Appl. Geophys.124, 415–430.Google Scholar
  6. Blanpied, M. L., Lockner, D. A., andByerlee, J. D. (1991),Fault Stability Inferred from Granite Sliding Experiments at Hydrothermal Conditions, Geophys. Res. Lett.18, 609–612.Google Scholar
  7. Chester, F. M. (1994),Effects of Temperature on Friction: Constitutive Equations and Experiments with Quartz Gouge, J. Geophys. Res.99, 7247–7261.Google Scholar
  8. Cox, S. J. D.,Velocity dependent friction in a large direct shear experiment on gabbro. InDeformation Mechanisms, Rheology, and Tectonics (eds. Knipe, R. J, and Rutter, E.H.) (Geol. Soc. London 1990) Spec. Pub.54, pp. 63–70.Google Scholar
  9. Dieterich, J. H. (1979),Modeling of Rock Friction: 1. Experimental Results and Constitutive Equations, J. Geophys. Res.84, 2161–2168.Google Scholar
  10. Dieterich, J. H.,Constitutive properties of faults with simulated gouge. InMechanical Behavior of Crustal Rocks (eds. Carter, N. L., Friedman, M., Logan, J. M., and Stearns, D. M.) (AGU Monograph24, 1981) pp. 103–120.Google Scholar
  11. Dieterich, J. H.,A model for the nucleation of earthquake slip. InEarthquake Source Mechanics (eds. Das, S.,Boatwright, J., andScholz, C H.) (AGU Monograph37, 1986) pp. 37–47.Google Scholar
  12. Gu, Y., andWong, T.-f. (1994),Development of Shear Localization in Simulated Quartz Gouge: Effect of Cumulative Slip and Gouge Particle Size, Pure and Appl. Geophys.143, 387–423.Google Scholar
  13. Ida, Y. (1973),The Maximum Ground Acceleration of Seismic Ground Motion. Bull. Seismol. Soc. Am.63, 959–968.Google Scholar
  14. Kuwahara, Y., Ohnaka, M., Yamamoto, K., andHirasawa, T. (1988),Accelerating Process of Rupture Propagation during Stick-slip Failure Instability, Seis. Res. Lett.59, 2.Google Scholar
  15. Li, V. C.,Mechanics of shear rupture applied to earthquake zones. InFracture Mechanics of Rock (ed. Atkinson, B.) (Academic Press, London, 1987) pp. 351–428.Google Scholar
  16. Lockner, D. A., Summers, R., andByerlee, J. D. (1986),Effects of Temperature and Sliding Rate on Frictional Strength of Granite, Pure and Appl. Geophys.124, 445–469.Google Scholar
  17. Marone, C. (1993),Micromechanics of Rate- and State-dependent Friction in Simulated Fault Gouge, EOS, Trans. Amer. Geophys. Un.74, 296.Google Scholar
  18. Marone, C., andScholz, C. H. (1988),The Depth of Seismic Faulting and the Upper Transition from Stable to Unstable Slip Regimes, Geophys. Res. Lett.15, 621–624.Google Scholar
  19. Marone, C., andKilgore, B. (1993),Scaling of the Critical Slip Distance for Seismic Faulting with Shear Strain in Fault Zones, Nature362, 618–621.Google Scholar
  20. Marone, C., Raleigh, C. B., andScholz, C. H. (1990),Frictional Behavior and Constitutive Modeling of Simulated Fault Gouge., J. Geophys. Res.95, 7007–7025.Google Scholar
  21. Marone, C., Hobbs, B. E., andOrd, A. (1992),Coulomb Constitutive Laws for Friction: Contrasts in Frictional Behavior for Distributed and Localized Shear, Pure and Appl. Geophys.139, 195–214.Google Scholar
  22. Ohnaka, M., andYamashita, T. (1989),A Cohesive Zone Model for Dynamic Shear Faulting Based on Experimentally Inferred Constitutive Relation and Strong Motion Source Parameters, J. Geophys. Res.94, 4089–4104.Google Scholar
  23. Ohnaka, M., andKuwahara, Y. (1990),Characteristic Features of Local Breakdown near a Crack-tip in the Transition Zone from Nucleation to Dynamic Rupture during Stick-slip Shear Failure, Tectonophys.175, 197–220.Google Scholar
  24. Okubo, P. G. (1989),Dynamic Rupture Modeling with Laboratory-derived Constitutive Relations, J. Geophys. Res.94, 12,321–12,335.Google Scholar
  25. Okubu, P. G., andDieterich, J. H. (1984),Effects of Physical Fault Properties on Frictional Instabilities Produced on Simulated Faults, J. Geophys. Res.89, 5817–5827.Google Scholar
  26. Pisarenko, D., andMora, P. (1994),Velocity Weakening in a Dynamical Model of Friction, Pure and Appl. Geophys.143, 61–87.Google Scholar
  27. Power, W. L., andTullis, T. E. (1992),The Contact between Opposing Fault Surfaces at Dixie Valley, Nevada, and Implications for Fault Mechanics, J. Geophys. Res.97, 14,425–14,435.Google Scholar
  28. Press, W. H., Flannery, B. P., Teukolshy, S. A., andVetterling, W. T.,Numerical Recipes in C (Cambridge, 1988) 475 pp.Google Scholar
  29. Rabinowicz, E. (1951),The Nature of the Static and Kinetic Coefficients of Friction, J. Appl. Phys.22, 1373–1379.Google Scholar
  30. Reinen, L. A., andWeeks, J. D. (1993),Determination of Rock Friction Constitutive Parameters using an Iterative Least-squares Inversion Method. J. Geophys. Res.98, 15,937–15,950.Google Scholar
  31. Reinen, L. A., Weeks, J. D., andTullis, T. E. (1991),The Frictional Behavior of Serpentinite: Implications for Aseismic Creep on Shallow Crustal Faults, Geophys. Res. Lett.18, 1921–1924.Google Scholar
  32. Reinen, L. A., Weeks, J. D., andTullis, T. E. (1994),The Frictional Behavior of Lizardite and Antigorite Serpentinites: Experiments, Constitutive Models, and Implications for Natural Faults, Pure and Appl. Geophys.143, 317–358.Google Scholar
  33. Rice, J. R. (1993),Spatio-temporal Complexity of Slip on a Fault, J. Geophys. Res.98, 9885–9907.Google Scholar
  34. Rice, J. R., andRunia, A. L. (1983),Stability of Steady Frictional Slipping, J. Appl. Mech.50, 343–349.Google Scholar
  35. Rice, J. R., andTse, S. T. (1986),Dynamic Motion of a Single Degree of Freedom System Following a Rate and State-dependent Friction Law., J. Geophys. Res.91, 521–530.Google Scholar
  36. Ruina, A. (1983),Slip Instability and State Variable Friction Laws, J. Geophys. Res.88, 10359–10370.Google Scholar
  37. Sammis, C. G., andSteacy, S. (1994),The Micromechanics of Friction in a Granular Layer, Pure and Appl. Geophys.142, 777–794.Google Scholar
  38. Scholz, C. H. (1988),The Critical Slip Distance for Seismic Faulting, Nature336, 761–763.Google Scholar
  39. Scholz, C. H.,The Mechanics of Earthquakes and Faulting (Cambridge University Press, 1990) 439 pp.Google Scholar
  40. Tse, S. T., andRice, J. R. (1986),Crustal Earthquake Instability in Relation to the Depth Variation of Frictional Slip Properties, J. Geophys. Res.91, 9452–9472.Google Scholar
  41. Tullis, T. E. (1988),Rock Friction Constitutive Behavior from Laboratory Experiments and its Implications for an Earthquake Prediction Field Monitoring Program, Pure and Appl. Geophys.126, 555–588.Google Scholar
  42. Tullis, T. E., andWeeks, J. D. (1986),Constitutive Behavior and Stability of Frictional Sliding of Granite, Pure and Appl. Geophys.124, 383–414.Google Scholar
  43. Wang, W., andScholz, C. H. (1994),Micromechanics of the Velocity and Normal Stress Dependence of Rock Friction, Pure and Appl. Geophys.143, 303–315.Google Scholar
  44. Wesnousky, S. G. (1990),Seismicity as a Function of Cumulative Geologic Offset: Some Observations from Southern California, Bull. Seismol. Soc. Am.80, 1374–1381.Google Scholar
  45. Wong, T.-f., Gu, Y., Yanagidani, T., andZhao, Y.,Stabilization of faulting by cumulative slip. InFault Mechanics and Transport Properties of Rock (eds. Evans, B., and Wong, T.-f.) (Academic Press Ltd., 1992) pp. 119–143.Google Scholar
  46. Yamada, K., Takeda, N., Kagami, J., andNaoi, T. (1978),Surface Density of Asperities and Real Distribution of Asperity Heights on Rubbed Surfaces, Wear47, 5–20.Google Scholar
  47. Yoshioka, N., andScholz, C. H. (1989),Elastic Properties of Contacting Surfaces under Normal and Shear Loads 1. Theory., J. Geophys. Res.94, 17,681–17,690.Google Scholar

Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • Chris Marone
    • 1
  • S. J. D. Cox
    • 2
  1. 1.Department of Earth, Atmospheric, and Planetary SciencesMassachusetts Institute of TechnologyCambridgeU.S.A.
  2. 2.CSIRO Division of Exploration and MiningNedlands

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