Advertisement

Constructing Constitutive Relationships for Seismic and Aseismic Fault Slip

  • N. M. Beeler
Chapter
Part of the Pageoph Topical Volumes book series (PTV)

Abstract

For the purpose of modeling natural fault slip, a useful result from an experimental fault mechanies study would be a physically-based constitutive relation that well characterizes all the relevant observations. This report describes an approach for constructing such equations. Where possible the construction intends to identify or, at least, attribute physical processes and contact scale physics to the observations such that the resulting relations can be extrapolated in conditions and scale between the laboratory and the Earth. The approach is developed as an alternative but is based on (1983) and is illustrated initially by constructing a couple of relations from that study. In addition, two example constitutive relationships are constructed; these describe laboratory observations not well-modeled by Ruina’s equations: the unexpected shear-induced weakening of silica-rich rocks at high slip speed (Goldsby and Tullis, 2002) and fault strength in the brittle ductile transition zone (Shimamoto, 1986). The examples, provided as illustration, may also be useful for quantitative modeling.

Key words

Friction dynamic fault slip brittle ductile transition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ampuero, J.-P. and Rubin, A. M. (2008), Earthquake nucleation on rate and state faults—Aging and slip laws, J. Geophys. Res. 113, doi: 10.1029/2007JB005082Google Scholar
  2. Blanpied, M. L., Lockner, D. A., and Byerlee, J. D. (1991), Fault stability inferred from granite sliding experiments at hydrothermal conditions, Geophys. Res. Lett. 18, 609–612.CrossRefGoogle Scholar
  3. Blanpied, M. L., Lockner, D. A. and Byerlee, J. D. (1995). Frictional slip of granite at hydrothermal conditions, J. Geophys. Res., 100, 13,045–13,064.CrossRefGoogle Scholar
  4. Blanpied, M. L., Marone, C. J., Lockner, D. A., Byerlee, J. D., and King, D. P. (1998), Quantitative measure of the variation in fault rheology due to fluid-rock interactions, J. Geophys. Res. 103, 9691–9712.CrossRefGoogle Scholar
  5. Boettcher, M. S., Hirth, J.G., and Evans, B. (2007), Olivine friction at the base of oceanic seismogenic zones, J. Geophys. Res. 112, B0125, doi: 10.1029/2006JB004301.CrossRefGoogle Scholar
  6. Brace, W. F. (1978), Volume changes during fracture and frictional sliding, Pure Appl. Geophys., 116, 603–614.CrossRefGoogle Scholar
  7. Brace, W. F., Paulding, B. W., and Scholz, C. H. (1966), Dilatancy in the fracture of crystalline-rock, J. Geophys. Res. 71, 3939–3953.Google Scholar
  8. Brown S. R. and Scholz, C. H. (1985), The closure of random elastic surfaces in contact, J. Geophys. Res. 90, 5531–5545.CrossRefGoogle Scholar
  9. Brune, J. N. (1970), Tectonic stress and the spectra of seismic shear waves from earthquakes, J. Geophys. Res. 75, 4997–50090.CrossRefGoogle Scholar
  10. Chester, F. M. (1994), Effects of temperature on friction: constitutive equations and experiments with quartz gouge, J. Geophys. Res. 99, 7247–7262.CrossRefGoogle Scholar
  11. Chester, F. M. (1995), A rheologic model for wet crust applied to strike-slip faults, J. Geophys. Res. 100, 13,033–13,044.CrossRefGoogle Scholar
  12. Chester, F. M. and Higgs, N. G. (1992), Multimechanism friction constitutive model for ultrafine quartz gouge at hypocentral conditions, J. Geophys. Res. 97, 1859–1870.CrossRefGoogle Scholar
  13. Dieterich, J. H. (1972), Time-dependent friction in rocks, J. Geophys. Res. 77, 3690–3697.CrossRefGoogle Scholar
  14. Dieterich, J. H. (1978), Time-dependent friction and the mechanics of stick slip, Pure Appl. Geophys. 116, 790–806.CrossRefGoogle Scholar
  15. Dieterich, J. H. (1979), Modeling of rock friction 1. Experimental results and constitutive equations, J. Geophys. Res. 84, 2161–2168.CrossRefGoogle Scholar
  16. Dieterich, J. H. and Kilgore, B. D. (1994), Direct observation of frictional contacts: New insights for sliding memory effects, Pure Appl. Geophys. 143, 283–302.CrossRefGoogle Scholar
  17. Dragert, H., Wang, K., and Rogers, G. (2004), Geodetic and seismic signatures of episodic tremor and slip in the northern Cascadia subduction zone, Earth Planets Space, 56, 1143–1150.Google Scholar
  18. DiToro, G., Goldsby, D. L., and Tullis, T. E. (2004), Friction falls towards zero in quartz rock as slip velocity approaches seismic rates, Nature, 47, 436–439.CrossRefGoogle Scholar
  19. Escartin, J., Hirth, G., and Evans, B. (1997). Nondilatant brittle deformation of serpentinites: implications for Mohr-Coulomb theory and the strength of faults, J. Geophys. Res. 102, 2897–2913.CrossRefGoogle Scholar
  20. Estrin, Y. and Brechet, Y. (1996), On a model of frictional sliding, Pure Appl. Geophys. 4, 745–762.CrossRefGoogle Scholar
  21. Goetze, C. and Evans, B. (1979), Stress and temperature in the bending lithosphere as constrained by experimental rock mechanics, Geophys. J. Roy. Astron. Soc. 59, 463–478.Google Scholar
  22. Goldsby, D. L. and Tullis, T. E. (2002), Low frictional strength of quartz rocks at subseismic slip rates, Geophys. Res. Lett. 29, 4 pp.Google Scholar
  23. Han, R., Shimamoto, T., Hirose, T., Ree, J.-H., and Ando, J-I. (2007), Ultralow friction of carbonate faults caused by thermal decomposition, Science 316, 878–881.CrossRefGoogle Scholar
  24. Hirose, T. and Shimamoto, T. (2005), Growth of molten zone as a mechanism of slip weakening of simulated faults in gabbro during frictional melting, J. Geophys. Res. 110.Google Scholar
  25. Ide, S., Beroza, G. C., Shelly, D. R., and Uchide, T. (2007), A scaling law for slow earthquakes, Nature 447, 76–79.CrossRefGoogle Scholar
  26. Ito, Y., Obara, K., Shiomi, K., Sekine, S., and Hirose, H. (2006), Slow earthquakes coincident with episodic tremors and slow slip events, Science 26, 503–506.Google Scholar
  27. Johnson, T. L., Wu, F. T., and Scholz, C. H. (1973), Source parameters for stick-slip and for earthquakes, Science 129, 278–280.CrossRefGoogle Scholar
  28. Kilgore, B. D., Blanpied, M. L., and Dieterich, J. H. (1993), Velocity dependent friction of granite over a wide randge of conditions, Geophys. Res. Lett. 20, 903–906.CrossRefGoogle Scholar
  29. Liu, Y. and Rice, J. R. (2005), Aseismic slip transients emerge spontaneously in 3D rate and state modeling of subduction earthquake sequences, J. Geophys. Res. 110, B08307, doi: 10.1029/2004JB003424.CrossRefGoogle Scholar
  30. Marone, C., Raleigh, C. B., and Scholz, C. H. (1990), Frictional behavior and constitutive modeling of simulated fault gouge, J. Geophys. Res. 95, 7007–7025.CrossRefGoogle Scholar
  31. McGarr, A. (1999), On relating apparent stress to the stress causing earthquake fault slip, J. Geophys. Res. 104, 3003–3011.CrossRefGoogle Scholar
  32. McGarr, A. and Fletcher, J. (2003), Maximum slip in earthquake fault zones, apparent stress, and stick-slip friction, Bull. Seismol. Soc. Am. 93, 2355–2362.CrossRefGoogle Scholar
  33. McGarr, A., Fletcher, J., and Beeler, N. M. (2004), Attempting to bridge the gap between laboratory and seismic estimates of fracture energy, Geophys. Res. Lett. 31 4 pp.Google Scholar
  34. Mizoguchi, K., Hirose, T., Shimamoto, T., and Fukuyama, E. (2007), Moisture-related weakening and strengthening of a fault activated at seismic slip rates, Geophys. Res. Lett. 33, doi: 10.1029/2006GL026980.Google Scholar
  35. Moore, D. E., Lockner, D. A., Ma, S., Summers, R., and Byerlee, J.D. (1997), Strengths of serpentinite gouges at elevated temperatures, J. Geophys. Res. 102 (B7), 14,787–14,801.CrossRefGoogle Scholar
  36. Nadeau, R. M. and Johnson, L. R. (1998), Seismological studies at Parkfield VI: Moment release rates and estimates of source parameters for small repeating earthquakes, Bull. Seismol. Soc. Am. 88, 790–814.Google Scholar
  37. Nakatani, M. and Scholz, C. H. (2004), Frictional healing of quartz gouge under hydrothermal conditions: I. Experimental evidence for solution transfer healing mechanism, J. Geophys. Res. 109, doi:10.1029/2001JB001522.Google Scholar
  38. Nakatani, M. and Scholz, C. H. (2006), Intrinsic and apparent short-time limits for fault healing: Theory observations and implications for velocity dependent friction, J. Geophys. Res. 111, doi:10.1029/2005JB004096.Google Scholar
  39. Obara, K., (2002), Nonvolcanic deep tremor associated with subduction in southwest Japan, Science 296, 1679–1681.CrossRefGoogle Scholar
  40. Okubo, P. G. and Dieterich, J. H. (1981), Fracture energy of stick-slip events in a large scale biaxial experiment, Geophys. Res. Lett. 8, 887–890.CrossRefGoogle Scholar
  41. Okubo, P. G. and Dieterich, J. H., (1986) State variable fault constitutive relations for dynamic slip. In Earthquake Source Mechanics (ed. S. Das, J. Boatwright, and C. H. Scholz) Geophys. Mono. 37, AGU, pp. 25–36.Google Scholar
  42. Perrin, G., Rice, J. R., and Zheng, G. (1995), Self-healing Slip Pulse on a Frictional Surface, J. Mech. Phys. Sol. 43, 1461–1495.CrossRefGoogle Scholar
  43. Rice, J. R. (1983), Constitutive relations for fault slip and earthquake instabilities, Pure Appl. Geophys. 121, 443–475.CrossRefGoogle Scholar
  44. Rice, J. R. (1993), Spatio-temporal complexity of slip on a fault, J. Geophys. Res. 98, 9885–9907.CrossRefGoogle Scholar
  45. Rice, J. R., Lapusta, N., and Ranjith, K. (2001), Rate-and state-dependent friction and the stability of sliding between elastically deformable solids, J. Mech. Phys. Sol. 49, 1865–1898.CrossRefGoogle Scholar
  46. Reinen, L. A., Weeks, J. D., and Tullis, T. E. (1994), The frictional behavior of lizardite and antigorite serpentinites: Experiments, constitutive models, and implications for natural faults, Pure Appl. Geophys. 143, 317–358.CrossRefGoogle Scholar
  47. Rimstidt, J. D. and Barnes, H. L. (1980), The kinetics of silica-water reactions, Geochimica et Cosmochimica Acta 44, 1683–1699.CrossRefGoogle Scholar
  48. Ruina, A. L. (1980), Friction laws and instabilities, a quasistatic analysis of some dry frictional behavior, Ph.D. Thesis, Brown University, 99 pp.Google Scholar
  49. Ruina, A. L. (1983), Slip instability and state variable friction laws, J. Geophys. Res. 88, 10359–10370.CrossRefGoogle Scholar
  50. Shibazaki, B. and Iio, Y. (2003) On the physical mechanism of silent slip events along the deeper part of the seismogenic zone, Geophys. Res. Lett. 30, 1489–1493, doi:10.1029/2003GL017047.CrossRefGoogle Scholar
  51. Shimamoto, T. (1986), Transition between frictional slip and ductile flow for halite shear zones at room temperature, Science 231, 711–714.CrossRefGoogle Scholar
  52. Stumm, W. and Morgan, J.J. Aquatic Chemistry (John Wiley and Sons, New York, (1981)), pp. 780.Google Scholar
  53. Tolstoi, D.M. (1967), Significance of the normal degree of freedom and natural normal vibrations in contact friction Wear 10, 199–213.CrossRefGoogle Scholar
  54. Tsutsumi, A. and Shimamoto, T. (1997), High-velocity frictional properties of gabbro, Geophys. Res. Lett. 24, 699–702.CrossRefGoogle Scholar
  55. Wong, T.-F. (1986), On the normal stress dependence of the shear fracture energy. In Earthquake Source Mechanics, Geophys. Monogr. Ser., Vol. 37 (eds. S. Das et al.), pp. 1–11, (AGU, Washington, D.C. 1986).Google Scholar

Copyright information

© Birkhäuser Verlag, Basel 2009

Authors and Affiliations

  • N. M. Beeler
    • 1
    • 2
    • 3
  1. 1.Cascades ObservatoryU. S. Geological SurveyVancouverUSA
  2. 2.U. S. Geological SurveyMenlo ParkUSA
  3. 3.Brown UniversityProvidenceUSA

Personalised recommendations