Advertisement

Can Damage Mechanics Explain Temporal Scaling Laws in Brittle Fracture and Seismicity?

  • Donald L. Turcote
  • Robert Shcherbakov
Chapter
Part of the Pageoph Topical Volumes book series (PTV)

Abstract

Time delays associated with processes leading to a failure or stress relaxation in materials and earthquakes are studied in terms of continuum damage mechanics. Damage mechanics is a quasiempirical approach that describes inelastic irreversible phenomena in the deformation of solids. When a rock sample is loaded, there is generally a time delay before the rock fails. This period is characterized by the occurrence and coalescence of microcracks which radiate acoustic signals of broad amplitudes. These acoustic emission events have been shown to exhibit power-law scaling as they increase in intensity prior to a rupture. In case of seismogenic processes in the Earth’s brittle crust, all earthquakes are followed by an aftershock sequence. A universal feature of aftershocks is that their rate decays in time according to the modified Omori’s law, a power-law decay. In this paper a model of continuum damage mechanics in which damage (microcracking) starts to develop when the applied stress exceeds a prescribed yield stress (a material parameter) is introduced to explain both laboratory experiments and systematic temporal variations in seismicity.

Key words

Fracture seismicity damage mechanics aftershocks power-law scaling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anifrani, J.C., Lefloch, C., Sornette, D., and Souillard, B. (1995), Universal log-periodic correction to renormalization-group scaling for rupture stress prediction from acoustic emissions, J. Phys. I 5, 631–638.CrossRefGoogle Scholar
  2. Ben-zion, Y. and Lyakhovsky, V. (2002), Accelerated seismic release and related aspects of seismicity patterns on earthquake faults, Pure Appl. Geophys. 159, 2385–2412.CrossRefGoogle Scholar
  3. Bowman, D.D. and King, G.C.P. (2001), Accelerating seismicity and stress accumulation before large earthquakes, Geophys. Res. Lett. 28, 4039–4042.CrossRefGoogle Scholar
  4. bowman, d.d., ouillon, g., sammis, c.g., sornette, a., and sornette, d. (1998), an observational test of the critical earthquake concept, j. geophys. res. 103, 24359–24372.CrossRefGoogle Scholar
  5. Bowman, D.D. and Sammis, C.G. (2004), Intermittent criticality and the Gutenberg-Richter distribution, Pure Appl. Geophys. 161, 1945–1956.CrossRefGoogle Scholar
  6. Brehm, D.J. and Braile, L.W. (1998), Intermediate-term earthquake prediction using precursory events in the New Madrid seismic zone, Bull. Seismol. Soc. Am. 88, 564–580.Google Scholar
  7. Brehm, D.J. and Braile, L.W. (1999a), Intermediate-term earthquake prediction using the modified time-to-failure method in Southern California, Bull. Seismol. Soc. Am. 89, 275–293.Google Scholar
  8. Brehm, D.J. and Braile, L.W. (1999b), Refinement of the modified time-to-failure method for intermediate-term earthquake prediction, J. Seismol. 3, 121–138.CrossRefGoogle Scholar
  9. Bufe, C.G., Nishenko, S.P., and Varnes, D.J. (1994), Seismicity trends and potential for large earthquakes in the Alaska-Aleutian region, Pure Appl. Geophys. 142, 83–99.CrossRefGoogle Scholar
  10. Bufe, C.G. and Varnes, D.J. (1993), Predictive modeling of the seismic cycle of the greater San Francisco Bay region, J. Geophys. Res. 98, 9871–9883.Google Scholar
  11. Ciliberto, S., Guarino, A., and Scorretti, R. (2001), The effect of disorder on the fracture nucleation process, Physica D 158, 83–104.CrossRefGoogle Scholar
  12. Coleman, B.D. (1957), Time dependence of mechanical breakdown in bundles of fibers. I Constant total load, J. Appl. Phys. 28, 1058–1064.CrossRefGoogle Scholar
  13. Coleman, B.D. (1958), Statistics and time dependence of mechanical breakdown in fibers, J.Appl. Phys. 29, 968–983.CrossRefGoogle Scholar
  14. Das, S. and Scholz, C.H. (1981), Theory of time-dependent rupture in the Earth, J. Geophys. Res. 86, 6039–6051.Google Scholar
  15. Freund, L.B., Dynamic Fracture Mechanics (Cambridge University Press, Cambridge 1990).Google Scholar
  16. Gluzman, S. and Sornette, D. (2001), Self-consistent theory of rupture by progressive diffuse damage, Phys. Rev. E 6306, Art. No. 066129.Google Scholar
  17. Guarino, A., Ciliberto, S., and Garcimartin, A. (1999), Failure time and microcrack nucleation, Europhys. Lett. 47, 456–461.CrossRefGoogle Scholar
  18. Guarino, A., Ciliberto, S., Garcimartin, A., Zei, M., and Scorretti, R. (2002), Failure time and critical behaviour of fracture precursors in heterogeneous materials, Eur. Phys. J. B 26, 141–151.CrossRefGoogle Scholar
  19. Guarino, A., Garcimartin, A., and Ciliberto, S. (1998), An experimental test of the critical behaviour of fracture precursors, Eur. Phys. J. B 6, 13–24.CrossRefGoogle Scholar
  20. Hild, F., Discrete versus continuum damage mechanics: A probabilistic perspective. In Continuum Damage Mechanics of Materials and Structures (O. Allix, F. Hild eds.) (Elsevier, Amsterdam 2002), pp. 79–114.Google Scholar
  21. Hirata, T. (1987), Omori’s power law aftershock sequences of microfracturing in rock fracture experiment, J. Geophys. Res. 92, 6215–6221.CrossRefGoogle Scholar
  22. Hirata, T., Satoh, T., and Ito, K. (1987), Fractal structure of spatial-distribution of microfracturing in rock, Geophys. J. R. Astr. Soc. 90, 369–374.Google Scholar
  23. Jaumé, S.C. and Sykes, L.R. (1999), Evolving towards a critical point: A review of accelerating seismic moment/energy release prior to large and great earthquakes, Pure Appl. Geophys. 155, 279–305.CrossRefGoogle Scholar
  24. Johansen, A. and Sornette, D. (2000), Critical ruptures, Eur. Phys. J. B 18, 163–181.CrossRefGoogle Scholar
  25. Kachanov, L.M.Introduction to Continuum Damage Mechanics (Martinus Nijhoff, Dordrecht 1986).Google Scholar
  26. Kachanov, M. (1994), On the concept of damage in creep and in the brittle-elastic range, Int. J. Damage Mech. 3, 329–337.Google Scholar
  27. Kattan, P.I. and Voyiadjis, G.Z.Damage Mechanics with Finite Elements: Practical Applications with Computer Tools (Springer, Berlin 2002).Google Scholar
  28. King, G.C.P. and Bowman, D.D. (2003), The evolution of regional seismicity between large earthquakes, J. Geophys. Res. 108, 2096.CrossRefGoogle Scholar
  29. Knopoff, L., Levshina, T., Keilis-Borok, V.I., and Mattoni, C. (1996), Increased long-range intermediate-magnitude earthquake activity prior to strong earthquakes in California, J. Geophys. Res. 101, 5779–5796.CrossRefGoogle Scholar
  30. Krajcinovic, D. (1989), Damage mechanics, Mech. Mater. 8, 117–197.CrossRefGoogle Scholar
  31. Krajcinovic, D.Damage Mechanics (Elsevier, Amsterdam 1996).Google Scholar
  32. Lockner, D. (1993), The role of acoustic-emission in the study of rock fracture, Int. J. Rock Mech. Min. Sci. 30, 883–899.CrossRefGoogle Scholar
  33. Lockner, D.A., Byerlee, J.D., Kuksenko, J.D., Ponomarev, V., and Sidorin, A.Observations of quasistatic fault growth from acoustic emissions. In Fault Mechanics and Transport Properties of Rocks (Academic Press, London 1992), pp. 3–31.Google Scholar
  34. Lyakhovsky, V., Ben-Zion, Y., and Agnon, A. (2001), Earthquake cycle, fault zones, and seismicity patterns in a rheologically layered lithosphere, J. Geophys. Res. 106, 4103–4120.CrossRefGoogle Scholar
  35. Lyakhovsky, V., Benzion, Y., and Agnon, A. (1997), Distributed damage, faulting, and friction, J. Geophys. Res. 102, 27635–27649.CrossRefGoogle Scholar
  36. Main, I.G. (1999), Applicability of time-to-failure analysis to accelerated strain before earthquakes and volcanic eruptions, Geophys. J. Int. 139, F1–F6.CrossRefGoogle Scholar
  37. Mogi, K. (1962), Study of elastic shocks caused by the fracture of hetergeneous materials and its relations to earthquake phenomena, Bull. Earthquake Res. Inst. 40, 125–173.Google Scholar
  38. Newman, W.I. and Phoenix, S.L. (2001), Time-dependent fiber bundles with local load sharing, Phys. Rev. E 6302, Art. No. 021507.Google Scholar
  39. Robinson, R. (2000), A test of the precursory accelerating moment release model on some recent New Zealand earthquakes, Geophys. J. Int. 140, 568–576.CrossRefGoogle Scholar
  40. Rundle, J., Klein, W., Turcotte, D.L., and Malamud, B.D. (2000), Precursory seismic activation and critical-point phenomena, Pure Appl. Geophys. 157, 2165–2182.CrossRefGoogle Scholar
  41. Sammis, C.G., Bowman, D.D., and King, G. (2004), Anomalous seismicity and accelerating moment release preceding the 2001 and 2002 earthquakes in northern Baja California, Mexico, Pure Appl. Geophys. 161, 2369–2378.CrossRefGoogle Scholar
  42. SCHOLZ, C.H., The Mechanics of Earthquakes and Faulting (Cambridge University Press, Cambridge 2002), 2nd ed.Google Scholar
  43. Scorretti, R., Ciliberto, S., and Guarino, A. (2001), Disorder enhances the effects of thermal noise in the fiber bundle model, Europhys. Lett. 55, 626–632.CrossRefGoogle Scholar
  44. Shcherbakov, R. and Turcotte, D.L. (2003), Damage and self-similarity in fracture, Theor. Appl. Frac. Mech. 39, 245–258.CrossRefGoogle Scholar
  45. Shcherbakov, R., Turcotte, D.L., and Rundle, J.B. (2004), A generalized Omori’s law for earthquake aftershock decay, Geophys. Res. Lett. 31, Art. No. L11613.Google Scholar
  46. Shcherbakov, R., Turcotte, D.L., and Rundle, J.B. (2005), Aftershock statistics, Pure Appl. Geophys. 162, 1051–1076.CrossRefGoogle Scholar
  47. Smith, R.L. and Phoenix, S.L. (1981), Asymptotic distributions for the failure of fibrous materials under series-parallel structure and equal load-sharing, J. Appl. Mech. 48, 75–82.CrossRefGoogle Scholar
  48. Sornette, D. and Andersen, J.V. (1998), Scaling with respect to disorder in time-to-failure, Eur. Phys. J. B 1, 353–357.CrossRefGoogle Scholar
  49. Sykes, L.R. and Jaumé, S.C. (1990), Seismic activity on neighboring faults as a long-term precursor to large earthquakes in the San Francisco Bay area, Nature 348, 595–599.CrossRefGoogle Scholar
  50. Turcotte, D.L., Newman, W.I., and Shcherbakov, R. (2003), Micro and macroscopic models of rock fracture, Geophys. J. Int. 152, 718–728.CrossRefGoogle Scholar
  51. Utsu, T., Ogata, Y., and Matsu’ura, R.S. (1995), The centenary of the Omori formula for a decay law of aftershock activity, J. Phys. Earth 43, 1–33.Google Scholar
  52. Varnes, D.J. and Bufe, C.G. (1996), The cyclic and fractal seismic series preceding an mb 4:8 earthquake on 1980 February 14 near the Virgin Islands, Geophys. J. Int. 124, 149–158.Google Scholar
  53. Yang, W.Z., Vere-Jones, D., and Li, M. (2001), A proposed method for locating the critical region of a future earthquake using the critical earthquake concept, J. Geophys. Res. 106, 4121–4128.CrossRefGoogle Scholar
  54. Zöller, G., Hainzl, S., and Kurths, J. (2001), Observation of growing correlation length as an indicator for critical point behavior prior to large earthquakes, J. Geophys. Res. 106, 2167–2175.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  • Donald L. Turcote
    • 1
  • Robert Shcherbakov
    • 2
  1. 1.Department of GeologyUniversity of CaliforniaDavisUSA
  2. 2.Center for Computational Science and EngineeringUniversity of CaliforniaDavisUSA

Personalised recommendations