Micro and macroscopic models of rock fracture

Geophysical Journal International

Volumn 152, Issue 3, 2003, Pages 718-728

  Turcotte, Donald L ^a,c   Newman, William I ^b,c   Shcherbakov, Robert ^a,c  

^a Department of Obstetrics Gynecology   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Critical point; Damage mechanics; Fibre bundle model; Fracture; Power law scaling

Indexed keywords

BRITTLE DEFORMATION; DAMAGE MECHANICS; EARTHQUAKE RUPTURE; EXPERIMENTAL STUDY; FRACTURE; POWER LAW;

EID: 0037339252     PISSN: 0956540X     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-246X.2003.01884.x     Document Type: Article

References (52)

1. Andersen, J.V., Sornette, D. & Leung, K.-T., 1997. Tricritical behaviour in rupture induced by disorder, Phys, Rev. Lett., 78, 2140-2143.
2. Anifrani, J.-C., Le Floc'h, C., Sornette, D. & Souillard, B., 1995. Universal log-periodic correction to renormalization group scaling for rupture stress prediction from acoustic emissions, J. Physique I. 5, 631-638.
3. Bak, P. & Tang, C., 1989. Earthquakes as a self-organized critical phenomenon, J. geophys. Res., 94, 15 635-15 637.
4. Ben-Zion, Y. & Lyakhovsky, V., 2002. Accelerated seismic release and related aspects of seismicity patterns on earthquakes faults, Pure appl. Geophys., 159, 2385-2412.
5. Ben-Zion, Y. & Rice, J.R., 1995. Slip patterns and earthquake populations along different classes of faults in elastic solids, J. geophys. Res., 100, 12 959-12 983.
6. Bowman, D.D., Ouillon, G., Sammis, C.G., Sornette, A. & Sornette, D., 1998. An observational test of the critical earthquake concept, J. geophys. Res., 103, 24 359-24 372.
7. Brehm, D.J. & Braile, L.W., 1998. Intermediate-term earthquake prediction using precursory events in the New Madrid seismic zone, Bull. seism. Soc. Am., 88, 564-580.
8. Brehm, D.J. & Braile, L.W., 1999. Intermediate-term earthquake prediction using the modified time-to-failure method in Southern California, Bull. seism. Soc. Am., 89, 275-293.
9. Buchel, A. & Sethna, J.P., 1997. Statistical mechanics of cracks: fluctuations, breakdown, and asymptotics of elastic theory, Phys. Rev., E, 55, 7669-7690.
10. Bufe, C.G. & Varnes, D.J., 1993. Predictive modeling of the seismic cycle of the greater San Francisco Bay region, J. geophys. Res., 98, 9871-9883.
11. Bufe, C.G., Nishenko, S.P. & Varnes, D.J., 1994. Seismicity trends and potential for large earthquakes in the Alaska-Alcutian region, Pure appl. Geophys., 142, 83-99.
12. Coleman, B.D., 1956. Time dependence of mechanical breakdown phenomena, J. appl. Phys., 27, 862-866.
13. Coleman, B.D., 1958. Statistics and time dependence of mechanical breakdown in fibers, J. appl. Phys., 29, 968-983.
14. Curtin, W.A., 1991. Theory of mechanical properties of ceramic-matrix composites, J. Am. Ceram. Soc., 74, 2837-2845.
15. Freund, L.B., 1990. Dynamic Fracture Mechanics, Cambridge University Press, Cambridge.
16. Gluzman, S. & Sornette, D., 2001. Self-consistent theory of rupture by progressive diffuse damage, Phys. Rev., E. 63, 066 129.
17. Guarino, A., Garcimartin, A. & Ciliberto, S., 1998. An experimental test of the critical behavior of fracture precursors, Eur. Phys. J., B, 6, 13-24.
18. Guarino, A., Ciliberto, S. & Garcimartin, A., 1999. Failure time and microcrack nucleation, Europhys. Lett., 47, 456.
19. Hemmer, P.C. & Hansen, A., 1992. The distribution of simultaneous fiber failures in fiber-bundles, J. appl. Mech., 59, 909-914.
20. Hirata, T., Satoh, E. & Ito, K., 1987. Fractal structure of spatial distribution of microfracturing in rock, Geophys. J. R. astr. Soc. 90, 369-374.
21. Jaume, S.C. & Sykes, L.R., 1990. Evolving towards a critical point: a review of accelerating seismic moment/energy release prior to large and great earthquakes, Pure appl. Geophys., 155, 279-306.
22. Johansen, A. & Sornette, D., 2000. Critical ruptures, Eur. Phys. J., B, 18, 163-181.
23. Kachanov, L.M., 1986, Introduction to Continuum Damage Mechanics, Martinus Nijhoff. Dordrecht.
24. Kloster, M., Hansen, A. & Hemmer, P.C., 1997. Burst avalanches in solvable models of fibrous materials, Phys. Rev., E, 56, 2615-2625.
25. Knopoff, L. & Newman, W.I., 1983. Crack fusion dynamics: a model for large earthquakes. Pure appl. Geophys., 121, 495-510.
26. Knopoff, L., Levshina, T., Keilis-Borok, V.I. & Mattoni, C., 1996. Increased long-range intermediate-magnitude earthquake activity prior to strong earthquakes in California, J. geophys. Res., 101, 5779-5796.
27. Krajcinovic, D., 1996. Damage Mechanics. Elsevier, Amsterdam.
28. Kun, F. & Henmann, H.J., 1999. Transition from damage to fragmentation in collision of solids, Phys. Rev., E, 59, 2623-2632.
29. Lemaitre, J. & Chaboche, J.-L., 1990. Mechanics of Solid Materials. Cambridge University Press, Cambridge.
30. Lockner, D.A., 1993. The role of acoustic emissions in the study of rock fracture, Int. J. Rock. Mech. Min. Sci. Geomech. Abs., 7, 883-889.
31. Lyakhovsky, V., Podladchikov, Y. & Poliakov, A., 1993. A rheological model of a fractured solid, Tectonophysics, 226, 187-198.
32. Lyakhovsky, V., Ben-Zion, Y. & Agnon, A., 1997. Distributed damage, faulting and friction, J. geophys. Res., 102, 27 635-27 649.
33. Mogi, K., 1962. Study of elastic shocks caused by the fracture of hetergeneous materials and its relations to earthquake phenomena, Bull. Earthq. Res. Inst., 40, 125-173.
34. Newman, W.I. & Knopoff, L., 1982. Crack fusion dynamics: a model for large earthquakes, Geophys. Res. Lett., 9, 735-738.
35. Newman, W.I. & Knopoff, L., 1983. A model for repetitive cycles of large earthquakes, Geophys. Res. Lett., 10, 305-308.
36. Newman, W.I. & Knopoff, L., 1990. Scale invariance in brittle fracture and the dynamics of crack fusion, Int. J. Fracture, 43, 19-24.
37. Newman, W.I. & Phoenix, S.L., 2001. Time dependent fiber-bundles with local load sharing, Phys. Rev., E, 63, 021 507.
38. Otani, H., Phoenix, S.L. & Petrina, P., 1991. Matrix effects on lifetime statistics for carbon fibre-epoxy microcomposites in creep rupture, J. Mat. Sci., 26, 1955-1970.
39. Robinson, R., 2000. A test of the precursory accelerating moment release model on some recent New Zeland earthquakes, Geophys. J. Int., 140, 568-576.
40. Rundle, J.B., Klein, W. & Gross, S., 1996. Dynamics of a traveling density wave model for earthquakes, Phys. Rev. Let., 76, 4285-4288.
41. Rundle, J.B., Klein, W. & Gross, S., 1999. Physical basis for statistical patterns in complex earthquakes populations: models, predictions and tests, Pure appl. Geophys., 155, 575-607.
42. Rundle, J.B., Klein, W., Turcotte, D.L. & Malamud, B.D., 2000. Precursory seismic activation and critical point phenomena, Pure appl. Geophys., 157, 2165-2182.
43. Selinger, R.L.B., Wang, Z.G., Gelbart, W.M. & Ben-Shaul, A., 1991. Statistical-thermodynamic approach to fracture, Phys. Rev., A. 43, 4396-4400.
44. Smith, R.L. & 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.
45. Sornette, D. & Andersen, J.V., 1998. Scaling with respect to disorder in time-to-failure, Eur. Phys. J., B, 1, 353-357.
46. Sykes, L.R. & Jaumé, S.C., 1990. Seismic activity on neighboring faults as a long-term precursor to large earthquakes in the San Francisco Bay region, Nature, 348, 595-599.
47. Turcotte, D.L., 1999. Seismicity and self-organized critically, Phys. Earth planet. Inter., 111, 275-293.
48. b = 4.8 earthquake on 1980 February 14 near the Virgin Islands, Geophys. J. Int., 124, 149-158.
49. Zapperi, S., Ray, P., Stanley, H.E. & Vespignani, A., 1997. First-order transition in the breakdown of disordered media, Phys. Res. Lett., 78, 1408-1411.
50. Zapperi, S., Ray, P., Stanley, H.E. & Vespignani, A., 1999. Avalanches in breakdown and fracture processes, Phys. Rev., E. 59, 5049-5057.
51. Zhurkov, S.N., 1965. Kinetic concept of strength of solids. Int. J. Fracture Mech., 1, 311-323.
52. Zoller, G., Hainzl, S. & 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.