A damage mechanics model for power-law creep and earthquake aftershock and foreshock sequences

Geophysical Journal International

Volumn 142, Issue 1, 2000, Pages 151-161

  Main, Ian G ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

Aftershocks; Creep; Earthquakes; Foreshocks; Rheology; Rock fracture

Indexed keywords

EARTHQUAKE; FLOW KINETICS; MECHANICS; MODEL; STEADY STATE;

AFTERSHOCK; CREEP; DAMAGE MECHANICS; EARTHQUAKE; FORESHOCK; POWER LAW; SEISMICITY;

EID: 0033949654     PISSN: 0956540X     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-246X.2000.00136.x     Document Type: Article

References (41)

1. Ashby, M.F. & Hallam, S.D., 1986. The failure of brittle solids containing small cracks under compressive stress states, Acta Metall., 34, 497-510.
2. Ashby, M.F. & Sammis, C.G., 1990. The damage mechanics of brittle solids in compression, Pure appl. Geophys., 133, 489-521.
3. Atkinson, B.K. & Meredith, P.G., 1987. The theory of subcritical crack growth with applications to minerals and rocks, in Fracture Mechanics of Rock, pp. 111-166, ed. Atkinson, B.K., Academic Press, London.
4. Bufe, C.G. & Varnes, D.J., 1993. Predictive modeling of the seismiccycle of the greater San Francisco Bay region, J. geophys. Res., 98, 9871-9883.
5. Costin, L.S., 1987. Time-dependent deformation and failure, in Fracture Mechanics of Rock, pp. 167-215, ed. Atkinson, B.K., Academic Press, London.
6. Das, S. & Scholz, C.H., 1981. Theory of time-dependent rupture in the Earth, J. geophys. Res., 86, 6039-6051.
7. Davy, P., Hansen, A., Bonnet, E. & Zhang, S.-Z., 1995. Localization and fault growth in layered brittle-ductile systems: implications for deformations of the continental lithosphere, J. geophys. Res., 100, 6281-6294.
8. Dieterich, J.H., 1978. Time-dependent friction and the mechanics of stick-slip, Pure appl. Geophys., 116, 790-806.
9. Hainzl, S., Zoeller, G. & Kurths, J., 1999. Similar power laws for foreshock and aftershock sequences in a spring-block model for earthquakes, J. geophys. Res., 104, 7243-7253.
10. Hobbs, B.E., Means, W.D. & Williams, P.F., 1976. An Outline of Structural Geology, Wiley, New York.
11. Horii, H. & Nemat-Nasser, S., 1985. Compression-induced microcrack growth in brittle solids: axial splitting and shear failure, J. geophys. Res., 90, 3105-3125.
12. Kagan, Y.Y. & Knopoff, L., 1978. Statistical study of the occurrence of shallow earthquakes, Geophys. J. R. astr. Soc., 55, 67-86.
13. Kostrov, 1974, Seismic moment and the energy of earthquakes and seismic flow of rock, Izv. Acad. Sci., USSR Phys. Solid Earth, 1, 23-44.
14. Lankford, J., 1981. The role of tensile microfracture in the strain rate dependence of compressive strength of fine-grained limestone. Int. J. Rock Mech. Min. Sci. Geomech. Abstract., 18, 173-175.
15. Lawn, B., 1993. Fracture of Brittle Solids, 2nd edn, Cambridge University Press, Cambridge.
16. Liakopoulou-Morris, F., Main, I.G., Crawford, B.R. & Smart, B.G.D., 1994. Microseismic properties of a homogeneous sandstone during fault development and frictional sliding, Geophys. J. Int., 119, 219-230.
17. Lockner, D., 1993a. Room temperature creep in saturated granite, J. geophys. Res., 98, 475-487.
18. Lockner, D., 1993b. The role of acoustic emission in the study of rock fracture, Int. J. Rock Mech. Min. Sci. Geomech. Abstract., 30, 883-899.
19. Lockner, D.A., 1998. A generalised law for brittle deformation of Westerley Granite, J. geophys. Res., 103, 5107-5123.
20. Main, I., 1988. Prediction of failure times in the earth for a timevarying stress, Geophys. J., 92, 455-464.
21. Main, I.G., 1999. Applicability of time-to-failure analysis to accelerated strain before earthquakes and volcanic eruptions, Geophys. J. Int., 139, F1-F6.
22. Main, I.G., Leonard, T., Papasouliotis, O., Hatton, C.G. & Meredith, P.G., 1999. One slope or two? - Detecting statistically-significant breaks of slope in geophysical data, with application to fracture scaling relationships, Geophys. Res. Lett., 26, 2801-2804.
23. Meredith, P.G. & Atkinson, B.K., 1983. Stress corrosion and acoustic emission during tensile crack propagation in Whin Sill Dolerite and other basic rocks. Geophys. J. R. astr. Soc., 75, 1-21.
24. Moore, D.E. & Lockner, D.A., 1995. The role of microcracking in shear-fracture propagation in granite, J. struct. Geol., 17, 95-114.
25. Ngwenya, B.T., Elphick, S.C., Maillot, B., Main, I.G. & Shimmield, G.B., 1999. Fluid-rock interactions during room temperature creep of porous sandstones: Implications for fault sealing, J. geophys. Res., submitted.
26. Okui, Y. & Horii, H., 1997. Stress and time-dependent failure of brittle rocks under compression: a theoretical prediction, J. geophys. Res., 102, 14 869-14 881.
27. Ranalli, G., 1995. Rheology of the Earth, 2nd edn, Chapman & Hall, London.
28. Reasenberg, P.A., 1999. Foreshock occurrence before large earthquakes, J. geophys. Res., 104, 4755-4768.
29. Reches, Z. & Lockner, D.A., 1994. Nucleation and growth of faults in brittle rocks, J. geophys. Res., 99, 18 159-18 173.
30. Renshaw, C.E. & Park, J.C., 1997. Effect of mechanical interactions on the scaling of fracture length and aperture, Nature. 386, 482-484.
31. Rice, J.R., 1978. Thermodynamics of quasi-static growth of Griffith cracks, J. Mech. Phys. Solids, 26, 61-78.
32. Ruina, A.L., 1983. Slip instability and state variable friction laws. J. geophys. Res., 88, 359-370.
33. Sammis, C.G. & Ashby, M.F., 1986. The failure of brittle porous solids under compressive stress states, Acta Metall., 34, 511-526.
34. Sano, O., Ito, I. & Terada, M., 1981. Influence of strain rate on dilatancy and shear strength of Oshima granite under uniaxial compression, J. geophys. Res., 86, 9299-9311.
35. Scholz, C.H., 1968a. Microfracturing and the inelastic deformation of rock in compression. J. geophys. Res., 73, 1471-1432.
36. Scholz, C.H., 1968b. Microfractures, aftershocks and seismicity, Bull. seism. Soc. Am., 58, 1117-1130.
37. Stanley, H. E., 1971. Introduction to Phase Transitions and Critical Phenomena, Oxford Science, Oxford.
38. Utsu, T., Ogata, Y. & Matsu'ura, R.S., 1995. The centenary of the Omori formula for the decay of aftershock activity, J. Phys. Earth, 43, 1-33.
39. Varnes, D.J., 1983. Time-dependent deformations in creep to failure of earth materials, in Proc. 7th East Asian Geotechnical Conf., 2, 107-130, Southeast Asian Geotechnical Society, Bangkok.
40. Voight, B., 1988. A method for predicting volcanic eruptions, Nature, 332, 125-130.
41. Voight, B., 1989. A relation to describe rate-dependent material failure, Science, 243, 200-203.