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Theoretical approach to dependence of crack growth mechanism on confining pressure
Earth, Planets and Space volume 52, pages 315–320 (2000)
We calculated the stress field on and around an elliptical open crack located in an elastic medium under various confining pressures. The problems were treated as two-dimensional ones by using complex potentials, and the considerable differences between uniaxial and triaxial crack growth mechanisms were recognized. A uniaxial condition allows a certain elliptical open crack to develop by itself (without any crack-crack interactions) along its major semi-axis, whereas a triaxial condition does not. This is the principal mechanism of transition from uniaxial to triaxial crack growth. Our transition model, derived using a theoretical approach, explains the dependence of experimental results, such as crack distribution and internal friction angle, on confining pressure well. We conclude that uniaxial and triaxial crack growth mechanisms fundamentally differ from each other, and that attention must be paid to experimental conditions when applying experimental results to phenomena in the Earth.
Baud, P., T. Reuschlé, and P. Charlez, An improved wing crack model for the deformation and failure of rock in compression, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr., 33, 539–542, 1996.
Berg, C. A., Deformation of fine cracks under high pressure and shear, J. Geophys. Res., 70, 3447–3452, 1965.
Brace, W. F., B. W. Paulding, Jr., and C. H. Scholz, Dilatancy in the fracture of crystalline rocks, J. Geophys. Res., 71, 3939–3953, 1966.
Digby, P. J. and S. A. F. Murrell, The deformation of flat ellipsoidal cavities under large confining pressures, Bull. Seism. Soc. Am., 66, 425–431, 1976.
Griffith, A. A., The phenomena of rupture and flow in solids, Phil. Trans. Roy. Soc. London, Ser. A, Math. Phys. Sci, 211, 163–198, 1921.
Hallbauer, D. K., H. Wagner, and N. G. W. Cook, Some observations concerning the microscopic and mechanical behaviour of quartzite specimens in stiff, triaxial compression tests, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr., 10, 713–726, 1973.
Horii, H. and S. Nemat-Nasser, Compression-induced microcrack growth in brittle solids: Axial splitting and shear failure, J. Geophys. Res., 90, 3105–3125, 1985.
Jaeger, J. C. and N. G. W. Cook, Fundamentals of Rock Mechanics, 2nd ed., 593 pp., Chapman and Hall, London, 1976.
Jeyakumaran, M. and J. W. Rudnicki, The sliding wing crack-Again!, Geophys. Res. Lett., 22, 2901–2904, 1995.
Kawakata, H. and M. Shimada, Frequency-magnitude relation of AE in fracture process of rocks athigh confining pressures, Proc. 8th Int. Congr. Rock Mech., 1, 207–210, 1995.
Kawakata, H., A. Cho, T. Yanagidani, and M. Shimada, The observations of faulting in Westerly granite under triaxial compression by X-ray CT scan, Int. J. Rock Mech. Min. Sci., 34: 3/4, Paper No. 151, 1997.
Kawakata, H., A. Cho, T. Kiyama, T. Yanagidani, and M. Shimada, The observations of fault formation in Westerly granite by X-ray CT scan, Tectonophys., 313, 293–305, 1999.
Lin, P. and J. M. Logan, The interaction of two closely spaced cracks: a rock model study, J. Geophys. Res., 96, 21,667–21,675, 1991.
Lockner, D. A. and T. R. Madden, A multiple-crack model of brittle fracture, 1. Non-time-dependent simulations, J. Geophys. Res., 96, 19,623–19,642, 1991.
Lockner, D. A., J. D. Byerlee, V. Kuksenko, A. Ponomarev, and A. Sidorin, Observations of quasi-static fault growth from acoustic emissions, in Fault Mechanics and Transport Properties of Rocks, edited by B. Evans and T.-F. Wong, pp. 3–31, Academic Press, San Diego, Calif., 1992.
McClintock, F. A. and J. B. Walsh, Friction on Griffith cracks in rocks under pressure, Proc. 4th U. S. Nat. Congr. Appl. Mech., 2, 1015–1022, 1962.
Murrell, S. A. F. and P. J. Digby, The theory of brittle fracture initiation under triaxial stress conditions - I, Geophys. J. Roy. Astron. Soc., 19, 309–334, 1970a.
Murrell, S. A. F. and P. J. Digby, The theory of brittle fracture initiation under triaxial stress conditions - II, Geophys. J. Roy. Astron. Soc., 19, 499–512, 1970b.
Orowan, E., Fracture and strength of solids, Repts. Prog. Phys., 12, 185–232, 1949.
Reches, Z. and D. A. Lockner, Nucleation and growth of faults in brittle rocks, J. Geophys. Res., 99, 18,159–18,173, 1994.
Scholz, C. H., The Mechanics of Earthquakes and Faulting, 439 pp., Cambridge University Press, Cambridge, 1990.
Segall, P. and D. D. Pollard, Mechanics of discontinuous faults, J. Geophys. Res., 85, 4337–4350, 1980.
Shimada, M. and A. Cho, Two types of brittle fracture of silicate rocks under confining pressure and their implication inthe earth’s crust, Tectonophys., 175, 221–235, 1990.
Wawersik, W. R. and W. F. Brace, Post-failure behavior of a granite and diabase, Rock Mech., 3, 61–85, 1971.
Yanagidani, T., S. Ehara, O. Nishizawa, K. Kusunose, and M. Terada, Localization of dilatancy in Ohshima granite under constant uniaxial stress, J. Geophys. Res., 90, 6840–6858, 1985.
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Kawakata, H., Shimada, M. Theoretical approach to dependence of crack growth mechanism on confining pressure. Earth Planet Sp 52, 315–320 (2000). https://doi.org/10.1186/BF03351642
- Fault Plane
- Tangential Stress
- Open Crack
- Crack Density
- Wing Crack