Skip to main content
SpringerLink
Log in

A phenomenological failure criterion for brittle rock

  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Summary

A phenomenological model is developed to represent failure in intact media as a consequence of shear-band formation. A stepped arrangement of connected flaws is assumed to be distributed within a planar shear-band inclined with respect to the applied deviatoric stresses. The flaws within the shear-band isolate a series of wedges that transmit tractions across the pre-failure zone. Gross stress transmission is controlled by static equilibrium with spatial stress inhomogeneity modulated through the distribution of flaws in the continuum adjacent to the shear-band. Under increased confinement, flaw closure beyond the shear-band results in a more homogeneous transmission of normal tractions across the failure plane. This stress dependent transition is based on physical arguments, related to mean flaw closure, to yield a distribution coefficient,W, that is controlled by macroscopic flaw rigidity,B. The model is able to replicate the power law dependency of ultimate strength with confining stress that is commonly observed. The model is specifically calibrated against experimental data for Daye marble. The phenomenological coefficients describing the failure process appear as material constants.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Batzle, M., Simmons, G., Siegfried, R. (1979) Direct observation of fracture closure in rocks under stress. EOS Trans. 60, 380.

    Google Scholar 

  • Bieniawski, Z. T. (1966): Mechanism of brittle fracture of rock. CSIR Report RMEG 580, Pretoria.

  • Bombolakis, E. G. (1968): Photoelastic study of initial stages of brittle fracture in compression. Tectonophysics 6, 461–473.

    Google Scholar 

  • Brace, W. F., Bombolakis, E. G. (1963): A note on brittle crack growth in compression. J. Geophys. Res. 68, 3709–3713.

    Google Scholar 

  • Brace, W. F., Paulding, B. W., Scholz, C. (1966): Dilatancy in the fracture of crystalline rocks. J. Geophys. Res. 71, 3939–3952.

    Google Scholar 

  • Brady, B. T. (1969a): A statistical theory of brittle fracture. Part I. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 6, 21–42.

    Google Scholar 

  • Brady, B. T. (1969b): A statistical theory of brittle fracture. Part II. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 6, 285–300.

    Google Scholar 

  • Dey, T. N., Wang, C.-Y. (1981): Some mechanics of microcrack growth and interaction in compressive rock failure. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 18, 199–209.

    Google Scholar 

  • Fairhurst, C., Cook, N. G. W. (1966): The phenomenon of rock splitting parallel to the direction of maximum compression in the neighborhood of a surface. In: Proc. 1st Int. Congress Int. Soc. Rock Mech. Liston, 687–692.

  • Fonseka, G. M., Murrell, S. A. F., Barnes, P. (1985): Scanning electron microscope and acoustic emission studies of crack development in rocks. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 22, 273–289.

    Google Scholar 

  • Griffith, A. A. (1921): The phenomena of rupture and flow in solids. Philosophical Transactions 221, 163–198.

    Google Scholar 

  • Griffith, A. A. (1924): Theory of rupture. In: Proc. 1st Int. Congress on Appl. Mechanics, Delft, 55–64.

  • Hallbauer, D. K., Wager, H., Cook, N. G. W. (1973): Some observations concerning the microscope and mechanical behavior of quartzite specimens in stiff triaxial compression tests. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 10, 713–726.

    Google Scholar 

  • Hoek, E., Bieniawski, Z. T. (1965): Brittle fracture propagation in rock under compression. Int. J. Fracture Mech. 1, 137–155.

    Google Scholar 

  • Janach, W. (1977): Failure of granite under compression. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 14, 209–215.

    Google Scholar 

  • Kranz, R. L. (1979a): Crack growth and development during creep in Barre granite. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 16, 23–36.

    Google Scholar 

  • Kranz, R. L. (1979b): Crack-crack and crack-pore interactions in stressed granite. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 16, 37–48.

    Google Scholar 

  • Liu, H. P., Livanos, A. C. R. (1976): Dilatancy and precursory bulging along incipient fracture zones in uniaxially compressed Westerly granite. J. Geophys. Res. 81, 3495–3510.

    Google Scholar 

  • Lundborg, N. A. (1974): A statistical theory of polyaxial strength of materials. In: Proc. 3rd Int. Congress Int. Soc. Rock Mech., Denver, 180–185.

  • McClintock, F. A., Walsh, J. B. (1962): Friction on Griffith cracks in rocks under pressure. In: Proc. 4th U.S. National Congress on Applied Mechanics, Vol. 2, 1015–1021.

  • Nesetova, V., Lajtai, E. Z. (1973): Fracture from compressive stress concentrations around elastic flaws. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 10, 265–284.

    Google Scholar 

  • Peng, S. D., Johnson, A. M. (1972): Crack growth and faulting in cylindrical specimens of Chelmsford granite. Int. J. Rock Mech. Min. Sci. 9, 37–86.

    Google Scholar 

  • Sholz, C. H. (1968a): Microfracturing, aftershocks and seismicity. Bull. Seism. Soc. Am. 58, 1117–1130.

    Google Scholar 

  • Scholz, C. H. (1968b): Macrofracturing and the inelastic deformation of rock in compression. J. Geophys. Res. 73, 1417–1432.

    Google Scholar 

  • Sokolinkoff, I. S. (1961): Mathematical theory of elasticity, 476 pp. J. Geophys. Res., 4237–4292.

  • Swain, M. V., Lawn, B. R., Burns, S. J. (1974): Cleavage step deformation in brittle solids. J. Mater. Sci. 9, 175–183.

    Google Scholar 

  • Tapponnier, P., Brace, W. F. (1976): Development of stress induced microcracks in Westerly granite. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 13, 102–113.

    Google Scholar 

  • Timoshenko, S. P., Goodier, J. N. (1970): Theory of elasticity. McGraw-Hill, New York, 109–112.

    Google Scholar 

  • Vutukuri, V. S., Lama, R. D., Saluja, S. S. (1974): Handbook on mechanical properties of rocks, Vol I, Trans. Tech. Publ. Clausthal.

  • Wang, T. F. (1982): Micromechanics of faulting in Westerly granite. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 19, 49–64.

    Google Scholar 

  • Wiebols, G. A., Cook, N. G. W. (1968): An energy criterion for the strength of rock in polyaxial compression. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 5, 529–549.

    Google Scholar 

  • Woronow, A. (1975): A new technique for determining the preferred failure angle of brittle rock. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 12, 289–293.

    Google Scholar 

  • Wu, F. T., Thomsen, L. (1975): Microfracturing and deformation of Westerly granite under creep condition. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 12, 167–173.

    Google Scholar 

Download references

Author information

Author notes

  1. Z. Ouyang

    Present address: Department of Mining Engineering, Wuhan Steel and Iron University, 430081, Wuhan, People's Republic of China

  2. D. Elsworth

    Present address: Department of Mineral Engineering, Pennsylvania State University, 16802, University Park, PA, USA

Authors and Affiliations

  1. Waterloo Centre for Groundwater Research, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    D. Elsworth

Authors
  1. Z. Ouyang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Elsworth
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ouyang, Z., Elsworth, D. A phenomenological failure criterion for brittle rock. Rock Mech Rock Engng 24, 133–153 (1991). https://doi.org/10.1007/BF01042858

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01042858

Keywords

Search

Navigation