pure and applied geophysics

, Volume 143, Issue 1–3, pp 117–149 | Cite as

Mechanisms of brittle fracture of rock with pre-existing cracks in compression

  • L. N. Germanovich
  • R. L. Salganik
  • A. V. Dyskin
  • K. K. Lee
Fault Mechanics, Rupture Processes, and Fracture: Theory and Observation


Fracture of rocks containing a multitude of pre-existing cracks is considered from both theoretical and experimental points of view, paying attention mainly to the underlying mechanisms. The competition between a number of mechanisms in producing tear or shear type fractures is discussed in relation to the properties of the rock and the system of pre-existing cracks on the one hand and the type of loading on the other hand. First, 2-D theoretical models and experimental results aimed at the explanation and description of brittle fracture under compression are considered. Their insufficiency and the necessity to address the 3-D peculiarities of crack growth in rock are shown on the basis of new experimental results on 3-D crack propagation in transparent rock-like brittle materials under uniaxial compression. The results show that in contrast to the 2-D case, a single 3-D crack cannot propagate any appreciable distance and the loading results in dynamic, burst-like failure of the sample. Possible mechanisms of the routinely observed extensive fracture propagation in rock samples (splitting), as well as the possibility of shear (oblique) fracture in uniaxial compression, are discussed in connection with these experiments.

Key words

Rock fracture in compression 3-D cracks laser technique of crack initiation 


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  1. Adams, M., andSines, G. (1978),Crack Extension from Flaws in a Brittle Material Subjected to Compression, Tectonophys.49, 97–118.Google Scholar
  2. Ashby, M. F., andHallam, S. D. (1986),The Failure of Brittle Solids Containing Small Cracks under Compressive Stress Sta es, Acta Metallurgica34, 497–510.CrossRefGoogle Scholar
  3. Ashby, M. F., andSammis, C. G. (1990),The Damage Mechanics of Brittle Solids in Compression. Pure and Appl. Geophys.133 (3), 489–521.Google Scholar
  4. Barenblatt, G. I., Marin, O. E., Pilipetskii, N. F., andUpadyshev, V. A. (1968),Effect of Stresses on the Orientation of Laser Damage Cracks in Transparent Dielectrics, Soviet Physics JETP,27 (5), 716–717.Google Scholar
  5. Brace, W. F., andBombolakis, E. G. (1963),A Note on Brittle Crack Growth in Compression, J. Geophys. Res.68 (12), 3709–3713.Google Scholar
  6. Brace, W. F., Paulding, B. M., andScholz, C. (1966),Dilatancy in the Fracture of Crystalline Rocks, J. Geophys. Res.71 (16), 3939–3953.Google Scholar
  7. Cannon, N. P., Schulson, E. M., Smith, T. R., andFrost, H. J. (1990),Wing Cracks and Brittle Compressive Fracture, Acta Metall. Mater.38 (10), 1955–1962.Google Scholar
  8. Cherepanov, G. P.,Mechanics of Brittle Fracture (McGraw-Hill, New York 1979).Google Scholar
  9. Cox, S. J. D., andScholz, C. H. (1988a),On the Formation and Growth of Faults: An Experimental Study, J. Struct. Geology10 (4), 413–430.Google Scholar
  10. Cox, S. J. D., andScholz, C. H. (1988b),Rupture Initiation in Shear Fracture of Rocks: An Experimental Study, J. Geophys. Res.93 (B4), 3307–3320.Google Scholar
  11. Dey, T. N., andChi-Yuen Wang (1981),Some Mechanisms of Microcrack Growth and Interaction in Compressive Rock Failure, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr.18, 199–209.Google Scholar
  12. Du, Y., andAydin, A. (1991),Interaction of Multiple Cracks and Formation of Echelon Crack Arrays, Int. J. Numer. and Analyt. Methods in Geomechanics15, 205–218.Google Scholar
  13. Dyskin, A. V., andGermanovich, L. N.,Rockburst model based on cracks growing near free surface. InRockbursts and Seismicity in Mines, Vol. 93, (ed. Young, R. P.) Proc. 3rd Internat. Symp., (Kingston, Ontario, Canada 1993a) pp. 169–173.Google Scholar
  14. Dyskin, A. V., andGermanovich, L. N. (1993b),Model of Crack Growth in Microcracked Rock, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr.30 (7), 813–820.Google Scholar
  15. Dyskin, A. V., Germanovich, L. N., andSalganik, R. L.,A mechanism of deformation and fracture of brittle rocks. InProc. 32nd U.S. Symp. on Rock Mechanics (A. A. Balkema Publishers, Rotterdam 1991) pp. 181–190.Google Scholar
  16. Dyskin, A. V., Germanovich, L. N., andUstinov, K. B.,On the pore-based mechanism of dilatancy and fracture of rocks under compression. InProc. 33rd U.S. Symposium on Rock Mechanics, Santa Fe 1992, pp. 797–806.Google Scholar
  17. Dyskin, A. V., Germanovich, L. N., andUstinov, K. B. (1993),Asymptotic Solution for Long Cracks Emanated from a Pore in Compression, Intern. J. Fract.62, 307–324.Google Scholar
  18. Dyskin, A. V., andSalganik, R. L. (1987),Model of Dilatancy of Brittle Materials with Cracks under Compression, Mech. Sol.22 (6), 165–173.Google Scholar
  19. Entov, V. M., andYagust, V. I. (1975),Experimental Studies of Behavior of Quasi-static Development of Microcracks in Concrete, Mech. Sol.4, 93–103.Google Scholar
  20. Fairhurst, C., andCook, N. G. W.,The phenomenon of rock splitting parallel to the direction of maximum compression in the neighborhood of a surface. InProc. First Congress International Society for Rocks Mechanics (Lisbon 1966). Vol. 1, pp. 687–692.Google Scholar
  21. Galybin, A. N. (1985),Formations of Cracks on Compressing an Unbounded Brittle Body with a Circular Opening, J. Appl. Math. and Mech.49, 797–799.Google Scholar
  22. Germanovich, L. N., andDyskin, A. V. (1988),A Model of Brittle Failure for Materials with Cracks in Uniaxial Loading, Mech. Sol.23 (2), 111–123.Google Scholar
  23. Germanovich, L. N., andDyskin, A. V. (1994a),Viral Expansions in Problems of Effective Characteristics. Part I. General Concepts, Mech. Comp. Mat.30 (2).Google Scholar
  24. Germanovich, L. N., andDyskin, A. V. (1994b),Viral Expansions in Problems of Effective Characteristics. Part II. Anti-plane Deformation of Fiber Composite. Analysis of Self-consistent Methods, Mech. Comp. Mat.30 (3).Google Scholar
  25. Germanovich, L. N., Dyskin, A. V., andTsyrulnikov, M. N. (1990),Mechanism of dilatancy and columnar failure of brittle rocks under uniaxial compression. Transactions (Doklady) of the USSR Academy of Sciences, Earth Science Sections313 (4) 6–10.Google Scholar
  26. Germanovich, L. N., Dyskin, A. V., andTsyrulnikov, M. N. (1993),A Model of Brittle Rock Deformations under Compression, Mech. Sol.28 (1), 116–128.Google Scholar
  27. Gol'dstein, R. V., Ladygin, V. M., andOsipenko, N. M. (1974),A Model of the Fracture of a Slightly Porous Material under Compression or Tension, Soviet Mining Sciences,10, 1–9.Google Scholar
  28. Gol'dstein, R. V., andKaptsov, A. V. (1982),The Formation of Structures of Fracture by Low-interacting Cracks, Mech. Sol.17 (4), 157–166.Google Scholar
  29. Griffith, A. A. (1924),The Theory of Rupture, Proc. 1st Int. Congr. on Applied Mech., Delft, 55–63.Google Scholar
  30. Hoek, E., andBieniawski, Z. T. (1965),Brittle Fracture Propagation in Rock under Compression, Int. J. Fract.1, 137–155.Google Scholar
  31. Hopper, R. W., andUhlmann, D. R. (1970),Mechanism of Inclusion Damage in Laser Glass, J. Appl. Phys.41 (10), 4023–4037.Google Scholar
  32. Horii, H., andNemat-Nasser, S. (1985),Compression-induced Microcrack Growth in Brittle Solids: Axial Splitting and Shear Failure, J. Geophys. Res.90 (B4), 3105–3125.Google Scholar
  33. Horii, H., andNemat-Nasser, S. (1986),Brittle Failure in Compression: Splitting, Faulting, and Brittle-ductile Transition, Phil. Trans. R. Soc. Lond. A319, 337–374.Google Scholar
  34. Huang Jiefan, Chen Ganglin, Zhao Yonghong, andWang Ren (1990),An Experimental Study of the Strain Field Development Prior to Failure of a Marble Plate under Compression, Tectonophys.175, 269–284.Google Scholar
  35. Ingraffea, A. R., andHeuze, F. E. (1980),Finite Element Models for Rock Fracture Mechanics, Int. J. Numer. and Analit. Methods in Geomech.4, 25–43.Google Scholar
  36. Ingraffea, A. R., andSchmidt, R. A.,Experimental verification of a fracture mechanics model for tensile strength prediction of Indiana limestone. InProc. 19th U.S. Symposium on Rock Mechanics, (University of Nevada, Reno) 1978, pp. 243–246.Google Scholar
  37. Isida, M., andNemat-Nasser, S. (1987),A Unified Analysis of Various Problems Relating to Circular Holes with Edge Cracks, Eng. Fract. Mech.27 (5), 571–591.Google Scholar
  38. Kemeny, J., andCook, N. G. W.,Micromechanics of Deformation in Rock. Toughening Mechanism in Quasi-brittle Materials (Kluwer Academic Publishers, Netherlands 1991) pp. 155–188.Google Scholar
  39. Kovalenko, Yu. F., Salganik, R. L., Sidorin, Y. V., andCherstvov, E. V. (1984),Study of the State of the Medium in a Laser Crack and the Mechanism of the Crack Growth in a Transparent Polymer Material, Soviet Physics Doklady29, 941–943.Google Scholar
  40. Kranz, R. L. (1979a),Crack Growth and Development during Creep of Barre Granite, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr.16, 23–35.Google Scholar
  41. Kranz, R. L. (1979b),Crack-crack and Crack-pore Interactions in Stressed Granite, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr.16, 37–47.Google Scholar
  42. Lamkin, S. J., Wawrzysgnek, P. A., andIngraffea, A. R.,Two-dimensional numerical simulation of interacting fractures in rock. InFracture of Concrete and Rock: Recent Developments (eds. Shah, S. P., Swartz, S. E., and Barr, B.) (Elsevier Applied Science, London and New York 1989), pp. 121–131.Google Scholar
  43. Lockner, D. A., Moore, D. E., andReches, Z.,Microcrack interaction leading to shear fracture. InRock Mechanics (eds. Tillerson, J. R., and Wawersik, W. R.) (Balkema, Rotterdam 1992), pp. 807–816.Google Scholar
  44. Melin, S. (1983),Why Do Cracks Avoid Each Other? Int. J. Fract.23 (1), 37–45.Google Scholar
  45. Murakami, Y.,Stress Intensity Factors Handbook, vol. 1 (Pergamon Press, Oxford, New York 1987).Google Scholar
  46. Nemat-Nasser, S., andHorii, H. (1982),Compression-induced Nonplanar Crack Extension with Application to Splitting, Exfoliation, and Rockburst, J. Geophys. Res.87, (B8), 6805–6821.Google Scholar
  47. Paul, B.,Macroscopic criteria for plastic flow and britle fracture. InFracture. An Advanced Treatise (ed. Liebowitz, H.) (Academic Press, New York and London 1968) Vol. II, pp. 313–496.Google Scholar
  48. Peng, S., andJohnson, A. M. (1972),Crack Growth and Faulting in Cylindrical Specimens of Chelmsford Granite, Int. J. Rock. Mech. Min. Sci. and Geomech. Abstr.9, 37–86.Google Scholar
  49. Rice, J.,The mechanics of earthquake rupture. InPhys. Earth Interior (eds. Dzievonsi, A. M., and Boschi, E.) (North-Holland, Amsterdam 1980) pp. 555–649.Google Scholar
  50. Reches, S., andLockner, D. A. (1990),Self-organized Cracking—A Mechanism for Brittle Faulting, EOS, AGU71, 1586.Google Scholar
  51. Salganik, R. L. (1973),Mechanics of Bodies with Many Cracks, Mech. Solids8 (4), 135–143.Google Scholar
  52. Sammis, C. G., andAshby, M. F. (1986),The Failure of Brittle Porous Solids under Compressive Stress States, Acta Metallurgica34 (3), 511–526.CrossRefGoogle Scholar
  53. Sangha, C. M., Talbot, C. J., andDhir R. K. (1974),Microfracturing of a Sandstone in Uniaxial Compression, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr.11 (3), 107–113.Google Scholar
  54. Sano, O., Ito, I., andTakeda, M. (1981),Influence of Strain Rate on Dilatancy and Strength of Oshima Granite under Uniaxial Compression, J. Geophys. Res.86 (B10), 9299–9311.Google Scholar
  55. Scholz, C. H. (1968),Microfracturing and the Inelastic Deformation of Rock in Compression, J. Geophys. Res.73, 1417–1432.Google Scholar
  56. Scholz, C. H.,The Mechanics of Earthquakes and Faulting (Cambridge University Press, Cambridge, New York, Sydney 1990).Google Scholar
  57. Segall, P., andPollard, D. D. (1980),Mechanics of Discontinuous Faults, J. Geophys. Res.85 (B8), 4337–4350.Google Scholar
  58. Spetzler, H., Mitzutani, H., andRummel, F.,Fracture and flow. InAnelasticity in the Earth, Geodyn. Ser., Vol. 4 (ed. Schreyer, W.) (Stuttgart, Germany 1982) pp. 85–93.Google Scholar
  59. Steacy, S. J., andSammis, C. G. (1992),A Damage Mechanics Model for Fault Zone Friction, J. Geophys. Res.97 (B1), 587–594.Google Scholar
  60. Tada, H., Paris, P. C., andIrwin, G. R.,The Stress Analysis of Cracks. Handbook. Second edition, Vol. II (Paris Productions, Inc. and Del Research Corporation. St. Louis, Missouri 1985).Google Scholar
  61. Talonov, A. V., andTulinov, B. M. (1989),Calculation of Strains for Brittle Materials Taking into Account Limiting Failure, J. Appl. Mech. Tech. Phys.30, 470–476.Google Scholar
  62. Wiederhorn, S. M. (1969),Fracture Surface Energy of Glass, J. Am. Ceram. Soc.52 (2), 99–105.Google Scholar
  63. Wong, T.-F.,Micromechanics of Faulting in Westerly Granite, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr.19, 49–63 (Pergamon Press, Oxfrod, New York, Seoul, Tokyo 1982).Google Scholar
  64. Zaitsev, Y.,Crack propogation in a composite material. InFracture Mechanics of Concrete, 1983 pp. 251–299.Google Scholar

Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • L. N. Germanovich
    • 1
  • R. L. Salganik
    • 2
  • A. V. Dyskin
    • 3
  • K. K. Lee
    • 1
  1. 1.The University of OklahomaNormanU.S.A.
  2. 2.Tel-Aviv UniversityTel-AvivIsrael
  3. 3.The University of Western AustraliaNedlandsAustralia

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