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Three-dimensional brittle shear fracturing by tensile crack interaction

Nature volume 439, pages 64–67 (2006)Cite this article

Abstract

Faults in brittle rock are shear fractures formed through the interaction and coalescence of many tensile microcracks1,2,3. The geometry of these microcracks and their surrounding elastic stress fields control the orientation of the final shear fracture surfaces3,4. The classic Coulomb–Mohr failure criterion5 predicts the development of two conjugate (bimodal) shear planes that are inclined at an acute angle to the axis of maximum compressive stress. This criterion, however, is incapable of explaining the three-dimensional polymodal fault patterns that are widely observed in rocks6,7,8,9. Here we show that the elastic stress around tensile microcracks in three dimensions promotes a mutual interaction that produces brittle shear planes oriented obliquely to the remote principal stresses, and can therefore account for observed polymodal fault patterns. Our microcrack interaction model is based on the three-dimensional solution of Eshelby10,11, unlike previous models4,12 that employed two-dimensional approximations. Our model predicts that shear fractures formed by the coalescence of interacting mode I cracks will be inclined at a maximum of 26° to the axes of remote maximum and intermediate compression. An improved understanding of brittle shear failure in three dimensions has important implications for earthquake seismology and rock-mass stability, as well as fluid migration in fractured rocks13.

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Figure 1: Contrasting patterns of conjugate (bimodal) and polymodal faults.
Figure 2: Elastic stress field around an isolated ‘penny-shaped’ crack.
Figure 3: Locus of maximum tensile interaction.
Figure 4: Comparison of model predictions with fault data from Triassic sandstones around Gruinard Bay.

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References

  1. Paterson, M. S. Experimental Rock Deformation—The Brittle Field Ch. 3 & 4 (Springer, Berlin, 1978)

    Book  Google Scholar 

  2. Lockner, D. A., Byerlee, J. D., Kuksenko, V., Ponomarev, A. & Sidorin, A. Observations of quasistatic fault growth from acoustic emissions. in Fault Mechanics and Transport Properties of Rocks (eds Evans, B. & Wong, T.) 3–31 (Academic, London, 1992)

    Google Scholar 

  3. Scholz, C. H. The Mechanics of Earthquakes and Faulting Ch. 1 & 3 (Cambridge Univ. Press, Cambridge, UK, 2002)

    Book  Google Scholar 

  4. Reches, Z. & Lockner, D. A. Nucleation and growth of faults in brittle rocks. J. Geophys. Res. 99, 18159–18173 (1994)

    Article  ADS  Google Scholar 

  5. Jaeger, J. & Cook, N. G. W. Fundamentals of Rock Mechanics, 3rd edn, Ch. 4 & 6 (Chapman & Hall, London, 1979)

    Google Scholar 

  6. Reches, Z. Analysis of faulting in three-dimensional strain fields. Tectonophysics 47, 109–129 (1978)

    Article  ADS  Google Scholar 

  7. Aydin, A. & Reches, Z. Number and orientation of fault sets in the field and in experiments. Geology 10, 107–112 (1982)

    Article  ADS  Google Scholar 

  8. Reches, Z. Faulting of rocks in three-dimensional strain fields. II. Theoretical analysis. Tectonophysics 95, 133–156 (1983)

    Article  ADS  Google Scholar 

  9. Reches, Z. & Dieterich, J. Faulting of rocks in three-dimensional strain fields. I. Failure of rocks in polyaxial, servo-control experiments. Tectonophysics 95, 111–132 (1983)

    Article  ADS  Google Scholar 

  10. Eshelby, J. D. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. A 241, 376–396 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  11. Eshelby, J. D. The elastic field outside an ellipsoidal inclusion. Proc. R. Soc. Lond. A 252, 561–569 (1959)

    Article  ADS  MathSciNet  Google Scholar 

  12. Du, Y. & Aydin, A. Interaction of multiple cracks and formation of echelon crack arrays. Int. J. Num. Analyt. Methods Geomech. 15, 205–218 (1991)

    Article  Google Scholar 

  13. Sternlof, K. R., Chapin, J. R., Pollard, D. D. & Durlofsky, L. J. Permeability effects of deformation band arrays in sandstone. AAPG Bull. 88, 1315–1329 (2004)

    Article  Google Scholar 

  14. Anderson, E. M. The Dynamics Of Faulting And Dyke Formation With Applications To Britain (Oliver and Boyd, Edinburgh, 1942)

    Google Scholar 

  15. De Paola, N., Holdsworth, R. E. & McCaffrey, K. J. W. The influence of lithology and pre-existing structures on reservoir-scale faulting patterns in transtensional rift zones. J. Geol. Soc. Lond. 162, 471–480 (2005)

    Article  Google Scholar 

  16. Crider, J. G. Oblique slip and the geometry of normal-fault linkage: mechanics and a case study from the Basin and Range in Oregon. J. Struct. Geol. 23, 1997–2009 (2001)

    Article  ADS  Google Scholar 

  17. Beacom, L. E., Anderson, T. B. & Holdsworth, R. E. Using basement-hosted clastic dykes as syn-rifting palaeostress indicators: an example from the basal Stoer group, northwest Scotland. Geol. Mag. 136, 301–310 (1999)

    Article  ADS  Google Scholar 

  18. Dewey, J. F., Holdsworth, R. E. & Strachan, R. A. in Continental Transpressional and Transtensional Tectonics (eds Holdsworth, R. E., Strachan, R. A. & Dewey, J. F.) Vol. 135 1–14 (Geological Society Special Publications, London, 1998)

    Google Scholar 

  19. Jones, R. R., Holdsworth, R. E., McCaffrey, K. J. W., Clegg, P. & Tavarnelli, E. Scale dependence, strain compatibility and heterogeneity of three-dimensional deformation during mountain building: a discussion. J. Struct. Geol. 27, 1190–1204 (2005)

    Article  ADS  Google Scholar 

  20. Moore, D. E. & Lockner, D. A. The role of microcracking in shear-fracture propagation in granite. J. Struct. Geol. 17, 95–114 (1995)

    Article  ADS  Google Scholar 

  21. Glover, P. W. J., Gomez, J. B. & Meredith, P. G. Fracturing in saturated rocks undergoing triaxial deformation using complex electrical conductivity measurements: experimental study. Earth Planet. Sci. Lett. 183, 201–213 (2000)

    Article  ADS  CAS  Google Scholar 

  22. Ju, J. W. & Sun, L. Z. Effective elastoplastic behaviour of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part 1: micromechanics based formulation. Int. J. Solids Struct. 38, 183–201 (2001)

    Article  Google Scholar 

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

    Article  Google Scholar 

  24. Pollard, D. D. & Segall, P. Theoretical displacements and stresses near fractures in rock: with applications to faults, joints, veins, dikes, and solution surfaces. in Fracture Mechanics of Rock (ed. Atkinson, B. K) 277–349 (Academic, London, 1987)

    Chapter  Google Scholar 

  25. McCaffrey, K. J. W. et al. Unlocking the spatial dimension: digital technologies and the future of geoscience fieldwork. J. Geol. Soc. Lond. 162, 927–938 (2005)

    Article  Google Scholar 

  26. Morris, A., Ferrill, D. A. & Henderson, D. B. Slip-tendency analysis and fault reactivation. Geology 24, 275–278 (1996)

    Article  ADS  Google Scholar 

  27. Petit, J.-P. & Barquins, M. Can natural faults propagate under mode II conditions? Tectonics 7, 1243–1256 (1988)

    Article  ADS  Google Scholar 

  28. Cox, S. J. D. & Scholz, C. H. On the formation and growth of faults: an experimental study. J. Struct. Geol. 10, 413–430 (1988)

    Article  ADS  Google Scholar 

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Acknowledgements

We thank L. Sun for help with benchmarking the external field solution of Eshelby, and Z. Reches for constructive reviews. Thanks also to N. Kusznir for help with conference funds and P. Meredith, N. de Paola and D. Faulkner for discussions.

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Authors and Affiliations

  1. Rock Deformation Laboratory, Department of Earth and Ocean Sciences, University of Liverpool, L69 3GP, Liverpool, UK

    David Healy

  2. e-Science Research Institute,

    Richard R. Jones

  3. Reactivation Research Group, Department of Earth Sciences, University of Durham, DH1 3LE, Durham, UK

    Robert E. Holdsworth

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  1. David Healy
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Correspondence to David Healy.

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Healy, D., Jones, R. & Holdsworth, R. Three-dimensional brittle shear fracturing by tensile crack interaction. Nature 439, 64–67 (2006). https://doi.org/10.1038/nature04346

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