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  • Print publication year: 2011
  • Online publication date: June 2012

10 - Toughness and fracture mechanics

Summary

Aims

Rock strengths, such as tensile and shear strength, are one measure of its resistance to brittle failure. Another measure of rock resistance to brittle failure is the energy absorbed by the rock during fracture propagation. The critical energy absorbed is referred to as material toughness. A third measure of resistance to fracture is the stress intensity at the fracture tip that must be reached if the fracture is to propagate. The critical stress intensity is referred to as fracture toughness. Toughness is a basic concept in fracture mechanics that provides a physical framework for understanding many processes associated with rock fractures. The main aims of this chapter are to:

Explain the concept of material toughness.

Explain the concept of fracture toughness.

Show how material and fracture toughness are related.

Relate the concept of toughness to the initiation of a fracture.

Introduce the concepts of process zone, fault core, and damage zone.

Show how to calculate the toughness associated with extension fractures.

Show how to calculate the toughness associated with faults.

Toughness

The toughness of a rock is a measure of its resistance to fracture. In other words, for a tough rock, large amounts of energy are needed to cause failure; much energy is absorbed by a tough rock as it fractures. This concept and the related concept of fracture toughness derive from materials science (Hull and Clyne, 1996; Chawla, 1998; Kobayashi, 2004) and fracture mechanics (Atkins and Mai, 1985; Broberg, 1999; Anderson, 2005).

References and suggested reading
Anderson, T. L., 2005. Fracture Mechanics: Fundamentals and Applications, 3rd edn. London: Taylor & Francis.
Ashby, M. F. and Jones, D. R. H., 2005. Engineering Materials 1, 3rd edn. Amsterdam: Elsevier.
Atkins, A. G. and Mai, Y. W., 1985. Elastic and Plastic Fracture. Chichester: Horwood.
Atkinson, B. K. (ed.), 1987. Fracture Mechanics of Rock. London: Academic Press.
Atkinson, B. K. and Meredith, P. G., 1987. Experimental fracture mechanics data for rocks andminerals. In: Atkinson, B. K. (ed.), Fracture Mechanics of Rock. London: Academic Press, pp. 477–525.
Balint, D. S. and Hutchinson, J. W., 2001. Mode II edge delamination of compressed films. ASME Journal of Applied Mechanics, 68, 725–730.
Balme, M. R., Rocchi, V., Jones, C., Sammonds, P. R., Meredith, P. G., and Boon, S., 2004. Fracture toughness measurements on igneous rocks using a high-pressure, high-temperature rock fracture mechanics cell. Journal of Volcanology and Geothermal Research, 132, 159–172.
Broberg, K. B., 1999. Cracks and Fracture. New York: Academic Press.
Carmichael, R. S., 1989. Practical Handbook of Physical Properties of Rocks and Minerals. Boca Raton, Boston, MA: CRC Press.
Chawla, K. K., 1998. Composite Materials: Science and Engineering, 2nd edn. Berlin: Springer-Verlag.
Dahlberg, T. and Ekberg, A., 2002. Failure, Fracture, Fatigue. Studentlitteratur, Lund, Sweden.
Delaney, P. and Pollard, D. D., 1981. Deformation of host rocks and flow of magma during growth of minette dikes and breccia-bearing intrusions near Ship Rock, New Mexico. US Geological Survey Professional Paper, 1202.
Fourney, W. L., 1983. Fracture control blasting. In: Rossmanith, H. P. (ed.), Rock Fracture Mechanics. New York: Springer-Verlag, pp. 301–319.
Geshi, N., Kusumoto, S., and Gudmundsson, A., 2010. The geometric difference between non-feeders and feeder dikes. Geology, 38, 195–198.
Griffith, A. A., 1920. The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London, A221, 163–198.
Griffith, A. A., 1924. Theory of rupture: In: Biezeno, C. B. and Burgers, J. M. (eds.), Proceedings of the First International Congress on Applied Mechanics. Delft: Waltman, pp. 55–63.
Gudmundsson, A., 1990. Emplacement of dikes, sills, and magma chambers at divergent plate boundaries. Tectonophysics, 176, 257–275.
Gudmundsson, A., 2004. Effects of Young's modulus on fault displacement. Comptes Rendus Geoscience, 336, 85–92.
Gudmundsson, A., 2009. Toughness and failure of volcanic edifices. Tectonophysics, 471, 27–35.
Gudmundsson, A., 2010. Deflection of dykes into sills and magma-chamber formation. Tectonophysics (on line October 2009).
Gudmundsson, A., Simmenes, T. H., Larsen, B., and Philipp, S. L., 2009. Effects of internal structure and local stresses on fracture propagation, deflection, and arrest in fault zones. Journal of Structural Geology, doi:10.1016/j.jsg.2009.08.013.
Hull, D. and Clyne, T. W., 1996. An Introduction to Composite Materials, 2nd edn. Cambridge: Cambridge University Press.
Jin, Z. H. and Johnson, S. E., 2008. Magma-driven multiple dike propagation and fracture toughness of crustal rocks. Journal of Geophysics Research, 113, B03206.
Janssen, M., Zuidema, J., and Wanhill, R., 2004. Fracture Mechanics, 2nd edn. Abingdon, UK: Spon Press.
Kobayashi, T., 2004. Strength and Toughness of Materials. Berlin: Springer-Verlag.
Larsen, B., Grunnaleite, I., and Gudmundsson, A., 2009. How fracture systems affect permeability development in shallow-water carbonate rocks: an example from the Gargano Peninsula, Italy. Journal of Structural Geology, doi:10.1016/jsg.2009.05.009
Li, V. C., 1987. Mechanics of shear rupture applied to earthquake zones. In: Atkinson, B. K. (ed.), Fracture Mechanics of Rock. London: Academic Press, pp. 351–428.
Li, H. X. and Xiao, X. R., 1995. An approach on mode-I fracture toughness anisotropy for materials with layered microstructures. Engineering and Fracture Mechanics, 52, 671–683.
Nasseri, M. H. B. and Mohanty, B., 2008. Fracture toughness anisotropy in granitic rocks. International Journal of Rock Mechanics and Mining Science, 45, 167–193.
Nasseri, M. H. B., Mohanty, B., and Young, R. P., 2006. Fracture toughness measurements and acoustic activity in brittle rocks. Pure and Applied Geophysics, 163, 917–945.
Newhall, C. G. and Dzurisin, D., 1988. Historical unrest of large calderas of the world. US Geological Survey Bulletin, 1855.
Oehler, J. F., Vries, B. V. W., and Labazuy, P., 2005. Landslides and spreading of oceanic hot-spot and arc basaltic edifices on low strength layers (LSLs): an analogue modelling approach. Journal of Volcanology and Geothermal Research, 144, 169–189.
Parker, A. P., 1981. The Mechanics of Fracture and Fatigue. London: Spon.
Paterson, M. S. and Wong, T. W., 2005. Experimental Rock Deformation – the Brittle Field, 2nd edn. Berlin: Springer-Verlag.
Rice, J. R., 2006. Heating and weakening of faults during earthquake slip. Journal of Geophysical Research, 111, B05311.
Rice, J. R. and Cocco, M., 2007. Seismic fault rheology and earthquake dynamics. In: Handy, M. R., Hirth, G., and Horius, N. (eds.), Tectonic Faults: Agents of Chance on a Dynamic Earth. Cambridge, MA: The MIT Press, pp. 99–137.
Rivalta, E. and Dahm, T., 2006. Acceleration of buoyancy-driven fractures and magmatic dikes beneath the free surface. Geophysical Journal International, 166, 1424–1439.
Rossmanith, H. P. (ed.), 1983. Rock Fracture Mechanics. New York: Springer-Verlag, pp. 301–319.
Rossmanith, H. P. (ed.), 1997. Fracture Research in Retrospect: An Anniversary Volume in Honour of George R. Irwin's 90th Birthday. Rotterdam: Balkema.
Rubin, A. M. and Pollard, D. D., 1987. Origins of blade-like dikes in volcanic rift zones. US Geological Survey Professional Paper, 1350, pp. 1449–1470.
Sanford, R. J., 2003. Principles of Fracture Mechanics. Upper Saddle River, NJ: Prentice-Hall.
Schultz, R. A., 1995. Limits on strength and deformation properties of jointed basaltic rock masses. Rock Mechancis and Rock Engineering, 28, 1–15.
Shah, S. P., Swartz, S. E., and Ouyang, C., 1995. Fracture Mechanics of Concrete: Applications of Fracture Mechanics to Concrete, Rock, and Other Quasi-Brittle Materials. New York: Wiley.
Shulka, A. (ed.), 2006. Dynamic Fracture Mechanics. London: World Scientific.
Sneddon, I. N. and Lowengrub, M., 1969. Crack Problems in the Classical Theory of Elasticity. New York: Wiley.
Tada, H., Paris, P. C., and Irwin, G. R., 2000. The Stress Analysis of Cracks Handbook, 3rd edn. New York: American Society of Mechanical Engineers.
Tibaldi, A., Bistacchi, A., Pasquare, F. A., and Vezzoli, L., 2006. Extensional tectonics and volcano lateral collapses: insights from Ollague volcano (Chile-Bolivia) and analogue modelling. Terra Nova 18, 282–289.
Tvergaard, V. and Hutchinson, J. W., 2008. Mode III effects on interface delamination. Journal of the Mechanics and Physics of Solids, 65, 215–229.
Wooller, L., Vries, B. V. W, Murray, J. B., Rymer, H., and Meyer, S., 2004. Volcano spreading controlled by dipping substrata. Geology, 32, 573–576.