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The Energetics of Cataclasis Based on Breakage Mechanics

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Mechanics, Structure and Evolution of Fault Zones

Part of the book series: Pageoph Topical Volumes ((PTV))

Abstract

We develop a constitutive model for rocks that are constituted from brittle particles, based on the theory of breakage mechanics. The model connects between the energetics and the micromechanics that drive the process of confined comminution. Given this ability, our model not only describes the entire stress-strain response of the material, but also connects this response to predicting the evolution of the grain size distribution. The latter fact enables us to quantify how the permeability reduces within cataclasite zones, in relation to aspects of grain crushing. Finally, our paper focuses on setting a framework for quantifying how the energy budget of earthquakes is expensed in relation to dissipation events in cataclasis. We specifically distinguish between the dissipation directly from the creation of new surface area, which causes further breakage dissipation from the redistribution of locked-in stored energy from surrounding particles, dissipations from friction and from the configurational reorganisation of particles.

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References

  • An, L.-J. and Sammis, C.G. (1994), Particle size distribution of cataclastic fault materials from Southern California: A 3-D study, Pure Appl. Geophys. 143(1), 203–227.

    Article  Google Scholar 

  • Aydin, A., Borja, R.I., and Eichhubl, P. (2006), Geological and mathematical framework for failure modes in granular rock, J. Struct. Geol. 28(1), 83–98.

    Article  Google Scholar 

  • Beeler, N.M., Tullis, T.E., Blanpied, M.L., and Weeks, J.D. (1996), Frictional behavior of large displacement experimental faults, J. Geophys. Res. 101(B4), 8697–8715.

    Article  Google Scholar 

  • Ben-Zion, Y. (2008), Collective behavior of earthquakes and faults: Continuum-discrete transitions, progressive evolutionary changes and different dynamic regimes, Rev. Geophys. 46, RG4006, doi: 10.1029/2008RG000260.

    Google Scholar 

  • Ben-Zion, Y. and Sammis, C.G. (2003), Characterization of fault zones, Pure Appl. Geophys. 160(3), 677–715.

    Article  Google Scholar 

  • Boria, R.I., Tamagnini, C. and Amorosi, A. (1997), Coupling plasticity and energy-conserving elasticity models for clays, J. Geotech. Geoenviron. Engin. 123(10), 948–957.

    Article  Google Scholar 

  • Brunauer, S., Emmett, P.H., and Teller, E. (1938), Adsorption of gases in multimolecular layers, J. Am. Chem. Soc. 60(2), 309–319.

    Article  Google Scholar 

  • Caine, J.S., Evans, J.P. and Forster, C.B. (1996), Fault zone architecture and permeability structure, Geology 24(11), 1025–1028.

    Article  Google Scholar 

  • Chester, J.S., Chester, F.M., and Kronenberg, A.K. (2005), Fracture surface energy of the Punchbowl fault, San Andreas system, Nature 437(7055), 133–136.

    Article  Google Scholar 

  • Cundall, P. and Strack, O. (1979), A discrete numerical model for granular assemblies, Geotechnique 29, 47–65.

    Article  Google Scholar 

  • Cuss, R.J., Rutter, E.H. and Holloway, R.F. (2003), The application of critical state soil mechanics to the mechanical behaviour of porous sandstones, Internat. J. Rock Mech. and Mining Sci. 40, 847–862.

    Article  Google Scholar 

  • Edwards, S.F. and Grinev, D.V. (2001), Transmission of stress in granular materials as a problem of statistical mechanics, Physica A 302, 162–186

    Article  Google Scholar 

  • Einav, I. (2007a), Breakage mechanics—Part I: Theory, J. Mechan. Phys. Sol. 55(6), 1274–1297.

    Article  Google Scholar 

  • Einav, I. (2007b), Breakage mechanics—Part II: Modelling granular materials, J. Mech. Phys. Sol. 55(6), 1298–1320

    Article  Google Scholar 

  • Einav, I. (2007c), Fracture propagation in brittle granular matter, Proc. Roy. Soc. A: Math., Phys. Eng. Sci. 463(2087), 3021–3035.

    Article  Google Scholar 

  • Einav, I. (2007d), Soil mechanics: breaking ground, Philosoph. Transac. Roy. Soc. A: Math., Phys. Engin. Sci. 365(1861), 2985–3002.

    Article  Google Scholar 

  • Einav, I., Vardoulakis, I., and Chan, A.H.C. (2008), Confined comminution and permeability reduction in expanding perforations, to be submitted.

    Google Scholar 

  • Einav, I. and Puzrin, A.M. (2004), Pressure-dependent elasticity and energy conservation in elastoplastic models for soils, J. Geotechn. Geoenviron. Engin. 130(1), 81–92.

    Article  Google Scholar 

  • Evans, J.P., Forster, C.B., and Goddard, J.V. (1997), Permeability of fault-related rocks, and implications for hydraulic structure of fault zones, J. Struct. Geol. 19(11), 1393–1404.

    Article  Google Scholar 

  • Griffith, A.A. (1921), The phenomena of rupture and flow in solids, Philosoph. Transact. Roy. Soc. London. Series A, Containing Papers of a Math. or Phys. Character (1896–1934) 221(1), 163–198.

    Article  Google Scholar 

  • Guo, Y. and Morgan, J.K. (2007), Fault gouge evolution and its dependence on normal stress and rock strength—Results of discrete element simulations: Gouge zone properties, J. Geophys. Res. 112(B10403), 1–17.

    Google Scholar 

  • Hamiel, Y., Lyakhovsky, V., and Agnon, A. (2004), Coupled evolution of damage and porosity in poroelastic media: theory and applications to deformation of porous rocks, Geophys. J. Internatl. 156, 701–713

    Article  Google Scholar 

  • Heilbronner, R. and Keulen, N. (2006), Grain size and grain shape analysis of fault rocks, Tectonophysics 427(1–4), 199–216.

    Article  Google Scholar 

  • Hoque, E. and Tatsuoka, F. (1998), Anisotropy in elastic deformation of granular materials, Soils Found. 38(1), 163–179.

    Google Scholar 

  • Houlsby, G.T. (1985), The use of a variable shear modulus in elastic-plastic models for clays, Comp. Geotechn. 1(1), 3–13.

    Article  Google Scholar 

  • Houlsby, G.T., Amorosi, A., and Rojas, E. (2005), Elastic moduli of soils dependent on pressure: A hyperelastic formulation, Geotechnique 55(5), 383–392.

    Google Scholar 

  • Kendall, K. (1978), The impossibility of comminuting small particles by compression, Nature 272, 710–711.

    Article  Google Scholar 

  • LoPkesti, D.C.F. and O’Neill, D.A. (1991), Laboratory investigation of small strain modulus anisotropy in sands, Proc. ISOCCTI, Clarkson University, Potsdam, 1991, pp. 213–224.

    Google Scholar 

  • Lund, M.G. and Austrheim, H. (2003), High-pressure metamorphism and deep-crustal seismicity: Evidence from contemporaneous formation of pseudotachylytes and eclogite facies coronas, Tectonophysics 372(1–2), 59–83.

    Article  Google Scholar 

  • Lyakhovsky, V., Ben-Zion, Y., and Agnon, A. (1977), Distributed damage, faulting, and friction, J. Geophys. Res. 102(B12), 27,635–27,649.

    Article  Google Scholar 

  • Mandl, G., de Jong, L.N.J., and Maltha, A. (1977), Shear zones in granular material, Rock Mech. Rock Engin. 9(2), 95–144.

    Article  Google Scholar 

  • Marone, C., Raleigh, C.B., and Scholz, C.H. (1990), Frictional behavior and constitutive modeling of simulated fault gouge, J. Geophys. Res. 95(B5), 7007–7025.

    Article  Google Scholar 

  • Marone, C., Vidale, J.E., and Ellsworth, W.L. (1995), Fault healing inferred from time-dependent variations in source properties of repeating earthquakes, Geophys. Res. Lett. 22(22), 3095–3098.

    Article  Google Scholar 

  • Matyka, M., Khalili, A., and Koza, Z. (2008), Tortuosity-porosity relation in porous media flow, Phys. Rev. E 78, 026306.

    Article  Google Scholar 

  • McGarr, A., Fletcher, J.B., and Beeler, N.M. (2004), Attempting to bridge the gap between laboratory and seismic estimates of fracture energy, Geophys. Res. Lett. 31, L14606.

    Article  Google Scholar 

  • Morrow, C., Shi, L. Q., and Byerlee, J. (1981), Permeability and strength of San Andreas fault gouge under high pressure, Geophys. Res. Lett. 8(4), 325–328.

    Article  Google Scholar 

  • Muthuswamy, M. and Tordesillas, A. (2006), How do interparticle contact friction, packing density and degree of polydispersity affect force propagation in particulate assemblies?, J. Stat. Mech.-Theory and Experiment, P09003.

    Google Scholar 

  • Okada, Y., Sassa, K., and Fukuoka, H. (2004), Excess pore pressure and grain crushing of sands by means of undrained and naturally drained ring-shear tests, Engin. Geol. 75(3–4), 325–343.

    Article  Google Scholar 

  • Olgaard, D.L. and Brace, W.F. (1983), The microstructure of gouge from a mining-induced seismic shear zone, Internatl. J. Rock Mechan. and Mining Sci. Geomechan. Abstracts 20(1), 11–19.

    Article  Google Scholar 

  • Olsen, M.P., Scholz, C.H. and Léger, A. (1998), Healing and sealing of a simulated fault gouge under hydrothermal conditions: Implications for fault healing, J. Geophys. Res. 103(B4), 7421–7430.

    Article  Google Scholar 

  • Olsson, W.A. (1999), Theoretical and experimental investigation of compaction bands in porous rock, J. Geophys. Res. 104(B4), 7219–7228.

    Article  Google Scholar 

  • Pittarello, L., Di Toro, G., Bizzarri, A., Pennacchioni, G., Hadizadeh, J. and Cocco, M. (2008), Energy partitioning during seismic slip in pseudotachylyte-bearing faults (Gole Larghe Fault, Adamello, Italy), Earth Planet. Sci. Lett. 269(1–2), 131–139.

    Article  Google Scholar 

  • Reches, Z. and Dewers, T.A. (2005), Gouge formation by dynamic pulverization during earthquake rupture, Earth Planet. Sci. Lett. 235(1–2), 361–374.

    Article  Google Scholar 

  • Renard, F., Gratier, J.-P., and Jamtveit, B. (2000), Kinetics of crack-sealing, intergranular pressure solution, and compaction around active faults, J. Struct. Geol. 22(10), 1395–1407.

    Article  Google Scholar 

  • Ricard, Y. and Bercovici, D. (2003), Two-phase damage theory and crustal rock failure: The theoretical ‘void’ limit, and the prediction of experimental data, Geophys. J. Internatil. 155, 1057–1064.

    Article  Google Scholar 

  • Rice, J.R. (1978), Thermodynamics of the quasi-static growth of Griffith cracks, J. Mechan. Phys. Sol. 26, 61–78.

    Article  Google Scholar 

  • Rockwell, T., Sisk, M., Girty, G., Dor, O., Wechsler, N., and Ben-Zion, Y. (2009), Chemical and physical characteristics of pulverized Tejon lookout Granite Adjacent to the San Andreas and Garlock faults: implications for earthquake physics, Pure Appl. Geophys., in press.

    Google Scholar 

  • Roscoe, K.H. and Schofield, A.N. (1963), Mechanical behaviour of an idealised ‘wet’ clay, European Conf. Soil Mechan. Foundation Engin. Essen, Germany: Deutsche Gesellschaft für Erd-und Grundbau, E.v., Wiesbaden, 46–54.

    Google Scholar 

  • Sammis, C.G. and Ben-Zion, Y. (2008), Mechanics of grain-size reduction in fault zones, J. Geophy. Res. 113, B02306.

    Article  Google Scholar 

  • Sammis, C.G., Osborne, R.H., Anderson, J.L., Banerdt, M., and White, P. (1986), Self-similar cataclasis in the formation of fault gouge, Pure Appl. Geophys. 124(1), 53–78.

    Article  Google Scholar 

  • Scholz, C. The Mechanics of Earthquakes and Faulting (Cambridge University Press 1990).

    Google Scholar 

  • Schultz, R.A. and Siddharthan, R. (2005), A general framework for the occurrence and faulting of deformation bands in porous granular rocks, Tectonophysics 411(1–4), 1–18.

    Article  Google Scholar 

  • Segall, P. and Rice, J.R. (1995), Dilatancy, compaction, and slip instability of a fluid-infiltrated fault, J. Geophys. Res. 100(B11), 22,155–122,171.

    Article  Google Scholar 

  • Shah, K.R. (1997), An elasto-plastic constitutive model for brittle-ductile transition in porous rocks, Internatl. J. Rock Mechan. Mining Sci. 34(3–4), 283.e281–283.e213.

    Google Scholar 

  • Sheldon, H.A., Barnicoat, A.C., and Ord, A., (2006), Numerical modelling of faulting and fluid flow in porous rocks: An approach based on critical state soil mechanics, J. Struct. Geol. 28(8), 1468–1482.

    Article  Google Scholar 

  • Shi, Z., Ben-Zion, Y. and Needleman, A. (2008), Properties of dynamic rupture and energy partition in a solid with a frictional interface, J. Mechan. Phys. Sol. 56, 5–24.

    Article  Google Scholar 

  • Sleep, N.H. and Blanpied, M.L. (1992), Creep, compaction and the weak rheology of major faults, Nature 359(6397), 687–692.

    Article  Google Scholar 

  • Steacy, S.J. and Sammis, C.G. (1991), An automaton for fractal patterns of fragmentation, Nature 353(6341), 250–252.

    Article  Google Scholar 

  • Templeton, E.L. and Rice, J.R., (2008), Off-fault plasticity and earthquake rupture dynamics, 1. Dry materials or neglect of fluid pressure changes, J. Geophys. Res. B (Solid Earth), 113, B09306, doi:10.1029/ 2007JB005529.

    Article  Google Scholar 

  • Tenthorey, E., Cox, S.F., and Todd, H.F. (2003), Evolution of strength recovery and permeability during fluidrock reaction in experimental fault zones, Earth Planet. Sci. Lett. 206(1–2), 161–172.

    Article  Google Scholar 

  • Wilson, B., Dewers, T., Reches, Z.E. and Brune, J. (2005), Particle size and energetics of gouge from earthquake rupture zones, Nature 434(7034), 749–752.

    Article  Google Scholar 

  • Wong, T., David, C., and Zhu, W. (1997), The transition from brittle faulting to cataclastic flow in porous sandstones: Mechanical deformation, J. Geophys. Res. 102(B2), 3009–3025.

    Article  Google Scholar 

  • Xia, K. (2006), Scaling of fracture energies: The rationalization of different laboratory measurements, Geophys. Res. Lett. 33, L01305.

    Article  Google Scholar 

  • Zhang, S. and Tullis, T.E. (1998), The effect of fault slip on permeability and permeability anisotropy in quartz gouge, Tectonophysics 295(1–2), 41–52.

    Google Scholar 

  • Zhu, W. and Wong, T. (1997), The transition from brittle faulting to cataclastic flow: Permeability evolution, J. Geophys. Res. 102(B2), 3027–3041.

    Article  Google Scholar 

  • Ziegler, H. An introduction to thermomechanics, Second Ed. (North Holland, Amsterdam 1983).

    Google Scholar 

  • Zytynski, M., Randolph, M.F., Nova, R. and Wroth, C.P. (1978), On modelling the unloading-reloading behaviour of soils, Internatl. J. Numer. Analyt. Methods in Geomechan. 2(1), 87–93.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Civil Engineering J05, The University of Sydney, Sydney, NSW, 2006, Australia

    Giang D. Nguyen & Itai Einav

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  1. Giang D. Nguyen
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  2. Itai Einav
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  1. Department Earth Sciences, University of Southern California College of Letters, Arts & Sciences, Los Angeles, CA, 900089-0740, USA

    Yehuda Ben-Zion  & Charles Sammis  & 

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Nguyen, G.D., Einav, I. (2009). The Energetics of Cataclasis Based on Breakage Mechanics. In: Ben-Zion, Y., Sammis, C. (eds) Mechanics, Structure and Evolution of Fault Zones. Pageoph Topical Volumes. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0138-2_8

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