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  • 1
    Publication Date: 2013-02-06
    Description: Rocks deformed at low confining pressure are brittle, meaning that after peak stress the strength decreases to a residual value determined by frictional sliding. The difference between the peak and residual value is the stress drop. At high confining pressure, however, no stress drop occurs. The transition pressure at which no loss in strength occurs is a possible definition of the brittle-ductile transition. Here we show, using numerical rock deformation, how this type of brittle-ductile transition emerges from a simple model in which rock is idealized as an assemblage of cemented spherical unbreakable grains. Three-dimensional failure and residual strength envelopes determined for this model material illustrate that the brittle-ductile transition is a smoothly-varying, mean stress dependent function in principal stress space. Neither the Mohr-Coulomb nor the Drucker-Prager failure criterion, which are the most commonly used empirical laws in rock and soil mechanics, respectively, adequately describe the dependence of peak strength and the brittle-ductile transition on the intermediate stress (or Lode angle). A semi-quantitative comparison between the modeled peak strength envelope with a selection of existing polyaxial rock data shows that the emergent intermediate stress dependence of strength in bonded particle models is comparable to that observed in rock. Deformation of particle models in which bond shear failure is inhibited illustrate that the non-linear pressure dependence of strength (concave failure envelopes) is, at high mean stress, the result of microscopic shear failure, a result consistent with earlier two-dimensional numerical multiple-crack simulations.
    Print ISSN: 0148-0227
    Topics: Geosciences , Physics
    Published by Wiley on behalf of American Geophysical Union (AGU).
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  • 2
    Publication Date: 2013-01-25
    Description: Rocks deformed at low confining pressure are brittle, meaning that after peak stress the strength decreases to a residual value determined by frictional sliding. The difference between the peak and residual value is the stress drop. At high confining pressure, however, no stress drop occurs. The transition pressure at which no loss in strength occurs is a possible definition of the brittle-ductile transition. Here we show, using numerical rock deformation, how this type of brittle-ductile transition emerges from a simple model in which rock is idealized as an assemblage of cemented spherical unbreakable grains. Three-dimensional failure and residual strength envelopes determined for this model material illustrate that the brittle-ductile transition is a smoothly-varying, mean stress dependent function in principal stress space. Neither the Mohr-Coulomb nor the Drucker-Prager failure criterion, which are the most commonly used empirical laws in rock and soil mechanics, respectively, adequately describe the dependence of peak strength and the brittle-ductile transition on the intermediate stress (or Lode angle). A semi-quantitative comparison between the modeled peak strength envelope with a selection of existing polyaxial rock data shows that the emergent intermediate stress dependence of strength in bonded particle models is comparable to that observed in rock. Deformation of particle models in which bond shear failure is inhibited illustrate that the non-linear pressure dependence of strength (concave failure envelopes) is, at high mean stress, the result of microscopic shear failure, a result consistent with earlier two-dimensional numerical multiple-crack simulations.
    Print ISSN: 0148-0227
    Topics: Geosciences , Physics
    Published by Wiley on behalf of American Geophysical Union (AGU).
    Location Call Number Expected Availability
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  • 3
    Publication Date: 2019
    Description: Abstract Opening‐mode fractures, such as joints, veins and dykes, frequently exhibit power‐law aperture‐to‐length scaling, with scaling exponents typically ranging from 0.5 to 2. However, published high quality outcrop data and continuum based numerical models indicate that fracture aperture‐to‐length scaling may be non‐universal, with scaling being superlinear for short fractures and sublinear for long fractures. Here we revisit these published results by means of a particle‐based lattice solid model, which is validated using predictions from linear elasticity and linear elastic fracture mechanics. The triangular lattice model comprised of breakable elastic beams, with strengths drawn from a Weibull distribution, is used to investigate the fracture aperture‐to‐length scaling that emerges in a plate subjected to extension. The modeled fracture system evolution is characterized by two stages which are separated by the strain at which peak‐stress occurs. During the pre‐peak‐stress stage aperture‐to‐length scaling is universal with a power‐law exponent of about one. Shortly after the material has attained its maximum load bearing capacity, which coincides with the formation of a multiple‐segment fracture zone, aperture‐to‐length scaling becomes non‐universal, with power‐law exponents being consistent with earlier studies. The results presented here confirm that deviation from universal scaling laws are a consequence of fracture interaction. More specifically, the onset of non‐universal aperture‐to‐length scaling coincides with the formation of a multiple‐segment fracture zone.
    Print ISSN: 2169-9313
    Electronic ISSN: 2169-9356
    Topics: Geosciences , Physics
    Published by Wiley on behalf of American Geophysical Union (AGU).
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