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Deformation and Strength of Transversely Isotropic Rocks

  • Yang Zhao
  • Ronaldo I. BorjaEmail author
Conference paper
Part of the Springer Series in Geomechanics and Geoengineering book series (SSGG)

Abstract

Transverse isotropy is characterized by a plane of isotropy and an axis of anisotropy. For rocks, the plane of isotropy is associated with the bedding plane, whereas the axis of anisotropy is the normal to the bedding plane. Transversely isotropic rocks are known to exhibit strength that depend on the orientation of the bedding plane relative to the direction of load. In this work, we present a constitutive framework for predicting the deformation and strength of transversely isotropic rocks. The model is based on anisotropic critical state plasticity with thermal softening. We conduct numerical simulations of boundary value problems to demonstrate the impact of bedding plane orientation on the deformation and strength of a transversely isotropic rock.

Notes

Acknowledgments

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Geosciences Research Program, under Award Number DE-FG02-03ER15454. Support for materials and additional student hours were provided by the National Science Foundation under Award Number CMMI-1462231.

References

  1. 1.
    Bennett, K.C., Borja, R.I.: Hyper-elastoplastic/damage modeling of rock with application to porous limestone. Int. J. Solids Struct. 143, 218–231 (2018).  https://doi.org/10.1016/j.ijsolstr.2018.03.011CrossRefGoogle Scholar
  2. 2.
    Bennett, K.C., Regueiro, R.A., Borja, R.I.: Finite strain elastoplasticity considering the Eshelby stress for materials undergoing plastic volume change. Int. J. Plast. 77, 214–245 (2016)CrossRefGoogle Scholar
  3. 3.
    Bennett, K.C., Berla, L.A., Nix, W.D., Borja, R.I.: Instrumented nanoindentation and 3D mechanistic modeling of a shale at multiple scales. Acta Geotech. 10, 1–14 (2015)CrossRefGoogle Scholar
  4. 4.
    Borja, R.I., Rahmani, H.: Computational aspects of elasto-plastic deformation in polycrystalline solids soils. J. Appl. Mech. 79(3), 031024 (2012)CrossRefGoogle Scholar
  5. 5.
    Borja, R.I.: Plasticity Modeling & Computation. Springer, Heidelberg (2013)zbMATHGoogle Scholar
  6. 6.
    Borja, R.I., Rahmani, H.: Discrete micromechanics of elastoplastic crystals in the finite deformation range. Comput. Methods Appl. Mech. Eng. 275, 234–263 (2014)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Borja, R.I., Aydin, A.: Computational modeling of deformation bands in granular media, I: geological and mathematical framework. Comput. Methods Appl. Mech. Eng. 193(27–29), 2667–2698 (2004)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Borja, R.I.: Computational modeling of deformation bands in granular media, II: numerical simulations. Comput. Methods Appl. Mech. Eng. 193(27–29), 2699–2718 (2004)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Borja, R.I.: Bifurcation of elastoplastic solids to shear band mode at finite strain. Comput. Methods Appl. Mech. Eng. 191(146), 5287–5314 (2002)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Laloui, L., Cekerevac, C.: Thermo-plasticity of clays: an isotropic yield mechanism. Comput. Geotech. 30(8), 649–660 (2003)CrossRefGoogle Scholar
  11. 11.
    Niandou, H., Shao, J.F., Henry, J.P., Fourmaintraux, D.: Laboratory investigation of the mechanical behaviour of Tournemire shale. Int. J. Rock Mech. Min. Sci. 34(1), 3–16 (1997)CrossRefGoogle Scholar
  12. 12.
    Semnani, S.J., Borja, R.I.: Quantifying the heterogeneity of shale through statistical combination of imaging across scales. Acta Geotech. 12, 1193–1205 (2017)CrossRefGoogle Scholar
  13. 13.
    Semnani, S.J., White, J.A., Borja, R.I.: Thermo-plasticity and strain localization in transversely isotropic materials based on anisotropic critical state plasticity. Int. J. Num. Anal. Methods Geomech. 40, 2423–2449 (2016)CrossRefGoogle Scholar
  14. 14.
    Tien, Y.M., Kuo, M.C.: A failure criterion for transversely isotropic rocks. Int. J. Rock Mech. Min. Sci. 38(3), 399–412 (2001)CrossRefGoogle Scholar
  15. 15.
    Tien, Y.M., Kuo, M.C., Juang, C.H.: An experimental investigation of the failure mechanism of simulated transversely isotropic rocks. Int. J. Rock Mech. Min. Sci. 43(8), 1163–1181 (2006)CrossRefGoogle Scholar
  16. 16.
    Tjioe, M., Borja, R.I.: On the pore-scale mechanisms leading to brittle and ductile deformation behavior of crystalline rocks. Int. J. Num. Anal. Methods Geomech. 39(11), 1165–1187 (2015)CrossRefGoogle Scholar
  17. 17.
    Tjioe, M., Borja, R.I.: Pore-scale modeling of deformation and shear band bifurcation in porous crystalline rocks. Int. J. Num. Methods Eng. 108(3), 183–212 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Zhao, Y., Semnani, S.J., Yin, Q., Borja, R.I.: On the strength of transversely isotropic rocks. Int. J. Num. Anal. Methods Geomech. 42, 1917–1934 (2018).  https://doi.org/10.1002/nag.2809CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Stanford UniversityStanfordUSA

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