Skip to main content
Log in

A transversely isotropic elastic model of geomaterials

  • Published:
Journal of Applied and Industrial Mathematics Aims and scope Submit manuscript

Abstract

Under consideration is the choice of parameters of a transversely isotropic elastic model for describing the linear deformation of geomaterials. We also discuss some analytical and numerical methods of solving the corresponding dynamic equations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. B. D. Annin and N. I. Ostrosablin, “Anisotropy of Elastic Properties ofMaterials,” J.Appl.Mech. Tech. Phys. 49(6), 998–1014 (2008).

    Article  MathSciNet  Google Scholar 

  2. S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Solid (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  3. S. A. Batugin and N. K. Nirenburg, “Approximate Dependence Between the Elastic Constants of Rocks and Anisotropy Parameters,” Fiz.-Tekh. Probl. Razrab. Polezn. Iskop. 7(1), 7–12 (1972).

    Google Scholar 

  4. D.M. Klimov, V. I. Karev, Yu. F. Kovalenko, and K. B. Ustinov, “Mathematical and Physical Modeling of Stability of Inclined and Horizontal Wells in Anisotropic Media,” Preprint No. 879 (Inst. Probl. in Mech., Russian Academy of Sciences, Moscow, 2008).

    Google Scholar 

  5. F. Gassmann, “Introduction to Seismic Travel Time Methods in Anisotropic Media,” Pure and Applied Geophysics 58, 63–113 (1964).

    Article  Google Scholar 

  6. S. V. Gol’din, Seismic Waves in Anisotropic Media (Sibirsk. Otdel., Russian Acad. of Sci., Novosibirsk, 2008) [in Russian].

    Google Scholar 

  7. G. E. Backus, “Long-Wave Elastic Anisotropy Produced by Horizontal Layering,” J. Geophys. Res. 67(11), 4427–4440 (1962).

    Article  Google Scholar 

  8. L. A. Molotkov, Wave Propagation in Porous and Fissured Media on the Basis of the Effective Biot Model and Layered Media Model (Nauka, St. Petersburg, 2001) [in Russian].

    Google Scholar 

  9. A. A. Baryakh, V. A. Asanov, and I. L. Pankov, Physical and Mechanical Properties of Salt Rocks of the Verkhnekamsk Potassium Deposit (Perm State Technical University, Perm, 2008) [in Russian].

    Google Scholar 

  10. R. Burridge, P. Chadwick, and A. N. Norris, “Fundamental Elastodynamic Solution for Anisotropic Media with Ellipsoidal Slowness Surface,” Proc. Roy. Soc. London, Ser. A, 440(1910), 655–681 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  11. N. I. Ostrosablin, “General Solutions and Reduction of a System of Equations of the Linear Theory of Elasticity to Diagonal Form,” J. Appl.Mech. Tech. Phys. 34(5), 700–710 (1993).

    Article  MathSciNet  Google Scholar 

  12. A. E. Green and W. Zerna, Theoretical Elasticity (Oxford, 1968).

  13. B. D. Annin, “Models of Elastoplastic Deformation of Transversely Isotropic Materials,” Sibirsk. Zh. Indust. Mat. 2(2), 3–7 (1999).

    MATH  Google Scholar 

  14. S. K. Godunov, Equations of Mathematical Physics (Nauka, Moscow, 1978) [in Russian].

    MATH  Google Scholar 

  15. A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Issues of the Numerical Solution of Hyperbolic Systems of Equations (Fizmatlit, Moscow, 2001) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. D. Annin.

Additional information

Original Russian Text © B.D. Annin, 2009, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2009, Vol. XII, No. 3, pp. 5–14.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Annin, B.D. A transversely isotropic elastic model of geomaterials. J. Appl. Ind. Math. 4, 299–308 (2010). https://doi.org/10.1134/S1990478910030014

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1990478910030014

Key words

Navigation