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.
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B. D. Annin and N. I. Ostrosablin, “Anisotropy of Elastic Properties ofMaterials,” J.Appl.Mech. Tech. Phys. 49(6), 998–1014 (2008).
S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Solid (Nauka, Moscow, 1977) [in Russian].
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).
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).
F. Gassmann, “Introduction to Seismic Travel Time Methods in Anisotropic Media,” Pure and Applied Geophysics 58, 63–113 (1964).
S. V. Gol’din, Seismic Waves in Anisotropic Media (Sibirsk. Otdel., Russian Acad. of Sci., Novosibirsk, 2008) [in Russian].
G. E. Backus, “Long-Wave Elastic Anisotropy Produced by Horizontal Layering,” J. Geophys. Res. 67(11), 4427–4440 (1962).
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].
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].
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).
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).
A. E. Green and W. Zerna, Theoretical Elasticity (Oxford, 1968).
B. D. Annin, “Models of Elastoplastic Deformation of Transversely Isotropic Materials,” Sibirsk. Zh. Indust. Mat. 2(2), 3–7 (1999).
S. K. Godunov, Equations of Mathematical Physics (Nauka, Moscow, 1978) [in Russian].
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].
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Original Russian Text © B.D. Annin, 2009, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2009, Vol. XII, No. 3, pp. 5–14.
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Annin, B.D. A transversely isotropic elastic model of geomaterials. J. Appl. Ind. Math. 4, 299–308 (2010). https://doi.org/10.1134/S1990478910030014
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DOI: https://doi.org/10.1134/S1990478910030014