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Determination of elastic parameters of the deformable solid bodies with respect to the Earth model

  • Guliyev, Hatam H. (Department of Tectonopysics and Geomechanics, Institute of Geology and Geophysics of Azerbaijan National Academy of Sciences (ANAS)) ;
  • Javanshir, Rashid J. (Azerbaijan National Academy of Sciences) ;
  • Hasanova, Gular H. (Department of Tectonopysics and Geomechanics, Institute of Geology and Geophysics of Azerbaijan National Academy of Sciences (ANAS))
  • Received : 2017.07.13
  • Accepted : 2018.02.06
  • Published : 2018.08.10

Abstract

The study of behavior and values of deformations in the geological medium makes the scientific basis of the methodology of synthesis of true values of parameters of its physico-mechanical and density properties taking into account the influence of geodynamic impacts. The segments of continuous variation of homogeneous elastic uniform deformations are determined under overall compression of the medium. The limits of these segments are defined according to the criteria of instability (on geometric form changes and on "internal" instability). Analytical formulae are obtained to calculate current and limiting (critical) values of deformations within the framework of various variants of small and large initial deformations of the non-classically linearized approach of non-linear elastodynamics. The distribution of deformation becomes non-uniform in the medium while the limiting values of deformations are achieved. The proposed analytical formulae are applicable only within homogeneous distribution of deformations. Numerical experiments are carried out for various elastic potentials. It is found that various forms of instability can precede phase transitions and destruction. The influence of these deformation phenomena should be removed while the physico-mechanical and density parameters of the deformed media are determined. In particular, it is necessary to use the formulae proposed in this paper for this purpose.

Keywords

Acknowledgement

Grant : Complex of researches of theoretical and experimental interdisciplinary problems of geomechanics

Supported by : ANAS

References

  1. Adushkin, V.V. and Vityazev, A.V. (2007), "The origin and evolution of the Earth: A modern view", Bull. Russ. Acad. Sci., 77(5), 396-402.
  2. Akbarov, S.D. (2013), Stability Loss and Buckling Delamination: Three-Dimensional Linearized Approach for Elastic and Viscoelastic Composites, Springer, Berlin, Germany.
  3. Akbarov, S.D. and Guz, A.N. (2000), Mechanics of Curved Composites, Kluwer Academic Publishers, Dordrecht, The Netherlands.
  4. Akbarov, S.D., Guliyev, H.H. and Yahnioglu, N. (2016), "Natural vibration of the three-layered solid sphere with middle layer made of FGM: Three-dimensional approach", Struct. Eng. Mech., 57(2), 239-263. https://doi.org/10.12989/sem.2016.57.2.239
  5. Akbarov, S.D., Guliyev, H.H. and Yahnioglu, N. (2017), "Threedimensional analysis of the natural vibration of the threelayered hollow sphere with middle layer made of FGM", Struct. Eng. Mech., 61(5), 563-576. https://doi.org/10.12989/sem.2017.61.5.563
  6. Altshuler, L.V., Krupnikov, K.K., Fortov, V.E. and Funtikov, A.I. (2004), "The beginning of physics of megabar pressures", Bull. Russ. Acad. Sci., 74(11), 1011-1022.
  7. Anderson, D. (2007), New Theory of the Earth, Cambridge University Press, New York, U.S.A.
  8. Anderson, O.L. (1995), Equations of State of Solids for Geophysics and Ceramic Science, Oxford University Press.
  9. Biot, M.A. (1965), Mechanics of Incremental Deformation, Willey, New York, U.S.A.
  10. Birch, F. (1952), "Elasticity and constitution of the Earth's interior", J. Geophys. Res., 57(2), 227-286. https://doi.org/10.1029/JZ057i002p00227
  11. Bullen, K.E. (1963), An Introduction to the Theory of Seismology, Cambridge University Press, Сambridge, U.K.
  12. Bullen, K.E. (1975), The Earth's Density, Chapman and Hall, London, U.K.
  13. Dziewonski, A.M. and Anderson, D.L. (1981), "Preliminary reference Earth model", Phys. Earth Planet. Inter., 25(4), 297-356. https://doi.org/10.1016/0031-9201(81)90046-7
  14. Gufeld, I.L. (2013), "The degassing at depths and structure of lithosphere and upper mantle", Elec. J. Glubinnaya neft, 1(2), 172-189.
  15. Guliyev, H.H. (2010), "A new theoretical conception concerning the tectonic processes of the Earth", New Concept. Global Tecton. Newslett., 56, 50-74.
  16. Guliyev, H.H. (2011), "Fundamental role of deformations in internal dynamics of the Earth", New Concept. Global Tecton. Newslett., 61, 33-50.
  17. Guliyev, H.H. (2013), "Deformations, corresponding to processes of consolidation, deconsolidation and phase transitions in internal structures of the Earth", Geophys. J., 35(3), 166-176.
  18. Guliyev, H.H. (2016), "Analysis of the physical parameters of the Earth's inner core within the mechanics of the deformable body", Trans. NAS Azerbaijan Issue Mech. Ser. Phys. Tech. Math. Sci., 36(7), 19-30.
  19. Guliyev, H.H. (2017), "Analysis of results of interpretation of elastic parameters of solid core of the Earth from the standpoint of current geomechanics", Geophys. J., 39(1), 79-96.
  20. Guz, A.N. (1977), Basis of the Theory of Stability of Mine Workings, Naukova Dumka, Kiev, Ukraine.
  21. Guz, A.N. (1989), Fracture Mechanics of Composite Materials under Compression, Naukova Dumka, Kiev, Ukraine.
  22. Guz, A.N. (1999), Fundamentals of the Three-dimensional Theory of Stability of Deformable Bodies, Springer, Berlin, Germany.
  23. Hofmeister, A.M. (1993), "Interatomic potentials calculated from equations of state: Limitations of finite strain to moderate K", Geophys. Res. Lett., 20(7), 635-638. https://doi.org/10.1029/93GL00388
  24. Kalinin, V.A. (2000), Properties of Geomaterials and Physics of the Earth, in The Selected Works, IPE RAS, Moscow, Russia.
  25. Knopoff, L. (1963), Solids: Equations of State of Solids at Moderately High Pressures, in High Pressure Physics and Chemistry, Academic Press, New York, U.S.A.
  26. Kuliev, G.G. (1987), "The stability of the bars under nonuniform compression by the dead and tracer loads", Proc. Acad. Sci. Azerbaijan SSR Ser. Phys. Tech. Math. Sci., (5), 43-48.
  27. Kuliev, G.G. (1988), Basis of Mathematical Theory of Stability of the Wells, Elm, Baku, Azerbaijan.
  28. Kuliev, G.G. (2000), "Determination of Poisson's ratio in the stressed media", Doklady Russ. Acad. Sci., 370(4), 534-537.
  29. Li, X. and Tao, M. (2015), "The influence of initial stress on wave propagation and dynamic elastic coefficients", Geomech. Eng., 8(3), 377-390. https://doi.org/10.12989/gae.2015.8.3.377
  30. Liu, J. and Lin, J.F. (2014), "Abnormal acoustic wave velocities in basaltic and (Fe,Al)-bearing silicate glasses at high pressures", Geophys. Res. Lett., 41(24), 8832-8839. https://doi.org/10.1002/2014GL062053
  31. Mao, Z., Lin, J.F., Jacobsen, S.D., Duffy, T.S., Chang, Y.Y., Smyth, J.R., Frost, D.J., Hauri, E.H. and Prakapenka, V.B. (2012), "Sound velocities of hydrous ringwoodite to 16 GPa and 673 K", Earth Planet. Sci. Lett., 331, 112-119.
  32. Molodenskii, S.M. and Molodenskaya, M.S. (2009), "On mechanical Q parameters of the lower mantle inferred from data on the Earth's free oscillations and nutation", Izvestiya Phys. Solid Earth, 45(9), 744-752. https://doi.org/10.1134/S1069351309090031
  33. Molodenskii, S.M. and Molodenskaya, M.S. (2015), "Attenuation of free spheroidal oscillations of the Earth after the M = 9 earthquake in Sumatra and super-deep earthquake in the Sea of Okhotsk: I. The admissible Q-factor range for the fundamental mode and overtones of the free spheroidal oscillations", Izvestiya Phys. Solid Earth, 51(6), 821-839. https://doi.org/10.1134/S1069351315060051
  34. Molodenskii, S.M. and Molodenskii, M.S. (2015), "Attenuation of free spheroidal oscillations of the Earth after the M = 9 earthquake in Sumatra and super-deep earthquake in the Sea of Okhotsk: II. Interpretation of the observed Q-factor", Izvestiya Phys. Solid Earth, 51(6), 840-858. https://doi.org/10.1134/S1069351315060063
  35. Navrotsky, A. (1994), Physics and Chemistry of Earth Materials, Cambridge University Press, Cambridge, U.K.
  36. Prodaivoda, G.T., Vyzhva, S.A. and Vershilo, I.V. (2012), Mathematical Modeling of Effective Geophysical Parameters, Publishing-polygraph center "Kiev University", Kiev, Ukraine.
  37. Ringwood, A.E. (1981), The Structure and the Petrology of the Earth's Mantle, Nedra, Moscow, Russia.
  38. Ritsema, R. (2005), Global Seismic Structure Maps, in Plates, Plumes and Paradigms, Geological Society of America, Special Paper 388, 11-18.
  39. Tateno, S., Hirose, K., Ohishi, Y. and Tatsumi, Y. (2010), "The Structure of Iron in Earth's Inner Core", Science, 330(6002), 359-361. https://doi.org/10.1126/science.1194662
  40. Trampert, J., Deschamps, F., Resovsky, J. and Yuen, D. (2004), "Probabilistic tomography maps chemical heterogeneities throughout the lower mantle", Science, 306 (5697), 853-856. https://doi.org/10.1126/science.1101996
  41. Truesdell, C. (1972), A First Course in Rational Continuum Mechanics, The Johns Hopkins University, Baltimore, Maryland, U.S.A.
  42. Van Der Hilst, R.D. and Karason, H. (1999), "Compositional heterogeneity in the bottom 1000 kilometers of the Earth's Mantle: Toward a hybrid convection model", Science, 283(5409), 1885-1888. https://doi.org/10.1126/science.283.5409.1885
  43. Webb, S.L. and Jackson, L. (1990), "Polyhedral rationalization of variation among the single crystal elastic moduli for uppermantle silicates, garnet, olivine and orthopyroxene", Am. Miner, 75, 731-738.
  44. Wei, J.G. and Yan, C.L. (2014), "Borehole stability analysis in oil and gas drilling in undrained condition", Geomech. Eng., 7(5), 553-567. https://doi.org/10.12989/gae.2014.7.5.553
  45. Zharkov, V.N. (2012), Physics of the Earth's Interior, Nauka i obrazovanie, Moscow, Russia.
  46. .
  47. .

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