Abstract
The paper proposes a non-Euclidean approach based on physical mesomechanics and a scale classification for modeling the hierarchical block structure of the Erath’s subsurface as a defects-containing continuum whose main element is an opening mode crack initiated by shear under multiaxial compression. It is shown that such shear-induced opening mode fracture in the subsurface block structure results in incompatibility between its elements, which favors the non-Euclidean description of the block structure on different scales. The efficiency of the approach is demonstrated on the example of mesostructures of the first two scales classified.
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31 August 2021
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REFERENCES
Panin, V.E., Grinyaev, Yu.V., Danilov, V.I., et al., Structural Levels of Plastic Deformation and Fracture, Novosibirsk: Nauka, 1990.
Panin, V.E., Grinyaev, Yu.V., and Egorushkin, V.E., Foundations of Physical Mesomechanics of Structurally Inhomogeneous Media, Mech. Solids, 2010, vol. 45, pp. 501–118.
Goldin, S.V., Macro- and Mesostructures of the Seismic Focal Zone, Phys. Mesomech., 2005, vol. 8, no. 1–2, pp. 5–14.
Makarov, P.V., Smolin, I.Yu., Stefanov, Yu.P., et al., Nonlinear Mechanics of Geomaterials and Geomedia, Zuev, L.B., Ed., Novosibirsk: Geo, 2007.
Guzev, M.A. and Makarov, V.V., Deformation and Fracture of Highly Compressed Rocks Around Mine Workings, Vladivostok: Dalnauka, 2007.
Kondo, K., On the Geometrical and Physical Foundations of the Theory of Yielding, Proc. 2nd Japan. Nat. Congress Appl. Mech., Tokyo, 1953, pp. 41–47.
Bilby, B.A., Bullough, R., and Smith, E., Continuous Distributions of Dislocations: A New Application of the Methods of Non-Riemannian Geometry, Proc. Roy. Soc. A, 1955, vol. 231, pp. 263–273.
Stojanovic, R., Equilibrium Conditions for Internal Stresses in Non-Euclidian Continua and Stress Space, Int. J. Eng. Sci., 1963, vol. 1, pp. 323–327. https://doi.org/10.1016/0020-7225(63)90010-7
Minagawa, S., On the Stress Functions in Elastodynamics, Acta Mech., 1976, vol. 24, no. 3, pp. 209–217. https://doi.org/10.1007/BF01190371
Kröner, E., Incompatibility, Defects, and Stress Functions in the Mechanics of Generalized Continua, Int. J. Solids Struct., 1985, vol. 21, no. 7, pp. 747–756. https://doi.org/10.1016/0020-7683(85)90077-0
Myasnikov, V.P. and Guzev, M.A., Thermo-Mechanical Model of Elastic-Plastic Materials with Defect Structures, Theor. Appl. Fract. Mech., 2000, vol. 33, no. 3, pp. 165–171. https://doi.org/10.1016/S0167-8442(00)00011-2
Preston, S. and Elżanowski, M., Material Uniformity and the Concept of the Stress Space, in Continuous Media with Microstructure, Albers, B., Ed., Berlin: Springer, 2010, pp. 91–101. https://doi.org/10.1007/978-3-642-11445-8_9
Yavari, A., Goriely, A., and Elżanowski, M., Nonlinear Dislocation Mechanics, Arch. Ration. Mech. Analysis, 2012, vol. 205, no. 1, pp. 59–118. https://doi.org/10.1007/s00205-012-0500-0
Godunov, S.K. and Romenskii, E.I., Elements of Continuum Mechanics and Conservation Laws, New York: Kluwer Academic/Plenum Publishers, 2003. https://doi.org/10.1007/978-1-4757-5117-8
Chernyshev, G.N., Popov, A.L., Kozintsev, V.M., and Ponomarev, I.I., Residual Stresses in Deformed Solids, Moscow: Nauka, 1996.
Withers, P.J., Residual Stress and Its Role in Failure, Rep. Prog. Phys., 2007, vol. 70, no. 12, pp. 2211–2264. https://doi.org/10.1088/0034-4885/70/12/r04
Burgers, J.M., Physics—Some Considerations on the Fields of Stress Connected with Dislocations in a Regular Crystal Lattice, in Selected Papers of J.M. Burgers, Nieuwstadt, F.T.M. and Steketee, J.A., Eds., Dordrecht: Springer, 1995, pp. 335–389. https://doi.org/10.1007/978-94-011-0195-0_11
Crosby, W.O., On the Classification and Origin of Joint Structures, Proc. Boston Society Natural History, 1882–1883, vol. 22, pp. 72–85, Boston: Printed for the Society, 1884.
King, W., Report on the Superinduced Divisional Structure of Rocks, Called Jointing, and Its Relation to Slaty Cleavage, Trans. Roy. Irish Acad., 1875, vol. 25, pp. 605–662.
Sadovsky M. A. Natural Lumpiness of Rocks, Dokl. AN SSSR, 1979, vol. 274, no. 4.
Rock Mechanics, Müller, L., Ed., Wien: Springer, 1982.
Oparin, V.N. and Tanaino, A.S., Conical Ranking of Sizes of Structural Units in Rocks Classifications, J. Min. Sci., pp. 551–562. https://doi.org/10.1007/s10913-009-0069-7
Goldin, S.V., Lithosphere Destruction and Physical Nesomechanics, Phys. Mesomech., 2002, vol. 5, no. 5–6, pp. 5–22.
Odintsev, V.N., Rupture of Rocks, Moscow: IPKON RAS, 1996.
Kochanov, A.N., Microcracks in a Solid for Example Rocks, Gorny Inform. Analit. Byul., 2015, no. 7, pp. 221–225.
Sedov, L.I., Similarity and Dimensional Methods in Mechanics, Moscow: Nauka, 1977.
Chernyshev, S.N., Rock Fractures, Moscow: Nauka, 1983.
Makarov, V.V., Guzev, M.A., Odintsev, V.N., and Ksendzenko, L.S., Periodical Zonal Character of Damage Near the Openings in Highly-Stressed Rock Massif Conditions, J. Rock Mech. Geotech. Eng., 2016, vol. 8, no. 2, pp. 164–169. https://doi.org/10.1016/j.jrmge.2015.09.010
Lushpei, V.P., Makarov, V.V., and Laptev, A.S., Tectonophysical Stress Estimation for the Natalkinsky deposit and Methods of Rock Outcrop Stability Enhancement, Kolyma, 1982, nos. 3–4, pp. 18–21.
Sadovsky, M.A., Bolkhovitinov, L.G., and Pisarenko, V.F., Discreteness of Rocks, Izv. Akad. Nauk SSSR. Fiz. Zemli, 1982, vol. 12, pp. 3–18.
Sadovsky M.A., Bolkhovitinov, L.G., and Pisarenko, V.F., Deformation of Geophysical Medium and Seismic Process, Moscow: Nauka, 1987.
Nikolaevsky, V.N., Mechanics of Porous and Fractured Media, Moscow: Nedra, 1984.
Guzev, M.A., Odintsev, V.N., and Makarov, V.V., Principals of Geomechanics of Highly Stressed Rock and Rock Massifs, Tunnel. Underground Space Technol., 2018, vol. 81, pp. 506–511.
Guzev, M.A., Non-Euclidean Models of Elastoplastic Materials with Structure Defects, Saarbruken: Lambert Academic Publishing, 2010.
Myasnikov, V.P. and Guzev, M.A., Geometric Model of Internal Self-Balanced Stresses in Solids, Dokl. Phys., 2001, vol. 46, no. 10, pp. 740–741. https://doi.org/10.1134/1.1415593
Makarov, V.V., Guzev, M.A., and Golosov, A.M., Multichannel Method of Reliable Precursors of Failure Define, in Proc. 14th Int. Congress on Rock Mech. and Rock Eng., Rock Mech. Natural Res. Infr. Dev., Foz Do Igvassu, Brazil, 13–18 September, 2019, CRC Press, 2020, pp. 1875–1882.
Guzev, M.A. and Makarov, V.V., Principles of the Non-Euclidian Model Application to the Problem of Dissipative Mesocracking Structures of Highly Compressed Rock and Massifs Modelling, in E3S Web of Conferences, EDP Sciences, 2018, vol. 56, p. 02001. https://doi.org/10.1051/e3sconf/20185602001
Myasnikov, V.P., Guzev, M.A., and Makarov, V.V., Periodic Deformation of Fractured Rocks, in Proc. XI Russian Conf. on Rock Mechanics, St. Petersburg, Sept. 9–11, 1997, St. Petersburg: SPbGASU, 1997, pp. 333–337.
Guzev, M.A. and Paroshin, A.A., Non-Euclidean Model of the Zonal Disintegration of Rocks Around an Under-Ground Working, J. Appl. Mech. Tech. Phys., 2001, vol. 42, no. 1, pp. 131–139. https://doi.org/10.1023/A:1018877015940
Funding
The work by M.A. Guzev was partially supported by the Russian Science Foundation (project No. 19-19-00408). The work by V.V. Makarov was supported by the Ministry of Education and Science of the Russian Federation (grant agreement identifier RFMEFI58418X0034).
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Guzev, M.A., Makarov, V.V. Physical Mesomechanics Approach to Modeling the Earth’s Subsurface. Phys Mesomech 24, 357–362 (2021). https://doi.org/10.1134/S1029959921040020
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DOI: https://doi.org/10.1134/S1029959921040020