Abstract
The authors construct a continuum approximation for the model of a medium with internal structure and internal self-balancing stresses. The presupposition of diffeomorphism, i.e. existence of partial space derivatives of displacements is largely slackened. The information brought to the closed model of a geomedium by this presupposition is comparable with the information brought by the constitutive equations. The new model includes the local bends of grains of the skeleton, plasticity and the elastic strains of the binding medium in the pore space. The model is of a gradient type.
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References
Leont’ev, A.V. and Popov, S.N., Experience of Practical Application of the Hydraulic Fracturing Method of Stress Measurement, Gornyi Zhurnal, 2003, no. 3, pp. 37–43.
Serdyukov, S.V., Kurlenya, M.V., Patutin, A.V., Rybalkin, L.A., and Shilova, T.V., Experimental Test of Directional Hydraulic Fracturing Technique, J. Min. Sci., 2016, vol. 52, no. 4, pp. 615–622.
Leont’ev, A.V., Lekomtsev, Yu.M., and Rubtsova, E.V., RF patent no. 2320870, Byull. Izobret., 2008, no. 9.
Kurlenya, M.V., Baryshnikov, V.D., Baryshnikov, D.V., Gakhova, L.N., Kachal’skii, V.G., and Khmelinin, A.P., Development and Improvement of Borehole Methods for Estimating anb Monitoring Stress-Strain Behavior of Engineering Facilities in Mines, J. Min. Sci., 2019, vol. 55, no. 4, pp. 682–694.
Kurlenya, M.V. and Popov, S.N., Teoreticheskie osnovy opredelinya napryazhenii v gornykh porodakh (Theoretical Framework for Determining Stresses in Rocks), Novosibirsk: Nauka, 1983.
Sadosvky, M.A. Bolkhovitinov, L.G., and Pisarenko, V.F., Discreteness Property of Rocks, Izv. AN SSSR. Fiz. Zemli, 1982, no. 12, pp. 13–18.
Kocharyan, G.G., Geomekhanika razlomov (Geomechanics of Faults), Moscow: Geos, 2016.
Revuzhenko, A.F. and Mikenina, O.A., Elastoplastic Model of Rocks with Internal Self-Balancing Stresses, J. Min. Sci., 2018, vol. 54, no. 3, pp. 368–378.
Kosykh, V., Effect of Multiple Weak Impacts on Evolution of Stresses and Strains in Geomaterials, Trigger Effects in Geosystems, Springer, Cham, 2019, pp. 95–103.
Peng, Z. and Gomberg, Y., An Integrated Perspective as the Continuum between Earthquakes and Slowslip Phenomena, Nature Geosciences, 2010, no. 3, pp. 599–607.
Khristianovich, S.A., Fundamentals of Seepage Theory, J. Min. Sci., 1989, vol. 25, no. 5, pp. 397–412.
Revuzhenko, A.F., Version of the Linear Elasticity Theory with a Structural Parameter, J. Appl. Mech. Tech. Phys., 2016, vol. 57, no. 5, pp. 801–807.
Trusov, P.V., Nonlinear Mechanics of Deformable Solid: Some Issues to Be Discussed Mat. Modelir. Sist. Protsess., 2009, no. 17, pp. 85–95.
Revuzhenko, A.F., Mekhanika uprugoplasticheskikh sred i nestandartnyi analiz (Mechanics of Elasto-Plastic Media and Non-Standard Analysis), Novosibirsk: NGU, 2000.
Revuzhenko, A.F. and Mikenina, O.A., Elastoplastic Model of Rocks with a Structural Parameter, J. Appl. Mech. Tech. Phys., 2018, vol. 59, no. 2, pp. 332–340.
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The study was supported by the Russian Foundation for Basic Research, project no. 20-05-00184.
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Russian Text © The Author(s), 2020, published in Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, 2020, no. 2, pp. 3–11.
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Revuzhenko, A.F., Mikenina, O.A. Elastoplastic Model of Rocks with Internal Self-Balancing Stresses. Continuum Approximation. J Min Sci 56, 159–166 (2020). https://doi.org/10.1134/S1062739120026601
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DOI: https://doi.org/10.1134/S1062739120026601