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Title of the article

DEVELOPMENT OF CALCULATION METHOD FOR TENSILE STRENGTH OF ROCK SAMPLES UNDER COMPRESSION
Authors

VASIL’EV Leonid M., D. Sc. in Eng., Prof., Head of the Department of Rock Destruction Issues, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine, Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

ZHURAVKOV Michael A., D. Sc. in Phys. and Math., Prof., Head of the Department of Theoretical and Applied Mechanics, Belarussian State University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

VASIL’EV Dmitriy L., D. Sc. in Eng., Senior Researcher, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine, Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

MALICH Mykola G., Ph. D. in Eng., Assoc. Prof., Associate Professor of the Department of Metallurgical Production Machines and Units, National Metallurgical Academy of Ukraine, Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

NAZAROV Oleksandr E., Second Category Engineer, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine, Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.
In the section GEOMECHANICS
Year 2020 Issue 4 Pages 85–91
Type of article RAR Index UDK 622.028:620.173.24; 539.3 Index BBK  
DOI https://doi.org/10.46864/1995-0470-2020-4-53-85-91
Abstract The paper describes a procedure for improving the approach to determining the ultimate strength of rock samples, the basic method is L. Prandtl’s method. In earlier works of the authors of this paper, the L. Prandtl’s method was improved in relation to rocks, using a general algebraic equation for calculating horizontal normal stresses depending on the vertical component and mechanical characteristics of the rock. Here, the authors reject the assumption that the tangent contact stresses resulting from L. Prandtl's solution do not depend on the abscissa x and on the variable vertical stresses, in contrast to the well-known Coulomb–Amonton law, according to which the tangent stresses are directly proportional to the vertical pressure. The regularities of contact normal and tangential stresses distribution at failure of prismatic samples are clarified. As result, the method was developed for calculating the tensile strength of samples with three characteristic values of mechanical properties: kп, yield strength of material in shear; ρ, angle of internal friction; fс, coefficient of contact friction. These characteristics can be established experimentally by simple experimental studies. The proposed approach is effective for constructing ultimate curves and diagrams of “stress — longitudinal strain” of rocks in the case of contact friction. A comparative evaluation is given for the proposed method for calculating the tensile strength of samples during their destruction with experimental data. Comparison of the calculated tensile strength with experimental data shows that the relative error of calculations according to the proposed method is significantly lower than the relative error of calculations performed using the E. Unksov’s method. The proposed method can be recommended for practical application.
Keywords

rock, tensile strength, contact friction, contact stresses, fracture
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Bibliography
  1. Zhuravkov M.A. Matematicheskoe modelirovanie deformatsionnykh protsessov v tverdykh deformiruemykh sredakh (na primere zadach mekhaniki gornykh porod i massivov) [Mathematical modeling of deformation processes in solid deformable media (on the example of problems of rocks and massifs mechanics)]. Minsk, Belorusskiy gosudarstvennyy universitet Publ., 2002. 456 p. (in Russ.).
  2. Vasil’ev L.M., Vasil’ev D.L., Malich N.G., Angelovskiy A.A. Mekhanika obrazovaniya form razrusheniya obraztsov gornykh porod pri ikh szhatii [Mechanics of formation of rock destruction of samples during compression]. Dnipro, IMA-press Publ., 2018. 175 p. (in Russ.).
  3. Gromov N.P. Teoriya obrabotki metallov davleniem [Theory of metal processing by pressure]. Moscow, Metallurgiya Publ., 1967. 340 p. (in Russ.).
  4. Storozhev M.V., Popov E.A. Teoriya obrabotki metallov davleniem [Theory of metal processing by pressure]. Moscow, Mashinostroenie Publ., 1967. 423 p. (in Russ.).
  5. Baron L.I. Kharakteristiki treniya gornykh porod [Friction characteristics of rocks]. Moscow, Nauka Publ., 1967. 272 p. (in Russ.).
  6. Petukhov I.M., Linkov A.M. Mekhanika gornykh udarov i vybrosov [Mechanics of rock impacts and emissions]. Moscow, Nedra Publ., 1983. 279 p. (in Russ.).
  7. Stavrogin A.N., Protosenya A.G. Prochnost gornykh porod i ustoychivost vyrabotok na bolshikh glubinakh [Strength of rocks and stability of mine workings at great depths]. Moscow, Nedra Publ., 1985. 271 p. (in Russ.).
  8. Chanyshev A.I., Abdulin I.M. Kharakteristiki i sootnosheniya na kharakteristikakh na zapredelnoy stadii deformirovaniya gornykh porod [Characteristics and the relations on them at the stage of post-limit deformation in rocks]. Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh, 2008, no. 5, pp. 27–41 (in Russ.).
  9. Chanyshev A.I. Zapredelnoe deformirovanie materialov pri antiploskoy deformatsii i ego uchet v zadache o rasprostranenii pryamolineynoy polubeskonechnoy treshchiny [Post-limit deformation of materials under antiplane deformation and its consideration in the problem of propagation of a rectilinear semi-infinite crack]. Deformirovanie i razrushenie materialov s defektami i dinamicheskie yavleniya v gornykh porodakh i vyrabotkakh. Materialy 20 Mezhdunarodnoy nauchnoy shkoly [Deformation and destruction of materials with defects and dynamic phenomena in rocks and workings. Proc. 20th International scientific school]. Simferopol, 2010, pp. 349–354 (in Russ.).
  10. Vasilev D.L., Us Yu.M., Kostandov Yu.A., Potapenko A.A., Angelovskiy A.A., Chugunkov I.F. Obosnovanie metodov rascheta kontaktnykh napryazheniy pri szhatii gornykh porod [A substitution of calculation methods for a contact stresses rock compression]. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, 2010, no. 9–10, pp. 56–60 (in Russ.).
  11. Vasil’ev L.M., Lokshina L.Y., Kostandov U.A. Raschet predela prochnosti khrupkikh materialov s uchetom vnutrennego treniya [Calculation of the tensile strength of brittle materials taking into account internal friction]. Geo-technical mechanics, 2010, iss. 82, pp. 199–206 (in Russ.).
  12. Vasil’ev D.L. Sovershenstvovanie metoda rascheta predela prochnosti gornykh porod pri odnoosnom szhatii [Improving the method for calculating the tensile strength of rocks under uniaxial compression]. Geo-technical mechanics, 2013, iss. 108, pp. 106–111 (in Russ.).
  13. Vasil’ev L.M., Vasil’ev D.L. Teoreticheskoe obosnovanie formirovaniya gorizontalnykh normalnykh napryazheniy v massivakh gornykh porod [Theoretical ground for origination of normal horizontal stresses in rock masses]. Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh, 2013, no. 2, pp. 81–90 (in Russ.).
  14. Vasil’ev L.M., Vasil’ev D.L. Theoretical ground for origination of normal horizontal stresses in rock masses. Journal of mining science, 2013, vol. 49, no. 2, pp. 240–247.
  15. Spravochnik (kadastr) fizicheskikh svoystv gornykh porod [Reference book (cadaster) of physical properties of rocks]. Moscow, Nedra Publ., 1975. 279 p. (in Russ.).
  16. State Standard 21153.2-84. Porody gornye. Metody opredeleniya predela prochnosti pri odnoosnom szhatii (s Izmeneniyami No. 1, 2) [Rocks. Methods for determining the strength limit under uniaxial compression (with Amendments no. 1, 2)]. Moscow, Standartov Publ., 2001. 15 p. (in Russ.).