Home

Theoretical and experimental aspects of plastic deformation and destruction of rocks

Скачать статью

Andrey Viktorovich Zhabko

A. V. Zhabko / News of the Ural State Mining University 1 (2018) 68–79 DOI 10.21440/2307-2091-2018-1-68-79

 

УДК 539.(4+4.011+42)+622.(011.4+02+023.23) DOI 10.21440/2307-2091-2018-1-68-79

 

The urgency of the problem. The main process in mining is the process of destruction of rocks, so the establishment of laws and criteria for plastic deformation and destruction of rocks is the most important and fundamental object. 

Purpose of the work. The work is devoted to the establishment of laws of plastic deformation of rocks (solids).

Methods of research. Analytical and experimental research methods are widely used in this work.

Results. On the basis of the earlier studies, which were carried out by the author, the functions of the yield surface and the plastic potential are proposed. The limiting surface for these functions is the surface of the ultimate strength of solids (rocks), described by the Coulomb criterion. The author indicated the fundamental similarity between the proposed criterion of plastic deformation and rock strength with the Mora criterion and with the dry friction law of Amonton. The possibility of applying the proposed criterion as passport dependence is demonstrated. The characteristics of rock strength for shear adhesion and the angle of internal friction act as the parameters of this dependence. The paper provides comparison of the proposed theoretical criterion of plasticity and strength to the experimental data under the conditions of the three-dimensional stress state. The detailed analysis of this comparison between theoretical and experimental data is given, the corresponding conclusions are drawn. An analytical dependence was derived on the basis of the stability criterion obtained earlier by the author. It determines the value of the fundamental parameter of the hierarchy during shear and discontinuous destruction of mountain ranges. The relationship of this parameter hierarchy with the so-called number of Phidias, which determines the “Golden ratio”, is indicated. The dependence for calculation of a large-scale factor of the phenomenon of zonal disintegration of rocks around mine workings is offered. The physical interpretation of the proposed dependences to determine the fundamental parameter of the hierarchy of mountain ranges is given. The scale factor of the phenomenon of zonal disintegration of rocks around the workings in the strongly stressed mountain ranges is represented as well. The relation between these parameters and constants characterizing the orbital distances of the solar system planets is indicated.

Summary. This paper presents an experimental confirmation of the previously proposed theory of plastic deformation and fracture of rocks; some theoretical aspects are given in the continuation of the mentioned theory.

Keywords: function of plastic potential; criterion of rock strength; criterion of Coulomb; criterion of plasticity; main stresses; tensile strength; hardening; parameter of hardening; plastic deformation; dilatancy; fundamental parameter of hierarchy; scale factor of zonal disintegration of rocks; passport dependence.

 

REFERENCES

1. Zhabko A. V. 2015, Predel'noye napryazhennoye sostoyaniye gornykh porod [Limiting stressed state of rocks]. Izv. vuzov. Gornyy zhurnal [News of the Higher Institutions. Mining Journal], no. 5, pp. 50–55.

2. Zhabko A. V. 2017, Zakony plasticheskogo deformirovaniya i destruktsii tverdykh tel [Laws of plastic deformation and destruction of solids]. Izv. UGGU [News of the Ural State Mining University], no. 2 (46), pp. 82–87.

3. Zhabko A. V. 2017, Prochnost' kontinuuma (tverdykh tel) [The strength of the continuum (solids)]. Izv. vuzov. Gornyy zhurnal [News of the Higher Institutions. Mining Journal], no. 4, pp. 47 – 55.

4. Stavrogin A. N., Tarasov B. G., Shirquez O. A., Pevzner Ye. D. 1981, Prochnost’ i deformatsiya gornykh porod v dopredelnoy i zapredel’noy oblastyakh [Strength and deformation of rocks in additional and beyond areas]. FTPRPI [Journal of Mining Science], no. 6, pp. 3–11.

5. Stavrogin, A. N., Protosenya A. G., 1985, Prochnost' gornykh porod i ustoychivost vyrabotok na bol’shikh glubinakh [The strength of rocks and stability of mine workings at great depths]. Moscow, 271 p.

6. Kartashov Yu. M., Matveyev B. V., Mikheyev G. V. and others. 1979, Prochnost' i deformiruyemost' gornykh porod [Strength and deformability of rocks], Moscow, 269 p.

7. Stavrogin A. N., Tarasov B. G. 2001, Eksperimental'naya fizika i mekhanika gornykh porod [Experimental physics and mechanics of rocks]. St. Petersburg, 343 p.

8. Nadai A. 1954, Plastichnost' i razrusheniye tverdykh tel. Per. s angl.; pod red. G. S. Shapiro [The theory of flow and fracture of solids. Translated from English, edited by G. S. Shapiro]. Moscow, 648 p.

9. Odintsev V. N. 1996, Otryvnoye razrusheniye massiva skalnykh gornykh porod [Avulsion fracture of the massif rocks]. Moscow, 166 p.

10. Morozov Ye. M., Friedman Ya. B. 1961, Trayektorii treshchin khrupkogo razrusheniya kak geodezicheskiye linii na poverkhnosti tela [Trajectory of cracks of brittle fracture as geodesic lines on the surface of a body]. DAN SSSR [Doklady of the Russian Academy of Sciences of the USSR], vol. 139, no. 1, pp. 87–90.

11. Stavrogin, A. N., Protosenya A. G. 1979, Plastichnost’ gornykh porod [Plasticity of rocks]. Moscow, 301 p.

12. Kiyoo Mogi. 2007, Experimental rock mechanics. London.

13. Sadovsky M. A. 1979, Yestestvennaya kuskovatost’ gornoy porody [Natural lumpiness of rocks]. DAN SSSR [Doklady of the Russian Academy of Sciences of the USSR], vol. 247, vol. 4, pp. 829–831.

14. Kuksenko V. S., Inzhevatkin I. E., Manzhikov C. B., and others. 1987, Fizicheskiye i metodicheskiye osnovy prognozirovaniya gornykh udarov [Physical and methodological basis of forecasting rock bursts]. FTPRPI [Journal of Mining Science], no. 1, pp. 9–22.

15. Oparin V. N., Kurlenya M. V. 1994, O skorostnom razreze Zemli po Gutenbergu i vozmozhnom ego geomekhanicheskom obyasnenii. Ch. I. Zonalnaya geodezintegratsiya i iyerarkhicheskiy ryad geoblokov [On the high-speed section of the Earth according to Gutenberg and its possible geomechanical explanation. Part 1. The zonal geo-disintegration and hierarchical set of geoblocks]. FTPRPI [Journal of Mining Science], no. 2, pp. 14–26.

16. Chechel’nitsky A. M. Zakony orbitalnykh rasstoyaniy. Titsiusa–Bode i postoyannaya tonkoy struktury – kak mikro i megaparametr volnovoy Vselennoy [The Laws of orbital distances, Titius–Bode and fine structure constant as a micro and mega parameter of the wave Universe], URL: http://lib.uni-dubna.ru

17. Shemyakin Ye. I. 1988, O svobodnom razrushenii tverdykh tel [Free destruction of solid bodies]. DAN SSSR [Doklady of the Russian Academy of Sciences of the USSR], vol. 300, pp. 1090–1094.

18. Zhabko A. V. 2016, Teoriya rascheta ustoychivosti otkosov i osnovaniy. Obshchaya teoriya rascheta ustoychivosti odnorodnykh otkosov [Theory of calculation of stability of slopes and foundations. The General theory for calculating the stability of homogeneous slopes]. Izv. UGGU [News of the Ural State Mining University], no. 1 (41), pp. 72–83.

19. M. V. Kurlenya, V. N. Oparin 1996, O masshtabnom faktore yavleniya zonalnoy dezintegratsii gornykh porod i kanonicheskikh ryadakh atomno-ionnykh radiusov [On the scale factor of phenomenon of zonal disintegration of rocks and canonical series of atomic-ionic radii]. FTPRPI [Journal of Mining Science], no. 2, pp. 3–14.

20. M. V. Kurlenya, V. N. Oparin 1999, Problemy nelineynoy geomekhaniki [Problems of nonlinear geomechanics]. FTPRPI [Journal of Mining Science], no. 3, pp. 12–26.

21. Oparin V. N. 1997, Masshtabnyy faktor yavleniya zonalnoy dezintegratsii gornykh porod i stratifikatsiya nedr Luny po seysmicheskim dannym [Large-scale factor of the phenomenon of zonal disintegration of rocks and stratification of the moon according to the seismic data] FTPRPI [Journal of Mining Science], no. 6, pp. 3–17.

22. Kashubin S. N., Vinogradov V. B., Kuzin A.V. 2005, Fizika Zemli / pod red. V. V. Filatova. 2-e izd., ispr. i pererab. [Physics of the Earth. edited by V. V. Filatov. 2nd ed., edited and revised]. Ekaterinburg, 188 p.

23. Chanyshev, A. I., Kurenkeyeva B. O. 2004, K voprosu postroyeniya pasportnykh zavisimostey dlya gornykh porod. Problemy i perspektivy razvitiya gornykh nauk [The problem of the building passport dependences for rocks. Problems and prospects of mining Sciences]. Sb. statey mezhdunar. konf. (1–5 noyabrya 2004 g.) [Collection of articles of the International conference (1–5 Nov. 2004)]. Novosibirsk, pp. 308–312.

Лицензия Creative Commons
All articles posted on the site are available under the Creative Commons Attribution 4.0 Global License.