Andrey Viktorovich ZHABKO

УДК 622.83


A. V. Zhabko / News of the Ural State Mining University. 2018. Issue 4(52), pp. 98-107


Relevance of the research is due to the fact that there are some problems in geomechanics associated with the incorrect presentation of the mountain mass by the continuum environment. In this regard, some fundamental problems may occur in determining the strength and deformation properties of mountain ranges, the calculation of their stress-strain behavior.
Purpose of the study is to summarize the existing problems of geomechanics, determination the most significant ones, as well as to discuss possible ways to overcome them.
Methods of the study. Analytical methods of the research with experimental verification of the specified results are used in this work. Results and their application. This paper is intended to propose analytical criteria for plasticity and strength for rocks and other artificial materials, as well as the function of plastic potential for the strike-slip character of plastic deformation and destruction, based on the representation of solid bodies as the continuum environment. The proposed criteria and function of plastic potential were compared and adjusted with some experimental studies on the destruction of mountain rocks in a complex stress pattern. A variational principle of the disintegration of mountain ranges is proposed, which makes it possible to determine the geometry of the surfaces of disintegration. It follows that the surface of disintegration minimizes areas (volumes) with reduced potential (plastic), and areas with increased potential (elastic, energy-intensive ones) increase while minimizing the energy spent on creating surfaces (their length). On the basis of this principle, dependence has occurred; it connects the radius of curvature of the surface of shear disintegration and the main stresses while destruction by body forces (for example, gravity). A criterion for a crack extension or a fundamental hierarchy parameter (linear factor of blocks) is proposed; it is established that its value is determined by the angle of shearing resistance, as a measure for energy dissipation during when shearing. When considering a mountain massif as a discretic block medium, the sine-Gordon equation was obtained, which describes the deformation dynamics.
Conclusions. According to the results of the research, a number of criteria, principles, and dependencies were proposed that determine the processes of plastic deformation and destruction (disintegration) of rocks based on continuum and block-hierarchical models of the mountain massif.

Keywords: problems of geomechanics, strength and deformation properties of mountain ranges, disintegration and destruction of rocks, plastic deformation, sin-Gordon equation.




1. Kocharyan G. G. 2009, Deformatsionnyye protsessy v massivakh gornykh porod [Deformation processes in rock masses]. Moscow, 378 p.
2. Sashurin A. D. 2014, Sovremennyye geodinamicheskiye dvizheniya i ikh rol’ v formirovaniinapryazhenno-deformirovannogo sostoyaniya massiva gornykh porod [Modern geodynamic movements and their role in the formation of the stress-strain behaviour of the rock mass]. Geomechanics in mining: proceedings of the All-Russian scentific and technical conference with international participation, June 4–5, pp. 3–12.
3. Balek A. Е. 2018, Consideration of the mosaic structure of the stress-strain behavior of massive rock mass in solving practical problems of subsoil use. Problemy nedropol’zovaniya [Issues of subsoil use], issue 3. Ekaterinburg, pp. 140–150. (In Russ.)
4. Zoteev O. V. 1999, Scientific basis for calculating the design parameters of underground ore mining systems, taking into account the structure of the massif and the order of mining operations. PhD thesis. Ekaterinburg, 44 p.
5. Zhabko A. V. 2018, About the problems and modern methods for assessing the sustainability of open cast mining. Problemy nedropol’zovaniya [Issues of subsoil use], issue 3, Ekaterinburg, pp. 96–107. (In Russ.)
6. Coulomb A. 1773, Essay on the application of the rules of maxima and minima to certain statics problems relavant to architecture. Memoires presentes a l'Academie. Paris: Academy of Science, pp. 343–384.
7. Zhabko A. V. 2017, Laws of plastic deformation and destruction of solids. Izvestiya UGGU [News of the Ural State Mining University], no. 2 (46), pp. 82–87. (In Russ.) https://doi.org/10.21440/2307-2091-2017-2-82-87
8. Zhabko A. V. 2017, The strength of the continuum (of solid bodies). Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal [News of the Higher Institutions. Mining Journal], no. 4, pp. 47–55. (In Russ.) URL: https://elibrary.ru/item.asp?id=29299923
9. Zhabko A. V. 2018, Theoretical and experimental aspects of plastic deformation and destruction of rocks. Izvestiya UGGU [News of the Ural State Mining University], no. 1 (49), pp. 68–79. (In Russ.) https://doi.org/10.21440/2307-2091-2018-1-68-79
10. Oparin V. N., Kurlenya M. V. 1994, About the velocity profile of the earth according to Guttenberg and a possible geo-mechanical explanation. Part I. Zonal geo-disruption and hierarchical row of geo-blocks. Fiziko-tekhnicheskiye problemy razrabotki poleznykh iskopayemykh [Journal of Mining Science], no. 2, pp. 14–26. (In Russ.)
11. Makarov P. V. 1998, Physical mesomechanics approach to modeling the processes of deformation and fracture. Fizicheskaya mezomekhanika [Physical mesomechanics], no. 1, pp. 61–81. (In Russ.) URL: https://elibrary.ru/item.asp?id=12913615
12. Bykov V. G. 2015, Nonlinear waves and soliton waves in fault block models of geological terrains. Geologiya i geofizika [Geology and Geophysics], Vol. 56, No 5, pp. 1008-1024. (In Russ.) URL: https://elibrary.ru/item.asp?id=23527753
13. Vikulin A. V., Ivanchin A., G. 2013, About the modern concept of the block-hierarchical structure of the geological terrain and some of its consequences in the Earth sciences. Fiziko-tekhnicheskiye problemy razrabotki poleznykh iskopayemykh [Journal of Mining Science], No 3, pp. 67-84. (In Russ.) URL: https://elibrary.ru/item.asp?id=19404459
14. Vikulin A. V., Makhmudov Kh. F., Ivanchin A. G. et al. 2016, On wave and rheidity properties of the Earth’s crust. Fizika tverdogo tela [Physics of the Solid State], vol. 58, issue 3, pp. 547–557. (In Russ.) URL: https://elibrary.ru/item.asp?id=25668922
15. Garagash I. А. 2016, Uyedinennyye tektonicheskiye volny v verkhney mantii [Solitary tectonic waves in the upper mantle]. Tectonophysics and current issues of Earth sciences. The fourth tectonic-physical conference of The Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences, pp. 456–460. (In Russ.)
16. Garagash I. A., Nikolaevsky V. N. 2009, Cosserat mechanics for the Earth Sciences. Vychislitel’naya mekhanika sploshnykh sred [Computational Continuum Mechanics], vol. 2, no. 4, pp. 44–66. (In Russ.) URL: https://elibrary.ru/item.asp?id=16355033
17. Panin V. Е. 1998, Fundamentals of physical mesomechanics. Fizicheskaya mezomekhanika [Physical mesomechanics], no. 1, pp. 5–22. (In
Russ.) URL: https://elibrary.ru/item.asp?id=12913611
18. Panin V. E., Grinyaev Yu. V., Psakhie S. G. 2004, Physical mesomechanics: advances for two decades of development, problems and prospects. Fizicheskaya mezomekhanika [Physical mesomechanics], vol. 7, issue S1-1, pp. 1–25. URL: https://elibrary.ru/item.asp?id=10365838
19. Kurlenya M. V., Oparin V. N. 1999, Problems of nonlinear geomechanics. Part I. Fiziko-tekhnicheskiye problemy razrabotki poleznykh iskopayemykh [Journal of Mining Science], no. 3, pp. 12–26. (In Russ.) URL: https://elibrary.ru/item.asp?id=14947953
20. Kurlenya M. V., Oparin V. N. 2000, Problems of nonlinear geomechanics. Part II. Fiziko-tekhnicheskiye problemy razrabotki poleznykh iskopayemykh [Journal of Mining Science], no. 4, pp. 3–26. (In Russ.) URL: https://elibrary.ru/item.asp?id=14954392
21. Zhabko A. V. 2016, Analiticheskaya geomekhanika [Analytical geomechanics]. Ekaterinburg, 224 p.


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