Pendulum waves and basics of «geomechanical thermodynamics»

Abstract

It is shown that modern achievements in the field of experimental and theoretical researches and developments of innovative measuring systems for monitoring of non-linear dynamic and kinematic characteristics allow to formulate basics of new academic discipline, designated as “geomechanical thermodynamics”. The following circumstances can be considered as the most important prerequisites for development of this new discipline.
(1) Practical completeness of the classical thermodynamics, based on kinetic gas theory and molecular movements in solid bodies; (2) Creation of “formular construction tool” for the description of dynamic and ki- nematic characteristics of pendulum waves and energy conditions of their occurrence and propagation from dynamic sources, located in multi-phased stressed rock mass and geomaterials with block-hierarchical structure; (3) Principal opportunity to establish formal relations between substantial energy carriers of “packages” of non- linear pendulum waves (geoblocks of certain hierarchical levels according to their diameters) and “molecules”: their movement, velocity and acceleration of the “molecules” ↔ “geoblock”; “force interactions between mole- cules” ↔ “non-linear elastic interaction between geoblocks”, etc.
The term of “geomechanical temperature” is introduced and its analytical expression, which is proportional to kinetic energy of movement of geoblocks with defined volume for their hierarchical subsequence at “confined” conditions of the stressed rock mass, is shown. The similar aspects are discussed, when emission acoustic- electromagnetic fields are fixed using corresponding coefficients of mechanical-electrical and mechanical- acoustic transformations. In order to quantitively describe the evolution of energy state of local zones of stress- strain concentration and surroundings of their non-linear influence from catastrophic events at the natural and mine-engineering systems (earthquakes, rock bursts, etc.), the terms of their geomechanical and thermodynamic stages are introduced and specified: $T_{i}(i \in 0,+, \pm,-, *)$‒ with background states $\left(i \in 0,{ }^{*}\right)$ and three major stages $(i \in+, \pm,-) $outlined, where (+) is the concentration, $( \pm,-)$ are the failure and relaxation and (*) is the quasi-recovering up to “background” level after the occurred catastrophic event. Using certain examples, the exis- tence of critical elastic energy content of local zones with “meta-stable state”, which is transforming to quasi-resonance process of failure and relaxation of “excessive” energy, is shown $\left(T_{ \pm}\right)$.

Keywords

Geomechanical thermodynamics / Pendulum waves / Energy approach / Geomechanical and thermodynamic stages / Geomechanical temperature / Block-hierarchical structure

References

[1] V.N. Oparin, A.A. Adushkin, A.A. Baryakh, M.A. Zhuravkov, V.P. Potapov, et al., Geomechanical Fields and Processes: the Experimental and Analytical Investigation of Forming and Evolution of Catastrophic Event Local Zones at Geotechnical and Natural-Technical Systems,in: N. N. Melnikov, Eds.) Novosibirsk (vol. 1, SB RAS Pupl., 2018, p. 549. Vol.2. - 2019. - 543pp.

[2] V.N. Oparin, V.P. Potapov, T.A. Kiryaeva, V.F. Yushkin, On the problem of development of methods and geoinformation means for integrated evaluation of non-linear strain-wave processes, induced by seismic impacts, on geomechanical state of open-pit slopes and gas-dynamic activity of Kuzbass coal mines, Mining informational and analytical bulletin (8) ( 2020) 5-39.

[3] V.V. Adushkin, V.N. Oparin, From the alternating-sign explosion response of rocks to the pendulum waves in stressed media, J. Min. Sci. 48 (2) (2012) 203–222. P. II:2013, Vol. 49, No. 2, pp. 175-209; P. III: 2014, Vol. 50, No. 4, pp. 623-645; P.IV: 2016, Vol. 52, No. 1, pp. 1-35.

[4] V.N. Oparin, T.A. Kiryaeva, V.G. Potapov, V.F. Yushkin, New methods and information technologies in the experimental geomechanics, Novosibirsk: SB RAS Publ ( 2021) 292, https://doi.org/10.53954/9785604642856.

[5] V.N. Oparin, V.V. Adushkin, V.I. Vostrikov, V.F. Yushkin, T.A. Kiryaeva, et al., The development of experimental and theoretical basics of non-linear geotomography, Mining informational and analytical bulletin. - Part I: Formulation and justification of research taks (1) ( 2019) 5-25. Part II: Dynamic and kinematic characteristics of pendulum waves in stressed geomedia and seismic-emission processes. - 2019. - No.11. - pp. 5 - 26;Part III: Perspective monitoring systems of strain-wave processes at underground and surface mining conditions. - 2019. - No.12. - pp. 5 - 29.

[6] V.N. Oparin, A.P. Tapsiev, V.I. Vostrikov, et al., On possible causes of increase in seismic activity of mine fields in the Oktyabrsky and Taimyrsky mines of the Norilsk deposit in 2003, Part I: Seismic Regime// J. of Mining Science 40 (4) ( 2004) 321-338.

[7] V.N. Oparin, B.F. Simonov, Nonlinear deformation-wave processes in the vibrational oil geotechnologies, J. Min. Sci. 46 (2) ( 2010) 95-112.865

[8] V.N. Oparin, V.V. Adushkin, T.A. Kiryaeva, V.P. Potapov, V.G. Tyukhrin, A.V. Glumov, Effect of pendulum waves from earthquakes on gas-dynamic behavior of coal seams in Kuzbass, J. Min. Sci. 40 (No. 1) ( 2018) 3-14.

[9] V.N. Oparin, Theoretical fundamentals to describe interaction of geomechanical and physicochemical processes in coal seams, J. Min. Sci. 53 (2) ( 2017) 201-215.

[10] V.N. Oparin, in: Pendulum Waves and “Geomechanical Temperature”/2nd Russian-Chinese International Conference “Non-linear Geomechanical and Geodynamic Processes at Deposit Exploitation under High Depths”, Novosibirsk: IGD SO RAN, 2012, pp. 169-172.

[11] I.I. Gurvich, G.N. Boganik, Seismic survey, Moscow Times: Nedra Publ ( 1980) 551.

[12] V.N. Oparin, B.F. Simonov, V.F. Yushkin, V.I. Vostrikov, Y.V. Pogarsky, L.A. Nazarov, Geomechanical and Technical Basics for Oil Recovery Seam Increase at Vibro-Wave Technologies, Nauka, Novosibirsk, 2010, p. 404.

[13] V.N. Oparin, V.V. Timonin, V.N. Karpov, B.N. Smolyanitsky, Energy-based volumetric rock destruction criterion in the rotary-percussion drilling technology improvement, J. Min. Sci. 53 (6) ( 2017) 1043-1065.

[14] V.N. Oparin, O.M. Usol'tseva, V.N. Semenov, P.A. Tsoi, Evolution of stress-strain state in structured rock specimens under uniaxial loading, J. Min. Sci. 49 (5) ( 2013)-877.

[15] V.N. Oparin, T.A. Kiryaeva, O.M. Usol'tseva, Nonlinear deformation-wave processes in various rank coal specimens loaded to failure under varied temperature, J. Min. Sci. 51 (4) ( 2015) 641-658.

[16] V.G. Levich, Y.A. Vdovin, V.A. Myamlin, Course of Theoretical Physics vol. II, Nauka, Moscow, 1971, p. 936.

[17] R. Feinman, R. Leiton, M. Sands, Feinman's lectures on physics, Moscow Times: Mir Publ. 3 ( 1976), 4. - 496 pp.

[18] A.N. Stavrogin, A.G. Protosenya, Rock strength and working stability under high depths, Moscow Times: Nedra ( 1985) 271.

[19] M.A. Guzev, V.V. Makarov, Deformation and destruction of highly compressed rock around workings, Vladivostok: Dalnauka ( 2007) 232.

[20] B.D. Annin, V.M. Zhigalkin, Material Behavior in Conditions of Complex Loading, Novosibirsk: SO RAN Publ, 1999, p. 342.

[21] E.I. Shemyakin, G.L. Fisenko, M.V. Kurlenya, V.N. Oparin, et al., Effect of zonal disintegration around underground workings, Dokl. Akad. Nauk 289 (5) ( 1986) 1088-1094.

[22] M.A. Sadovsky, G.G. Kocharyan, V.N. Rodionov, On mechanics of block rock mass, Dokl. Akad. Nauk 302 (2) ( 1988) 306-307.

[23] M.A. Sadovsky, Hierarchy form dust particles to planets, The Earth and the Universe (6) ( 1984) 5-9.

[24] V.G. Bykov, Strain waves of the Earth: concept, observations and models, Geology and geophysics 46 (11) ( 2005) 1176-1190.

[25] A.V. Vikulin, Physics of Wave-Seismic Process, Petropavlovsk-Kamchatsky: KGPU Publ, 2003, p. 151.

[26] G.A. Sobolev, Basics of Earthquakes Prediction, Nauka, Moscow, 1993, p. 314.

[27] N.I. Korchuganov, A.K. Korsakov, Remote methods of geological mapping, Moscow Times ( 2009) 158.

[28] V.V. Donov, The development of the multi-layered lineament analysis method of aerospace images, Moscow Times ( 2009) 120.

[29] M. Bath, Spectral analysis in geophysics, Transl. from Eng. - Moscow: Nedra ( 1980) 535.

[30] N.Oparin V, et al., in:M.D. Novopashin (Ed.), Modern Geodynamics of Rock Mass in Upper Part of the Lithosphere:Origins, Parameters, Impact Om Mining Facilities, Novosibirsk: SO RAN Publ, 2008, p. 449.

[31] N.Oparin V, et al., in: N.N. Melnikov (Ed.), Crust Destruction and Processes of Self- Arrangement in Areas of High Artificial Impact, Novosibirsk: SO RAN Publ, 2012, p. 632.

[32] V.N. Oparin, G.E. Yakovitskaya, A.G. Vostretsov, V.M. Seryakov, Mechanical-electromagnetic transformations in rocks on failure, J. Min. Sci. 49 (3) ( 2013) 343-356.

[33] V.N. Oparin, B.D. Annin, Y.V. Chugui, et al., in: V.L. Shkuratnik (Ed.), Methods and Measuring Tools for Simulation and Field Investigations of Non-linear Strain-Wave Processes in Block Rock Mass, Novosibirsk: SO RAN Publ, 2007, p. 320.

[34] V.N. Oparin, S.N. Bagaev, A.A. Malovichko, et al., in: N.N. Melnikov (Ed.), Methods and Systems of Seismic-Strain Monitoring of Artificial Earthquakes and Rock Bursts, vol. 1, Novosibirsk:SO RAN Publ., 2009, p. 304. Vol. 2. - 2010.-261 pp.

[35] V.N. Oparin, A.S. Tanaino, Classical Scale of Hierarchical Representations in Mining Petrology, Nauka, Novosibirsk, 2011, p. 259.

[36] Wu Hao, Fang Qin, Yu Dong-xun, Advances in the study on pendulum-type wave phenomenon in the deep block rock mass, Advances in mechanics 38 (5) ( 2008) 601-609.

[37] K.-X. Wang, L.-M. Dou, Y.-S. Pan, V.N. Oparin, Еxperimental study of incompatible dynamic response feature of block rock mass, Rock Soil Mech. 41 (4) ( 2020) 1227-1234. &#8210.

[38] S.N. Zhurkov, Kinetic concept of solid body strength (thermofluctuationalmechanism), Bulletin AS USSR (3) ( 1968) 46-52.

[39] S.N. Zhurkov, V.S. Kuksenko, V.A. Petrov, On rock destruction prediction, Earth physics (6) ( 1977) 11-18.