The development of coal deposits is accompanied by the release of methane from the destroyed coal and the formation of dust-gas-air mixtures predisposed to chemical reaction, manifested in the form of deflagration or detonation, as a result of which the shock waves are formed in the mine atmosphere, which in the conditions of coal mines can lead to catastrophic consequences. In order to prevent the propagation of shock waves and thermodynamic processes in the mine atmosphere at coal mines, various designs of shaft jumpers are used, for which the technological construction schemes were developed. However, scientifically substantiated and reliable methods for calculating jumpers have not yet been created. To date, the design parameters of the jumpers, primarily their thickness, are assigned on the basis of rather primitive strength calculations, which are based on the design scheme of a thin plate, the thickness of which, by definition, is significantly less than its other dimensions. The thickness of the shaft jumper is comparable to the dimensions of its cross section, which fundamentally contradicts the main requirement for the design scheme of a thin plate. In this regard, it can be said that the existing methods for determining the parameters of the jumpers based on the calculation scheme of a thin plate do not correspond to the actual operating conditions of the jumpers, therefore, they cannot be recommended to ensure the reliability of the shaft jumpers.
This article discusses the stress-strain state in a shaft jumper with a circular cross section based on the classical theory of elasticity. The paper formulates a boundary value problem of the stress-strain state of a jumper in a linear formulation, constructs its solution, as a result of which the stress components in the jumper under the action of static pressure caused by a shock wave are found.
2. Cherdantsev N.V. About One Approach to the Calculation of Coal Outburst from Gas-bearing Seam Hosting Geological Disturbances. Bezopasnost Truda v Promyshlennosti = Occupational Safety in Industry. 2019. № 8. pp. 13–18. (In Russ.). DOI: 10.24000/0409-2961-2019-8-13-18
3. Lindenau N.I., Maevskaya V.M., Krylov V.F. Origin, prevention and extinguishing of the endogenous fires in the coal mines. Moscow: Nedra, 1977. 319 p. (In Russ.).
4. Chanyshev A.I. A method to determine a body’s thermal state. Journal of Mining Science. 2012. Vol. 48. Iss. 4. pp. 660–668.
5. Cherdantsev S.V., Shlapakov P.A., Shlapakov E.A., Lebedev K.S., Erastov A.Yu. Thermophysical and gas-dynamic conditions of deflagration and detonation processes in dust-gas-air flows of mine workings near the centers of self-heating. Khimicheskaya fizika i mezoskopiya = Chemical Physics and Mesoscopy. 2019. Vol. 21. № 2. pp. 179–189. (In Russ.). DOI: 10.15350/17270529.2019.2.20
6. Cherdantsev S.V., Shlapakov P.A., Lebedev K.S., Kolykhalov V.V. Creation of detonation process during gas outburst in roadway at supersonic speed. Gornyy informatsionno-analiticheskiy byulleten (nauchno-tekhnicheskiy zhurnal) = Mining informational and analytical bulletin (scientific and technical journal). 2019. № 7. pp. 62–73. (In Russ.). DOI: 10.25018/0236-1493-2019-07-0-62-73
7. Valger S.A., Fedorova N.N., Fedorov A.V. Mathematical Modeling of Propagation of Explosion Waves and Their Effect on Various Objects. Combustion, Explosion, and Shock Waves. 2017. Vol. 53. № 4. pp. 433–443. DOI: 10.1134/S0010508217040074
8. Fomin V.M., Postinkov B.V., Kolotilov V.A., Shalaev V.S., Shalaev Yu.V., Florya N.F. Modeling shock wave processes in a mine opening with permeable barriers. Journal of Mining Science. 2019. Vol. 55. Iss. 1. pp. 18–22. DOI: 10.1134/S106273911901524X
9. Erofeev V.I., Korsakov M.I., Leontieva A.V. Linear and Nonlinear Plane Longitudinal Waves in the Slepyan-Palmov Medium. Mechanics of Solids. 2022. Vol. 57. № 6. pp. 1385–1395. DOI: 10.3103/S0025654422060218
10. Zhuravlev V.Ph. Effect of Inertia of Elastic Waves in Elastic Systems with Axial Symmetry. Mechanics of Solids. 2018. Vol. 53. Iss. 1. pp. 68–72. DOI: 10.3103/S0025654418010089
11. Ilyashenko A.V. Propagation of a plane shock front in an elastic layer. Izvestiya Rossiyskoy akademii nauk. Mekhanika tverdogo tela = Bulletin of the Russian Academy of Sciences. Mechanics of Solids. 2022. № 5. pp. 141–149. (In Russ.). DOI: 10.31857/S0572329922050075
12. Nurgaliev E.I. Substantiation and development of technology for isolation of reservoir workings by pipe-less monolithic jumpers with simultaneous construction of grouting curtains: abstract of the thesis ... Candidate of Technical Sciences. Kemerovo, 2020. 22 p. (In Russ.).
13. Timoshenko S.P., Voynovskiy-Kriger S. Theory of Plates and Shells. Moscow: Nauka, 1966. 636 p. (In Russ.).
14. Solyanik-Krassa K.V. Axisymmetric problem of elasticity theory. Moscow: Stroyizdat, 1987. 336 p. (In Russ.).
15. Koshlyakov N.S., Gliner E.B., Smirnov M.M. Equations in the partial derivatives of the mathematical physics. Moscow: Vysshaya shkola, 1970. 712 p. (In Russ.).