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Modeling displacements and stress relief in coal-bearing rock mass

The article analyzes the key stress redistribution patterns in coal-bearing rock mass and in the coal seam roof and floor at the stage of pre-mine gas drainage. The known experimentally revealed property of coal samples to change their linear sizes in methane absorption– desorption is used to construct theoretical models of the influence exerted by gas emission from coal seam on the stress–strain behavior of enclosing rock mass. Naturally, coal mining greatly changes the rock mass behavior and induces zones of stress relief and stress increase in rocks. On the other hand, rock mass undergoes impact of gas drainage activities as early as before mining, and stress relief zones also appear in this case although they are weaker. As known, these zones induce or stimulate permeability in rock mass and, accordingly, promote mass transfer of methane to drainage boreholes among other things. The analytical problem is solved by means of adaptation of the known relations from theory of functions of complex variable and the solution of the Kelvin problem on an elastic half-space subject to a load. The article shows that beyond the stress relief zone, there is a stress increase zone in rock mass, which is the strongest nearby the gas drainage zone boundary, and the stress relief front is simultaneously the stress increase front.

Keywords: methane, coal-bearing rock mass, permeation, stress–strain behavior, permeability, drainage borehole, stress relief, theory of functions of complex variable, Kelvin problem.
For citation:

Zakharov V. N., Trofimov V. A., Shlyapin A. V. Modeling displacements and stress relief in coal-bearing rock mass. MIAB. Mining Inf. Anal. Bull. 2022;(12):109-127. [In Russ]. DOI: 10.25018/0236_1493_2022_12_0_109.


The study was supported by the Ministry of Science and Higher Education of the Russian Federation, Agreement No. 075-15-2021-943 and European Commission Research Fund for Coal and Steel (RFCS) funded project «Advanced methane drainage strategy employing underground directional drilling technology for major risk prevention and green-house gases emission mitigation» GA: 847338-DD-MET-RFCS-2018/RFCS-2018.

Issue number: 12
Year: 2022
Page number: 109-127
ISBN: 0236-1493
UDK: 622.81
DOI: 10.25018/0236_1493_2022_12_0_109
Article receipt date: 03.10.2022
Date of review receipt: 08.11.2022
Date of the editorial board′s decision on the article′s publishing: 10.11.2022
About authors:

V.N. Zakharov1, Аcademician of Russian Academy of Sciences, Director ICEMR RAS, e-mail:, ORCID ID: 0000-0002-9309-2391,
V.A. Trofimov1, Dr. Sci. (Eng.), Head of Laboratory, e-mail:, ORCID ID: 0000-0001-9010-189X,
A.V. Shlyapin1, Cand. Sci. (Eng.), Deputy Director for Science, e-mail:, ORCID ID: 0000-0002-9442-0983,
1 Institute of Problems of Comprehensive Exploitation of Mineral Resources of Russian Academy of Sciences, 111020, Moscow, Russia.


For contacts:

A.V. Shlyapin, e-mail:


1. Zakharov V. N., Trofimov V. A., Shlyapin A. V. Patterns of the formation of the stressed state of rocks in the roof of the mined-out area during its development. Russian Mining Industry. 2021, no. 6, pp. 68—75. [In Russ]. DOI: 10.30686/1609-9192-2021-6-68-75.

2. Trofimov V. A., Filippov Yu. A. Peculiarities of the formation of methane mass transfer in the rocks of the interlayer. Equipment and technologies for oil and gas complex. 2021, no. 3, pp. 71—78. [In Russ]. DOI: 10.33285/1999-6934-2021-3(123)-71-78.

3. Zakharov V. N., Shlyapin A. V., Trofimov V. A., Filippov Yu. A. Change in stress–strain behavior of coal-rock mass during coal mining. MIAB. Mining Inf. Anal. Bull. 2020, no. 9, pp. 5—24. [In Russ]. DOI: 10.25018/0236-1493-2020-9-0-5-24.

4. Trofimov V. A., Kubrin S. S., Filippov Yu. A., Kharitonov I. L. Numerical modeling of stress–strain state for host rock mass and thick gently dipping coal seam after mining completion in extraction panel. MIAB. Mining Inf. Anal. Bull. 2019, no. 8, pp. 42—56. [In Russ]. DOI: 10.25018/0236-1493-2019-08-0-42-56.

5. Trofimov V. A., Filippov Y. A. Influence of stress variation in roof rocks of coal seam on strata gas conditions in longwalling. Journal of Mining Science. 2019, vol. 55, no. 5, pp. 722— 732. DOI: 10.1134/S1062739119056099.

6. Kai L., Daiyin Y., Yeheng S. The mathematical model of stress sensitivities on tight reservoirs of different sedimentary rocks and its application. Journal of Petroleum Science and Engineering. 2020, vol. 193, article 107372. DOI: 10.1016/j.petrol.2020.107372.

7. Ignatov E. V. Dependences and features of displacements and formation of zones of destruction of the roof and the marginal part of the reservoir when interacting with the element base of the non-pillar technology. Journal of Mining and Geotechnical Engineering. 2020, no. 4, pp. 4—41. [In Russ]. DOI: 10.26730/2618-7434-2020-4-4-41.

8. Lubosik Z., Waclawik P., Horak P., Wrana A. The influence of in-situ rock mass stress conditions on deformation and load of gateroad supports in hard coal mine. Procedia Engineering. 2017, vol. 191, pp. 975—983. DOI: 10.1016/j.proeng.2017.05.269.

9. Akilu S., Padmanabhan E., Sun Z. A review of transport mechanisms and models for uncon-ventional tight shale gas reservoir systemst. International Journal of Heat and Mass Transfer. 2021, vol. 175, article 121125. DOI: 10.1016/j.ijheatmasstransfer.2021.121125.

10. Liu T., Lin B. Q., Fu X. H., Liu S. M. A new approach modeling permeability of miningdisturbed coal based on a conceptual model of equivalent fractured coal. Journal of Natural Gas Science & Engineering. 2020, vol. 79, article 103366. DOI: 10.1016/j.jngse.2020.103366.

11. Li Y., You X., Zhao J., Zhang X. Production forecast of a multistage fractured horizontal well by an analytical method in shale gas reservoir. Environmental Earth Sciences. 2019, vol. 78, no. 9, article 27220. DOI: 10.1007/s12665-019-8156-9.

12. Hosseini N., Khoei A. R. Modeling fluid flow in fractured porous media with the interfacial conditions between porous medium and fracture. Transport in Porous Media. 2021, vol. 139, no. 1, pp. 109—129. DOI: 10.1007/s11242-021-01648-5.

13. Zhang R., Cheng Y. P., Yuan L., Zhou H. X., Wang L., Zhao W. Enhancement of gas drainage efficiency in a special thick coal seam through hydraulic flushing. International Journal of Rock Mechanics and Mining Sciences. 2019, vol. 124, no. 3-4, article 104085. DOI: 10.1016/j.ijrmms.2019.104085.

14. Fan J. Y., Liu P., Li J. J., Jiang D. Y. A coupled methane/air flow model for coal gas drainage: model development and finite-difference solution. Process Safety and Environmental Protection. 2020, vol. 141, pp. 288—304. DOI: 10.1016/j.psep.2020.05.015.

15. Kang P. K., Lei Q., Dentz M., Juanes R. Stress-induced anomalous transport in natural fracture networks. Water Resources Research. 2019, vol. 55, no. 5, pp. 4163—4185. DOI: 10.1029/2019WR024944.

16. Lei Q., Wang X., Xiang J., Latham J-P. Polyaxial stress-dependent permeability of a three-dimensional fractured rock layer. Hydrogeology Journal. 2017, vol. 25, no. 8, pp. 2251— 2262. DOI: 10.1007/s10040-017-1624-y.

17. Wang Z., Pan J., Hou Q., Niu Q. Changes in the anisotropic permeability of low-rank coal under varying effective stress in Fukang mining area, China. Fuel. 2018, vol. 234, no. 15, pp. 1481—1497. DOI: 10.1016/j.fuel.2018.08.013.

18. Zafar A., Su Y. L., Li L., Fu J., Mehmood A. Tight gas production model considering TPG as a function of pore pressure, permeability and water saturation. Petroleum Science. 2020, vol. 17, no. 1, pp. 1356—1369. DOI: 10.1007/s12182-020-00430-4.

19. Zhong X., Zhu Y., Liu L., Yang H., Li Y., Xie Y., Liu L. The characteristics and influencing factors of permeability stress sensitivity of tight sandstone reservoirs. Journal of Petroleum Science and Engineering. 2020, vol. 191, article 107221. DOI: 10.1016/j.petrol.2020.107221.

20. Wang S. G., Elsworth D., Liu J. S. Permeability evolution during progressive deformation of intact coal and implications for instability in underground coal seams. International Journal of Rock Mechanics and Mining Sciences. 2013, vol. 58, pp. 34—45. DOI: 10.1016/j. ijrmms.2012.09.005.

21. Tao S., Tang D., Xu H., Li S. The influence of flow velocity on coal fines output and coal permeability in the Fukang Block, southern Junggar Basin, China. Scientific Reports. 2017, vol. 7, no. 1, article 14124, pp. 1—10. DOI: 10.1038/s41598-017-14295-y.

22. Lu Y. Y., Ge Z. L., Yang F., Xia B. W., Tang J. R. Progress on the hydraulic measures for grid slotting and fracking to enhance coal seam permeability. International Journal of Mining Science and Technology. 2017, vol. 27, no. 5, pp. 867—871. DOI: 10.1016/j.ijmst.2017.07.011.

23. Zhao Y., Lin B. Q., Liu T., Kong J., Zheng Y. N. Gas flow in hydraulic slotting-disturbed coal seam considering stress relief induced damage. Journal of Natural Gas Science & Engineering. 2020, vol. 75, article 103160. DOI: 10.1016/j.jngse.2020.103160.

24. Chen D. D., He W. R., Xie S. R., He F. L., Zhang Q., Qin B. B. Increased permeability and coal and gas outburst prevention using hydraulic flushing technology with cross-seam borehole. Journal of Natural Gas Science & Engineering. 2020, vol. 73, article 103067. DOI: 10.1016/j. jngse.2019.103067.

25. Nozhkin N. V. Zablagovremennaya degazatsiya ugol'nykh mestorozhdeniy [Early degassing of coal deposits], Мoscow, Nedra, 1979, 271 p.

26. Crouch S., Starfield A. Metody granichnykh elementov v mekhanike tverdogo tela [Boundary element methods in solid mechanics], Мoscow, Mir, 1987, 328 p.

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