Thaw depth prediction in cylindrical underground openings

The study aims to determine a correction factor to minimize estimation error in thaw depth prediction using the methods of plane-symmetry long-span openings for cylindrical openings of circular symmetry. With an assumption of equal rock volumes involved in heat exchange, a simple expression was obtained for finding the correction factor. A potential variation range was assessed for the correction factor in the conditions typical of a mine operating in the permafrost zone in the natural (uncontrolled) thermal environment. In particular, it is shown that the correction factor can exceed sometimes the allowable value in the engineering practice. This can lead to an essential error in the thaw depth value and, as a consequence, can bring erroneous design engineering solutions. In order to embrace the maximum possible source data, the correction factor expression is presented in a dimensionless form as a function of the Fourier and Stefan criteria. The 3D plots allow finding the correction factor within a wide range of the source data to improve the accuracy of the thaw depth in rock mass around openings of cylindrical symmetry. The cross-sections of the underground openings, for which the thaw depth error is below the value allowable in the engineering practice and the correction factor is inapplicable, are determined.

Keywords: permafrost zone, underground structure, underground opening, symmetry, thaw depth, equivalent radius, calculation error.
For citation:

Galkin A. F., Pankov V. Yu. Thaw depth prediction in cylindrical underground openings. MIAB. Mining Inf. Anal. Bull. 2022;(1):72-83. [In Russ]. DOI: 10.25018/0236_ 1493_2022_1_0_72.

Acknowledgements:
Issue number: 1
Year: 2022
Page number: 72-83
ISBN: 0236-1493
UDK: 536:24:622.413
DOI: 10.25018/0236_1493_2022_1_0_72
Article receipt date: 14.10.2021
Date of review receipt: 21.10.2021
Date of the editorial board′s decision on the article′s publishing: 10.12.2021
About authors:

A.F. Galkin, Dr. Sci. (Eng.), Professor, Chief Researcher, e-mail: afgalkin@mail.ru, https://orcid.org/0000-0002-5924-876X, Melnikov Permafrost Institute of Siberian Branch of Russian Academy of Sciences, 677010, Yakutsk, Russia
V.Yu. Pankov, Cand. Sci. (Geol. Mineral.), Assistant Professor, M.K. Ammosov North-Eastern Federal University, 677000, Yakutsk, Russia, e-mail: viu.pankov@s-vfu.ru.

For contacts:

A.F. Galkin, e-mail: afgalkin@mail.ru.

Bibliography:

1. Skuba V. N. Issledovanie ustoychivosti gornykh vyrabotok v usloviyakh mnogoletney merzloty [Study of the stability of mine workings in the conditions of permafrost], Novosibirsk, Nauka, 1974, 118 p.

2. Sherstov V. A. Povyshenie ustoychivosti vyrabotok rossypnykh shakht Severa [Increase in sustainability of the mining of the North], Novosibirsk, Nauka, 1980, 56 p.

3. Dyad‘kin Yu. D. Osnovy gornoy teplofiziki dlya shakht i rudnikov Severa [Basics of mining themo physics for underground mines in the North], Moscow, Nedra, 1968, 256 p.

4. Kuzmin G. P. Podzemnye sooruzheniya v kriolitozone [Underground structures in the permafrost zone], Novosibirsk, Nauka, 2002, 176 p.

5. Greth A., Roghanchi P., Kocsis K. A review of cooling system practices and their applicability to deep ad hot underground US mines. Proccedings of the 16th North American Mine Ventilation Symposium. Golden. 2017, vol. 11, pp. 1—9.

6. Danko G. Ventilation and climate control of deep mines. McGraw-Hill Yearbook of Science and Technology. 2012, рр. 296—299.

7. Kazakov B. P., Zaitsev A. V. The study of the formation of the thermal regime of deep mines. Vestnik Permskogo natsional’nogo issledovatel’skogo politekhnicheskogo universiteta. Geologiya. Neftegazovoe i gornoe delo. 2014, no. 10, pp. 91—97. [In Russ].

8. Lapshin A. A. The effect of hardening bookmarks in treatment chambers on the microclimate of deep mines. East European Journal of Advanced Technology. 2014, no. 10, pp. 3—11. [In Russ].

9. Vernigor V. M., Morozov K. V., Bobrovnikov V. N. About approaches to designing thermal regime of mines in permafrost. Journal of Mining Institute. 2013, vol. 205, pp. 139—140. [In Russ].

10. Galkin A. F. Thermal regime of cryolithozone mines. Journal of Mining Institute. 2016, vol. 219, pp. 377—381. [In Russ]. DOI: 10.18454/pmi.2016.3.377.

11. Parshakov O. S., Levin L. Yu., Semin M. A. Thawing of rocks in shaft sinking with artificial ground freezing. MIAB. Mining Inf. Anal. Bull. 2021, no. 8, pp. 51—69. [In Russ]. DOI: 10.25018/0236149320218051.

12. Semin M. A., Brovka G. P., Pugin A. V., Bublik S. A., Zhelnin M. S. Effects of temperature field nonuniformity on strength of frozen wall in mine shafts. MIAB. Mining Inf. Anal. Bull. 2021, no. 9, pp. 79—93. [In Russ]. DOI: 10.25018/0236149320219079.

13. Gorelik Ya. B., Pazderin D. S. Correctness of formulation and solution of thermomechanical problems in forecasting temperature field dynamics in the foundations of constructions on permafrost. Earth's Cryosphere. 2017, vol. XXI, no. 3, pp. 49—59. [In Russ].

14. Khalid M. Z., Zubair M., Ali M. An analytical method for the solution of two phase Stefan problem in cylindrical geometry. Applied Mathematics and Computation. 2019, vol. 342, pp. 295—308.

15. McCord D., Crepeau J., Siahpush A., Brogin J. Analytical solutions to the Stefan problem with internal heat generation. Applied Thermal Engineering. 2016, vol. 103, pp. 443—451.

16. Galkin A. F. Calculation of parameters of cryolithic zone mine openings thermal protection coating. Metallurgical and Mining Industry. 2015, no. 8, pp. 68—73.

17. Mitchell S. L., Vynnycky M. On the numerical solution of two-phase Stefan problems with heat-flux boundary conditions. Journal of Computational and Applied Mathematics. 2014, vol. 264, pp. 49—64.

18. Li M., Chaouki H., Robert J. L., Ziegler D., Martin D., Fafard M. Numerical simulation of Stefan problem with ensuing melt flow through XFEM/level set method. Finite Elements in Analysis and Design. 2018, vol. 148, pp. 13—26.

19. Turkyilmazoglu M. Stefan problems for moving phase change materials and multiple solutions. International Journal of Thermal Sciences. 2018, vol. 126, pp. 67—73.

20. Goodman T. R. The use of integral methods in nonlinear problems of unsteady heat transfer. Problemy teploobmena [Heat transfer problems], Moscow, Atomizdat, 1967, pp. 41—95.

21. Khokholov Y. A., Kurilko A. S., Solov’ev D. E. Temperature field analysis in salty rocks at shaft mouth under operation of a freezing system. Journal of Mining Science. 2016, vol. 52, no. 3, pp. 593—600.

22. Kurilko A. S., Khokholov Y. A., Drozdov A. V., Solov'ev D. E. Control of ground temperatures under headframes and collars of vertical shafts. A case study of the Udachny diamond mine (Yakutia). Earth's Cryosphere. 2017, vol. 21, no. 5, pр. 82—91. [In Russ]. DOI: 10.21782/ KZ1560-7496-2017-5(82-91).

23. Galkin A. F., Kurta I. V., Pankov V. Yu. Comparison of heat flows in underground openings of plane and spherical symmetry. MIAB. Mining Inf. Anal. Bull. 2020, no. 10, pр. 133— 141. [In Russ]. DOI: 10.25018/0236-1493-2020-10-0-133-141.

24. Posobie po raschetu ustoychivosti podzemnykh gornykh vyrabotok pri razmeshchenii v nikh ob'ektov narodnogo khozyaystva [Manual for calculating the stability of underground mine workings when placing objects of the national economy in them], Moscow, TsITP, 1990, 71 p. [In Russ].

Подписка на рассылку

Раз в месяц Вы будете получать информацию о новом номере журнала, новых книгах издательства, а также о конференциях, форумах и других профессиональных мероприятиях.