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].