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.

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:,, 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:

For contacts:

A.F. Galkin, e-mail:


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