Effect of temperature on thaw depth in frozen rocks

Authors: Галкин А. Ф., Курта И. В.

The estimates of the initial temperature effect on thaw depth in frozen rocks are presented. The calculation relations were the simple analytical solutions of a Stephan problem under first-order boundary conditions. The expression is obtained for finding error in calculations of thaw depth with mathematical model of the assumed equality between the initial temperature of frozen rocks and the ice melting temperature. The calculation formulas take into account the functional dependence of rock density and heat capacity on ice content. By way of illustration, a quartz sandstone-and-water mix is tested in frozen condition under the change in ice content from zero (dry quartz sandstone) to one (pure ice). The calculations from the obtained formulas are presented as 2D and 3D graphs for a wide range of variation in initial values typical of various-purpose underground openings in the permafrost zone. The calculation analysis shows that the main parameter to govern the calculation error is the value of the Stephan number. The error of the thaw depth prediction as function of the determinants represented by the ice content and initial temperature in frozen rocks is quantified. The expression is obtained to find the initial temperature and ice content relation such that the error of engineering design of thaw depth in frozen rocks is less than allowable value.

Keywords: rocks, prediction, thawing, error, temperature, designing, ice content, permafrost zone.
For citation:

Galkin A. F., Kurta I. V. Effect of temperature on thaw depth in frozen rocks. MIAB. Mining Inf. Anal. Bull. 2020;(2):82-91. [In Russ]. DOI: 10.25018/0236-1493-2020-2-0-82-91.

Acknowledgements:
Issue number: 2
Year: 2020
Page number: 82-91
ISBN: 0236-1493
UDK: 622.536.24
DOI: 10.25018/0236-1493-2020-2-0-82-91
Article receipt date: 05.09.2019
Date of review receipt: 29.10.2019
Date of the editorial board′s decision on the article′s publishing: 20.01.2020
About authors:

A.F. Galkin1, Dr. Sci. (Eng.), Professor, e-mail: afgalkin@mail.ru,
I.V. Kurta1, Cand. Sci. (Eng.), Assistant Professor, Vice-Rector for Research, e-mail: ivankurta@ya.ru,
1 Ukhta State Technical University, 169300, Ukhta, Republic of Komi, Russia.

 

For contacts:

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

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