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Solution of an Inverse Stefan Problem in Analyzing the Freezing of Groundwater in a Rock Mass

  • L. Yu. LevinEmail author
  • M. A. Semin
  • A. V. Zaitsev
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A one-dimensional inverse Stefan problem is formulated in cylindrical coordinates. The problem is of interest in the analysis of freezing a mass of rock and forming an iced rock barrier around a single freezing column in building shafts as well as solving the problem of controlling the process of thawing. Additional conditions in the formulation of the inverse problem are the data of experimental measurements of temperatures in thermal boreholes located at a certain given distance from a freezing column and the magnitudes of temperatures and of the cold-carrier flow rate in freezing columns. An analytical expression is presented for the functional that determines the measure of proximity of the obtained solution to the exact one. A numerical method has been developed for solving the posed inverse problem by minimizing the functional.

Keywords

iced rock barrier coefficient inverse Stefan problem minimization of functional freezing column controlling-thermal borehole mass of rock phase transition building of shafts 
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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mining InstituteUral Branch of the Russian Academy of SciencesPermRussia

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