Mathematical Prediction of Ice-and-Rock Shield Thickness in Shaft Sinking
L. YU. LEVIN, M. A. SEMIN, O. S. PARSHAKOV
Mining Institute, Ural Branch, Russian Academy of Sciences, ul. Sibirskaya 78a, Perm, 614007 Russia
Keywords: ледопородное ограждение, проходка стволов, задача Стефана, диффузионная теплопроводность, фазовый переход, математическое моделирование, ice-and-rock shield, shaft sinking, Stefan problem, diffusion thermal conductions, phase transition, mathematical modeling
Abstract
A Stefan problem is analyzed for the case of rock freezing during shaft sinking, It is shown that the rate of thermal diffusion in rock mass is comparable with the velocity of the boundary between different phases. The Stefan problem is solved for a single shaft using the finite difference method. The procedure for the generalization of the calculation data on thickness of an ice-and-rock shield in a single shaft for the case of many shafts is improved. The ice-and-rock shield thickness forming around freezing pipes is calculated in terms of shaft 1 in the mine of Petrikovsky Mining and Processing plant of Belaruskali.
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