Natural Convection in Water-Saturated Rock Mass under Artificial Freezing
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______________________________ MINING _________________________________ THERMOPHYSICS
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Natural Convection in Water-Saturated Rock Mass under Artificial Freezing M. A. Semina*, L. Yu. Levina, M. S. Zhelninb, and O. A. Plekhovb a
Mining Institute, Ural Branch, Perm, 614007 Russia *e-mail: [email protected] b Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences, Perm, 614013 Russia
Received January 1, 2020 Revised February 4, 2020 Accepted April 10, 2020 Abstract—The authors study theoretically the non-isometric natural convection of pore water in rock mass subjected to artificial ground freezing. The mathematical model is developed for a permeable watersaturated layer of rocks under artificial freezing. The model assumptions allowed transition to a twodimension axially symmetric model. The numerical computation gives critical Rayleigh number values such that natural convection of pore water has a significant influence on temperature and position of phase transition front. Three possible convection regimes of pore water are determined as function of alternatingsign ability of thermal expansion factor. Keywords: Artificial ground freezing, natural convection, porous medium, ground water seepage, mathematical modeling, frozen wall. DOI: 10.1134/S1062739120026782
INTRODUCTION
Artificial ground freezing is commonly applied in construction of underground roadways and tunnels in soil and rocks heavily saturated with water. In this technology, a freezing borehole loop is drilled around a mine opening under construction and freezing pipes with circulating refrigerant are installed in the boreholes. Water-saturated rock mass freezes as a result of contact with freezing pipes, and hydrodynamic permeability of the rock mass lowers eventually while physical strength grows [1, 2]. Conditionally, rock mass subjected to thermal influence from freezing pipes is divided into frozen and unfrozen zones [1]. Some researches distinguish a third, quasi-equilibrium two-phase zone of rocks containing both ice and unfrozen water—a mushy zone [3, 4]. Heat transfer in the frozen zone occurs due to thermal conduction, whereas the unfrozen zone and mushy zone permit both heat conduction and heat convection. Heat convection might be connected with the presence of natural particle velocity field in permeable rock mass due to specific features of hydrological regime [5]. Most scientific papers on artificial ground freezing consider only enforced convection [3, 5–7] while natural convection remains nearly neglected. The studies of natural convection in frozen ground in a general case are described in [8–10]. The theoretical research of groundwater flow effect on frozen wall construction [8] focuses on enforced convection and touches upon the influence of n
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