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FREE CONVECTION OF PORE WATER IN SATURATED PERMEABLE ROCK MASS DURING ARTIFICIAL FREEZING
Abstract
This paper presents a theoretical study on the free convection of pore water in saturated permeable rock mass during artificial freezing. Artificial freezing technology is widely used in the construction of mine shafts, tunnels and other types of excavation that take place under high water content conditions or conditions of high levels of groundwater seepage in soil and rock. A qualitative analysis of artificial freezing in water-saturated permeable rock mass shows that the effect of free convection can be significant in practical situations. Based on this result, a deeper theoretical study of the non-isothermal free convection of pore water in permeable rock mass has been carried out by formulating a mathematical model. The case of freezing using a single freezing column was considered, and the stages of frozen wall growth and holding were studied. The temperature dependence of water density was found using the Boussinesq approximation. The coefficient of thermal expansion of water was considered to be a function of temperature ? it is important to note that this function changes its sign at 4 °C. These model simplifications made it possible to consider the two-dimensional axisymmetric Darcy?Stefan problem. The system of equations used to solve the Darcy?Stefan problem was transformed into dimensionless form and solved numerically using the finite-difference method. The numerical algorithm was implemented in C#, using the Microsoft Visual Studio environment. Through a series of numerical calculations, the critical Rayleigh numbers were obtained, where the free convection of pore water had a significant effect on the temperature field and on the position of the phase-transition front ? three possible modes of free convection of pore water were identified.
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