ON THE AMBIGUITY OF INTERPRETATION OF THE TEMPERATURE FIELD OF THE FROZEN ROCK MASS USING BOREHOLE THERMOMETRY

Abstract

The relevance. Sinking vertical mine shafts using artificial ground freezing requires controlling the state of the frozen wall formed around the shaft under construction. The most widespread and informative method of experimental control of the frozen wall state is borehole thermometry. The borehole thermometry data is used to adjust the parameters of the model (thermophysical properties of rocks) to re-create the temperature field in the entire volume of the frozen rock mass by means of mathematical modeling. Adjustment of the model parameters under certain conditions can lead to ambiguity in determining the model parameters, the reason for which is currently not studied. The main aim is to study the conditions for ambiguity occurrence in the calculated thermophysical properties of the rock mass as a result of the adjusting the parameters of the model according to the measurement data in the control boreholes. The object of the research is a frozen water-saturated rock mass around two mine shafts of the potash mine of the Nezhinsky mining and processing complex under construction. Research methods included the collection and processing of borehole thermometry data, the formulation of a mathematical model of heat transfer in the frozen rock mass, the numerical solution of the direct and inverse Stefan problems and the theoretical interpretation of the mismatch between the measured and calculated temperatures of the rocks. Results. We studied the mismatch between the measured and numerically calculated temperatures in the control boreholes on the phase plane of the adjusted parameters of the model – the thermal conductivities of frozen and unfrozen rocks. It is shown that the minimum of the mismatch functional under certain conditions moves over time or is not unique. The analysis of the arising ambiguity is carried out on the basis of a simplified mathematical model of the heat balance at the boundary of the phase transition front. It was found that at the ice growing stage, an unreliable determination of thermal conductivity in the frozen rock is possible due to the high temperature gradient in the rock mass near the control boreholes and the error of borehole inclinometry. At the ice holding stage, an unreliable determination of both thermal conductivities is possible, since the solution of the problem depends mainly on their ratio.

Keywords

• artificial freezing of rocks
• frozen wall
• control boreholes
• inverse stefan problem
• mathematical modeling
• thermal conductivity of rocks