Adjustment of Thermophysical Rock Mass Properties in Modeling Frozen Wall Formation in Mine Shafts under Construction
L. Yu. Levin, M. A. Semin, A. V. Zaitsev
Mining Institute, Ural Branch, Russian Academy of Sciences, Perm, 614007 Russia
Keywords: Ледопородное ограждение, обратная задача Стефана, калибровка параметров модели, метод градиентного спуска, метод конечных разностей, шахтный ствол, Frozen wall, inverse Stefan problem, model parameter adjustment, gradient descent method, finite difference method, mine shaft
Abstract
Modeling of heat exchange processes in water-saturated rock mass during shafting with artificial freezing is performed. The problem of adjusting thermophysical properties of rock layers by the experimental measurements of temperature in the check thermal wells spaced from the freezing perimeter is analyzed. In terms of the abuilding shafts at Nezhinsky Mining and Processing Plant, significance of adjusting the the thermophysial parameters borrowed from the geological engineering survey data is illustrated. The number of independent adjustment parameters is determined from the analysis of the system of equations in two-dimensional two-phase Stefan problem in the dimensionless form. An inverse Stefan problem is formulated for a horizontal layer of rocks. The numerical algorithm is proposed for the inverse Stefan problem solution based on the gradient descent method. The algorithm minimizes functional of discrepancies between the model and measurement temperatures at the locations of the check wells. The functional of discrepancies in the phase space of the thermophysical properties and the algorithm convergence are analyzed.
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