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MATHEMATICAL ANALYSIS OF THE SUBSIDENCE CURVE APPROXIMATION ACCURACY ON THE EXAMPLE OF THE FUNCTION BY S.P. KOLBENKOV
Abstract
The article presents the results of statistical processing of field surveying observations data of the displacement process on the earth's surface. Currently, the main method to monitor displacements and deformations of the earth?s surface during mining operations is to determine the coordinates of reference points of observation stations. This method allows you to obtain reliable data on the movements of points in the displacement trough and form an idea of both the shape of the trough and the values of deformations in the trough. The actual question is the mathematical description of the shape of the mold curve, as well as the rational choice of the necessary number of reference points for observations in each specific case. In the Russian methodology for estimating displacements and deformations, it is common to use the exponential function proposed by Professor S.P. Kolbenkov. The coefficients a, b, c are empirically determined for all major coal basins. In this research, a mathematical Monte Carlo simulation was performed, which resulted in the evaluation of the effect of displacements measurement errors and parameters characterizing the trough size on the calculation errors of the distribution characteristics of the subsidence in the trough. Based on the analysis of the relationship between the half-trough length and the determination error value in the approximation, it was concluded that it is necessary to increase the coverage area of the expected displacement zone by 1.1-1.2 times to improve the accuracy of determining the actual borders of the trough. Analysis of the effect of errors in determining the displacement of reference points on the approximation accuracy showed that the error in calculating the maximum subsidence and the size of trough is largely influenced by the number of input data involved in the solution. The functional connection between them and errors in the source data most accurately describes by the linear function. At the same time, errors in approximation of the trough will be more with a small value of the maximum subsidence in the trough. Based on the research, we made a conclusion of the necessary accuracy of geodetic observations of the displacement process when performing deformation monitoring of undermined buildings and structures.
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