MATHEMATICAL MODEL OF CORRELATION ANALYSIS FOR DETERMINING THE CONVEX SHAPE OF OPEN-PIT MINE SLOPES
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This article is devoted to determining the most safe trajectory of the sides based on a comprehensive analysis of the convex-shaped quarry sides. Based on experimental data, the trajectory of various shapes of the sides was determined according to their various dimensions (height and width). For the purpose of analytical representation of these trajectories, the least squares method was used, and they were approximated using an algebraic function of degree n. This approach allows minimizing the deviations between the experimental data and the mathematical model (minimizing the difference between the theoretical model and the experimental data in mathematical modeling) and determining the curve as close as possible to the profile of the real quarry side. At the next stage, a correlation analysis was carried out based on the obtained functional relationships, and the degree of statistical dependence between the geometry of the quarry sides and their stability indicators was assessed. As a result, a mathematical model was developed that takes into account the correlation dependence, based on the approximation of flight trajectories by an n-th power function. With the help of this model, it is possible to determine the most stable and safe shape of the sides for various geometric parameters. It is also shown that, based on this model, it is possible to choose several alternative geometric shapes or optimal configurations that ensure the stability of the quarry side.
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References
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