Mathematical modeling of trajectory of the maximum subsidence of points on the earth surface caused by working out of coal layers

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Authors:

N.I. Antoshchenko,Dr. Sci. (Tech.), Professor, State Higher Educational InstitutionDonbass State Technical University”, Rector, Professor of the Department of Labour Protection, Alchevsk, Ukraine

L.A. Chepurnaya,State Higher Educational InstitutionDonbass State Technical University”, Postgraduate Student, Alchevsk, Ukraine

Abstract:

Purpose. The aim of the research isusing boundary values of parameters related to terrestrial surface displacement and clearing wastes of the rated scheme for forecasting a trajectory of the maximum subsidence points on the terrestrial surface at the stage of clearing works development.

Methodology. Empirical coefficients of mathematical dependences are determined in two ways: on the basis of processing experimental data by a method of least squares and according to the rated scheme using boundary values of parameters of terrestrial surface displacement and clearing wastes. The technique aims at establishment of the equivalence of these methods and the type of mathematical dependence, most accurately describing a trajectory of the maximum subsidence points on the terrestrial surface.

Findings. The exponential equation most precisely describes a trajectory of the maximum subsidence points on the terrestrial surface. The equivalence of ways of empirical coefficients determination has been established.

Originality. On the basis of the proximity of empirical coefficients determined by different ways, it has been proved that forecasting the trajectory of the maximum subsidence points on the terrestrial surface on the basis of boundary values of parameters of terrestrial surface displacement and clearing wastes is possible.

Practical value. Determination of empirical coefficients of the mathematical equations by the offered way will allow to further avoid labor- and time-consuming direct supervisions to receive experimental data and perform their processing by the method of least squares.

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