Mathematical Model for Determining Optimal Size Mining Blocks Iron Ore Mining According to the Creterea Economic Efficiency

Sustainable development is one of the priority areas of society. However, the replacement of natural minerals with artificial ones, in particular iron ore, has not yet taken place. Therefore, the authors of scientific work are constantly looking for optimal ways to use natural resources, including iron ore. Thus, the following problems of iron ore mining were considered in the works of the authors: 1) parametric resonance in the process of movement of hoisting vessels in the trenches of ore and coal mines; 2) expert system of selection of competitive options of systems of underground development of ore deposits; 3) the automated system for selection for optimal solution for the process of iron ore mining based on artificial intelligence methodology. However, another problem of iron ore mining has not been considered by the authors - an integrated economic and mathematical model the geomechanical state of rock mass at ultrahigh depths and to determine the optimal geometric dimensions of structural elements of mining blocks. This model is developed on the basis of the method of dimensionless functional characteristics for calculating the dimensions of the structural elements of the block, ensuring their stability. The authors have expanded the capabilities of this method by introducing into its mathematical apparatus elements that make it possible to perform vibrational economic and mathematical calculations of an optimization nature to find the sizes of block elements that are optimal according to economic criteria, ensuring the simultaneous achievement of the necessary stability of the block elements for the entire period of ore mining in the block and the maximum possible economic efficiency of developing its reserve in specific geomechanical and economic conditions for carrying out mining operations.