Purpose is to determine a function of the reduced expenditures connected with drilling-and-blasting operations, loading and hauling operations, and rock fragmentation depending upon the cost of machine-shift of the applied facility, its operation modes, hardness of rock being blasted, cost of the used explosive, and rock fragmentation quality based upon the developed optimization mathematical model. Methods. Method of statistical evaluation of natural blockiness structure of the rock as well as quality of its fragmentation by means of explosive energy has been applied. Statistical studies have been carried out concerning the basic indices of rock fragmentation depending upon its largeness and block hardness. Purposely-designed experimental equipment has been applied for sampling analysis of the rock fracturing in the process of its drilling by means of rotary drilling rig. The abovementioned supported representativeness of the sampling. Findings. Statistical distributions of the rock blockiness structure in terms of each bar length involving its place within the drilling assembly as well as in terms of the well depth have been compiled. Visual comparison of experimental data and theoretical data has helped determine that the statistical distributions of natural blockiness structure of the rock have the closest correlation with gamma distribution which differential function has two positive parameters. Statistical dependence has been defined between drilling-and-blasting results and the total expenditures connected with hard rock mining. Originality. A concept of oversize crushing coefficient has been introduced; its statistical dependence upon the mined rock hardness and specific consumption of the applied explosive has been derived. An alternative has been proposed concerning changes in parameters of the differential function of the assumed gamma distribution relative to the predicted granulometric composition of rock mass. Practical implications. Economic and mathematical model has been developed involving a target function of the total expenditures connected with the listed operations as well as a set of constraints avoiding incorrect decisions. The optimization method makes it possible to control drilling-and-blasting parameters at each stage of hard rock mining.

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This article deals with production planning in the context of providing technology at each mining stage with developed and ready-tostoping reserves. In order to address the problem, the ore body is represented by a geological block model. Numerical data is used to represent the attributes of each block, such as mass, density, ore grade, rock type. The mining plan provision with reserve standards on the degree of reconnaissance for production is reduced to the optimization task solution. The main condition for ensuring the planned production productivity of the mine is to provide the minimum necessary developed reserves. In the proposed mathematical model, it is taken into account by one of the objective function’s terminators for solving the set task. As the results of the calculations have shown, such a scheduling ensures approach that there is developed ore’s sufficient amount for at least 6 months at the beginning of each period, which is a clear advantage of the proposed model.

Purpose. An algorithm development for calculating the optimum depth for cyclical-and-continuous method schemes introduction when cleaning-up the deep iron ore quarries.Methods. When developing an algorithm for calculating the optimum depth for cyclical-and-continuous method schemes introduction under the conditions of the Kacharsky mine, abstraction and analytical techniques were used to distinguish the parameters that most significantly influence on the depth value of the cyclical-and-continuous method schemes introduction. The developed algorithm has been applied when constructing a mathematical model based on mining-engineering parameters for cleaning-up the Kacharsky Iron Ore Mine.Findings. An algorithm is presented for calculating the optimum depth to put into operation the railway transport and a conveyor hoister in the cyclical-and-continuous method schemes, taking into account the mining-engineering and economic parameters for cleaning-up the deep quarries in surface mining. It has been substantiated that the transition from a combined automobile-railway to a combined automobile-conveyor-railway mode of transport is economically viable and will expand the limits of the effective use of surface mining of iron ore deposits. It is recommended to restrict the depth of commissioning the railway transport to 149 m, and the conveyor hoister -to 344 m into the cyclical-and-continuous method schemes using automobile-conveyor and automobile-railway modes of transport.Originality. Based on the constructed mathematical model, the dependences have been obtained of the prime costs for transporting the total volume of rocks mined on the depth of the cyclical-and-continuous method schemes introduction under the conditions of the Kacharsky Iron Ore Mine. Practical implications.For the conditions of cleaning-up the Kacharsky Iron Ore Mine, the optimum parameters have been set for the mining-transport scheme of the cyclical-and-continuous method, which ensure the minimum prime costs of the rock mass transportation.

A 3D model of optimal contours phased development of oval-shaped open pit mines is proposed in the article. It is assumed that with enough accuracy the volumetric contour of the open pit mine is interpolated by an elongated elliptic hyperboloid. The calculation formulas for mineral resources are derived and optimal volumes of overburden are determined depending on the mining phase. In this case, the total number of mining phases is set in advance. The stripping ratio is used as a quality criterion of the optimization task. The problem of optimal control is solved using the Bellman function in dynamic programming. All the necessary calculation formulas are obtained in the final form by solving the optimization problem. Their simplicity and substantiation of each conclusion ensure that the results of this study can be successfully applied in practical calculations of the design and planning of mining operations in open pit mining.