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.

Purpose. A methodology development for predicting the geomechanical situation when mining an ore deposit with steep-dipping layers, taking into account the uncertainty in determining the rock properties, which is a consequence of the rock mass heterogeneity. Methods. The assessment of the open-pit wall stability is based on a combination of numerical simulation of the rock stress-strain state (SSS) and probabilistic analysis. The finite element method is used to determine the changes in the SSS that occur at various stages of mining operations due to design changes in the overall open-pit slope angle. The elastic-plastic model of the medium and the Mohr-Coulomb failure criterion are implemented in the codes of the 3D finite element analysis program RS3 (Rocscience). Stochastic simulation is used to assess random risks associated with natural object state variations. Findings. The distribution of maximum shear strains, which localizes the real or potential sliding surfaces in the open-pit wall at various stages of ore mining, has been identified. Based on the Shear Strength Reduction procedure, the open-pit wall Strength Reduction Factor (SRF) has been determined. The probabilities of open-pit wall stability loss, as well as the decrease in the strength reduction factor below the standard level at all stages of the ore body mining, have been revealed. Originality. For the first time, for real mining-geological conditions of a deep ore open pit, the dependence of the strength reduction factor on the overall wall slope angle, which changes during mining of each steep layer, has been determined. For each stage of mining operations, for the first time, the probability of a decrease in the open-pit wall stability below the standard level has been determined based on stochastic simulation. Practical implications. The ratio between the open-pit contour characteristic (overall slope angle) and the probabilistic safety factor is the basis for practical solutions to ensure the efficiency and safety of mining at various stages of friable and hard overburden excavation, ore extraction, as well as for the subsequent optimization of the open-pit design contours.

ApproBAtIon of the technoloGy of effIcIent ApplIcAtIon of excAvAtor-AutoMoBIle coMplexes In the Deep open MInes purpose. To establish the feasibility of implementing the technology for working out the overburden rock ledges and ore min ing by transverse panels in steeply sloped layers within a single open mine until the end of its operation. Methodology. In substantiating the spatial position of the staged contours of steeply sloped layers in roundshaped open mine fields and their optimization, the following methods were used: Bellman's analytical and optimal control methods in dynamic programming in combination with an integrated mining and geological information complex basing on a digital model of an iron ore field. To study the reserves of increasing the productivity of excavatorcar complexes, when switching to the technology of working out pit banks with transverse panels in steeply inclined layers from top to bottom with a shift of the open pit spacing, methods of correlation and regression analysis were used. findings. Based on the distinction between the concepts of the nearcontour and deep zones of deep open mines and the in troduction of two new parameters for the relationship between the contours of the ore field and the dynamics of the open mine formation, a method of justification of the spatial position of the staged contours of steeply sloped layers in roundshaped open mine fields has been developed. Compared to the deadend turn of automotive dumping trucks according to the used technology for working out ledges with longitudinal panels, the transition to working them out with transverse panels with a width of 60-80 m, with a loop turn of the automotive dumping trucks for loading will increase the productivity of excavators at least by 25-30 %, which, along with a decrease in the spacing of the open mine sides, compensates the intensity of the ore field overburden from top to bottom within the boundaries of steeply sloped layers even with a significant lag of overburden operations. originality. The transition to the technology of working out ledges with transverse panels in steeply sloped layers is the only solution if the overburden lag exceeds the current design overburden volumes when mining approaches the limit contour of the open mine surface. In the studied extremely deep iron ore open mine, even when the design volume of the current (annual) over burden operations increases by more than 3 times, this technology allowed reducing the overburden lag by 25 % and shortening the period for the development of the ore production capacity from 8 to 5 years. A mathematical model has been created to optimize the contours of working out stages for steeply sloped fields when working out ledges with transverse panels in steeply sloped layers, in which the functional contains the fourthorder nonlinearity in relation to the required value-the width of the panels. Automa tion of calculations for optimizing the parameters of the design of the working open mine sides in the dynamics of the development of minin...

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