Geometrization of Kryvbas iron ore deposits

Mining and geometrical prediction of iron ore deposit quality indices to solve problems of long-term and current planning intended to provide the most efficient performance of mining enterprises in terms of ore blending quality and increase rationalization of deposit development is an important aspect of geometrization. Investigations carried out to develop a mining-geometrical method for predicting indices of iron ore deposit quality are topical nowadays. The present study aims to enhance the methodology for geometrization of iron ore deposit quality indices for developing a mining-geometrical method of their prediction to provide rational mining. The research methodology consists in mining and geometrical modeling of quality indices and properties of the deposit, thus enabling determination of a certain relationship between components of a mineral, and, thereby, identification of the nature of these components’ location in the mineral. The latter is essential in design, construction and operation of a mineral deposit. The obtained results allow predicting quality indices of the deposit, assessing mineral reserves and consequently planning and optimizing performance of mining enterprises. The developed methods enable increased efficiency of mining iron ore deposits of Kryvbas.


Introduction
Ukraine ranks third in the world as to calculated iron ore reserves which make over 62 Bn t.Most of these reserves (over 32 Bn t) are concentrated in Kryvyi Rih iron ore basin [1][2][3][4][5] and mined by open pit and underground methods.Distribution of iron ore reserves by enterprises of the Kryvyi Rih Basin is given in table 1.According to the US Geological Survey, during the past 15 years, Ukraine ranks sixth in terms of the amount of the ore mass mined (70-86 M t/y) [6][7][8][9][10].
To maintain a high level of annual ore production, mining enterprises are continuously enhancing technological processes.
Thus, in open pit mining, special attention is paid to drilling and blasting (enhancement of explosives and initiation methods) and technological operations (application of imported equipment during loading and transportation of the broken ore mass).
Underground mining systems are constantly being enhanced as well.To ensure appropriate quality of the extracted ore mass, enterprises widely apply open stoping systems.Imported self-propelled delivery equipment used in mining at considerable depths (over 1250 m) helps provide annual productivity of 2-3 M t [11][12][13][14].It should be noted that in working out Kryvyi Rih iron ore deposit, mining enterprises fail to increase annual ore production due to the fact that when designing or enhancing the technology, they use the data of mining and geometrical assessment of the deposit obtained in the previous century.
Planning mining production processes and performance of a mining enterprise is an important task even at the stage of deposit opening [15][16][17][18][19].It can be ensured by application of mining and geometrical methods.At this, an important role is played by mining, geological and geometrical parameters and the nature of the deposit position which can be determined by methods of subsoil geometry [20][21][22][23].
A very important task that can be solved by geometrization methods is to determine stability of a rock massif under the stress-strain state.This enables determining measures to maintain rock massif stability [24][25][26][27].
Planning operation of a mining enterprise on the basis of mining and geometrical methods results in high economic indicators [53][54][55][56][57] ensured by rationalizing and optimizing mining operations.
Mining and geometrical assessment of the deposit is the most expedient when based on methods of analyzing geological data, among which geostatistical methods are the most effective [58][59][60][61][62].This problem is closely related to the task of assessing and predicting the quality of IOP Publishing doi:10.1088/1755-1315/1254/1/0120673 reserves applying self-organization methods [63][64][65].

Purpose
The purpose of the study is geometrization of the iron ore deposit.A particularly important aspect of geometrization of iron ore mineral deposits involves mining and geometrical prediction of their quality indices to solve problems of long-term and current planning intended to provide the most efficient performance of mining enterprises in terms of ore blending and increase rationalization of deposit development.
The most promising methods for assessing indicators of the deposit include geometrization ones based on the use of a set of self-organizing methods and geostatistical methods of assessment [66,67] which are developed and enhanced in the present work.

Methods
Processing the initial geological data requires a lot of sampling; the content of samples influences the quality in a certain block or area of the deposit.The problem of sampling is associated with application of various methods for determining weighted averages.The following two aspects of the problem are of great importance: the search procedure and a criterion for its completion.This criterion can be based on the value of the distance from the sample to the block or to the point where the composition is to be determined.In the most complex programs for calculating weighted averages, the search for points in an area is carried out on a plane or in a cone to ensure relative representativeness of all directions.This enables avoiding the effect of accumulation of samples in certain directions and their absence in others.
This step is, however, superfluous in case of kriging, since with accumulation of points, introduction of sample covariances allows considering automatically the influence of components of the cluster eliminating its excessive influence.Kriging helps to distribute weights among the nearest samples, if a constant density of sampling is not provided.
The grid density does not really influence the number of samples to be considered.Any kriging method does not indicate the number of samples required when assessing the ore composition in this block.From a theoretical standpoint, all available samples should be used.Nevertheless, it is clear that far-removed samples are of little interest.Therefore, it is obvious that the number of samples should not be too large.For example, considering sixteen points instead of twelve increases the calculation time by a factor of about 3, and sixteen samples instead of eight -by a factor of 8.
A sample removed from the block in a given direction for more than an influence interval (if any) is assumed to have a zero weight and should not be used.As an example, let us assess the exploration grid of Skelevatske deposit of ferruginous quartzites mined by the PivdGZK open pit.The deposit has for a long time been sampled in two ways.Detailed exploration is carried out by sampling the sludge of boreholes located irregularly with an interval of 50 to 200 meters.Operational exploration is carried out in the exploded mass by the point method.In case of homogeneous ores, pieces from an area of about a 50 m long (in the direction parallel to the bench slope) with a width determined by the size of the block to be exploded are selected in one sample.In case of heterogeneous ores, each type of quartzites is sampled separately.The sample weight is about 30 kg.
The data for assessment were selected along axis 77 along the strike towards the main direction of mining operations advance.The best method of assessment for actual conditions of Kryvbas iron ore deposits can be chosen by comparison.First, dependency of the natural component of variability on the sampling interval is assessed (figure 1-6), and then autocorrelation coefficients are determined at different sampling intervals (figure [7][8][9][10][11][12].
According to figures 1-6, at Skelevatske deposit, the minimum critical interval of geological exploration for both magnetite and total iron is 600 m.This enables the conclusion that   As is seen from figure 7-12, the autocorrelation coefficient provides ambiguous results.This is due to the fact that this coefficient inherently estimates, to this or that degree, deviation from the sample average value.Thus, in order to qualitatively assess a deposit with a nonlinear nature of index variability, the volume and interval of the sample should be selected with great accuracy and the initial data should be smoothed over as well, this being very time consuming and not always possible.In this very case, the graphs are sine curves with a growing amplitude.Deviations of the indices of nearby points from the average also change in the close to sinusoidal manner, so the deposit can be said to actually have a sinusoidal component when obtaining the indices, and the autocorrelation coefficient is not quite relevant for assessing the exploration grid   of Kryvbas iron ore deposits.
Determining the size of blocks under assessment can be set as a detailed assessment task,   distinguishing blocks of the smallest possible sizes.But this trend leads to an inexpedient cost of work and unreliable results.It turns out that small closely located blocks are characterized by very similar estimates.It should be kept in mind that as the block sizes decrease, estimation errors increase.Thus, a halving in linear dimensions of blocks leads to an 8-fold increase in the number of blocks to be assessed and, probably, the number of systems of linear equations to be solved.Accordingly, it can be assumed that the minimum block size should be at least a quarter of the average interval of the drilling grid.For example, blocks should have a side of 50 meters with a drilling grid pitch of 200 meters or a side of 200 meters at a pitch of 800 meters.
The most important geological and technological indices of ores of Skelevatske deposit of ferruginous quartzites include the content of magnetic iron which is associated with the total iron content.The nature of magnetic iron content in the exploded mass can be predicted based on the borehole sample data.At that, it is advisable to take the content of total and magnetic iron according to borehole sample data as arguments of prediction.Argument values in the inter-hole space can be determined through interpolation.It is advisable to use kriging as an interpolation method.

Results and discussion
The experiment was carried out at the PivdGZK open pit within axes 80-108 along and 89-109 across the strike at horizons -165÷-180 m, -180÷-195 m and -195÷-210 m.The area is located in the north-eastern part of the deposit, the area of oxidized ores makes its southern boundary.Structurally, the area is the eastern wing of the deposit synclinal.In the east, it is bounded by Tarapakiv fault, and its western border coincides with the deposit boundary.
The area is characterized by a sustained occurrence of rocks, weak development of folded deformations.Rocks dip to the north-north-east according to the general deposit sinking.
In the southern part of the area, i.e. on the boundary between the fourth ferruginous quartzites horizon and the fourth schistous horizon, there emerge a number of open folds the size and position of which are clearly seen on the map of the deposit as alternative outbreaks of schists (anticlinal) and quartzites (synclinal).
The initial geological data was obtained from horizon mining plans at a scale of 1:1000.Operational exploration was carried out to sample the exploded mass.At that, sampling areas were of irregular shape and different sizes.The dimensions of the areas ranged from 20 to 50 meters across.The content of total and magnetic iron by detailed exploration boreholes data and horizontal and vertical coordinates of the centers of the sampling areas were taken as arguments for prediction using the multidimensional heuristic prediction algorithm (MHPA).An irregular sampling grid was used for drilling detailed exploration boreholes.Distances between the boreholes ranged from 50 to 200 meters.With the help of kriging, isolines of the content of magnetic iron in the inter-hole space were built.In the center of each sampling area of the exploded mass, the value of magnetic iron was determined based on the available electronic model of isolines.All the acquired values were summarized in spreadsheets, which made the basis for building a predictive function according to the MHPA method.At that, at each stage of its building, credibility of the results obtained was proportional to the inverse distance between the center of the area of sampling the exploded mass and the nearest borehole of detailed exploration, as the greater this distance is, the greater the interpolation error becomes.Thus, the results of building a more accurate function had a greater priority in assessing the quality of the built predictive function.
The basic set of initial data enabled determining dependencies of the magnetic iron content in the exploded mass on that of magnetic iron determined by boreholes of detailed exploration and on the horizontal and vertical coordinates of the points.Three equations of predictive functions obtained by the MHPA method are presented in figures 13-15.
The found dependencies demonstrate that there is a dependency of the magnetic iron content in the exploded mass on that of the sampling data of detailed exploration boreholes, as of all the arguments involved in the MHPA procedure, significant numerical coefficients were determined   only for this value.During calculations, several types of ores with different properties were identified in the area under consideration and that resulted in determining different functional dependencies.
Areas with properties corresponding to these dependencies on a simulated set of data were obtained and grouped according to the MHPA procedure.At that, the iron content data obtained from detailed exploration boreholes were interpolated for 50 by 50 m square grid nodes.
Interpolation was performed using kriging.Predictive values of the content of magnetic iron associated with the content of magnetic iron in the exploded mass were determined in the squaregrid nodes applying the MHPA procedure.Via kriging, these values were interpolated, which became the basis for long-term planning.Based on the interpolation, there were built plans of isolines of the predicted magnetite iron content which are presented in figures [16][17][18].Predicted data for current planning was received by adjusting the obtained electronic model according to operational exploration data at points spatial position of which was determined on the basis of production needs and was irregular.Each author's specific role and expertise greatly enriched the research across various stages, ultimately leading to the comprehensive findings and conclusions presented in this article.

Conclusions
As a result of the study, an effective geometrization technique has been developed that meets the requirements of mining production.It enables assessment of mineral reserves and significantly increases efficiency of planning mining operations.The use of geostatistical methods makes it possible to assess and process the initial geological data.The developed self-organizing prediction algorithm is flexible in application, efficient, and can be used in various mining and geological conditions for geometrization of the deposit in order to provide planning and assessment of various mining technologies.
The relative error of the predicted value of the magnetic iron content in the exploded mass according to the developed method for long-term planning does not exceed 6.8%.
The positive results of prediction at the area under consideration are the basis for using the developed methods in other areas of the PivdGZK open pit.
Proceeding from the results, methods of geometrization of mineral deposits based on selforganization and geostatistical assessment are a very promising direction for further research.The considered methods require further development and enhancement in order to increase their efficiency and application at deposits of Kryvbas as well as other regions that produce both ore and non-metallic minerals.

Figure 7 .
Figure 7. Dependency of the autocorrelation coefficient for the magnetite iron content on the sampling interval, hor.-165÷-180 m.

Figure 8 .
Figure 8. Dependency of the autocorrelation coefficient for the magnetite iron content on the sampling interval, hor.-180÷-195 m.

Figure 9 .
Figure 9. Dependency of the autocorrelation coefficient for the magnetite iron content on the sampling interval, hor.-195÷-210 m.

Figure 10 .
Figure 10.Dependency of the autocorrelation coefficient for the total iron content on the sampling interval, hor.-165÷-180 m.

Figure 11 .
Figure 11.Dependency of the autocorrelation coefficient for the total iron content on the sampling interval, hor.-180÷-195 m.

Figure 12 .
Figure 12.Dependency of the autocorrelation coefficient for the total iron content on the sampling interval, hor.-195÷-210 m.

Figure 13 .
Figure 13.Relationship between the magnetic iron content according to the exploded rock mass sampling data and that of detailed exploration borehole data at hor. -165÷-180 m.

Figure 14 .
Figure 14.Relationship between the magnetic iron content according to the exploded rock mass sampling data and that of detailed exploration borehole data at hor. -180÷-195 m.

Figure 15 .
Figure 15.Relationship between the magnetic iron content according to the exploded rock mass sampling data and that of detailed exploration borehole data at hor. -195÷-210 m.

Table 1 .
Distribution of iron ore reserves by enterprises of the Kryvyi Rih Basin