Enhancement of the technology of caved ore drawing from the ore deposit footwall “triangle”

In mining iron ore, over 60% of underground mines at Kryvyi Rih iron ore basin apply a system with the bulk caving of ore and overlying rocks. However, when the deposit dip is 45-60 degrees, application of this mining system leads to losses of about 30-40% of the footwall ore. Available methods of the loss reduction result in an increase in production costs or a decrease in the iron content in the mined ore mass. After analyzing the mechanism of forming the figure of drawing, it is proposed to change its parameters without significant costs due to the use of an inclined plane and an overcompacted ore layer. The presented study enables stating that with an increase in the inclined plane angle from 45 to 75 degrees the draw crater radius increases from 2 to 7.5 m, and a decrease in the factor of first loosening of ore leads to an increase in the radius of the crater to 10 m. Thus, for the first time it is proved that a decrease in the first loosening factor leads to the increased semi-minor axis of the ellipsoid of drawing and the width of the active drawing area, which will reduce losses of caved ore when drawing it from the stoping block in the footwall area. It is established that in order to minimize losses and dilution of ore when using level mining systems, the drawpoint should be located in the block sill at a distance ensuring formation of the 20 to 25 m high ellipsoid of drawing. In case of an overcompacted 22 m thick ore layer, it is possible to significantly reduce ore losses from 14 to 10% and ore dilution from 16 to 9%, thereby enhancing ore mass extraction indices without additional costs.


Introduction
Kryvyi Rih iron ore deposit is a narrow strip of metamorphic rocks and it is an integral part of Kryvyi Rih-Kremenchuk deposit extending from south to north.The length of the ore deposits along the strike varies from 0.8 to 2.5 km due to different mining and geological conditions at different enterprises, [1][2][3][4].
The geological cross-section of the deposit along the shaft of the KRYVORIZKA underground mine of the joint-stock company KRYVBASZALIZRUDKOM is given (figure 1).As is seen from figure 1, mining operations are carried out below level -1350 m.The analysis of mining enterprises shows that physical and mechanical properties, the shape of occurrence, the dip angle and stability change depending on the mining depth.In mining blocks there occur inclusions of waste rocks with the horizontal thickness of 0.5-12.0m [16][17][18][19][20].
Rocks of the hanging wall and footwall are represented by strong, stable martite hornfels with ultimate compression strength of 100-130 MPa and goethite-hematite-martite hornfels with ultimate compression strength of 70-90 MPa.Physical properties of rocks are given in table 1.
As is seen from table 1, physical and mechanical properties of the rocks are wide in range.According to the geological data [1,21,22], the rich ores are of hematite composition and differ only in the number and proportion of mineral varieties [23][24][25][26].
Strength of iron ores declines with depth, and this deteriorates mining conditions.Thus, -120-160 every 500 m of the depth increase reduces the gradient of the compression strength of rocks by 0.6-0.7,and for the central part it makes 0.9-1.0[27][28][29][30].
When mining iron ore, over 60% of underground mines of Kryvyi Rih iron ore basin apply a system with the bulk caving of ore and overlying rocks [31][32][33][34].
These mining systems have the following disadvantages [35][36][37][38]: ore losses on the footwall (up to 30-50% of the total ore losses); ore dilution (by 3-5% more than standard); reduced content of the useful component in the mined ore mass.
When the deposit dip is 45-60 degrees, application of these mining systems results in about 30-40% of ore lost on the footwall [39][40][41][42][43]. Increased losses of ore during mining lead to an increase in the specific volume of mining and capital works, pre-term mining of levels [21].
In this regard, the scientific and technical task of studying and enhancing the technology of mining ore deposits by the underground method for Kryvyi Rih iron ore basin in the "triangle" of the footwall (in the "dead" area) when working out ore deposits with a dip of 45-60 degrees to minimize ore losses is topical.

Purpose
One of the solutions for this scientific and technical problem involves developing a method to reduce ore losses in the footwall "triangle" without increasing the cost of caved ore drawing.
The present work aims to study and enhance the technology of mining ore deposits by enhancing the mode of drawing, which will reduce ore losses on the footwall in underground mining at Kryvyi Rih iron ore basin.
To achieve this goal it is necessary to solve the following tasks: (i) Analyzing iron ore mining practices and ways to reduce ore losses in the footwall influence area.(ii) Conducting studies to reduce ore losses in the "dead" area of the ore deposit.The idea behind the work is to use regularities of ore movement under an inclined plane when working out ore deposits with a 45-60 degrees dip by bulk caving systems.

Analysis of researches and publications
Caved ore drawing from blocks when using systems with the bulk caving of ore is one of the most important production processes.Depending on the accepted method of ore drawing, ore losses and dilution are calculated, and the main parameters of the mining system are determined.This is due to the fact that 30-45% of the caved ore reserves is drawn from a block under overlying rocks, while losses in the block make 14-16%, and ore dilution is 12-20% [44][45][46][47][48].
A significant number of publications are devoted to the issue of reducing losses and dilution of caved ore from the stoping block [49][50][51][52][53]. Scientists of Kryvyi Rih National University (Ukraine) have made a significant contribution concerning ore drawing under caved rocks [54][55][56][57][58][59][60][61].The panel enclosed by vertical walls of the ore massif from four sides is more favorable in terms of drawing from blocks as such conditions increase extraction indicators.
According to studies, the following factors significantly impact extraction indices [31,62,63]: • intensification of ore drawing under caved rocks; • the distance between the axes of drawpoints; • structural elements of the mining system.
It is proved that the optimal distance between the axes of drawpoints is 4-6 m when drawing ore using scraper winches or vibration equipment, and 8-12 m -when using self-propelled loading machines or underground excavators.This enables significant reduction of ore losses and dilution but increases costs for driving and maintaining workings.
The authors of [1,6,31,54] argue that the distance between drawpoints is inversely proportional to the height of the sublevel and proportional to losses in ore drawing.Therefore, depending on the height of the sublevel, the ore deposit thickness and the dip angle, it is necessary to use the appropriate drawing mode: even, sequential, advance and others, thus allowing reduction of ore losses on: the stoping block sill; the footwall of the ore deposit.
However, when working out a block, a significant amount of broken ore remains in the footwall influence area, especially when using the bulk caving system in unstable rocks.When drawing ore under caved rocks, about 25-35% of the reserves remains in the footwall influence area, and when working out deposits in unstable rocks of the hanging wall, ore losses reach 50% [64][65][66][67].
Practices of mining ore deposits with a dip of over 75 degrees applying systems with the bulk caving of ore and country rocks show that ore losses in the footwall influence area are minimal and do not exceed 5-7%.However, the number of such deposits in Kryvyi Rih iron ore basin is less than 15-17% [68][69][70].
To reduce ore losses on the footwall when mining deposits with a dip of less than 60 degrees.the following technological solutions are applied (figure 2) [31,32,54,64,71]: • working out the "triangle" of the footwall as the first stage (figure 2 When working out the "triangle" of the footwall as the first stage (figure 2(a)), a scraper drift is driven 10-20 m above the main receiving level in the footwall of the deposit.An additional working of the receiving level can be driven in both ore and rocks of the footwall with drawpoints on one side.
Disadvantages include: • significant costs for creation and maintenance of an additional receiving level; • the specific volume of subsidiary development increased by 1.0-1.2m/kt of reserves; • significant dilution of ore with waste rocks as the height of the drawn ore layer increases.
The idea behind the method of mining the "triangle" of the footwall as the second stage (figure 2(b)) involves extraction of the main reserves of the panel with the help of delivery workings of the main receiving level, and the reserves of the footwall are broken and drawn afterwards.It should be noted that mining the "triangle" of the footwall in this way is carried out in difficult mining conditions, and in some cases it is hardly possible at all.
Disadvantages of this method of mining the footwall "triangle" include: • increased unsafety of stoping; significant ore losses (up to 30-50%); • a significant amount of subsidiary development (10-15 m/kt); • low efficiency; • high labor intensity and material costs.
Extracting ore from the "triangle" of the footwall with cutting footwall waste rocks (selective mining) (figure 2(c)) involves creating a compensation room at the footwall on which the ore massif is broken.Due to movement of the massif, the broken ore is shifted from the footwall to the center at the level of undercutting.Thus, the broken ore enters the drawing area and is located on the footwall.The ore is drawn from the first row of drawpoints located in the footwall.After extracting the ore mass from the first row of drawpoints, drawing continues from the second row, and so on.
Advantages of this method consists in the following: on the footwall, the minimum amount of ore remains (up to 10%); driving additional workings in the footwall allows an increase in the size of the compensation room; a simplified scheme of preparatory-development operations is applied; a small part of the "triangle" at the top of the panel remains unmined; location of workings on the same level enhances occupational safety.
Disadvantages include the following: additional costs for creating a compensation room; a significant amount of additional work on driving workings in the footwall rocks; increased costs for maintaining additional workings; increased volume of mined waste rocks due to creation of the compensation room in the footwall.
To reduce ore losses on the footwall of the panels, the method of driving additional draw workings in footwall rocks is used (figure 2(d)).This scheme has found wide application in complete mining of the ore massif within the stoping block.The main requirements for application of this scheme of mining the "triangle" of the footwall are [54,64]: relatively stable rocks of the hanging wall; medium thickness of ore deposits; the distance between the rows of drawpoints of additional receiving levels is determined such that ellipsoids of drawing touch waste rocks.
According to [54,55], depending on the horizontal thickness of the ore deposit and the height of the caved layer, ore losses are formed in different ways (figure 3).It is proved that when ore is being drawn, the figure of drawing is formed to the maximum height equal to the vertical thickness of the deposit.After reaching the contact with the inclined surface, the axis of the ellipsoid of drawing deviates and runs parallel to the footwall, forming a draw crater with the radius R r .

Methods
A significant contribution to development of the theory of ore drawing has been made by Agoshkov et al [31], Malakhov et al [54], Korzh [64].According to the results of their research, it is established that when caved ore is drawn from the mining block, the following figures are formed: ellipsoid of drawing, ellipsoid of loosening and draw crater (figure 4) [31,54,72,73].
At the first stage, before the ellipsoid of drawing reaches the inclined surface, the figure of drawing is formed according to previous studies [1,18,54].
According to [31,32,54], the small and large semi-minor and semi-major axes of the ellipsoid of drawing are determined by empirical expressions (1) and ( 2) for fine and coarse ores respectively, m: where b is the semi-minor axis of the ellipsoid of drawing, m; h el is the height of the caved ore layer (height of the ellipsoid of drawing), m; d is the diameter of the drawpoint, m; a is the semi-major axis of the ellipsoid of drawing, m.The volume of the ellipsoid of drawing for ores with homogeneous loose properties is determined by the empirical formula, m 3 where k 1 is the tangent of the straight line inclination angle; k 2 is the empirical coefficient.
The volume of the ellipsoid of loosening Q l is about fifteen times larger than that of the ellipsoid of drawing for loose non-compacted materials [21,74,75].Therefore, the volume of the ellipsoid of loosening can be determined by the expression, m 3 where µ 0 is the volume factor, assumed to be equal to 2.11.Knowing the ratio of the volume of the ellipsoid of loosening to that of drawing, the latter can be determined according to the expression, m where Q l is the volume of the ellipsoid of loosening, m 3 ; n is the ratio of the volume of the ellipsoid of loosening Q l to the volume of the ellipsoid of drawing q.
The ratio of the volume of the ellipsoid of loosening Q l to that of the ellipsoid of drawing q that are formed during caved ore drawing depends on loose properties of the ore and is described by the dependency [33,62,71] where n is the angular caved ore drawing factor; k l is the first loosening factor, unit fr.; dyn is the dynamic component of subsequent loosening; kl is the component of the subsequent loosening; k l.is is the subsequent loosening factor.For magnetite ore, the indicators k l and dyn , are 1.0204 and 1.05 respectively [21,33], the calculation results are given in table 2.
As is seen from table 2, when the caved ore first loosening factor decreases from 1.5 to 1.25, the ratio of the volume of the loosening figure to the volume of the drawing figure changes from 15.0 to 2.84.In compacted ore, there is an intensive extinction of an increase in the volume of figures of loosening and ore drawing.Consequently, extinction of the increase in the volume of loosening figures is more intensive than that of the figure of drawing, as a result of which the ratio of their volumes decreases [76][77][78][79].
According to Korzh [33], the semi-minor axis of the ellipsoid of drawing is determined by the expression, m where r is the radius of the ore drawing flow, m; m 0 is the factor of increase in the semi-minor axis of the ellipsoid of drawing, m; k ext is the factor of intensity extinction for the semi-minor axis increase; h 0 is the minimum height of the ellipsoid of drawing, m.When drawing caved ore under overlying rocks [5,21,54], particle flow velocities throughout the entire period remain phase shifted by the constant value ϕ.
The trajectory of particles (the boundary of the ellipsoid of loosening) is determined by the expression [32] y where ϕ is the distance between points A0 and A1, m; y, x are coordinates of a point relative to the horizontal and vertical axes of the ellipsoid of loosening, m; k is the distance to which a piece of ore moves vertically, m; is eccentricity of the ellipsoid of loosening.
The second stage of ore drawing from a single drawpoint is characterized by the fact that with further caved ore drawing, parameters of the ellipsoid of drawing remain unchanged, and subsequent formation of the ellipsoid of drawing occurs parallel to the hanging wall, thus forming the draw crater.
It is proved that the normal ellipsoid of loosening is formed until the cutoff height h = m × tan α [31].
The draw crater radius R r , which is equal to the vertical thickness of the ore body, is determined by the formula where H l is the height of the ellipsoid of loosening, m; h is the height of the caved ore layer, m.
In [4,33,62,64] it is argued that the curve forming the draw crater within the range H l -H moves parallel to the footwall.Thus, ore losses in the "triangle" of the deposit footwall are calculated by the expression, unit fractions IOP Publishing doi:10.1088/1755-1315/1254/1/012065 where M is the horizontal thickness of the ore deposit, m; α is the dip angle of the ore deposit, degrees; H is the height of the caved ore, m.

Results
Laboratory studies enable establishing that the figure of drawing changes depending on the surface inclination angle.The results of studying changes in ore drawing angles depending on the surface inclination, distances between the drawpoint and the inclined surface and the width of the caved layer in the lower and upper parts of the "triangle" of the footwall are given in table 3. Based on the results of the calculations performed, dependencies of the angle of the caved ore flow under the inclined plane on the angle of the ore deposit dip and the distance between a drawpoint and the inclined surface can be built (figure 5).
The graphs in figure 5 enable the conclusion that an increase in the ore deposit dip angle results in an increased angle of ore drawing under the inclined plane.Thus, an increase in the deposit dip from 45 to 60 degrees leads to increases of the angle of drawing from 57.2 to 77.2 at the distance of 10 m between a drawpoit and the inclined surface.When the distance between a drawpoint and the inclined surface increases from 10 to 20 m at the ore deposit dip of 60 degrees, the angle of ore drawing decreases from 77.2 to 68.1 degrees.
The dependency of the change in the angle of ore drawing under the inclined plane on the distance between a drawpoint and the inclined surface and the caved layer width in the lower part of the mining block of the "triangle" of the footwall shown in figure 6.
Figure 6 enables the conclusion that an increase in the distance between a drawpoint and the inclined surface from 10 to 20 m results in a decrease of the angle of caved ore drawing from 76.4 to 50.5 degrees.The graph shows that changing the caved layer in the lower part of the mining block of the "triangle" of the footwall and the distance between a drawpoint and the inclined surface approximate the angle of ore drawing to that of the deposit dip.Let us consider how the angle of inclination of the enclosing plane and the angle of caved ore drawing impact the draw crater radius.The calculation scheme is given in figure 7.
Considering the right triangle ABC and knowing the width of the ore layer under breaking, the angle of inclination of the enclosing plane, the radius of the draw crater R r (triangle BCD) is determined by the formula where γ is the angle of internal friction, degrees; β r.r is the angle of inclination of the enclosing plane, degrees; d is the width of the base of the ore layer under breaking, m.Thus, according to the known values from the theory of drawing caved ore under the country rocks, the radius of the draw crater is determined.The results of the calculations are given in table 4. According to the obtained values, the dependency of the drawing crater radius on the angle of the enclosing plane inclination can be built (figure 8).
As is seen in figure 8, an increase in the angle of plane inclination leads to the increase of the draw crater radius from 2.0 to 7.5 m at the first loosening factor of 1.5.A decrease in the first loosening factor from 1.5 to 1.1 results in the increase of the draw crater radius from 2.0-7.5 m to 4.4-10.0m.Thus, by changing the angle of plane inclination and increasing the width of the active drawing area, it is possible to reduce ore losses on the footwall.
Ore reserves remaining outside the active drawing area are determined by the expression, t The volume of diluting rocks, when drawing caved ore, is determined by the formula, m 3 where l d is the distance between the drawpoint and the inclined plane, m.Caved ore losses during its drawing under the overcompacted layer are determined by the expression, % where k r is the ratio of ore extraction from the overcompacted layer, unit fr.; Q r is the ore reserve in the overcompacted layer, t; N is the number of drawpoints; γ r.o is the volumetric weight of loosened ore, t/m 3 ; d cr is the diameter of the draw crater, m.Depending on physical and mechanical properties of the caved ore, ridges remaining on the block sill depend on the angle of ore drawing.At Kryvyi Rih iron ore basin, the angle of ore drawing does not exceed 68 degrees.
Analytical calculations of losses and dilution of ore during deposit mining using an overcompacted layer for the ore deposit dip of 60 degrees and an angle of the inclined plane of 70 degrees are given in table 5.
Based on the results of the analytical calculations performed, dependencies of changes in losses and dilution of ore during its drawing under the overcompacted layer are built figure 9.
As is seen in figure 9, an increase in the thickness of the overcompacted layer of ore decreases ore losses from 15 to 8%, and dilution increases from 6 to 16%.This is due to the fact that a decrease in the thickness of the overcompacted layer decreases the semi-minor axis of the ellipsoid of drawing, and the radius of the drawing flow under the inclined plane decreases accordingly.To minimize ore losses and dilution, it is advisable to locate the drawpoint in the block sill at a distance that provides formation of the 20 to 25 m high ellipsoid of drawing.
Thus, when applying the sublevel forced caving system using an overcompacted ore layer, it is possible to significantly reduce ore losses and dilution to enhance extraction of ore mass without additional costs.With the 22 m thick overcompacted layer, ore losses and dilution can be reduced from the actual 14 and 16% to 10 and 9% respectively.

Conclusions
The results of the analysis of methods for determining parameters of figures of caved ore drawing from stoping blocks enable the conclusion that there is no single methodology.Each of the methods has its own conditions of application.However, parameters of the figure of drawing are significantly impacted by the degree of crushing, the material mobility ratio, the shape and condition of the surface, the compaction factor, the mode of drawing.The results of the studies performed enable proving that the width of the active drawing area is impacted by not only rock pressure, but also the ore deposit dip angle and the enclosing surface represented by the hanging wall or created by gradual ore breaking.Thus, losses of ore on the footwall can be reduced by changing the angle of inclination of the plane and increasing the width of the active drawing area.
It is established for the first time that an increase in the thickness of the overcompacted ore layer leads to increases in the semi-minor axis of the ellipsoid of drawing and the width of the active area, which results in decreased losses and dilution of ore during its drawing from the stoping block.It is established that in order to minimize ore losses and dilution when using level mining systems, the drawpoint should be located in the block sill at a distance that provides formation of the 20 to 25 m high ellipsoid of drawing.
Using an overcompacted ore layer can significantly reduce ore losses and dilution and enhance extraction of ore mass without additional costs.Thus, the 22 m thick overcompacted layer enables ore losses and dilution reduction from the actual 14 and 16% to 10 and 9% respectively.

Figure 1 .
Figure 1.Geological cross-section of Kryvyi Rih iron ore basin along the shaft of the mine KRYVORIZKA, the JSC KRYVBASZALIZRUDKOM.
(a)); • extracting the "triangle" of the footwall as the second stage (figure 2(b)); • cutting waste rocks in the footwall (figure 2(c)); • creating an additional receiving level with the complete working out of the ore massif and a single compensation room (figure 2(d)).

Figure 2 .
Figure 2. Methods of mining ore reserves in the footwall influence area: 1 -the ore massif; 2overlying rocks; 3 -the working of the additional receiving level; 4 -the delivery working of the main receiving level; 5 -the compensation room; 6 -losses of ore in the footwall influence area; 7 -cutting footwall rocks.

Figure 3 .
Figure 3. Ore losses in the footwall influence: a) formation of a "triangle" of the footwall at an ore drawing angle of 75-81 degrees; b) formation of a "triangle" of the footwall parallel to the hanging wall; 1 -the ore massif; 2 -losses of ore in the footwall influence area; 3 -overlying rocks.

Figure 4 .
Figure 4. Formation of figures of drawing and loosening in drawing caved ore.

Figure 5 .
Figure 5. Dependency of the ore drawing angle on the ore deposit dip and the distance between a drawpoint and the inclined surface when the caved layer width at the lower part of the mining block is 4 m: 1, 2, 3 -the distance between a drawpoint and the inclined surface, 10, 15 and 20 m respectively.

Figure 6 .
Figure 6.Dependency of the angle of ore drawing on the distance between a drawpoint and the inclined surface at the ore deposit dip of 45 degrees and the width of the caved layer in the lower part of the mining block of the "triangle" of the footwall: 1, 2, 3 and 4 -the width of the caved layer, 4, 6, 8 and 10 m respectively.

Figure 7 .
Figure 7. Scheme for determining the radius of the draw crater depending on the angle of the inclined plane.

Figure 8 .
Figure 8. Dependencies of the change in the radius of the draw crater on the angle of the plane inclinatione.

13 Table 5 .Figure 9 .
Figure 9. Dependencies of changes in losses and dilution of ore during its drawing under the over-compacted layer and the inclined plane located at the angle of 70 degrees and with the ore deposit dip of 60 degrees.

Table 1 .
Stratigraphic index and ultimate strength of rocks, Kryvyi Rih iron ore basin.

Table 2 .
Volume to volume ratio for loosening and drawing figures.

Table 3 .
The angle of the caved ore movement under the inclined plane.

Table 4 .
Change in the radius of the drawing crater depending on the angle of the enclosing plane inclination.