Research of borehole drilling parameters for determining the optimum size of granite stone blocks

The optimal geometrical parameters of boreholes in dimension stone quarries, whose impact on granite blocks separation and splitting efficiency, are determined, taking into account the stress-deformed state of rock massif. The crack initiation process is analysed considering the flat problem of elasticity theory. Determine destruction parameters of natural stone by borehole methods using the calculations of the required distance between the boreholes in the row along the splitting line with the specified borehole diameters, and created forces of stone destruction are proposed. The optimal shape of splitting block from massif depends on the specific plane of splitting is determined. The possible directions of borehole deviation from ideal ones, their extension due to drilling and tensions in the boreholes are studied. The introduction of the borehole’s overlapping coefficient, which influences the weakening of the massif along the directed (designed) split line, is proposed to define further necessary tensions for mechanical ways of separating blocks. The equations for determining drilling operations parameters at granite blocks splitting from dimension stone quarries massifs are proposed. The coefficient of limit values of deviation angles is defined.


Introduction
Extraction of natural stone in dimension stone quarries consists of different processes such as: drilling, blasting, splitting, cutting, crushing, excavation, etc.Besides mining, many of those operations also apply to civil engineering [1].
Extraction technology of dimension stones is characterized by specific factors that aim to keep the physical and mechanical natural stone properties and get blocks with a straight shape and effective commercial size [2].
All used methods for dimension stone block extraction can be divided into crack-forming, split-shaping, physical, technical and combined methods.Still, the most common ones are crack-forming and split shaping.
Used split-shaping (fracturing methods) methods for the creation of critical tensions in the splitting planes are formed by drilling boreholes.Fracturing methods into splitting with shims, control blasting processes or thermal procedures and using non-explosive destructive mixtures are divided.
Using the technology of dimension stone extraction during the process of splitting blocks from the massif mostly the splitting methods by shims are used.In practice, due to drilling deformation and borehole deviation, the horizontal projections of the hole's tops and bottoms usually do not be projected one on one.Sometimes boreholes curvature causes the intersection of the next holes in the middle of the length or near their bottoms.In such case, it causes the formation of large rough surfaces after splitting on the block's surfaces, that result in significant losses of stone in further processing operations.The incorrect position of the boreholes' bottom causes the unequal concentration of splitting tensions.It is the result of diagonal fracture formation.
Extraction of natural stone blocks has a large amount of drilling.The quality of drilling operations performance determines the effectiveness of further operations for splitting blocks from the massif.Borehole deviation from the design position causes an increase in the volume of drilling operations due to an increase in the length of drilled boreholes.When using fractureforming methods, the deflection of borehole axes causes a change in the geometry of splitting forces spreading, affecting the efficiency and quality of the splitting and separation process.Borehole deviation when performing drilling operations of stone massif drilling can cause increased separation area, tool costs, and poor quality of block production.The quality of drilling boreholes is determined by a number of indicators: mode parameters of the drilling process, type and condition of drilling tools, and state of the rock mass.One of the most promising directions of improving extraction processes is optimizing drilling operating parameters, considering the natural fracturing and physical and mechanical properties of dimension stone [3].
Thus, the research of the impact of these factors on the efficiency of drilling operations is a topical scientific and practical task, the solution of which will improve the efficiency of extraction natural stone technology and the quality of natural stone blocks.

Statement of the problem
Recently many researchers were based on such important operations as drilling, which was performed with different materials, particularly dimension stones drilling in quarries.Drilling is an important process during dimension stone extraction because an inefficient drilling process can cause huge operational losses [4].That's why mining enterprises should attempt to optimize those losses.Optimizing drilling losses is also sufficiently effective for further developing mining technologies [5].
Many studies and research for increasing drilling process efficiency are based on determining the optimal speed of penetration of the drill steel (jackrod) and sintered diamond coring a bit into massif.It is based on the optimal choice of the type of drilling equipment according to the current condition of massif and determination of the sufficient force for penetration into the rock [6].Assessing drilling efficiency considering rocks' properties is also an important part of research [7].
Another scientific and applied drilling problem is the problem of geometric linearity deformation and extension of the boreholes.During drilling, the drill steel and the sintered diamond core bit strike the rock mass, forming a borehole [8].As a result, a circular borehole wall becomes deformed, and the total borehole area is also changing.This process can cause further crack creation and reduce tensions in the splitting plane [5].
Calculating the optimal tensions for splitting blocks from massif is also important to analyze the micro-cracking process.Particularly this analysis can be found in the following work [9,10], where are described the micro-cracking process and analysis of mechanical features of rocks during splitting [11].The crack creation and the process of further formation of cracks are described by Huang et al [12].
The optimization of technological mining parameters in the quarry for dimension stone blocks quality improvement, which is based on photogrammetric measurement techniques, is researched by Levytskyi et al [13].
During extraction of the dimension stone, it is important to study the massif's deformation mode (stress-deformed state) in detail.The boreholes drill along the splitting line of the monolith.
All previous studies do not indicate how much the hole deviation line from the designed direction reduces the coefficient of massif weakening.Also, the problem of the loss stone coefficient changing after the deflection of boreholes is not considered earlier as a result of a change in the shape of stone blocks, causing to increase in the costs of further processing.

Methodology
The method of determining the destruction of stone by hole methods is to determine the required distance between boreholes in the line of splitting with given borehole diameters, creating splitting tensions.Throughout the studies, full-scale measurements of lengths and diameters were carried out of boreholes.After the block was splitted off, the azimuths of boreholes deviation from the optimal directions and the dimensions of the directly extracted blocks with all inequalities were considered (figure 1).According to this method, it was determined that the optimal shape of the splitted block from the massif (the equality of splitting planes and their mutual perpendicularity) depends on the specific area of splitting, i.e. the correlation of the area formed by the split plane to the total area of splitted block or monolith.

Results
The study about the causes of the drilled borehole's deviation shows that it occurs due to geological, technical and technological factors.During the drilling of the borehole, deviations can occur due to the following reasons: encounter with a crack, a stress state factors of the massif, inaccuracies in the installation of the perforator, a clearance due to physical tool wear or structural defects in the particular part of the drilling machine and influence of the surface roughness on which the machine is installed for the accuracy of the installation.
The least studied and the most actual research on borehole drilling is the definition of the influence of the zone of overlapping holes on the deviation of the borehole according to the designed position [14].
The criterion for determining the maximum permissible values of the hole deviation angle from the vertical is the condition of excluding its intersection with the next holes.It should be noted that the limit criterion is valid in such cases when the borehole axis coincides with the plane of borehole lines.In case the difference between the azimuthal borehole axis angle and the plane of borehole lines, the maximum deviation angle will be determined by additional geomechanical determination of the stone blocks splitting process.
In practice, vertically drilled boreholes are over-crossed with one or a series of sub-horizontal cracks.Each of these cracks adds value to the axis deviation angle.For the linear drilling method, the criterion for the quality of drilling is also the geometric parameters, namely the orientation of boreholes that may intersect with each other.
Only for different dimension stones, the method of line drilling, which is combined with the mechanical stresses initiation in the boreholes, the quality of drilling operations will be determined in addition to the geometric parameters, also by parameters of formation of the stone massif tenses.Methods of calculation of the borehole parameters, which are based on practical experience and conducted scientific research, are used in the technology of dimension stone block extraction.
The dimension stone extraction calculation methodology by splitting boreholes method is determined by the required distance between holes within the boreholes line of the given diameter and splitting stone forces.
The research has established that the quality of the stone splitting from the massif (the equality of splitting planes and their mutual perpendicularity) depends on the specific splitting plane.That is the ratio of the area formed by the holes to the overall area of splitted block or the monolith.
One of the important technological parameters of the extraction of granite blocks is the required distance between the holes that are drilled in the designed splitting plane.These formulas were obtained empirically and analytically and provided a diagram of the stress state of the rock monolith, where the static stress acts inside the wells without stress concentrators.
For calculation of the distance between boreholes, it is proposed to use an equation that, when used further, obtains the most accurate results: where d h − diameter of the borehole; l h − borehole length; p(t) − pressure on the walls of the borehole; H − granite monolith height; σ p − ultimate rock tensile strength; p(t) − a coefficient that takes into account the reduction of the strength of the stone from the time of loading, which varies from 0,1 to 0,7, depending on the orientation of the splitting plane along the layer, or at an angle to it (anisotropic properties).During the drilling of the borehole line for splitting, in addition to the basic equations of the flat problem of elasticity theory, the plane of borehole displacement from its ideal location has to be considered.It means that the borehole has neither deviation in the azimuthal direction (α), nor in a circular direction (φ) (figure 2).
To determine the specific splitting area for one shim, a dependence which takes into account both geometric parameters of splitting and the anisotropic properties of natural stone, which makes it possible to use it in different deposits, was used: where k a − coefficient defines the anisotropic properties of the rock (for erupting rocks k a = 0,2− 1,0).For the best splitting stone direction k a = 1,0, and in the direction π/2, 3π/2, for labradorite k a = 0,6, gabbro-norite k a = 0,2, granite k a = 0,4; P − pressure in the system, Pa; r g step between elements of hydro rock splitting systems installation, m; σ p − tensile strength of granite, MPa; U − specific relaxation ratio of the splitting plane by drilled boreholes, which depends on the location of the boreholes in the splitting plane: where z − total drilled holes length in the splitting plane, m; d b − diameter of the hole, m; S − the block cut-off area with the length (a) and the height (h), m 2 .The values of z are determined from the dependence: where l bg , l bg -length of boreholes where there are hydro rock splitting systems installed (l bg = h) and additional boreholes for massif weakening (l bp = k n ), m; n p , n bp -number of boreholes respectively for the installation of hydro rock splitting systems and additional boreholes for massif weakening; k dr -uneven rate of drilling (k dr = 0, 9); r p -distance between additional boreholes for massif weakening, m; k n − coefficient of reducing the length of weakening holes (k n = 0 − 1).
Reducing the above expressions and also taking into account that splitting is performed in the vertical plane of the dimension stone blocks with the length a and height h for l bg = h and l bp = h/3, we obtain the following relation (correlation): As it seens from the expression, the specific splitting area by hydro rock splitting systems does not depend on the height h of the ledge.
The technological coefficient of losses from the drill-split shim method of separating granite blocks k tl is determined by the following equation: An ideal borehole area and an actual overlapping area are introduced.The ideal borehole area can be described by equation S i = l n d n .The actual overlapping area can be described by equation The coefficient of splitting plane weakening: K alap = S i S h .
In the limit values at the maximum deviation, the coefficient of massif weakening will be for α = 0 0 -S h = πR ln cos φ , for α = 90 0 -S h = πR 2 l 2 = πR 2 2 sin φ .So in all other possible positions, the actual boreholes overlapping area will be: Taking to according that the loss coefficient and the weakening massif coefficient depend on such parameters as hole diameter and depth, which in most cases equals the height of the bench.It can be argued that when splitting the block, it is also necessary to take into account the split-line direction if the designed directions of drilling operations are not kept.
As a result of field measurements, experimental values of the reduction of the weakening massif coefficient were obtained due to the deviation of holes from the designed direction.As a result, the values of the weakening coefficient were determined for different values of the directional angle and the vertical deviation angle; the graphic representation of this dependence is shown in figure 3. The above formula of technological loss coefficients, Eq. ( 7), allows you to determine the coefficient of removal of blocks and the complex productivity of equipment for preparing blocks for extraction.
In an ideal three-dimensional model of massif cracking, the geological coefficient of loss kg.l = 0, since the main systems of cracks are parallel with each other and their planes intersect at right angles.Separate this three-dimensional model on the SQL, SQS, SSL planes, the simple models of individual location crack systems location in the dimension stone massif we obtained (figure 4).
Considering the absence of ideal conditions on natural stone deposits, a non-orthogonal model was introduced in which the basic systems of cracks do not intersect at a right angle γ.At the  same time, it is considered that the angles of falling cracks in the massif are constant; that is, all the cracks of one system are parallel.Given all the above, a three-dimensional model of the fracture of an array (figure 5) was developed, which will allow determining the most optimal directions of drilling operations with the subsequent minimal losses of minerals.
The following dependencies determine areas of separation planes in the case with: (n q l q sin γ QS + 0, 5n l l l sin 2α q )(n s l s sin γ QS + 0, 5n i l i sin 2α s ) sin γ 2 QS sin α q sin α s ; where H m , L m , B m -height, length and width of the monolith, respectively, m; n q , n s , n lamount of blocks between planes respectively of transverse Q, longitudinal S and smooth L cracks of the massif, within the linear dimensions of the monolith, units; l q , l s , l l -distance between the planes of the corresponding systems of cracks, m; α q , α s , α l -falling angles of the corresponding cracks systems, degrees; γ QL , γ QS , γ SL -angles between the corresponding cracks systems that determine the non-orthogonally of the cracks systems with each other, degrees.
The indicator, which characterizes the overall geometric parameter of breaking, is the specific plane of splitting.In mining practice, the line of drilled holes in a certain vertical plane, due to some deviation of their axis, will only partially intersect the designed plane.Only in the case of a deviation of the hole along the planned plane of splitting its section throughout its length will it keep in this plane.

Conclusion
The value of the specific splitting area during the monolith preparation to the extraction will be less than the estimated, which effect to splitting parameters of blocks from the dimension stone massif.Therefore, the overall quality index of drilling can be taken as a performance criterion for splitting blocks from the massif.
The values of tensions allow analysing the conditions for the creation of cracks for splitting blocks from the dimension stone massif.It should be borne in mind that the theory of failure considers only the most significant stresses, not taking into account that other present stresses also affect the achievement of the critical state.The critical value is σ γ for a dimension stone massif.It can be determined the critical tension initiates cracking formation.
The quality of the stone preparation for splitting depends first of all on the plane of designed split plane, the main characteristic of which is the specific value of splitting plane.As proved by the calculations, this value depends on the angle of borehole inclination.It was researched that boreholes have different values of deviations from vertical, which cause a decrease of the specific value of splitting plane, which depends on the azimuthal α and the zenith angles φ of hole axis along the designed split-line.It is obtained that the most negative values of the azimuthal angle α are observed in the range from 72°to 90°, and the zenith angle φ from 0,75°to 1,4°.

Figure 3 .
Figure 3. Change the coefficient of the massif mitigation.

Figure 4 .
Figure 4. Orthogonal models of the propagation of Q LS systems in the natural stone massif: a) the longitudinal vertical plane of S QL ; b) the blanket horizontal plane S QS ; c) the lateral vertical plane of S SL .

Figure 5 .
Figure 5. Three-dimensional model of a natural stone massif fracture.