EXPERIMENTAL DETERMINATION OF ANGLE VALUES OF THE ROCKS FULL DISPLACEMENT WHEN UNDERMINING THEM BY BREAKAGE HEADINGS

Purpose. Experimental determination of angle changes of full displacement of rocks by removing the breakage face from the face entry in different mining and geological conditions. Methods. On the basis of experimental data on parameters of the earth’s surface subsidence and the breakage headings size the full displacement angles of undermined rocks are determined graphically. Findings. The angle changes of the earth’s surface maximal subsidence are determined from the ratio of breakage heading size and mining operations depth. Originality. The maximal earth’s surface subsidence values correspond to the minimal values of the displacement angles above the face entry. Practical implications. The obtained results make it possible to estimate the displacement zones possible boundaries of undermined rocks with their discontinuity.


INTRODUCTION
According to the normative document (Minpalyvenerho Ukrainy, 2004), full displacement angles (ψ 1 , ψ 2 , ψ 3 ) are used in the calculation of displacements and deformations of the earth's surface after its complete undermining by breakage headings (the trough flat bottom formation).These angles are internal with respect to worked-out area.They are formed on the vertical cuts along the main sections of trough by the seam sheet and lines connecting the borders of mine working and trough flat bottom.Angle ψ 1 is laid off near the bottom border, angle ψ 2 -near the upper border, angle ψ 3 -near the border of mine working along the strike (Salehnia, Collin, & Charlier, 2016;Suchowerska Iwanec, Carter, & Hambleton, 2016;Filatiev, 2017a;Filatiev, 2017b).
When mining coal seams, the angle of maximal subsidence of undermined rocks (θ) is used to determine the location of the most characteristic places of trough displacement of the earth's surface -highs of soil subsidence.According to the normative document, this parameter is determined from the drop of the reservoir in vertical section in the main part of the trough across the stretch of the reservoir by a horizontal line and by a line connecting the middle of the working with the point of maximal subsidence in the incomplete part of the earth's surface.Academician S.G.Aversion assumed that undermined massif line of the maximal displacements is not straightforward and tends to become steeper as it ap-proaches the earth's surface.To simplify the calculations at the present time, the angles θ are accepted, including constant for the whole of undermined rocks strata in compliance with the normative document.
It is believed that the angle of maximal subsidence of rocks in particular geological-mining and mining-technical conditions depends only on the angle of slope of coal seam development (Khomenko, Kononenko, & Petlyovanyy, 2014;Ghabraie, Ren, Barbato, & Smith, 2017;Salmi, Nazem, & Karakus, 2017).For individual coal deposits θ is calculated according to the General equation: where: k -is an empirical coefficient taken equal from 0 to 1.With the exception of recommendation for seams with coal grades T and A: Recommended values of edge angles of undermined rocks maximal subsidence for different coal basins are in the wide range from 300 to 950 (Fig. 1).

Figure 1. Examples of change of maximal subsidence angles of rocks (θ) and angles of slope of the mined seam (α) for different coal basins
This indicates the possible influence of other factors, besides the angles of slope (Kuz'menko, Petlyovanyy, & Stupnik, 2013;Mohammed, Wan, & Wei, 2015;Petlovanyi, 2016).The reliability of the parameter definition θ influences largely the effectiveness of the developed rational measures for the protection of objects on the earth's surface from the harmful effects of wastewater treatment works.Therefore, it is important to establish additional influencing factors, besides the angle of slope.
In case of incomplete undermining, in addition to full displacement angles (ψ 1 , ψ 2 , ψ 3 ) in the computational schemes (Minpalyvenerho Ukrainy, 2004) the angles of maximal subsidence of the earth's surface (θ) are used.For the Lviv-Volyn basin angle θ is assumed constant and equal to 90°.For the rest coal deposits of Ukraine a correction to the angle of slope of the mined seam θ = 90° -0.8 α is applied.

MAIN PART
Based on the calculated schemes (Minpalyvenerho Ukrainy, 2004) of the trough displacement size determination with incomplete and complete undermining of the earth's surface, it follows that the angles of full displacement in both cases are taken up the same and constant regardless of the degree of broken working development.
Full displacement angles can be constant only after trough flat bottom formation.As studies have shown (Filat'yev, Antoshchenko, Gasyuk, & Pyzhov, 2015), until full undermining of the earth's surface, the angles of maximal subsidence of the earth's surface (θ) change under the influence of broken working.If to determine the full displacement angles on the basis of the breakage heading size and the maximal subsidence values of the earth's surface corresponding to them, the values of full displacement angles cannot be constant.
The angle changes of full displacement with the position of the earth's surface maximal subsidence by removing the breakage face from the face entry is characterized by diagram (Fig. 2).
For its implementation it is necessary to know the location of the experimental points 1, 2, 3 ... i and their maximal subsidence η 1 , η 2 , η 3 … η i .This calculated scheme and experimental data on the trough's parameters make it possible to determine the angle changes of full displacement above the face entry (ψ 01 , ψ 02 , ψ 03 ... ψ 0i ), and above the removing breakage face (ψ 1 , ψ 2 , ψ 3 ... ψ i ).Knowing of these angles is necessary for the development of measures for the rational protection of objects on the earth's surface.Until now, their ratios have not been studied, so research in this direction is relevant.The purpose of work is the experimental determination of the angle changes of full displacement when removing the breakage face from the face entry in different mining and geological conditions.
The methods of angles (ψ 01 , ψ 02 , ψ 03 ... ψ 0i and ψ 1 , ψ 2 , ψ 3 ... ψ i ) determination according to the experimental data are represented in diagram (Fig. 2).Each experimental point of the earth's surface maximal subsidence is connected by one line segment with a face entry fixed wall, and by another line segment each point is connected with a position of this breakage face, corresponding to it.The angle between the first segment and the seam sheet is the full displacement angle above the face entry and the angle between the second segment and the seam sheet is the full displacement angle above the moving breakage face.The total of the experimental points of the earth's surface maximal subsidence corresponds to the trajectory curve 4 of the maximal subsidence.
The trajectory curves of maximal subsidence points of dependence η m on their projection distances to face entry (L r ) are chosen by least squares method based on the results of observations (Iofis & Shmelev, 1985;Larchenko, 1998;Borzykh & Gorovoy, 1999;Babenko, 2009;Averin, Kir'yazev, & Dotsenko, 2010;Nazarenko & Yoshchenko, 2011) on twelve sites of seven mines in different coal basins.The dependence m = f (L) is described more precisely by way of exponential equation.Taking up in the equation of the curve m = f (L) value of m = 0 we have found the position of point 1 (Fig. 1), in which the earth's surface displacement begins for each of the studied object.The position of the breakage face 1, which corresponds to the beginning of the earth's surface displacement at the point 1 has been determined in the same way, using the dependence η m on the distance between the face entry and breakage face L.
This analysis of experimental observations made it possible to supplement the initial data (Iofis & Shmelev, 1985;Larchenko, 1998;Borzykh & Gorovoy, 1999;Babenko, 2009;Averin, Kir'yazev, & Dotsenko, 2010;Nazarenko & Yoshchenko, 2011) with values of ψ 01 and ψ 1 angles on twelve objects for η m = 0 at the moment when displacement processes reach the undermined rocks of the earth's surface (Table 1).(Babenko, 2009) The following values of full displacement angles above the face entry (ψ fe ) and breakage face (ψ bf ) were determined graphically from the experimental data of the earth's surface maximal subsidence (η m ) and from corresponding to them breakage face removals from face entry (L).
The results of such ψ fe and ψ bf determinations are exemplified for "Stepova Mine", "P.L. Voikov Mine", "M.V. Frunze Mine" and "Appalach Basin Mine" (Fig. 3).Mining and geological conditions of these mines differ significantly.The differences are in the different depth of mining operations, the strength of the host rocks, the metamorphic grade of coals and other indicators.For example, in "Stepova Mine" the seam C 6 was mined at a depth of 107 m with G grade of coal.The host rocks for these grades are less strong within the range of coal metamorphism.On the contrary, the anthracite seams, which were mined at a depth of about 700 m in such mines as "P.L. Voikov" and "M.V. Frunze", differ by the most strong host rocks.Mining and geological conditions of the objects have determined the different location of curves, which describe the angle changes of full displacement when removing the breakage face from the face entry.In all cases, the full displacement angles above the moving breakage face exceed their values above the face entry.It indicates that angle changes, despite the difference in mining and geological conditions happened approximately in the same direction.Such changes could cause the main factors influencing the earth's surface displacement.According to (Yagunov, 2007), it is the ratio of breakage heading sizes (L) and the depth of mining operations (H) that determine the parameters of undermined rocks displacement by 80%.To verify this conclusion a joint statistical analysis of all data obtained on the basis of experimental observations (Iofis & Shmelev, 1985;Larchenko, 1998;Borzykh & Gorovoy, 1999;Babenko, 2009;Averin, Kir'yazev, & Dotsenko, 2010;Nazarenko & Yoshchenko, 2011) has been held.The results of this analysis (Fig. 4) have proved a close correlation dependence of the angle changes of the earth's surface maximal subsidence as from the side of face entry (ψ fe ), so above the breakage face (ψ bf ) with the complex parameter L/H.Correlation ratios for these dependences amounted respectively to 0.88 and 0.97.Almost functional dependences of ψ fe and ψ bf on L/H for different coal deposits confirmed the conclusion concerning the main effect of this parameter.The parameter L/H determines the degree of the earth's surface undermining.If its value is less than 1, there is approximately the same change of angles ψ fe and ψ bf .When L/H ˃ 1, the angles ψ bf exceed ψ fe , ψ bf substantially.Angle values with sufficient breakage heading development (L/H ˃ 1) are stabilized in the range of 50 -60°.Such their values are close to their value (55°) recommended by the normative document (Minpalyvenerho Ukrainy, 2004).
The ψ fe angles above the face entry reduced to 30° (Fig. 4), with a significant broken working development (L/H ≈ 3.0).This situation is explained by dislocation of points of the earth's surface maximum subsidence in the direction of removing breakage face.
It should be noted that the earth's surface maximal subsidence values correspond to the minimal values of ψ fe angles.Obviously, using the ratio of the ψ fe and ψ bf angles and calculated scheme (Fig. 2) it is possible to estimate the displacement zones possible boundaries of undermined rocks with their discontinuity.

CONCLUSIONS
Full displacement angles of undermined rocks, determined by the earth's surface maximal subsidence and degree of the broken working development do not remain constant.
The main factor, which influences the displacement angle changes above the face entry and breakage face, is the ratio of a linear size of the breakage heading and the depth of mining operations.
Full displacement angles above the face entry and breakage face depend almost functionally on a complex parameter -a ratio of the breakage face removal from the face entry (L) and the broken working depth (H).
When the degree of broken working development L/H ≤ 1, there are approximately the same displacement angle changes above the face entry and removing breakage face.
When L/H ˃ 1, the displacement angles above the breakage face substantially exceed their value above the face entry.
With sufficient broken working development (L/H ˃ 1), the displacement angles above the breakage face are stabilized and equal approximately to 55°.
Displacement angles above the face entry can reach up to 30° when the parameter L/H ≈ 3.0, and this is caused by dislocation of points of the earth's surface maximum subsidence in the direction of removing breakage face.
The earth's surface maximal subsidence values correspond to the minimal displacement angles values of face entry.
Comparing the values of the displacement angles above the face entry and the breakage face, and using the trough's parameters of the earth's surface it is possible to estimate the displacement zones possible boundaries of undermined rocks with their discontinuity.

Figure 2 .
Figure 2. Diagram of the angle changes of displacement of rocks, undermined by removing the breakage face from the face entry: 1, 2, 3 ... i -positions of the breakage face and the points corresponding to them of the trajectory curve of the earth's surface maximal subsidence; 4 -trajectory curve of the earth's surface maximal subsidence points; i + n -random position of breakage face after complete undermining of the earth's surface; η1, η2, η3, ηi -maximal subsidence of the earth's surface, respectively, for the positions of the breakage face 1, 2, 3 ... i; ηo -depth of the displacement through flat bottom; δo, δi -adjoining angles of the impact on the earth's surface, respectively, from side of the face entry and moving breakage face; ψ01, ψ02, ψ03 ... ψ0i -angles from side of the face entry, which characterize earth's surface maximal subsidence at positions of the breakage face 1, 2, 3 ... i, corresponding to them; ψ1, ψ2, ψ3 ... ψi -angles from side of the breakage face, respectively, at its positions 1, 2, 3 ... i