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UDC 622.1
ANGLES OF TOTAL SHIFTS AND ANGLES OF MAXUMUM CROP DURING DEVELOPMENT OF FACES DIAGONAL TO SEAM STRIKE
DIRECTIONS
Natal'ya A. KOLESNIK1, Gennadii I KOZLOVSKIY1, Aleksandra A. KANAVETS1
1 Donetsk National Technical University, Donetsk
When predicting deformations and determining measures to protect underworked objects, angular parameters are used: the boundary angles, the angles of total shift, the angle of maximum crop. The values of these angular parameters are given in the normative documents, but only for sections across and along the strike of the formation. However, at present, longwall face mining is mainly being carried out along a diagonal direction to the strike of the formation. In connection with this, the determination of the values of the angular parameters for such conditions is a topical task.
The method of determination and the analytical dependences of the angles of total shifts and angles of maximum crop in sections of the longitudinal and transverse axes of coal-mining faces developed along diagonal directions to the strike of the formation are proposed. These angular parameters are used for prognosis of deformations of the earth's surface and for determining the characteristic zones of influence of mine workings on the local places.
Key words: angles of total shifts, angles of maximum crop, diagonal directions of contour of working, deformation of earth surface
Hot to cite this article: Kolesnik N.A., Kozlovskiy G.I., Kanavets A.A. Angles of Total Shifts and Angles of Maximum Crop During Development of Faces Diagonal to Seam Strike Directions. Zapiski Gornogo instituta. 2017. Vol. 225, p. 298-306. DOI: 10.18454/PMI.2017.3.298
Introduction. Angular parameters are used to determine the boundaries of the zones of mine workings influence on the earth's surface and predict the deformations of the latter when working and protecting buildings, structures and natural objects [8, 12, 15]. Their normative values are determined by many years of research by many authors [2, 4, 6, 9-11, 13, 14] and are given in the «Rules for underworking ...» [1] only for the main cross-sections of the trough across and along the strike of the formation.
Currently, longwall faces are often mined along diagonal directions to the strike of the formation [5, 7]. The main sections of the trough should be considered cross sections along the longitudinal and transverse axis of a working. Therefore, the determination of the angular parameters in these sections is very important.
The analytic dependences of the boundary angles in cross sections, which are diagonal to the strike of the formation, were published by the authors of this article in [3]. Therefore, in this paper only the angles of total shifts and the angles of maximum draw are considered.
Methods for determining angles of total shifts and angles of maximum draw. Let us consider the coal seam working (a = 20°) developed by «diagonal» longwall face in the contour I-II-III-IV (Fig. 1). Let's assume we will replace the seam cutting area with short faces (with a slight discontinuity in time) along the strike (Fig.1, a) and across the strike of the formation (Fig.1, b) with the stopping of the bottom lines along the contour specified above. Then, according to the «Rules of underworking ...» [10], we get a flat bottom of the trough, bounded by lines 2, 3, with boundary points Еаi, Еbi on the axes of the «diagonal» face (where i is the number of points). In this case, the distances АiЕaj ^ AE^. Now the problem is reduced to finding the average weight points E. This principle is also the basis of the methodology proposed here.
Since the lines at the angles ¥ and 0 have a constant angle of inclination in the bedrock and incrop deposits, in order to simplify the calculations, the process will be considered as occurring only in bedrock, assuming the depth seam incrop line equal to ± 0.0. Let us draw conditional advance of the «diagonal» face line to seam incrop point (Fig.2, b). Then M1 point will be both the pit limit and flat bottom of the trough, since the depth H = 0.
From Fig.2, b, the seam inclination angle along the production line I-II and the distance A1M1 are:
HA
tgaj_n = tga • sin s , AjMj =-1— ,
tga • sin s
where a, s, HA1 - seam inclination angle, acute angle between longitudinal axis of working and seam strike line, seam depth at point A1.
Seam incrop
Nominal H = ±0,0
50 ■
100
200 ■
H
Fig. 1. Layout of «diagonal» face with seam inclination angle of a = 20° with conditional replacement of area with short faces
along the strike (a) and across the strike (b) of the formation 1, 2, 3 - pit limit points: coal seam mining with «diagonal» face; flat bottom of trough with conditional replacement of are with short faces along the strike and across the strike of the formation; 4 - when a > 90° - T the trough flat bottom boundary of angle T (with replacement of faces across the strike) is set outside the contour of «diagonal» face; 5 - longitudinal axes of short faces; e - acute angle between longitudinal axis of «diagonal» face and seam strike line; ArA2, A3-A4 - lateral (short) and longitudinal (long) axes of the face
a
I
A3
W
Seam incrop
M4
M1
Nominal H = 0,0
\\ .-V
II
\ / /
M2
G4
III
M2
P3' 4
Fig. 2. Design layout for determining angles of total shifts in axial cross-sections of «diagonal» face:
a - orientation pattern of «diagonal» face along the seam strike line; b - a pattern of geometrical relations between angle and linear parameters
of horizontal alignment. Also see p. 300
I
b
a
Ha
d a,
Pi
Pi
p; Ai
a > 90° - T1
g
—) / a < 90° -
HAi
I Ebi
a > 90° - T1
9Ea
N>Eb/
-> ^ a < 90° -
HAi ATtie N^jei ^a'ie j
E' E
s.T1je
\9Ea aje
AEa > AEb
Fig. 2. Ending. Design layout for determining angles of total shifts in axial cross-sections of «diagonal» face: c-j - the same in vertical cross-sections; Ai, Ci, Pi, Pi - boundary points (where i - point number): contours of «diagonal» face at axial lines; flat bottom pf trough, determined by angle T3 (with conditional replacement with faces along the strike); the same with angles T^ T2 (with replacement of faces across the strike) with a < 90°- T1; the same for angle T (when replacing faces across the strike) with a > 90° - T1; Ei, Ei', E^, Egi - boundary points of flat bottom of trough at axial lines of «diagonal» face: with a < 90°- T1; with a > 90°- T (i, j); with a > 90°- T and replacement with faces along the strike; with a > 90°- T and replacement with faces across the strike: a, a', e - angles: seam inclination; seam inclination at axial cross-sections of «diagonal» face; acute angle between longitudinal axis of the face and seam strike line; T1, T2, T3, Tj T2j, T1e, T2e - angles of total shifts at cross-sections across and along the strike and in cross-sections of «short» and «long» axes of «diagonal» face; p1, 92, 93, 9^, 92j, 91e, 92e - angles of inclination of lines corresponding to angles of total shift and linear parameters of horizontal alignment
Let us determine the distance A1E1 (between working boundary and flay bottom of trough boundary) separately with conditional replacement of face mining along the strike (a) and across the strike (b) accordingly in left and right columns:
a)
AC -
F1C1 -
A1F1 -
Ha.
tg^3
HAi sin 8
tg^3
HA cos 8
(Fig.2, c), (Fig.2, b),
A1E1(a) =
A1E1(a) =
tg^3
AM 1 • FC1
F1M1
HA sin 8
tgy3 - tga • sin 8 • cos8
b)
A1P1 =
H
P1G1 -
AG -
tg^2
H^ cos 8
tg^2 HA sin 8
tg^2
(Fig.2, e), (Fig.2, b),
HA sin 8
A E -
tg% + tga • sin 8
A E -
A1M1 • P1G1 G1M1
A
c
e
E
h
where 92, 93 - inclination angles of total shift lines at cross-sections across and along the strike at point A1 (Fig.2 b, e).
We obtain two values A1E1 - the distance from the working face boundary to the boundary of the flat bottom of the trough in the section of the transverse axis A1-A2 of the «diagonal» face I-II-III-IV. At s = 0°, the line (boundary) I-II is oriented along the strike of the formation and only the angle 92 affects the distance A1E1, i.e. the expression A1E1 (b). Similarly, at s = 90°, only A1E1 (a) affects A1E1. For s = s = 45° there must be an equivalent effect of the equalities with the indices (a) and (b). To fulfill these conditions, we take weighting coefficients P(a) = sin s the average weighting coefficient value of distance A1E1 is:
P(b) = cos s. Then
AE = H,
sin2 s
(tg93 - tga • sins • coss)(sins + coss)
+ -
- +
cos2 s
From Fig.2, c, d, e, g:
Then
(tg<p2 + tga • sin s)(sins + coss)
HA
93 = ^3, 92 = ^2 - a, 92 = arctg-—r .
AiEi
A,E, = H.
sin2 s
(tg¥3 - tga • sins • coss)(sins + coss)
■ +
+ -
cos2 s
(tg(¥2 - a) + tga • sin s)(sins + coss)
(1)
92, = arctg
1:
sin2 s
(tg¥3 - tga • sins • coss)(sins + coss)
- +
+ -
cos2 s
(tg(Y2 - a) + tga • sin s)(sins + coss)
(2)
The formula is cumbersome, but simple in calculations. Nevertheless, to simplify it (and subsequent formulas) we introduce the notation: A = tga-sins-coss, B = tga• sin2s, C = tga-cos2s,
D = sin s + coss . Then
92, = arctg 11:
sin2 s
- + -
cos2 s
From Fig.2, g
(tg^3 - A) D (tg (^2 -a) + B) D
= + «' A,-A2;
y2j = 92j + arctg(tga • coss).
(3)
(4)
where ¥2j, 92j - angle of total shift and angle of inclination of total shift lines from the up dip in cross-section of longitudinal axis of working (in point A, at Fig.2, b).
Similarly, analytical dependencies are obtained for determining the angles of total shifts: ¥2e (with a < 70°), (with a < 90° - ¥,), (with a < 90° - ¥,) respectively from the up dip of the longitudinal axis, from the down dip in the section of the transverse axis and from the down dip in the section of the longitudinal axis of the «diagonal» face. The corresponding formulas are given in Table 1, where the accepted notations are also indicated.
In addition, we will look at at the angles of total shifts from the down dip side of the formation in the axial sections of the «diagonal» face with a > 90° - In this case when replacing the coal mining area developed with faces across the strike the boundary of flat bottom of trough is located above the coal pillar, outside the mining contour (Fig.2, f). The details will be given on the examples of angle at point A2 (Fig.2, b). Here the distance A2E2, when replacing the coal mining area developed by faces along the strike we calculate (applying the same method) using the formula:
A2E2(a) -
ha2 sin S
tg% + tga • sin s • cos s
(5)
When replacing the coal mining area developed with faces across the strike the point Eb is located outside the contour of «diagonal» face and distance A2E2(b) is determined using the formula (Fig.2, j):
A2 E2(b )
H . cose
2(b ) tg^j + tga • sin2e
According to the justification stated above, we take weighting coefficients: P^E w Then average weighting coefficient value is
sin2 s
(6)
sin s .
PA2£2(b) - cos S
A2 E2 - HA2
(tg% + tga • sine • cose)(sin s + cos s) cos2 s
(tg^j + tga • sin2e)(sin s + cos s)
Let us substitute the values 93 = ¥3 (Fig.2, c), 91 = 180°- (¥1 + a) (puc.2, f) u -Then
sin2 S
H
A2E2
A2 E2 - H A
(tg¥3 + tga • sine • cose)(sin s + cos s)
cos2 S
- arctg
1:
(tga • sin e - tg(Yj + a))(sin s + coss) sin2e
(7)
(tg¥3 + tga • sine • cose)(sine + cose)
2
cos e
(tga • sin e - tg(¥1 + a))(sine + cose)
(8)
or with the above given notations
91j - arctg11 :
sin2e
cos2e
(tg¥ + A)D (B - tg(^1 + a))D
(9)
If according to the calculations it will be ^1j2 > 0° (i.e. AEa> AEbi), then the boundary point E of flat bottom of trough of «diagonal» face is located inside the contour I-II-III-IV (Fig.2, j) and angle of total shifts equals:
^ij - - arctg(tga • cose).
(10)
2
2
With cpij2 < 0° (Fig.2, j)
y = 180° -
j2
-a
A1- A2 j
= 180°
arctg(tga • cose). (11)
Similarly, the analytic dependence is determined for the angle T1 (at point A3 in Fig. 2, b) of total shifts on the down dip in the section of the longitudinal axis of the «diagonal» working. The formulas are given in Table. 1.
The method of determining the angles of maximum seam crop will be considered using the example of a section along the transverse axis A1-A2 of a «diagonal» working (Fig.3).
From triangle A1MA2 (Fig.3)
y
\0j
\Yj
M
Fig.3. Cross-section of longitudinal axis A1-A2 of «diagonal» working
A A2 sin A A2 sin ;
AM = -V-A2M = -V-j.
1 sin(^„ ) 2 sinl^j + ^2, )
The OM line drawn from the middle of working at the angle of the maximum crop is the median of the triangle and its length is determined by the formula
OM - 1a/2(a1M2 + A2M2)- A1A22 ;
OM =
From triangle OMA2
A1A2 2sin(^1j + ^2j)
2(sin2^1j + sm%)-sin2(^1j + ^2j) .
sin y
A2M sin ^ OM
y. = arcsin
2sin ^1jsin^2j
/2(sin2^1j + sin%) - sin2^ + Yj The angle of maximum crop 9j at the cross-section of traverse axis of «diagonal» working is:
(12)
6- = arcsin
0j = y, - arctga'a1 _
2sin Y1jsin
^(sin2, sin2T2|)-sin2 (TI| + vj
- arctg(tga • coss )
(13)
The same is for cross-section of longitudinal axis of «diagonal» working
Yf = arcsin
2 • sin¥1fsin¥2f
■yj 2 (sin 2y1f + sin 2y2f )- sin2 (y1f + y2f )
(14)
0f = arcsin
2sin¥1fsin¥2f
V 2(sin X + sin 2y2f )- sin2 (^1f + y2f )
- arctg(tga • coss )
(15)
os o
iU.
o c
a>
3
3'
<Q
C
3'
3'
tQ
Table 1
Formulas for determining angles of line inclinations (<p) and angles of total shifts (*P) at cross- section of traverse (index j) and longitudinal (index f) axes of «diagonal» working
Cross-sections
Along traverse (short) axis of working (Ai-A2 at Fig. 2)
Along longitudinal (long) axis of working C43-44at Fig. 2)
Working boundaries (Fig. 2 b)
At the upper boundary of the working (at point Ai) with a < 70°
At the lower boundary of the working (at point Ai) with a < 90°
At the lower boundary of the working (at point A2) with a > 90°
At the upper boundary of the working (at point Ait with a < 70°
At the lower boundary of the working (at point Ai) with a < 90°-Ti
At the lower boundary of the working (at point
Ai with a > 90° - ¥ !
Angles of line inclinations at angles of total shifts
<P2j = arc1H 1
2
COS E
(tg y3-A)D (tg (W2-a) + B)D
. 2
Sill E
2
COS E
(tg%+A)D (tg(V1+a )-E)D
. 2
Sin E
2
COS E
(lg%+Ä)D (S-tgf^ +a))D_
<p2f = arctg^ 1 :
<Pif = arctg^l
9if = arctg^ 1 :
2
COS s
. 2
sin s
(tg%-A)D (tg(%-a)+ C)D
2
COS E
. 2 SHI E
(tgV 3+A)D (tg^ + a )-C)D
2
COS s
. 2
sin s
(tg^3 + A)D (C - tg(^ + a))D
Angles of total shifts
~ ^2, + ^Ig " cos £)
fjj = (py - arctg(tga ■ cos e ) With (ptj > 0°
^lj = fij ~~ arctg(tga ■ cos e ) With (ptj < 0°
^lj = 180" - jtpjj j - arctg(lga ■ cos e)
lP2f = tp2f + arctg(tga - sins)
= ^lf ~ arctg(tga - sins)
With (plf > 0°
= "Pif ~~ arctg(tga ■ sin e ) With (plf < 0°
'Pjj = 180° - Jq^f J - arctg(tga ■ sins)
Note. A — tga-sins-cosE, B — tga-sin2s, C = tga-cos2E, D = sin e + cos e; "iS, ¥3 _ angles of total shifts at cross-sections across and along the seam strike [1]); a - angle of seam dip; s - acute angle between longitudinal (long) axis of working and seam strike line.
S ^
CD '—
Co ^
o a>
S. at g g
co 5" =j- «
3» 3. «
§ O
Q. <D £ =
4 a
CD 5*: co ^
¡I
ï< o
II
5 fe S-
D « c a>
g- à I
£ a
a> ^
o>
O O
-tx
Ol
o ---
>1 00 k> <0 00
Conclusions. Thus, the authors of the article proposed a method for determining and analyzing the dependences of the angles of total shifts and the angles of maximum crop in sections of the longitudinal and transverse axes of coal-mining faces developed along diagonal directions to the strike of the formation.
Table 2
Angles of inclinations of total shifts lines 9 (at cross-section) and angles of total shifts ¥ at cross-sections of axes of «diagonal» workings calculated according to formulas from Table 1
(¥j = 55°; ¥2 = 55° + 0,3a; ¥3 = 55°)
Seam inclination angle a, degree Angle between longitudinal axis of working and seam strike e, degree Angles of total shifts lines inclination at cross-section of traverse axis of working, degree Angles of total shifts at cross-section of traverse axis of working, degree
From up dip side 92j From down dip side 9ij From up dip side ^ From down dip side Ty
20 0 41.0 75.0 61.0 55.0
20 50.5 76.2 69.4 57.3
40 57.2 73.4 72.8 57.8
60 59.4 68.2 69.7 57.9
80 57.6 60.3 61.2 56.7
90 55.0 55.0 55.0 55.0
40 0 27.0 -85.0 67.0 55.0
20 39.5 -89.7 77.8 52.1
40 52.2 82.9 84.9 50.2
60 55.9 73.8 78.7 51.0
80 56.1 62.1 64.4 53.8
90 55.0 55.0 55.0 55.0
60 0 13.0 -65.0 73.0 55.0
20 30.6 -76.1 89.0 45.5
40 46.5 -89.0 99.5 38.0
60 47.1 78.7 88.0 37.9
80 53.0 64.4 69.8 47.7
90 55.0 55.0 55.0 55.0
Note. When 9 < 0° the boundary of flat bottom of the trough is located outside the working contour, i.e. above the coal pillar (point E' at Fig.2, j)
Table 3
Angles of inclinations of total shifts lines 9 (at cross-section) and angles of total shifts ¥ at cross-section of longitudinal axes of «diagonal» workings calculated according to formulas from Table 1
(¥j = 55°; ¥2 = 55°+ 0,3a; ¥3 = 55°)
Seam inclination angle a, degree Angle between longitudinal axis of working and seam strike e, degree Angles of total shifts lines inclination at cross-section of longitudinal axis of working, degree Angles of total shifts at cross-section of longitudinal axis of working, degree
From up dip side 92f From down dip side 91f From up dip side T2f From down dip side
20 0 55.0 55.0 55.0 55.0
20 58.9 64.7 66.0 57.6
40 58.9 71.1 72.0 57.9
60 54.4 75.1 71.9 57.6
80 45.9 76.4 65.6 56.7
90 41.0 75.0 61.0 55.0
40 0 55.0 55.0 55.0 55.0
20 56.3 68.3 72.3 52.3
40 54.9 78.6 83.2 50.3
60 46.9 86.9 82.9 50.8
80 32.2 -86.8 71.8 53.7
90 27.0 -85.0 67.0 55.0
Ending of Table 3
Seam inclination angle a, Angle between longitudinal axis of working and Angles of total shifts lines inclination at cross-section of longitudinal axis of working, degree Angles of total shifts at cross-section of longitudinal axis of working, degree
degree. seam strike e, degree. From up dip side 92f From down dip side 9if From up dip side Tf From down dip side Tif
60 0 55.0 55.0 55.0 55.0
20 49.9 72.1 80.5 41.5
40 46.2 84.9 94.3 36.8
60 42.4 -82.7 98.7 41.0
80 18.5 -69.9 78.2 50.5
90 13.0 -65.0 73.0 55.0
Note. When 9 < 0° boundary of flat bottom of the trough is located outside the working contour, i.e. above the coal pillar (point E' at Fig.2, j).
For visual perception in Table 2, 3 show values of the angles of inclination of total shifts (9) and the angles of total (T) shifts in the axial sections of the "diagonal" faces are calculated according to the formulas of Table 1. They make it possible to trace the nature of the variation of the named angles as a function of the angle of incidence of the formation a and the angle e between the longitudinal axis of working and the strike of the formation. This, in turn, facilitates the forecast of deformations of the earth's surface from the influence of workings.
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Authors: Natal'ya A. Kolesnik, Candidate of Engineering Sciences, Associate Professor, kolesniknatalka@gmail.com (Donetsk National Technical University, Donetsk), Gennadii I Kozlovskiy, Candidate of Engineering Sciences, Associate Professor, kolesnikna-talka@gmail.com (Donetsk National Technical University, Donetsk), Aleksandra A. Kanavets, Assistant Lecturer, yahy@meta.ua (Donetsk National Technical University, Donetsk).
The article was accepted for publication on 13 March, 2017.
