ENERGY
OF
FRACTURE
BURST-PRONE A.
A.
OF
COAL
IN
SEAMS
Borisenko
The crushing of coal in g a s b u r s t s has c e r t a i n f e a t u r e s . F i r s t , t h e r e i s an exceedingly l a r g e d i f f e r e n c e between the f r a g m e n t s i z e s of the coal b e f o r e and a f t e r crushing - five o r d e r s of m a g n i t u d e . Secondly, b u r s t p r o n e s e a m s have high jointing (endogenous f r a c t u r e ) . Thirdly, the specific e n e r g y expended on c r u s h i n g the coal in a b u r s t r a n g e s o v e r a wide r a n g e - t h r e e o r d e r s of magnitude (according to m e a s u r e m e n t s , f r o m 0 A to 44.0 kgf 9c m ] c m 3 ). All this m a k e s it n e c e s s a r y to evaluate the p o s s i b i l i t y of applying the known laws of c r u s h i n g to the c a s e of g a s b u r s t s ; f o r this purpose, coals of v a r i o u s d e g r e e s of f r a c t u r e and s t r e n g t h s in b u r s t - p r o n e and b u r s t - f r e e s e a m s of the Donets and P e c h o r a coalfields w e r e c r u s h e d by v a r i o u s static and dynamic m e a n s . The b r o k e n coal was s c r e e n e d on s t a n d a r d s c r e e n s into 13 f r a c t i o n s with p a r t i c l e radii f r o m +0.5 to - 0 . 0 0 2 c m . F r o m the r e s u l t s of a d i s p e r s i o n a n a l y s i s we calculated the c o r r e c t e d radius of the coal p a r t i c l e s (according to weight), r n [1]. It is known that the e n e r g y of s u r f a c e f o r m a t i o n does not depend on the method of b r e a k i n g ; however, the l a t t e r m a y g o v e r n the e n e r g y expended on m e c h a n i c a l p r o c e s s e s a c c o m panying the f o r m a t i o n of s u r f a c e . T h e r e f o r e , to d e t e r m i n e the law of c r u s h i n g of b u r s t - p r o n e coals, we b r o k e coals not only with a falling weight, but also by static crushing in a p r e s s and by grinding in a m i l l . To g e n e r a l i z e the e x p e r i m e n t a l r e s u l t s and to elucidate the law of c r u s h i n g of the coal, the value of r n f o r e a c h e x p e r i m e n t was reduced to unity f o! r a work of crushing of 1.0 k g f . c m / c m 3. The c o r r e c t i o n coefficient was d e t e r m i n e d as n = 1 / r n , where r n is the c o r r e c t e d radius of the p a r t i c l e s for a work of crushing of 1.0 k g f . c m / c m 3. The dependence of the specific w o r k o f crushing on the d i m e n s i o n l e s s v a r i a b l e r n / r n is shown g r a p h i c a l l y in Fig. 1. The d i m e n s i o n s of the p a r t i c l e s in the original m a t e r i a l w e r e 2-3 o r d e r s of m a g nitude l a r g e r than t h o s e in the c r u s h e d coal; t h e r e f o r e we neglected the initial work of c r u s h i n g . With a f a i r l y c l o s e c o r r e l a t i o n ( c o r r e l a t i o n r a t i o 0.86), the dependence of the c o r r e c t e d p a r t i c l e r a d i u s on the specific w o r k of c r u s h i n g is given by A'
A = (.,)17s,
(1)
w h e r e A' = 1.0 k g f . c m / c m 3. Thus, for c o a l s the dependence of the work of c r u s h i n g on the p a r t i c l e s i z e i s r e p r e s e n t e d by the equation of C h a r l e s [2] with an exponent of 2 o75. This law of crushing f o r c o a l s a g r e e s with the e x p e r i m e n t a l data b e t t e r than the e m p i r i c a l laws, both for the c o a r s e and for the fine p a r t i c l e s (Fig. 1). We t e s t e d coals f r o m four s e a m s in the P e c h o r a coalfield and 10 s e a m s in the D o n b a s s . The s t r e n g t h s of the coals under uniaxial c o m p r e s s i o n ranged f r o m 6.7 to 250 k g f / c m 2, and the d e g r e e of f r a c t u r e f r o m I to V on the s c a l e of S h t e r e n b e r g and Yablokov. T h e r e f o r e , Eq. (1) i s f a i r l y u n i v e r s a l f o r c o a l s . We m u s t note that, despite the unavoidable e r r o r s in d e t e r m i n a t i o n of rn, f o r e a c h e x p e r i m e n t the r e l a tion between the work done and r n was e x p r e s s e d by p o w e r functions with v a r i o u s different exponents, with v e r y high c o r r e l a t i o n r a t i o s close to unity. We m a y suppose that the exponent in the e m p i r i c a l laws of c r u s h ing (including Charles, law) is not constant but depends on the m e c h a n i c a l p r o p e r t i e s of the m a t e r i a l . But for a c l a s s of m a t e r i a l s with s i m i l a r p r o p e r t i e s (such as coals), to a c e r t a i n a p p r o x i m a t i o n we can a s s u m e that the exponent in the law of crushing is constant. F r o m the data in the method of c r u s h i n g . c r u s h i n g the solid coal p r a c t i c a l l y no effect on
Fig. 1 it follows that the r e s u l t s of crushing a r e n e a r l y o r c o m p l e t e l y independent of This conclusion follows f r o m a c o m p a r i s o n of the 11 m e t h o d s of crushing, including [3]. According to other data [4], i n c r e a s i n g the r a t e of c r u s h i n g b y a f a c t o r of 1000 had the r e s u l t s of c r u s h i n g . This i m p o r t a n t fact p e r m i t s us to extend the law of crushing
A. A. Skochtnskii Institute of Mining, L y u b e r t s y . T r a n s l a t e d f r o m F i z i k o - T e k h n i c h e s k i e P r o b l e m y R a z rabotki Poleznykh I s k o p a e m y k h , No. 5, pp. 96-101, S e p t e m b e r - O c t o b e r , 1979. Original a r t i c l e s u b m i t t e d A p r i l 11, 1977.
0038-5581/79/1505-0509507.50
9 1980 Plenum Publishing C o r p o r a t i o n
509
~/rn
;,2
~=
0,8
,,I
0,4
=2
AJ
+4
§
ee e
ei
o-
i
o
10
20
JO
kgf'cm/cm3
Fig. 1. G r a p h of r n c o r r e c t e d to unity v s w o r k of crushing 9 1) I m p a c t crushing; 2) i m p a c t c r u s h i n g of coal f r o m g a s b u r s t ; 3) crushing in p r e s s ; 4) in m i l l . in Eq. (1) to c r u s h i n g by a g a s b u r s t . We i n v e s t i g a t e d the shape of the coal p a r t i c l e s b r o k e n b y g a s b u r s t s and b y v a r i o u s methods of crushing in the l a b o r a t o r y . F r a c t i o n s m e a s u r i n g f r o m 1 c m to 0.025 c m w e r e studied under the m i c r o s c o p e with a known r a t i o between the m a x i m u m and m i n i m u m p a r t i c l e d i m e n s i o n s . In e a c h e x p e r i m e n t we counted about 1000 p a r t i c l e s for each of eight f r a c t i o n s ; in all we i n v e s t i g a t e d 33 coal s a m p l e s . It was found that the r a t i o between the m a x i m u m and m i n i m u m d i m e n s i o n s of the p a r t i c l e s r a n g e s f r o m 1.02 to 1.64, a v e r a g i n g 1.24. Taking account of the actual l i n e a r d i m e n s i o n s of the coal p a r t i c l e s , we found that the a r e a of the s u r f a c e s f o r m e d by c r u s h i n g the coal is 6~ l e s s than the a r e a of the s u r f a c e s of s p h e r i c a l o r cubical p a r t i c l e s . T h e r e f o r e , in d e t e r m i n i n g the c o r r e c t e d p a r t i c l e radius we can neglect the deviation f r o m t r u e s p h e r i c a l o r cubical shape (and this is what we did). An investigation of the shape of the p a r t i c l e s of b r o k e n coal (including t h o s e b r o k e n b y g a s b u r s t s ) r e v e a l e d that the bulk of t h e s e p a r t i c l e s a r e h e x a h e d r a with s m o o t h f a c e s . Hence we can i n f e r that the p a r t i c l e s f o r m e d by crushing the coal coincide with n a t u r a l s t r u c t u r a l units of the s e a m . It would be i n t e r e s t i n g to i n v e s t i g a t e p a r t i c l e s m e a s u r i n g l e s s than 0.025 c m in the s a m e way; however, such an investigation was obs t r u c t e d by aggregation of the p a r t i c l e s . In coal b r o k e n by g a s b u r s t s , p a r t i c l e s m e a s u r i n g m o r e than 0.025 c m constitute 75-94% by weight. About half the total e n e r g y of f r a c t u r e of the s e a m is expended on f o r m i n g t h e s e p a r t i c l e s . F r o m t h e s e r e s u l t s it follows that at l e a s t half the e n e r g y r e a l i z e d in f r a c t u r e of the s e a m in the f o r m of gas b u r s t s is not due to d i s s o c i a t i o n of c h e m i c a l bonds in coal m o l e c u l e s . To elucidate the physical e s s e n c e and to e s t i m a t e the p r o p o r t i o n a l i t y coefficient n, we p e r f o r m e d an investigation which involved testing coal s p e c i m e n s under uniaxial c o m p r e s s i o n p e r p e n d i c u l a r to the c l e a v a g e , followed by c r u s h i n g the coal and m e a s u r i n g the specific work of f r a c t u r e and the v a l u e s of r n. F i g u r e 2 is a plot of ~ c / r n v s the specific w o r k of f r a c t u r e . This dependence has a c o r r e l a t i o n r a t i o of 0.78 and i s e x p r e s s e d b y the equation AA
~ '~ ( I
w h e r e AA is the s p e c i f i c w o r k of c r u s h i n g of the coal in kgf 9c m / c m 3 ; ~rc, u l t i m a t e r e s i s t a n c e to uniaxial c o m p r e s s i o n , k g f / c m 3 ; rn, i and rn,2, initial and final c o r r e c t e d p a r t i c l e radii, c m ; and a = 597 kgf3/7[cmi3/~, an e m p i r i c a l coefficient. The specific w o r k of f r a c t u r e of the s e a m in a g a s b u r s t (rn, i ~ ~o) can be found f r o m the e x p r e s s i o n
A = (oc/597r.) ].Ts,
(3)
w h e r e r n is the c o r r e c t e d radius of the coal p a r t i c l e s b r o k e n b y the g a s b u r s t , in c e n t i m e t e r s . F r o m Eq. (2) we get an e x p r e s s i o n for the c r u s h a b i l i t y 1~ of the coal a s an e n e r g y index of its m e c h a n i -
510
oc/r
~ i
i
400(]
2000
" ~
./~,
/. 0
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I
"
i
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20
30
Fig. 2. G r a p h of a o / r n v s w o r k of f r a c t u r e . cal p r o p e r t i e s : R = hA.r~ '~5 [kgf.cm-~
(4)
According to the available data, g a s b u r s t s o c c u r when R = 0.062-0.214. H a r d c o a l s with d e g r e e s of f r a c t u r e I and II have higher v a l u e s of R - 1.736 o r higher. Thus f o r the s a m e d e g r e e of c r u s h i n g of the coal, b u r s t - p r o n e s e a m s r e q u i r e about o n e - t e n t h as m u c h e n e r g y as b u r s t - f r e e o n e s . In Eq. (4) we have a s s u m e d that the v a l u e of R is independent of the p a r t i c l e s i z e of the original s a m p l e r n I. F o r coals, this a s s u m p t i o n does not lead to l o s s of a c c u r a c y i f the s p e c i f i c w o r k of f r a c t u r e i s s u f f i c z e n t l y g r e a t - A = 5.0 k g f - c m / e m 3 o r m o r e . It is s i m p l e s t to d e t e r m i n e the index of c r u s h a b i l i t y with the aid of s t a n d a r d equipment for d e t e r m i n i n g the h a r d n e s s of the coal u n d e r c r u s h i n g . The index of c r u s h a b i l i t y of the c o a l s can be used to e s t i m a t e the m e c h a n i c a l p r o p e r t i e s and b u r s t h a z a r d of s e a m s in the regional prediction of b u r s t h a z a r d . It is known that coal s a m p l e s e x t r a c t e d f r o m g e o l o g i cal e x p l o r a t o r y b o r e h o l e s usually consist of b r o k e n coal, and it is difficult to d e t e r m i n e the s t r e n g t h of the coal f r o m t h e s e s a m p l e s . However, this p r o b l e m can e a s i l y be solved by d e t e r m i n i n g the c r u s h a b i l i t y index. If a s a m p l e f r o m a b o r e h o l e is of s t r r o n g l y c r u s h e d coal, it is convenient to d e t e r m i n e the c r u s h a b i l i t y index with allowance f o r the initial p a r t i c l e dimension by s c r e e n i n g the s a m p l e b e f o r e and a f t e r c r u s h i n g and using the e x p r e s s i o n
R = AA (r~.,5 rf , ). n,2
(5)
n,1
Since 1~ is an e n e r g y index, the b u r s t h a z a r d of a s e a m a c c o r d i n g to the m e c h a n i c a l p r o p e r t i e s f a c t o r i s i n v e r s e l y p r o p o r t i o n a l to B. In this r e s p e c t ~{ is i m p o r t a n t and differs f a v o r a b l y f r o m o t h e r indices of the m e c h a n i c a l p r o p e r t i e s of coal; for e x a m p l e , a twofold i n c r e a s e in the s t r e n g t h a c does not at all m e a n that f r o m the a s p e c t of e n e r g y the b u r s t h a z a r d is halved. F o r known v a l u e s of AA and r n f r o m E q s . (2) o r (3) we can d e t e r m i n e the s t r e n g t h of the coal (its u l t i m a t e r e s i s t a n c e to uniaxial c o m p r e s s i o n ) . As shown in [5], the c r u s h a b i l i t y indices c o r r e l a t e c l o s e l y with o t h e r m e c h a n i c a l indices of r o c k s . It is also of i n t e r e s t to elucidate the laws of distribution of the f r a c t i o n s of the c r u s h e d coal, including that c r u s h e d in g a s b u r s t s . The f r a c t i o n a l distribution of c r u s h e d r o c k s is, of c o u r s e , u s u a l l y r e p r e s e n t e d b y m e a n s of the Rozin-- R a m m l e r law. By using this law, o r any o t h e r known law, in d e t e r m i n i n g the w o r k of crushing we can l i m i t o u r s e l v e s to m e a s u r i n g the yield of an individual f r a c t i o n . F i g u r e 3 shows the c u m u l a t i v e c u r v e s of the yields of f r a c t i o n s of c r u s h e d coal f r o m b u r s t - p r o n e s e a m s (minus). F r o m t h e s e g r a p h s we s e e that in double l o g a r i t h m i c c o o r d i n a t e s the c u m u l a t i v e c u r v e s b e c o m e s t r a i g h t lines (i.e., s a t i s f y the R o z i n - R a m m l e r law) only f o r s m a l l specific w o r k of crushing, high strength, and c o r r e s p o n d i n g l y low d e g r e e of d i s p e r s i o n of the coal. As the w o r k of c r u s h i n g i n c r e a s e s , the actual d i s tribution of the coal f r a c t i o n s i n c r e a s i n g l y d e v i a t e s f r o m the distribution c o r r e s p o n d i n g to the R o z i n - R a m m l e r law. To v e r i f y whether this deviation is due to p e r s i s t e n t e r r o r s , we c a r r i e d out crushing (by the u s u a l method) and d i s p e r s i o n a n a l y s i s on g l a s s and m a r b l e . As seen f r o m the g r a p h s in Fig. 3, the p a r t i c l e d i m e n sion distributions for t h e s e m a t e r i a l s do fit the R o z i n - R a m m l e r law, like those f o r strong coals o r for low s p e c i f i c work e x p e n d i t u r e s . F r o m t h e s e r e s u l t s it follows that as the amount of w o r k expended on c r u s h i n g i n c r e a s e s , t h e r e i s a r e l a t i v e d e c r e a s e in the yield of fine f r a c t i o n s ; t h i s tendency i s m o r e m a r k e d in weak b u r s t - p r o n e c o a l s . T h i s
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Fig. 3. Cumulative distribution curves of particle sizes on Weibull net. a) Mazurka seam, Donbass; degree of fracture. IV; specific work of crushi~4;: 1) 15.6; 2) 6.9; 3) 2.15; 4) 0.78 kgfocm/cm3; marble: 5) 36.1; 6) 18.0 k g f - c m / c m 3. b) Livenskii seam, Donbass; degree of fracture, HI; specific work of crushing: 1) 6.4; 2) 4.8; 3) 3.1; 4) 1.55 k g f . c m / c m 3. c) Chetvertyi seam, Pechera coalfield; degree of fracture, I-H; specific work of crushing: 1) 12.6; 2) 4.9; 3) 1.6 k g f o c m / c m 3. Troinoi seam, Pechora coalfield; degree of fracture, V; specific work of crushing: 4) 0.8; 5) 0.4; 6) 0.09 k g f - c m / c m 3. d) Berestovskii seam, Donbass; degree of fracture, IH; specific work of crushing: 1) 7.4; 2) 4.9; 3) 2.5 kgf-cm/cm3; glass 18.3 k g f - c m / c m 3 (4). phenomenon can be explained as follows~ Since the coal p o s s e s s e s an initial jointtng fracture, in the first stages of crushing the breakage of the fragments involves separation of the coal into its natural structural elements; this breakage requires minimal energy ex1~enditure. But the formation of fragments with radii l e s s than the radius of the structural elements of the seams requires greater energy expenditure. Therefore, it is natural that as the energy expenditure and the overall degree of dispersion increase, the yield by weight of particles of small radius relatively decreases. A similar hypothesis concerning the role of structural elements in rocks has been advanced, in particular, by Koshelev et al. [6]. The cumulative curves for coal from a single seam, obtained for various specific values of the work of crushing, have a constant slope (Fig. 3). However, the slope differs from one coal to another. Clearly, the an~gle of slope of the curves characterizes the properties of the coals corresponding to the above hypotheses their endogenous fracture (jointing). It is characteristic that deviations from the Rozin-- Rammler law are not observed for unjointed materials such as glass and marble. Attempts have also been made to represent the experimental particle radius distribution using other two-parameter equations [7]; however, these were not successful. Since no specific law of particle-size distribution has been found for burst-prone coals, the yields of the individual fractions do not characterize the work of fracture of the coal with sufficient accuracy. In this respect, the most acceptable index for determin512
ing the results of crushing of coal is the c o r r e c t e d particle radius. The above results can be used to develop a theory of gas bursts for practical purposes - in estimating the mechanical properties of the coal and in methods of predicting burst hazard. LITERATURE 1. 2. 3.
4. 5. 6. 7.
CITED
S . E . Andreev, V. V. Tovarov, and V. A. Perov, Laws of Crushing and Calculation of Part i cl e Size Composition Characteristics [in Russian], Metallurgizdat, Moscow (1959). R . J . Charles, "Energy--size reduction relationship in comminution," T r a n s . Am. Soc. Mech. E n g , 208 (1957). J. Grantmure and J. Hawkes, "High-energy impact rock breaking," Can. Mining Met. Bull., No. 760
(1975). B. Kh. Bergstrom, "The energy and dimensional aspects of crushing of a single particle," in. Rock Mechanics [in Russian], Nedra, Moscow (1966). L.I. Baron, Yu. G. Konyashin, and V. M. Kurbatov, The Crushability of Rocks [in Russian], Izd. Akad. Nauk SSSR, Moscow(1963). E.A. Koshelev, V. M. Kuznetsov, S. T. Safronov, and A. G. Chernikov, "The statistics of fragments formed by blasting solid bodies," Zh. Prikl. Mekho Tek_h. Fiz., NOo2 (1971). P.A. Kouzov, Principles of Analysis of the State of Dispersion of Industrial Dusts and Crushed Materials [in Russian], Khimiya, Leningrad (1971).
513