PREDICTING

T H E B U R S T H A Z A R D OF C O A L

S E A M S FROM P H Y S I C A L G.

INDICES

N. F e l t

UDC 622.815:622.23.02

Contemporary ideas on the nature of rock bursts lead to the logical conclusion that a comprehensive outburst hazard index for coal seams should be a function of indices which describe the gas and rock pressure factors and take account of the physical and m e c h a n i c a l properties of the seams themselves. The gas factor W can be specified quantitatively by the amount of energy which can be developed by the expanding gas emitted by the coal when it disintegrates over a period of time comparable to that of a burst, i.e., not more than 30 sec. It is extremely difficult to give an exact solution to the problem of the expansion energy of the gas when the coal disintegrates, because we are dealing with a polytropic process. But it may be solved to a first approximation quite satisfactorily if we assume that, in a rock burst, it approximates most closely to an adiabatic problem, so that the change in the internal energy of the gas when it passes from state (PI, T1) to state (Pz, T2) is given by: k--1

k -- 1

22414

,-~-j

cal/ton,

(i)

where R is the gas constant (R = 1.98 c a l / m o l e , deg), k is the adiabatic index (for methane, k = 1.32), Pl and P2 are the initial and final gas pressures in kilograms per square centimeter, V is the volume of gas capable of doing work when the pressure drops from Pi to Pz, and T is the absolute temperature of the coal-gas system in degrees Centigrade, Substituting for R and k in (1) and assuming that T = 273 + 30 = 303~ the burst falls from Pl to 1 atm, the equation simplifies to

l~/

"-'- 8 0 0

and that the gas pressure at the time of

V [l -- (___~1 ~0,24] cal/ton. \Pl

/

(2)

J

The volume V of gas capable of doing work when the pressure drops from Pl to P2 depends on the sorption c a pacity of the coal, apl, at pressure p t , a n d i t s capacity to emit gas at the initial moment. The capacity of a coal to emit gas per unit t i m e depends basically on the breakability of the coal (the size of the fractions obtained on disintegration), and can be represented by the coefficient of gas transfer b30 which shows the ratio of the amount of gas emitted, in the first 30 sec after disintegration, from coal of given size to the total sorption capacity of this coal. The amount V30 of gas which can take part in a burst at a known coal sorption capacity ap and gas transfer c a pacity c30 is found by known experimental methods [1, 2] or by means of a nomogram [3]. The rock pressure factor k can be expressed quantitatively as the ratio of the m a x i m u m abutment pressure on the seam in the face area to the compressive strength of the seam:

X=S/R,

(3)

where k is an ~!r representing the stress or load state of the seam in tons per square meter, 8 is the abutment pressure on the ,~gm due to the surrounding rock in tons per square meter, and R is the compressive strength of the seam

Skochinskii Mining Institute, Moscow. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 2, pp. 23-26, March-April, 1968. Original article submitted December 26, 1966.

112

t=1,7 9

in tons per square meter. Where a seam has a complex structure and consists of several bands of different strengths, the average strength of the seam as a whole is determined by taking into account the weakening effect of soft partings using the VNIMI ( A l l Union Mine Surveying Research Institute) formulas [4].

s W=1,76 9

t,O-

o

|

o

9

"

O

--o

-

'%-o,4e)(~-o, le)-o, xe~

? I

I u

u

I

i

I

0,5

i

i

I

l.O

u

~_

W

Gas energy Fig. 1. Burst hazard of coal seams, plotted versus seam stress k and occluded gas energy W. o) Dangerous seams; O) safe seams.

Thus, having found two indices W and X which express the gas and rock pressure factors, we can obtain a comprehensive i ndex for the burst hazard which is a function of these: A B = at(W, X). This is done by defining the burst-prone areas of W and X in a graph of W versus X (see Fig. 1). This method was used to find a n u m er i cal v al u e for the comprehensive burst hazard index for coal seams in the Central and Donetsk-Makeevka areas of the Donbass. The gas pressure in the seam was c a l c u l a t e d by the e m p i r i c a l formula used in the Donbass: p ~ 0.1 ( H - H 0 ) , where p is the methane pressure in the seam in atmospheres, H is the depth from the surface in meters, and H0 is the depth of the upper l i m i t of the m e t h ane zone in meters.

The sorption capacity of the coal ap at pressure p, the gas: transfer coefficient of the coal %0, and the quantity of gas which can be emitted in the first 30 sec when the coal disintegrates, Va0, were found for each seam individually by means of a nomogram [3]. The energy of the gas capable of participating in the burst was found by means of (2); the rock pressure was found from the formula S = . k 1[ H a,,,

(3')

where k is the stress concentration coefficient (from field observations and models, this coefficient is 1.5-3.0; for calculations it is taken to a first approximation as k = 2), }, is the m e a n v o l u m e t r i c weight of the rock in tons per cubic meter, H is the depth from the surface in meters, and ac~ is the coefficient of the e f f e c t of the gradient c~ (when cx < 30 ~ acx = 1; when ot = 30-60 ~ acx = cos cx; and when c~ = 60 ~ or more, ac~ = 0.5). The m e a n compressive strength of the seam was found e x p e r i m e n t a l l y in the field using a P-1 strength gauge by a method described in [5]. The load coefficient of the seam can be found from (3). Figure 1 shows the d e t e r m i nations of indices W and X for 18 seams in nine collieries of the Central and Donetsk-Makeevka regions of the Donbass. For co n ev n i e n c e in data processing, the indices are plotted along the axes of abscissae and ordinates in standard form: X = X/3.72; ~ /= W/3400. It will be seen that the values of W and X at which bursts tend to occur (dangerous seams) and those at which no bursts occur (safe seams) lie in different parts of the graph. The burst-prone region can be demarcated from the safe area by a hyperbolic curve, ( ~ - 0 . 4 2 ) x ( W - 0 . 1 8 ) - 0 . 0 1 2 = 0, or, replacing ~ a n d Wby k and W,

(7, -- 1,6) Beginning

from (4), the burst hazard

A~-

(W--

index for a seam

().-

600)

-- 150----.0.

(4)

can be found from the formula

1,6)(W--

600) -- 150.

(5)

Where AB >-- 0 the seam is prone to bursts, whereas where A B < 0 it is safe. The graph and (5) show that bursts cannot take p l ace even where the seam is highly stressed, provided that the energy of the gas e m i t t a b l e in 30 sec when the coal disintegrates is less than W = 600 c a l / t o n , or, where high gas energy values are involved, provided that the index of the seam load (stress) lies below X = 1.6. The burst index of the seam, AB, is not constant, but depends on variations in the mining or g e o l o g i c a l c o n ditions under which the seam is being worked (this index in fact increases with en h an cem en t of the burst-promoting factors). Therefore if the burst index is to be reliably determined, we must introduce a safety factor which takes account of the variability of mining and geological conditions. Eq. (5) then becomes

113

'A.

= ()"av-;-- %, -- 1.6) ( ~ a v +

v v / - - 600)

(6)

150.

The average values of the seam load index (stress) Xav and the gas energy Wav and their coefficients of v a r i a tion (v x and Vw) are found for a sector of the seam which is t y p i c a l in terms of mining and g e o l o g i c a l conditions and which is at least 20 m long and 20 m to the strike. The burst hazard of seams and the effectiveness of measures to combat bursts can be found, provided that a quantitative determination of burst probability is carried out under specific mining and g e o l o g i c a l conditions. If the probability of a burst is taken as the probable attainment by the index of a c r i t i c a l value A~ at which bursts will occur, then the burst probability X can be c a l c u l a t e d by statistical methods: X = 1 - P , where P is the probability that a normally distributed random variate A B wii1 fall in the interval ( 0 , A ~ ) , i.e., the probability that a burst will not take place. The value of P can be found from the expression A x - Yl B

0 -- AB B

2~

Z~

1

~

• =,0(

e

9

)

2 dz

__

(I) 0

1

(

e

)

2

p

where 40 is the normalized Laplace function, found n u m e r i c a l l y from tables, AB is the mean value of the index in the zone, o is the standard deviation (o = AB VA)' and A~ is the critical v a l u e of the index at which a burst occurs (from preliminary data, this m a y be taken as ~ 4000). As an e x a m p l e , we give calculations of the probability for the Mazur seam of the Yunkom colliery. The i n i t i a l data are as follows: _(13o(

0 - 39oo 600

-A~ ~--- 3600; A~ = 4250; 0=900.

) = 0.7641.

/9(0 < AB • A~)

~b0

(

4250--3600 900

)

Thus the burst probability is X = 1 - P = 0.3359. CONCLUSIONS

A method is proposed for predicting bursts in coal seams by means of an index which for the first time takes comprehensive account of the seam stress and the energy of the gas which can take part in the burst, these values being determined in the light of the physical and m e c h a n i c a l properties of the coals themselves. The author shows how it is possible to determine quantitatively the burst probabilities for various mining and g e o l o g i c a l conditions. LITERATURE 1.

2. 3. 4. 5,

114

CITED

A. A. Skochinskii, V. V. Khodot, M. F. Yanovskaya,et al., Methane in Coal Seams [in Russian], Ugletekhizdat, Moscow (1988). M. F. Yanovskaya, "An approximate method for c a l c u l a t i n g desorption of methane during disintegration of coal in a burst," in: Combating Bursts in Coal Seams [in Russian], Oosgortekhizdat, Moscow (1962). M. F. Yanovskaya and Yu. S. Premysler, Nomograms for Calculating Gas Emission during Disintegration of Coal [in Russian], izd. IGD im. A. A. Skochinskogo, Moscow (1967). G. N. Kuznetsov, F. P. Bublik, and S. O. Kuznetsov, The Strength of Nonuniform Interchamber Pillars [in Russian], Co11. 18, izd. VNIMI, Leningrad (1962). G. N. FeAt, The Strength Properties and Stabilities of BUrSt-Prone Coal Seams [in Russian], "Nauka," Moscow (1966).