Prediction of rock and gas outburst occurrence

Engineering Geology, 33 (1993) 241-250 Elsevier Science Publishers B.V., Amsterdam

241

Prediction of rock and gas outburst occurrence T. C y r u l Polish Academy o[ Sciences, Strata Mechanics Research Institute, Reymonta 27, 30-059 Krakow, Poland (Received March 31, 1992; revised version accepted August 26, 1992)

ABSTRACT Cyrul, T., 1993. Prediction of rock and gas outburst occurrence. Eng. Geol., 33: 241-250. The concept of a rock and gas outburst as an event in a random field is presented. Within the framework of the concept a non-physical approach to outburst prediction is demonstrated. The approach employs a cause-effect scheme to study relations between the causes and effects of outbursts. The effects are recognized as dychotomic functions of space that take value one when an outburst occurred and value zero in the opposite case. The effects are real-valued functions of space that are interpreted as realizations of a random field. The division of the cause space and the approximation of the effects by simple functions with regard to the division under the criterion of the minimum mean squared error lead to a model that allows outburst prediction. The parameters of the model was were estimated on the basis of measured data from the "Nowa Ruda" coal mine. An example of the application of the model is also presented.

Introduction The great variability o f rock and gas outbursts has caused controversy and a range o f opinions a b o u t the nature o f the p h e n o m e n o n and inspired the formulation o f different hypotheses o f origin. Some attempts to systematize these opinions and hypotheses were have been undertaken by several authors (for example, Pieczuk, 1969; Cis, 1971; Gil and Swidzinski, 1982; H y m a n , 1987). Gil and Swidzinski (1982) devide the hypotheses on the initiation mechanism o f rock and gas outbursts into three categories: (a) Hypotheses that ascribe the main role in the initiation mechanism to gas. (b) Hypotheses that prescribe the main role in outburst initiation to rock stresses. (c) C o n t e m p o r a r y hypotheses, that treat outbursts as resulting from a n u m b e r o f factors including gas content, stress level, mechanical properties o f rocks, tectonics, etc. Correspondence to: T. Cyrul, Polish Academy of Sciences, Strata Mechanics Research Institute, Reymonta 27, 30-059 Krakow, Poland. 0013-7952/93/$06.00

C o n t e m p o r a r y theories, which treat the outburst multi-parametrically, are undoubtly the closest to explaining the outburst mechanism. Nevertheless, there is to date little agreement concerning the relative importance o f particular parameters in the outburst process, while the role o f each o f the parameters in the outburst process has also not been determined. F o r example, Cyrul (Cyrul, 1987) in his poll o f 25 Polish experts on outbursts compiled a list o f 47 different factors that have been pointed out as important. Olchoviczenko (1982) indentifies 70 factors which play a role in rock and gas outbursts occurrence. This dispersion o f opinions make us d o u b t the possibility o f arriving at an explanation o f its mechanism, and obtaining an operational formula for practical applications, in the near future. On the other hand, mine personel face this hazard which has accounted for some 15,000 victims in the last ten years (Airuni, 1987). One m a y suspect that the divergence o f opinions on the n u m b e r and relative importance o f particular factors affecting outbursts originate from the shortage o f quantitative in situ data. To fill this information gap, industrial research laboratories

~ 1993 -- Elsevier Science Publishers B.V. All rights reserved.

242

were created in Poland at the beginning of 80"s. The main duties of these laboratories were the conducting of in situ measurements and the sampling of deposits, as well as the creation of data files characterizing rock and gas outbursts. Results of the laboratories activity have been stored in a data bank and are accessible to industrial and academic research institutions. Some of the results of these measurements have been presented earlier (Cyrul, 1988; Cyrul and Piotrowski, 1990). In this paper we will use some of the data to estimate a model for the prediction of rock and gas outbursts in the "Nowa Ruda" coal mine. Rock and gas outburst

Outbursts are described as sudden and violent releases of gases and rocks that result from a complex combination of factors including geology, stresses, gas content and rock properties. The force of the released gases and transported materials can not only disrupt mine ventilation but also debilitate ground control structures. Since outbursts first began occurring about a century ago, extensive research has been conducted onto their occurrence. There is a great body of literature on the different aspects of outbursts (Backer, 1984; Pieczuk, 1968, Hyman, 1987). Theories have been developed to gain an understanding of the causes and mechanisms of outbursts. Pieczuk (Pieczuk, 1969) subjected 141 outburst theories and hypotheses to a critical analysis. Since then numerous models has been proposed, for example those of Litwiniszyn (1983) or of Barton and Kullmann (1990), enlarging the literature. Some authors have grouped the further hypotheses according to the dominant cause(s) of outbursts. According to them the "pocket", the "dynamic" (Hyman, 1987; Backer, 1984) and the "multiparameter'" (Gil and Swidzinski, 1982) theories selected from the body of literature can describe the basis of the outburst mechanism. A paradoxical situation results from the study of the literature. Despite great disagreement among experts, even on very basic questions, concerning dominant causes and mechanisms (Szewczyk, 1985), scientists and researchers tend to describe the mechanism in very sophisti-

~ ~ ~ ~ 'i

cated terms, while mining geologists and engineers vainly try to predict this hazard with any degree of reliability. A c o n c e p t o f r o c k and g a s outburst description

In practice we mostly lace the following situation. We excavated various types of workings in deposit and usually unexpectedly we "'induce" an outburst. Except for so called "compact outbursts" (Kozlowski, 1980), there is no rule for predicting outburst occurence. The outburst, as a discrete phenomenon, can be represented in space by a single point. It can be regarded as the observed effect resulting from the performance of a natural system that can be isolated in the rock mass environment. Figure I shows a schematic representation of such a system. Vectors P and S, depending on particular discipline, are referred to, respectively, as causes and effects, input and output (or excitation and response). Each system can be characterized by measurable quantities called features of the system. All of the measurable outburst features are functions of space. According to the previous reports (Cyrul, 1988, 1990) they are very erratic, as are most geological data (Agterberg, 1974), and are often best dealt with in terms of a probabilistic interpretation. Accordingly, we can characterize an outburst environment by a vectorial random field Z of the following form: Z(x, (o)= (So(x, (o), Sl (x, ~,3)..... &(x, ~,)), x PI(x, (o)..... Pro(x, co))

(I)

where x ~ ~v is a point in space and (o ~ ~ is an elementary event. The component So assumes only two values: {~ - - outburst So =

(2) --

no outburst

Components SI ..... Sk of the vector S=(S~ ..... Sk)

)

)

)

¢:p

)

Fig. I. C a u s e

effect scheme.

) S

S )

PREDICTION OF ROCK AND GAS OUTBURST OCCURRENCE

243

describe observable effects of the outburst. They have non-zero values at that time when So = 1. Components P1 ..... Pm of the vector P = (P1 ,'",Pro) r represent observable causes of the outburst. Let D c ~P be a set of points. It is known that the best approximation of a component Si within the class of random fields F = a [ P ( x , to), x~D] measurable with regard to the a-field (Halmos, 1950) is a posteriori mean E(SiIF). To find the conditional expectation we need full probabilistic information, i.e., the distribution. This is a pity since we ususally have at our disposal only a matrix Z, of n observations of the form: Sol , ...,

Son

811 , ...,

Sin

•

Z=

.

[Sol,

...,

SOn-

Skl ..... Skn

= LS1 ..... Sn

Pin

P1 ..... P.

Pll

.....

(3)

conditional expectation: E(SIa(P1 ..... P,) ^ So = 1) gives relations between the outburst effects and causes P~ ..... P, under the condition that the outburst have actually occured. Certain aspects of this model have been discussed in Cyrul (1992). Model 3 (cause-effect) in the form: go =f(P1

..... Pn)

(5)

being an approximation of the conditional expectation:

E [So Ia(P, ..... P.)] gives the probability of the outburst occurring when causes P1,...,P, have been observed• From the pragmatic point of view of predicting outbursts, model 3 as represented by Eq. 5 is of special interest• The construction of an operationl form of the model as well as a demonstration of its application will be the scope of the subsequent sections of this paper. The model

Pro1, " " ,

Pmn

i.e., the set D = {xl .... ,x,} is in this case a discrete set. We have to introduce some assumptions to narrow down the class F. To achieve a reasonable compromise between an optimal, but in practice unrealistic, model, and a possible one (i.e., a simplified model) we have to carefully introduce assumptions and verify them using the available data. To fully characterize the outburst environment for the purpose of outburst prediction we need three models. Model 1 (structural) should describe space relations in the vectorial random field P(x, co). Within this model characterization of the outburst environment should be conducted. The theory of regionalized variables or classical statistics are the options to be employed. The subject has been discussed at length in Cyrul (1990). Model 2 (cause-effect) in the form: 'S = ($1 ..... Sk) T = ¢b(P 1 ..... P,)

(4)

(see Halmos, 1950) being an approximation of the

Let us consider a random field: Z(x, to) = (So(x, ¢o), P1 (x, to) ..... P,,,(x, to))

(6)

where x ~ ~P is a point in the "geographic" space (the deposit) and to ~ O is an random event• S can assume only one of two values as in Eq. 2. We treat the components P1,...,P,, as causes of an outburst and assume that component So does not depend on x directly, but only through the causes Pl(X, to) ..... P,,(x, to) which depend on x directly. Let P be a set of values of causes P1 ..... P,,, being a specific or non-specific subset of II~" and represent P by a finite sum of separable sets B 1, i= 1..... k, e.g.: k

P = U B, ^ i # j ~ B, ~ Bj = ~ ,

(7)

i=1

The dichotomic component So(to, x) will be approximated by simple functions with respect to the division {B1} in such a way as to minimize the mean squared error of that approximation. Denoting by Zs(x) an indicator of the set B, e.g.,

244

,

the function:

Accordingly:

xeB O, x C B 1.

)~B(X)=

(~ ]~ll

k

~'~o(X, co) = ~ P[So(x, co) i=l

= I I(PI(x, c0)..... Pro(x, CO)• Bi] the component So can be approximated by the equation: k

So(x, co)= ~ OqZn,[Pl(x, co)..... P,.(x, CO)]

(8)

i=l

and: ( ~ ..... ~k) = arg min Ep[So(x, CO) k

- ~. cq){B,(PI(x, co)..... Pro(x, co)]

x ZB, [PI( x, co)..... Pro(x, CO)]

(12)

It is easy to prove, that the above expression is a version of the expected value of the component So(x, co) with regard to the sub-field generated by the division {Bi} of the space of the values of causes P1 ..... Pro, because So(x, co) is a measurable function on that sub-field and satisfies the proper functional equation (Szczepankiewicz, 1985):

(9)

i=1

where Ep is the expected value with regard to the (unknown) distribution P on the space £2 of elementary events. It is easy to see that:

VBi ft~i S(x, co)P(dco) -- ~

E(S(x, co)P(dco)]a(Bi ..... B.))P(dco)

dB i 82 = Ep[So(x

-

, (I))

(13) Moreover, the mean squared e r r o r •2 of the above approximation is expressed as:

1

~iXB,(Px(x, co)..... P,.(x, co)

-

i=1 k

k

= ~ i-1

k

2 °q°'gEp{XB,[P'(x, co)..... P,,(x, CO)]I

~,2= P(ISo(x, co)= l~)- Y~ P [So(x, co)

j=l

i=1

X ZBj[PI(X, ra))..... P,,(x, ¢o)]

= 11[PI(x, co)..... Pro(x, co)] • Bi]

k

x P({[PI[(X, CO)..... Pm(x,~o)]eBi})

2 Z aiEp{So(x, co)

-

(14)

i=1

x ZB,[Pa(X, CO)..... P,.(x, co)]} + Ep{S2(x, co)}

We can estimate values 8i being an assessments of conditional probabilities

k

= ~ a2n({[nl(x, co)..... P,.(x, CO)] • S i } )

P({So(X,

i=1

co) = 11(Pl(X, CO). . . . .

P.,(x, CO))~ Bi})

(15)

k -

-

2 ~ aiP({[P,(x, co)..... P.,(x, co)] i--1

• B i A S o ( x , co)=l})+P({So(x, CO)=l})

Finally we have the model: (10) k

Finding the minimum of this function we obtain:

So(x, co) = ~ ~i,~n,[Pl(x, co)..... Pr~(X, CO)]

(16)

i=l

~i ~-

P( { [ P I (x, co), ..., P,,(x, co)]• Bi /x So(X, CO)= 1}) P({[P,(x, CO)..... P,.(x, co)] • Bi}) = P(So(x, co) = 11[Px(x, co)..... P,.(x, co)] • Bi)

(1])

that allows us, on the basis of measurements or as a result of the prediction of values of causes P1 .... ,P,., to determine the probability of occurrence of an outburst at an arbitrary point x of the geographic space and to evaluate the mean squared error of that approximation.

PREDICTION

Data

OF

ROCK

AND

for the model

GAS

245

OCCURRENCE

OUTBURST

estimation

methane content [m3/t]; (CH4) carbon dioxide content [m3/t]; (CO2) - - desorption [mm H20]; (Dp) - - gas pressure [kPa]; (P) - - volatile matter [%]; (Vb) - - ash content [%]; (Aa) - - moisture content [%] (Wc) - - Protodiakonof's coefficient [ - ] ; (F) - - seam thickness [m]; (Mi) Figure 3 shows histograms of values of all the features measured at outburst (So = 1) and nonoutburst (So=0) points within the deposit. To make the comparison easier, histograms of a given cause for S o = O and for So= 1 are placed in the same column one above another and the value (horizontal) axis of the lower histogram only is named. It is easy to see that histograms of some causes (Vb, Mi, F, Wc, Aa) cannot be differentiated in terms of the value of the dichotomic component So, i.e., they are irrelevant to outburst occurrence. Histograms of some others (P, CO2, Dp or CH4) differ substantially for different values of So and can be recognized as principal cause of outbursts. For example, the histogram of gas pressure (P) has the same shape for So = 0 and S O= l; however, the range of values for the latter case is almost two times larger than the range of the former. The modal value of P for the first Case is l l0 [kPa] while for So = 1 it is close to 200 [kPa]. The range of values of desorption (Dp) is similar for both cases (547 and 557 [mm H20]); the histograms, however, differ significantly. For 'So = 1 the histogram of Dp is almost symmetrical with the modal value around 270 [mm H20], while for S o = 0 the histogram of Dp is highly positively skewed with a modal value of 100 [mm H20]. Histograms of Z1 are very irregular and difficult to interpret. Nevertheless one can see that higher Z1 values are more frequent for So = 1, i.e., for outburst occurrence. In terms of the scheme in Fig. i, the principal causes can be recognized as signals; the irrelevant ones as noise. --

--

The data comes from the "Piast" coal basin of the "Nowa Ruda" coal mine. The mine is located in the southwestern part of Poland and is one of the most hazardous mine in the world (Backer, 1984; Cyrul and Piotrowski, 1989). According to Eq. 1 both outburst locations and sampling locations without outbursts can be represented by points in space. Figure 2 shows the two types of points within the coal seam of the "Piast" field. The points marked by ( + ) represent locations of outburst occurrences for which S o = 1. The remaining points, marked by (o) show sampling locations at which there were no outbursts and, therefore, So=0. Figure 2 represents only such points at which in addition to geographic coordinates X, Y, Z, the following features (outburst causes) have been measured: - - depth from the surface [m]; (Zi)

PLANE VIEW

,f°÷ ?

,

l:)

+

N

Z

o_l_ I--- U3 (JILl _J~
ILl >

g ~e +

,'-

i

':e-"° + o .....

VERTICAL SECTION FACING NORTH

C)

So-So :

1 0

i

4-60

rn

Fig. 2. Location of sampling points in the coat seam of the " N o w a R u d a " mine at which an outburst occurred ( + ) and did not occur (o).

Probability

of rock

and gas outbursts

occurrence

--

An example

With the use of the model represented by Eq. 16 one can predict the occurrence of an outburst

246

t (3Rtl

i t./) ,

,

12

m

o

34

~

40

,

o ,

600

r ~

.8

o

22

,

406

829

o

2

3.5

on

cP

12

o

Vb

50

40

\

P

"2 320

o 0

22

C02

c, 557

,

o 824

Z1

, .3

M;

, 3.7

I

CO •

,

0

, 0

,

0

2.0

, ~

CH4

O ,

0

o 2.8

557

m , 2

5,¢7

,

rl]']

.1

. 0.2

Dp

_

1.'4

,

F

'2 l.O

o

,

~

.4 o~

m

7.9

35

o.i[lL

m .e

2.0

774.

2.1

Wc

Ao

~ 37

Fig. 3. Histograms of values of outburst features measured at points at which outbursts occurred (S = l) and did not occur (S=0).

at an arbitrary point Xo of the deposit. This can be done in two steps: Step I. For an arbitrary point x0 e R p in the geographic space, we estimate values of causes Pl(Xo, O~)..... P,,(x,co using well-known methods such as, for example, kriging or co-kriging, developed by Matheron (1971), for vectorial data. Resulting from the first step we obtain the assessments:

l - S ( x o, e)). The above-mentioned reasoning can be presented graphically as in Fig. 4. In the proposed prediction procedure, step lI is especially simple for it is limited only to the classification of the point (['l(Xo, co) ..... #,,(Xo, co)) to one of the sets B~ and to the substitution:

(t61 (Xo, co)..... /3m(xo, co))

The procedure that has been proposed is flexible. Each of the steps can be improved. At this moment we will consider as an example the prediction of rock and gas outbursts in the "Piast" field of the Nowa Ruda mine. Since we have only

(17)

Step II. We then calculate the value of: k

~o(Xo, ~o)= ~
P.(x,co)]

i=l

(0, l )

So(xo, ~o) = ~i = P{So(x, co) = 1 ][Pl(x, ~o)..... P,,(x,e))]}EBi

(19)

(18)

which is interpreted as the probability of an outburst occurrence at point Xo (or as the degree of the rock and gas outburst hazard). The proposed method of rock and gas outburst prediction c a n b e seen as a randomized decision rule. The particular decision can be made after completing the random experiment, which ascribes to the outburst the probability S(xo, co) and to the non-occurrence of an outburst the probability

st ep_~

0 %(xo,t~)

geogrclphic space

sp(Ic~ of ccluses

Fig. 4. Schematic representation of the developed prediction procedure.

247

PREDICTION OF ROCK AND GAS OUTBURST OCCURRENCE

data from 369 sampling points we will consider only three (out of ten) "causes" of outburst. Let us divide the range of variability of the first 'cause' (see upper horizontal CO2 axis in Fig. 5 and F in Fig. 6) of outbursts into three sub-ranges in such a way as to assure that a similar number of observations falls into each sub-range. For CO2 in Fig. 5, the respective limits of these sub-ranges are (min - 2.775), (2.775 - 6.3), (6.3 - max). The denominators of the simple fractions ascribed to these sub-ranges are equal to the number of observations to fall into the given sub-ranges. For CO2 in Fig. 5 the numbers, are respectively, 123,

121 and 125. Within each of the sub-ranges, the range of variability of the second cause (see vertical P axis in Fig. 5) also is divided into three sub-ranges, thus resulting in a total of 3 × 3 = 9 fields of variability for two causes. Similarly the third cause (see small horizontal Dp axis in Fig. 5) is divided into three, sub-ranges, possibly of equal size, within each of the nine fields. The results of this is that of ~3 is divided into 27 fields. For each field we count the number of observations falling into it and then we chose those of the observations which are related to outburst, i.e., to So =1. The ratio of the number of these

co / P n ~ 2

82 121

22 123

113 I

125

)

i

6.3

2. 778 0

0

4

1

I'll 41

1

4 39

1

3

)Dp

51

27

16

130

-165 . . . . . . . . . . . . . . . . 0

3"/

78

141

0

>Dp

258

2

/P/Dp

18

i 23

i 2o

130

23

>Dp

258

44

130

258

>Dp

>Dp

42 44

= 0.21

23

1

255 .............

44 44

P CO

0

44

'Dp

15

C

)Dp

41 44

19

40

,p

296

165 ..............

11

130 . . . . . . . . . . . . . . . 15

8

130

28 36

3 44

2

28 37

-145 . . . . . . . . . . . . . . . .

0

0

)Dp

12 41

415 ................

0

116

71

20

0

10

>Dp 54

CO

P

c

CO

2

/P

= 0.27

Fig. 5. Probabilities of outburst occurence for 27 divisions of the cause space composed of values of CO2, P and Dp.

24S

I ( b I
F/Aa/Vb

73 123

64 129 I

80

10

3

13

I 13 I 16 21.0

0.565 11

lO

i 14

t 13

S

>Vb

14

25.4

21 . 0

26 43 -5.5

4

-5.4

5

9

~1~t7~ 22 . 6

-14.0

~- I

24 . 0

10

)Vb

lO

13113

26 . 4

>Vb

39

6.4

4

9

8

14

>Vb

6

. . . . . . . . . . . . . .

9

]

14

21 .9

22

26

41

41

-12.0 . . . . . . . . . . . . . . 7 14

~ 2 7I . 51~ >Vb 6

9

9

] 13

2O 41 'Aa

>Vb

=

F/Aa/Vb

0.463

8

I0

11

13

I 12

t 13

23 . 35

27.5

25

29

41

38

~Aa c

)Vb

-13.0 . . . . . . . . . . . .

i 14

23.5

9

113 26.8

18

6

)Vb

26.2

45

5

13

25

~2 13 .~1 1 ~2 6 .

26 . 5

S I

21.2

. . . . . . . . . . . . . . . .

9

...............

9

F

26 41

................

->

i

O. 405

14

117

I

)Vb

27 . 16

'Aa

c

=

F/Aa

0.483

Fig. 6. Probabilities of outburst occurence for 27 divisions of the cause space composed by values of F, Aa and Vb.

observations to the total number of observations within a given field will be an estimation of the probability of outburst occurrence under the condition that the causes have been realized within the given field. For the example in Fig. 5, the number of observations falling into the central sub-range of CO2, <2.775- 6.3), is 121 (denominator) and the number of outbursts, i.e. observations for So-- 1, equals 82 (numerator). The number of observations falling into the central sub-range of CO2 and the central sub-range of P (central P axis in Fig. 5) under the above-mentioned condition is 36, while number of outbursts for the subranges is 28. Finally, for the above sub-ranges

of CO2 and P the number of observations for D p < 130 m m H 2 0 equals 9 (denominator) while the number of outbursts is 1. For the next subrange of Dp, i.e. for 1 3 0 < D p < 2 5 8 , there are 16 observations and all of them are outbursts. The main disadvantage of the method is, that while dividing the set of causes of outburst into a larger number of fields, the minimum sample size for which the reasoning makes sense increases very rapidly. In our example the minimum number of observations per field was assumed to be ten. Further research into considering the spatial structures of causes shall eliminate this shortcoming.

249

PREDICTION OF ROCK AND GAS O U T B U R S T O C C U R R E N C E

Calculations have been performed in accordance with the above rule for two sets of causes CO2/ P/Dp and F/Aa/Vb. This choice is supported by Fig. 3 where the first triplet of features indicates a high sensitivity with regard to the value of So. The second triplet represents the causes that appear irrelevant to outburst occurrence. The results are presented in Fig. 5 and Fig. 6. The common fractions represent estimators of the conditional probabilities of outburst occurrence within particular ranges of values for the features. Additionally, for each set of causes, calculations for two first causes only have been performed and the values of e for triplets and pairs of causes have been compared (Figs. 5 and Fig. 6). The value of e, which characterizes the quality of model fitting is in both cases lower for triplets of causes than for pairs. Figure 7 shows a map of the probability of outburst occurrence within that section of the coal seam of the "Nowa Ruda" coal mine shown in Fig. 2. For clarity the mine lay-out has not been included. Crosses represent the locations of outburst occurrence while triangles represent the sampling points with no outbursts. Conclusions

Due to the complexity of the mechanism of rock and gas outbursts the commonly practicized approach to outburst prediction through the 424-00

-43soo - 3000

~

explanation of the mechanism on the ground of physics leads mainly to non operative and qualitative solutions. The proposed concept of outburst as an event in a random field, associated with the cause - concept of outburst modeling represents an alternative approach to effective outburst modeling and prediction. To use this concept measurements have to be carried out in outburst-prone areas. The data should consists of numerical values characterizing the outburst causes and effects. This concept let us develop a model that allows prediction of outburst occurrence at an arbitrary point of the coal seam. Our approach eliminates assumptions and simplifications concerning the outburst mechanism. The simplifications usually originate from a poor understanding of the outburst mechanism. The proposed procedure is flexible and can be improved. Especially the spatial structures of the functions describing the outburst causes require further investigation. To further improve the precision of outburst prediction it is of primary importance to complete the list of principal causes of outbursts, i.e., the necessary causes for the outburst occurrence, and distinguish them from the irrelevant ones that should be treated as a noise. In the face of the considerable disagreement amongst outburst experts on the issue, i.e., which

/

\

\

- 1000

Fig. 7. Contours of probabilities of rock and gas outburst occurrence within the coal seam of the " N o w a R u d a " coal mine; ( + ) locations of outbursts; ( A ) locations of sampling points with no outbursts.

250

cause is the dominant one in the occurrence of outbursts the dychotomic component So({O, x) (2) of the model (1) can help in solving this problem. Only those causes that are, on average, sensitive to the value of So(~o,x) (Fig. 3), should be recognized as significant ones for the modeling and prediction of outbursts. This conclusion is supported by Fig. 5 and Fig. 6. The set of irrelevant causes (Fig. 6), poorly differentiates the coal seam into high and low hazard regions (most of the probabilities of the outburst occurrence are close to 0.5 and the value of ~: is high) while the set of principal causes allows a distinguishing between high and low hazard areas while the adjustment of the model to the data is better (low value of e; Fig. 5). References Agterberg, F.P., 1974. Geomathematics - - Mathematical Background and Geoscience Applications. Elsevier, Amsterdam, 596 pp. Airuni A.T., 1987. Prediction and prevention of gazodynamic phenomena in coal mines. Nauka, Moscow (in Russian), 309 pp. Backer, A., 1984. Outbursts in Coal Mines, IEA Coal Res. Rep. ICT1S/TR25, 55 pp. Barron, K. and Kullmann, D., 1990. Modelling of outbursts at # 2 6 Colliery, Galace Bay, Nova Scotia. Part 2: Proposed outburst mechanism and model. Min, Sci. Technol., 11(3): 261-268. Cis, J., 1971. Rock and Gas Outbursts in the Lower Silesian Coal Basin. Slask, Katowice (in Polish), 332 pp. Cyrul, T., 1987. Evaluation of the in situ full scale experiment of outburst. IMG PAN Res. Rep., Krakow (in Polish), 34 pp.

J ,.', ~.~LI

Cyrul T., 1988. Multiwuqable characterization ol" outburst prone seams. Proc. 12th Conf. Tendcncies in Gas and Rock Outburst, Hazard Prevention in Underground Mines. Nowa Ruda Radkow, Poland, pp. I23 144 (in Polish). Cyrul, T., 1990. Some aspects of outburst prediction m the Lower Silesian coal basin, in rock as a mulliphase medium. In: J. Litwiniszyn (Editor), AGH Publ. Krakow, pp. 643 676 (in Polish). Cyrul, T., 1992. A concept of prediction of rock and gas outbursts. Int. J. Geotech, Geol. Eng., [0:1 17. Cyrul, T. and Piotrowski, P., 1989. Some global structural characteristics of a rock and gas outburst prone area. Sekitangiken, Coal Min. Res. Center Jpn., 29(5): I 12 (in Japanese). Gil, H. and Swidzinski, A., 1982. Rock and gas outbursts in underground mines. Silesian Univ. Publ., 1035, Gliwice (in Polish), 312 pp. Halmos, P.R., 1950. Measure Theory. Van Norstrand, Princeton, N.J., 304 pp. Hyman, D., 1987. A review of the mechanisms of gas outbursts in coal. US Bur. Mines IC, 9155, 31 pp. Kozlowski, B., 1980. Rock and gas outbursts hazard in coal mining. Komitet Gornictwa PAN Publ., Warszawa (in Polish), 232 pp. Litwmiszyn, J., 1983. A model of rock and gas mass outburst. Archivum Gornictwa, 28:453 466. Matheron, G., 1971. The theory of regionalized variables and its applications. Les Cahiers du Centre de Morphologie Mathematique de Fontainebleau, 5, 211 pp. Olchoviczenko A.E., 1982. Prediction of rock and gas outbursts in coal seams. Niedra Publ., Moscow (in Russian), 315 pp. Pieczuk, A.J., 1969. Critical review of theoretical developments concerning rock and gas outbursts. Niedra Publ., Moscow (in Russian), 325 pp. Szewczyk, K., 1985. Descripton of fragments of the Discussion on "'The Prediction and Fighting the Outburst Hazard". Bull. Outburst Hazard Committee, Sobotka Gorka (31 May 2 June), 8:296 326 (in Polish). Szczepankiewicz, E., 1985. Applications of Random Fields. BNI Publ., Warszawa (in Polish), 390 pp.