ZE = C 9 V B, where C and B are parameters characterizing mining works and the state of rock mass. Assuming that the measure of seismic hazard is the ...
PAGEOPH, Vol. 129, Nos. 3/4 (1989)
Continuous
00334553/89/040523-1151.50 + 0.20/0 9 1989 Birkh~iuser Verlag, Basel
E v a l u a t i o n o f Seismic H a z a r d I n d u c e d b y the D e p o s i t E x t r a c t i o n in Selected C o a l M i n e s in P o l a n d E. GLOWACKA l and A. KIJKO I
Abstract--A probabilistic relation between seismic activity and the volume V of extracted deposits in mines is derived Z E = C 9 VB, where C and B are parameters characterizing mining works and the state of rock mass. Assuming that the measure of seismic hazard is the amount of seismic energy released in a given time interval, it is shown how the hazard can be evaluated continuously, The derived relations were tested in selected coal mines in Upper Silesia.
Key words: Induced seismicity, seismic hazard, seismic energy, Polish coal mines.
1. Introduction
Tremors of rock mass occurring in underground mines are typical examples of induced seismic activity caused by the rock deformation due to the extraction of some of its volume. The dependence of seismic activity on the extracted deposit volume has long been known from observations (e.g., SKLENAR, and RUDAJEV, 1975). KIJKO (1985) introduced the dependence of seismic activity on the amount of extracted deposit as a deterministic relation, and he also pointed out that it is necessary to interpret this dependence as a probabilistic relation. This paper describes briefly the way of deriving this dependence and the possibility of applying it in a continuous evaluation of the seismic hazard.
2. Formulation of the Problem
On the basis of earlier solutions by RANDALL (1971) and additional assumptions, MCGARR (1976) showed that the seismicity resulting from the extraction of
J Institute o f Geophysics, Polish Academy o f Sciences, 00-973 Warsaw, P.O. Box 155, Pasteura 3, Poland.
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rock volume, expressed by the sum of seismic moments EMo, has the form EMoI= k . # . AVe,
(1)
where A V~ is the induced volume change of rocks as a result of mining activity,/~ is the shear modulus and k is a constant. Assuming (KIJKO, 1985) that the AVc is proportional to the volume AV of extracted deposits AVc
=
19. a V
(2)
relation (1) becomes ~Mo = k - ~ . |
AV.
(3)
The parameter (9 in general depends on the state of primary and secondary stresses in the rock mass. The primary stresses combine the geostatic and tectonic stresses, while the secondary stresses are induced by mining. In general, the parameter O is a function of time, but, when it is evaluated from a large set ot tremors, its averaged value represents the scale of rock fracturing in the whole working area. On the basis of observations MCGARR (1976) assumed that the direction and value of the maximum stress el coincided with the direction and value of the stress induced by the overburden pressure. This assumption neglects the fact that both the tectonic and mining stresses can locally take a maximum value with a direction other than the vertical one. This problem will be discussed later. For relation (3) to be applicable in practice when the seismic moments are not determined routinely, M0 must be ,replaced by equivalent parameters. It can be shown that in some special cases the seismic moment can be replaced by seismic energy which is routinely determined in Polish mines. It should be emphasized that all our formalism could have been well formulated in terms of Mo. Assuming that local magnitude M of small earthquakes is proportional to the logarithm of seismic moment Mo log Mo = c + d" M
(4)
and that the averaged relation which links the seismic energy E with the local magnitude M is log E = c~ + fl 9M
(5)
the relation (3) takes the form (KIJKO, 1985) E E a/~
= const 919 9AV,
(6)
where const = k 9 # 9 1 0 ~a/~ " In order to simplify relation (6), which is inconvenient for calculations, it was assumed in addition that the magnitude distribution is described by the Gutenberg-
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Richter law l o g N = a - b 9M It was shown by KIJKO (1985) that such a distribution of magnitude simplifies expression (6) to E E = const 9( O . AV) B,
(7)
where | and B = (fl - b ) / ( d - b ) are parameters dependent on the state of the rock mass. Relation (7) can be further simplified as follows EE = C 9AV B.
(8)
It can readily be demonstrated that the applicability range of relation (8) is much wider than it follows from the original assumption. For example, if the linear relation (2) is replaced by the more general relation AV
c --m- { ~ .
(AV) p,
where p is a constant, equation (8) does not change its form. In the following consideration we will use the symbol V instead of A V to simplify the notation. The purpose of this study is to apply relation (8) in evaluating the seismic hazard in mines. For this purpose, relation (8) is represented in a probabilistic form. Let us assume that the seismic activity is observed in a mining area far enough from the time and space effects of other workings. Let us assume, moreover, that as the volume AVt was extracted, the seismic energy (ZE)i is released in the time At,-. Identifying the scisrnic hazard with a value of the seismic energy Ei by determining the difference (ZE), = C - ( V ~ - V~_,),
(9)
we can evaluate the seismic hazard for each successive time interval Ati (and the corresponding extraction of A V3. In the last relation (XE)i denotes the most probable sum of seismic energy expected in time interval Ati to which the extracted rock volume A Ve = Vi - V~_ 1 corresponds. C and B are constants calculated from the previous course of dependence (8) (i.e., for t~_ 1). Also, the value of (ZE)~ is evaluated as (ZE) 7 = (ZE); + AE;_,,
(10)
where; (ZE)7 denotes the most probable energy sum expected in the time interval Ate enlarged by the value o f energy accumulated in the rock mass AE~_ 1= (ZE)~_ l (ZE)~ ~, where (ZE)i_~ denotes the observed sum of energy/'eleascd in the rock mass in the time interval Ati_ 1. The value of AEi_~> 0 means that the seismic energy observed in the time interval Atg_ ~ was below the expected value. We assume that the energy accumulated in this way cannot be dissipated and it will increase the seismic hazard in the next time interval. If AE~_ ~ < 0 the seismic hazard decreases and we assume that (ZE)~ = (ZE)i.
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The sum of seismic energy EE accompanying the extracted rock volume A V does not have to be treated deterministically, but could be understood as a random variable as well. In view of the available data and mathematical models of physical phenomena there seems to be little evidence to dictate the choice of any particular distribution of EE. For all these reasons, following common engineering practice, normal distribution was adopted. Let P(E~) = P ( E E > Ej) to denote that the most probable sum of seismic energy exceeds the predetermined threshold energy Ej. Following our assumption of normal distribution, the probability P(Ej) takes the form: -
t
exp( - ( l12aZ)(E - Z E ' ) 2) dE,
(11)
dO where a is the standard deviation of the energy. The presented method for evaluating the seismic hazard changing during the extraction was applied in two coal mines in Upper Silesia with different geological and excavation conditions.
3. The Results The first of the discussed regions (Figure 1) is situated in the "Wujek" mine, covering part of seam 501 lying there at a depth of 600-700 m and inclined at an angle of 4-6 ~ to the south (G~OWACKA et al., 1987). The layer thickness ranges between 3.5 and 8.5 m. The analyzed area is bounded on two sides by faults with displacement of the order of 120 m, and in the longwall there are practically no tectonic perturbations. At a depth of about 20 m under seam 501, there lies the partly extracted seam 504, its edge is marked in Figure 1. Its presence affects slightly the seismicity of bed 501. The basic deposit of seam 501 was excavated in 1974-1979 at 5 retreating longwalls with a mechanized support with caving. The walls were worked successively from I-V, keeping the outstripping character of their fronts. In the periods when 2 or 3 walls were worked at the same time the rate of extraction reached 100 m per month. During the exploitation there occurred 2 tremors with the energy of the order of 10 7 J, 68 tremors with the energy of the order of 10 6 J, 528 tremors with the energy of the order of 105 J and several thousands of smaller events. In the analysis of the seismic hazard tremors were used with energy no less than 105 J for each of the walls separately and for the whole region as well. In Figure 2 the results for wall V, and in Figure 3 the results for the whole region are given. In both figures, the output volume of extraction is marked on the horizontal axis. Under this axis, dots mark the progress of work in each month. The arrows mark the tremors with the energy bigger than 107j and 5 9 106 J. The upper part "a" of the two figures represents the measured results: the seismic energy observed in each
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1978.09.04 E=5.2~lOTJ
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st/h.o
~
~'_-
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.--.- I
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Figure 1 Sketch of the geological and mining situation in a chosen region of seam 501 at the "Wujek" coal mine.
month (curve 1), the total energy sum (curve 2) and the theoretical dependence ZE(V) (curve 3). The lower part "b" of the figures illustrates the predicted seismic hazard calculated from relation (9) (curve 4) and that taking into account the accumulation of seismic energy calculated from formula (10) (curve 4a), and the predicted probability that the energy of 107j will be exceeded in each month (curve 5). Figure 2 shows several month-long periods of energy accumulation (where curves 4 and 4a diverge) and the increased probability preceding the two largest tremors with energy exceeding 10 7 J, which occurred close to wall V. Similarly, in Figure 3 covering all the 5 walls, one can notice several months long periods of increasing accumulation and probability preceding tremors with energies greater than 106 J. In Figure 3c dots mark the periods of energy accumulation occurring at particular walls. It can be seen that tremors with energy greater than 107j were preceded by accumulation at 2 or 3 longwalls at the same time, so they had a more regional nature, unconnected directly with the extraction of individual walls. This means that the region where very strong seismic events are originated considerably exceeded the dimensions of longwalls. The probable cause of this phenomenon is the extraction of the whole region rather than that of a single wall.
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Figure 2 Seismic energy v e r s u s volume of extracted rock for longwall V at the "Wujek" coal mine. Arrows mark the tremors with energy bigger than 107 J and 5 9 106 J. a) l - - m o n t h l y sums of seismic energy, 2--total seismic energy, 3---energy calculated from relation E E = C 9 V n. b) 4--predicted seismic hazard calculated from relation (9), 4a--predicted seismic hazard, taking into account the energy accumulation calculated from relation (10), 5--probability of exceeding the energy 107 J.
Different behaviour is characteristic of longwalls worked out under complex mining and tectonic conditions. As an example we consider longwaU 614 of seam 501 at the "Gottwald" coal mine in Upper Silesia (GLoWACKA e t al., 1988). The analysis was also carried out for a region consisting of 5 longwalls worked out with caving in the top slice of a layer lying in this area at a depth of 580-650 m (Figure 4). The results are shown in Figure 5 (longwall 614) and 6 (the whole analyzed area). Contrary to the other longwalls, longwall 614 w~s a closing wall worked out under extremely difficult mining conditions. Thus it is'characterized by high seismic activity, low energy accumulation and high probability of the 105 J energy being exceeded (Figure 5). The analysis of this wall, treated as part of the
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Evaluation of Seismic Hazard in Polish Coal Mines
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