GOSPODARKA SUROWCAMI MINERALNYMI Tom 24 2008 Zeszyt 3/1 VIOLETTA SOKO A-SZEWIO A* Method of evaluating the probability of a strong tremor Introduction Tremor and crump emergency conditions are fundamentally connected with the technology of conducted mining. The forecast can be prepared for tremors connected with the conducted mining. The data obtained during conducted mining in similar mining and geological conditions or statistical or analytical methods are used. The reliability of statistical methods for forecasting can be evaluated at 70 80% [5]. Unfortunately, those methods do not have an option of taking into account a variable tectonic stress field and local dislocations of the field resulting from the past exploitation. In the case of applying statistical methods and the analysis limited to the area around a single working the postulate of the stationary process of generating the seismic phenomena is possible for the assumption only for particular segments determined for a moving longwall front by evaluating the parameters of energy distribution in time windows. This is more difficult in the case of a small number of recorded tremors. The mid- and short-term seismic treat forecast is often prepared with the help of statistical parametric methods which on the basis of theoretical conceptions and empirical relationships allow us to build a model describing the process of generating tremors, which in turn allows us to create a probability distribution function which describes the data. The method of determining the probability of a stronger tremor based on the relationship linking the total seismic energy with an exploited volume was presented in the work [2]. The level of the induced seismicity can also be characterized by taking into consideration the indices which describe the deformation processes of the tremor-inducing strata of a rock mass and ground surface [1, 3, 6, 9]. Institute of Mining of the Silesian University of Technology realized a research project in the years 2004 2007, the aim of which was to * The Silesian University of Technology, Gliwice, Poland.
42 determine the relationship between a recorded induced seismic activity and the size of the ground surface deformation. As a result of these works a index was assumed which describes the size of the ground surface deformation through the cross-section area of a subsiding trough P w along the observation line situated according to the direction of an advancing wall front [7, 8]. Using this index in the article a method of evaluating the probability of a tremor with established seismic energy was presented. The method was applied for the area of the longwall mining conducted in the region of the Halemba hard coal mine. 1. Indices which characterize the size of the surface deformation andinducedseismicityassumedinthemethod For describing the size of the ground surface deformation resulting from mining the P w cross-section area of the subsiding trough along the observation line situated according to the direction of an advancing wall front was assumed in a described method. The index was established making a simplifying assumption that the volume V w of a created subsiding trough on the surface changes in time proportionally to the cross-section area P w created along the observation line. At the same time, the assumption was made that there is a relationship between the volume of the subsiding trough created on the surface and observed seismicity of a rock mass. The assumption was based on the relationship established by A. Kijko [4]. The detailed argument was discussed in the work [7, 8]. The measured subsidence of the ground surface points (on the observation line ) observed in a few selected levelling surveying cycles conducted within the project were shown in the Fig. 1. The level of the seismicity induced by the conducted mining was characterized by: N i the number of tremors recorded in a given time period (time-period of the realized geodesic levelling surveying cycles), Fig. 1. Measured subsidence w [mm] of selected ground surface points in a few levelling surveying cycles [8] Rys. 1. Wartoœæ osiadania w [mm] wybranych punktów powierzchni mierzona w kilku cyklach pomiarów niwelacyjnych
E i total energy of tremors recorded in a given time period (time-period of the realized geodesic levelling surveying cycles). The coal mine geophysical stations calculate the coordinates of the tremor focuses and seismic energies as standard, hence the choice of the indices. 43 2. Method of evaluating the probability of a strong tremor The research conducted within the project 4T12A 032 26 [8] showed that there is a statistically significant relationship between the increasing total seismic energy of the tremors (increasing total number of tremors) and the increasing cross-section area of the subsiding trough P w along the observation line situated according to the direction advancing wall front, approximately in the middle of the longwall area. On this basis it was assumed that based on the changes in P w and changes in observed seismic activity we can estimate the probability of a strong tremor. Analyzing the relationship between the seismic activity and cross-section area of a subsiding trough showed the validity of applying the E i quantity (total seismic energy of the tremors released in i time-period of realized geodesic surveying) and P w for predicting strong tremors. It was assumed that the increasing area P w is proportional to the seismic energy which should be released. The aim of the forecast is to determine the probability of a strong tremor based on the increasing area P w and total seismic energy E i. It was assumed that the relationship will be searched that will allow us to determine the probability of a strong tremor with the energy of the order of above 5 10 4 [J] on the basis of the determined logit model. The relationship between the occurrence frequency of the particular values of the dependent variable and the selected independent variables was described in the model. It was assumed that the variable E (tremor energy) assumes values ordered in m groups (m time-periods of the levelling surveying cycles). The symbols were assumed: y j the number of the variants of the variable Y(E)occurring in j group (variant E 5 10 5 [J]), p j y m j j (1) j variant frequency m j number of elements in j-group (number of tremors in a period) for j{ 1,..., m} N m m j j1 (2) The probability p j is an empirical probability of an event consisting in y j variants occurring of the variable Y(E) inj-group.
44 Let p be the function of variables X 1,..., X k,thatis: p f( X1,..., X K ) it was assumed: X 1 cross-section area of the subsiding trough P w along the observation line, X 2 total seismic energy in i period E (time-period of the surveying cycles), k number of independent variables. It was assumed that f is a linear function, thus: k p i X i1 i (3) Monotonic transformations of the probability into an interval were carried out: (0,1) ( ; ) Through the logit transformation, turning empirical probability into logit L: p L log p for p ( 01,) 1 (4) The general form of a model was searched: where: i unknown parameter for i{ 1,..., k}, X i independent variables (Ei, Pw) fori{ 1,..., k} random factor, k number of independent variables. The model of multiple regression was searched: L0 1X1... k X k (5) L X (6) where: unknown parameter vector, X observation matrix created from the observations of the independent variables, random factor.
The generalized least squares method was applied. Estimator of the logit model unknown parameter vector has the following form: where: T ( T ) X W X X W L 45 1 1 1 (7) w W 0 1 0 w m w j 1 m p ( 1 p ) j j j for j{ 1,..., m} (8) p j known empirical probability. Based on the empirical observations we calculate the value of estimator b in the logit model and we calculate the number variance. The parameters of the model was then determined on the basis of the research on ground surface deformation in the region of the mining conducted by Halemba hard coal mine, longwall 6, bed 415/1 on average depth 600 m. The length of the longwall was 258 m and longwall life 1070 m. The longwall working was conducted with caving up to 3.5 m high with the coal left in the thill about 0.9 m thick. The bed in this region is rated the 3rd crump treat level. The research in detail was described in the work [8]. Seismic activity induced by conducted works was medium and high at the beginning. 339 tremors were recorded with the seismic energies in the order of 10 3 to 10 6 [J] in the period from December 2004 till November 2006. Maximum seismic tremor energy amounted to 3 10 6 [J]. Pw area was determined on the basis of the periodical geodesic surveying: levelling and angular linear on the observation line 1. Figure 2 shows the outline of the mining conducted in the region in the research period and the draft of the observation net was used to testing of the worked out method for evaluating the probability of a strong tremor. Figure 3 shows the relationship of the growing area of the cross-section of the subsiding trough and the total seismic energy in the time-periods of the levelling surveying cycles with the probability of the tremor with energy E 5 10 4 [J] on the basis of the empirical data. In the analyzed set of the observations the functional relationship between L and P w, E i was determined in the following form: L = 0,002607587 0,00093676 P w 0,000000485748 E i (9) Calculated standard deviation of the remainders of the set for the model amounts to: Su = 0,592637105
46 Fig. 2. The outline of the observation network Rys. 2. Zarys siatki obserwacyjnej Fig. 3. The relationship of the increasing area of the cross-section of the subsiding trough P w and the total seismic energy in the time-period of the levelling surveying cycles E i with the probability p i of the tremor with energy E 5 10 4 [J] on the basis of the empirical data Rys. 3. Zale noœæ pomiêdzy wzrastaj¹c¹ powierzchni¹ przekroju osiadaj¹cej synkliny P w a ca³kowit¹ energi¹ sejsmiczn¹ w poszczególnych okresach czasu cykli pomiarów niwelacyjnych E i z prawdopodobieñstwem p i wyst¹pienia wstrz¹sów o energii E 5 10 4 [J] na podstawie danych empirycznych
The calculated multiple correlation coefficient R = 0.528 is on the level p <0.05 significantly different from zero. The above-mentioned model can be used for forecasting the probabilities of strong tremors. The probability forecast p can be calculated according to the formula: 47 L 10 p 1 10 L (10) Summary The article discusses the method of evaluating the probability of a strong tremors devised on the basis of the results of the research on the relations between the induced seismicity and the size of the ground surface deformation. The total seismic energy of the tremors induced by mining and the number of tremors were assumed as indices of the seismic activity in this method. The assumption was made that there is a relationship between the volume of the subsiding trough created on the surface and the observed seismicity of a rock mass. On this basis the increasing area of the cross-section Pw of the subsiding trough along the observation line situated according to the direction of the advancing wall front was assumed as an index of the deformation of the ground surface in the model. These indices were applied for evaluating the probability of the strong tremor with the help of a logit model. The example of applying the method with the results of research project 4T12A 032 26 was discussed in the article. The method requires verification based on the results of research conducted in other regions of mining exploitation, where high seismic activity of a rock mass appears. REFERENCES [1] DrzêŸla B., Bia³ek J., Jaworski A., Bañka P., Ko³odziejczyk P., 1994 Badanie zwi¹zków sejsmicznoœci indukowanej eksploatacj¹ górnicz¹ z parametrami opisuj¹cymi deformacje oœrodka skalnego. Sprawozdanie koñcowe z realizacji projektu badawczego KBN nr 903759101. Gliwice 1994, praca niepublikowana. [2] G ³ o w a c k a E., 1991 Ocena zagro enia sejsmicznego górotworu z uwzglêdnieniem przebiegu eksploatacji. Praca doktorska. Warszawa 1991. [3] G o s z c z A.,1988 Wp³yw gradientu prêdkoœci obni ania siê powierzchni pod wp³ywem robót górniczych na stan zagro enia wstrz¹sami górniczymi. ZN AGH s.górnictwo z. 141, Kraków 1988. [4] K i j k o A., 1985 Theoretical model for relationship between minning seismicity and excaviation area. Acta geoph. Pol. vol. 33, 1985. [5] L a s o c k i S., 1990 Predykcja silnych wstrz¹sów górniczych. ZN AGH, Geofizyka Stos. Nr 7, 1990. [6] M a r c a k H., 1996 Struktura zapisów sejsmologicznych wstrz¹sów górniczych z punktu widzenia prognozy zagro enia sejsmicznego. Mat. Szko³y Eksploatacji Podziemnej. Seria Wyk³ady nr 12. CPPGSMIE PAN, Kraków 1996.
48 [7] Soko³a-Szewio³a V.,2006 Obserwowanezmianyobni eñpunktówpowierzchniterenuarejestrowana aktywnoœæ sejsmiczna górotworu. XIII Miêdzynarodowa Konferencja Naukowo-Techniczna nt. Górnicze zagro enia naturalne 2006. GIG, 319 328. Katowice, 2006. [8] Soko³a-Szewio³a V.,Bia³ek J.,Bañka P.,iin.,2007 Zale noœcipomiêdzywielkoœciamideformacji powierzchni terenu i aktywnoœci¹ sejsmiczn¹ górotworu. Projekt badawczy KBN 4T12A 032 26. Gliwice, 2007. [9] W a n i o r J., 1982 Metoda prognozowania wstrz¹sów i t¹pniêæ w oparciu o wyniki pomiarów geodezyjnych. PTPNOZ. Czêstochowa 1982. METODA OKREŒLANIA PRAWDOPODOBIEÑSTWA WYST PIENIA SILNEGO WSTRZ SU PODZIEMNEGO S³owa kluczowe Aktywnoœæ sejsmiczna spowodowana górnictwem, prawdopodobieñstwo, wstrz¹sy podziemne Streszczenie Metoda szacowania prawdopodobieñstwa wyst¹pienia silnego wstrz¹su podziemnego wykorzystuj¹ca zale noœæ pomiêdzy odkszta³ceniem powierzchni i zarejestrowan¹ aktywnoœci¹ sejsmiczn¹ górotworu. Aktywnoœæ sejsmiczna wywo³ana przez górnictwo okreœlona zosta³a jako ca³kowita energia sejsmiczna wstrz¹sów E, a iloœæ wstrz¹sów jako N. Za³o ona zosta³a zale noœæ pomiêdzy objêtoœci¹ koryta osiadaj¹cej na powierzchni a zaobserwowan¹ aktywnoœci¹ sejsmiczn¹. Za wskaÿnik modelowej deformacji powierzchni przyjêto powierzchniê przekroju P w osiadaj¹cej synkliny wzd³u linii obserwacyjnej usytuowanej równolegle do posuwaj¹cego siê przodka œcianowego. Opisana metoda wykorzystuje model logitowy. Na podstawie wyników, w których okreœlono P w, w modelu wykorzystano ca³kowit¹ energiê sejsmiczn¹ E i zarejestrowan¹ w poszczególnych okresach czasu pomiarów geodezyjnych. Przyjêto za³o enie, e energia sejsmiczna, która powinna zostaæ uwolniona jest proporcjonalna do wzrastaj¹cej powierzchni P w. Szacunki maj¹ na celu okreœlenie prawdopodobieñstwa wyst¹pienia silnego wstrz¹su na podstawie powiêkszaj¹cej siê powierzchni P w oraz E i (ca³kowitej energii sejsmicznej uwolnionej w okresie czasu i przeprowadzonych okresowych geodezyjnych pomiarów niwelacyjnych). Przyjêto za³o enie, e znaleziona zostanie zale noœæ, która pozwoli na obliczenie prawdopodobieñstwa wyst¹pienia silnego wstrz¹su podziemnego posiadaj¹cego energiê rzêdu ponad 5. 10 4 [J] na podstawie modelu logitowego. W modelu opisano zale noœæ pomiêdzy wystêpuj¹c¹ czêstotliwoœci¹ okreœlonych wartoœci zale nych zmiennych oraz wybranych niezale nych zmiennych. Metodê zastosowano dla szeregu obserwacji uzyskanych w wyniku projektu badawczego 4T12A 032 26. Okreœlono funkcjonaln¹ zale noœæ pomiêdzy E i, P w oraz L (logit). Obliczony wspó³czynnik korelacji wielokrotnej R = 0,528 znajduje siê na poziomie p <0,05, ró ni¹cym siê znacz¹co od 0. Model mo e zostaæ wykorzystany do prognozowania prawdopodobieñstw wystêpowania silnych wstrz¹sów podziemnych. METHOD OF EVALUATING THE PROBABILITY OF A STRONG TREMOR Mining induced seismicity, probability, tremors Key words Abstract The method of evaluating the probability of a strong tremor using the relationship between the size of the ground surface deformation and recorded seismic activity of a rock mass. Seismicity induced by conducted mining was characterized by total seismic energy of the tremors E and the number of tremors N. The assumption was made
that there is a relationship between the volume of the subsiding through created on the surface and observed seismicity of a rock mass. The cross-section area P w of the subsiding through along the observation line situated parallel to the direction of an advancing wall front was assumed as an index of the deformation of the ground surface in the model. The method described uses a logit model. The total seismic energy E i recorded in time-periods of realized geodesic surveying was used in the model, on the basis of the results, in which the P w was determined. It was assumed that the seismic energy which should be released is proportional to the increasing area P w.theaim of the evaluation is to determine the probability of a strong tremor occurrence on the basis of the increasing area P w and E i (total seismic energy released in i time-period of realized periodical geodesic levelling surveying). It was assumed that the relationship will be searched that will allow us to calculation the probability of a strong tremor with the energy of the order of above 5 10 4 [J] on the basis of the determined logit model. The relationship between the occurring frequency of particular values of the dependent variable and the selected independent variables was described in the model. The method was applied for the set of observations obtained as a result of the research project 4T12A 032 26. The functional relation between E i, P w and L (logit) was determined. The calculated multiple correlation coefficient R = 0.528 is on the level p < 0.05 significantly different from zero. The model can be used for forecasting the probabilities of strong tremors occurrence. 49