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Studies on temporal and spatial variation of microseismic activities in a deep metal mine
International Journal of Rock Mechanics & Mining Sciences 60 (2013) 171–179
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International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms
Studies on temporal and spatial variation of microseismic activities in a deep metal mine Jian-po Liu a,n, Xia-ting Feng a,b, Yuan-hui Li a, Shi-da Xu a, Yu Sheng c a
Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang, Liaoning 110819, China State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China c Beijing SCR Instruments Ltd., Beijing 100048, China b
a r t i c l e i n f o
abstract
Article history: Received 1 May 2012 Received in revised form 21 September 2012 Accepted 21 December 2012 Available online 5 February 2013
Aiming at forecasting techniques of ground pressure hazards in deep metal mines, a microseismic monitoring system was established at a deep stope in Hongtoushan copper mine in China. Based on theories of geophysics and rock mechanics, a forecasting approach was introduced using microseismic multi-parameters including cumulative apparent volume, energy index, spatial correlation length, fractal dimension and b value. The approach was used to predict large scale fractures and ground pressure hazards in rock masses. The results showed that microseismic activities were very weak before mining commenced. However, activities became significant when mining started. When mining finished, microseismic activities remained at a higher level for about one week then became weakened. Before large scale fractures occurred, all microseismic multi-parameters behaved differently. The apparent volume and spatial correlation length were continually increasing, while energy index, fractal dimension and b value were gradually dropping to their minimum values. Therefore, these parameters could be used as precursory indicators for great ground pressure hazards. Comprehensive analysis on microseismic multi-parameters changes could improve reliability of forecasting, which is of great significance to deep metal mines in managing ground pressure failure risks. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Deep metal mine Microseismic (MS) monitoring Energy index Apparent volume Spatial correlation length Fractal dimension b value
1. Introduction With the continued rapid development of national economy and increased demands for mineral resources, deep mineral resources exploitation gradually becomes the trend of future mining in China. It is anticipated that over thirty mines whose depths will beyond 1000 m by 2015. Ten of them will be deeper than 1300 m. Deep extraction of minerals creates large volume of cavities and leads to high stresses surrounding the excavation which may cause failures in rock mass, in some cases, dynamic failures would occur. Therefore, it is important to investigate and to understand rock mass behavior in deep mining environment. The microseismic (MS) monitoring technique, using elastic waves generated by rock damage to evaluate the stability of rock mass, has been proven to be a useful tool for assessing rock mass stability and for forecasting dynamic hazards, hence to better manages disastrous rock failures. With the advances in computer technology over past decades, ability of fast processing of seismic waves has made the MS technology more applicable. It now becomes a routine technology in the deep mining operation and is widely used in South Africa, Australia, the United States, Canada, Chile, Poland and other countries
n
Corresponding author. Tel.: þ86 24 83684690. E-mail address: [email protected] (J.-p. Liu).
1365-1609/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijrmms.2012.12.022
[1–7]. Additionally, this technology was also gained much attention and was adopted in other applications, e.g. tunnel [8], hot dry rock power generation [9], open pit slope [10], deep-buried underground powerhouse [11,12], etc. Application of the MS monitoring technology in China only commenced after 2000. Li et al. [13] established a 64-channels digital MS monitoring system in Fankou lead–zinc mine with an ESG system. It was basically used to identify threedimensional locations of MS events in real-time through on-line monitoring. In 2003, Jiang et al. [14] in collaboration with the Commonwealth Scientific and Industrial Research Organization (CSIRO) of Australia performed a pilot trial seeking applicability of MS technology towards detecting and preventing coal mine hazards. Following the initial effort, a new explosion-proof MS monitoring system was developed and some meaningful results were obtained. In 2005, Tang [15,16] established an ISS MS monitoring system at Dongguashan copper mine to study stress changes and deformation characteristics in rock mass due to mining. Other mines such as Shizhuyuan polymetallic mine [17], Huize lead–zinc mine [18], Zhangmatun iron mine [19] are also established MS monitoring systems successively. In addition, Feng [20,21] carried out MS monitoring technique in the deeply and long buried tunnel of JinPing hydropower station in southwestern China, meaningful results were obtained. Much of applications of the MS technology to date are limited to qualitatively categorize seismic hazards. Great efforts have
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been made by many researchers in attempting use MS technology as a tool to predict dynamic disastrous failures. However, limited successes were achieved in this aspect. The inhomogeneous natures of rock structures and complexity of mining process makes difficulties in identifying and understanding key influences of MS activities and their evolution. Therefore, how to fully utilize and analyze those MS monitoring data and get the precursory characteristics before dynamic hazards happened has become an urgently problem need to be solved. Hongtoushan copper mine is one of the deepest nonferrous metal mines in China. Seismic hazards, e.g. rock burst, roof collapses and side wall failures under high rock stresses were presented at the mine since late 1990 s. To enhance management of seismic hazards, the mine decided to adopt seismic monitoring technology. As such, an ISS MS system was established in June 2010. The present paper describes the use of multi-parameters, including accumulation apparent volume, energy index, spatial correlation length, fractal characteristic and b value, to analyze the spatial and temporal evolution characteristics of MS events. Attempt is made to establish a framework of forecasting for large scale fractures in rock mass using seismic data.
2. Establishment of a MS monitoring system at Hongtoushan copper mine 2.1. Mining layout and selected sensor array Hongtoushan copper mine has been in operation since 1958. It is one of the deepest nonferrous metal mines in China. The deepest stope is 1357 m below the ground surface. With continued mining operation, high ground pressures have been causing seismic hazards, eg. rock burst and roof collapses, which impact on safety of operators and disrupt production, hence cause financial losses. Aiming to mitigate seismic hazards and to enhance safety management, a MS monitoring system was installed around Stope 27 at depth of 1137 m. It was the largest stope with an exposed area of 2400–3000 m2 and about 67,000 t of ores were expected to being recovered. The overhead cut-and-fill stoping method was used for mining at Stope 27, four layers have been mined and the fifth layer is being stopped at present. Stopes 19 to 26, along side of stope 27, were mined using the room-and-pillar method. Among them, stope 16, 18, 20, 22, 24 and 26 were mined and filled. The layout surrounding stope 27 is showed in Fig. 1(a). The mining facilities around stope 27 include hanging wall haulage tunnel, across-vein roadway, slope ramp and pipe well showed in Fig. 1(b). MS sensors arrangement is on basis of those existed facilities. Five sensors, including one triaxial accelerometer and four uniaxial geophones, were permanently installed on slope ramp between the fourth and the fifth platforms. In addition, two uniaxial geophones were installed in acrossvein roadway.
Fig. 1. Mining layout for No.27 stope at 707 m level and the MS sensors array. 1-filled layer cavities, 2-mined layer cavities, but not filled, 3-layers to be mine, 4-pipe well, 5-slope ramp, 6-platform. (a) Plan view and (b) side view.
2.2. Establishment of a MS monitoring system A high performance ISS system [22] was adopted for this research project. The hardware system include sensors, seismic data acquisition unit (GS), DSL 2-wire modem for GS, server, electric cable, telephone line, optical fiber and photoelectric converter, etc. The sensor array consists of one triaxial and six uniaxial heavy duty 14 Hz borehole geophones with a performance range of 7–2000 Hz and sensitivity of 80 V/ms 1. These intelligent sensors have self-checking function that can automatically identify the sensor ID, coordinates, azimuth and dipping angle when installed. The data acquisition GS unit has specification of a 32 bit AD conversion accuracy and the maximum sampling frequency of
Fig. 2. Install methods of MS sensors. (a) Schemetic diagram for permanent installation , (b) schematic diagram for temporary installation and (c) device for temporary installation.
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48,000 Hz. A sampling rate of 6000 Hz was adopted for this system. Each GS unit was equipped with an intelligent uninterruptible power suppliery (iUPS) to enhance the performance of GS units. Through the system, MS wave signals are sensed by the sensors, which concerted them into electrical analog signals and received by the GS data acquisition units, where the signals are further converted to digital signals. A DSL technology based communication system, which synchronizes the system and transmits the digital data through a telephone line from GS units to a central server at an underground center at 707 m level. The digital seismic data can be processed at the server and results can be downloaded by the central office of the mine and by a remote research center at Northeast University (NEU) via internet. The sensors were installed in either way of permanent or temporary installation. The procedure for a permanent
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installation Fig. 2(a) included following steps: (1) to position a sensor, bound with an air-exhausting pipe, into the boreholes with a special installation tool; (2) to apply a wooden plug, with a hole in the middle allowing passes of an exhausting pipe, an grouting pipe and an signal cable, to hold grout at the entrance of the boreholes; (3) to inject the grout until its overflowing from the exhausting pipe; (4) to block and to cut both the injecting and the exhausting pipes. It is worth noting that sensors need to be tied a certain distance from the end of the exhaust pipe to ensure sensors were grouted firmly. The temporarily installed sensors were shown in Fig. 2(b). A special device was developed as shown in Fig. 2(c) for such a purpose. It consisted of an inner and an outer sleeve. The outer sleeve was permanently placed at the bottom of the borehole by capsule resin. A sensor was attached to an inner sleeve, which remained in place during the monitoring. Upon complete the monitoring work, the sensor could be retrieved by withdrawn the inner sleeve using the installation tool and could be used elsewhere. A weekly inspection procedure was adopted to ensure it in a firmly fixed state and was not affected by ground shaking due to blasting operation. Signal testing suggests that the P-wave arrival time could be clearly identified. It was noticeable that coda waves presented. However, they have little influence on location accuracy of MS events. 2.3. Mining sequence The mining of the fifth layer at stope 27 was carried out from January 11 to January 19, 2011, except January 16. The thickness of ore body was about 3–4 m and the total area was about 1600 m2. Blasting design on timing, position, sequence, amount of explosives and excavate volume are showed in Fig. 3 and Table 1 respectively. Before this mining work, two areas, Region A and B showed in Fig. 3 had been mined. Regions C and D will be mined at the later stage. The mining in Regions 1 to 8, shown in Fig. 3 was completed on January 19, 2011.
Fig. 3. Sequence and location of mining work.
Table 1 Blasting parameters of mining work. Number Data
1 2 3 4 5 6 7 8
2011.01.11 2011.01.12 2011.01.13 2011.01.14 2011.01.15 2011.01.17 2011.01.18 2011.01.19
Explosive/ Weight of box explosive/ kg
Numbers of millisecond blasting
Ore volume/ m3
25 26 30 30 30 30 30 6
5 5 6 6 6 6 6 6
660 686 792 792 792 792 792 158
600 624 720 720 720 720 720 144
3. Spatial and temporal characteristics of micro-seismicity 3.1. Daily micro-seismicity Many blasting events were recorded during the course of monitoring. The blasting events could be identified from characteristics of waveforms, such as high energy, high frequency and quick decay etc. They were not analyzed in this study. By contrast, Signals of MS events were usually much weaker with lower energy, longer duration, lower frequency and slow decay. Fig. 4 shows recorded MS activities from January 1 to February 25,
Fig. 4. Law of MS activities with time (2011.01.01-02.25).
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2011. It is interested to see that features of the MS activities were much different before, during and after the mining operation. Before January 11, the operations at Stope 27 were mainly related to ore transportation and backfill, the MS events were less than five every day. Since mining resumed on January 11, a sharp increase in MS events is visible. Due to blast operation in the duration from January 11 to January 19, the average rate of MS activities was at 20–30 events a day. It suggests that the mining work has great disturbance to surrounding rock mass, which accelerate generation and propagation of cracks. When the mining operation finished on January 19, MS activities remained at a higher level for a week, indicating influences of stress-field redistribution and adjustment. The MS activities remarkably decreased to relatively stable state from January 26, one week after mining operation and the MS events are at a rate of fifteen a day. It is noticeable to see that event generation remains at this rate one month after the complete of mining, indicating the stress redistribution is a relatively long process.
3.2. Laws of accumulative apparent volume and energy index Due to the complexity of underground mining environment, rock mass damage cannot be estimated from single MS event. According to the view of seismology, statistical analysis on temporal and spatial evolution laws of MS events is widely used to judge rock mass stability by studied MS events within somewhat time and space. General statistical parameters of
microseismic activity include apparent volume, apparent stress, and energy index. The apparent stress sA [23] is defined as the ratio of the radiated seismic energy E and seismic scalar seismic potency P, expressed as:
sA ¼
ð1Þ
Apparent volume VA [23] is a much stable parameter, and it measures the volume of rock with the inelastic change, expressed as: VA ¼
mP2 E
ð2Þ
where m is the rigidity of the rock. Apparent volume, like apparent stress, depends on seismic potency P and radiated energy E, and, because of its scalar nature, can easily be manipulated in the form of cumulative or contour plots. Apparent volume and apparent stress are two important parameters in seismology theory, which are often used to describe the changes within rock mass before hazards occurred. When rocks closing to peak stress, the deformation growth will speed up and the stress growth will reduce. After peak stress, the stress is gradually reduce while deformation growing quickly. During the strain-softening stage, the more quickly stress dropping, the more serious rocks failure. Energy index EI [23] of a MS event is the ratio of the observed radiated seismic energy of that event E, to the average energy EðPÞ radiated by events of the observed potency P taken from logEðPÞ ¼ dlogP þc, for the monitoring area showed in Fig. 5: EI ¼
Fig. 5. Relationship between MS energy and potency.
E P
E E E ¼ ¼ 10c d EðPÞ P 10dlogP þ c
ð3Þ
which for d ¼1.0 would be proportional to the apparent stress. The higher the energy index, the higher the driving stress at the source of the event at the time of its occurrence. Therefore, the changes of apparent volume VA and energy index EI can be applied to obtain precursor information of rock mass hazards. Fig. 6 shows the changes of accumulative apparent volume and energy index from January 15 to February 15, 2011. Before February 2, apparent volume was gradually growing, while the logarithm of energy index log (EI) fluctuating changed and gradually reached to its maximum value. It illustrated that the elastic deformation volume of rock mass within monitoring area was increasing, and the driving stress at the source of the MS events reached the maximum value. During the period from February 2 to 7, logarithm of energy index log (EI) was decreased sharply but accumulated apparent volume kept increasing, which indicated that parts of rock mass within monitoring area was
Fig. 6. Changes of accumulative apparent volume and energy index with time.
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becoming unstable status. This period could be seen as strainsoftening stage, which was an onset of a potential underground pressure hazard and could be regarded as a warning indicator. With the time going, apparent volume was continually increasing and log (EI) was resume increasing, and the rock mass was entering into an unstable state. Finally, two large scales of MS events occurred on February 8 and 11 that are second day and fourth day after the warnings issues, respectively. These two events were located at the areas between stope 27 and other stopes that had been filled showed in Fig. 7. Their magnitudes the two events were 0.1 and 0.2, respectively. The waveforms of large MS event on February 8 showed in Fig. 8. Apparent volume and energy index can be seen to a stain– stress curve, representing laboratory behavior of a hard rock
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sample under compression test. The phenomenon of logarithm of energy index log (EI) dynamically deceasing and accumulated apparent volume obviously increasing could be regarded as precursory characteristics. The quicker log (EI) decreasing and accumulated apparent volume increasing, the larger risk of an underground pressure hazards would be happened. The mining operation would disturb surrounding rock mass and induce stress redistribution within rock mass. Fig. 9 shows the cloud plots of distribution of displacement and log (EI). The average displacement can be calculated by the ratio of seismic potency and source area. It could be seen that the regions of large deformation in horizontal plans at stope 27 roof are expending, while the areas of large log (EI) are reducing, particularly near slope ramp. This phenomenon indicated that serious degradation of rock mass, and slope ramp was damaged in forms of bulging, slabbing and splitting, etc. Because changes in stress and deformation were independently obtained from MS events, therefore they can reflect the difference of physics mechanics of different areas within rock mass. The source of a MS event associated with a weaker geological feature or with a softer patch in the rock mass yields more slowly under lower differential stress, and radiates less seismic energy per unit of inelastic co-seismic deformation, than an equivalent source within strong and highly stressed rock mass. The phenomenon of deformation increasing and stress reducing indicated that the rock mass become degradation. In contrast, the integrity of rock mass is much better.
3.3. Spatial correlation length of MS events
Fig. 7. Spatial position of the two large magnitude MS events.
In accordance with the hypothesis of the critical point [24], two characteristic parameters, i.e. growing of correlation length
Fig. 8. Waveforms of large MS event on February 8.
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Fig. 9. Cloud charts distribution of displacement and lg (EI).
and increasing of critical sensitivity before unstable failure of materials such as rocks, can be considered as the precursors. In seismology, the spatial correlation can be considered as a characteristic distance or cluster size of events in a certain time interval [25]. If the system approaches the critical point, there will be a long-range interaction characterized by power-law function. ¨ Zoller et al. [25] have studied the accelerated growing phenomenon of correlation length of 9 earthquakes (M Z6.5) between 321–401N in California in 1952. It was suggested that the accelerated growth of correlation length might be seen as a predictive indicator before large earthquakes. Rong et al. [26] and Tyupkin and Giovambattista [27] were also obtained the similar results from studying on earthquakes and laboratory tests, respectively. Li et al. [28] found that two factors may influence the change of spatial correlation length: stress release and stress re-distribution. The former leads to a decrease in correlation length, while the latter leads to an increase in correlation length. The growth of correlation length x of MS events can be expressed as [29]:
xðtÞ tf t
k
ð4Þ
where tf is rock failure time and k is power-law fitting parameter. The spatial correlation length of MS events was calculated by Single-Link Cluster (SLC) presented by Frohlich and Davis [30]. The
SLC method [25,30,31] assumes that the time-space distances of MS events can be written as a matrix D1. The distance of events i and j, dij, in line i and column j of the matrix D1, can be expressed as: dij ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 xj xi þ yj yi þ zj zi þ c2 t j t i
ð5Þ
where x, y and z are the three-dimensional coordinates of MS event, t is the time of MS events occurred, c is the associated constant of time and spatial distance. In this work, we only study the spatial characteristics of MS events. Therefore c¼ 0 and the dij indicates the spatial distance between the MS events. Firstly, when a distribution of N events is taken into account, for each MS event s and its nearest event w, the distance of the two events, dsw, is the minimum distance in a serial of distances in line s of the matrix D1. The straight line connected event s and event w is a single link. Similarly, the nearest event of event w will be found. This process is repeated to generate a subset of SLC frame. There may be M (0oMoN/2) subsets with M-1 single links between them. Secondly, a new matrix D2 is established according to these subsets. It define dlm ¼min(dsw) (sAl, wAm), as the spatial distance of subset l and subset m. Thirdly, this process is repeated, recursively, until the N MS events are connected with N-1 links to establish the entire SLC frame. The probability density function o(l) gives the probability that a link is smaller than or equal to l. In this paper, the spatial correlation length
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x would be defined under the condition of o(x)¼0.5 according to ¨ Zoller et al. [25]. The temporal evolution of the spatial correlation length of MS events is calculated with sliding window that moves with a certain count of MS events. There were 730 MS events generated from January 1 to February 25, 2011, so we chosen 55 MS events to calculate x and 15 MS events as sliding window DN, seen in Fig. 10. The change of spatial correlation length of MS events from January 15 to February 15, 2011, showed in Fig. 11. Before January 25, spatial correlation length and energy release rate sustained in high level caused by mining operation. It indicated that the different areas in rock mass nearby stope 27 showed much large correlation resulted from mining disturbance. However, the spatial correlation length dropped to its minimum value on January 25 2011 along with weakened MS activities. From January 26 to February 6, 2011, spatial correlation lengths returned to increase with the cracks propagating in rock mass. It illustrated that the long-range correlations were being established by redistribution of stress from smaller to larger scales between different areas in rock mass. This process can be regarded as warning period of underground pressure hazard. On February 6, 2011, spatial correlation length reached its maximum value and then decreased rapidly. Under the high correlated stress field, a small rupture could jump over barriers and grow into a large fracture. When the stress field within rock mass was highly correlated, stress would transfer in a long range and large numbers of micro-cracks coalesce, leading the rock mass into an instable phase. Therefore, rock mass nearby stope 27 entered a state of high underground pressure hazard would occur, and two large scale MS events generated in the night February 8 and 11 showed as Fig. 9. Along with the occurrence of two large MS events, stress was released, the correlation of different areas in rock mass and the interaction between cracks were weakened. Rock mass was re-entered to relatively stable status and spatial correlation length also fallen back from high level. It is worth noting that when the large magnitude events occurred, spatial correlation length dropped quickly, which was in accordance with a description by Li et al. [28]. In his studies, in a case where the specimens showed clear cracking localization, spatial correlation length of acoustic emission events would drop in zones of cracks localization. Such a phenomenon appeared to be useful that the
Fig. 10. Sketch map of sliding window.
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spatial correlation length could be used as an indicator to forecast underground pressure failures. 3.4. Fractal characteristic of MS events Fractal geometry focuses on description of irregular or disorder phenomenon in nature. Xie [32] has gained many important conclusions from studies on microcracks propagation, characterization of fracture surface and rock burst in mine by use of fractal theory. Lei and Satoh [33] have investigated the change of fractal dimension of acoustic emission events through experiments and showed the fractal dimension would reduce to its minimum value before rock failure. In this paper, Box dimension was used to study fractal characteristic of MS events. Assuming F as a non-empty bounded subset, Nd (F) as the number of cover the set of F by max diameter d, then the lower and upper box dimension of F are respectively defined as follows: Dim B F ¼ lim
lg Nd ðFÞ lg d
ð6Þ
Dim B F ¼ lim
lg Nd ðFÞ lg d
ð7Þ
d-0
d-0
If the two values are equal, they can be regarded as box dimension of F and expressed as: DimB F ¼ lim
d-0
lg N d ðFÞ lg d
ð8Þ
Thus, the minimum number to cover the set of F by d is about
d s orders, where s equal to DimBF. This paper used cubes with side length r to cover monitoring areas for calculating fractal dimension. Thus, some cubes are empty with no MS events, while others contain MS events. The number of non-empty cubes N(r) with r changed to zero would be calculated. Then fractal dimension D is calculated as followed: D ¼ lim r-0
lg NðrÞ lg r
ð9Þ
Usually, a series of r and N(r) would be calculated, and the slope of fitting curve of ln NB ln r be taken as fractal dimension D. In this study, 55 MS events were selected for calculating fractal dimension using a sliding window approach. Each sliding window included 15 MS events, which was consistent with the calculation process of spatial correlation length in order to compare analyses. Considering the self-similarity and scale invariance, the cube side length r ranged from 10 to 40 m. Fig. 12 showed the plots of ln N(r)B ln r on January 22, January 23, January 29, February 1 and February 6.
Fig. 11. Changes of MS spatial correlation length and energy release with time (2011.01.16-02.15).
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The changes of fractal dimension of MS events from January 15 to February 15, 2011, showed as Fig. 13. Before January 22, fractal dimension of MS events were relatively higher, which indicated that the distribution of cracks within rock mass was very scatter. Since then, fractal dimension were continuously fluctuated descending, which suggested the cracks within rock mass were gradually changing from disorder to order. On February 6, fractal dimension reduced to its minimum value, illustrated the cracks were highly concentrated in some areas nearby stope 27, and rock mass came into dangerous period of underground pressure hazard occurred. The phenomenon of fractal dimension of MS events reduced to its minimum value before large scale rock mass fracture reflects the cracks distribution is an evolutionary process from disorder to order. The spatial distribution of MS events during mining process of stope 27 is irregularly, and is much less correlated with blasting position and stoping sequence. It is much difficult to judge the ground pressure hazard occurrence by MS events depend on naked-eye observation. Therefore, fractal theory is a very useful method to find out the regularity of MS events from its irregular spatial distribution.
where M is magnitude, N is the number of earthquakes with magnitude equal or above M, a and b are constants. In the G–R relationship, b value is a useful parameter for analyzing magnitude and frequency in seismology. It is of great significance for studying the proportion of different scale cracks and the process of small-scale cracks grow into large-scale cracks [35]. 55 MS events and 15 events were adopted as calculated window and sliding window, respectively. The magnitude of MS events during this monitoring period was from -5 to 0.5. Thus, we adopted DM¼0.5 to calculate b value. Fig. 14 shows the evolution law of b value with time. Before January 29th, b value was gradually increasing, which indicates there were much more small scale cracks within rock mass during this period, occupied by higher proportion. After February 2, the proportion of large scale cracks was increasing and the b value decreased extremely. It suggests that small scale cracks gradually coalescence into larger scale cracks. When the two large scale MS events happened on 8th and 11 February, b value had slightly rising back. The reason for that is the amount of small scale cracks was also re-increase with large scale rock fracture occurred.
3.5. Change of b value of MS events
4. Conclusion and discussion
Gutenberg and Richter [34] proposed the well known G–R relationship between earthquake magnitude and frequency by studying the global seismicity in 1944 showed as follows:
In this paper, temporal and spatial activities of MS events were studied during mining process of a deep stope based on the theory of geophysics and rock mechanics. During mining operation, MS activities can be divided into three stages: MS events generated much fewer prior to mining, while grew significantly during mining process; MS activities remains at a higher level for one week followed by a relative low activities. The mining process induced stress redistribution and deformation within rock mass. The regions of large deformation at horizontal plan of stope roof are expending, while the areas of large energy index, log (EI), are reducing, particularly near slope ramp, which indicated that the rock mass was seriously degradation. Before large scale fractures occurred, MS multi-parameters appeared distinct precursory characteristics can be called warning period. The apparent volume and spatial correlation length were continually increasing, while energy index, fractal dimension and b value were gradually dropping to their minimum values, which can be seen as precursory characteristics of ground pressure hazards. The monitoring results show it is feasible to forecast ground pressure hazards through comprehensive analysis by MS multi-parameters. When studying on MS activities, some parameters may be influenced by monitoring data uncertainty, such as located precision of MS events, monitoring system sensitivity and artificial processing error. Therefore, comprehensive analysis by multi-parameters changes can improve
lg N ¼ a2bM
ð10Þ
Fig. 12. ln N(r)B ln r plot of MS events.
Fig. 13. Changes of fractal dimension and energy release with time (2011.01.16-02.15).
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Fig. 14. Changes of b value and energy release with time (2011.01.16-02.15).
forecasting accuracy, which is much meaningful to the application of MS monitoring technology in deep metal mine. Geological conditions and mining process are usually complex in deep mining environment. Variety of hazards of rock masses could encounter in practice. It is demonstrated that the microseismic data are very useful in understanding seismic responses of rock masses to mining. Though studies of great quantities of seismic data and characterization of behavior of rock masses, useful indicators, such as energy index, spatial correlation length, could be developed as precursors of failures in rock masses.
Acknowledgments The Projects (2013BAB02B01, 2013BAB02B03) supported by the Key Projects in the National Science & Technology Pillar Program during the Twelfth Five-year Plan Period, the National Natural Science Foundation of China (51204030, 51274055, 51204031, 51109035) and the Fundamental Research Funds for the Central Universities (N110301006, N110501001, N110401003).
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Contents lists available at SciVerse ScienceDirect
International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms
Studies on temporal and spatial variation of microseismic activities in a deep metal mine Jian-po Liu a,n, Xia-ting Feng a,b, Yuan-hui Li a, Shi-da Xu a, Yu Sheng c a
Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang, Liaoning 110819, China State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China c Beijing SCR Instruments Ltd., Beijing 100048, China b
a r t i c l e i n f o
abstract
Article history: Received 1 May 2012 Received in revised form 21 September 2012 Accepted 21 December 2012 Available online 5 February 2013
Aiming at forecasting techniques of ground pressure hazards in deep metal mines, a microseismic monitoring system was established at a deep stope in Hongtoushan copper mine in China. Based on theories of geophysics and rock mechanics, a forecasting approach was introduced using microseismic multi-parameters including cumulative apparent volume, energy index, spatial correlation length, fractal dimension and b value. The approach was used to predict large scale fractures and ground pressure hazards in rock masses. The results showed that microseismic activities were very weak before mining commenced. However, activities became significant when mining started. When mining finished, microseismic activities remained at a higher level for about one week then became weakened. Before large scale fractures occurred, all microseismic multi-parameters behaved differently. The apparent volume and spatial correlation length were continually increasing, while energy index, fractal dimension and b value were gradually dropping to their minimum values. Therefore, these parameters could be used as precursory indicators for great ground pressure hazards. Comprehensive analysis on microseismic multi-parameters changes could improve reliability of forecasting, which is of great significance to deep metal mines in managing ground pressure failure risks. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Deep metal mine Microseismic (MS) monitoring Energy index Apparent volume Spatial correlation length Fractal dimension b value
1. Introduction With the continued rapid development of national economy and increased demands for mineral resources, deep mineral resources exploitation gradually becomes the trend of future mining in China. It is anticipated that over thirty mines whose depths will beyond 1000 m by 2015. Ten of them will be deeper than 1300 m. Deep extraction of minerals creates large volume of cavities and leads to high stresses surrounding the excavation which may cause failures in rock mass, in some cases, dynamic failures would occur. Therefore, it is important to investigate and to understand rock mass behavior in deep mining environment. The microseismic (MS) monitoring technique, using elastic waves generated by rock damage to evaluate the stability of rock mass, has been proven to be a useful tool for assessing rock mass stability and for forecasting dynamic hazards, hence to better manages disastrous rock failures. With the advances in computer technology over past decades, ability of fast processing of seismic waves has made the MS technology more applicable. It now becomes a routine technology in the deep mining operation and is widely used in South Africa, Australia, the United States, Canada, Chile, Poland and other countries
n
Corresponding author. Tel.: þ86 24 83684690. E-mail address: [email protected] (J.-p. Liu).
1365-1609/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijrmms.2012.12.022
[1–7]. Additionally, this technology was also gained much attention and was adopted in other applications, e.g. tunnel [8], hot dry rock power generation [9], open pit slope [10], deep-buried underground powerhouse [11,12], etc. Application of the MS monitoring technology in China only commenced after 2000. Li et al. [13] established a 64-channels digital MS monitoring system in Fankou lead–zinc mine with an ESG system. It was basically used to identify threedimensional locations of MS events in real-time through on-line monitoring. In 2003, Jiang et al. [14] in collaboration with the Commonwealth Scientific and Industrial Research Organization (CSIRO) of Australia performed a pilot trial seeking applicability of MS technology towards detecting and preventing coal mine hazards. Following the initial effort, a new explosion-proof MS monitoring system was developed and some meaningful results were obtained. In 2005, Tang [15,16] established an ISS MS monitoring system at Dongguashan copper mine to study stress changes and deformation characteristics in rock mass due to mining. Other mines such as Shizhuyuan polymetallic mine [17], Huize lead–zinc mine [18], Zhangmatun iron mine [19] are also established MS monitoring systems successively. In addition, Feng [20,21] carried out MS monitoring technique in the deeply and long buried tunnel of JinPing hydropower station in southwestern China, meaningful results were obtained. Much of applications of the MS technology to date are limited to qualitatively categorize seismic hazards. Great efforts have
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been made by many researchers in attempting use MS technology as a tool to predict dynamic disastrous failures. However, limited successes were achieved in this aspect. The inhomogeneous natures of rock structures and complexity of mining process makes difficulties in identifying and understanding key influences of MS activities and their evolution. Therefore, how to fully utilize and analyze those MS monitoring data and get the precursory characteristics before dynamic hazards happened has become an urgently problem need to be solved. Hongtoushan copper mine is one of the deepest nonferrous metal mines in China. Seismic hazards, e.g. rock burst, roof collapses and side wall failures under high rock stresses were presented at the mine since late 1990 s. To enhance management of seismic hazards, the mine decided to adopt seismic monitoring technology. As such, an ISS MS system was established in June 2010. The present paper describes the use of multi-parameters, including accumulation apparent volume, energy index, spatial correlation length, fractal characteristic and b value, to analyze the spatial and temporal evolution characteristics of MS events. Attempt is made to establish a framework of forecasting for large scale fractures in rock mass using seismic data.
2. Establishment of a MS monitoring system at Hongtoushan copper mine 2.1. Mining layout and selected sensor array Hongtoushan copper mine has been in operation since 1958. It is one of the deepest nonferrous metal mines in China. The deepest stope is 1357 m below the ground surface. With continued mining operation, high ground pressures have been causing seismic hazards, eg. rock burst and roof collapses, which impact on safety of operators and disrupt production, hence cause financial losses. Aiming to mitigate seismic hazards and to enhance safety management, a MS monitoring system was installed around Stope 27 at depth of 1137 m. It was the largest stope with an exposed area of 2400–3000 m2 and about 67,000 t of ores were expected to being recovered. The overhead cut-and-fill stoping method was used for mining at Stope 27, four layers have been mined and the fifth layer is being stopped at present. Stopes 19 to 26, along side of stope 27, were mined using the room-and-pillar method. Among them, stope 16, 18, 20, 22, 24 and 26 were mined and filled. The layout surrounding stope 27 is showed in Fig. 1(a). The mining facilities around stope 27 include hanging wall haulage tunnel, across-vein roadway, slope ramp and pipe well showed in Fig. 1(b). MS sensors arrangement is on basis of those existed facilities. Five sensors, including one triaxial accelerometer and four uniaxial geophones, were permanently installed on slope ramp between the fourth and the fifth platforms. In addition, two uniaxial geophones were installed in acrossvein roadway.
Fig. 1. Mining layout for No.27 stope at 707 m level and the MS sensors array. 1-filled layer cavities, 2-mined layer cavities, but not filled, 3-layers to be mine, 4-pipe well, 5-slope ramp, 6-platform. (a) Plan view and (b) side view.
2.2. Establishment of a MS monitoring system A high performance ISS system [22] was adopted for this research project. The hardware system include sensors, seismic data acquisition unit (GS), DSL 2-wire modem for GS, server, electric cable, telephone line, optical fiber and photoelectric converter, etc. The sensor array consists of one triaxial and six uniaxial heavy duty 14 Hz borehole geophones with a performance range of 7–2000 Hz and sensitivity of 80 V/ms 1. These intelligent sensors have self-checking function that can automatically identify the sensor ID, coordinates, azimuth and dipping angle when installed. The data acquisition GS unit has specification of a 32 bit AD conversion accuracy and the maximum sampling frequency of
Fig. 2. Install methods of MS sensors. (a) Schemetic diagram for permanent installation , (b) schematic diagram for temporary installation and (c) device for temporary installation.
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48,000 Hz. A sampling rate of 6000 Hz was adopted for this system. Each GS unit was equipped with an intelligent uninterruptible power suppliery (iUPS) to enhance the performance of GS units. Through the system, MS wave signals are sensed by the sensors, which concerted them into electrical analog signals and received by the GS data acquisition units, where the signals are further converted to digital signals. A DSL technology based communication system, which synchronizes the system and transmits the digital data through a telephone line from GS units to a central server at an underground center at 707 m level. The digital seismic data can be processed at the server and results can be downloaded by the central office of the mine and by a remote research center at Northeast University (NEU) via internet. The sensors were installed in either way of permanent or temporary installation. The procedure for a permanent
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installation Fig. 2(a) included following steps: (1) to position a sensor, bound with an air-exhausting pipe, into the boreholes with a special installation tool; (2) to apply a wooden plug, with a hole in the middle allowing passes of an exhausting pipe, an grouting pipe and an signal cable, to hold grout at the entrance of the boreholes; (3) to inject the grout until its overflowing from the exhausting pipe; (4) to block and to cut both the injecting and the exhausting pipes. It is worth noting that sensors need to be tied a certain distance from the end of the exhaust pipe to ensure sensors were grouted firmly. The temporarily installed sensors were shown in Fig. 2(b). A special device was developed as shown in Fig. 2(c) for such a purpose. It consisted of an inner and an outer sleeve. The outer sleeve was permanently placed at the bottom of the borehole by capsule resin. A sensor was attached to an inner sleeve, which remained in place during the monitoring. Upon complete the monitoring work, the sensor could be retrieved by withdrawn the inner sleeve using the installation tool and could be used elsewhere. A weekly inspection procedure was adopted to ensure it in a firmly fixed state and was not affected by ground shaking due to blasting operation. Signal testing suggests that the P-wave arrival time could be clearly identified. It was noticeable that coda waves presented. However, they have little influence on location accuracy of MS events. 2.3. Mining sequence The mining of the fifth layer at stope 27 was carried out from January 11 to January 19, 2011, except January 16. The thickness of ore body was about 3–4 m and the total area was about 1600 m2. Blasting design on timing, position, sequence, amount of explosives and excavate volume are showed in Fig. 3 and Table 1 respectively. Before this mining work, two areas, Region A and B showed in Fig. 3 had been mined. Regions C and D will be mined at the later stage. The mining in Regions 1 to 8, shown in Fig. 3 was completed on January 19, 2011.
Fig. 3. Sequence and location of mining work.
Table 1 Blasting parameters of mining work. Number Data
1 2 3 4 5 6 7 8
2011.01.11 2011.01.12 2011.01.13 2011.01.14 2011.01.15 2011.01.17 2011.01.18 2011.01.19
Explosive/ Weight of box explosive/ kg
Numbers of millisecond blasting
Ore volume/ m3
25 26 30 30 30 30 30 6
5 5 6 6 6 6 6 6
660 686 792 792 792 792 792 158
600 624 720 720 720 720 720 144
3. Spatial and temporal characteristics of micro-seismicity 3.1. Daily micro-seismicity Many blasting events were recorded during the course of monitoring. The blasting events could be identified from characteristics of waveforms, such as high energy, high frequency and quick decay etc. They were not analyzed in this study. By contrast, Signals of MS events were usually much weaker with lower energy, longer duration, lower frequency and slow decay. Fig. 4 shows recorded MS activities from January 1 to February 25,
Fig. 4. Law of MS activities with time (2011.01.01-02.25).
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2011. It is interested to see that features of the MS activities were much different before, during and after the mining operation. Before January 11, the operations at Stope 27 were mainly related to ore transportation and backfill, the MS events were less than five every day. Since mining resumed on January 11, a sharp increase in MS events is visible. Due to blast operation in the duration from January 11 to January 19, the average rate of MS activities was at 20–30 events a day. It suggests that the mining work has great disturbance to surrounding rock mass, which accelerate generation and propagation of cracks. When the mining operation finished on January 19, MS activities remained at a higher level for a week, indicating influences of stress-field redistribution and adjustment. The MS activities remarkably decreased to relatively stable state from January 26, one week after mining operation and the MS events are at a rate of fifteen a day. It is noticeable to see that event generation remains at this rate one month after the complete of mining, indicating the stress redistribution is a relatively long process.
3.2. Laws of accumulative apparent volume and energy index Due to the complexity of underground mining environment, rock mass damage cannot be estimated from single MS event. According to the view of seismology, statistical analysis on temporal and spatial evolution laws of MS events is widely used to judge rock mass stability by studied MS events within somewhat time and space. General statistical parameters of
microseismic activity include apparent volume, apparent stress, and energy index. The apparent stress sA [23] is defined as the ratio of the radiated seismic energy E and seismic scalar seismic potency P, expressed as:
sA ¼
ð1Þ
Apparent volume VA [23] is a much stable parameter, and it measures the volume of rock with the inelastic change, expressed as: VA ¼
mP2 E
ð2Þ
where m is the rigidity of the rock. Apparent volume, like apparent stress, depends on seismic potency P and radiated energy E, and, because of its scalar nature, can easily be manipulated in the form of cumulative or contour plots. Apparent volume and apparent stress are two important parameters in seismology theory, which are often used to describe the changes within rock mass before hazards occurred. When rocks closing to peak stress, the deformation growth will speed up and the stress growth will reduce. After peak stress, the stress is gradually reduce while deformation growing quickly. During the strain-softening stage, the more quickly stress dropping, the more serious rocks failure. Energy index EI [23] of a MS event is the ratio of the observed radiated seismic energy of that event E, to the average energy EðPÞ radiated by events of the observed potency P taken from logEðPÞ ¼ dlogP þc, for the monitoring area showed in Fig. 5: EI ¼
Fig. 5. Relationship between MS energy and potency.
E P
E E E ¼ ¼ 10c d EðPÞ P 10dlogP þ c
ð3Þ
which for d ¼1.0 would be proportional to the apparent stress. The higher the energy index, the higher the driving stress at the source of the event at the time of its occurrence. Therefore, the changes of apparent volume VA and energy index EI can be applied to obtain precursor information of rock mass hazards. Fig. 6 shows the changes of accumulative apparent volume and energy index from January 15 to February 15, 2011. Before February 2, apparent volume was gradually growing, while the logarithm of energy index log (EI) fluctuating changed and gradually reached to its maximum value. It illustrated that the elastic deformation volume of rock mass within monitoring area was increasing, and the driving stress at the source of the MS events reached the maximum value. During the period from February 2 to 7, logarithm of energy index log (EI) was decreased sharply but accumulated apparent volume kept increasing, which indicated that parts of rock mass within monitoring area was
Fig. 6. Changes of accumulative apparent volume and energy index with time.
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becoming unstable status. This period could be seen as strainsoftening stage, which was an onset of a potential underground pressure hazard and could be regarded as a warning indicator. With the time going, apparent volume was continually increasing and log (EI) was resume increasing, and the rock mass was entering into an unstable state. Finally, two large scales of MS events occurred on February 8 and 11 that are second day and fourth day after the warnings issues, respectively. These two events were located at the areas between stope 27 and other stopes that had been filled showed in Fig. 7. Their magnitudes the two events were 0.1 and 0.2, respectively. The waveforms of large MS event on February 8 showed in Fig. 8. Apparent volume and energy index can be seen to a stain– stress curve, representing laboratory behavior of a hard rock
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sample under compression test. The phenomenon of logarithm of energy index log (EI) dynamically deceasing and accumulated apparent volume obviously increasing could be regarded as precursory characteristics. The quicker log (EI) decreasing and accumulated apparent volume increasing, the larger risk of an underground pressure hazards would be happened. The mining operation would disturb surrounding rock mass and induce stress redistribution within rock mass. Fig. 9 shows the cloud plots of distribution of displacement and log (EI). The average displacement can be calculated by the ratio of seismic potency and source area. It could be seen that the regions of large deformation in horizontal plans at stope 27 roof are expending, while the areas of large log (EI) are reducing, particularly near slope ramp. This phenomenon indicated that serious degradation of rock mass, and slope ramp was damaged in forms of bulging, slabbing and splitting, etc. Because changes in stress and deformation were independently obtained from MS events, therefore they can reflect the difference of physics mechanics of different areas within rock mass. The source of a MS event associated with a weaker geological feature or with a softer patch in the rock mass yields more slowly under lower differential stress, and radiates less seismic energy per unit of inelastic co-seismic deformation, than an equivalent source within strong and highly stressed rock mass. The phenomenon of deformation increasing and stress reducing indicated that the rock mass become degradation. In contrast, the integrity of rock mass is much better.
3.3. Spatial correlation length of MS events
Fig. 7. Spatial position of the two large magnitude MS events.
In accordance with the hypothesis of the critical point [24], two characteristic parameters, i.e. growing of correlation length
Fig. 8. Waveforms of large MS event on February 8.
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Fig. 9. Cloud charts distribution of displacement and lg (EI).
and increasing of critical sensitivity before unstable failure of materials such as rocks, can be considered as the precursors. In seismology, the spatial correlation can be considered as a characteristic distance or cluster size of events in a certain time interval [25]. If the system approaches the critical point, there will be a long-range interaction characterized by power-law function. ¨ Zoller et al. [25] have studied the accelerated growing phenomenon of correlation length of 9 earthquakes (M Z6.5) between 321–401N in California in 1952. It was suggested that the accelerated growth of correlation length might be seen as a predictive indicator before large earthquakes. Rong et al. [26] and Tyupkin and Giovambattista [27] were also obtained the similar results from studying on earthquakes and laboratory tests, respectively. Li et al. [28] found that two factors may influence the change of spatial correlation length: stress release and stress re-distribution. The former leads to a decrease in correlation length, while the latter leads to an increase in correlation length. The growth of correlation length x of MS events can be expressed as [29]:
xðtÞ tf t
k
ð4Þ
where tf is rock failure time and k is power-law fitting parameter. The spatial correlation length of MS events was calculated by Single-Link Cluster (SLC) presented by Frohlich and Davis [30]. The
SLC method [25,30,31] assumes that the time-space distances of MS events can be written as a matrix D1. The distance of events i and j, dij, in line i and column j of the matrix D1, can be expressed as: dij ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 xj xi þ yj yi þ zj zi þ c2 t j t i
ð5Þ
where x, y and z are the three-dimensional coordinates of MS event, t is the time of MS events occurred, c is the associated constant of time and spatial distance. In this work, we only study the spatial characteristics of MS events. Therefore c¼ 0 and the dij indicates the spatial distance between the MS events. Firstly, when a distribution of N events is taken into account, for each MS event s and its nearest event w, the distance of the two events, dsw, is the minimum distance in a serial of distances in line s of the matrix D1. The straight line connected event s and event w is a single link. Similarly, the nearest event of event w will be found. This process is repeated to generate a subset of SLC frame. There may be M (0oMoN/2) subsets with M-1 single links between them. Secondly, a new matrix D2 is established according to these subsets. It define dlm ¼min(dsw) (sAl, wAm), as the spatial distance of subset l and subset m. Thirdly, this process is repeated, recursively, until the N MS events are connected with N-1 links to establish the entire SLC frame. The probability density function o(l) gives the probability that a link is smaller than or equal to l. In this paper, the spatial correlation length
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x would be defined under the condition of o(x)¼0.5 according to ¨ Zoller et al. [25]. The temporal evolution of the spatial correlation length of MS events is calculated with sliding window that moves with a certain count of MS events. There were 730 MS events generated from January 1 to February 25, 2011, so we chosen 55 MS events to calculate x and 15 MS events as sliding window DN, seen in Fig. 10. The change of spatial correlation length of MS events from January 15 to February 15, 2011, showed in Fig. 11. Before January 25, spatial correlation length and energy release rate sustained in high level caused by mining operation. It indicated that the different areas in rock mass nearby stope 27 showed much large correlation resulted from mining disturbance. However, the spatial correlation length dropped to its minimum value on January 25 2011 along with weakened MS activities. From January 26 to February 6, 2011, spatial correlation lengths returned to increase with the cracks propagating in rock mass. It illustrated that the long-range correlations were being established by redistribution of stress from smaller to larger scales between different areas in rock mass. This process can be regarded as warning period of underground pressure hazard. On February 6, 2011, spatial correlation length reached its maximum value and then decreased rapidly. Under the high correlated stress field, a small rupture could jump over barriers and grow into a large fracture. When the stress field within rock mass was highly correlated, stress would transfer in a long range and large numbers of micro-cracks coalesce, leading the rock mass into an instable phase. Therefore, rock mass nearby stope 27 entered a state of high underground pressure hazard would occur, and two large scale MS events generated in the night February 8 and 11 showed as Fig. 9. Along with the occurrence of two large MS events, stress was released, the correlation of different areas in rock mass and the interaction between cracks were weakened. Rock mass was re-entered to relatively stable status and spatial correlation length also fallen back from high level. It is worth noting that when the large magnitude events occurred, spatial correlation length dropped quickly, which was in accordance with a description by Li et al. [28]. In his studies, in a case where the specimens showed clear cracking localization, spatial correlation length of acoustic emission events would drop in zones of cracks localization. Such a phenomenon appeared to be useful that the
Fig. 10. Sketch map of sliding window.
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spatial correlation length could be used as an indicator to forecast underground pressure failures. 3.4. Fractal characteristic of MS events Fractal geometry focuses on description of irregular or disorder phenomenon in nature. Xie [32] has gained many important conclusions from studies on microcracks propagation, characterization of fracture surface and rock burst in mine by use of fractal theory. Lei and Satoh [33] have investigated the change of fractal dimension of acoustic emission events through experiments and showed the fractal dimension would reduce to its minimum value before rock failure. In this paper, Box dimension was used to study fractal characteristic of MS events. Assuming F as a non-empty bounded subset, Nd (F) as the number of cover the set of F by max diameter d, then the lower and upper box dimension of F are respectively defined as follows: Dim B F ¼ lim
lg Nd ðFÞ lg d
ð6Þ
Dim B F ¼ lim
lg Nd ðFÞ lg d
ð7Þ
d-0
d-0
If the two values are equal, they can be regarded as box dimension of F and expressed as: DimB F ¼ lim
d-0
lg N d ðFÞ lg d
ð8Þ
Thus, the minimum number to cover the set of F by d is about
d s orders, where s equal to DimBF. This paper used cubes with side length r to cover monitoring areas for calculating fractal dimension. Thus, some cubes are empty with no MS events, while others contain MS events. The number of non-empty cubes N(r) with r changed to zero would be calculated. Then fractal dimension D is calculated as followed: D ¼ lim r-0
lg NðrÞ lg r
ð9Þ
Usually, a series of r and N(r) would be calculated, and the slope of fitting curve of ln NB ln r be taken as fractal dimension D. In this study, 55 MS events were selected for calculating fractal dimension using a sliding window approach. Each sliding window included 15 MS events, which was consistent with the calculation process of spatial correlation length in order to compare analyses. Considering the self-similarity and scale invariance, the cube side length r ranged from 10 to 40 m. Fig. 12 showed the plots of ln N(r)B ln r on January 22, January 23, January 29, February 1 and February 6.
Fig. 11. Changes of MS spatial correlation length and energy release with time (2011.01.16-02.15).
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The changes of fractal dimension of MS events from January 15 to February 15, 2011, showed as Fig. 13. Before January 22, fractal dimension of MS events were relatively higher, which indicated that the distribution of cracks within rock mass was very scatter. Since then, fractal dimension were continuously fluctuated descending, which suggested the cracks within rock mass were gradually changing from disorder to order. On February 6, fractal dimension reduced to its minimum value, illustrated the cracks were highly concentrated in some areas nearby stope 27, and rock mass came into dangerous period of underground pressure hazard occurred. The phenomenon of fractal dimension of MS events reduced to its minimum value before large scale rock mass fracture reflects the cracks distribution is an evolutionary process from disorder to order. The spatial distribution of MS events during mining process of stope 27 is irregularly, and is much less correlated with blasting position and stoping sequence. It is much difficult to judge the ground pressure hazard occurrence by MS events depend on naked-eye observation. Therefore, fractal theory is a very useful method to find out the regularity of MS events from its irregular spatial distribution.
where M is magnitude, N is the number of earthquakes with magnitude equal or above M, a and b are constants. In the G–R relationship, b value is a useful parameter for analyzing magnitude and frequency in seismology. It is of great significance for studying the proportion of different scale cracks and the process of small-scale cracks grow into large-scale cracks [35]. 55 MS events and 15 events were adopted as calculated window and sliding window, respectively. The magnitude of MS events during this monitoring period was from -5 to 0.5. Thus, we adopted DM¼0.5 to calculate b value. Fig. 14 shows the evolution law of b value with time. Before January 29th, b value was gradually increasing, which indicates there were much more small scale cracks within rock mass during this period, occupied by higher proportion. After February 2, the proportion of large scale cracks was increasing and the b value decreased extremely. It suggests that small scale cracks gradually coalescence into larger scale cracks. When the two large scale MS events happened on 8th and 11 February, b value had slightly rising back. The reason for that is the amount of small scale cracks was also re-increase with large scale rock fracture occurred.
3.5. Change of b value of MS events
4. Conclusion and discussion
Gutenberg and Richter [34] proposed the well known G–R relationship between earthquake magnitude and frequency by studying the global seismicity in 1944 showed as follows:
In this paper, temporal and spatial activities of MS events were studied during mining process of a deep stope based on the theory of geophysics and rock mechanics. During mining operation, MS activities can be divided into three stages: MS events generated much fewer prior to mining, while grew significantly during mining process; MS activities remains at a higher level for one week followed by a relative low activities. The mining process induced stress redistribution and deformation within rock mass. The regions of large deformation at horizontal plan of stope roof are expending, while the areas of large energy index, log (EI), are reducing, particularly near slope ramp, which indicated that the rock mass was seriously degradation. Before large scale fractures occurred, MS multi-parameters appeared distinct precursory characteristics can be called warning period. The apparent volume and spatial correlation length were continually increasing, while energy index, fractal dimension and b value were gradually dropping to their minimum values, which can be seen as precursory characteristics of ground pressure hazards. The monitoring results show it is feasible to forecast ground pressure hazards through comprehensive analysis by MS multi-parameters. When studying on MS activities, some parameters may be influenced by monitoring data uncertainty, such as located precision of MS events, monitoring system sensitivity and artificial processing error. Therefore, comprehensive analysis by multi-parameters changes can improve
lg N ¼ a2bM
ð10Þ
Fig. 12. ln N(r)B ln r plot of MS events.
Fig. 13. Changes of fractal dimension and energy release with time (2011.01.16-02.15).
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Fig. 14. Changes of b value and energy release with time (2011.01.16-02.15).
forecasting accuracy, which is much meaningful to the application of MS monitoring technology in deep metal mine. Geological conditions and mining process are usually complex in deep mining environment. Variety of hazards of rock masses could encounter in practice. It is demonstrated that the microseismic data are very useful in understanding seismic responses of rock masses to mining. Though studies of great quantities of seismic data and characterization of behavior of rock masses, useful indicators, such as energy index, spatial correlation length, could be developed as precursors of failures in rock masses.
Acknowledgments The Projects (2013BAB02B01, 2013BAB02B03) supported by the Key Projects in the National Science & Technology Pillar Program during the Twelfth Five-year Plan Period, the National Natural Science Foundation of China (51204030, 51274055, 51204031, 51109035) and the Fundamental Research Funds for the Central Universities (N110301006, N110501001, N110401003).
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