Fractal analysis on the spatial distribution of acoustic emission in the failure process of rock spe

International Journal of Minerals, Metallurgy and MaterialsVolume 16, Number 1, February 2009, Page 19MineralsEL SEVIERFractal analysis on the spatial distribution of acoustic emission in thefailure process of rock specimensRuifu Yuan) and Yuan-hui L?)1) Energy Science and Engincering School, Henan Polytechnic University, Jiaozuo 454000 China2) Cllege of Resouree and Civil Enginering, Northeastern University, Shenyang 10004,0 China(Received 2008-02-02)Abstract: The spatial distribution of acoustic emission (AE) events in the failure process of several rock specimens was acquired us-ing an advanced AE acquiring and analyzing system. The box counting method (BCM) was employed to calculate the fractal dimen-sion (FD) of AE spatial distribution. There is a similar correlation between the fractal dimension and the load strength for dfferentrock specimens. The fractal dimension presents a decreasing trend with the increase of load strength. For the same kind of specimens,their FD values will decrease to the level below a relatively same value when they reach failure. This value can be regarded as thecritical value, which implies that the specimen will reach failure soon. The results reflect that it is possible to correlate the damage ofrock with a macroscopic paramcter, the FD value of AE signals. Futhermore, the FD value can be also used to forecast the final fail-ure of rock. This conclusion alws identifying or predicting the damagc in rock with a great advantagc over the classic theory and isvery crucial for forecasting rockburst or other dynamic disasters in mines.Key words: rockburst; acoustic emision; spatial distribution; fractal dimension; critical value; damage[This work was financially supported by the Special Subject of the National High- Tech Research and Development Program ofChina (No.2007AA06Z107), Supporting Project of New Century Excellence Talents in Chinese Universities (No.NCET-07-0163),Opening Research Foundation of CAS Key Laboratony of Rock and Soil Mechanics (No.Z110607) and Youth Foundation of HenanPolytechnic University (No.Q2008-51)]1. Introductionworth more than the simple statistic parameters. Withthe rapid development of location technique, the re-Rock is a typically inhomogenous and anisotropicsearch on the spatial distribution of AE sourcesmaterial, which contains several natural defects withemerged after the 1990s. Fox example, Lockner [10]various scales, such as microcracks, pores, fissures,observed the complete nucleation and growth processjoints inclusions, and precipitates. Large numbers ofof a fault from the locations of AE events. Xu et al.acoustic emission (AE) signals will be generated when[11] preliminarily analyzed the temporal and spatialrock is loaded till failure. Since AE signals are gener-distribution of microcracks in several specimens usingated by propagating and expanding of microcracks,an 8-channel, high-speed AE signal sampling and ana-ach AE signal contains plentiful information olyzing system. Li et al. [12] achieved thestructure change inside the rock [1-3]. Therefore, it is3-dimensional distribution of AE events during thenot surprising that in geological science, the acousticwhole failure process of rock specimens under uniax-emission phenomenon has atracted considerable at-ial compression and observed the emergence and fll-tention of rock engineering researchers [4-7]. Owinging process of the gap.to facility and technical reasons, early AE studies in中国煤化工rock engineering were limited to the statistics of AEmn is extremelynumber, counts, energy, and magnitude [8-9]. ThedisordMYHCNMHGhthebridgebe-spatial distribution of AE events reflects the propaga-tween the distribution of AE events and thetion of microcracks inside the rock, and therefore, it ismacro-mechanical behavior of rock. In recent years,Also avaiable online at www.sciencedirect.com。2009 University of Sciene and Technology Bejig All rights reserve.20International Journal of Minerals, Metallurgy and Materials, VoL16, No.1, Feb 2009fractal geometry has been widely used to describeThe aim of this article was to propose a new diag-some iregular phenomena in the fracture behavior ofnostic methodology based on data processing of AEmaterials. Biancolini et al. [13] used fractal analysissignals for the study of microcrack nucleation andand the box-counting method to characterize the spa-propagation in rock. The result of fractal analysis bytial distribution of the prime AE sources through thethe box-counting method (BCM) in particular is thefractal dimension. Nanjo [14] researched the relation-characterization of the signal from the point of view ofship between the fractal dimensions of spatial distri-the spatial distribution of the prime AE sources. Frombution of aftershocks and the pre-existing active faults.BCM, it was possible to extract a parameter (ractalXie [15] founded the fractal rock mechanics and ana-dimension) that could be correlated with the damagelyzed the fractal dimension of spatial distribution ofof the material.microseism events before a main rockburst in GalenaMine, USA. However, till now, only a few successful2. Experimental procedurecases forecasting rockburst by microseism technique2.1. Specimensindicate that the understanding and knowledge of themechanical behavior of AE distribution in rock stillSeveral kinds of brittle rock, such as granite, mar-remains in the primary stage and cannot yet fully meetble, and limestone were chosen and processed tothe needs of engineering design. As a result, the fur-specimens to meet the requirements suggested byther investigation of the laws of damage evolution andISRM. Table 1 shows the specification of the speci-the mechanisms of AE distribution has theoretical andmens used in the test.practical significance.Table 1. Specification of the specimensSerial numberLithologySizeWave velocity 1 (m:s_)Home _UG-192 mmx101 mmx151 mm4100Yiwula MountainUG-2Granite99 mmx 100 mmx151 mm4500Yiwulu MountainUG-3100 mmx103 mmx151 mm3800Yiwuli MountainUG-4102 mmx103 mmx151 mm4400Yiwuliu MountainUG-592 mmx102 mmx 150 mm3500UG-871 mmx75 mmx 154 mmUS-1Sandstoneφ80mmx182mm5100Zhaogu Coal MineUS-2.φ 65 mmx101 mm4300US-3φ64mmx102mm3000φ66mmx102mmUM-1Marble61 mm*61 mmx151 mm6000NanyangUM-262 mmx63 mmx 128 mm6100UM-3φ 60 mmx118 mm4200UM4中61 mmx120 mmUD-1Doleriteφ 56 mmx125 mmHongtoushan Copper MineUD-2φ 56 mmx126 mm5000UD-3UD-4φ 56 mmx124 mmUD-5φ56mmx124mm2.2. Acoustic emission monitoringments.Monitoring of AE signals was achieved using eightAE acquiring and analyzing systempiezelectric sensors with response frequencies at 125to 750 kHz. These sensors were positioned on theSpecimen习sides of specimens and were coupled with silicone中国煤化工grease. The signals were amplified with pre-amplifiersSen(40 dB) and main amplifiers (0-20 dB, auto-adjustive).'lasYHCNMH(A PC with AE analyzing software was used for thePressing machineServocontral systemacquisition and mermorization of AE signals. Fig. 1shows the arrangement of the experimental equip-Fig. 1. Arrangement of the experimental instruments.R.F. Yuan et al, Fractal aoalysis on the spatial distribution of acoustic emission in the...212.3. Experimental resultsevents is formed in the center area of the specimen. InFig. 2 plots the AE rate and the load versus dis-the third stage (>80% of peak load), the intensity ofplacement of UG-1 specimen. It reports signals withAE signals rises drastically till the specimen failure,frequencies between 125 and 750 kHz. It can be seenand most of these AE events appear in the specimen'sfrom Fig. 2 that as the load increases, the intensity ofcenter area and fill the gap.AE signals grows accordingly. The greatest emission,120expressed by AE rate and energy intensity, occurs400-Load| 100when the load approaches the maximum level of 400一AErate.kN. Fig. 3 shows the spatial distribution of AE signals+ 80during the load process for UG-1 specimen. It can beobserved in Figs. 2 and 3 that the AE events show thei 200following stages, which are similar to those inl 40Figs.4-6. In the first stage ( 20% of peak load), the100-rate of AE events presents a low value and most of| 20these events are located at the two ends of the speci-mens. In the second stage (20%-80% of the peak load),the AE rate increases stably, and the location of AEDisplacement 1 mmevents gradually extends to the center area of theFig.2. Load and AE rate vs. displacement for the UG-1specimen from the two ends. A gap with few AEspecimen.(a(b)(d)Fig, 3. Spatial distribution of AE signals in different stages of load process for the UG-1 specimen: (3) 0-20% of peak load;(b) 20%-80% of peak load; (C) 80%-100% of peak load; (d) whole process.1 18016a)”(b300160140一Load+250. AE rateAE ratef 140t 200二200t 120至100150崔f 10080岁言0F1006010--40500t0.81.60.00.10.20.30.40.5060中国煤化工Fig. 4. Load and AE rate vs. displacement for differMHCNMHG22International Journal of Minerals, Metallurgy and Materials, VoL.16, No.1, Feb 2009a)(b(c)Fig. 5. Spatial distribution of AE signals in different stages of load process for US-1 specimen: (a) 0-20% of peak load; (b)20%-80% of peak load; (C) 80%-100% of peak load; (d) whole process.(a，(cFig. 6. Spatial distribution of AE signals in different stages of load process for UM-1 specimen: (a) 0-20% of peak load; (b)20%-80% of peak load; (C) 80%- 100% of peak load; (d) whole process.3. Fractal dimension of spatial distributionr and N(r) and drew the lgN(r) to lg1/r line in lg-lggrid. The slope of the IgN(r) to lgl/r line was the frac-of AE eventstal dimension value Dp.Data processing of AE signals was achievedthrough the fractal algorithm using, in particular, the4. Results and discussionbox-counting method, described below.As mentioned above, the activity of AE events, es-The space that the specimen occupies could be Cov- pecially AE spatial distribution, reflected the evolve-ered by cubes with the side length of r. Then, somement of damage inside the specimen. Several re-cubes were empty and some others contain AE events.searches indicated that the behaviors of rock material,It indicated that these unempty cubes covered the spa-such as the distribution of microcracks, the shape oftial distribution of AE signals. The unempty cubesfracture surface, and the envelopment of damage,were counted and recorded as N(r). When r-→0, theshowed the fractal character. Of course, the disorderlyfractal dimension could be calculated as follows:distribution of AE signals generated in the failureprocess also had the fractal character.lgN(r)Dzlimo-lgrFigs. 7-10 show the correlation between the fractaldimension and the Inad etrenoth nf the specimens ofHowever, the set of AE events was composed ofgranit中国煤化工:rite, respectively.limited points. When r was lower than the value |UThere!YHCNMHGenthefractaldi-(|U=inf {|X-Y: X, Y∈U}, where U is the set of AEmenston ana the loaa strengun Ior al tests. The fractalevents), N(r) will be a constant value, which is the to-dimension shows a decreasing trend with the increasetal number of AE events. Therefore, in practical opof load strength. The whole load process is dividederation, the usual method was to find a series values ofinto 5 stages. In the first stage of the load processRF. Yuan et al, Fractal analysis on the spatial distribution of acoustic emission in the...23(<20% of peak load), the fractal dimension remainsnotice that all specimens' FD values decrease to thehigh in a range of 0.45-0.85. This implies that duringlevel below a relatively same value when the speci-the initial damage of the specimens, there is no or-mens reach failure. This value can be regarded as theganization in the spatial distribution of AE events, andcritical value, which implies that the specimen willtherefore, there is no organization or nucleation ofreach failure soon.microcracks inside the specimens. Moreover, after the0.first half of the load process, the fractal dimension be-0.8gins to decrease, reaching Dg <0.3 or 0.4 at the failurepoint. It is possible to correlate the fatigue damage0.7with the distribution of AE events, showing that the0.6nucleation and propagation of cracks begin after the0.5first half of the total load process. The most excitingphenomenon is that the FD values will descend to thelevel below a critical value for the same kind ofCritical value0.2specimens when they approach failure (at >80% of2060100peak load), such as 0.3 for granite and sandstoneLoad strength 1 %specimens and 0.4 for dolerite and marble specimens(notice the dashed line in Figs. 7-10). The FD valuesFig. 9. Values of fractal dimension in failure process for4of the specimens in different load stages are reportedmarble specimens.in Table 2.0.9.8-0.8 UD-30.7+UD-4,UID-,JUD-3.6-rUG-2vG-3:0.4-UG-40.3|UD-2Critical valuc0.2-0.1L406030280Load strength / %Fig. 10. Values of fractal dimension in failure process forFig. 7. Values of fractal dimension in failure process for 55 dolerite specimens.granite specimens.5. Conclusion0.7个一US-IIt is seen in this article that it is possible to correlate-- US-2_-US-3.the damage of the material with a macroscopic pa-rameter, namely the fractal dimension of AE signals.雷0.5This result suggests that it is possible to use the fractals 0.4-analysis of AE signals as a valuable diagnostic meth-odology for the study of microcrack nucleation andE0.3 --propagation in rock. The tests emphasize a relation-ship between the damage during a load process and810the fractal dimension of AE signals. Furthermore, theresults can be repeated by changing the condition ofLoad strengh 1 %Fig. 8. Values of fractal dimension in failure process for 4the test. It is verified that the valucs of fractal dimen-sion will decrease to a critical value for all tests per-sandstone specimens.forme中国煤化工1od allows identi-The decrease of fractal dimension implies that thefyingHCNMHGsverycrucialforvith a great ad-sources of emission are ordering. They will assemblevantagon a plane (or several planes sometimes). The plane(s)forecasting rockburst or other dynamic disasters inis just the position of macro-cracks which lead to themines.completely failure of the specimen. It is possible to24International Journal of Minerals, Metallurgy and Materials, VoL16, No.1, Feb 2009Table 2. Fractal dimension of AE events in diferent specimens during the uniaxial compressive load processLoad strengthNo.0-20%20%-40%40%-60%60%6-80%80%- 100%Critical valueUG-I0.480.680.550.540.19UG-20.450.350.560.15UG-30.570.590.310.27).30.440.410.370.25UG-50.770.600.460.28US-10.750.610.23US-20.760.580.510.17US-30.470.500.26US-40.650.20UM-10.490.360.300.210.720.3UM-30.670.40UM-40.64_0.850.24UD-I0.390.32UD-20.530.50.40.22UD-30.62).40.83_UD-50.AcknowledgementsTechnol. Beijing, 15(2008), p.215.[7] M. Cai, H. Morioka, and P.K. Kaiser, Back analys ofThe authors would like to thank Mr. J. Tian, J.P.rock mass strength parameters using AE monitoring data,Liu, and J.Y. 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