煤与砂岩复合岩声发射统计效应的试验与最大似然理论
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摘要
岩石类材料破裂损伤的声发射统计效应近年来在理论、试验和模拟方面已开展了大量研究,并且近年来以声发射为实验基础,采用统计物理学的方式分析声发射信号,继而关于材料内部损伤机制的相关研究也得到了发展,但是针对不同材料声发射统计效应及其相互作用与临界行为研究还较为缺乏。为此在实验室条件下采用日本岛津AGI-250高精度材料试验机对由分别取自内蒙古和重庆地区的煤与砂岩组成的复合岩开展了单轴压缩试验,利用DISP系列全数字声发射工作站采集压缩条件下试样中煤与砂岩层位的声发射信号,对信号进行了概率密度分布分析,并建立了考虑叠加效应的幂律指数最大似然估计方法。研究发现:复合岩在单轴压缩条件下煤层和砂岩层的声发射信号与纯煤和纯砂岩表现出了不同的统计性质,其整体声发射能量概率密度分布受煤层影响较大,砂岩层整体服从单幂律分布,而煤层则服从双幂律分布;叠加效应的幂律指数最大似然估计方程由上下限幂律指数α,β,与声发射数量比例x三参数控制,方程预测结果与试验中拥有较低幂律指数层位的分析结果一致,且随着声发射能量的增加逐渐趋近于下限幂律指数值;随着声发射能量级的增加,复合岩中煤层对整体统计结果的影响程度逐渐增加,而砂岩层的影响程度变化不明显。
A lot number of studies have been carried out on the acoustic emission statistic effect of rock material fracture damage in theory,experiments and simulation recently. Based on the test approach of acoustic emission,the research on the mechanism of internal damage of materials has also been conducted to analyze the AE signal by statistical physics method. However,the study on acoustic emission statistic effect and critical behavior of different materials is rare. In this paper,the uniaxial compression test was carried out on the composite rock composed of coal and sandstone from Inner Mongolia and Chongqing using Japan Shimazu AGI-250 high-precision material testing machine,and the AE signal was captured by the DISP AE station. The probability density distribution analysis has been applied for the AE signals captured in different layers of sample composited by coal and sandstone under uniaxial compression,and a maximum likelihood estimation method for power-law exponent considering superposition effect has been established. The results showed that more influenced by the coal layer of composite rock,the acoustic emission energy probability density distribution of the composite sample was different from that of pure coal and sandstone,in which coal layer and sandstone layer followed single and double power-law respectively in general. The maximum likelihood estimation equation of power-law exponent under superposition effect was determined by power-law exponent's upper limitationα,the lower limitationβand the ratioxof AE amounts,which showed consistency with the experimental results of the layer with lower limitation,and gradually approached to the lower limitation with the increase of acoustic emission energy. With increasing level of acoustic emission energy,the influence degree of coal layer on the whole composite rock increased gradually,while that of sandstone layer had no significant change.
A lot number of studies have been carried out on the acoustic emission statistic effect of rock material fracture damage in theory,experiments and simulation recently. Based on the test approach of acoustic emission,the research on the mechanism of internal damage of materials has also been conducted to analyze the AE signal by statistical physics method. However,the study on acoustic emission statistic effect and critical behavior of different materials is rare. In this paper,the uniaxial compression test was carried out on the composite rock composed of coal and sandstone from Inner Mongolia and Chongqing using Japan Shimazu AGI-250 high-precision material testing machine,and the AE signal was captured by the DISP AE station. The probability density distribution analysis has been applied for the AE signals captured in different layers of sample composited by coal and sandstone under uniaxial compression,and a maximum likelihood estimation method for power-law exponent considering superposition effect has been established. The results showed that more influenced by the coal layer of composite rock,the acoustic emission energy probability density distribution of the composite sample was different from that of pure coal and sandstone,in which coal layer and sandstone layer followed single and double power-law respectively in general. The maximum likelihood estimation equation of power-law exponent under superposition effect was determined by power-law exponent's upper limitationα,the lower limitationβand the ratioxof AE amounts,which showed consistency with the experimental results of the layer with lower limitation,and gradually approached to the lower limitation with the increase of acoustic emission energy. With increasing level of acoustic emission energy,the influence degree of coal layer on the whole composite rock increased gradually,while that of sandstone layer had no significant change.
引文
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[23]SALJE E K H,LIU H,JIN L,et al.Intermittent flow under constant forcing:Acoustic emission from creep avalanches[J].Applied Physics Letters,2018,112(5):054101.
[24]KIM K,FRANKLIN J A,BOWLING A J,et al.International society for rock mechanics commission on testing methods[J].International Journal of Rock Mechanics&Mining Sciences&Geomechanics Abstracts,1999,24(1):53.
[25]张伯虎,李东林,胡万雨.岩石声发射信号频谱与能量特征分析[J].东北大学学报(自然科学版),2015,36(S1):185-188.ZHANG Bohu,LI Donglin,HU Wanyu.Spectrum and energy characteristics analysis of rock acoustic emission signal[J].Journal of Northeastern University(Natural Science),2015,36(S1):185-188.
[26]VAN DER ELST N J,BRODSKY E E.Connecting near-field and far-field earthquake triggering to dynamic strain[J].Journal of Geophysical Research:Solid Earth,2010,115:B07311.
[27]SALJE E K H,LAMPROSI G I,SOTO-PARRA D E,et al.Noise of collapsing minerals:Predictability of the compressional failure in goethite mines[J].American Mineralogist,2013,98(4):609-615.
[28]CLAUSET A,SHALIZI C R,NEWMAN M E J.Power-law distributions in empirical data[J].SIAM Review,2009,51(4):661-703.
[2]CARRILLO L,MA?OSA L,ORTíN J,et al.Experimental evidence for universality of acoustic emission avalanche distributions during structural transitions[J].Physical Review Letters,2010,81(9):1889-1892.
[3]LüP,WU K,JIAO Y,et al.The experimental study of acoustic emission during creep of rocks[J].Acta Seismologica Sinica,1991,5(1):169-176.
[4]SALJE E K H,DAHMEN K A.Crackling noise in disordered materials[J].Annual Review of Condensed Matter Physics,2014,5:233-254.
[5]BISMAYER U.Early warning signs for mining accidents:Detecting crackling noise[J].American Mineralogist,2017,102(1):3-4.
[6]BARóJ,PLANES A,SALJE E K H,et al.Fracking and labquakes[J].Philosophical Magazine,2016,96(35):3686-3696.
[7]BARóJ,CORRALá,ILLA X,et al.Statistical similarity between the compression of a porous material and earthquakes[J].Physical Review Letters,2013,110(8):088702.
[8]NATAF G F,CASTILLO-VILLA P O,BARóJ,et al.Avalanches in compressed porous SiO2-based materials[J].Physical Review E.,2014,90(2):022405.
[9]NICCOLINI G,DURIN G,CARPINTERI A,et al.Crackling noise and universality in fracture systems[J].Journal of Statistical Mechanics-Theory and Experiment,2009(1):P01023.
[10]SETHNA J P,DAHMEN K A,MYERS C R.Crackling noise[J].Nature,2001,410(6825):242-250.
[11]SALJE E K H,PLANES A,VIVES E.Analysis of crackling noise using the maximum-likelihood method:Power-law mixing and exponential damping[J].Physical Review E,2017,96(4):042122.
[12]KUN F,VARGA I,LENNARTZ-SASSINEK S,et al.Approach to failure in porous granular materials under compression[J].Physical Review E,2013,88(6):062207.
[13]KUN F,VARGA I,LENNARTZ-SASSINEK S,et al.Rupture cascades in a discrete element model of a porous sedimentary rock[J].Physical Review Letters,2014,112(6):065501.
[14]姜德义,岳好学,张璇,等.砂岩单轴压缩声发射和纤维束模型模拟[J].岩土力学,2017,38(S2):1-8.JIANG Deyi,YUE Haoxue,ZHANG Xuan,et al.Acoustic emission of sandstone under uniaxial compression and simulation of fiber bundle model[J].Rock and Soil Mechanics,2017,38(S2):1-8.
[15]SALJE E K H,WANG X,DING X,et al.Simulating acoustic emission:The noise of collapsing domains[J].Physical Review B,2014,90(6):064103.
[16]SALJE E K H,SOTO-PARRA D E,PLANES A,et al.Failure mechanism in porous materials under compression:Crackling noise in mesoporous Si O2[J].Philosophical Magazine Letters,2011,91(8):554-560.
[17]姜德义,谢凯楠,蒋翔,等.页岩单轴压缩破坏过程中声发射能量分布的统计分析[J].岩石力学与工程学报,2016,35(S2):3822-3828.JIANG Deyi,XIE Kainan,JIANG Xiang,et al.Statistical analysis of acoustic emission energy distribution during uniaxial compression of shale[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(S2):3822-3828.
[18]谢凯楠,姜德义,蒋翔,等.页岩巴西劈裂试验的能量分布与临界特征分析[J].煤炭学报,2017,42(3):613-620.XIE Kainan,JIANG Deyi,JIANG Xiang,et al.Energy distribution and criticality characteristics analysis of shale Brazilian splitting test[J].Journal of China Coal Society,2017,42(3):613-620.
[19]张树文,鲜学福,周军平,等.基于巴西劈裂试验的页岩声发射与能量分布特征研究[J].煤炭学报,2017,42(S2):346-353.ZHANG Shuwen,XIAN Xuefu,ZHOU Junping,et al.Acoustic emission characteristics and the energy distribution of the shale in Brazilian splitting testing[J].Journal of China Coal Society,2017,42(S2):346-353.
[20]JIANG X,JIANG D,CHEN J,et al.Collapsing minerals:Crackling noise of sandstone and coal,and the predictability of mining accidents[J].American Mineralogist,2016,101(12):2751-2758.
[21]JIANG X,LIU H,MAIN I.G,et al.Predicting mining collapse:Superjerks and the appearance of record-breaking events in coal as collapse precursors[J].Physical Review E,2017,96(2):023004.
[22]姜德义,何怡,欧阳振华,等.砂岩单轴蠕变声发射能量统计与断面形貌分析[J].煤炭学报,2017,42(6):1436-1442.JIANG Deyi,HE Yi,OUYANG Zhenhua,et al.Acoustic emission energy statistical properties of sandstone during uniaxial creep and its fracture surfaces morphology[J].Journal of China Coal Society,2017,42(6):1436-1442.
[23]SALJE E K H,LIU H,JIN L,et al.Intermittent flow under constant forcing:Acoustic emission from creep avalanches[J].Applied Physics Letters,2018,112(5):054101.
[24]KIM K,FRANKLIN J A,BOWLING A J,et al.International society for rock mechanics commission on testing methods[J].International Journal of Rock Mechanics&Mining Sciences&Geomechanics Abstracts,1999,24(1):53.
[25]张伯虎,李东林,胡万雨.岩石声发射信号频谱与能量特征分析[J].东北大学学报(自然科学版),2015,36(S1):185-188.ZHANG Bohu,LI Donglin,HU Wanyu.Spectrum and energy characteristics analysis of rock acoustic emission signal[J].Journal of Northeastern University(Natural Science),2015,36(S1):185-188.
[26]VAN DER ELST N J,BRODSKY E E.Connecting near-field and far-field earthquake triggering to dynamic strain[J].Journal of Geophysical Research:Solid Earth,2010,115:B07311.
[27]SALJE E K H,LAMPROSI G I,SOTO-PARRA D E,et al.Noise of collapsing minerals:Predictability of the compressional failure in goethite mines[J].American Mineralogist,2013,98(4):609-615.
[28]CLAUSET A,SHALIZI C R,NEWMAN M E J.Power-law distributions in empirical data[J].SIAM Review,2009,51(4):661-703.