Bedding effect on multifractal characteristics of acoustic emissions in coal specimens under indirect tension
ZHAO Bingchao1, 2, WAN Xin1, WANG Wei1, 2, GUO Yaxin1, HE Shenglin1
(1. College of Energy and Mining Engineering, Xi?an University of Science and Technology, Xi?an, Shaanxi 710054, China; 2. Key Laboratory of Western Mine Exploitation and Hazard Prevention, Ministry of Education, Xi?an University of Science and
Technology, Xi?an, Shaanxi 710054, China)
Abstract：To investigate the impact of bedding on the multifractal characteristics of acoustic emission (AE) signals during the tensile failure process of coal rock, Brazilian tests were conducted on coal samples with varying bedding angles. AE systems were employed for real-time monitoring, and analyses were performed on the mechanical properties, failure patterns, and ringing counts. The multifractal spectrum of the coal samples was estimated using the MF-DFA method. The time-varying response characteristics of the spectrum width Δα and the frequency spectrum measure subset Δf(?) were examined, which facilitated the identification of precursors to tensile failure in coal rock through multifractal analysis. The research findings indicate that as the bedding angle increases from 0°to 90°and subsequently to C0°, the tensile strength of coal samples initially decreases before increasing again. The failure mode transitions from bedding tensile failure to bedding shear sliding failure, and eventually to matrix tensile failure or a composite failure characterized by bedding shear sliding. Throughout the loading process, the coal samples display a fluctuating decrease followed by an increase in , while Δf(?) exhibits an overall fluctuating decrease. The fractal aggregation activity of cracks is enhanced, and when significant primary fractures develop, both and Δf(?) reach their extreme values, maximizing the non-uniform distribution characteristics of the signals and the proportion of large-scale fractures. The propagation mode of cracks is significantly influenced by bedding, with the bedding dip controlling the direction of crack propagation. This indicates that as the bedding dip increases, cracks transition from bedding-parallel to bedding-perpendicular propagation, resulting in a greater variety of macroscopic cracks. The evolution of crack patterns in coal samples shifts from a “unidirectional gradual” mode to a “multidirectional multifocal” mode. Consequently, the parameter initially decreases and then increases, while the variation of Δf(?) is inconsistent. Overall, the more singular the crack propagation mechanism in coal samples, the smaller the Δf(?). The time-varying response characteristics of the multifractal parameters and Δf(?) in coal samples are closely linked to their crack evolution, with a sudden increase in and a sudden decrease in Δf(?) serving as precursors to tensile failure in coal rock.
1] 刘恺德，刘泉声，朱元广，等. 考虑层理方向效应煤岩巴西劈裂及单轴压缩试验研究[J]. 岩石力学与工程学报，2013，32(2)：308– 316.(LIU Kaide，LIU Quansheng，ZHU Yuanguang，et al. Experimental study of coal considering directivity effect of bedding plane under Brazilian splitting and uniaxial compression[J]. Chinese Journal of Rock Mechanics and Engineering，2013，32(2)：308–316.(in Chinese))
[2] 吴基文，闫立宏. 煤岩抗拉强度两种室内间接测定方法比较与成果分析[J]. 岩石力学与工程学报，2004，23(10)：1 643–1 647.(WU Jiwen，YAN Lihong. Comparison study on two kinds of indirect measurement methods of tensile strength of coal in laboratory[J]. Chinese Journal of Rock Mechanics and Engineering，2004，23(10)：1 643–1 647.(in Chinese))
[3] 张庆贺，袁 亮，杨 科，等. 深井煤岩动力灾害的连续卸压开采防治机制[J]. 采矿与安全工程学报，2019，36(1)：80–86.(ZHANG Qinghe，YUAN Liang，YANG Ke，et al. Mechanism analysis on continuous stress-relief mining for preventing coal and rock dynamic disasters in deep coal mines[J]. Journal of Mining and Safety Engineering，2019，36(1)：80–86.(in Chinese))
[4] 王 伟，赵毅鑫，高艺瑞，等. 层理和预制裂纹方向对煤断裂力学性质影响规律试验研究[J]. 岩石力学与工程学报，2022，41(3)：433–445.(WANG Wei，ZHAO Yixin，GAO Yirui，et al. Experimental research of influences of bedding and pre-crack directions on fracture characteristics of coal[J]. Chinese Journal of Rock Mechanics and Engineering，2022，41(3)：433–445.(in Chinese))
[5] LAUBACH S E，MARRETT R A，OLSON J E，et al. Characteristics and origins of coal cleat：a review[J]. International Journal of Coal Geology，1998，35(1/4)：175–207.
[6] 中华人民共和国国家标准编写组. GB/T 50266―2013 工程岩体试验方法标准[S]. 北京：中国计划出版社，2013.(The National Standard Compilation Group of People?s Republic of China. GB/T 50266―2013 Standard for test methods of engineering rockmass[S]. Beijing：China Planning Press，2013.(in Chinese))
[7] 中华人民共和国国家标准编写组. GB/T 23561.10—2010煤和岩石物理力学性质测定方法，第10部分：煤和岩石抗拉强度测定方法[S]. 北京：中国标准出版社，2010.(The National Standard Compilation Group of People?s Republic of China. GB/T 23561.10—2010 Methods for determination of physical and mechanical properties of coal and rocks，the tenth part：Determination of tensile strength of coal and rock[S]. Beijing：Standards Press of China，2010.(in Chinese))
[8] 李德建，祁 浩，李春晓，等. 含层理面煤试样的巴西圆盘劈裂实验及数值模拟研究[J]. 矿业科学学报，2020，5(2)：150–159.(LI Dejian，QI Hao，LI Chunxiao，et al. Brazilian disc splitting test and numerical simulation on coal samples containing bedding planes[J]. Journal of Mining Science and Technology，2020，5(2)：150–159.(in Chinese))
[9] WANG W，ZHAO Y，TENG T，et al. Influence of bedding planes on mode i and mixed-mode (I–II) dynamic fracture toughness of coal：analysis of experiments[J]. Rock Mechanics and Rock Engineering，2021，54(1)：173–189.
[10] 刘晓辉，戴 峰，刘建锋，等. 考虑层理方向煤岩的静动巴西劈裂试验研究[J]. 岩石力学与工程学报，2015，34(10)：2 098–2 105. (LIU Xiaohui，DAI Feng，LIU Jianfeng，et al. Brazilian splitting tests on coal rock considering bedding direction under static and dynamic loading rate[J]. Chinese Journal of Rock Mechanics and Engineering，2015，34(10)：2 098–2 105.(in Chinese))
[11] 赵毅鑫，肖 汉，黄亚琼. 霍普金森杆冲击加载煤样巴西圆盘劈裂试验研究[J]. 煤炭学报，2014，39(2)：286–291.(ZHAO Yixin，XIAO Han，HUANG Yaqiong. Dynamic split tensile test of Brazilian disc of coal with split Hopkinson pressure bar loading[J]. Journal of China Coal Society，2014，39(2)：286–291.(in Chinese))
[12] 雷瑞德，粟 罗，贺 培，等. 不同高径比煤样巴西劈裂声发射特征及能量演化机制研究[J]. 煤炭科学技术，2024，52(10)：63–77. (LEI Ruide，SU Luo，HE Pei，et al. Study on acoustic emission characteristics and energy evolution of Brazilian splitting tests of coal samples with different height-diameter ratio[J]. Coal Science and Technology，2024，52(10)：63–77.(in Chinese))
[13] 刘 斌，赵毅鑫，张 汉，等. 单轴压缩及劈裂试验下煤的声发射特征研究[J]. 采矿与安全工程学报，2020，37(3)：613–621.(LIU Bin，ZHAO Yixin，ZHANG Han，et al. Acoustic emission characteristics of coal under uniaxial compression and Brazilian splitting[J]. Journal of Mining and Safety Engineering，2020，37(3)：613–621.(in Chinese))
[14] 付军辉，黄炳香，刘长友，等. 煤试样巴西劈裂的声发射特征研究[J]. 煤炭科学技术，2011，39(4)：25–28.(FU Junhui，HUANG Bingxiang，LIU Changyou，et al. Study on acoustic emission features of coal sample Brazilian splitting[J]. Coal Science and Technology，2011，39(4)：25–28.(in Chinese))
[15] 尹贤刚，李庶林，唐海燕. 岩石破坏声发射强度分形特征研究[J]. 岩石力学与工程学报，2005，24(19)：3 512–3 516.(YIN Xiangang，LI Shulin，TANG Haiyan. Study of strength fractal features of acoustic emission in process of rock failure[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(19)：3 512–3 516.(in Chinese))
[16] 李元辉，刘建坡，赵兴东，等. 岩石破裂过程中的声发射b值及分形特征研究[J]. 岩土力学，2009，30(9)：2 559–2 563.(LI Yuanhui，LIU Jianpo，ZHAO Xingdong，et al. Study on b-value and fractal dimension of acoustic emission during rock failure process[J]. Rock and Soil Mechanics，2009，30(9)：2 559–2 563.(in Chinese))
[17] 龚 囱，赵 坤，包 涵，等. 红砂岩蠕变破坏声发射震源演化及其分形特征[J]. 岩土力学，2021，42(10)：2 683–2 695.(GONG Cong，ZHAO Kun，BAO Han，et al. Acoustic emission source evolution and fractal features during creep failure of red sandstone[J]. Rock and Soil Mechanics，2021，42(10)：2 683–2 695.(in Chinese))
[18] 谢和平，陈至达. 分形(fractal)几何与岩石断裂[J]. 力学学报，1988，(3)：264–271.(XIE Heping，CHEN Zhida. Fractal geometry and rock fracture[J]. Chinese Journal of Theoretical and Applied，1988，(3)：264–271.(in Chinese))
[19] 谢和平，高 峰，周宏伟，等. 岩石断裂和破碎的分形研究[J]. 防灾减灾工程学报，2003，(4)：1–9.(XIE Heping，GAO Feng，ZHOU Hongwei，et al. Fractal study on rock fracture and fracture[J]. Journal of Disaster Prevention and Mitigation Engineering，2003，(4)：1–9.(in Chinese))
[20] 蔡江东，陈亚东，张道明. 基于多重分形的岩石声发射信号特征解构分析[J]. 地下空间与工程学报，2012，8(5)：963–968.(CAI Jiangdong，CHEN Yadong，ZHANG Daoming. Study on the feature of acoustic emission of rock under compression experiment based on multi-fractal theory[J]. Chinese Journal of Underground Space and Engineering，2012，8(5)：963–968.(in Chinese))
[21] ZHANG R，LIU J，SA Z，et al. Experimental investigation on multi-fractal characteristics of acoustic emission of coal samples subjected to true triaxial loading-unloading[J]. Fractals，2020，28(5)：1–25.
[22] KONG X，WANG E，HE X，et al. Time-varying multifractal of acoustic emission about coal samples subjected to uniaxial compression[J]. Chaos，Solitons and Fractals，2017，103：571–577.
[23] 刘 杰，王恩元，李忠辉，等. 煤样破裂表面电位多重分形特征[J]. 煤炭学报，2013，38(9)：1 616–1 620.(LIU Jie，WANG Enyuan，LI Zhonghui，et al. Multi-fractal characteristics of surface potential of coal during the fracture[J]. Journal of China Coal Society，2013，38(9)：1 616–1 620.(in Chinese))
[24] 许福乐，王恩元，宋大钊，等. 煤岩破坏声发射强度长程相关性和多重分形分布研究[J]. 岩土力学，2011，32(7)：2 111–2 116.(XU Fule，WANG Enyuan，SONG Dazhao，et al. Long-range correlation and multifractal distribution of acoustic emission of coal-rock[J]. Rock and Soil Mechanics，2011，32(7)：2 111–2 116.(in Chinese))
[25] ISRM. Suggested methods for determining tensile strength of rock materials[J]. International Journal of Rock Mechanics and Mining Sciences，1978，15(6)：99–103.
[26] 侯 鹏，高 峰，杨玉贵，等. 黑色页岩巴西劈裂破坏的层理效应研究及能量分析[J]. 岩土工程学报，2016，38(5)：930–937.(HOU Peng，GAO Feng，YANG Yugui，et al. Effect of bedding plane direction on acoustic emission characteristics of shale in Brazilian tests[J]. Rock and Soil Mechanics，2016，38(5)：930–937.(in Chinese))
[27] 董 超，王恩元，晋明月，等. 分形计盒维数的微震波初至自动识别[J]. 煤矿安全，2013，44(6)：198–201.(DONG Chao，WANG Enyuan，JIN Mingyue，et al. Automatic identification first arrival of microseismic waves by fractal box-counting dimension[J]. Safety in Coal Mines，2013，44(6)：98–201.(in Chinese))
[28] HALSEY T C，JENSEN M H，KADANOFF L P，et al. Fractal measures and their singularities：The characterization of strange sets[J]. Physical Review A，1986，33(2)：1 141–1 151.
[29] YANG P，YANG Q. Empirical mode decomposition and rough set attribute reduction for ultrasonic flaw signal classification[J]. International Journal of Computational Intelligence Systems，2014，7(3)：481–492.
[30] MUZY J F，BACRY E，ARNEODO A. Wavelets and multifractal formalism for singular signals：Application to turbulence data[J]. Physical Review Letters，1991，67(25)：3 515–3 518.
[31] TURIEL A，PEREZ-VICENTE C J，GRAZZINI J. Numerical methods for the estimation of multifractal singularity spectra on sampled data：A comparative study[J]. Journal of Computational Physics，2006，216(1)：362–390.
[32] 毛浩宇，张 敏，蒋若辰，等. 基于微震信号多重分形特征的岩石边坡变形预警研究[J]. 岩石力学与工程学报，2020，39(3)：560–571.(MAO Haoyu，ZHANG Min，JIANG Ruochen，et al. Study on deformation pre-warning of rock slopes based on multi-fractal characteristics of microseismic signals[J]. Chinese Journal of Rock Mechanics and Engineering，2020，39(3)：560–571.(in Chinese))
[33] 奚彩萍，张淑宁，熊 刚，等. 多重分形降趋波动分析法和移动平均法的分形谱算法对比分析[J]. 物理学报，2015，64(13)：335–348. (XI Caiping，ZHANG Shuning，XIONG Gang，et al. A comparative study of multifractal detrended fluctuation analysis and multifractal detrended moving average algorithm to estimate the multifractal spectrum[J]. Acta Physica Sinica，2015，64 (13)：335–348.(in Chinese))
[34] KANTELHARDT J W，ZSCHIEGNER S A，KOSCIELNY-BUNDE E，et al. Multifractal detrended fluctuation analysis of nonstationary time series[J]. Physica A：Statistical Mechanics and its Applications，2002，316(1/4)：87–114.
[35] MALI P，MUKHOPADHYAY A. Multifractal characterization of gold market：A multifractal detrended fluctuation analysis[J]. Physica A：Statistical Mechanics and its Applications，2014，413：361–372.
[36] WANG F，FAN Q，STANLEY H E. Multiscale multifractal detrended- fluctuation analysis of two-dimensional surfaces[J]. Physical Review E，2016，93(4)：1–12.
[37] WU Z，ZHANG L，YUE M. Low-rate DoS attacks detection based on network multifractal[J]. IEEE Transactions on Dependable and Secure Computing，2016，13(5)：559–567.
[38] LU S，WANG J，XUE Y. Study on multi-fractal fault diagnosis based on EMD fusion in hydraulic engineering[J]. Applied Thermal Engineering，2016，103：798–806.
[39] SEO S K，KIM K，CHANG K-H，et al. Determination of the dynamical behavior of rainfalls by using a multifractal detrended fluctuation analysis[J]. Journal of the Korean Physical Society，2012，61(4)：658–661.
[40] 王小林，温仕轩，王煜东，等. 高温作用下砂岩声发射特征及破坏前兆[J]. 长江科学院院报，2023，40(11)：118–124.(WANG Xiaolin，WEN Shixuan，WANG Yudong，et al. Acoustic emission characteristics and failure precursor of sandstone in high temperature[J]. Journal of Yangtze River Scientific Research Institute，2023，40(11)：118–124.(in Chinese))
[41] 李 楠，李保林，陈 栋，等. 冲击破坏过程微震波形多重分形及其时变响应特征[J]. 中国矿业大学学报，2017，46(5)：1 007–1 013. (LI Nan，LI Baolin，CHEN Dong，et al. Multi-fractal and time-varying response characteristics of microseismic waves during the rockburst process[J]. Journal of China University of Mining and Technology，2017，46(5)：1 007–1 013.(in Chinese))
[42] XIE X，LI S，GUO J. Study on multiple fractal analysis and response characteristics of acoustic emission signals from goaf rock bodies[J]. Sensors，2022，22(7)：1–20.
[43] OSWIECIMKA P，KWAPIEN J，DROZDZ S. Wavelet versus detrended fluctuation analysis of multifractal structures[J]. Physical Review E，2006，74(1)：1–37.
[44] 孙 博，任富强，刘冬桥. 基于声发射多重分形特征的层状板岩失稳前兆研究[J]. 岩土力学，2022，43(3)：749–760.(SUN Bo，REN Fuqiang，LIU Dongqiao. Research on the failure precursors of layered slate based on multifractal characteristics of acoustic emission[J]. Rock and Soil Mechanics，2022，43(3)：749–760.(in Chinese))
[45] 赵 菲，孟世卓，刘冬桥，等. 基于声发射信号特征的花岗岩岩爆破坏前兆信息研究[J]. 岩石力学与工程学报，2024，43(11)：2 669–2 686.(ZHAO Fei，MENG Shizhuo，LIU Dongqiao，et al. Failure precursor of granite rockburst based on acoustic emission signal characteristics[J]. Chinese Journal of Rock Mechanics and Engineering，2024，43(11)：2 669–2 686.(in Chinese))
[46] 王笑然，王恩元，刘晓斐，等. 裂隙砂岩裂纹扩展声发射响应及速率效应研究[J]. 岩石力学与工程学报，2018，37(6)：1 446–1 458. (WANG Xiaoran，WANG Enyuan，LIU Xiaofei，et al. Macro-crack propagation process and corresponding AE behaviors of fractured sandstone under different loading rates[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(6)：1 446–1 458.(in Chinese))
[47] CARPINTERI A. Scaling laws and renormalization groups for strength and toughness of disordered materials[J]. International Journal of Solids and Structures，1994，31(3)：291–302.
[48] CARPINTERI A. Fractal nature of material microstructure and size effects on apparent mechanical properties[J]. Mechanics of Materials，1994，18(2)：89–101.
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