Research on the evolution law of microcracks in sandstone based on rectangular tensor inversion and RA-AF analysis
LIU Gang1, 2*, SHI Xiang1, 2, ZAN Yonglong1, 2, WANG Shengxuan1, 2
(1. School of Mining Engineering, Heilongjiang University of Science and Technology, Harbin, Heilongjiang 150022, China;
2. Heilongjiang Provincial Key Laboratory of Ground Pressure Control and Gas Control in Deep Coal Mine Mining,
Heilongjiang University of Science and Technology, Harbin, Heilongjiang 150022, China)
Abstract：To investigate the mesoscopic crack evolution behavior and the dominant mechanisms during the failure process of sandstone, an integrated approach combining acoustic emission moment tensor inversion with RA-AF parameter analysis was employed to quantitatively characterize the types, spatiotemporal distribution, and stress response characteristics of microcracks. Based on moment tensor theory and incorporating sensor coupling coefficients calibrated through pencil-lead break experiments, microcracks were classified into five categories—shear cracks, tensile-shear mixed-mode cracks, compressive-shear mixed-mode cracks, tensile cracks, and compressive cracks—using the crack tensile angle criterion. Furthermore, an RA-AF empirical model was established to support the analysis. The results indicate the following: (1) Under various loading paths, microcracks resulting from sandstone failure are predominantly shear cracks. The number of each of the five microcrack types exhibits a positive correlation with stress level, with shear cracks showing the most significant increase. (2) As stress increases, microcracks initiate, propagate, and gradually coalesce, forming a fracture zone that corresponds to the macroscopic failure surface. (3) RA-AF analysis reveals that shear cracks account for more than 50% of all microcracks in sandstone, which aligns with findings from moment tensor inversion. (4) Waveforms generated by tensile cracks exhibit abrupt characteristics, with concentrated signal energy in the frequency domain, whereas waveforms associated with shear cracks display oscillatory behavior, featuring dispersed frequency-domain energy and higher amplitude. This distinction provides a physical mechanism that explains the heterogeneity observed in RA-AF parameters. (5) Moment tensor inversion is well-suited for theory-driven, detailed analysis of crack mechanisms, while RA-AF analysis is more appropriate for rapid identification of crack types in engineering practice. This study elucidates the dominant micromechanical mechanism of shear failure in sandstone and the co-evolutionary behavior of multiple crack types, thereby providing a theoretical foundation for rock fracture prediction.
刘 刚1，2*，石 翔1，2，昝永龙1，2，王盛旋1，2. 基于矩张量反演与RA-AF分析砂岩微裂纹演化规律研究[J]. 岩石力学与工程学报, 2026, 45(2): 381-396.
LIU Gang1, 2*, SHI Xiang1, 2, ZAN Yonglong1, 2, WANG Shengxuan1, 2. Research on the evolution law of microcracks in sandstone based on rectangular tensor inversion and RA-AF analysis. , 2026, 45(2): 381-396.
[1] PAN Y S，WANG A W. Disturbance response instability theory of rock bursts in coal mines and its application[J]. Geohazard Mechanics，2023，1(1)：1–17.
[2] 吴顺川，黄小庆，陈 钒，等. 岩体破裂矩张量反演方法及其应用[J]. 岩土力学，2016，37(增1)：1–18.(WU Shunchuan，HUANG Xiaoqing，CHEN Fan，et al. Moment tensor inversion of rock failure and its application[J]. Rock and Soil Mechanics，2016，37(Supp.1)：1–18.(in Chinese))
[3] GILBERT F. Excitation of the normal modes of the Earth by earthquake sources[J]. Geophysical Journal International，1971，22(2)：223–226.
[4] 刘培洵，陈顺云，郭彦双，等. 声发射矩张量反演[J]. 地球物理学报，2014，57(3)：858–866.(LIU Peixun，CHEN Shunyun，GUO Yanshuang，et al. Moment tensor inversion of acoustic emission[J]. Chinese Journal of Geophysics，2014，57(3)：858–866.(in Chinese))
[5] FEIGNIER B，YOUNG R P. Moment tensor inversion of induced microseisnmic events：evidence of non-shear failures in the－4＜M＜－2 moment magnitude range[J]. Geophysical Research Letters，1992，19(14)：1 503–1 506.
[6] OHTSU M. Acoustic emission theory for moment tensor analysis[J]. Journal of Research in Nondestructive Evaluation，2009，6(3)：169–184.
[7] 秦子森，郭宦富. 基于声发射的不同粒径花岗岩细观破裂机理研究[J]. 价值工程，2024，43(8)：140–142.(QIN Zisen，GUO Huanfu. Study on mesoscopic fracture mechanism of granite with different particle sizes based on acoustic emission[J]. Value Engineering，2024，43(8)：140–142.(in Chinese))
[8] 李江哲. 基于声发射时频域及矩张量反演技术的岩石材料破裂试验研究[硕士学位论文][D]. 邯郸：河北工程大学，2023.(LI Jiangzhe，Experimental study on fracture of rock materials based on acoustic emission time-frequency domain and moment tensor inversion technique[M. S. Thesis][D]. Handan：Hebei University of Engineering，2023.(in Chinese))
[9] 王桂林，王润秋，孙 帆，等. 单轴压缩下溶隙灰岩声发射RA-AF特征及破裂模式研究[J]. 中国公路学报，2022，35(8)：118–128. (WANG Guilin，WANG Runqiu，SUN Fan，et al. RA-AF characteristics of acoustic emission and failure mode of karst-fissure limestone under uniaxial compression[J]. China Journal of Highway and Transport，2022，35(8)：118–128.(in Chinese))
[10] 葛振龙，孙 强，王苗苗，等. 基于RA/AF的高温后砂岩破裂特征识别研究[J]. 煤田地质与勘探，2021，49(2)：176–183.(GE Zhenlong，SUN Qiang，WANG Miaomiao，et al. Fracture feature recognition of sandstone after high temperature based on RA/AF[J]. Coal Geology and Exploration，2021，49(2)：176–183.(in Chinese))
[11] 李江哲，南博文. 基于声发射RA-AF值岩石破裂细观裂纹动态演化特征试验研究[J]. 吉林水利，2023，(11)：1–6.(LI Jiangzhe，NAN Bowen. Experimental study on dynamic evolution characteristics of meso-cracks in rock fracture based on acoustic emission RA-AF value[J]. Jilin Water Resources，2023，(11)：1–6.(in Chinese))
[12] 王聚贤，梁 鹏，张艳博，等. 基于声发射RA-AF值与kneedle算法的岩石拉剪破裂分类研究[J]. 岩石力学与工程学报，2024，43(增1)：3 267–3 279.(WANG Juxian，LIANG Peng，ZHANG Yanbo，et al. Research on classification of rock tensile-shear fracture based on acoustic emission RA-AF values and kneedle algorithm[J]. Chinese Journal of Rock Mechanics and Engineering，2024，43(Supp.1)： 3 267–3 279.(in Chinese))
[13] 邓朝福，刘建锋，陈 亮，等. 不同粒径花岗岩断裂力学行为及声发射特征研究[J]. 岩土力学，2016，37(8)：2 313–2 320.(DENG Chaofu，LIU Jianfeng，CHEN Liang，et al. Fracture mechanical behaviors and acoustic emission characteristics of Beishan granites with different particle sizes[J]. Rock and Soil Mechanics，2016，37(8)：2 313–2 320.(in Chinese))
[14] 许海亮，任合欢，宋义敏. 带裂纹花岗岩试件三点弯变形演化及破裂机制[J]. 地下空间与工程学报，2022，18(4)：1 199–1 207.(XU Hailiang，REN Hehuan，SONG Yimin. Deformation evolution and failure mechanism of three-point bending granite specimen with cracks[J]. Chinese Journal of Underground Space and Engineering，2022，18(4)：1 199–1 207.(in Chinese))
[15] 王宗炼，王怀伟，任会兰，等. 基于声发射矩张量理论的混凝土裂纹机制反演[J]. 兵工学报，2022，43(1)：181–189.(WANG Zonglian，WANG Huaiwei，REN Huilan，et al. Inversion of crack mechanism in concrete materials based on moment tensor theory of acoustic emission[J]. Acta Armamentarii，2022，43(1)：181–189.(in Chinese))
[16] 任会兰，宁建国，宋水舟，等. 基于声发射矩张量分析混凝土破坏的裂纹运动[J]. 力学学报，2019，51(6)：1 830–1 840.(REN Huilan，NING Jianguo，SONG Shuizhou，et al. Investigation on crack growth in concrete by moment tensor analysis of acoustic emission[J]. Chinese Journal of Theoretical and Applied Mechanics，2019，51(6)：1 830–1 840.(in Chinese))
[17] 郑 喜. 基于声发射的预制裂纹岩样细观破裂机制研究[硕士学位论文][D]. 沈阳：东北大学，2015.(ZHENG Xi. Microfracture mechanism of pre-cracked rock specimens from the acoustic emission[M. S. Thesis][D]. Shenyang：Northeastern University，2015. (in Chinese))
[18] 何云松. 基于矩张量的岩石破裂微观机制声发射研究[硕士学位论文][D]. 成都：成都理工大学，2017.(HE Yunsong. Study on AE testing method of microscopic mechanism of rock failure based on moment tensor[M. S. Thesis][D]. Chengdu：Chengdu University of Technology，2017.(in Chinese))
[19] 郭宦富. 基于声发射的不同加载条件下岩石细观破裂机制反演[硕士学位论文][D]. 沈阳：东北大学，2020.(GUO Huanfu. Inversion of micro fracture mechanism of rock under different loading conditions based on acoustic emission[M. S. Thesis][D]. Shenyang：Northeastern University，2020.(in Chinese))
[20] Federation of Construction Materials Industries. JCMS-III B5706 Monitoring method for active cracks in concrete by acoustic emission[S]. [S. l.]：Federation of Construction Materials Industries，2003.
[21] 刘 刚，王盛旋，王冬伟，等. 非均匀应力下含不同缺陷形态砂岩损伤破坏特征及能量演化规律[J]. 采矿与岩层控制工程学报，2025，7(5)：053013.(LIU Gang，WANG Shengxuan，WANG Dongwei，et al. Damage characteristics and energy evolution of sandstone with defect of different geometric profiles under heterogeneous loads[J]. Journal of Mining and Strata Control Engineering，2025，7(5)：053013.(in Chinese))
[22] 王晓丹. 基于矩张量的钢筋混凝土结构损伤声发射检测方法研究[硕士学位论文][D]. 西安：西安建筑科技大学，2015.(WANG Xiaodan. Research on the method of the damage in the reinforced concrete by the acoustic emission testing based on the moment tensor[M. S. Thesis][D]. Xi?an：Xi?an University of Architecture and Technology，2015.(in Chinese))
[23] 程铁栋，吴义文，戴聪聪，等. 岩石破坏全过程声发射信号去噪及特征提取方法研究[J]. 煤炭科学技术，2019，47(12)：24–31. (CHENG Tiedong，WU Yiwen，DAI Congcong，et al. Study on method of acoustic emission signal denoising and feature extraction in whole process of rock failure[J]. Coal Science and Technology，2019，47(12)：24–31.(in Chinese))
2026, Vol. 45 
