基于FEM研究含孔隙介质中裂纹矩张量反演精度
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摘要
基于矩张量理论的动态裂纹扩展监测方法,利用裂纹开裂产生的声发射信号获取裂纹开裂信息,而介质中的孔隙结构会影响监测结果的准确性。使用二维平面应变有限单元方法(FEM)建立孔隙分布数值模型,给出特定裂纹在不同孔隙率介质下的反演结果,并分析其成因。数值结果表明,双力偶成分对孔隙率的敏感度最高。对于纯剪切裂纹,反演结果中双力偶成分的占比随孔隙率的增大而减小;对于面内各向同性和拉伸裂纹,双力偶成分的占比随孔隙率的增大而增大。原因是孔隙结构对弹性波的散射导致弹性波幅值的空间分布发生变化,效果体现在两方面:一方面,能量转移作用导致不同传播方向弹性波的幅值趋于接近;另一方面,孔隙分布的差异导致临近传播方向的弹性波幅值差异增大。两种影响因素的权重差异导致不同裂纹的反演结果受孔隙的影响不同。
The monitoring method for the dynamic growth of cracks,which is based on the moment-tensor theory,utilizes the acoustic-emission signal of crack opening to obtain the information of cracks. The pore in media has an effect on the accuracy of monitoring results. The two-dimensional plane strain finite element method( FEM) was applied to build the numerical model with pore involved. The inversion results for specific cracks in media with different poriness were provided and the mechanism was analyzed. The numerical results show that the double-couple component is more sensitive to poriness than the other two components. For pure shear cracks,the proportion of double-couple component decreases with the increase of the poriness. For isotropic and pure tensile cracks,the proportion of double-couple component increases with the increase of the poriness. The reason is the wave scattering of pore changes the spatial distribution of elastic-wave amplitude and the effect contains the two aspects. The energy transfer results in the fact that the wave amplitudes of different directions become closer to each other. Meanwhile,the difference of pore distribution increases the difference between the wave amplitudes of different directions. The effect of pore on inversion results varies for different cracks,because the weight of the two aspects is different.
The monitoring method for the dynamic growth of cracks,which is based on the moment-tensor theory,utilizes the acoustic-emission signal of crack opening to obtain the information of cracks. The pore in media has an effect on the accuracy of monitoring results. The two-dimensional plane strain finite element method( FEM) was applied to build the numerical model with pore involved. The inversion results for specific cracks in media with different poriness were provided and the mechanism was analyzed. The numerical results show that the double-couple component is more sensitive to poriness than the other two components. For pure shear cracks,the proportion of double-couple component decreases with the increase of the poriness. For isotropic and pure tensile cracks,the proportion of double-couple component increases with the increase of the poriness. The reason is the wave scattering of pore changes the spatial distribution of elastic-wave amplitude and the effect contains the two aspects. The energy transfer results in the fact that the wave amplitudes of different directions become closer to each other. Meanwhile,the difference of pore distribution increases the difference between the wave amplitudes of different directions. The effect of pore on inversion results varies for different cracks,because the weight of the two aspects is different.
引文
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[20]谭子翰,徐松林,刘永贵,等.含多种尺寸缺陷岩体中的弹性波散射[J].应用数学和力学,2013,34(1):38-48.TAN Z H,XU S L,LIU Y G,et al.Scattering of elastic waves by multi-size defects in rock mass[J].Applied Mathematics and Mechanics,2013,34(1):38-48(in Chinese).
[21]郑阳,周进节.兰姆波在裂纹处的模态转换及散射特性研究[J].工程力学,2014,31(6):21-29.ZHENG Y,ZHOU J J.Mode conversion and scattering properties of Lamb waves near localized cracking[J].Engineering Mechanics,2014,31(6):21-29(in Chinese).
[22]OHTSU M,OHNO K,HAMSTAD M A.Moment tensors of inplane-waves analyzed by Si GMA-2D[J].Journal of Acoustic Emission,2005,23:47-63.
[23]孙成禹,李振春.地震波动力学基础[M].北京:石油工业出版社,2011:46.SUN C Y,LI Z C.Foundation of seismic wave dynamics[M].Beijing:Petroleum Industry Press,2011:46(in Chinese).
[24]OHTSU M.Source inversion of acoustic emission waveform[J].Doboku Gakkai Ronbunshu,1988,398:71-79.
[25]曹丹平,周建科,印兴耀.三角网格有限元法波动模拟的数值频散及稳定性研究[J].地球物理学报,2015,58(5):1717-1730.CAO D P,ZHOU J K,YIN X Y.The study for numerical dispersion and stability of wave motion with triangle-based finite element algorithm[J].Chinese Journal of Geophysics,2015,58(5):1717-1730(in Chinese).
[2]AKI K,RICHARDS P G.Quantitative seismology[M].San Francisco:W.H.Freeman and Co.,1980.
[3]OHTSU M.Acoustic emission theory for moment tensor analysis[J].Research in Nondestructive Evaluation,1995,6(3):169-184.
[4]KNOPOFF L,RANDALL M J.The compensated linear-vector dipole:A possible mechanism for deep earthquakes[J].Journal of Geophysical Research,1970,75(26):4957-4963.
[5]SIPKIN S A.Interpretation of non-double-couple earthquake mechanisms derived from moment tensor inversion[J].Journal of Geophysical Research,1986,91(B1):531-547.
[6]JULIAN B R,MILLER A D,FOULGER G R.Non-double-couple earthquakes 1.Theory[J].Reviews of Geophysics,1998,36(4):525-549.
[7]HUDSON J A,PEARCE R G,ROGERS R M.Source type plot for inversion of the moment tensor[J].Journal of Geophysical Research,1989,94(B1):765-774.
[8]VAVRYCˇUK V.Moment tensor decompositions revisited[J].Journal of Seismology,2014,19(1):231-252.
[9]吴微微,杨建思,苏金蓉,等.2013年吉林前郭-乾安震源区中强地震矩张量反演与区域孕震环境研究[J].地球物理学报,2014,57(8):2541-2554.WU W W,YANG J S,SU J R,et al.Moment inversion of moderate earthquakes and seismogenic environment in QianguoQian’an source region,2013,Jilin province[J].Chinese Journal of Geophysics,2014,57(8):2541-2554(in Chinese).
[10]柴金飞,金爱兵,高永涛,等.基于矩张量反演的矿山突水孕育过程[J].工程科学学报,2015,37(3):267-274.CHAI J F,JIN A B,GAO Y T,et al.Water inrush inoculation process in mines based on moment tensor inversion[J].Chinese Journal of Engineering,2015,37(3):267-274(in Chinese).
[11]康清清,缪发军,刘红桂,等.利用矩张量反演法研究江苏高邮-宝应MS4.9级地震震源机制解和震源深度[J].地球物理学报,2015,58(1):204-215.KANG Q Q,MIAO F J,LIU H G,et al.Focal mechanism and focal depth of the Gaoyou-Baoying,Jiangsu,China MS4.9earthquake on 20 July 2012 derived from moment tensor inversion[J].Chinese Journal of Geophysics,2015,58(1):204-215(in Chinese).
[12]RSSLER D,RMPKER G,KRGER F.Ambiguous moment tensors and radiation patterns in anisotropic media with applications to the modeling of earthquake mechanisms in W-Bohemia[J].Studia Geophysica et Geodaetica,2004,48(1):233-250.
[13]VAVRYCUK V.Focal mechanisms in anisotropic media[J].Geophysical Journal International,2005,161(2):334-346.
[14]CHAPMAN C H,LEANEY W S.A new moment-tensor decomposition for seismic events in anisotropic media[J].Geophysical Journal International,2012,188(1):343-370.
[15]BAIG A,URBANCIC T.Microseismic moment tensors:A path to understanding frac growth[J].The Leading Edge,2010,29(3):320-324.
[16]BAIG A,URBANCIC T I,PRINCE M.Microseismic moment tensors:A path to understanding growth of hydraulic fractures[C]∥Canadian Unconventional Resources and International Petroleum Conference:Society of Petroleum Engineers,2010:137771.
[17]CARCIONE J M,HELLE H B,PHAM N H.White’s model for wave propagation in partially saturated rocks:Comparison with poroelastic numerical experiments[J].Geophysics,2003,68(4):1389-1398.
[18]WHITE J E.Computed seismic speeds and attenuation in rocks with partial gas saturation[J].Geophysics,1975,40(2):224-232.
[19]刘宁,李敏,陈伟民.基于EMT采用FEM研究含裂纹介质中弹性波传播机制[J].北京航空航天大学学报,2015,41(9):1686-1692.LIU N,LI M,CHEN W M.Wave propagation in cracked elastic media based on EMT using FEM[J].Journal of Beijing University of Aeronautics and Astronautics,2015,41(9):1686-1692(in Chinese).
[20]谭子翰,徐松林,刘永贵,等.含多种尺寸缺陷岩体中的弹性波散射[J].应用数学和力学,2013,34(1):38-48.TAN Z H,XU S L,LIU Y G,et al.Scattering of elastic waves by multi-size defects in rock mass[J].Applied Mathematics and Mechanics,2013,34(1):38-48(in Chinese).
[21]郑阳,周进节.兰姆波在裂纹处的模态转换及散射特性研究[J].工程力学,2014,31(6):21-29.ZHENG Y,ZHOU J J.Mode conversion and scattering properties of Lamb waves near localized cracking[J].Engineering Mechanics,2014,31(6):21-29(in Chinese).
[22]OHTSU M,OHNO K,HAMSTAD M A.Moment tensors of inplane-waves analyzed by Si GMA-2D[J].Journal of Acoustic Emission,2005,23:47-63.
[23]孙成禹,李振春.地震波动力学基础[M].北京:石油工业出版社,2011:46.SUN C Y,LI Z C.Foundation of seismic wave dynamics[M].Beijing:Petroleum Industry Press,2011:46(in Chinese).
[24]OHTSU M.Source inversion of acoustic emission waveform[J].Doboku Gakkai Ronbunshu,1988,398:71-79.
[25]曹丹平,周建科,印兴耀.三角网格有限元法波动模拟的数值频散及稳定性研究[J].地球物理学报,2015,58(5):1717-1730.CAO D P,ZHOU J K,YIN X Y.The study for numerical dispersion and stability of wave motion with triangle-based finite element algorithm[J].Chinese Journal of Geophysics,2015,58(5):1717-1730(in Chinese).
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