基于DDA方法的不利地质结构对弹性纵波传播规律的影响研究
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摘要
基于黏性边界理论,在DDA程序中实现了适用于底部输入地震波的人工边界条件,并通过算例验证了其合理性。采用改进的DDA方法研究了节理的刚度和间距、软弱夹层的厚度和波阻抗对弹性纵波传播规律的影响。计算结果表明:节理面透射系数的理论解与DDA数值解差别较小;随着法向刚度的降低,节理对弹性纵波的衰减作用增大;节理间距存在门槛值和临界值,在不同的取值范围,对弹性纵波的衰减规律不同;弹性纵波在分界面上的透射系数的理论解和DDA数值解基本一致;软弱夹层厚度影响多重透射波的干涉效应,厚度越小,干涉效应越强;随着软弱夹层与周围岩石的波阻抗比值的降低,软弱夹层对地震波的衰减作用越来越明显。
Based on viscous boundary theory,the artificial boundary was implemented in DDA method and well proved with a specific example.Using the modified DDA method,the influence of joint stiffness,joint spacing,weak intercalation thickness,and impedance on elastic P-wave propagation were studied.The results showed that,the difference of transmission coefficient of joint surface between DDA calculation and theoretical solution is very small.The attenuation of elastic P-wave increases with the decrease of joint stiffness.There exists threshold value and critical value for joint space.In different ranges,the wave attenuation law is different.The transmission coefficient of elastic P-wave on interface calculated by DDA method is very close to the theoretical solution.Weak intercalation thickness affects the interference effect of multiple transmission.The attenuation of elastic P-wave increases with the decrease of weak intercalation impedance.
Based on viscous boundary theory,the artificial boundary was implemented in DDA method and well proved with a specific example.Using the modified DDA method,the influence of joint stiffness,joint spacing,weak intercalation thickness,and impedance on elastic P-wave propagation were studied.The results showed that,the difference of transmission coefficient of joint surface between DDA calculation and theoretical solution is very small.The attenuation of elastic P-wave increases with the decrease of joint stiffness.There exists threshold value and critical value for joint space.In different ranges,the wave attenuation law is different.The transmission coefficient of elastic P-wave on interface calculated by DDA method is very close to the theoretical solution.Weak intercalation thickness affects the interference effect of multiple transmission.The attenuation of elastic P-wave increases with the decrease of weak intercalation impedance.
引文
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[15]Tian Zhennong,Zhang Lewen.Numerical analysis of blast wave propagation in rock mass containing weak interlayer[J].Journal of Shenyang University of Technology,2010,32(3):349-354.[田振农,张乐文.岩体中软弱夹层影响爆炸波传播规律的数值分析[J].沈阳工业大学学报,2010,32(3):349-354.]
[16]Du Xiaoli,Song Hongwei,Wei Jingsheng.Numerical simu-lation research on stabil ity of slope with weak sandwich un-der seismic loadings[J].J of China Three Gorges Univ:Natural Sciences,2010,32(1):39-42.[杜晓丽,宋宏伟,魏京胜.地震对软弱夹层边坡稳定性影响数值模拟研究[J].三峡大学学报:自然科学版,2010,32(1):39-42.]
[17]Jiao Y Y,Zhang X L,Zhao J,et al.Viscous boundary of DDA for modeling stress wave propagation in jointed rock[J].International Journal of Rock Mechanics and Mining Sciences,2007,47:1070-1076.
[18]Schoenberg M.Elastic wave behavior across linear slip in-terfaces[J].Journal of Acoustics Society of America,1980,68(5):1516-1521.
[19]Cai J G,Zhao J.Effects of multiple parallel fractures on ap-parent attenuation of stress waves in rock masses[J].Inter-national Journal of Rock Mechanics and Mining Sciences,2000,37(4):661-682.
[2]石根华.数值流形方法与非连续变形分析[M].裴觉民,译.北京:清华大学出版社,1997.
[3]Maclaughlin M M,Doolin D M.Review of validation of the discontinuous deformation analysis(DDA)method[J].Inter National Journal for Numerical and Analytical Methods in Geomechanics,2006,30(4):271-305.
[4]Zhang Yonghui,Zheng Rongming.The extension and appli-cation of DDA method[J].Chinese Geotechnical Engineer-ing,1998,20(2):109-111.[张勇慧,郑榕明.DDA方法的改进及应用[J].岩土工程学报,1998,20(2):109-111.]
[5]Liu Jun,Li Zhongkui.Current situation and development of DDA method[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(5):839-845.[刘军,李仲奎.非连续变形分析(DDA)方法研究现状及发展趋势[J].岩石力学与工程学报,2004,23(5):839-845.]
[6]Zheng Hong,Jiang Wei.Discontinuous deformation analysis based on complementary theory[J].Science in China Series E:Technological Science,2009,39(10):1702-1708.[郑宏,江巍.基于互补理论的非连续变形分析方法[J].中国科学E辑:技术科学,2009,39(10):1702-1708.]
[7]Hatzor Y H,Arzi A A,Zaslavskyc Y,et al.Dynamic stability analysis of jointed rock slopes using the DDA method:King Herod’s Palace,Masada,Israel[J].International Journal of Rock Mechanics&Mining Sciences,2004,41:813-832.
[8]陈国兴.岩土地震工程学[M].北京:科学出版社,2007.
[9]廖振鹏.工程波动理论导论[M].第2版.北京:科学出版社,2002.
[10]Lysmer J,Kuhlemeyer R L.Finite dynamic model for in fi-nite media[J].Journal of the Engineering Mechanics Divi-sion,ASCE,1969,95:859-877.
[11]Lysmer J,Udaka T,Tsai C-F,et al.FLUSH,a computer program for approximate3D analysis of soil-structure inter-action problems[R].Report No.EERC75-30,Earthquake Engineering Research Center,College of Engineering,Uni-versity of California,Berkeley,California.
[12]Fu Xiaodong,Sheng Qian,Zhang Yonghui,et al.Prelimina-ry research on wave problem calculation using DDA method[J].Journal of Sichuan University:Engineering Science Edi-tion,2012,44(2):70-75.[付晓东,盛谦,张勇慧,等.DDA方法在波动问题计算中的初步研究[J].四川大学学报:工程科学版,2012,44(2):70-75.]
[13]Guo Yiyuan,Li Shihai.Distinct element analysis of propa-gation characteristics of P-wave in rock pillar with finite length[J].Chinese Journal of Rock Mechanics and Engi-neering,2002,21(8):1124-1129.[郭易圆,李世海.有限长岩柱中纵波传播规律的离散元数值分析[J].岩石力学与工程学报,2002,21(8):1124-1129.]
[14]Ru Zhongliang,Jiang Yujing.Research on transmission be-haviors of rough joint surfaces with elastic p-wave incidence[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(12):2535-2539.[茹忠亮,蒋宇静.弹性纵波入射粗糙节理面透射性能研究[J].岩石力学与工程学报,2008,27(12):2535-2539.]
[15]Tian Zhennong,Zhang Lewen.Numerical analysis of blast wave propagation in rock mass containing weak interlayer[J].Journal of Shenyang University of Technology,2010,32(3):349-354.[田振农,张乐文.岩体中软弱夹层影响爆炸波传播规律的数值分析[J].沈阳工业大学学报,2010,32(3):349-354.]
[16]Du Xiaoli,Song Hongwei,Wei Jingsheng.Numerical simu-lation research on stabil ity of slope with weak sandwich un-der seismic loadings[J].J of China Three Gorges Univ:Natural Sciences,2010,32(1):39-42.[杜晓丽,宋宏伟,魏京胜.地震对软弱夹层边坡稳定性影响数值模拟研究[J].三峡大学学报:自然科学版,2010,32(1):39-42.]
[17]Jiao Y Y,Zhang X L,Zhao J,et al.Viscous boundary of DDA for modeling stress wave propagation in jointed rock[J].International Journal of Rock Mechanics and Mining Sciences,2007,47:1070-1076.
[18]Schoenberg M.Elastic wave behavior across linear slip in-terfaces[J].Journal of Acoustics Society of America,1980,68(5):1516-1521.
[19]Cai J G,Zhao J.Effects of multiple parallel fractures on ap-parent attenuation of stress waves in rock masses[J].Inter-national Journal of Rock Mechanics and Mining Sciences,2000,37(4):661-682.
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