岩体中弹性波传播尺度效应的初步分析
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摘要
含缺陷岩体具有尺度效应,此类岩体中传播的弹性波也有尺度效应。对现场测点EC37-201-06,在3.0×3.2 m2的范围内采用动态有限元方法进行了15种尺度的弹性波传播规律的分析研究。对现场测点EC37-101-06,在1.2×1.2 m2的范围内采用准静态有限元方法进行了60种尺度的弹性波波速与围压及计算尺度的关系的计算分析。前者采用了射线理论分析思想,而后者采用等效介质分析思想,得到了相应的弹性波的尺度效应,但二者规律有差异。为建立二者间的联系,也为了工程应用,基于量纲理论分析方法,给出了一个半理论的波速与入射波频率的计算公式。与现场声波和地震波测试结果,以及考虑随机分布单节理散射模型的计算结果进行比较,初步分析结果表明,此公式基本可行。
The propagation rules of elastic wave in rock mass with defects take on scale effect,just like the rock mass.The dynamic finite element method(DFEM) is employed to investigate the propagation rules of elastic waves at site-EC37-201-06.The whole computation area is 3.0?3.2 m2 and 15 kinds of computation scales are applied.A static finite element method(FEM) is used to study the relations of elastic wave velocities to the confined pressure and computation scales at site-EC37-101-06.The whole computation area is 1.2?1.2 m2 and 60 kinds of computation scales are applied.The ray theory is used in the former method,and the effective media theory is used in the later.The scale effect of elastic waves is obtained,but there are differences for the two methods.To establish their relations and provide a simple model for engineering computation,a semi-theoretical phase velocity equation is proposed based on the dimensionless method.Compared with the in-situ sonic velocities,seismic velocities and velocities computed by the theoretical model with randomly distributed joints,the proposed equation can be well used in rock mass.
The propagation rules of elastic wave in rock mass with defects take on scale effect,just like the rock mass.The dynamic finite element method(DFEM) is employed to investigate the propagation rules of elastic waves at site-EC37-201-06.The whole computation area is 3.0?3.2 m2 and 15 kinds of computation scales are applied.A static finite element method(FEM) is used to study the relations of elastic wave velocities to the confined pressure and computation scales at site-EC37-101-06.The whole computation area is 1.2?1.2 m2 and 60 kinds of computation scales are applied.The ray theory is used in the former method,and the effective media theory is used in the later.The scale effect of elastic waves is obtained,but there are differences for the two methods.To establish their relations and provide a simple model for engineering computation,a semi-theoretical phase velocity equation is proposed based on the dimensionless method.Compared with the in-situ sonic velocities,seismic velocities and velocities computed by the theoretical model with randomly distributed joints,the proposed equation can be well used in rock mass.
引文
[1]陈颙,黄庭芳.岩石物理学[M].北京:北京大学出版社,2001.(CHEN Yong,HUANG Ting-fang.Rock physics[M].Beijing:Beijing University Press,2001.(in Chinese))
[2]HUDSON J A.Wave speeds and attenuation of elastic waves in material containing cracks[J].Geophys JR Astr Soc,1981,64:133–150.
[3]MURPHY W F,WINKLER K W,KLEINBERG R L.Acoustic relaxation in sedimentary rocks:dependence on grain contacts and fluid saturation[J].Geophysics,1986,15(3):757–766.
[4]WINKLER K W.Dispersion analysis of velocity and attenuation in Berea sandstone[J].Journal of Geophysical Research,1985,90(B8):6793–6800.
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[6]MAVKO G.Estimating grain-scale fluid effects on velocity dispersion in rocks[J].Geophysics,1991,56(12):1940–1949.
[7]GETTEMY G L,TOBIN H J,HOLE J A,et al.Multi-scale compressional wave velocity structure of the San Gregorio fault zone[J].Geophysical Research Letters,2004,31(6):1–5.
[8]MAVKO G,MUKERJI T,Dvorikin J edition.岩石物理手册:孔隙介质中地震分析工具[M].徐海滨,戴建春,译.合肥:中国科学技术大学出版社,2008.(MAVKO G,MUKERJI T,Dvorikin J.The rock Physics Handbook:Tools for seismic analysis in porous media[M].XU Hai-bin,DAI Jian-chun,trans.Hefei:University of Science and Technology of China Press,2008.(in Chinese))
[9]YING CF,TRUELL R.Scattering of a plane longitudinal wave by a spherical obstacle in an isotropically elastic solid[J].Applied Physics,1956,27(9):1086–1097.
[10]ACHENBACH J D,WANG C Y.Two-dimensional time domain BEM for scattering of elastic waves in solids of general anisotropy[J].International Journal of Solids and Structures,1996,33(26):3843–3864.
[11]ERIKSSON A S,BOSTROM A,DATTA SK.Ultrasonic wave propagation through a cracked solid[J].Wave Motion,1995,22:297–310.
[12]钟伟芳,聂国华.弹性波的散射理论[M].武汉:华中理工大学出版社,1997.(ZHONG Wei-fang,NIE Guo-hua.Scattering theory of elastic wave[M].Wuhan:Huazhong University of Science and Technology Press,1997.(in Chinese))
[13]GUBERNATIS J E,DOMANY E.Effects of microstructure on the speed and attenuation of elastic waves in porous materials[J].Wave Motion,1984,6:579–589.
[14]MUKERJI T.Waves and scales in heterogeneous rocks[D].Stanford:Stanford University,1995.
[15]石安池,唐鸣发,周其健.金沙江白鹤滩水电站柱状节理玄武岩岩体变形特性研究[J].岩石力学与工程学报,2008,27(10):2079–2086.(SHI An-chi,TANG Ming-fa,ZHOU Qi-jian.Research of deformation characteristics of columnar jointed basalt at Baihetan hydropower station on Jinsha river[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(10):2079–2086.(in Chinese))
[16]赵坚,蔡军刚,赵晓豹,等.弹性纵波在具有非线性法向变形本构关系的接力出的传播特征[J].岩石力学与工程学报,2003,22(1):9–17.(ZHAO Jian,CAI Jun-gang,ZHAO Xiao-bao,et al.Transmission of elastic P-waves across single fracture with nonlinear normal deformation behavior[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(1):9–17.(in Chinese))
[17]刘永贵,徐松林,席道瑛,等.节理玄武岩体弹性波频散效应研究[J].岩石力学与工程学报,2010,29(增刊1):3314–3320.(LIU Yong-gui,XU Song-lin,XI Dao-ying,et al.Dispersion effect of elastic wave in jointed basalt[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(S1):3314–3320.(in Chinese))
[2]HUDSON J A.Wave speeds and attenuation of elastic waves in material containing cracks[J].Geophys JR Astr Soc,1981,64:133–150.
[3]MURPHY W F,WINKLER K W,KLEINBERG R L.Acoustic relaxation in sedimentary rocks:dependence on grain contacts and fluid saturation[J].Geophysics,1986,15(3):757–766.
[4]WINKLER K W.Dispersion analysis of velocity and attenuation in Berea sandstone[J].Journal of Geophysical Research,1985,90(B8):6793–6800.
[5]WINKLER K W.Estimation of velocity dispersion between seismic and ultrasonic frequencies[J].Geophysics,1986,51(1):183–189.
[6]MAVKO G.Estimating grain-scale fluid effects on velocity dispersion in rocks[J].Geophysics,1991,56(12):1940–1949.
[7]GETTEMY G L,TOBIN H J,HOLE J A,et al.Multi-scale compressional wave velocity structure of the San Gregorio fault zone[J].Geophysical Research Letters,2004,31(6):1–5.
[8]MAVKO G,MUKERJI T,Dvorikin J edition.岩石物理手册:孔隙介质中地震分析工具[M].徐海滨,戴建春,译.合肥:中国科学技术大学出版社,2008.(MAVKO G,MUKERJI T,Dvorikin J.The rock Physics Handbook:Tools for seismic analysis in porous media[M].XU Hai-bin,DAI Jian-chun,trans.Hefei:University of Science and Technology of China Press,2008.(in Chinese))
[9]YING CF,TRUELL R.Scattering of a plane longitudinal wave by a spherical obstacle in an isotropically elastic solid[J].Applied Physics,1956,27(9):1086–1097.
[10]ACHENBACH J D,WANG C Y.Two-dimensional time domain BEM for scattering of elastic waves in solids of general anisotropy[J].International Journal of Solids and Structures,1996,33(26):3843–3864.
[11]ERIKSSON A S,BOSTROM A,DATTA SK.Ultrasonic wave propagation through a cracked solid[J].Wave Motion,1995,22:297–310.
[12]钟伟芳,聂国华.弹性波的散射理论[M].武汉:华中理工大学出版社,1997.(ZHONG Wei-fang,NIE Guo-hua.Scattering theory of elastic wave[M].Wuhan:Huazhong University of Science and Technology Press,1997.(in Chinese))
[13]GUBERNATIS J E,DOMANY E.Effects of microstructure on the speed and attenuation of elastic waves in porous materials[J].Wave Motion,1984,6:579–589.
[14]MUKERJI T.Waves and scales in heterogeneous rocks[D].Stanford:Stanford University,1995.
[15]石安池,唐鸣发,周其健.金沙江白鹤滩水电站柱状节理玄武岩岩体变形特性研究[J].岩石力学与工程学报,2008,27(10):2079–2086.(SHI An-chi,TANG Ming-fa,ZHOU Qi-jian.Research of deformation characteristics of columnar jointed basalt at Baihetan hydropower station on Jinsha river[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(10):2079–2086.(in Chinese))
[16]赵坚,蔡军刚,赵晓豹,等.弹性纵波在具有非线性法向变形本构关系的接力出的传播特征[J].岩石力学与工程学报,2003,22(1):9–17.(ZHAO Jian,CAI Jun-gang,ZHAO Xiao-bao,et al.Transmission of elastic P-waves across single fracture with nonlinear normal deformation behavior[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(1):9–17.(in Chinese))
[17]刘永贵,徐松林,席道瑛,等.节理玄武岩体弹性波频散效应研究[J].岩石力学与工程学报,2010,29(增刊1):3314–3320.(LIU Yong-gui,XU Song-lin,XI Dao-ying,et al.Dispersion effect of elastic wave in jointed basalt[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(S1):3314–3320.(in Chinese))
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