节理岩体双重非线性弹性介质中的纵波传播特性
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摘要
基于应力-应变关系中包含三阶非线性项的岩石介质和非线性法向变形节理模型,结合波动方程特征线法,得到在非线性岩石介质中纵波法向入射单节理时透射波的半数值解,并编写计算程序。对波源参数、节理参数和岩石非线性、节理位置等进行一系列参数研究,探讨节理岩石双重非线性弹性介质对透射波波形、透射系数和频谱分布的影响。研究结果表明,岩石的非线性系数会对节理的高频滤波作用以及节理面质点位移的恢复路径产生影响。双重非线性作用下的透射波除了和线性岩石中一样受节理参数、波源参数的影响外,还与节理位置和岩石的非线性系数有关。在纵波受岩石非线性作用较大的情况下,频率相同振幅较小的纵波的透射系数较大。大振幅波在双重非线性的影响下,透射波中会产生一系列高谐波,该高谐波是应力波受岩石和节理综合作用的结果。
Based on the nonlinear rock mechanics with third order nonlinearity and nonlinear normal deformation behaviour joint model,by using wave equation characteristic method,the semi-numerical solutions of P-wave across single joint in dual nonlinear elastic medium are obtained.Computational programs are compiled.Studies of parameters of joint and wave source,nonlinear coefficient of soft rock,position of joint are conducted to get an insight into transmitted waveform,transmission coefficient and frequency spectra distribution under the influence of dual nonlinear elasticity.The results show that the nonlinear coefficient of rock affects the high-frequency filter of joint and displacement recovery path of particle on joint surface.The wave propagation is not only affected by the same factors in linear wave,but also by the nonlinear coefficient and joint position.When P-wave with the same frequency is influenced greatly by the nonlinear behaviour of rock;the transmission coefficient of P-wave with smaller amplitude is bigger.When P-wave with large amplitude is influenced by dual nonlinearity;a series of higher harmonics are produced in transmitted wave;and this higher harmonics is affected by the combined effect of rock and joint.
Based on the nonlinear rock mechanics with third order nonlinearity and nonlinear normal deformation behaviour joint model,by using wave equation characteristic method,the semi-numerical solutions of P-wave across single joint in dual nonlinear elastic medium are obtained.Computational programs are compiled.Studies of parameters of joint and wave source,nonlinear coefficient of soft rock,position of joint are conducted to get an insight into transmitted waveform,transmission coefficient and frequency spectra distribution under the influence of dual nonlinear elasticity.The results show that the nonlinear coefficient of rock affects the high-frequency filter of joint and displacement recovery path of particle on joint surface.The wave propagation is not only affected by the same factors in linear wave,but also by the nonlinear coefficient and joint position.When P-wave with the same frequency is influenced greatly by the nonlinear behaviour of rock;the transmission coefficient of P-wave with smaller amplitude is bigger.When P-wave with large amplitude is influenced by dual nonlinearity;a series of higher harmonics are produced in transmitted wave;and this higher harmonics is affected by the combined effect of rock and joint.
引文
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[3]MCALL K R,GUYER R A.Equation of state and wave propagation in hysteretic nonlinear elastic materials[J].Journal of Geophysical Research,1994,99(B12):23 887-23 897.
[4]HOKSTAD K.Nonlinear and dispersive acoustic wave propagation[J].Geophysics,2004,69(3):840-848.
[5]CHENG N.Nonlinear wave propagation in sandstone:a numerical study[J].Geophysics,1996,61(6):1 935-1 938.
[6]ZHENG H S,ZHANG Z J,YANG B J.A numerical study of 1D nonlinear P-wave propagation in solid[J].Acta Seismologica Sinica,2004,17(1):80-86.
[7]那仁满都拉.流体与固体介质中有限振幅波、孤立波的传播和相互作用的理论与求解方法研究[博士学位论文][D].长春:吉林大学,2005.(NARANMANDULA.Study on theory and solving method for propagation and interaction of finite-amplitude waves and solitary waves in fluid and solid media[Ph.D.Thesis][D].Changchun:Jilin University,2005.(in Chinese))
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[11]MALAMA B,KULATILAKE P H S W.Models for normal fracture deformation under compressive loading[J].International Journal of Rock Mechanics and Mining Sciences,2003,40(6):893-901.
[12]ZHAO J,CAI J G.Transmission of elastic P-waves across single fractures with a nonlinear normal deformational behavior[J].Rock Mechanics and Rock Engineering,2001,34(1):3-22.
[13]王卫华,李夕兵,左宇军,等.非线性法向变形节理对弹性纵波传播的影响[J].岩石力学与工程学报,2006,25(6):1 218-1 225.(WANG Weihua,LI Xibing,ZUO Yujun,et al.Effects of single joint with nonlinear normal deformation on P-wave propagation[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(6):1 218-1 225.(in Chinese))
[14]石崇,徐卫亚,周家文.二维波穿过非线性节理面的透射性能研究[J].岩石力学与工程学报,2007,26(8):1 645-1 652.(SHI Chong,XU Weiya,ZHOU Jiawen.Research on transmission behaviours of nonlinear joints with 2D wave propagation[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(8):1 645-1 652.(in Chinese))
[15]王观石,胡世丽,李贵荣,等.爆破地震波在结构面的传播特性与结构面倾角判断[J].岩石力学与工程学报,2010,29(9):1 790-1 798.(WANG Guanshi,HU Shili,LI Guirong,et al.Transmission attributes of blasting seismic wave in interface and judgment of interface obliquity[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(9):1 790-1 798.(in Chinese))
[16]鞠杨,李业学,谢和平,等.节理岩石的应力波动与能量耗散[J].岩石力学与工程学报,2006,25(12):2 426-2 434.(JU Yang,LI Yexue,XIE Heping,et al.Stress wave propagation and energy dissipation in jointed rocks[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(12):2 426-2 434.(in Chinese))
[17]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):2 535-2 539.(RU Zhongliang,JIANG Yujing.Research on transmission behaviors of rough joint surfaces with elastic P-wave incidence[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(12):2 535-2 539.(in Chinese))
[18]俞缙,钱七虎,林从谋,等.纵波在改进的弹性非线性法向变形行为单节理处的传播特性研究[J].岩土工程学报,2009,31(8):1 156-1 164.(YU Jin,QIAN Qihu,LIN Congmou,et al.Transmission of elastic P-wave across one fracture with improved nonlinear deformational behaviors[J].Chinese Journal of Geotechnical Engineering,2009,31(8):1 156-1 164.(in Chinese))
[19]FAN L F,REN F,MA G W.An extended displacement discontinuity method for analysis of stress wave propagation in viscoelastic rock mass[J].Journal of Rock Mechanics and Geotechnical Engineering,2011,3(1):73-81.
[20]TENCATE J A,VAN DEN ABEELE K E A,SHANKLAND T J,et al.Laboratory study of linear and nonlinear elastic pulse propagation in sandstone[J].Journal of the Acoustical Society of America,1996,100(3):1 383-1 391.
[21]JOHNSON P A,ZINSZNER B,RASOLOFOSAON P N J.Resonance and elastic nonlinear phenomena in rock[J].Journal of Geophysical Research,1996,101(B5):11 553-11 564.
[22]SWAN G.Determination of stiffness and other joint properties from roughness measurements[J].Rock Mechanics and Rock Engineering,1983,16(1):19-38.
[23]SUN Z,GERRARD C,STEPHANSSON O.Rock joint compliance tests for compression and shear loads[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1985,22(4):197-213.
[2]MEEGAN G D,JOHNSON P A,GUYER R A,et al.Observations of nonlinear elastic wave behavior in sandstone[J].Journal of the Acoustical Society of America,1993,94(6):3 387-3 391.
[3]MCALL K R,GUYER R A.Equation of state and wave propagation in hysteretic nonlinear elastic materials[J].Journal of Geophysical Research,1994,99(B12):23 887-23 897.
[4]HOKSTAD K.Nonlinear and dispersive acoustic wave propagation[J].Geophysics,2004,69(3):840-848.
[5]CHENG N.Nonlinear wave propagation in sandstone:a numerical study[J].Geophysics,1996,61(6):1 935-1 938.
[6]ZHENG H S,ZHANG Z J,YANG B J.A numerical study of 1D nonlinear P-wave propagation in solid[J].Acta Seismologica Sinica,2004,17(1):80-86.
[7]那仁满都拉.流体与固体介质中有限振幅波、孤立波的传播和相互作用的理论与求解方法研究[博士学位论文][D].长春:吉林大学,2005.(NARANMANDULA.Study on theory and solving method for propagation and interaction of finite-amplitude waves and solitary waves in fluid and solid media[Ph.D.Thesis][D].Changchun:Jilin University,2005.(in Chinese))
[8]李延,席道瑛,徐松林.动荷载作用下岩石非线性弹性响应研究[J].地学前缘,2006,13(3):206-212.(LI Ting,XI Daoying,XU Songlin.Investigation of the nonlinear elastic responses of rock under impact loading[J].Earth Science Frontier,2006,13(3):206-212.(in Chinese))
[9]钱祖文.非线性声学[M].北京:科学出版社,1992:324-338.(QIAN Zuwen.Nonlinear acoustics[M].Beijing:Science Press,1992:324-338.(in Chinese))
[10]BARTON N R,BANDIS S C,BAKHTAR K.Strength,deformation and conductivity coupling of rock joints[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1985,22(3):121-140.
[11]MALAMA B,KULATILAKE P H S W.Models for normal fracture deformation under compressive loading[J].International Journal of Rock Mechanics and Mining Sciences,2003,40(6):893-901.
[12]ZHAO J,CAI J G.Transmission of elastic P-waves across single fractures with a nonlinear normal deformational behavior[J].Rock Mechanics and Rock Engineering,2001,34(1):3-22.
[13]王卫华,李夕兵,左宇军,等.非线性法向变形节理对弹性纵波传播的影响[J].岩石力学与工程学报,2006,25(6):1 218-1 225.(WANG Weihua,LI Xibing,ZUO Yujun,et al.Effects of single joint with nonlinear normal deformation on P-wave propagation[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(6):1 218-1 225.(in Chinese))
[14]石崇,徐卫亚,周家文.二维波穿过非线性节理面的透射性能研究[J].岩石力学与工程学报,2007,26(8):1 645-1 652.(SHI Chong,XU Weiya,ZHOU Jiawen.Research on transmission behaviours of nonlinear joints with 2D wave propagation[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(8):1 645-1 652.(in Chinese))
[15]王观石,胡世丽,李贵荣,等.爆破地震波在结构面的传播特性与结构面倾角判断[J].岩石力学与工程学报,2010,29(9):1 790-1 798.(WANG Guanshi,HU Shili,LI Guirong,et al.Transmission attributes of blasting seismic wave in interface and judgment of interface obliquity[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(9):1 790-1 798.(in Chinese))
[16]鞠杨,李业学,谢和平,等.节理岩石的应力波动与能量耗散[J].岩石力学与工程学报,2006,25(12):2 426-2 434.(JU Yang,LI Yexue,XIE Heping,et al.Stress wave propagation and energy dissipation in jointed rocks[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(12):2 426-2 434.(in Chinese))
[17]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):2 535-2 539.(RU Zhongliang,JIANG Yujing.Research on transmission behaviors of rough joint surfaces with elastic P-wave incidence[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(12):2 535-2 539.(in Chinese))
[18]俞缙,钱七虎,林从谋,等.纵波在改进的弹性非线性法向变形行为单节理处的传播特性研究[J].岩土工程学报,2009,31(8):1 156-1 164.(YU Jin,QIAN Qihu,LIN Congmou,et al.Transmission of elastic P-wave across one fracture with improved nonlinear deformational behaviors[J].Chinese Journal of Geotechnical Engineering,2009,31(8):1 156-1 164.(in Chinese))
[19]FAN L F,REN F,MA G W.An extended displacement discontinuity method for analysis of stress wave propagation in viscoelastic rock mass[J].Journal of Rock Mechanics and Geotechnical Engineering,2011,3(1):73-81.
[20]TENCATE J A,VAN DEN ABEELE K E A,SHANKLAND T J,et al.Laboratory study of linear and nonlinear elastic pulse propagation in sandstone[J].Journal of the Acoustical Society of America,1996,100(3):1 383-1 391.
[21]JOHNSON P A,ZINSZNER B,RASOLOFOSAON P N J.Resonance and elastic nonlinear phenomena in rock[J].Journal of Geophysical Research,1996,101(B5):11 553-11 564.
[22]SWAN G.Determination of stiffness and other joint properties from roughness measurements[J].Rock Mechanics and Rock Engineering,1983,16(1):19-38.
[23]SUN Z,GERRARD C,STEPHANSSON O.Rock joint compliance tests for compression and shear loads[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1985,22(4):197-213.
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