SH波在地裂缝界面处的传播规律
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摘要
在弹性力学和波动理论的基础上,运用时域和频域计算方法分析出平面SH波穿越地裂缝介质时的传播规律。通过引入地裂缝界面等效切向刚度等有关参数,对出平面波传播的频域及时域分析方法进行对比验证,分析地裂缝界面的等效切向刚度、入射波频率、入射角和裂缝面剪切强度对穿越地裂缝时出平面SH波的传播规律的影响。多个参数的交叉对比分析结果表明,等效切向刚度或入射角度越小,地裂缝界面的低通滤波效应越明显。裂缝面的剪切滑移导致透射波速在达到临界值时被截止。输入实际地震波时,随着透射系数的减小,透射波幅值减小不明显但波形变化较大;反射波幅值和波形将逐渐趋近入射波,但相位相对于入射波存在一定的滞后。为得到真实有效的波动传播规律,采用线性内插对波动时程数据进行处理,结果表明本文方法不会影响计算的精度。
It is important to study seismic wave propagation through fractures in the field of earthquake engineering.Based on elasticity mechanics and wave motion theories,the propagation law of an anti-plane SH-wave across a ground fissure interface is analyzed using time-domain and frequency-domain calculation methods in this paper.Recursion equations are established and a contrast verification between the two methods is conducted.The influence of certain related parameters on the propagation law of anti-plane SH-waves are discussed,including the equivalent shear stiffness of the ground fissure interface,incidence wave frequency,incident angle,and shear strength of the fissure surface.Furthermore,a cross-comparison of these parameters is performed,and recursion equations considering the shear strength of fissure are established.Results indicate that the transmission coefficient increases with an increase in equivalent shear stiffness and the incident angle,but decreases with an increase in incident frequency.In addition,the lowpass filtering effect of the ground fissure interface is more evident with a decrease in equivalent shear stiffness and the incident angle.Under the input of a real seismic wave,there is a decrease of transmission coefficient but no obvious decrease in the amplitude of the transmission wave.However,the waveform change is obvious.The amplitude and wave form of the reflection wave gradually approach the incident wave,but the effect of hysteresis occurs in the phase relative to incident wave.To obtain an effective and real propagation law of wave motion,fluctuation timehistory data were processed using linear interpolation,and results indicate that there are no changes to the precision of calculation results using this method.
It is important to study seismic wave propagation through fractures in the field of earthquake engineering.Based on elasticity mechanics and wave motion theories,the propagation law of an anti-plane SH-wave across a ground fissure interface is analyzed using time-domain and frequency-domain calculation methods in this paper.Recursion equations are established and a contrast verification between the two methods is conducted.The influence of certain related parameters on the propagation law of anti-plane SH-waves are discussed,including the equivalent shear stiffness of the ground fissure interface,incidence wave frequency,incident angle,and shear strength of the fissure surface.Furthermore,a cross-comparison of these parameters is performed,and recursion equations considering the shear strength of fissure are established.Results indicate that the transmission coefficient increases with an increase in equivalent shear stiffness and the incident angle,but decreases with an increase in incident frequency.In addition,the lowpass filtering effect of the ground fissure interface is more evident with a decrease in equivalent shear stiffness and the incident angle.Under the input of a real seismic wave,there is a decrease of transmission coefficient but no obvious decrease in the amplitude of the transmission wave.However,the waveform change is obvious.The amplitude and wave form of the reflection wave gradually approach the incident wave,but the effect of hysteresis occurs in the phase relative to incident wave.To obtain an effective and real propagation law of wave motion,fluctuation timehistory data were processed using linear interpolation,and results indicate that there are no changes to the precision of calculation results using this method.
引文
[1]PYRAK-NOLTE L J,MYER L R,COOK N G W.Transmission of Seismic Waves Across Single Natural Fractures[J].Journal of Geophysical Research(Solid Earth),1990,95(B6):8617-8638.
[2]巴振宁,冯领香,梁建文.无破碎带断层场地对SH波的散射[J].地震工程学报,2015,37(4):919-925,937.BA Zhenning,FENG Lingxiang,LIANG Jianwen.Scattering of Plane SH-wave by a Fault Site Without a Fracture Zone[J].China Earthquake Engineering Journal,2015,37(4):919-925,937.
[3]徐平,铁瑛,夏唐代.半空间饱和介质内圆形洞室对平面P1波的散射[J].西北地震学报,2008,24(4):369-375.XU Ping,TIE Ying,XIA Tangdai.Scattering of Plane P1Waves by a Circular Cavity Buried in Semi-infinite Space Saturated Media[J].Northwestern Seismological Journal,2008,24(4):369-375.
[4]HUDSON J A.Wave Speeds and Attenuation of Elastic Waves in Material Containing Cracks[J].Geophysical Journal International,1981,64(1):133-150.
[5]GU B,SUáREZ-RIVERA R,NIHEI K T,et al.Incidence of Plane Waves Upon a Fracture[J].Journal of Geophysical Research:Solid Earth,1996,101(B11):25337-25346.
[6]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.
[7]ZHAO X B,ZHAO J,CAI J G.P-wave Transmission Across Fractures with Nonlinear Deformational Behaviour[J].International Journal for Numerical and Analytical Methods in Geomechanics,2006,30(11):1097-1112.
[8]LI Jianchun,MA Guowei.Analysis of Blast Wave Interaction with o Rock Joint[J].Rock Mech Rock Eng,2010,48:777-787.
[9]ZHU J B,PERINO A,ZHAO G F,et al.Seismic Response of Asingle and a Set of Filled Joints of Viscoelastic Deformational Behaviour[J].Geophysical Journal International,2011,186(3):1315-1330.
[10]宋林,邵珠山,吴敏哲,等.考虑剪切滑移效应时节理岩体中剪切S波的传播特性探析[J].西安建筑科技大学学报(自然科学版),2011,43(4):494-500.SONG Lin,SHAO Zhushan,WU Minzhe,et al.Theoretical Analysis on the Propagation Characteristic of S-wave Across Single Fracture with Consideration of Shear Slide Behavior[J].Journal of Xi’an University of Architecture&Technology(Natural Science Edition),2011,43(4):494-500.
[11]宋林,闫玉湛,韩八晓,等.非线性变形节理中纵波传播特性的理论研究[J].应用力学学报,2012,29(2):133-140.SONG Lin,YAN Yuzhan,HAN Baxiao,et al.Theoretical Research into the Wave Propagation of P-wave Across Rock Joint with Nonlinear Deformation[J].Chinese Journal of Applied Mechanics,2012,29(2):133-140.
[12]刘立波,李建春,李海波,等.应力波斜入射粘弹性节理的传播规律[J].岩石力学与工程学报,2012,32(增刊2):3593-3598.LIU Libo,LI Jianchun,LI Haibo,et al.Propagation Law of Oblique Incidence of Stress Wave Across a Viscoelastic Joint[J].Chinese Journal of Rock Mechanics and Engineering,2012,32(Supp2):3593-3598.
[13]LI J C,WU W,LI H B,et al.A Thin-layer Interface Model for Wave Propagation Through Filled Rock Joints[J].Journal of Applied Geophysics,2013,19:31-38.
[14]LI J C,LI H B,JIAO Y Y,et al.Analysis for Oblique Wave Propagation Across Filled Joints Based on Thin-layer Interface Model[J].Journal of Applied Geophysics,2014,102:39-46.
[15]柴少波,李建春,李海波,等.平面P波入射含结构面岩体并引起地表面的振动研究[J].岩石力学与工程学报,2015,34(增刊2):3888-3895.CHAI Shaobo,LI Jianchun,LI Haibo,et al.Study of P-wave Propagation Across a Natural Structural Plane and Its Influence of Ground Motion[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(Supp2):3888-3895.
[16]柴少波,李建春,李海波.柱面波在节理岩体中的传播特性[J].岩石力学与工程学报,2014,33(3):523-530.CHAI Shaobo,LI Jianchun,LI Haibo.Propagation Characteristics of Cylindrical Wave in Joint Rock Masses[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(3):523-530.
[17]LI Jianchun,MA Guowei,ZHAO Jian.Analysis of Stochastic Seismic Wave Interaction with a Slippery Rock Fault[J].Rock Mech Rock Eng,2011,44:85-92.
[18]刘天云,刘光廷.拱坝河谷三维地震动分析[J].水利学报,2000(9):79-85.LIU Tianyun,LIU Guangting.The Seismic Field Analysis of Arch Dam Canyon[J].Journal of Hydraulic Engineering,2000(9):79-85.
[19]苑韦虹.地裂缝计算模型及参数研究[D].西安:长安大学,2014.YUAN Weihong.Study on Calculating Model and Parameters of Ground Fissure[D].Xi’an:Chang’an University,2014
[20]LI J C,LIU T T,LI H B,et al.Shear Wave Propagation Across Filled Joints with the Effect of Interfacial Shear Strength[J].Rock Mechanics and Rock Engineering,2015,48(4):1547-1557.
[21]SCHOENBERG M.Elastic Wave Behavior Across Linear Slip Interfaces[J].The Journal of the Acoustical Society of America,1980,68(5):1516-1521.
[22]ZHAO X B,ZHAO J,HEFNY A M,et al.Normal Transmission of S-wave Across Parallel Fractures with Coulomb Slip Behavior[J].Journal of Engineering Mechanics,2006,132(6):641-650.
[23]LI J C.Wave Propagation Across Non-linear Rock Joints Based on Time-domain Recursive Method[J].Geophysical Journal International,2013,193(2):970-985.
[2]巴振宁,冯领香,梁建文.无破碎带断层场地对SH波的散射[J].地震工程学报,2015,37(4):919-925,937.BA Zhenning,FENG Lingxiang,LIANG Jianwen.Scattering of Plane SH-wave by a Fault Site Without a Fracture Zone[J].China Earthquake Engineering Journal,2015,37(4):919-925,937.
[3]徐平,铁瑛,夏唐代.半空间饱和介质内圆形洞室对平面P1波的散射[J].西北地震学报,2008,24(4):369-375.XU Ping,TIE Ying,XIA Tangdai.Scattering of Plane P1Waves by a Circular Cavity Buried in Semi-infinite Space Saturated Media[J].Northwestern Seismological Journal,2008,24(4):369-375.
[4]HUDSON J A.Wave Speeds and Attenuation of Elastic Waves in Material Containing Cracks[J].Geophysical Journal International,1981,64(1):133-150.
[5]GU B,SUáREZ-RIVERA R,NIHEI K T,et al.Incidence of Plane Waves Upon a Fracture[J].Journal of Geophysical Research:Solid Earth,1996,101(B11):25337-25346.
[6]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.
[7]ZHAO X B,ZHAO J,CAI J G.P-wave Transmission Across Fractures with Nonlinear Deformational Behaviour[J].International Journal for Numerical and Analytical Methods in Geomechanics,2006,30(11):1097-1112.
[8]LI Jianchun,MA Guowei.Analysis of Blast Wave Interaction with o Rock Joint[J].Rock Mech Rock Eng,2010,48:777-787.
[9]ZHU J B,PERINO A,ZHAO G F,et al.Seismic Response of Asingle and a Set of Filled Joints of Viscoelastic Deformational Behaviour[J].Geophysical Journal International,2011,186(3):1315-1330.
[10]宋林,邵珠山,吴敏哲,等.考虑剪切滑移效应时节理岩体中剪切S波的传播特性探析[J].西安建筑科技大学学报(自然科学版),2011,43(4):494-500.SONG Lin,SHAO Zhushan,WU Minzhe,et al.Theoretical Analysis on the Propagation Characteristic of S-wave Across Single Fracture with Consideration of Shear Slide Behavior[J].Journal of Xi’an University of Architecture&Technology(Natural Science Edition),2011,43(4):494-500.
[11]宋林,闫玉湛,韩八晓,等.非线性变形节理中纵波传播特性的理论研究[J].应用力学学报,2012,29(2):133-140.SONG Lin,YAN Yuzhan,HAN Baxiao,et al.Theoretical Research into the Wave Propagation of P-wave Across Rock Joint with Nonlinear Deformation[J].Chinese Journal of Applied Mechanics,2012,29(2):133-140.
[12]刘立波,李建春,李海波,等.应力波斜入射粘弹性节理的传播规律[J].岩石力学与工程学报,2012,32(增刊2):3593-3598.LIU Libo,LI Jianchun,LI Haibo,et al.Propagation Law of Oblique Incidence of Stress Wave Across a Viscoelastic Joint[J].Chinese Journal of Rock Mechanics and Engineering,2012,32(Supp2):3593-3598.
[13]LI J C,WU W,LI H B,et al.A Thin-layer Interface Model for Wave Propagation Through Filled Rock Joints[J].Journal of Applied Geophysics,2013,19:31-38.
[14]LI J C,LI H B,JIAO Y Y,et al.Analysis for Oblique Wave Propagation Across Filled Joints Based on Thin-layer Interface Model[J].Journal of Applied Geophysics,2014,102:39-46.
[15]柴少波,李建春,李海波,等.平面P波入射含结构面岩体并引起地表面的振动研究[J].岩石力学与工程学报,2015,34(增刊2):3888-3895.CHAI Shaobo,LI Jianchun,LI Haibo,et al.Study of P-wave Propagation Across a Natural Structural Plane and Its Influence of Ground Motion[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(Supp2):3888-3895.
[16]柴少波,李建春,李海波.柱面波在节理岩体中的传播特性[J].岩石力学与工程学报,2014,33(3):523-530.CHAI Shaobo,LI Jianchun,LI Haibo.Propagation Characteristics of Cylindrical Wave in Joint Rock Masses[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(3):523-530.
[17]LI Jianchun,MA Guowei,ZHAO Jian.Analysis of Stochastic Seismic Wave Interaction with a Slippery Rock Fault[J].Rock Mech Rock Eng,2011,44:85-92.
[18]刘天云,刘光廷.拱坝河谷三维地震动分析[J].水利学报,2000(9):79-85.LIU Tianyun,LIU Guangting.The Seismic Field Analysis of Arch Dam Canyon[J].Journal of Hydraulic Engineering,2000(9):79-85.
[19]苑韦虹.地裂缝计算模型及参数研究[D].西安:长安大学,2014.YUAN Weihong.Study on Calculating Model and Parameters of Ground Fissure[D].Xi’an:Chang’an University,2014
[20]LI J C,LIU T T,LI H B,et al.Shear Wave Propagation Across Filled Joints with the Effect of Interfacial Shear Strength[J].Rock Mechanics and Rock Engineering,2015,48(4):1547-1557.
[21]SCHOENBERG M.Elastic Wave Behavior Across Linear Slip Interfaces[J].The Journal of the Acoustical Society of America,1980,68(5):1516-1521.
[22]ZHAO X B,ZHAO J,HEFNY A M,et al.Normal Transmission of S-wave Across Parallel Fractures with Coulomb Slip Behavior[J].Journal of Engineering Mechanics,2006,132(6):641-650.
[23]LI J C.Wave Propagation Across Non-linear Rock Joints Based on Time-domain Recursive Method[J].Geophysical Journal International,2013,193(2):970-985.