P波在弹性介质与饱和冻土介质分界面上的透反射问题研究

基于弹性波在冻结饱和多孔介质与单相弹性介质中的传播理论,研究了平面P波在饱和冻土介质与单相弹性介质分界面上的透反射问题。利用Helmholtz矢量分解定理,根据分界面上的边界条件,获得了平面P波从单相弹性介质入射到饱和冻土介质分界面上透反射振幅比的理论表达式。通过数值计算,分析了在不同入射频率、胶结参数、孔隙率、饱和度和接触参数下,弹性波的透反射振幅比随入射角变化的关系。研究结果表明：P波从单相弹性介质垂直入射到饱和冻土介质分界面上时只有反射P波和3种透射P波产生,当掠入射时只产生反射而没有透射现象发生。入射频率、胶结参数、孔隙率、饱和度以及接触参数等参数对反射波和透射波的振幅比影响显著。     

非饱和土地基中P1波通过波阻板的传播特性研究

基于单相弹性介质与非饱和多孔介质中波的传播理论和Snell定律,研究了P1波从非饱和土介质中入射到波阻板（wave impeding block,WIB）时的传播特性。推导了P1波在非饱和土地基中通过波阻板后反射波和透射波振幅比的解析解,分析了反射波振幅比和透射波振幅比与波阻板的剪切模量、密度以及入射角、入射频率、饱和度等各种参数的关系曲线,从而得到这些参数对非饱和土地基中波阻板隔振效果的影响规律。数值结果表明：波阻板隔振屏障的剪切模量和密度对其隔振性能影响较为显著,当波阻板剪切模量和密度在一定范围内时波阻板隔振屏障可获得较好的隔振性能;入射角对波阻板隔振性能影响较大,而入射频率对其隔振效果影响很小。     

节理面透射模型及其隔振性能研究

振动波入射到节理界面上,与软弱断层一样会产生波场的分解,能够起到隔振作用。根据线性变形节理的透反射规律研究发现,隔振后各点的波场可由透射P波与透射S波叠加而成,其能量分配服从Zoeppritz方程,不连续位移造成了透射波的衰减;法向刚度增加透射纵波系数会增加,而切向刚度与透射纵波无关,法向与切向刚度对透射S波均有影响,刚度增加透射S波振幅逐渐降低,逐步逼近于0;由于透射后波场相互干涉,不同波场延时不同,透射合成波与入射波相比,振幅降低,持续时间增加,波形尾段有畸变;总能量系数与节理面的刚度无关,而随入射角增加不断降低。     

非饱和土中Rayleigh波的传播特性分析

基于对非饱和多孔介质的研究成果,考虑孔隙中液相和气相的相互影响,研究了非饱和土地基中Rayleigh波的传播特性。通过非饱和土中固相、液相和气相的质量平衡方程、动量平衡方程和非饱和土有效应力原理,建立了问题的弹性波动方程。通过引入势函数及考虑自由透水（透气）的边界条件,经过理论推导给出了非饱和土中Rayleigh波的弥散特征方程。通过数值算例分析了Rayleigh波的波速和衰减系数随饱和度、频率和固有渗透系数等因素的变化规律。结果表明：不同饱和度下波速随频率和固有渗透系数的变化均是先不变,然后小幅下降,再急剧增加,最后趋于一致;衰减系数在不同饱和度下随频率的增大而增大,随固有渗透系数的增大而先增大后减小。     

斜入射线弹性节理应力波传播特征的数值模拟

依据弹性波理论,应力波斜入射线弹性节理时会发生波场分解。根据入射、透射及反射各波形的不同到时,运用离散元软件UDEC模拟应力波在含倾斜节理岩体中的传播并计算其透射、反射系数,并分析其波型转换规律。应力波斜入射单节理时,模拟得到的透射、反射系数随节理刚度、入射角度的变化规律,与已有的理论解是吻合的。应力波斜入射一组平行节理时,随着节理间距的增大,其同类波的透射系数Tpp、Tss先增大后减小,最后趋于稳定值;节理条数越多,Tpp、Tss越小。此外,不同条数的节理,透射系数达到最大值的临界节理间距值基本一致,但趋于稳定时的节理间距值随节理条数的增加而逐渐增大。     

P波作用下饱和土中输流管道动力响应

根据Biot波动理论,采用复变函数与多级坐标法,求解了P波作用下饱和土体中地下输流管道的波动散射方程,分析了管道中流体介质性质、入射波角度及管道埋深等对地下输流管道周边动应力集中系数及孔压集中系数分布的影响。计算结果表明：在低频弹性波入射时,管道周边动应力集中系数及孔压集中系数分布相对均匀,而随入射频率的增加,其分布变得复杂化,但其峰值有所减小;中低频波入射作用下,管道内为水、石油介质时,动应力集中系数和孔压集中系数较空气介质时小,而在高频波作用时情况相反;对于管道内流体介质为水时,随着入射角度的变化,应力集中分布也沿一定角度的方向发生转动,入射波自管道下方垂直入射时,管道周边动应力集中系数峰值相对较大;随埋深的增加,动应力集中系数和孔压集中系数均呈震荡减小的趋势。     

动测法桩基检测过程中弹性波能量在桩体界面上的反射和透射

本文分别就(1)变阻抗桩(2)变截面桩(3)阻抗截面均有变化的桩阐述了在动测过程中弹性波能量的传输过程,即弹性波能量在截面上的入射、反射和透射的关系及分配特性。     

P波入射下土饱和度对土层交界面运动的影响

给出波从基本饱水土层入射到弹性土层时在土层交界面上的水平位移和竖向位移分量的表达式。通过数值计算分析,研究了饱和度对交界面上反射、透射系数以及水平、竖向位移分量幅值的影响。     

基于VSP的透射PS波成像

利用弹性波动方程进行了非零偏移距VSP波场的数值模拟,通过偏振投影和中值滤波技术相结合进行波场分离,对分离后的反射P波和透射PS波利用动校正(NMO)和VSPCDP叠加技术进行成像。成像结果表明:透射PS波成像与反射P波成像具有同样良好的效果,而且透射PS波成像是反射波成像很好的补充。利用透射PS波成像不需要增加数据采集的成本,所以透射波成像技术将会在石油工业中被广泛采用。     

三相非饱和松散颗粒介质中弹性波的弥散性分析

由已建立了的非饱和土这种三相松散介质中的动力控制方程,得到波动方程的解,表明在非饱和土中存在3种P波（P1、P2和P3波）和1种S波。根据推导出的波速以及衰减的解析表达式,以实际工程中的尾砂土这种非饱和多孔介质为例,通过Matlab计算工具对非饱和土中的4种体波的弥散特性进一步数值分析,给出了典型的弥散和衰减曲线。结果表明,在一定的频率范围内,4种波的波速及衰减随频率的升高而增大,其中P2、P3波受频率影响强烈,而P1、S波受频率影响则相对较小。此外,饱和度的增加也将导致P1波波速的增大,但对P2、P3波和S波影响不大。     

非饱和土地基中复合多层波阻板对S波的隔离效应

基于弹性波在非饱和多孔介质与单相弹性介质中的传播理论,考虑在非饱和土地基中设置一定厚度的复合多层波阻板（复合多层波阻板以3层为例）,利用Helmholtz矢量分解定理,推导了非饱和土地基中S波通过复合多层波阻板的透射、反射振幅比的解析解。通过数值算例,分析了层间波阻板剪切模量和密度等物理力学参数对非饱和土地基中S波通过复合多层波阻板时传播特性的影响规律。结果表明：复合多层波阻板中层间波阻板材料的剪切模量和密度对透反射系数影响显著。复合多层波阻板是一种有效的隔振屏障,严格控制层间波阻板的剪切模量和密度可以获得最佳隔振效果,这为复合多层波阻板在地基振动控制领域中的应用提供理论指导。     

Effect of pore connectivity on reflection amplitudes of an inhomogeneous wave in a composite porous solid saturated by two immiscible fluids

Present paper aims to study the phenomenon of reflection and transmission when an inhomogeneous wave strikes some discontinuity in a composite porous medium saturated by two immiscible viscous fluids. The incident wave splits into six reflected and six transmitted waves at the interface. All reflected and transmitted waves are inhomogeneous in nature with different directions of propagation vector and attenuation vector. A dimensionless parameter \(\varsigma \in [0, 1]\) is introduced to represent the extent of connection among the pores at the interface. Expression of Umov–Poynting vector is derived to obtain energy flux vector. Continuity of energy flux vector at the interface gives the required boundary conditions for the system. Connecting parameter \(\varsigma \) is also employed in boundary conditions to model the partial connection of pores at the interstices of two media. For numerical discussion we consider a porous medium composed of sandstone and ice, saturated with oil and water. The effect of parameter \(\varsigma \) and angle of incidence is determined numerically on the amplitude and the energy ratios of reflected and transmitted waves.     

REFLECTION AND TRANSMISSION OF SHEAR WAVES IN MONOCLINIC MEDIA

This paper deals with the propagation, reflection and transmission of shear waves in monoclinic media. The dispersion equation for a monoclinic layer overlying a monoclinic half-space has been obtained and curves are plotted. The amplitude ratios for both the reflected and transmitted waves due to reflection of shear waves at the interface of two monoclinic half-spaces have also been computed and the numerical results are presented graphically. The results are compared with the isotropic case. It has been observed that, in monoclinic media, the amplitude ratios for reflected and transmitted wave increases approximately by 25 and 50 per cent respectively, in comparison to the isotropic case. © 1997 John Wiley & Sons, Ltd.     

Elastic waves at a corrugated interface between two dissimilar fibre‐reinforced elastic half‐spaces

The reflection and transmission phenomena of elastic waves incident at a corrugated interface between two dissimilar fibre‐reinforced elastic half‐spaces have been analysed. Using Rayleigh method of approximation, the expressions of the reflection and transmission coefficients are obtained in closed form for the plane interface as well as for the first order approximation of the periodic interface ζ = d cos px. All these reflection and transmission coefficients of regular and irregular waves are found to be the functions of angle of incidence and elastic parameters of the media. Moreover, the coefficients of irregularly reflected and transmitted waves are found to be proportional to the amplitude of the corrugated interface and are functions of the frequency of the incident wave. Numerical computations have been performed for a specific model to compute these coefficients and results obtained are shown graphically. The results of Singh and Singh (Sadhana 2004; 29 :249–257) and Ben‐Menahem and Singh (Seismic Waves and Sources. Springer: New York) have been derived from our analysis as particular cases. Copyright © 2006 John Wiley & Sons, Ltd.     

岩体夹层应力波能量演化及应力响应特征分析

夹层是常见的地质结构,在地震或爆破荷载作用下,夹层对应力波的传播以及对岩体的响应具有重要的影响。以往对应力波在夹层介质中传播的研究多集中于夹层对应力波的隔振或透射性能,而对应力波在夹层中的多次折、反射过程中能量的演化规律缺乏讨论,对夹层介质的应力响应与破坏没有开展较好地分析。通过理论方法对应力波在夹层内部传播过程中的能量系数的变化规律进行了研究,分析了岩体介质波阻抗和应力波入射角对夹层内外介质中累积波动能量系数的影响规律,以及平面型边坡中软弱夹层的应力响应特征和动态稳定性。研究发现,应力波在夹层内部往复反射过程中,夹层内剩余应力波能量随折、反射发生次数呈指数曲线下降,第4次折、反射后产生的应力波能量可以忽略;夹层内外介质中应力波的累积能量系数的差异随着夹层内外介质波阻抗的相对差异的增大而增大。在平面谐波入射下,边坡内部的夹层中的剪应力和抗剪强度呈波动变化;相对P波,SV波入射会产生较高水平的剪应力,对边坡稳定性影响最大。且SV波入射时,边坡的安全系数对夹层的倾角变化更为敏感,随倾角增大而迅速降低。     

Reflection and refraction of SH‐waves at a corrugated interface between two monoclinic elastic half‐spaces

A problem of reflection and transmission of shear wave incident upon a corrugated interface between two monoclinic solid half‐spaces have been investigated. Rayleigh's method of approximation is used to investigate the reflection and transmission coefficients for first and second approximation of the corrugation. For a special interface, closed‐form expressions of these coefficients for the first order approximation of the corrugation are obtained. It is found that these coefficients are functions of amplitude of corrugation, elastic parameters of the media, frequency of the incident wave and angle of incidence. The numerical computations are performed for a specific model and the results obtained are presented graphically. It is found that the reflection and transmission coefficients are strongly influenced by the corrugation and the elastic properties of the media. Results of some earlier workers in this field have been reduced as particular case from the present formulation. Copyright © 2004 John Wiley & Sons, Ltd.