Ultrasonic beam focusing characteristics of shear-vertical waves for contact-type linear phased array in solid

We investigate the beam focusing technology of shear-vertical(SV) waves for a contact-type linear phased array to overcome the shortcomings of conventional wedge transducer arrays. The numerical simulation reveals the transient excitation and propagation characteristics of SV waves. It is found that the element size plays an important role in determining the transient radiation directivity of SV waves. The transient beam focusing characteristics of SV waves for various array parameters are deeply studied. It is particularly interesting to see that smaller element width will provide the focused beam of SV waves with higher quality, while larger element width may result in erratic fluctuation of focusing energy around the focal point. There exists a specific range of inter-element spacing for optimum focusing performance. Moreover, good beam focusing performance of SV waves can be achieved only at high steering angles.

Diffraction of plane SV waves by a cavity in poroelastic half-space

This paper presents an indirect boundary integration equation method for diffraction of plane SV waves by a 2-D cavity in a poroelastic half-space.The Green＇s functions of compressive and shear wave sources are derived based on Biot＇s theory. The scattered waves are constructed using fictitious wave sources close to the boundary of the cavity, and their magnitudes are determined by the boundary conditions. Verification of the accuracy is performed by： （1） checking the satisfaction extent of the boundary conditions, （2） comparing the degenerated solutions of a single-phased case with well- known solutions, and （3） examining the numerical stability of the solutions. The nature of diffraction of plane SV waves around a cavity in a poroelastic half-space is investigated by numerical examples.

Effect of seawater on incident plane P and SV waves at ocean bottom and engineering characteristics of offshore ground motion records off the coast of southern California, USA

The effect of seawater on vertical ground motions is studied via a theoretical method and then actual offshore ground motion records are analyzed using a statistical method. A theoretical analysis of the effect of seawater on incident plane P and SV waves at ocean bottom indicate that on one hand, the affected frequency range of vertical ground motions is prominent due to P wave resonance in the water layer if the impedance ratio between the seawater and the underlying medium is large, but it is greatly suppressed if the impedance ratio is small; on the other hand, for the ocean bottom interface model selected herein, vertical ground motions consisting of mostly P waves are more easily affected by seawater than those dominated by SV waves. The statistical analysis of engineering parameters of offshore ground motion records indicate that:(1) Under the infl uence of softer surface soil at the seafl oor, both horizontal and vertical spectral accelerations of offshore motions are exaggerated at long period components, which leads to the peak spectral values moving to a longer period.(2) The spectral ratios(V/H) of offshore ground motions are much smaller than onshore ground motions near the P wave resonant frequencies in the water layer; and as the period becomes larger, the effect of seawater becomes smaller, which leads to a similar V/H at intermediate periods(near 2 s). These results are consistent with the conclusions of Boore and Smith(1999), but the V/H of offshore motion may be smaller than the onshore ground motions at longer periods(more than 5 s).

A series solution for surface motion amplification due to underground twin tunnels:incident SV waves

A series solution of displacement response of the ground surface in the presence of underground twin tunnels subjected to excitation of incident plane SV waves is derived by using Fourier-Bessel series expansion method.The numerical parametric study shows that underground twin tunnels significantly amplify the nearby surface ground motion.It is suggested that the effect of subways on ground motion should be considered when the subways are planned and designed.

2.5D scattering of incident plane SV waves by a canyon in layered half-space

This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green＇s fi.mctions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.

斜入射SV波作用下设置减震层隧道的地震响应

对于距离隧道较远的浅源地震,地震波是以一定角度倾斜传播到隧道近场并对隧道造成破坏。本文采用有限元方法研究了SV波入射角和减震层对隧道地震响应的影响。利用黏弹性人工边界和等效节点力公式建立了二维斜入射SV波的输入方法,并通过算例验证了该方法的准确性。基于所建立的输入方法,研究了有和无减震层隧道在不同入射角下的地震响应,并分析了减震层环向长度的影响。数值结果表明:1)二次衬砌的拉伸损伤和内力峰值随着入射角的增大而增大;2)减震层在不同的地震波入射角下具有良好的减震效果,减震效果随着入射角的增大而减小,且减震层可以减小二次衬砌的竖向加速度分量;3)减震层的环向长度会影响隧道的减震效果。

Surface motion of a semi-cylindrical hill for incident plane SV waves: Analytical solution

An analytical solution for surface motion of a semi-cylindrical hill for incident plane SV waves was derived by using the wave function expansion method and the auxiliary function technique, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and angle as well as hill width on the surface motion of the hill was discussed by numerical examples. It was shown that, a hill greatly amplifies incident plane SV waves, and the maximal amplification may reach 4 times of that for free-field response; and for incident waves of low frequency, the maximal displacement amplitudes emerge mostly at the half-space, however, for incident waves of high frequency, the maximal displacement amplitudes appear mostly at the hill.

Effects of a covering layer in a circular-arc canyon on incident plane SV waves

An analytical solution for scattering of incident plane SV waves by a circular-arc canyon with a covering layer was derived by Fourier-Bessel series expansion technique, and the solution was utilized to analyze the effects of the covering layer on incident plane SV waves. It was shown that the covering layer in a canyon, even if it is very thin, amplifies incident plane SV waves tremendously, and the amplification can be two and half times more than that for a simple canyon; the stiffness and thickness of the covering layer also have great effects on incident plane SV waves.

SV波斜入射下海底沉管隧道地震响应研究

为避免近场斜入射地震波对海底沉管隧道造成灾难性后果,对沉管隧道及其剪力键在斜入射地震作用下的动力响应规律进行深入研究。首先,基于时域有限元方法并结合黏弹性人工边界,将地震波转换为模型边界节点的等效节点力,建立基于波动理论的三维平面SV波斜入射方法,并采用半空间算例验证该方法的准确性;然后,在该地震波输入方法的基础上,利用ABAQUS软件建立土体-沉管隧道节段三维精细化有限元模型,研究地震SV波斜入射作用下不同入射角度对沉管隧道及其剪力键动力响应的影响。研究结果表明:1)当SV波入射角接近临界角时,斜入射对隧道竖向和纵向响应达到最大值,水平响应与入射角呈反比关系;2)斜入射会使结构中对称部位产生非对称剪力,剪力键的剪力承担比也发生改变;3)剪力键根部易产生拉伸裂缝,端角也可能因应力集中而产生局部破坏。

SV波斜入射时不同水体模拟方法下超高水头船闸地震反应分析

基于黏弹性人工边界的地震动斜入射方法模拟平面SV波不同角度入射情况,分别采用声固耦合法和附加质量法模拟闸室内水体,研究超高水头船闸闸室位移、应力和塑性损伤等地震反应,对比两种水体模拟方法计算结果的异同。结果表明:(1)整体上,两种方法计算得出的左、右闸墙地震反应结果随入射角度变化的规律基本一致;左闸墙受拉损伤的最大值均出现在入射角15°时,右闸墙受拉损伤的最大值均出现在入射角35°时;地震波入射角度对超高水头船闸动力响应影响较大,设计时应考虑地震波斜入射的影响。(2)当入射角较大时,采用声固耦合法计算的闸墙相对位移极值、主应力极值和受拉损伤结果偏保守的概率更大,对超高水头船闸结构设计来说更为安全。(3)建议两种计算方法相互参考和校核,推荐采用偏安全的结果进行超高水头船闸结构设计。

Dynamic soil-tunnel interaction in layered half-space for incident P-and SV-waves

The dynamic soil-tunnel interaction is studied by the model of a rigid tunnel embedded in layered half-space, which is simplified as a single soil layer on elastic bedrock to the excitation of P- and SV-waves. The indirect boundary element method is used, combined with the Green＇ s function of distributed loads acting on inclined lines. It is shown that the dynamic characteristics of soil-tunnel interaction in layered half-space are different much from that in homoge- neous half-space, and that the mechanism of soil-tunnel interaction is also different much from that of soil-founda- tion-superstructure interaction. For oblique incidence, the tunnel response for in-plane incident SV-waves is com- pletely different from that for incident SH-waves, while the tunnel response for vertically incident SV-wave is very similar to that of vertically incident SH-wave.

Broadband Analytical Solution to the Scattering of Plane SV Waves by Circular Cylindrical Canyons

Based on Fourier-Bessel series expansion of wave functions,an analytical solution to 2-D scattering ofincident plane SV waves by circular cylindrical canyons with variable depthto-width ratios is deduced in this paper. Unlike other analytical solutions,this paper uses the asymptotic behavior of the cylindrical function to directly define the undetermined coefficients of scattered waves,thus,avoiding solving linear equation systems and the related numerical computation problems under high-frequency incident waves,thereby broadening the applicable frequency range of analytical solutions. Through comparison with existing analytical solutions,the correctness of this solution is demonstrated. Finally, the incident plane SV wave scattering effect under circular cylindrical canyons in wider frequency bands is explored.

TI介质中P-SV波传播的SBP-SAT模拟

基于速度-应力形式的弹性波动方程,采用分部求和和同时逼近项技术建立的SBP-SAT方法,推导了横向各向同性(transversely isotropy,TI)介质的矩阵对称型(symmetric matrix form,SMF)弹性波动方程离散形式,并通过能量法进行了稳定性分析。将该方法应用于倾斜横向各向同性(tilted transverse isotropic,TTI)介质模型、垂直横向各向同性(transverse isotropy with a vertical axis of symmetry,VTI)介质和含裂缝及曲线域的复杂介质模型,对所得的速度幅值和单炮记录分析并总结规律;对不同时间步长、单元网格数的结果进行对比,得出计算效率并验证该方法在求解P-SV波传播问题上的正确性。数值模拟结果表明,该方法模拟精度高,适用性好,在地震数值模拟领域有很好的应用价值和前景。

SV波任意角度入射下地铁车站结构地震响应分析

地震波入射角度对地铁车站结构地震响应的影响问题已受到学者的关注和重视。SV波斜入射时存在临界角情况,超过临界角时,场地水平向运动与竖向运动的相位差会发生改变,同时在超临界角入射下场地具有较大的竖向地震作用;然而SV波超临界角入射下的这些特征对地铁车站地震响应的影响规律还未见公开报道。通过ABAQUS有限元软件,首先验证了基于频域刚度矩阵的地震动输入计算方法求解地下隧道对任意角度SV波散射问题的计算精度,然后研究了SV波0°~80°范围内入射时II类、III类、IV类场地条件下两层三跨地铁车站结构的地震响应。研究表明:在较硬的场地中,SV波超临界角入射下场地同时具有较大的水平向和竖向地震作用,这将显著增大车站中柱的轴力幅值,与垂直入射情况相比,轴力幅值最高被增大至3.28倍,同时,SV波临界角附近入射时,轴力分布显著区别于其他情况;车站中柱的弯矩与剪力最大值均出现在地震波垂直入射时,且总体上,弯矩、剪力幅值随着SV波入射角度的增大而减小;车站与周围地基的动力相互作用,对车站结构所受到的水平地震作用具有一定的增大效应,场地越软,增大效应越显著。建议将SV波垂直入射和临界角附近入射2种工况均作为地铁车站结构抗震设计的不利工况。

SV波全反射作用下地震动的合成及振动特性

越来越多的研究表明来自基岩的地震波并不是垂直地面向上传播的。地震波在斜入射与垂直入射时所产生的场地效应有很大不同,由于存在全反射现象,SV波在斜入射时产生的场地效应更为复杂。文章基于均匀弹性半空间地震波传播理论,分别推导得到SV波入射角在小于、大于等于临界角时地震动的计算表达式,通过模型算例研究SV波全反射作用下的地震动特性。研究发现:由SV波产生的地震动主要由入射波和反射波构成,滑行波作用可以忽略;地面运动轨迹具有面波旋转振动特点;随着入射角的增大,地面震动从以水平方向振动为主逐渐过渡到以垂直方向振动为主,两个方向的振动均小于入射波峰值的2倍。

多空沟对弹性波的散射及隔振性能分析:平面P-SV波入射

在地基振动控制中,较浅的单空沟由于散射效率低,隔振效果并不理想,而多空沟可以通过提高散射效率而达到理想的隔振效果。根据弹性动力学基本理论,在复数域上进行波函数展开,由空沟周边应力自由边界条件,并借助保角映射理论和多极坐标变换技术建立了问题的控制方程,给出了多空沟对平面P‑SV波散射的解析解答。以双空沟为例,参数分析了激励频率、空沟长度和空沟间距等因素对隔振效果的影响规律。结果表明:双空沟的隔振效果明显优于单空沟,并且随着空沟长度增加,隔振效果越好;存在一定的空沟间距使双空沟能发挥出更好的隔振效果。

空沟对弹性波散射的时域分析:平面SV波入射

基于土‑结构相互作用理论,利用比例边界有限元法,将含有空沟地形条件的场地分解为近场系统和无穷远场系统。利用四叉树对近场计算区域进行网格精细化离散,并利用位移单位‑脉冲响应矩阵来表示近场和远场交界面上的相互作用力,从而将斜入射的平面SV波转化为作用在近场系统边界上的等效节点力来模拟入射波对近场系统的激励作用,建立了时域‑空间域弹性波传播问题的数值模型,通过数值算例验证了方法的有效性,分析了入射角和空沟深度等参数对隔振效果的影响。结果表明:隔振效果随着入射角的增大而增大;当入射角较大时,通过进一步增大空沟深度,可使得空沟发挥出更优的隔振效果。

Separation of P. and SV-wavefields from multi-componen seismic data

在多分量地震勘探资料中,水平和垂直分量都记录有P波和SV波。本文研究了P波和SV波波场分解的方法。当上行P波和S波分别入射时,通过研究它们引起的水平和垂直位移,把地震记录的水平和垂直分量进行分解,得到纵波和转换波;在已知海底介质中纵横波速度和介质密度的情况下,可以在τ-P域内实现波场分解,然后变换到时间域,得到时间域内的纵波和转换波剖面。把本文研究的波场分解方法应用于合成资料,能够有效地分解得到纵波波场和转换波波场。最后,海上多分量实际资料的实例应用表明,本文研究的波场分解方法是可行有效的。本方法也适用于自由表面的资料。

Seismic stability of jointed rock slopes under obliquely incident earthquake waves

Seismic stability of slopes has been traditionally analyzed with vertically propagated earthquake waves.However,for rock slopes,the earthquake waves might approach the outcrop still with a evidently oblique direction.To investigate the impact of obliquely incident earthquake excitations,the input method for SV and P waves with arbitrary incident angles is conducted,respectively,by adopting the equivalent nodal force method together with a viscous-spring boundary.Then,the input method is introduced within the framework of ABAQUS software and verified by a numerical example.Both SV and P waves input are considered herein for a 2 D jointed rock slope.For the jointed rock mass,the jointed material model in ABAQUS software is employed to simulate its behavior as a continuum.Results of the study show that the earthquake incident angles have significance on the seismic stability of jointed rock slopes.The larger the incident angle,the greater the risk of slope instability.Furthermore,the stability of the jointed rock slopes also is affected by wave types of earthquakes heavily.P waves induce weaker responses and SV waves are shown to be more critical.

Scattering and diffraction of plane P-waves in a 2-D elastic half-space Ⅱ：shallow arbitrary shaped canyon

Scattering and Diffraction of elastic in-plane P-and SV-waves by a surface topography such as an elastic canyon at the surface of a half-space is a classical problem which has been studied by earthquake engineers and strong-motion seismologists for over forty years. The case of out-of-plane SH waves on the same elastic canyon that is semi-circular in shape on the half-space surface is the first such problem that was solved by analytic closed form solutions over forty years ago by Trifunac. The corresponding case of in-plane P-and SV-waves on the same circular canyon is a much more complicated problem because, the in-plane P-and SV-scattered waves have different wave speeds and together they must have zero normal and shear stresses at the half-space surface. It is not until recently in 2014 that analytic solution for such problem is found by the author in the work of Lee and Liu. This paper uses the technique of Lee and Liu of defining these stress-free scattered waves to solve the problem of the scattered and diffraction of these in-plane waves on an almost-circular surface canyon that is arbitrary in shape.