Antiplane response of isoceles triangular hill to incident SH waves

In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can satisfy the governing equation and boundary condition, is provided. Furthermore, numerical examples are presented; the influences of wave number and angle of the incident waves and the angle of the hill's peak on ground motion are discussed.     

Scattering of plane P waves by a semi-cylindrical hill： analytical solution

An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and incident angle on the surface motion of the hill was discussed, and it was shown that a hill greatly amplifies incident plane P waves, and maximum horizontal displacement amplitudes appear mostly at the inclined incidence of waves, which are located at the half-space; and maximum vertical displacement amplitudes emerge mostly at the vertical incidence of waves, which are situated at the hill.     

平面S波在饱和多孔热弹性介质边界的反射问题研究

针对饱和多孔介质中热弹性波的传播特性问题,基于多孔介质理论和广义的热弹性模型,研究平面S波在饱和多孔热弹性介质边界上的反射问题。以考虑流-固耦合的饱和多孔介质波动方程和热-弹耦合的广义热弹性基本方程出发,建立饱和多孔介质的热-流-固耦合弹性波动模型。通过引入势函数并考虑自由透水和绝热的边界条件,经过理论推导最终给出在饱和多孔热弹性介质边界上的四种反射波的振幅反射率的理论表达式。在此基础上进行数值计算,分别讨论平面S波的入射频率、入射角和热膨胀系数等参数对四种反射波的振幅反射率的影响情况。结果表明:各反射波的振幅反射率分别随频率和热膨胀系数的增大而增大,同时也受到平面S波入射角变化的影响。该结论对于土动力学的理论研究及其相关的工程勘探具有一定的指导意义。     

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。     

声波在两种多孔介质界面上的反射和透射

本文导出了声波在两种多孔介质界面上反射、透射的一般计算公式.作为例子,数值计算了P₁波入射于界面时,P₁、P₂和S波的反射、透射系数与声波频率、入射角等量之间的关系.结果表明,各种模式波的反射、透射系数与入射角、多孔介质性质有关,在Biot特征频率附近与频率有关,并用界面两侧的法向能流相等验证了结果的正确性.若把多孔介质当作均匀固体处理,将会得到显著不同的结果.     

倾斜入射快纵波在饱和土中单个圆柱体周围的散射

在Biot饱和土波动理论的基础上,采用波函数展开法,研究了饱和土体中单个圆柱体对倾斜入射PI波的散射特性,计算了背向散射谱和总散射截面积。结果表明,饱和土体中PI波倾斜入射时,随着倾斜入射角的增大,总散射截面积在减小,产生的散射波主要以PI波和SV波为主;随着饱和土体渗透系数的减小,PI波、PⅡ波和SV波背向散射谱平均幅值均呈增大趋势,但PI波背向散射谱幅值变化程度较小。     

平面SV波入射下半圆凸起地形地表运动解析解

采用波函数展开法,并借助辅助函数思想,给出了平面SV波入射下半圆凸起地形地表运动的一个解析解,并对解答的收敛性和截断计算精度进行了检验;最后通过若干算例分析了入射频率和入射角度以及凸起地形宽度对地表运动的影响. 数值结果表明,凸起地形对入射SV波具有显著的放大作用, 该放大作用可达自由场的4倍以上. 当入射频率较低时, 位移峰值多位于半空间地表; 而当入射频率较高时,位移峰值多位于凸起地形表面.      

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

Introduction Scattering of incident waves by local topographies is one of the most attractive topics in the field of engineering seismology. They can be resolved by either a numerical method or an analyti-cal method. The numerical methods include finite difference method, finite element method, boundary element method, etc. The analytical method is the wave function expansion method. Al-though numerical methods can be used for arbitrary-shaped topographies, the analytical solutions are still …     

P波入射下断层参数对地表地震动的影响

基于应用透射人工边界条件的显式有限元法计算断层破碎带宽度及力学参数变化、地震动入射角变化时二维断层场地模型P波入射下地表地震动场的分布。结果表明:(1)低速度破碎带的存在导致整个场地都有P波转换为SV波的分量,且在断层破碎带的区域出现断层陷波;(2)低速度破碎带的存在使输入场地恒定的能量向破碎带集聚放大,随着破碎带宽度增大或其介质波速降低集聚放大效应增大;(3)场地放大效应是频率相关的,宽度较宽或介质波速较低的断层破碎带对输入地震动中较低的频率成份放大显著;(4)竖向断层破碎带能阻隔斜入射地震P波,随着入射角增加隔震效应更显著。     

In-plane foundation-soil interaction for embedded circular foundations

Foundation soil interaction is studied using an analytical two-dimensional model, for circular foundations embedded in a homogeneous elastic half-space and for incident plane P- and SV- and for surface Rayleigh waves. The scattered waves are expanded in complete series of cyclindrical wave functions. A detailed analysis is presented of the foundation response to unit amplitude incident waves as a function of the type of incident waves and angle of incidence, the depth of the embedment and the foundation mass per unit length.It is shown that free-field translations and point rotation approximate well the foundation input motion only for very long incident waves. For shorter incident waves, those in general overestimate the foundation input motion. Neglecting the rotation of the foundation input motion (which is usually done in practice) may eliminate a major contribution to the base excitation of buildings and may cause nonconservative estimates of the forces in these buildings. Incident waves appear as ‘longer’ to a shallow foundation than to a deeper foundation. Therefore, deeper foundations are more effective in reflecting and scattering the short incident waves.     

复杂场地条件下地震动空间效应研究

产生地震动空间效应的主要原因是地质构造的变化会极大地改变复杂场地条件下到达不同观测点的地震波,因此地震波振幅和相位发生明显变化。本文利用有限元和边界元耦合的方法,通过建立雷克子波入射时的非线性响应模型求解复杂场地条件下的波动积分方程,进行复杂近地表构造中地震波场数值模拟,旨在分析复杂场地条件下入射方向不同的地震波的动力响应规律。研究结果显示近地表会极大地改变地震波传播特征,导致地震波传播趋向不一致性的因素是由于复杂场地条件重建了地震波的传播路径,尤其须指出的是非一致性地表位移响应源于软土层中低频子波的传播。在地震响应分析中导致系统不同动力响应的其他原因是主频和地震波速度结构的改变,同时地震波入射角度的改变会引起到达观测点的时间滞后,地表位移响应随着入射角度的增大而增加,地震动的空间效应随着入射角度的减小而愈趋明显。     

三维沉积盆地对地震动的放大效应间接边界元法模拟

基于一种高精度间接边界元法(IBEM), 实现了沉积盆地三维地震响应的频域、 时域精细求解, 并以半空间中椭球形沉积盆地对平面P波和SV波的散射为例, 着重探讨了入射角度、 入射波型、 入射频率、 盆地长宽比和深宽比对沉积盆地地震动放大效应的影响规律． 结果表明: 盆地形状对地震波的放大效应和空间分布状态具有显著影响, 且具体规律受控于入射波频段． ① 随着盆地深度增大, 盆地边缘面波发育更为充分, 在较宽频段内均会出现显著的地震动放大效应, 且深盆地的放大区域集中于盆地中部． ② 圆形盆地对地震波的汇聚效应最为显著, 而狭长盆地对地震波的汇聚作用相对较弱, 高频情况下可在盆地内部形成多个聚焦区域． ③ 不同波型入射下, 盆地对地震动放大效应的机制有所差异: P波入射下, 竖向位移放大主要是由于盆地边缘面波由四周向中部汇聚所致; SV波入射下, 边缘面波汇聚效应相对较弱, 而当盆地较深时, 底部透射体波和边缘面波易形成同相干涉从而显著放大地震动． 按盆地内外介质波速比为1/2, P波和SV波垂直入射下频域最大放大倍数分别为25和15, 时域放大倍数约为4.0和3.7(雷克子波)． ④ 低频波入射下, 位移从盆地中部向边缘逐渐减小, 且浅层沉积盆地对地表位移幅值的放大作用不明显． ⑤ P波和SV波的入射角度对盆地地震动放大幅值及空间分布特征也具有显著影响．      

大型引水隧道在平面地震波入射下动力响应的解析解

本文以波函数展开法为基础,给出了SV波与P波入射时大型引水隧道平面地震响应的解析解.并根据解析解,利用数值方法对建立的场地模型进行了计算分析,研究了隧道结构-水体体系的地震响应.重点讨论了入射波频率、入射角、衬砌力学性能对衬砌结构动力响应的影响.分析表明,大型引水隧道动力响应受入射波频率和入射角的影响较为明显,而衬砌力...     

The Effect Analysis of Topography on the Spectrum Properties of Anti-Plane Movement

An explicit finite difference method is performed to evaluate the significance of topography effects on the seismic response of viscoelastic sites. The real accelerograms and bell-shape impulse wavelets, slope angle of cliff and angle of incidence on the spectrum property of the incoming waves are all discussed in detail. The conclusions show that the presence of topographic factors and the direction of the incident waves not only significantly affect the peak ground acceleration of a site, but also affect the spectrum properties of the incoming waves, and the effect on the direction of the incident waves is especially remarkable. The study also finds that it is reasonable to analyse spectrum properties with the input of impulse wavelets in the finite element simulation of wave motion.     

局部地形对出平面运动谱特性的影响分析

本文利用显式有限元有限差分方法进行了脉冲和实际地震动输入下的粘弹性场地地形影响的分析计算,研究了坡地地形在高宽比不同、体波入射角度不同时出平面运动谱特性的差异。结果显示:地形的特征尺寸和入射角度不仅对地震动的峰值有影响,而且对地震动的谱特性有较大的影响,其中入射角度的影响尤为显著。另外,研究还表明,基于脉冲输入研究粘弹性地形谱特性的影响仍不失为一种有效的方法。     

地震波斜入射下层状场地中地下综合管廊地震响应分析

利用黏弹性人工边界和等效地震荷载时域波动输入方法,结合土层和半空间的精确动力刚度矩阵,实现了地震波斜入射下层状场地地下综合管廊地震反应分析,建立了不同场地条件下地下综合管廊分析模型。计算结果表明:地震波倾斜入射情况下,综合管廊结构地震响应与垂直入射时具有显著差异,一般SV波以30°临界角附近入射时结构地震反应最为剧烈;地下综合管廊动应力集中主要分布在管廊角部、中柱上下端;成层土波速结构变化对地下综合管廊地震反应亦具有显著影响。总体上看:当穿越软夹层时管廊结构地震反应更为剧烈,且覆盖层越厚,管廊结构内力幅值越大。因此地下综合管廊结构抗震设计宜考虑地震波倾斜入射及场地土层性质的影响。     

Kelvin wave generation by a semi-infinite barrier

A closed form solution is given for the problem of simple harmonic plane waves incident obliquely on a semi-infinite barrier. The amplitude of the Kelvin wave component is considered and it is found that increased amplitudes of the Kelvin waves can be expected for certain wave numbers, depending upon the angle of incidence.     

Modelling the response of a double-barred sandy beach system to time-varying wave angles

Sandy beaches typically have one or more shore-parallel bars with superimposed smaller-scale three-dimensional (3D) bars. Knowledge of their morphodynamic behaviour under more realistic wave conditions is limited. This study investigates the response of beaches with two shore-parallel bars to sinusoidally time-varying angles of incidence, using a non-linear morphodynamic model. Different periods and amplitudes of this sinusoidal variation are considered, as well as different time-mean wave angles. For time-invariant and normally incident waves, results show that alongshore rhythmic 3D bars form in the domains of inner and outer shore-parallel bars. The 3D bars in the inner domain are coupled at half the outer-bars wavelength. This phase coupling breaks up when the wave angle varies in time. Initially, regular 3D bars form in the inner domain (free behaviour), which become irregular when 3D bars develop in the outer domain (forced behaviour). The heights of the 3D bars oscillate with time, reaching maximum values when the forcing period is comparable to the system adjustment time scale (∼ 10–20 days). For a time-varying wave angle around an oblique mean, alongshore migrating 3D bars emerge in both inner and outer domains. In contrast, for an oblique (constant) wave angle, 3D bars only form in the inner domain and they hardly migrate alongshore. For any forcing period, the dominant response period of the oscillating bar heights is at half the forcing period when waves are (on average) normally incident, and it equals the forcing period when waves are on average obliquely incident. Compared with time-invariant angles, heights of inner and outer 3D bars are (on average) smaller and larger, respectively, when the angle varies with time, particularly for forcing periods in the order of the system adjustment time scale. Increasing the amplitude of the time-varying wave angle weakens bar growth. Explanations of these results are also provided.     

埋地双排复合式管体结构在SH波作用下的动力分析

以波动理论为基础,采用复变函数法,给出了地下双排复合式管体结构在SH波作用下的解析解。分析了入射波角度、频率变化,管体埋深、内管的厚度变化等参数对管体动应力集中的影响。结果表明:复合式管体内侧的动应力集中峰值明显高于外侧;高频入射时,双排管体在给定距离之间的相互影响较大,动应力集中峰值向邻侧偏移;复合式管体内管越薄,动应力集中峰值越大;垂直入射时,动应力集中峰值受埋深的影响呈周期性变化。     

Numerical study on transient harbor oscillations induced by successive solitary waves

Tsunamis are traveling waves which are characterized by long wavelengths and large amplitudes close to the shore. Due to the transformation of tsunamis, undular bores have been frequently observed in the coastal zone and can be viewed as a sequence of solitary waves with different wave heights and different separation distances among them. In this article, transient harbor oscillations induced by incident successive solitary waves are first investigated. The transient oscillations are simulated by a fully nonlinear Boussinesq model, FUNWAVE-TVD. The incident successive solitary waves include double solitary waves and triple solitary waves. This paper mainly focuses on the effects of different waveform parameters of the incident successive solitary waves on the relative wave energy distribution inside the harbor. These wave parameters include the incident wave height, the relative separation distance between adjacent crests, and the number of elementary solitary waves in the incident wave train. The relative separation distance between adjacent crests is defined as the ratio of the distance between adjacent crests in the incident wave train to the effective wavelength of the single solitary wave. Maximum oscillations inside the harbor excited by various incident waves are also discussed. For comparison, the transient oscillation excited by the single solitary wave is also considered. The harbor used in this paper is assumed to be long and narrow and has constant depth; the free surface movement inside the harbor is essentially one-dimensional. This study reveals that, for the given harbor and for the variation ranges of all the waveform parameters of the incident successive solitary waves studied in this paper, the larger incident wave heights and the smaller number of elementary solitary waves in the incident tsunami lead to a more uniform relative wave energy distribution inside the harbor. For the successive solitary waves, the larger relative separation distance between adjacent crests can cause more obvious fluctuations of the relative wave energy distribution over different resonant modes. When the wave height of the elementary solitary wave in the successive solitary waves equals to that of the single solitary wave and the relative separation distance between adjacent crests is equal to or greater than 0.6, the maximum oscillation inside the harbor induced by the successive solitary waves is almost identical to that excited by the single solitary wave.