半空间异质隆起的出平面动力响应:地表运动

采用闭合解析解对水平地表圆形非匀质隆起出平面运动特征进行详细分析。结果表明：（1）隆起区域介质软硬程度对其出平面地表运动影响非常大，软质隆起表面的地表位移较匀质隆起情况有显著放大，地表运动波动效应明显增强，而硬质隆起则减弱地表运动；（2）软质隆起地表位移幅值最大反应和平均反应增大的程度一般来说至少不低于隆起区域波速降低的程度，很多情况是远大于波速降低的程度，但最大反应出现的位置和频段主要受入射波角度控制；（3）当波垂直传播时，地表位移放大出现在隆起顶部，频率随隆起区变软，明显向低频移动，可出现在很低频段内，且随隆起区变软放大更为显著；（4）当波掠入射时，地表最大位移出现在隆起后表面，地表运动仍然十分强烈，甚至比波垂直入射时隆起顶部反应还要大，但出现在较高频段内。     

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。     

弹性层状半空间中凸起地形对入射平面SH波的放大作用

对Wolf理论进行拓展,使之可解决凸起地形对波的散射问题,进而利用间接边界元法,求解了弹性层状半空间中凸起地形对入射平面SH波的放大作用问题。本文模型的显著特点之一是考虑了层状半空间的动力特性以及层状半空间和凸起地形的阻尼;特点之二是计算精度高。文中以基岩上单一土层中半圆凸起地形对入射平面SH波的放大作用为例进行了数值计算分析。研究表明,基岩上单一土层中凸起地形对入射平面SH波放大作用和均匀半空间中凸起地形有着本质的差别;土层动力特性不仅影响凸起地形地表位移的幅值,还会影响地表位移的频谱;阻尼会显著降低凸起地形对高频波的放大作用。     

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.     

Antiplane response of isosceles 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 anti-plane (SH) waves by a semi-elliptical hill: II—deep hill

The ground motion and wave propagation resulting from the scattering of anti-plane (SH) waves by a deep semi-elliptical hill on an elastic half-space are investigated. The solution is the closed-form one based on the method of wave-function expansion, and the expansion of elliptical sine and cosine over the half-range [−π/2, π/2]. The analysis shows that the interference of ground motion depends on several factors such as frequency of the incident waves, incident angle, and the aspect ratio of elliptical hills. Similar to part I: Shallow Hill, numerical results when semi-elliptical tends to semi-circular are compared with the work done by Lee et al. [17].     

Scattering of plane sh waves by a semi-cylindrical canyon

The two-dimensional scattering and diffraction of plane SH waves by a semi-cylindrical canyon is analysed for a general angle of wave incidence. The closed-form solution of the problem shows that the surface topography can have prominent effects on incident waves only when the wavelengths of incident motion are short compared to the radius of a canyon. The surface amplification of displacement amplitudes around and in the canyon changes rapidly from one point to another, but the amplification is always less than 2. The over-all trends of amplification pattern are determined by two principal parameters: (1) γ, the angle of incidence of plane SH waves, and (2) η, the ratio of radius of the canyon to one-half wave length of incident waves. The higher η leads to greater complexity of the pattern of surface displacement amplitudes characterized by more abrupt changes of amplification from one point to another, while γ mainly determines the over-all trends of displacement amplitudes. For grazing and nearly grazing incidences, for example, a strong shadow zone is developed behind the canyon. The qualitative analysis of the topographic effects on the Pacoima Dam accelerogram,¹ based on the semi-cylindrical canyon, suggests that this strong-motion record was not seriously affected by surface topography of the recording site.     

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 …     

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.      

Scattering of SH waves by a scalene triangular hill

<正>The influence of local landforms on ground motion is an important problem.The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function,moving coordinates and auxiliary functions.First,the model is divided into two domains:a scalene triangular hill with a semi-circular bottom;and a half space with a semi-circular canyon.Wave functions that satisfy the zero-stress condition at the triangular wedges and at the horizontal surface are constructed in both domains.Then,considering the displacement continuity and stress equilibrium, algebraic equations are established.Finally,numerical examples are provided to illustrate the influence of the geometry of the hill and the characteristics of the incident waves on the ground motions.     

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.     

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．      

Scattering of plane sh waves by a semi-elliptical canyon

In this paper we analyse the two-dimensional scattering and diffraction of plane SH waves by a semi-elliptical canyon. The exact series solution of the problem, for general angle of incidence of the plane SH waves, has been used to examine the dependence of surface amplifications inside and near the canyon. The nature of ground motion has been found to depend on two key parameters: (a) The angle of incidence. (b) The ratio of the canyon width to the wave length of incident SH waves. For short incident waves surface displacement amplitudes change rapidly from one point to another, while for the long waves and shallow canyons displacement amplitudes display only minor departure from the uniform half-space amplification of 2. For shallow canyons and long incident waves, the angle of incidence introduces only minor changes into the overall behaviour of surface amplitudes. For deep canyons and nearly grazing incidences, a prominent shadow zone is realized behind the canyon.     

Effect of topography and subsurface inhomogeneity on seismic rayleigh waves

The effect of topography and subsurface inhomogeneity on surface motion is investigated in the case of Rayleigh waves. In the previous paper, the same effect was investigated in the case of SV waves. Several types of topography, such as cliffs both with and without a soft layer at the foot of the slope, are considered. Computations are made using a new hybrid method combining a particle model with a finite element method. In cases of harmonic Rayleigh waves, surface motions with amplitudes as large as 1.5 to 5 times the horizontal surface displacement of the incident Rayleigh waves are produced near the slope and the sloping interface. When a Rayleigh wave propagating through a hard single-layered ground encounters a sloping interface where hard ground and soft ground make contact with each other, Rayleigh waves having two different, phase velocities are produced and they correspond to the fundamental mode, and the first mode determined by Haskell's method. In addition, the transient response when Rayleigh waves propagate through the cliff is also simulated. Assuming the vertical component of the Tokachi-oki Earthquake (1968) measured on the surface to be a Rayleigh wave, the incident Rayleigh wave can be obtained by a Fourier synthesis of eigenfunctions of Rayleigh waves.     

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。     

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).     

山谷地形对入射SV波地震反应分析

基于黏弹性人工边界的显式动力有限元方法,研究了突出平台状山谷地形场地的地形效应,分析了山谷地形对地表地震动的影响.结果表明:(1)沿着地震动输入方向地表反应较其他方向上的反应强烈;(2)与单一凸起山体地形对地表地震动的放大效应相比,相邻地形的存在对地表地震动位移傅里叶谱谱比曲线的形状影响不大,但是对PGD有着较大的影响...     

Dynamic stress concentration of an elliptical cavity in a semi-elliptical hill under SH-waves

The method of wave-function expansion in elliptical coordinates,elliptical cosine half-range expansion and Mathieu function were applied to obtain an exact analytical solution of the dynamic stress concentration factor(DSCF)around an elliptical cavity in a shallow,semi-elliptical hill.An infinite system of simultaneous linear equations for solving this problem was established by substituting the wave expression obtained by the Mathieu function including the standing wave expression of elliptical lining given herein into the boundary condition obtained by the region-matching method.The finite equations system with unknown coefficients obtained by truncation were solved numerically,and the results in the case of an ellipse degenerating into a circle were compared with previous results to verify the accuracy of the method.The effects of different aspect ratios,incident wave angles and aperture ratios on the dynamic stress concentration around the elliptical cavity were described.Some numerical results,when the elliptical hill was changed into a circular one,were analyzed and compared in detail.In engineering,this model can be regarded as a semi-cylindrical hill with an elliptical cylindrical unlined tunnel under the action of SH waves,and the results are significant in aseismic design.     

Oblique flexural-gravity wave scattering by a submerged semi-circular ridge

This study examines the flexural-gravity wave scattering by a semi-circular ridge submerged in the ocean covered by a thin ice sheet. The ice sheet is treated as an elastic plate and its deflection is modelled using the Euler-Bernoulli beam equation. The fluid motion is described by linear potential theory. The series solutions of velocity potentials for obliquely and normally incident waves are both developed using multipole expansions. The unknowns in the series solutions are determined in terms of the impermeable condition on the ridge surface. Accurate results for the reflection and transmission coefficients of ridge and the deflection of ice sheet are presented. The effects of ridge radius, ice thickness, wave frequency and wave incident angle on the hydrodynamic quantities are shown.     

On the interaction of rayleigh surface waves with structures

A two-dimensional soil-structure interaction analysis is carried out for transient Rayleigh surface waves that are incident on a structure. The structure is modelled by a three-degree of freedom rigid basemat to which is attached a flexible superstructure, modelled by a single mass-spring system. The structural responses to a given Rayleigh wave train are compared with those that would have been obtained if the free-field acceleration-time history had been applied as a normally incident body wave. The results clearly exhibit the [frequency filtering] effects of the rigid basemat on the incident Rayleigh waves. It is shown that, if seismic excitation of a structure is, in fact, due to Rayleigh surface waves, then an analysis assuming normally incident body waves can considerably over-estimate structural response, both at basemat level for horizontal and vertical motions and for vertical oscillations of the superstructure. However, in the examples considered here, relatively large rocking effects were induced by the Rayleigh waves, thus giving maximum horizontal accelerations in the superstructure that were of comparable magnitude for Rayleigh and normally incident body waves.