Effects of wave passage on the relevant dynamic properties of structures with flexible foundation

An evaluation of the wave passage effects on the relevant dynamic properties of structures with flexible foundation is presented. A simple soil–structure system similar to that used in practice to take into account the inertial interaction effects by the soil flexibility is studied. The kinematic interaction effects due to non‐vertically incident P, SV and Rayleigh waves are accounted for in this model. The effective period and damping of the system are obtained by establishing an equivalence between the interacting system excited by the foundation input motion and a replacement oscillator excited by the free‐field ground motion. In this way, the maximum structural response could be estimated from standard free‐field response spectra using the period and damping of the building modified by both the soil flexibility and the travelling wave effects. Also, an approximate solution for the travelling wave problem is examined over wide ranges of the main parameters involved. Numerical results are computed for a number of soil–structure systems to identify under which conditions the effects of wave passage are important. It comes out that these effects are generally negligible for the system period, but they may significantly change the system damping since the energy dissipation within the soil depends on both the wave radiation and the diffraction and scattering of the incident waves by the foundation. Copyright © 2001 John Wiley & Sons, Ltd.     

基于反卷积干涉法的土层地震反应特性研究

美国阿拉斯加安克雷奇德兰尼公园的土层地震反应观测台阵建有6个井下观测点和1个地表观测点, 每个观测点设置一个三分量加速度传感器, 该台阵建成后记录了多次地震事件. 本文通过反卷积地震干涉法对这些地震记录进行土层反应分析, 根据该分析结果提取土层结构的等效剪切波速和阻尼比. 所有层位的地震记录对地表记录的反卷积波形均反映出在土层中传播的上、 下行波, 其上行与下行至每一层的时间差别明显. 根据每一层的到时差, 确定土层中的等效剪切波速和分层等效剪切波速, 该结果与现场土层等效剪切波速测试结果吻合较好; 根据等效剪切波速计算出的土层卓越频率, 其一致性亦较好; 根据上、 下行波的峰值分析确定该场地土层的等效阻尼比, 也与软土的阻尼比经验值相当. 这些参数为后续的土层反应模拟和土结相互作用研究奠定了良好的数据基础. 结果表明, 反卷积干涉法能够用于土层反应分析和土层地震反应特性的提取.      

Analysis on influence of seismic travelling wave effect on semi-active control for long-span rigid-continuous bridge

Introduction The methods of enhancing ability of bridge to resist earthquake disaster can be divided into two aspects. One is enhancing the resisting earthquake ability from the designing ways; the other is adding control devices on the existing structures to effectively control the seismic responses of bridge from the vibration control ways. The great progress has been made in structure control technique in the last years. It has the advantages of security, validity, economical and wide appli…     

行波效应对大跨刚构连续桥梁半主动控制影响分析

给出了地震动行波输入下大跨刚构连续桥梁的半主动控制分析方法,在桥梁支座部位设置磁流变阻尼器,对一座五跨刚构连续桥梁进行了不同视波速行波输入下的半主动控制计算分析. 结果表明,行波效应对该大跨刚构连续桥梁的无控制地震反应、半主动控制地震反应和减震效果均有显著影响,对主梁和桥墩均会在较低视波速地震行波输入时表现出不利影响,并且使半主动控制减震效果明显降低. 因此,在确定半主动控制系统的参数时应考虑地震行波效应的影响以确保控震效果.      

任意空间取向TI介质qP和qSV波解耦的波动方程

由于构造运动等作用,TI介质对称轴往往沿空间任意方向分布,具有任意空间取向对称轴的TI（ATI）介质更符合实际地质情况.VTI介质与ATI介质的相速度在形式上具有一致性,VTI介质中地震波的相角对应ATI介质对称轴与地震波传播方向的夹角.本文基于Tsvankin的VTI介质精确相速度公式,利用TI介质对称轴和地震波传播方向上单位向量的数量积和向量积来计算ATI介质的精确相速度.根据弱各向异性假设,导出qP波和qSV波的近似相速度,分析了近似公式的误差,讨论总结了ATI介质qP波和qSV波的相速度特征.本文中的单位向量采用观测坐标系表示,通过相角关系,可以较为方便地由ATI介质近似相速度导出频散关系,然后借助傅里叶逆变换推导出时间-波数域qP波和qSV波解耦的波动方程.数值算例表明本文的波动方程是qP波和qSV波解耦的,波场计算结果稳定,未出现明显的数值频散,验证了本文方法的有效性.     

Wave-induced setup of the mean surface over a sloping beach

A new theoretical approach for the wave-induced setup over a sloping beach is presented that takes into consideration the explicit variations of the surface waves due to bottom slope and viscosity. In this way, the wave forcing of the mean Lagrangian volume fluxes is calculated without assuming that the local depth is constant. The analysis is valid in the region outside the surf zone and is based on the shallow-water assumption. A novel approach for separating the viscous damping of the waves from the frictional damping of the mean flow is introduced, where the mean Eulerian velocity is applied in the bottom stress for the mean fluxes. In the case where the onshore Lagrangian mean transport is zero, a new formula is derived for the Eulerian mean free surface slope, in which the effects of bottom slope, viscous wave damping and frictional bottom drag on the mean flow are clearly identified. The analysis suggests that viscous damping of the waves and frictional dissipation of the Eulerian near-bed return flow could lead to setup outside the surf zone.     

Acoustic gravity wave growth and damping in convecting plasma

The propagation of acoustic gravity waves through steadily convecting plasma in the thermosphere has been analysed theoretically. The growth and damping rates of internal gravity waves due to the feedback effects of wave-modulated Joule heating and Laplace forcing have been calculated. It is found that large convection flow velocities lead to the growth of large-scale internal gravity waves, whilst small- and medium-scale waves are heavily damped, under similar conditions. It has also been shown that wave growth is favoured for waves travelling against the plasma flow direction. The effects of critical coupling when wave phase speeds match the plasma flow speed have also been investigated. The results of these calculations are discussed in the context of the atmospheric energy budget and thermosphere-ionosphere coupling.     

Momentum transfer at the ocean–atmosphere interface: the wave basis for the inertial coupling approach

 The inertial coupling approach for the momentum transfer at the ocean–atmosphere interface, which is based on the assumption of a similarity hypothesis in which the ratio between the water and air reference velocities is equal to the square root of the ratio between the air and water densities, is reviewed using a wave model. In this model, the air and water reference velocities are identified, respectively, with the spectrally weighted phase velocity of the gravity waves and the Stokes velocity at the water roughness length, which are evaluated in terms of the dimensionless frequency limits in Toba's equilibrium spectrum. It is shown that the similarity hypothesis is approximately satisfied by the wave model over the range of wave ages encountered in typical sea states, and that the predicted values of the dimensionless surface drift velocity, the dimensionless water reference velocity, and the Charnock constant are in reasonable agreement with observational evidence. The application of the bulk relationship for the surface shear stress, derived from the inertial coupling hypothesis in general circulation modeling, is also discussed. Received: 6 January 2001 / Accepted: 28 June 2001     

Oblique wave scattering by undulating porous bottom in a two-layer fluid: Fourier transform approach

The problem involving scattering of oblique waves by small undulation on the porous ocean bed in a two-layer fluid is investigated within the framework of linearised theory of water waves where the upper layer is free to the atmosphere. In such a two-layer fluid, there exist waves with two different wave numbers (modes): wave with lower wave number propagates along the free surface whilst that with higher wave number propagates along the interface. When an oblique incident wave of a particular mode encounters the undulating bottom, it gets reflected and transmitted into waves of both modes so that some of the wave energy transferred from one mode to another mode. Perturbation analysis in conjunction with Fourier transform technique is used to derive the first-order corrections of velocity potentials, reflection and transmission coefficients at both modes due to oblique incident waves of both modes. One special type of undulating bottom topography is considered as an example to evaluate the related coefficients in detail. These coefficients are shown in graphical forms to demonstrate the transformation of water wave energy between the two modes. Comparisons between the present results with those in the literature are made for particular cases and the agreements are found to be satisfactory. In addition, energy identity, an important relation in the study of water wave theory, is derived with the help of the Green’s integral theorem.     

行波效应对大跨度空间结构随机地震响应的影响

深入研究了行波效应对大跨度空间结构随机地震响应的影响,进一步完善了大跨度空间结构随机地震响应分析理论。推导了双支座、单自由度体系地震响应功率谱密度函数的解析表达式,研究了不同频率体系的响应峰值随地面视波速的变化规律,分析了多支撑点、多自由度体系的地震响应功率谱矩阵的特点,发现多自由度体系地震响应随地面视波速的变化规律与单自由度体系相似。数值模拟了某体育馆网壳结构在不同地面视波速情况下的随机地震响应,结果表明,考虑地震动行波效应后,结构地震响应随地面视波速的变化而显著变化,当视波速较低时其变化规律很复杂;且支撑点附近、受拟静力位移影响较大的部分杆件的地震响应明显增大,远离支撑点处、受拟静力位移影响较小的部分杆件的地震响应稍有减小。由此得出结论,对于大跨度空间结构的随机地震响应分析,必须考虑地震动的行波效应,尤其当受拟静力位移影响较大的部分杆件对结构抗震设计起控制作用时;且应对可能出现的地面视波速进行全面分析,作为结构抗震设计依据。     

On the attenuation of transient spherical waves in a four-element viscoelastic model and its implications

Summary In a four-element model, which consists of two Voigt elements in series, the impulse responses of spherical waves for particle displacement, velocity, acceleration and strain are computed numerically. These impulse responses are shown to be useful in synthesis for the desired wave response through convolution, between the input of the source function and the impulse responses. The rate of decay of peak amplitude versus distance, as waves radiate out, is examined in the region close to the source which may be nuclear or dynamite explosives and found to be linear in log-log scale. The amplitude spectra of the unit impulse response are obtained through Fourier analysis, and the model is found to behave as a low pass filter. With the properly chosen elastic constants for springs in the model and damping coefficients for dashpot, it is seen that, like the earth materials, the attenuation exponent (in neper/1000 ft) versus frequency in the model is approximately linear. One of the results observed byCollins andLee [1] is fitted by the model. The model thus simulates more nearly the wave in earth materials close to the source than the Voigt solid.     

横向各向同性多孔介质中的地震波传播

基于各向异性多孔介质中的广义Ｂｉｏｔ理论，导出了横向各向同性多孔介质中波传播的特征方程．指出在多孔介质中有４种类型的频散和耗散波传播：准纵波ＱＰ１（快纵波）、准纵波ＱＰ２（慢纵波）、准横波ＱＳＶ和横渡ＳＨ．文中给出了４种波速度的解析表达式．数值计算频率曲线和衰减曲线与Ｓｃｈｍｉｔｔ（１９８９）用均值处理得到的结果类似．还给出了波传播过程中３种类型准体波之间的耦合系数（或称转换系数）．     

The effect of inertial coupling on seismic reflection amplitudes

A problem of reflection and transmission of elastic waves at a plane interface between a uniform elastic solid half-space and a porous elastic half-space containing two immiscible fluids is investigated. The theory developed by Lo, Sposito and Majer for porous media containing two immiscible fluids is employed to find out the reflection and transmission coefficients. The incident wave is assumed to propagate through the uniform elastic half-space and two cases are considered. In the first case, a beam of plane longitudinal wave is assumed to be incident and in the second case, a beam of transverse wave is assumed to be incident at the interface. By taking granite as impervious elastic medium and columbia fine sandy loam containing air-water mixture as porous medium, reflection and transmission coefficients are obtained. By neglecting the inertial coupling coefficients, these coefficients are reduced to those obtained by Tomar and Arora using the theory of Tuncay and Corapcioglu. It is found that the inertial coupling parameters significantly affect the phase speeds and the amplitude ratios of the transmitted waves.     

Effects of seismic wave propagation upon buried pipelines

The behaviour of long straight buried pipelines subjected to seismic wave propagation is investigated. Well-known relationships for determining upper bounds for the axial strain and curvature in the pipeline as well as relationships for relative displacement and rotation at the pipeline joints are discussed. The assumption that the seismic excitation can be modelled as a travelling wave having a shape which remains unchanged as it traverses the pipeline is examined in detail. It is shown that this assumption is unconservative when the effective propagation velocity of the seismic waves with respect to the pipeline is such that the actual time lag (separation distance between points divided by effective propagation velocity) is less than a ‘cross-over’ time lag. Cross-over time lags for 22 pairs of ground displacements recorded during the 1971 San Fernando Earthquake are presented in this paper. Finally, methods for estimating the propagation speed of the seismic waves along or with respect to the pipeline are discussed.     

Response spectra for torsion,rocking and rigid foundations

Simple procedures are proposed for computing response spectra for torsional and rocking input ground motions assuming horizontally travelling waves of constant shape. It is shown that harmonic relationships exist between the rotational spectra and the corresponding translational spectra, and that SV rather than PSV is the correct basis for deriving the angular displacement, velocity and acceleration response spectra. An approximation enabling the use of the standard tripartite logarithmic response spectra is discussed. Simple expressions for ‘accidental’ eccentricity and rocking input effects are presented. Also proposed are multipliers to spectral ordinates to account for the filtering effects of rigid base mats resting on Winkler type foundations. For wave transit times shorter than half the natural period of the structure, these multipliers can be approximated by the frequency dependent averaging coefficients given in the literature, which are dependent, however, on the response, rather than the input, frequency.     

Sloshing analysis of rectangular tanks with a submerged structure by using small-amplitude water wave theory

A new sloshing analysis method for rectangular tank systems with a submerged structure are proposed by using the velocity potential and the linear water wave theory. The velocity potential functions are obtained by decomposing the surface wave into a wall-induced wave, reflected and transmitted waves, and a scattered wave. A simplified method using a response spectrum for zero damping is also proposed. The results of the simplified method are in good agreement with those of the analytical method. The sloshing response of the fluid-structure system is found to be very sensitive to the characteristics of the ground motion and the configuration of the system. Under typical earthquakes, the submerged structure shows a tendency to decrease sloshing amplitude, hydrodynamic pressure, and base shear, while it shows a tendency to increase the overturning moment. For the ground excitation dominated by low-frequency contents, the sloshing response increases significantly and the contribution of the higher sloshing modes increases. Copyright © 1999 John Wiley & Sons, Ltd.     

Wave patterns generated by disturbances travelling horizontally in rotating stratified fluids

The pattern and propagation of waves generated by steady or oscillatory disturbances travelling horizontally in a rotating, stratified fluid are studied following a technique developed by Lighthill. Both two‐ and three‐dimensional distrubances are investigated. The results show how rotation modifies internal wave patterns in a stratified fluid and how stratification modifies inertial wave patterns in a rotating fluid. The results are used to compute the effective diminution of Taylor column length due to the presence of density stratification. They also show that the appearance of wave crests upstream of a disturbance is possible only when the disturbance is unsteady and that observations of upstream blocking in a two‐dimensional stratified flow can be explained by the existence of a certain class of plane waves as modified by viscosity.     

Characteristics of disturbances in the atmosphere and oceans

The characteristics of the disturbances in the atmosphere and oceans and in other stably stratified and rotating fluids are analyzed according to their phase and group velocities. It is shown that both stable stratification and rotation augment the velocity of the sound waves, and that the internal gravity waves and inertial waves are mutually exclusive when the Brunt-Väisälä frequency is different from the Coriolis parameter. It is also shown that both the barotropic and the internal Rossby waves are well separated from the gravity waves and that they can be represented accurately by the quasi-geostrophic potential vorticity equation, even close to the equator, except for the one member withn=0 which is coupled with an eastward propagating gravity wave.     

The instability of internal gravity waves to localised disturbances

The instability of an internal gravity wave due to nonlinear wave-wave interaction is studied theoretically and numerically. Three different aspects of this phenomenon are examined. 1. The influence of dissipation on both the resonant and the nonresonant interactions is analysed using a normal mode expansion of the basic equations. In particular, the modifications induced in the interaction domain are calculated and as a result some modes are shown to be destabilised by dissipation. 2. The evolution of an initial unstable disturbance of finite vertical extent is described as the growth of two secondary wave packets travelling at the same group velocity. A quasi-linear correction to the basic primary wave is calculated, corresponding to a localised amplitude decrease due to the disturbance growth. 3. Numerical experiments are carried out to study the effect of a basic shear on wave instability. It appears that the growing secondary waves can have a frequency larger than that of the primary wave, provided that the shear is sufficient. The instability of waves with large amplitude and long period, such as tides or planetary waves, could therefore be invoked as a possible mechanism for the generation of gravity waves with shorter period in the middle atmosphere.     

Effects of foundation embedment during building–soil interaction

A numerical solution for evaluating the effects of foundation embedment on the effective period and damping and the response of soil–structure systems is presented. A simple system similar to that used in practice to account for inertial interaction effects is investigated, with the inclusion of kinematic interaction effects for the important special case of vertically incident shear waves. The effective period and damping are obtained by establishing an equivalence between the interacting system excited by the foundation input motion and a replacement oscillator excited by the free-field ground motion. In this way, the use of standard free-field response spectra applicable to the effective period and damping of the system is permitted. Also, an approximate solution for total soil–structure interaction is presented, which indicates that the system period is insensitive to kinematic interaction and the system damping may be expressed as that for inertial interaction but modified by a factor due to kinematic interaction. Results involving both kinematic and inertial effects are compared with those obtained for no soil–structure interaction and inertial interaction only. The more important parameters involved are identified and their influences are examined over practical ranges of interest. © 1998 John Wiley & Sons, Ltd.