Seismic behaviour of pile groups by hybrid experiments

Non-linear seismic soil-pile interaction was studied with a hybrid procedure that used a pseudo-dynamic testing (PDT) method modified to account for frequency dependence and developed for foundation-soil systems. The numerical scheme used in the conventional PDT was improved by the introduction of a time-dependent pseudo-forcing function derived from the frequency-dependent dynamic characteristics of the system by Hilbert transformation in the frequency domain. Single, 2-, 3- and 9-pile group foundation models were used, their mechanical characteristics later being determined from static and forced vibration dynamic tests. Amplitude scaling was used for three recorded accelerograms. Data recorded during an earthquake at the site of the experiments revealed that the proposed methodology predicts well seismic nonlinear interaction and accounts for frequency dependence and non-linearity in the time domain.     

涡流地震检波器的特性及测试方法的研究

本文介绍了涡流地震检波器的工作原理、结构及其频率响应特性--涡流检波器的输出特性在固有频率之上是按外界激励频率的平方递增。高频灵敏度随着激励频率的增加而增高有助于弥补高频信号通过地层传播时的急剧衰减,从而提高了地震勘探的分辨率。在固有频率之下,则加强了低频滤波作用。 本文还以对单自由度线性振动系统的动态分析为基础,研究了利用实验幅频特性曲线来求该系统的固有频率和阻尼系数的方法,推导出必要的计算公式。最后举出一个应用实例,并检验了这种方法的可信度。     

Monitoring the structural dynamic response of a masonry tower: comparing classical and time-frequency analyses

The monitoring of the evolution of structural dynamic response under transient loads must be carried out to understand the physical behaviour of building subjected to earthquake ground motion, as well as to calibrate numerical models simulating their dynamic behaviour. Fourier analysis is one of the most used tools for estimating the dynamic characteristics of a system. However, the intrinsic assumption of stationarity of the signal imposes severe limitations upon its application to transient earthquake signals or when the dynamic characteristics of systems change over time (e.g., when the frequency of vibration of a structure decreases due to damage). Some of these limitations could be overcome by using the Short Time Fourier Transform (STFT). However, the width of the moving window adopted for the analysis has to be fixed as a function of the minimum frequency of interest, using the best compromise between resolution in both the time and frequency domains. Several other techniques for time-frequency analysis of seismic signals recorded in buildings have been recently proposed. These techniques are more suitable than the STFT for the application described above, although they also present drawbacks that should be taken into account while interpreting the results. In this study, we characterize the dynamic behaviour of the Falkenhof Tower (Potsdam, Germany) while forced by ambient noise and vibrations produced by an explosion. We compare the results obtained by standard frequency domain analysis with those derived by different time-frequency methods. In particular, the results obtained by the standard Transfer Function method, Horizontal to Vertical Spectral Ratio (HVSR), Short Time Fourier Transform (STFT), Empirical Mode Decomposition (EMD) and S-Transform are discussed while most of the techniques provide similar results, the EMD analyses suffer some problems derived from the mode mixing in most of the Intrinsic Mode Functions (IMFs).     

Frequency-independent impedances of soil-structure systems in horizontal and rocking modes

The frequency-independent foundation impedances, commonly used in soil-structure dynamic interaction problems, are developed for a circular footing resting on a homogeneous halfspace. As they ignore the structure attached to the foundation, the error introduced in the structural response may be 50 per cent or more in the neighbourhood of the fundamental frequency of the soil-structure system. The present study proposes a new method developed for most dynamic soil-structure interaction problems. The key idea is to retain for the frequency-independent impedances values computed for the fundamental frequency of the soil-structure system; thus these values include the dynamic characteristics of the whole soil-structure system and lead to a satisfactory approximation of the exact solution over a wide frequency range. The method is developed here for the horizontal and rocking modes of a structure with a circular base resting on a homogeneous halfspace. Numerical applications are given for a simple linear oscillator in order to make possible a thorough parametric study. The response of some idealized building-foundation systems to harmonic excitation or to a seismic input is next examined in order to illustrate the efficiency of the proposed model.     

Optimal design of SDOF envelope systems for the responses of MDOF dynamic systems

The concept of envelope system for a given dynamic system is proposed in this paper which refers to those systems whose module of transfer function in the whole range of frequency domain is always bigger than that of a given system. This concept opens a new way to study the problems of robust design and modelling for dynamic systems. The condition that an envelope system has to satisfy is rendered as the determination of the positiveness of a real polynomial function and Sturm's sequence method is used to establish an easily implemented criterion for evaluating the positiveness of the polynomial in terms of its coefficients. The optimization for the envelope system is expressed as the minimization of the 2-norm of its transfer function and simplex method is employed to search for the optimal solution. Two dynamic systems are used to illustrate the optimal design for the envelope systems of some of their responses. © 1998 John Wiley & Sons, Ltd.     

Damped vibration mode superposition method for dynamic response analysis

In the dynamic response analysis of extremely complex structural systems in which the damping characteristics of each element are independent, the damping matrix is not always diagonalized by the use of undamped free vibration mode shapes. In the present paper, a mode-superposition method by the use of damped free vibration mode shapes is developed for such structural systems. It is also shown that the Fast Fourier Transform (FFT) procedures, that are available for the dynamic response analysis of linear structural systems, are used effectively in this mode-superposition method with good accuracy.     

地震作用下低层建筑砌体结构的动力特性分析

传统低层建筑砌体结构动力特性分析中,易受到外界环境的干扰,砌体结构的完整性欠缺,导致动力特性分析的准确度较低。为提高低层建筑砌体结构的抗震性能,提出地震作用下低层建筑砌体结构的动力特性分析方法。首先利用低层建筑砌体结构反应自功率谱,完成砌体结构的自振频率辨认;然后通过941B型超低频率测振仪测试自振频率,筛出振动波形中噪声干扰的区域,获取时域波形和频域波形;最后依据时域波形和频域波形塑造低层建筑砌体三维精细化模型,在该模型基础上,通过子空间迭代算法获取低层建筑砌体结构的模拟结果,分析地震作用下芯柱、圈梁等构造措施对建筑砌体结构动力特征的影响,完成砌体结构的动力特性分析。实验结果表明,利用所提方法对地震作用下低层建筑砌体结构的动力特性进行分析,得到的分析结果准确度较高。     

CFRP composite retrofitting effect on the dynamic characteristics of arch dams

The purpose of this study is to investigate the effect of retrofitting dynamic characteristics of a damaged laboratory arch dam model, subsequently repaired with high-strength structural mortar and strengthened with composite carbon fiber reinforced polymer. This study constructed in laboratory conditions is a prototype arch dam–reservoir–foundation model. Five test cases of ambient vibration on the arch dam model illustrate the changes in dynamic characteristics: natural frequency, mode shape, and damping ratio, before and after retrofitting. The ambient vibration tests collected data from the dam body during vibrations by natural excitations which provided small impacts and response signals from sensitivity accelerometers placed at crest points. Enhanced Frequency Domain Decomposition Method in the frequency domain extracts the experimental dynamic characteristics. At the end of the study, experimentally identified dynamic characteristics obtained from all test cases have been compared with each other. Apparently, after the retrofitting, the natural frequencies of the dam body increased considerably, demonstrating that the retrofitting, including repairing and strengthening is very effective on the flashback of initial dynamic characteristics.     

Criterion of stability and implementation issues of hybrid frequency-time-domain procedure for non-linear dynamic analysis

A criterion of stability pertaining to the hybrid frequency-time-domain procedure is derived. It stems from the initial-value theorem on one side and from the condition of convergence which applies to the harmonic counterpart of the procedure on the other side. The criterion depends on the dynamic stiffnesses of both the original non-linear system and the pseudo-linear system evaluated at the Nyquist frequency. Since at this frequency both stiffnesses are usually controlle by the mass, the criterion of stability is satisfied for most structural systems. The procedure must, however, be applie sequentially to individual time segments. The validity of this criterion is confirmed by a numerical investigation performe for a SDOF system. The solution of non-linear dynamic problems requires consideration of implementation issues which are also discusse in the paper. The analysis of a non-linear soil-structure-interaction system in which the soil's stiffness coefficients an directly defined in the frequency domain also demonstrates the accuracy of the hybrid frequency-time-domain procedure.     

地震作用下黄土边坡动力响应的时频特征分析

地震作用下黄土边坡的动力响应特征与变形失稳机制是具有重要理论与实践意义的课题,但从动力响应频谱特性方面开展的研究还相对较少.以大型振动台模型试验获得的黄土边坡地震动峰值加速度数据为基础,通过分析其变化规律,着重从频谱特性的角度分析,讨论黄土边坡的动力失稳机制.进一步通过对坡面不同高程测点、边坡内部垂直方向以及水平方向上测点的加速度时程进行绝对加速度反应谱分析,从频谱变化角度提出黄土边坡的动力失稳机制.研究表明,黄土边坡在地震动作用下的响应过程可以分为三个阶段:弹性阶段、塑性阶段与破坏阶段;黄土边坡进入破坏阶段时均会伴随反应谱峰值的增幅或者主周期的变化,在弹性阶段反应谱加速度峰值增幅与输入地震动幅值增幅一致,进入塑性阶段后反应谱峰值增幅比输入地震动幅值增幅小;研究提出将反应谱首峰的凸显情况作为坡体破坏程度的判断依据之一.     

Dynamic properties analysis of a stay cable-damper system in consideration of design and construction factors

A numerical solution based on the Steffensen stable point iterative method is proposed to resolve the transcendental frequency equation of a stay cable-damper system. The frequency equation, which considers clamped supports and fl exural rigidity of the cable, is intended to investigate the infl uence of the parameters of the cable damper system on its dynamic characteristics. Two factors involved in the design and construction phases, the damping coeffi cient induced by external dampers and the cable tension, are the focus of this study. Their impact on modal frequencies and damping ratios in these two phases of cable-damper systems are investigated by resolving the equation with the proposed solution. It is shown that the damping coeffi cient and cable tension exert more noticeable effects on the modal damping ratios than on the modal frequencies of stay cable-damper systems, and the two factors can serve as design variables in the design phase and as adjustment factors in the construction phase. On the basis of the results, a roadmap for system-level optimal design of stay cable-damper systems that can achieve global optimal vibration suppression for the entire bridge is proposed and discussed.     

Implementation of configuration dependent stiffness proportional damping for the dynamics of rigid multi-block systems

The distinct element method (DEM) has been used successfully for the dynamic analysis of rigid block systems. One of many difficulties associated with DEM is modeling of damping. In this paper, new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid multi-block systems. The stiffness proportional damping is constructed for the prescribed damping ratio, based on the non-zero fundamental frequency effective during the time interval while the boundary conditions remain essentially constant. At this time interval, the fundamental frequency can be estimated without complete eigenvalue analysis. The damping coefficients will vary while the damping ratio remains the same throughout the entire analysis. A new numerical procedure is developed to prevent unnecessary energy loss that can occur during the separation phases. These procedures were implemented in the development of the distinct element method for the dynamic analyses of piled multi-block systems. The analysis results for the single-block and two-block systems were in a good agreement with the analytic predictions. Applications to the seismic analyses of piled fourblock systems revealed that the new procedures can make a significant difference and may lead to much-improved results.     

Dynamic characteristics and seismic response of adjacent buildings linked by discrete dampers

Coupling adjacent buildings using discrete viscoelastic dampers for control of response to low and moderate seismic events is investigated in this paper. The complex modal superposition method is first used to determine dynamic characteristics, mainly modal damping ratio and modal frequency, of damper-linked linear adjacent buildings for practical use. Random seismic response of linear adjacent buildings linked by dampers is then determined by a combination of the complex modal superposition method and the pseudo-excitation method. This combined method can effectively and accurately determine random seismic response of non-classically damped systems in the frequency domain. Parametric studies are finally performed to identify optimal parameters of viscoelastic dampers for achieving the maximum modal damping ratio or the maximum response reduction of adjacent buildings. It is demonstrated that using discrete viscoelastic dampers of proper parameters to link adjacent buildings can reduce random seismic responses significantly. Copyright © 1999 John Wiley & Sons Ltd.     

The specification of wide-band recorders

Working models for signal, path and earth-noise characteristics are developed which collectively define the input expected to a seismic recorder. These are used to elucidate the problems of frequency and dynamic ranges of wide-band recorders designed to record the whole body-wave signal received above earth noise. An optimised recorder characteristic is derived which minimises dynamic range.     

双向地震作用下锯末混合土场地动力特性分析

在北京工业大学振动台台阵系统上开展了一系列锯末混合土地基自由场振动台模型试验,试验中模型箱采用装配式连续体刚性模型箱,试验中输入地震动时程采用El Centro地震动记录、Taft地震动记录和天津地震动记录,地震动输入方向分为水平单向和水平双向。文中,重点考察了双向地震动输入下锯末混合土模型场地的动力特性及其变化规律,主要指标包括模型场地地震动反应的峰值加速度及其动力放大系数、加速度时程及其傅氏谱。试验结果表明:随着输入地震动强度的增大,同一测点反应的峰值加速度总体上在增大,而其加速度动力放大系数总体上呈现减小的趋势,反应的频谱组成从较高频率向较低频率移动;双向地震作用下锯末混合土模型场地的动力变化规律与单向地震作用下较为一致。     

Full frequency-range transient solution for compressional waves in a fluid-saturated viscoacoustic porous medium1

An analytical transient solution is obtained for propagation of compressional waves in a homogeneous porous dissipative medium. The solution, based on a generalization of Biot's poroelastic equations, holds for the low- and high-frequency ranges, and includes viscoelastic phenomena of a very general nature, besides the Biot relaxation mechanism. The viscodynamic operator is used to model the dynamic behaviour associated with the relative motion of the fluid in the pores at all frequency ranges. Viscoelasticity is introduced through the standard linear solid which allows the modelling of a general relaxation spectrum. The solution is used to study the influence of the material properties, such as bulk moduli, porosity, viscosity, permeability and intrinsic attenuation, on the kinematic and dynamic characteristics of the two compressional waves supported by the medium. We also obtain snapshots of the static mode arising from the diffusive behaviour of the slow wave at low frequencies.     

DYNAMIC RESPONSE OF EQUIPMENT IN STRUCTURES WITH SLIDING SUPPORT

The dynamic behaviour of a single degree-of-freedom (DOF) equipment mounted on a sliding primary structures subjected to harmonic and earthquake ground motions is studied numerically. To deal with the discontinuity nature of sliding structural systems, in this work the fictitious spring model is adopted. With the problem formulated in a state space form, an incremental numerical scheme capable of dealing with multi-DOF sliding structural systems is proposed for solving the time history responses. Numerical examples excited by harmonic and real earthquake ground motions are considered in order to study the following three effects: (1)the variation of the frictional coefficient of the sliding support, (2)subharmonic resonance and (3)effect of tuning (i.e. when the frequency of the equipment is coincident with or close to the fundamental frequency of the primary structure) on the mounted equipment. The dynamic characteristics of the mounted equipment are highlighted in the analysis of the numerical examples. © 1997 by John Wiley & Sons, Ltd.     

Centrifugal modelling of dynamic soil-structure interaction

This paper presents a centrifuge model that is capable of realistically representing soil-structure systems subjected to earthquake-like excitation. The model is validated by performing (i) free field soil tests, (ii) dynamic soil-structure interaction tests and (iii) a numerical analysis of the experimental results. The free field experiments show that the simulated earthquake, which is generated by the hammer-exciter plate method, is similar in amplitude and frequency content to a real earthquake. The experiments also demonstrate that a confined soil sample can satisfactorily model a horizontal soil stratum of infinite lateral extent when the containment walls are lined with an absorptive material to attenuate wave reflections that would otherwise occur. Measurements of the acceleration at different locations on the free soil surface indicate that the surface motion is fairly uniform over a relatively large area. This is further confirmed by a comparison made between the measured free and scattered field motions for a surface foundation. Next, a series of soil-structure interaction tests are performed which examine the dependence of radiation damping on the natural frequencies of the structure relative to the fundamental frequency of the soil stratum. The experimental results are shown to be consistent with established theories. Finally, the experimental results are used to compute the stiffness and damping parameters of a two degree of freedom numerical model of the soil-structure system. The experimental parameters are shown to be in good agreement with calssical text book formulae. This study demonstrates that the centrifuge model consistently behaves as expected for simple, but realistic, dynamic soil and soil-structure systems, and can, therefore, be used with confidence to examine more complicated systems that are not yet fully understood.