Periodic response of a rigid block resting on a footing subjected to harmonic excitation

This study presents the dynamic behaviour of a rigid block which rests on a footing supported by a spring and a dashpot on a rigid base. The response of the rigid body is examined carefully when the base is excited by a harmonic force. It is found that a periodic motion appears in three different modes: stick-stick, stick-slip and slip-slip. The conditions that initiate the stick-stick and slip-slip modes are derived in explicit forms and the maximum sliding displacement is also obtained analytically. Useful dimensionless parameters are proposed for the presentation of the dynamic behaviour. The accuracy of results is confirmed by the response history computed by the Nigam-Jennings method.     

Neural network analysis of overturning response under near-fault type excitation

Under strong seismic excitation, a rigid block will uplift from its support and undergo rocking oscillations which may lead to （complete） overturning. Numerical and analytical solutions to this highly nonlinear vibration problem are first highlighted in the paper and then utilized to demonstrate how sensitive the overturning behavior is not only to the intensity and frequency content of the base motion, but also to thc presence of strong pulses, to their detailed sequence, and even to their asymnletry. Five idealised pulses capable of representing ＂rupture-directivity＂ and ＂fling＂ affected ground motions near the fault, are utilized to this end ： the one-cycle sinus, the one-cycle cosinus, the Ricker wavelet, the truncated （T）-Ricker wavelet, and the rectangular pulse ＂Overturning-Acceleration Amplification＂ and ＂Rotation＂ spectra are introduced and presented. Artificial neural network modeling is then developed as an alternative numerical solution. The neural network analysis leads to closed-form expressions for predicting the overturning failure or survival of a rigid block, as a function of its geometric properties and the characteristics of the excitation time history. The capability of the developed neural network modeling is validated through comparisons with the numerical solution. The derived analytical expressions could also serve as a tool for assessing the destructiveness of near-fault ground motions, for structures sensitive to rocking with foundation uplift.     

特殊长周期地震动的参数特征研究

近断层脉冲型地震动和远场软土层场地类谐和地震动是两类特殊的长周期地震动,当前的规范均很少对这两类地震作用进行具体的规定。研究了近断层脉冲型和远场类谐和地震动的幅值、幅值比（V／A,D／V）、傅里叶幅值谱和反应谱的差别,分析了相位角和作用循环周期数对简单脉冲的影响,并用于解释两类特殊地震动的工程特征。以集集地震动为数据基础,分析了两类长周期地震动的傅里叶谱和反应谱特征;将平均加速度和位移规准反应谱分别与规范设计谱进行了比较。建议设计谱在长周期段考虑近断层作用和软土场地面波效应的影响。     

A new spatial coherence model and analytical coefficients for multi-support response spectrum combination

In this paper, a new spatial coherence model of seismic ground motions is proposed by a fi tting procedure. The analytical expressions of modal combination (correlation) coeffi cients of structural response are developed for multi-support seismic excitations. The coeffi cients from both the numerical integration and analytical solutions are compared to verify the accuracy of the solutions. It is shown that the analytical expressions of numerical modal combination coeffi cients are of high accuracy. The results of random responses of an example bridge show that the analytical modal combination coeff icients developed in this paper are accurate enough to meet the requirements needed in practice. In addition, the computational effi ciency of the analytical solutions of the modal combination coeff icients is demonstrated by the response computation of the example bridge. It is found that the time required for the structural response analysis by using the analytical modal combination coeffi cients is less than 1/20 of that using numerical integral methods.     

海域地震动研究现状分析

海域地震动是海洋工程建设必须考虑的因素,近年来学者们对海域地震动做了大量研究,这些研究涵盖海域地震动的各方面。为总结对海域地震动特性的研究成果并分析存在的问题,分类阐述了不同学者对海域地震的研究结果。根据采用的研究方法可分为解析方法、数值模拟方法和统计方法。在此基础上,归纳了不同研究方法得出的海域地震动场地影响与传播规律的结论:解析方法与数值方法得出的结论侧重于分析海域地震动受海水、淤泥沉积层与地形等场地条件的影响;统计方法得出的结论集中在海域地震动与陆地地震动在地震动特性与传播规律方面的差异,这些结论可以为采用相同方法的研究提供参考。最后,对当前研究中存在的问题进行探讨,由于数据相对匮乏,导致缺少对海域地震动与陆域地震动差异的定量分析,也缺少对海域地震动不确定性的分析。     

Experimental and theoretical simulations of seismic poundings between two adjacent structures

Shaking table tests have been carried out to investigate the pounding phenomenon between two steel towers of different natural frequencies and damping ratios, subject to different combinations of stand‐off distance and seismic excitations. Both harmonic waves and ground motions of the 1940 El Centro earthquake are used as input. Subjected to sinusoidal excitations, poundings between the two towers could appear as either periodic or chaotic. For periodic poundings, impact normally occurs once within each excitation cycle or within every other excitation cycle. A type of periodic group poundings was also observed for the first time (i.e. a group of non‐periodic poundings repeating themselves periodically). Chaotic motions develop when the difference of the natural frequency of the two towers become larger. Under sinusoidal excitations, the maximum relative impact velocity always develops at an excitation frequency between the natural frequencies of the two towers. Both analytical and numerical predictions of the relative impact velocity, the maximum stand‐off distance, and the excitation frequency range for pounding occurrences were made and found to be comparable with the experimental observations in most of the cases. The stand‐off distance attains a maximum when the excitation frequency is close to that of the more flexible tower. Pounding appears to amplify the response of the stiffer structure but suppress that of the more flexible structure; and this agrees qualitatively with previous shaking table tests and theoretical studies. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic analysis of structures with a fractional derivative model of viscoelastic dampers

Viscoelastic dampers are now among some of the preferred energy dissipation devices used for passive seismic response control. To evaluate the performance of structures installed with viscoelastic dampers, different analytical models have been used to characterize their dynamic force deformation characteristics. The fractional derivative models have received favorable attention as they can capture the frequency dependence of the material stiffness and damping properties observed in the tests very well. However, accurate analytical procedures are needed to calculate the response of structures with such damper models. This paper presents a modal analysis approach, similar to that used for the analysis of linear systems, for solving the equations of motion with fractional derivative terms for arbitrary forcing functions such as those caused by earthquake induced ground motions. The uncoupled modal equations still have fractional derivatives, but can be solved by numerical or analytical procedures. Both numerical and analytical procedures are formulated. These procedures are then used to calculate the dynamic response of a multi-degree of freedom shear beam structure excited by ground motions. Numerical results demonstrating the response reducing effect of viscoelastic dampers are also presented.     

Response of rigid body assemblies to dynamic excitation

Shaking table tests were conducted to investigate the response of rectangular wooden blocks and block assemblies of various sizes and slenderness to harmonic and earthquake base excitation. The shaking tests were followed by an analytical and a numerical study of response of single blocks and block assemblies. The analytical study was aimed at establishing criteria for the initiation of rocking and of overturning in response to harmonic base motion and consisted of solving numerically the differential equations of motion of a rigid block on a rigid foundation. The numerical study, in the course of which the response of both single blocks and block assemblies was examined, was implemented by means of the Distinct Element Method (DEM). Prior to the DE simulation of actual shaking tests, preliminary analyses were conducted to confirm numerical stability and to evaluate material and damping parameters. Comparing the recorded time histories with those given by the analytical study and the DE simulation, good agreement was found. The distinct element model in use appeared to follow the highly non-linear motion of rigid body assemblies faithfully to reality. On the basis of the results, provided that the necessary parameters are carefully estimated, the employed DE model can be regarded as an appropriate tool to simulate response of rigid body assemblies to dynamic base excitation.     

基于分解方法的脉冲型地震动非弹性反应谱分析

本文旨在分析脉冲型地震动中不同频率的地震动分量对于原始地震动幅值及其非弹性反应谱的影响.首先以近期12次大地震的53条典型脉冲型地震动为数据基础,基于多尺度分解方法获取脉冲型地震动中的高频分量和低频分量.为与传统方法对比,本文获取了能够表征地震动脉冲特性的卓越分量及滤除卓越分量的剩余分量.然后对比分析原始地震动和4种地震动分量的幅值特征和非弹性反应谱的特性,以讨论地震动分量对原始地震动幅值参数及其非弹性反应谱的影响.最后结合简谐地震动模型和地震动分量的性质,讨论脉冲型地震动非弹性反应谱诸多特征的产生原因.分析发现,低频分量不仅是控制脉冲型地震动速度和位移幅值的主要因素,其对原始地震动的加速度幅值也具有不可忽略的影响.低频分量也是导致脉冲型地震动非弹性位移比谱偏大以及强度折减系数谱偏小的直接原因,从而造成结构在脉冲型地震动作用下需要具有更大的非弹性位移以及更高的强度需求.     

Semi-analytical techniques for the determination of the dynamic response of equipment in structures supported on coulomb friction elements

Techniques for the analysis of equipment in structures supported on a Coulomb friction type support that is subjected to harmonic and earthquake ground motion are presented. The behaviour is governed by two phases—a sliding phase and a non-sliding phase. Since the behaviour in each of the phases is linear, an analytical expression for equipment response can be obtained in terms of the roots of an appropriate characteristic polynomial. The times of phase transition are determined by an iterative scheme. The methodology is accurate, less computationally intensive, and avoids the difficulties that can be encountered with standard numerical integration techniques for highly non-linear systems.     

Effects of near-fault and far-fault ground motions on nonlinear dynamic response and seismic damage of concrete gravity dams

As the forward directivity and fling effect characteristics of the near-fault ground motions, seismic response of structures in the near field of a rupturing fault can be significantly different from those observed in the far field. The unique characteristics of the near-fault ground motions can cause considerable damage during an earthquake. This paper presents results of a study aimed at evaluating the near-fault and far-fault ground motion effects on nonlinear dynamic response and seismic damage of concrete gravity dams including dam-reservoir-foundation interaction. For this purpose, 10 as-recorded earthquake records which display ground motions with an apparent velocity pulse are selected to represent the near-fault ground motion characteristics. The earthquake ground motions recorded at the same site from other events that the epicenter far away from the site are employed as the far-fault ground motions. The Koyna gravity dam, which is selected as a numerical application, is subjected to a set of as-recorded near-fault and far-fault strong ground motion records. The Concrete Damaged Plasticity (CDP) model including the strain hardening or softening behavior is employed in nonlinear analysis. Nonlinear dynamic response and seismic damage analyses of the selected concrete dam subjected to both near-fault and far-fault ground motions are performed. Both local and global damage indices are established as the response parameters. The results obtained from the analyses of the dam subjected to each fault effect are compared with each other. It is seen from the analysis results that the near-fault ground motions, which have significant influence on the dynamic response of dam–reservoir–foundation systems, have the potential to cause more severe damage to the dam body than far-fault ground motions.     

Analytical earthquake response of 1D hybrid base isolation systems

The work presents several dynamic analyses of an actual base isolation system previously identified by using a non-linear 1D model and full scale free vibration tests. After a short introduction to the building and the base isolation system considered, reference is made to previous studies where the model used was developed. The analytical model, originally derived for free vibration analyses and system identification applications, is extended in the present paper to earthquake response simulations. First a theoretical harmonic ground motion is considered, in order to identify resonance conditions for the system and stress how these should be avoided in actual design, by carefully studying the seismological and site conditions. The response of the system to a nearly harmonic natural ground motion is then predicted. Next the performance of the system under several significant ground motions from the Friuli 1976, Irpinia 1980 and L'Aquila 2009 earthquakes is considered, and the reasons for its satisfactory or unsatisfactory behaviour are pointed out and explained. Means for correcting unsatisfactory performances are also suggested and discussed. The behaviour of the system under near fault records from the L'Aquila 2009 earthquake is then considered, the conditions leading to the maximum demands are highlighted and the reasons behind them are clearly explained. Finally the 1D model presented is used to predict the 2D response to 2D ground motions.     

Dynamic displacements and stresses in the vicinity of a cylindrical cavity embedded in a half-space

The two-dimensional response of a viscoelastic half-space containing a buried, unlined, infinitely long cylindrical cavity of circular cross-section subjected to harmonic plane SH, P, SV and Rayleigh waves is obtained by an indirect boundary integral method based on the two-dimensional Green's functions for a viscoelastic half-space. An extensive critical review of the existing numerical results obtained by other techniques is presented together with some new numerical results describing the motion on the ground surface and the motion and stresses on the wall of the cavity for P, SV, SH and Rayleigh waves.     

TRANSFER FUNCTIONS FOR RIGID RECTANGULAR FOUNDATIONS

Closed-form expressions and comprehensive numerical solutions are presented for the transfer functions of surface-supported, rigid, rectangular foundations excited by horizontally polarized, incoherent shear waves for which the motions are parallel to one of the foundation sides. The free-field ground motion is specified stochastically in terms of a local power spectral density function and an orthotropic incoherence function which decays exponentially with the square of the excitation frequency and the separation distance. The response quantities examined include the lateral and torsional components of the foundation motion. Displayed graphically, the results elucidate the effects and relative importance of the numerous parameters involved. For vertically incident incoherent wave fields, the lateral transfer function of a rectangular foundation is related to that of a judiciously selected square foundation, and the interrelationship of the results is examined. © 1997 by John Wiley & Sons, Ltd.     

3-D shell analysis of cylindrical underground structures under seismic shear (S) wave action

The 3-D shell theory is employed in order to provide a new perspective to earthquake-induced strains in long cylindrical underground structures, when soil-structure interaction can be ignored. In this way, it is possible to derive analytical expressions for the distribution along the cross-section of axial, hoop and shear strains and also proceed to their consistent superposition in order to obtain the corresponding principal and von Mises strains. The resulting analytical solutions are verified against the results of 3-D dynamic FEM analyses. Seismic design strains are consequently established after optimization of the analytical solutions against the random angles which define the direction of wave propagation relative to the longitudinal structure axis, the direction of particle motion and the location on the structure cross-section. The basic approach is demonstrated herein for harmonic shear (S) waves with plane front, propagating in a homogeneous half-space or in a two layer profile, where soft soil overlays the bedrock.     

A numerical approach for modeling near-fault ground motion and its application in the 1994 Northridge earthquake

An approach for simulating near-fault ground motion was presented by combining the finite fault model with a numerical algorithm, named investigated lump method presented in this paper for wave propagation. The investigated lumps are constructed from the auxiliary quadrilateral grids. The dynamic equilibrium equations of a typical investigated lump have been derived and obtained by integrating the stresses along the contour of the investigated lump. The stresses are calculated using the constitutive relations and the interpolation techniques. The investigated lump method is then implemented using the equilibrium equations of investigated lumps and the calculations of stresses alternately in time domain. The stability criterion of the algorithm has been given. Comparisons with the discrete wave-number method solutions for predicting the ground motions at the Pacoima Dam during the San Fernando earthquake show the validity of the method presented in this paper for simulating near-field ground motions. A finite fault source model has been implemented in the algorithm here. The source parameters given by Wald et al. (1996) [18] are applied to synthesize the ground motions at three stations during the 1994 Northridge earthquake. The simulating results qualitatively match to the corresponding ground motion records. The studies demonstrated that the approach presented in this paper is an effective tool for the numerical simulation of near-fault ground motion.     

Analytical solution for vertical site response analysis and its validation

Existing studies for site response analysis in geotechnical earthquake engineering have widely concentrated on the horizontal component of the ground motion. However, strong vertical ground motions have been repeatedly observed, resulting in significant vertical compression damage of engineering structures. Furthermore, for the seismic design of critical structures(e.g. large-scale dams and nuclear power plants), the ground motions in all three directions should be considered. Therefore, there is a need to investigate the site response subjected to the vertical component of the ground motion, especially for the seismic design of critical structures. Consequently, in this study, a numerical program for vertical site response analysis is proposed based on the commonly used analytical transfer function method. The proposed program is then validated against well-documented case studies obtained from the Japanese KiK-net(Kiban Kyoshin network) downhole array monitoring system. Results show that the response spectra at the ground surface are well predicted in the low frequency range(5 Hz), while discrepancies are observed in the high frequency range. However, the high frequency discrepancies do not significantly affect the overall prediction accuracy, as the overall seismic response of geotechnical structures are usually dominated by low frequency vibrations. Furthermore, the limitations in the analysis are also discussed.     

含峭壁V形峡谷对地震SH波散射的解析解

地表地形常引起地震动的局部放大,这是由于地震波传播至局部地形时产生了散射现象.本文利用波函数展开方法和区域匹配技术,提出了含峭壁V形峡谷对平面SH波散射问题的解析解,并进行了退化验证.通过频域内的参数分析,揭示了峭壁深度、入射波频率和角度等因素对峡谷场地地面运动的影响规律,发现上部峭壁会增强峡谷对地震动的地形放大效应....     

面向设计应用的地震动空间相干函数模型

本文对现有的常用地震动空间相干模型进行了总结,提出了一个新的面向工程抗震设计应用的形式统一的地震动空间相干函数模型,在此基础上推导出了多点地震反应谱和功率谱计算所需要的振型组合系数的解析表达式,避免了耗费时间的数值积分运算。本文模型与计算方法使多点地震激励下结构响应的计算时间减低至积分方法的1/20以下,使多点地震反应谱方法和多点地震功率谱方法在计算时间方面实用化。     

Is rocking motion predictable?

An argument of engineers and researchers against the use of rocking as a seismic response modification technique is that the rocking motion of a structure is chaotic and the existing models are incapable of predicting it well. This argument is supported by the documented inability of rocking models to predict the motion of a specimen excited by a single ground motion. A statistical comparison of the experimental and the numerical responses of a rigid rocking oscillator not to a specific ground motion, but to ensembles of ground motions that have the same statistical properties, is presented. It is shown that the simple analytical model proposed by Housner in 1963 is capable of predicting the statistics of seismic response of a rigid rocking oscillator.