Seismic drift demands in multi‐storey cross‐laminated timber buildings

This paper investigates the seismic response of multi‐storey cross‐laminated timber (CLT) buildings and its relationship with salient ground‐motion and building characteristics. Attention is given to the effects of earthquake frequency content on the inelastic deformation demands of platform CLT walled structures. The response of a set of 60 CLT buildings of varying number of storeys and panel fragmentation levels representative of a wide range of structural configurations subjected to 1656 real earthquake records is examined. It is shown that, besides salient structural parameters like panel aspect ratio, design behaviour factor, and density of joints, the frequency content of the earthquake action as characterized by its mean period has a paramount importance on the level of nonlinear deformations attained by CLT structures. Moreover, the evolution of drifts as a function of building to ground‐motion periods ratio is different for low‐ and high‐rise buildings. Accordingly, nonlinear regression models are developed for estimating the global and interstorey drifts demands on multi‐storey CLT buildings. Finally, the significance of the results is highlighted with reference to European seismic design procedures and recent assessment proposals.     

Ground motion characteristics of the Chi‐Chi earthquake of 21 September 1999

The purpose of this paper is to investigate the ground motion characteristics of the Chi‐Chi earthquake (21 September 1999) as well as the interpretation of structural damage due to this earthquake. Over 300 strong motion records were collected from the strong motion network of Taiwan for this earthquake. A lot of near‐field ground motion data were collected. They provide valuable information on the study of ground motion characteristics of pulse‐like near‐field ground motions as well as fault displacement. This study includes: attenuation of ground motion both in PGA and spectral amplitude, principal direction, elastic and inelastic response analysis of a SDOF system subjected to near‐field ground motion collected from this event. The distribution of spectral acceleration and spectral velocity along the Chelungpu fault is discussed. Based on the mode decomposition method the intrinsic mode function of ground acceleration of this earthquake is examined. A long‐period wave with large amplitude was observed in most of the near‐source ground acceleration. The seismic demand from the recorded near‐field ground motion is also investigated with an evaluation of seismic design criteria of Taiwan Building Code. Copyright © 2000 John Wiley & Sons, Ltd.     

Dynamic interaction of bridge–train system under non‐uniform seismic ground motion

The probability that an earthquake occurs when a train is running over a bridge in earthquake‐prone regions is much higher than before, for high‐speed railway lines are rapidly developed to connect major cities worldwide. This paper presents a finite element method‐based framework for dynamic analysis of coupled bridge–train systems under non‐uniform seismic ground motion, in which rail–wheel interactions and possible separations between wheels and rails are taken into consideration. The governing equations of motion of the coupled bridge–train system are established in an absolute coordinate system. Without considering the decomposition of seismic responses into pseudo‐static and inertia‐dynamic components, the equations of motion of the coupled system are formed in terms of displacement seismic ground motions. The mode superposition method is applied to the bridge structure to make the problem manageable while the Newmark‐β method with an iterative computation scheme is used to find the best solution for the problem concerned. Eight high‐speed trains running over a multi‐span steel truss‐arch bridge subject to earthquakes are taken as a case study. The results from the case study demonstrate that the spatial variation of seismic ground motion affects dynamic responses of the bridge–train system. The ignorance of pseudo‐static component when using acceleration seismic ground motions as input may underestimate seismic responses of the bridge–train system. The probability of separation between wheels and rails becomes higher with increasing train speed. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic response of a cable‐stayed bridge deck under multi‐component non‐stationary random ground motion

A Markov method of analysis is presented for obtaining the seismic response of cable‐stayed bridges to non‐stationary random ground motion. A uniformly modulated non‐stationary model of the random ground motion is assumed which is specified by the evolutionary r.m.s. ground acceleration. Both vertical and horizontal components of the motion are considered to act simultaneously at the bridge supports. The analysis duly takes into account the angle of incidence of the earthquake, the spatial correlation of ground motion and the quasi‐static excitation. A cable‐stayed bridge is analysed under a set of parametric variations in order to study the non‐stationary response of the bridge. The results of the numerical study indicate that (i) frequency domain spectral analysis with peak r.m.s. acceleration as input could provide more r.m.s. response than the peak r.m.s. response obtained by the non‐stationary analysis; (ii) the longitudinal component of the ground motion significantly influences the vertical vibration of the bridge; and (iii) the angle of incidence of the earthquake has considerable influence on the deck response. Copyright © 2003 John Wiley & Sons, Ltd.     

The effects of repeated earthquake ground motions on the non‐linear response of SDOF systems

In many parts of the world, the repetition of medium–strong intensity earthquake ground motions at brief intervals of time has been observed. The new design philosophies for buildings in seismic areas are based on multi‐level design approaches, which take into account more than a single damageability limit state. According to these approaches, a sequence of seismic actions may produce important consequences on the structural safety. In this paper, the effects of repeated earthquake ground motions on the response of single‐degree‐of‐freedom systems (SDOF) with non‐linear behaviour are analysed. A comparison is performed with the effect of a single seismic event on the originally non‐damaged system for different hysteretic models in terms of pseudo‐acceleration response spectra, behaviour factor q and damage parameters. The elastic–perfect plastic system is the most vulnerable one under repeated earthquake ground motions and is characterized by a strong reduction of the q‐factor. A moment resisting steel frame is analysed as well, showing a reduction of the q‐factor under repeated earthquake ground motions even larger than that of an equivalent SDOF system. Copyright © 2002 John Wiley & Sons, Ltd.     

Evaluation of dynamic eccentricities obtained using a probabilistic approach,response spectrum methods and modern building codes

In this paper a probabilistic approach has been adopted to study both the effects of uncertainty in earthquake frequency content and the correlation between earthquake frequency content and ground motion intensity on the response of a single-storey torsionally coupled elastic structure. The earthquake ground motion has been assumed to be a Gaussian, zero mean, stationary random process which is fully characterized by a power spectrum. The ground acceleration power spectrum is idealized as a probabilistic normalized power spectrum computed from actual earthquake records. The advantage of such an idealization is that it enables the effect of the natural frequency as a controlling structural parameter in torsional coupling to be assessed. Comparisons of the dynamic amplifications of eccentricity with those obtained from modern codes of practice and conventional response spectrum analyses have been made. The results of this study have shown that the variation in the frequency content has a significant effect on the response of low frequency structures, while the correlation between the frequency content and the intensity of seismic ground motion is insignificant for the wide range of structures considered. The structure natural frequency has been shown to be an important controlling parameter in the torsionally coupled response of structures subject to seismic loading. The frequency dependence of the dynamic amplification of eccentricity was found not to be reflected in the response spectrum analysis and the torsional provisions of modern building codes.     

A new approximation for spectral velocity ordinates at short periods

Response spectrum methods in earthquake‐resistant design sometimes require information on the spectral velocity (SV) for a given single‐degree‐of‐freedom oscillator and specified seismic hazard. SV has been conventionally approximated as pseudo spectral velocity (PSV) in the case of lightly damped structures that are not too flexible. This study shows that the PSV approximation may lead to large overestimation errors when the structure is stiffer to the ground motion and the ground motion is a long‐period motion. It is also shown that a new approximation requiring the use of peak ground acceleration of the motion may significantly reduce these errors. Copyright © 2008 John Wiley & Sons, Ltd.     

Constant‐ductility response spectra for sequential earthquake and tsunami loading

Simplified approaches for examining structural system response under sequential earthquake and tsunami loading are helpful for understanding response trends. To aid understanding, nonlinear (constant‐ductility) response spectra are developed for elastoplastic single degree of freedom systems subjected to seismic loads followed by hydrodynamic tsunami loads. The forcing function is composed of long‐duration earthquake motion concatenated with a range of tsunami hydrodynamic forces that are proportional to the pseudo‐spectral acceleration produced by the earthquake motion. The constant‐ductility spectra are thus constructed for scenarios where the loading imposed by one hazard is not dominant over the other. The spectra and basic intensity measures indicate that the amplification of response for sequential earthquake and tsunami loading over the earthquake only case is most significant for systems with long natural periods and high‐ductility capacity under seismic loading. Copyright © 2017 John Wiley & Sons, Ltd.     

地震动强度非平稳特性参数与结构响应之间的近似定量关系分析

本文在对实际地震加速度记录统计分析的基础上,给出了能够合理描述地震动强度非平稳特性的参数及其取值范围;然后引入实验设计方法,建立了适合于地震动强度非平稳特性参数分析的实验设计算法,用来分析地震动强度非平稳特性参数的变化对结构响应的影响;最后通过与近似技术相结合,建立了地震动强度非平稳特性参数与结构响应之间的近似定量关系模型.结果表明,本文提出的实验设计方法适合于对地震动强度非平稳特性参数进行分析,该方法在有效地减小计算量的同时,获得了结构响应与参数变化之间的对应关系.基于实验设计方法进行的特性参数方差分析结果表明:地震动的稳态持时对结构地震响应的影响比较显著;对于周期较小的结构,特性参数之间的交互作用对结构地震响应的影响显著,但当周期大于1 s时,则不显著.本文建立的近似定量关系模型能够较好地反映不同特性参数、不同周期结构动力响应之间的联系,为工程实践中基于结构特性合理设置地震动特性参数、合成或挑选地震加速度时程提供理论依据.      

Multi‐angle,multi‐damage fragility curves for seismic assessment of bridges

The scope of this study is to investigate the effect of the direction of seismic excitation on the fragility of an already constructed, 99‐m‐long, three‐span highway overpass. First, the investigation is performed at a component level, quantifying the sensitivity of local damage modes of individual bridge components (namely, piers, bearings, abutments, and footings) to the direction of earthquake excitation. The global vulnerability at the system level is then assessed for a given angle of incidence of the earthquake ground motion to provide a single‐angle, multi‐damage probabilistic estimate of the bridge overall performance. A multi‐angle, multi‐damage, vulnerability assessment methodology is then followed, assuming uniform distribution for the angle of incidence of seismic waves with respect to the bridge axis. The above three levels of investigation highlight that the directivity of ground motion excitation may have a significant impact on the fragility of the individual bridge components, which shall not be a priori neglected. Most importantly, depending on the assumptions made for the component to the system level transition, this local sensitivity is often suppressed. It may be therefore necessary, based on the ultimate purpose of the vulnerability or the life cycle analysis, to obtain a comprehensive insight on the multiple damage potential of all individual structural and foundation components under multi‐angle excitation, to quantify the statistical correlation among the distinct damage modes and to identify the components that are both most critical and sensitive to the direction of ground motion and carefully define their limit states which control the predicted bridge fragility. Copyright © 2015 John Wiley & Sons, Ltd.     

Stochastic analysis of rigid foundation filtering

The effect of the space–time variation of earthquake ground motion on the translational response of structures supported on large rigid mat foundations is considered. A stochastic space–time ground motion model, based on the analysis of recordings from the SMART-1 seismograph array in Lotung, Taiwan, is used. Random vibration theory is utilized to obtain an expression for the reduction in the maximum structural response, for a specified probability level and strong motion duration. Numerical computations are performed to examine the sensitivity of the reduction in structural response to various ground motion and structural parameters. The results indicate that spatial correlation and travelling wave effects give rise to significant reductions in structural responses when the seismic waves have low apparent propagation velocities. Utilization of this result in the design of structures on large foundations should yield substantial cost savings.     

基于SDOF体系和高层结构的地震动强度指标研究

合理的地震动强度指标是预测和评价结构抗震响应的重要基础。选取24个周期点的单自由度体系和一个高层框架核心筒长周期结构,基于不同震源机制的100条地震动记录时程分析结果,研究16种地震动强度指标与结构地震响应的相关性,并提出考虑高阶振型影响的改进反应谱相关型地震动强度指标。研究表明：（1）不同地震动强度指标与结构地震响应的相关性差别较大,随着单自由度体系自振周期的增大,地震动强度指标与单自由度体系地震响应的相关性大致呈减小的趋势;（2）对于高层长周期结构,综合对比分析各地震动强度指标分别与顶点最大位移、最大基底剪力、最大层间位移的相关性,从工程实用角度出发,推荐地面运动峰值速度为最佳地震动强度指标;（3）由于高层长周期结构受高阶振型影响显著,采用含有高阶振型因素的反应谱强度指标可提高与结构地震响应的相关性。     

Influence of time‐varying frequency content in earthquake ground motions on seismic response of linear elastic systems

Earthquake ground motion records are nonstationary in both amplitude and frequency content. However, the latter nonstationarity is typically neglected mainly for the sake of mathematical simplicity. To study the stochastic effects of the time‐varying frequency content of earthquake ground motions on the seismic response of structural systems, a pair of closely related stochastic ground motion models is adopted here. The first model (referred to as ground motion model I) corresponds to a fully nonstationary stochastic earthquake ground motion model previously developed by the authors. The second model (referred to as ground motion model II) is nonstationary in amplitude only and is derived from the first model. Ground motion models I and II have the same mean‐square function and global frequency content but different features of time variation in the frequency content, in that no time variation of the frequency content exists in ground motion model II. New explicit closed‐form solutions are derived for the response of linear elastic SDOF and MDOF systems subjected to stochastic ground motion model II. New analytical solutions for the evolutionary cross‐correlation and cross‐PSD functions between the ground motion input and the structural response are also derived for linear systems subjected to ground motion model I. Comparative analytical results are presented to quantify the effects of the time‐varying frequency content of earthquake ground motions on the structural response of linear elastic systems. It is found that the time‐varying frequency content in the seismic input can have significant effects on the stochastic properties of system response. Copyright © 2016 John Wiley & Sons, Ltd.     

唐山地区强震动记录的应用研究初探

本文给出了唐山地区强震动记录应用研究的两个实例,提出了建筑结构采用时程分析时选用强震动记录的原则和方法,通过对唐山地区强震动记录的分析处理,得到了其峰值加速度及加速度反应谱,确定了本地区进行弹性时程分析时选用的强震动记录;研究了局部场地条件对地震动影响的唐山响堂三维强震动观测台阵,以唐山响堂台阵2号测井(地下32m)的基岩强震动作为输入,通过2号测井的土层剖面,利用2个一维土层地震反应分析程序,分别计算得到地表的峰值加速度和加速度反应谱,并把计算结果与同次地震相应的地表强震动记录峰值加速度与加速度反应谱进行了对比分析。     

基于小波变换的层间隔震结构地震响应分析

利用小波多分辨率分析将地震动加速度分解为多频段小波分量,并运用复模态方法推导其计算层间隔震体系在地震作用下的动力响应公式,讨论各频段地震信号及结构响应的能量分配。同时利用小波时频工具分析地震动能量在时频域内的分布对层间隔震结构响应的影响,进而为考察地震动非平稳性对层间隔震结构非线性分析的影响提供方法。利用小波分析的以上优势,对一典型层间隔震结构分别进行弹性和弹塑性分析,结果表明弹性体系在地震作用下的响应可由该地震波各小波分量的响应叠加而得,地震动能量在时间上的集中会对层间隔震结构响应产生不利影响。     

空间网格结构多维多点随机地震响应分析的高效算法

将林家浩教授提出的“虚拟激励法”进一步推广应用于空间网格结构多维多点非平稳随机地震响应分析,推导了多维虚拟激励随机振动分析方法的理论公式,给出了峰值响应估计方法,并讨论了多维地震动的随机模型及参数选取,通过编制的专用计算机程序分析了网壳结构的随机地震响应。本方法自动包含了参振振型间及各输人地震分量间的相关项,计算精确、快速,非常适合分析频率密集型空间网格结构的随机地震响应,是一种高效的随机振动分析算法。     

Estimation of hysteretic energy demand using concepts of modal pushover analysis

Hysteretic energy dissipation in a structure during an earthquake is the key factor, besides maximum displacement, related to the amount of damage in it. This energy demand can be accurately computed only through a nonlinear time‐history analysis of the structure subjected to a specific earthquake ground acceleration. However, for multi‐story structures, which are usually modeled as multi‐degree of freedom (MDOF) systems, this analysis becomes computation intensive and time consuming and is not suitable for adopting in seismic design guidelines. An alternative method of estimating hysteretic energy demand on MDOF systems is presented here. The proposed method uses multiple ‘generalized’ or ‘equivalent’ single degree of freedom (ESDOF) systems to estimate hysteretic energy demand on an MDOF system within the context of a ‘modal pushover analysis’. This is a modified version of a previous procedure using a single ESDOF system. Efficiency of the proposed procedure is tested by comparing energy demands based on this method with results from nonlinear dynamic analyses of MDOF systems, as well as estimates based on the previous method, for several ground motion scenarios. Three steel moment frame structures, of 3‐, 9‐, and 20‐story configurations, are selected for this comparison. Bias statistics that show the effectiveness of the proposed method are presented. In addition to being less demanding on the computation time and complexity, the proposed method is also suitable for adopting in design guidelines, as it can use response spectra for hysteretic energy demand estimation. Copyright © 2008 John Wiley & Sons, Ltd.     

Sliding fragility of block‐type non‐structural components. Part 2: Restrained components

This paper focuses on seismic vulnerability assessment of restrained block‐type non‐structural components under sliding response on the basis of seismic inputs specified by current seismic codes. The general representation of restrained equipment considered in this study consists of a rigid block restrained by four post‐tensioned, symmetrically arranged cables. Two sliding‐related failure modes are considered: restraint breakage and excessive absolute acceleration. Fragility analysis is proposed as an appropriate tool to evaluate these failure modes. Sample fragility curves developed through Monte‐Carlo simulations show that the restraint breakage limit state is sensitive to the parameters of the equation of motion. For instance, fragility estimates obtained without taking into account vertical base accelerations can be significantly unconservative for relatively large values of the coefficient of friction. In contrast, the excessive absolute acceleration limit state exhibits little sensitivity to the parameters of the equation of motion. Peak absolute acceleration response is almost always equal to or greater than the horizontal peak base acceleration. Representative results suggest that reasonable response estimates for blocks located at stories other than the ground in multistorey buildings can in general be obtained by simply scaling the ground acceleration to the peak acceleration at the corresponding storey. Copyright © 2002 John Wiley & Sons, Ltd.     

Application of a Monte‐Carlo simulation approach for the probabilistic assessment of seismic hazard for geographically distributed portfolio

The conventional integral approach is very well established in probabilistic seismic hazard assessment (PSHA). However, Monte‐Carlo (MC) simulations can become an efficient and flexible alternative against conventional PSHA when more complicated factors (e.g. spatial correlation of ground shaking) are involved. This study aims at showing the implementation of MC simulation techniques for computing the annual exceedance rates of dynamic ground‐motion intensity measures (GMIMs) (e.g. peak ground acceleration and spectral acceleration). We use multi‐scale random field technique to incorporate spatial correlation and near‐fault directivity while generating MC simulations to assess the probabilistic seismic hazard of dynamic GMIMs. Our approach is capable of producing conditional hazard curves as well. We show various examples to illustrate the potential use of the proposed procedures in the hazard and risk assessment of geographically distributed structural systems. Copyright © 2015 John Wiley & Sons, Ltd.