A modified method for simulating non-stationary multi-point earthquake ground motion

A spectral-representation-based algorithm is proposed to simulate non-stationary and stochastic processes with evolutionary power,according to a prescribed non-stationary cross-spectral density matrix. Non-stationary multi-point seismic ground motions at different locations on the ground surface are generated for use in engineering applications. First,a modified iterative procedure is used to generate uniformly modulated non-stationary ground motion time histories which are compatible with the prescribed power spectrum. Then,ground motion time histories are modeled as a non-stationary stochastic process with amplitude and frequency modulation. The characteristic frequency and damping ratio of the Clough-Penzien acceleration spectrum are considered as a function of time in order to study the frequency time variation. Finally,two numerical examples are presented to validate the efficiency of the proposed method,and the results show that this method can be effectively applied to the dynamic seismic analysis of long and large scale structures.     

A procedure for simulating synthetic accelerograms compatible with correlated and conditional probabilistic response spectra

The modeling of seismic load is a major topic that has to be addressed thoroughly in the framework of performance based seismic analysis and design. In this paper, a simple procedure for simulating artificial earthquake accelerograms matching the statistical distribution of response spectra, as given by median ground motion prediction equations, the standard deviation and correlation coefficients, is proposed. The approach follows the general ideas of the (natural) ground motion selection algorithms proposed by Baker [4] and Wang [43] but using simulated (artificial) “spectrum-compatible” accelerograms. This allows to simulate spectrum-compatible accelerograms featuring variability similar to the one of recorded accelerograms when the match of median and ±1 standard-deviation response spectra is imposed by the regulator. The procedure is illustrated by an application to the NGA ground motion data and models.     

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.      

非平稳空间相关多点地震动合成方法研究

根据地震波的传播特点,在现有的非平稳空间相关多点地震动合成方法的基础上进行了改进。通过修正随机相位角,使生成的多点地震动在局部场地上具有收敛性。给出了未知和已知相位差谱统计规律2种情况下非平稳多点地震动的合成方法。进一步提出了基于实际地震纪录的空间相关多点地震动合成方法。这些方法可用于大尺度结构的多点输入分析。     

Enrichment of seismic ground motion databases using Karhunen–Loève expansion

Best estimate seismic analysis are generally based on time‐domain simulations of structural responses. The seismic load is then modeled by a stochastic process representing ground motion. For this purpose, the analyst can use recorded accelerograms or work with synthetically generated ones. The number of ground motion time‐histories available for a given scenario and site condition is limited and generally not sufficient for carrying out more advanced probabilistic structural response analysis. It is then necessary to have at our disposal methods that allow for generating synthetic accelerograms that realistically characterize earthquake ground motions. However, most of the methods proposed in literature for generating synthetic accelerograms do not accurately reproduce the natural variability of ground motion parameters (such as PGA, cumulative absolute velocity, and Arias intensity) observed for recorded time histories. In this paper, we introduce a new method for generating synthetic ground motion, based on Karhunen‐Loève decomposition and a non‐Gaussian stochastic model. The proposed method enables the structural analyst to simulate ground motion time histories featuring the properties mentioned above. To demonstrate its capability, we study the influence of the simulation method on different ground motion parameters and on soil response spectra. We finally compute fragility curves to illustrate the practical application of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Simulation of artificial random field considering the temporal-spatial variation

Introduction For the seismic design of special structures such as nuclear power station, marine platform, long-span bridge and dam, generally the time-history response analysis of the structure under seismic excitation is imperative, which was coded in most seismic design codes. The earthquake records suitable for the seismic situation and site condition are necessary to be used as the seismic input in the dynamic analysis of structures. As a result of the limited observational condition of st…     

基于希尔伯特变换的非平稳地震动模拟方法的验证

基于希尔伯特变换的非平稳地震动模拟方法能够生成一系列地震动样本,具有与给定天然地震动相似的非平稳特征. 该方法在模拟天然地震动时域波形的形态和能量的时频分布方面,效果非常显著且已得到验证. 本文以理想单自由度体系弹塑性地震反应为基础,深入验证该方法在模拟天然地震动对结构影响效应方面的效果. 研究结果表明,该方法能够较好地模拟天然地震动的工程特性,其生成的地震动样本的峰值特性及其引起的结构弹塑性地震响应具有与天然地震动相似的特征.      

Influence of irregular topography and random soil properties on coherency loss of spatial seismic ground motions

Coherency functions are used to describe the spatial variation of seismic ground motions at multiple supports of long span structures. Many coherency function models have been proposed based on theoretical derivation or measured spatial ground motion time histories at dense seismographic arrays. Most of them are suitable for modelling spatial ground motions on flat‐lying alluvial sites. It has been found that these coherency functions are not appropriate for modelling spatial variations of ground motions at sites with irregular topography (Struct. Saf. 1991; 10 (1):1–13). This paper investigates the influence of layered irregular sites and random soil properties on coherency functions of spatial ground motions on ground surface. Ground motion time histories at different locations on ground surface of the irregular site are generated based on the combined spectral representation method and one‐dimensional wave propagation theory. Random soil properties, including shear modulus, density and damping ratio of each layer, are assumed to follow normal distributions, and are modelled by the independent one‐dimensional random fields in the vertical direction. Monte‐Carlo simulations are employed to model the effect of random variations of soil properties on the simulated surface ground motion time histories. The coherency function is estimated from the simulated ground motion time histories. Numerical examples are presented to illustrate the proposed method. Numerical results show that coherency function directly relates to the spectral ratio of two local sites, and the influence of randomly varying soil properties at a canyon site on coherency functions of spatial surface ground motions cannot be neglected. Copyright © 2010 John Wiley & Sons, Ltd.     

空间相关的多点地震动合成(Ⅱ)合成实例

本文应用已提出的自功率谱、相干函数、视速度模型生成了空间相关的多点地震动时程。采用分段合成、乘强度包络函数的方法近似地考虑了地震动强度和频率尬发的非平稳性、生成的地震动符合空间相关性、传播性、随机性和非平稳性,可用于长结构多点输入地震反应分析。     

基于非平稳随机地震动模型的重力坝抗震可靠度分析

基于正交展开的非平稳随机地震动模型,并考虑混凝土材料的非线性和坝体与库水之间的流固耦合,对印度Koyna重力坝进行有限元分析,得到坝顶水平位移和坝颈拉应力,结合概率密度演化方法和等价极值事件的思想,获得丰富的概率信息。这为坝体结构的随机地震反应分析和可靠度研究提供新的途径。     

Random vibration analysis of long-span structures subjected to spatially varying ground motions

On the basis of the pseudo-excitation method (PEM), a random vibration methodology is formulated for the seismic analysis of multi-supported structures subjected to spatially varying ground motions. The ground motion spatial variability consists of the wave passage, incoherence and site–response effects. Advantages of this method are that less computation effort is required and that the cross-correlations both between normal modes and between excitations are automatically included. Random seismic responses of a realistic long-span bridge due to the wave passage, incoherence and site–response effects are extensively investigated. It is shown that all these effects have significant influence on the seismic response of the structure.     

Physically compliant,conditionally simulated spatially variable seismic ground motions for performance‐based design

The performance‐based design of lifeline systems requires spatially variable seismic excitations at the structures' supports that are consistent with prescribed seismic ground motion characteristics and an appropriate spatial variability model—such motions can be obtained through conditional simulation. This work revisits the concept of conditional simulation and critically examines the conformity of the generated motions with the characteristics of the target random field and observations from data recorded at dense instrument arrays. Baseline adjustment processing techniques for recorded earthquake accelerograms are extended to fit the requirements of simulated and conditionally simulated spatially variable ground motions. Emphasis is placed on the use of causal vs acausal filtering in the data processing. Acceleration, velocity and displacement time histories are evaluated in two example applications of the approach. The first application deals with a prescribed synthetic time history that incorporates nonstationarity in the amplitude and frequency content of the motions and depends on earthquake magnitude, source–site distance and local soil conditions; this example results in zero residual displacements. The second application considers as prescribed time history a recording in the vicinity of a fault and yields nonzero residual displacements. It is shown that the conditionally simulated time histories preserve the characteristics of the prescribed ones and are consistent with the target random field. The results of this analysis suggest that the presented methodology provides a useful tool for the generation of spatially variable ground motions to be used in the performance‐based design of lifeline systems. Copyright © 2006 John Wiley & Sons, Ltd.     

A new energy-based ground motion selection and modification method limiting the dynamic response dispersion and preserving the median demand

A novel ground motion selection and modifications method to perform response history analysis of structures is presented in this paper. Currently, the accessibility of ground motion information permits the analysis of structures using real ground motion data. Predicting the dynamic behavior of structures is a primary objective; therefore, the selection of a set of ground motions that shows a reduction in the variability of the structural response and accuracy in preserving the median demand is a challenging task. The new selection and scaling procedure emerges from comparing a set of horizontal ground motions at various ranges of frequency. In this study, the conditional mean spectrum and the design response spectrum are used as target spectra, and the records that give an applicable and compelling contribution to the hazard are considered. It is possible to obtain a set of ground motions with similar seismic severity by matching the target spectrum at the period of interest T _ref , where the scaled spectrum should have an equivalent Housner intensity in the period range 0.2T _ref –2T _ref . The horizontal components for every band of frequency is obtained using a specific index that depends on the energy-frequency trend’s shape as well as on its scattering degree around the mean value. This allows obtaining a set of spectrum-compatible records with almost identical severity and low dispersion of the structural response parameters. The methodology has been tested showing a significant effectiveness in terms of low variability of parameters and accuracy in preserving the median demand for a given hazard scenario.     

Analyzing the effect of moving resonance on seismic response of structures using wavelet transforms

There is a complex interaction between the seismic response (i.e., peak displacements) of a nonlinear structure and the characteristics of a ground motion. One ground motion characteristic that contributes to record‐to‐record variability is spectral nonstationarity, or the variation of signal's frequency content with time. When the predominant natural periods of a nonlinear structure elongate in such a way as to match with the predominant frequency content in the ground motion, a phenomenon called moving resonance occurs. The effect of moving resonance on the response of nonlinear structures is investigated. Continuous complex wavelet transforms are used to examine the spectral nonstationarity of ground motion acceleration histories and associated structural displacement histories to identify the occurrences of moving resonance. A three‐dimensional displacement response spectrum is used to determine which combinations of initial period and strength create the largest displacements and thus are candidate configurations for experiencing moving resonance. A method is then proposed for quantifying the effect of moving resonance on structural response. The method utilizes discrete wavelet transforms to decompose a ground motion into component signals with limited frequency band and examines the structural response due to each individual component. A discussion is provided as to how these tools can be used to identify ground motion characteristics that may be conducive to moving resonance. Copyright © 2013 John Wiley & Sons, Ltd.     

地震动空间效应对大跨度桥梁非线性地震响应的影响

由于大跨度桥梁的桥墩间距离较大,其地震响应分析应考虑地震动输入的空间效应。本文建立了多点激励下大跨度桥梁地震响应分析方法,采用损伤塑性本构模型模拟混凝土材料特性,考虑地震动空间效应对大跨度连续刚构桥进行非线性地震响应分析,从而分析地震动空间效应对大跨度桥梁地震响应的影响。研究表明:考虑行波激励或多点激励时桥梁地震响应较一致激励而言有所差异,考虑地震动空间效应时可能会夸大或减小桥梁结构的动力响应;多点激励时桥梁地震响应会随视波速的改变而变化。由此得出结论,对于大跨度桥梁地震响应分析应合理的考虑地震动空间效应。     

拟合加密控制点反应谱的地震动时程合成

在传统地震动反应谱频域拟合方法的基础上,提出了拟合加密控制点目标反应谱的地震动合成方法,并在此基础上利用实际算例与传统方法进行了对比.本文方法在每次迭代调整过程中均考虑了对地震动加速度强度包络函数的模拟,并且对调整后的地震动进行了基线校正,从而确保最终合成的地震动时程既能以一定精度拟合加密目标反应谱,又能满足目标包络函数的要求,同时保证积分所得位移曲线不产生基线漂移.数值算例分析结果表明,本文方法与传统非加密控制点目标谱拟合方法相比,在地震动时程曲线合成、反应谱拟合精度以及收敛速度等方面均具有一定的优势.      

Scenario-Based Seismic Risk Analysis: An Engineering Approach to the Development of Source and Site-Specific Ground Motion Time Histories in Areas of Low Seismicity

Modern engineering design methods require ground motion time histories as input for non-linear dynamic structural analysis. Non-linear dynamic methods of analysis are increasingly applied in the context of probabilistic risk assessments and for cost-effective design of critical infrastructures. In current engineering practice artificial time histories matching deterministic design spectra or probabilistic uniform hazard spectra are most frequently used for engineering analysis. The intermediate step of generation of response spectra can lead to a biased estimate of the potential damage from earthquakes because of insufficient consideration of the true energy content and strong motion duration of earthquakes. Thus, assessment of seismic risk may seem unrealistic. An engineering approach to the development of three-component ground motion time histories has been established which enables consideration of the typical characteristics of seismic sources, regional ground motion attenuation, and the main geotechnical characteristics of the target site. Therefore, the approach is suitable for use in scenario-based risk analysis a larger number of time histories are required for representation of the seismic hazard. Near-field effects are implemented in the stochastic source model using engineering approximations. The approach is suggested for use in areas of low seismicity where ground motion records of larger earthquakes are not available. Uncertainty analysis indicates that ground motions generated by individual earthquakes are well constrained and that the usual lognormal model is not the best choice for predicting the upper tail of the distribution of the ground motions.     

Response spectrum analysis of structures subjected to spatially varying motions

An important aspect of earthquake loads exerted on extended structures, or structures founded on several foundations, is the spatial variability of the seismic motion. Hence, a rigorous earthquake resistant design of lifeline structures should account for the spatial character of the seismic input, at least in an approximate way. A procedure is proposed which enables addressing the problem of multiply supported structures, subjected to imperfectly correlated seismic excitations, by means of an extension to the response spectrum method. A modified response spectrum model is developed for the design of extended facilities subjected to single and multicomponent ground motion. The modification procedure is based on adjusting each spectral value of the given design response spectrum by means of a correction factor, which depends on the structural properties and on the characteristics of the wave propagation phenomenon. Finally, the theoretical model is validated through digital simulation of seismic ground motion, whereby model predictions are found to be in good agreement with exact results.     

Inelastic dynamic analysis of RC bridges accounting for spatial variability of ground motion,site effects and soil–structure interaction phenomena. Part 2: Parametric study

The methodology for dealing with spatial variability of ground motion, site effects and soil–structure interaction phenomena in the context of inelastic dynamic analysis of bridge structures, and the associated analytical tools established and validated in a companion paper are used herein for a detailed parametric analysis, aiming to evaluate the importance of the above effects in seismic design. For a total of 20 bridge structures differing in terms of structural type (fundamental period, symmetry, regularity, abutment conditions, pier‐to‐deck connections), dimensions (span and overall length), and ground motion characteristics (earthquake frequency content and direction of excitation), the dynamic response corresponding to nine levels of increasing analysis complexity was calculated and compared with the ‘standard’ case of a fixed base, uniformly excited, elastic structure for which site effects were totally ignored. It is concluded that the dynamic response of RC bridges is indeed strongly affected by the coupling of the above phenomena that may adversely affect displacements and/or action effects under certain circumstances. Evidence is also presented that some bridge types are relatively more sensitive to the above phenomena, hence a more refined analysis approach should be considered in their case. Copyright @ 2003 John Wiley & Sons, Ltd.     

Inelastic dynamic analysis of RC bridges accounting for spatial variability of ground motion,site effects and soil–structure interaction phenomena. Part 1: Methodology and analytical tools

During strong ground motion it is expected that extended structures (such as bridges) are subjected to excitation that varies along their longitudinal axis in terms of arrival time, amplitude and frequency content, a fact primarily attributed to the wave passage effect, the loss of coherency and the role of local site conditions. Furthermore, the foundation interacts with the soil and the superstructure, thus significantly affecting the dynamic response of the bridge. A general methodology is therefore set up and implemented into a computer code for deriving sets of appropriately modified time histories and spring–dashpot coefficients at each support of a bridge with account for spatial variability, local site conditions and soil–foundation–superstructure interaction, for the purposes of inelastic dynamic analysis of RC bridges. In order to validate the methodology and code developed, each stage of the proposed procedure is verified using recorded data, finite‐element analyses, alternative computer programs, previous research studies, and closed‐form solutions wherever available. The results establish an adequate degree of confidence in the use of the proposed methodology and code in further parametric analyses and seismic design. Copyright © 2003 John Wiley & Sons, Ltd.