Conditional simulation of spatially variable seismic ground motions based on evolutionary spectra

This paper proposes a computational procedure for the conditional simulation of spatially variable seismic ground motions for long span bridges with multiple supports. The seismic ground motions, with part of their time histories measured at some supports, are regarded as zero‐mean nonstationary random processes characterized by predefined evolutionary power spectral density. To conditionally simulate unknown seismic ground motion time histories at other supports, the Kriging method is first described briefly for the conditional simulation of a random vector comprised of zero‐mean Gaussian variables. The multivariate oscillatory processes characterized by the evolutionary power spectral density matrix are then introduced, and the Fourier coefficients of the oscillatory processes and their covariance matrix are derived. By applying the Kriging method to the random vector of the Fourier coefficients and using the inverse Fourier transform, unknown nonstationary seismic ground motion time histories can be simulated. A numerical example is selected to demonstrate capabilities of the proposed simulation procedure, and the results show that the procedure can ensure unbiased time‐varying correlation functions, especially the cross correlation between known and unknown time histories. The procedure is finally applied to the Tsing Ma suspension bridge in Hong Kong to generate ground accelerations at its multiple supports using limited seismic records. Copyright © 2012 John Wiley & Sons, Ltd.     

Ground-motion prediction equations for the intermediate depth Vrancea (Romania) earthquakes

We present the regional ground-motion prediction equations for peak ground acceleration (PGA), peak ground velocity (PGV), pseudo-spectral acceleration (PSA), and seismic intensity (MSK scale) for the Vrancea intermediate depth earthquakes (SE-Carpathians) and territory of Romania. The prediction equations were constructed using the stochastic technique on the basis of the regional Fourier amplitude spectrum (FAS) source scaling and attenuation models and the generalised site amplification functions. Values of considered ground motion parameters are given as the functions of earthquake magnitude, depth and epicentral distance. The developed ground-motion models were tested and calibrated using the available data from the large Vrancea earthquakes. We suggest to use the presented equations for the rapid estimation of seismic effect after strong earthquakes (Shakemap generation) and seismic hazard assessment, both deterministic and probabilistic approaches.     

华北地区地震危险性分析和地面运动预测的一致性方法

利用华北地区地震活动性资料,建立了地震危险性计算的一致性模型.在此模型的基础上,得出了北京、天津、唐山和济南等7个城市未来2500年内地震的时空强度分布,并计算了2500年回复周期的地震动峰值加速度(PGA).结果表明,唐山和太原的PGA最大(>0.2g),石家庄和北京次之(≈0.17g).对华北地区2500年地震记录的正演计算结果表明,太原和唐山地区的潜在地震危险最有可能来源于震级在6.0～7.0、震中距离在12～15km的地震活动;而北京、天津和石家庄地区则可能来源于震级在5.5～6.0、震中距离在10km左右的地震活动.采用IBC(International Building Code)方法计算后的结果显示,太原、唐山等地区的PGA与2001年我国地震动峰值加速度值基本一致,与此地区的较高地震活动性特征相符.利用随机震源模型,还给出了影响此7个城市的最大地震记录的加速度、速度及位移时程曲线,这对本区工程建筑的抗震性设计以及对救援设施的选址等有重要作用.     

Evolutionary properties of stochastic models of earthquake accelerograms: Their dependence on magnitude and distance

An approach to generate artificial earthquakeaccelerograms on hard soil sites is presented. Eachtime-history of accelerations is considered as arealization of a non-stationary gaussian stochasticprocess, with statistical parameters depending onmagnitude and source-to-site distance. In order tolink the values of these parameters for each groundmotion record with the corresponding magnitude andsource-to-site distance, semi-empirical functionalrelations called generalized attenuationfunctions are determined. The set of realground-motion time histories used to obtain thesefunctions correspond to shocks generated at differentsources and recorded at different sites in thevicinity of the southern coast of Mexico. The resultsshow significant dispersion in the parameters of themodel adopted, which reflect that associated with thereal earthquakes included in the sample employed.The problem of conditional simulation of artificialacceleration time histories for prescribed intensitiesis briefly presented, but its detailed study is leftfor a companion paper. The criteria and modelsproposed are applied to generate two families ofartificial acceleration records for recurrenceintervals of 100 and 200 years at a specific sitelocated in the region under study. The results shownin this article correspond to acceleration timehistories recorded on firm ground for earthquakesgenerated at the subduction zone that runs along thesouthern coast of Mexico, and cannot be generalized tocases of earthquakes generated at other sources orrecorded at other types of local conditions. Thismeans that the methods and functional forms presentedhere are applicable to these other cases, but thevalues of the parameters that characterize thosefunctions may differ from those presented here.     

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.     

基于工程特性的主余震型地震动降维模拟

余震是由主震孕育而来,两者之间存在着一定的关联性,如何构造主余震型地震动模型,是工程结构抗震分析的基础。着眼于地震动的工程特性,根据主余震之间的峰值加速度、强震持时、场地卓越频率等要素,分别建立主震和余震自身的演变功率谱模型,基于非平稳随机过程的谱表示,通过引入随机函数降维模拟方法,实现仅用三个基本随机变量即可精确模拟主余震型地震动过程。研究表明,采用该降维模拟方法的效率和精度均满足工程需求,且与实测主余震型地震动记录的反应谱和幅值谱拟合一致,验证该模型与方法的优越性,为工程结构在主余震型随机地震作用下的抗震分析提供有效途径。     

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.     

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.     

Characteristics of radiation and propagation of seismic waves in the Baikal Rift Zone estimated by simulations of acceleration time histories of the recorded earthquakes

The regularities in the radiation and propagation of seismic waves within the Baikal Rift Zone in Buryatia are studied to estimate the ground motion parameters from the probable future strong earthquakes. The regional parameters of seismic radiation and propagation are estimated by the stochastic simulation (which provides the closest agreement between the calculations and observations) of the acceleration time histories of the earthquakes recorded by the Ulan-Ude seismic station. The acceleration time histories of the strongest earthquakes (M _W ~ 3.4–4.8) that occurred in 2006–2011 at the epicentral distances of ~96–125 km and had source depths of ~8–12 km have been modeled. The calculations are conducted with estimates of the Q-factor which were previously obtained for the region. The frequency-dependent attenuation and geometrical spreading are estimated from the data on the deep structure of the crust and upper mantle (velocity sections) in the Ulan-Ude region, and the parameters determining the wave forms and duration of acceleration time histories are found by fitting. These parameters fairly well describe all the considered earthquakes. The Ulan-Ude station can be considered as the reference bedrock station with minimum local effects. The obtained estimates for the parameters of seismic radiation and propagation can be used for forecasting the ground motion from the future strong earthquakes and for constructing the seismic zoning maps for Buryatia.     

Earthquake motion input and its dissemination via the Internet

Objectives of this task are to conduct research on seismic hazards, and to provide relevant input on the expected levels of these hazards to other tasks. Other tasks requiring this input include those dealing with inventory, fragility curves, rehabilitation strategies and demonstration projects. The corresponding input is provided in various formats depending on the intended use: as peak ground motion parameters and/or response spectral values for a given magnitude, epicentral distance and site conditions; or as time histories for scenario earthquakes that are selected based on the disaggregated seismic hazard mapped by the U.S. Geological Survey and are incorporated in building codes. The user community for this research is both academic researchers and practicing engineers who may use the seismic input generated by the synthesis techniques that are developed under this task for a variety of applications. These include ground motions for scenario earthquakes, for developing fragility curves and in specifying ground motion input for critical facilities (such as hospitals) located in the eastern U.S. Supported in part by the Earthquake Engineering Research Centers Program of the National Science Foundation under Award Number EEC-9701471 to the Multidisciplinary Center for Earthquake Engineering Research.     

Spectral parameters of ground motion in different regions: comparison of empirical models

Fourier-amplitude spectrum is one of the most important parameters describing earthquake ground motion, and it is widely used for strong ground motion prediction and seismic hazard estimation. The relationships between Fourier-acceleration spectra, earthquake magnitude and distance were analysed for different seismic regions (the Caucasus and Taiwan island) on the basis of ground motion recordings of small to moderate (3.5≤M_L≤6.5) earthquakes. It has been found that the acceleration spectra of the most significant part of the records, starting from S-wave arrival, can be modelled accurately by the Brune's “ω-squared” point-source model. Parameters of the model are found to be region-dependent. Peak ground accelerations and response spectra for condition of rock sites were calculated using stochastic simulation technique and obtained models of source spectra. The modelled ground-motion parameters are compared with those predicted by recent empirical attenuation relationship for California.     

A method for generating fully non-stationary and spectrum-compatible ground motion vector processes

Earthquake ground motion spatial variability can influence significantly the response of certain structures. In order to accurately evaluate probabilistic characteristics of the seismic response of structures, the Monte Carlo simulation technique is still the only universal method of analysis when strong nonlinearities and input uncertainties are involved. Consequently, realizations of ground motion time histories taking into account both time and spatial variability need to be generated. Furthermore, for some design applications, the generated time histories must also satisfy the provision imposed by certain seismic codes stating that they have to be also response-spectrum-compatible. For these purposes, a spectral-representation-based methodology for generating fully non-stationary and spectrum-compatible ground motion vector processes at a number of locations on the ground surface is proposed in this paper. The simulated time histories do not require any iterations on the individual generated sample functions so that Gaussianity and prescribed coherence are suitably preserved. The methodology has also the advantage of providing the fully non-stationary and spectrum-compatible cross-spectral density matrix of the ground motion time-histories that can be used for reliability studies in an analytic stochastic fashion.     

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.     

Rating damage potential of ground motion records

In this study, a total of 115,246 ground motions recorded during earthquakes of Moment magnitudes ranging from M_w 5.0 to M_w 9.0 are analyzed statistically. A total of 21 ground motion parameters characterising the recorded acceleration time histories are used in the analysis. Classification of these parameters through statistical correlation is reported and a parameter called "distance from zero-amplitude axis," or d_Z-A, is formulated in the principal component space. The ability for d_Z-A to rate the damage potentials of strong motion records is evaluated through correlation of d_Z-A with Japan Meteorological Agency(JMA) instrumental seismic intensities. This parameter can be used to rate damage potential of any strong motion record irrespective of the magnitude and location of the earthquake. It can also be used in selecting ground motion records of appropriate damage potential in seismic design and probabilistic analysis.     

Ground motion prediction equation considering combined dataset of recorded and simulated ground motions

Himalayan region is one of the most active seismic regions in the world and many researchers have highlighted the possibility of great seismic event in the near future due to seismic gap. Seismic hazard analysis and microzonation of highly populated places in the region are mandatory in a regional scale. Region specific Ground Motion Predictive Equation (GMPE) is an important input in the seismic hazard analysis for macro- and micro-zonation studies. Few GMPEs developed in India are based on the recorded data and are applicable for a particular range of magnitudes and distances. This paper focuses on the development of a new GMPE for the Himalayan region considering both the recorded and simulated earthquakes of moment magnitude 5.3–8.7. The Finite Fault simulation model has been used for the ground motion simulation considering region specific seismotectonic parameters from the past earthquakes and source models. Simulated acceleration time histories and response spectra are compared with available records. In the absence of a large number of recorded data, simulations have been performed at unavailable locations by adopting Apparent Stations concept. Earthquakes recorded up to 2007 have been used for the development of new GMPE and earthquakes records after 2007 are used to validate new GMPE. Proposed GMPE matched very well with recorded data and also with other highly ranked GMPEs developed elsewhere and applicable for the region. Comparison of response spectra also have shown good agreement with recorded earthquake data. Quantitative analysis of residuals for the proposed GMPE and region specific GMPEs to predict Nepal–India 2011 earthquake of Mw of 5.7 records values shows that the proposed GMPE predicts Peak ground acceleration and spectral acceleration for entire distance and period range with lower percent residual when compared to exiting region specific GMPEs.     

地震波双模态时变修正Kanai-Tajimi非平稳随机模型的改进及参数识别

在Vlachos等提出的双模态时变修正Kanai-Tajimi功率谱模型及其参数识别方法的基础上,利用杜修力等提出的Kanai-Tajimi功率谱滤波方法并引进遗传算法及二次优化识别技术进行改进,建立地震动时变功率谱的参数模型化方法。通过集集地震波的时变功率谱模型参数识别及模拟地震动算例,验证改进后的双模态时变修正Kanai-Tajimi功率谱模型的可行性和有效性,其方法可运用到重大工程结构抗震分析的设计地震动输入中。     

随机方法在地震烈度速报中的应用

我国地震监测台网间距大,很难实现大震发生时地震烈度分布图的快速编制.基于随机方法,利用历史小震数据反演地震动估计模型的参数,参考地震发生时获取的少量强震动数据,选取合适的震源参数,正演地震动场的分布.根据地震烈度与地震动参数的经验关系,实现地震烈度速报.本方法可以模拟大震的近断层地震动特征,对高烈度区的判断较目前常用的烈度速报方法更为合理.研究成果既可以用于首张烈度分布图的发布,还能够用于地震烈度的动态修正.     

Seismic reliability assessment of classical columns subjected to near‐fault ground motions

A methodology for the performance‐based seismic risk assessment of classical columns is presented. Despite their apparent instability, classical columns are, in general, earthquake resistant, as proven from the fact that many classical monuments have survived many strong earthquakes over the centuries. Nevertheless, the quantitative assessment of their reliability and the understanding of their dynamic behavior are not easy, because of the fundamental nonlinear character and the sensitivity of their response. In this paper, a seismic risk assessment is performed for a multidrum column using Monte Carlo simulation with synthetic ground motions. The ground motions adopted contain a high‐ and low‐frequency component, combining the stochastic method, and a simple analytical pulse model to simulate the directivity pulse contained in near source ground motions. The deterministic model for the numerical analysis of the system is three‐dimensional and is based on the Discrete Element Method. Fragility curves are produced conditional on magnitude and distance from the fault and also on scalar intensity measures for two engineering demand parameters, one concerning the intensity of the response during the ground shaking and the other the residual deformation of the column. Three performance levels are assigned to each engineering demand parameter. Fragility analysis demonstrated some of the salient features of these spinal systems under near‐fault seismic excitations, as for example, their decreased vulnerability for very strong earthquakes of magnitude 7 or larger. The analysis provides useful results regarding the seismic reliability of classical monuments and decision making during restoration process. Copyright © 2013 John Wiley & Sons, Ltd.