Kriging metamodeling in seismic risk assessment based on stochastic ground motion models

An efficient computational framework is presented for seismic risk assessment within a modeling approach that utilizes stochastic ground motion models to describe the seismic hazard. The framework is based on the use of a kriging surrogate model (metamodel) to provide an approximate relationship between the structural response and the structural and ground motion parameters that are considered as uncertain. The stochastic character of the excitation is addressed by assuming that under the influence of the white noise (used within the ground motion model) the response follows a lognormal distribution. Once the surrogate model is established, a task that involves the formulation of an initial database to inform the metamodel development, it is then directly used for all response evaluations required to estimate seismic risk. The model prediction error stemming from the metamodel is directly incorporated within the seismic risk quantification and assessment, whereas an adaptive approach is developed to refine the database that informs the metamodel development. The ability to efficiently obtain derivative information through the kriging metamodel and its utility for various tasks within the probabilistic seismic risk assessment is also discussed. As an illustrative example, the assessment of seismic risk for a benchmark four‐story concrete office building is presented. The potential that ground motions include near‐fault characteristics is explicitly addressed within the context of this example. The implementation of the framework for the same structure equipped with fluid viscous dampers is also demonstrated. Copyright © 2015 John Wiley & Sons, Ltd.     

基于强度和能量控制的随机地震动模型

考虑地震动的随机性和频率与强度非平稳性,通过理论分析,提出了一般随机地震动模型,并给出了确定模型参数的原则和方法。该模型以地震动强度、地震动能量以及地震动持时等宏观指标作为控制随机地震动模型参数的指标,而对其内在的频谱组成等指标只要求满足一般地震动的特征。该模型可以用于描述平稳随机过程、强度非平稳随机过程以及强度和频率完全非平稳随机过程。通过与常用功率谱模型的比较,验证了该模型的合理性。     

Structural performance assessment under near‐source pulse‐like ground motions using advanced ground motion intensity measures

This paper demonstrates the effectiveness of utilizing advanced ground motion intensity measures (IMs) to evaluate the seismic performance of a structure subject to near‐source ground motions. Ordinary records are, in addition, utilized to demonstrate the robustness of the advanced IM with respect to record selection and scaling. To perform nonlinear dynamic analyses (NDAs), ground motions need to be selected; as a result, choosing records that are not representative of the site hazard can alter the seismic performance of structures. The median collapse capacity (in terms of IM), for example, can be systematically dictated by including a few aggressive or benign pulse‐like records into the record set used for analyses. In this paper, the elastic‐based IM such as the pseudo‐spectral acceleration (S_a) or a vector of S_a and epsilon has been demonstrated to be deficient to assess the structural responses subject to pulse‐like motions. Using advanced IMs can be, however, more accurate in terms of probabilistic response prediction. Scaling earthquake records using advanced IMs (e.g. inelastic spectral displacement, S_di, and IM _1I&2E; the latter is for the significant higher‐mode contribution structures) subject to ordinary and/or pulse‐like records is efficient, sufficient, and robust relative to record selection and scaling. As a result, detailed record selection is not necessary, and records with virtually any magnitude, distance, epsilon and pulse period can be selected for NDAs. Copyright © 2008 John Wiley & Sons, Ltd.     

Selection and ranking of ground motion models for seismic hazard analysis in the Pyrenees

The issue addressed in this paper is the objective selection of appropriate ground motion models for seismic hazard assessment in the Pyrenees. The method of Scherbaum et al. (2004a) is applied in order to rank eight published ground motion models relevant to intraplate or to low deformation rate contexts. This method is based on a transparent and data-driven process which quantifies the model fit and also measures how well the underlying model assumptions are met. The method is applied to 15 accelerometric records obtained in the Pyrenees for events of local magnitude between 4.8 and 5.1, corresponding to moment magnitudes ranging from 3.7 to 3.9. Only stations at rock sites are considered. A total of 720 spectral amplitudes are used to rank the selected ground motion models. Some control parameters of these models, such as magnitude and distance definitions, may vary from one model to the other. It is thus important to correct the selected models for their difference with respect to the magnitude and distance definitions used for the Pyrenean data. Our analysis shows that, with these corrections, some of the ground motion models successfully fit the data. These are the Lussou et al. (2001) and the Berge-Thierry et al. (2003) models. According to the selected ground motion models, a possible scenario of a magnitude 6 event is proposed; it predicts response spectra accelerations of 0.08–0.1 g at 1 Hz at a hypocentral distance of 10 km.     

Numerical simulation of strong ground motion for the M_s8.0 Wenchuan earthquake of 12 May 2008

The Wenchuan earthquake of 12 May 2008 is the most destructive earthquake in China in the past 30 years in terms of property damage and human losses. In order to understand the earthquake process and the geo-morphological factors affecting the seismic hazard, we simulated the strong ground mo-tion caused by the earthquake, incorporating three-dimensional (3D) earth structure, finite-fault rupture, and realistic surface topography. The simulated ground motions reveal that the fault rupture and basin structure control the overall pattern of the peak ground shaking. Large peak ground velocity (PGV) is distributed in two narrow areas: one with the largest PGV values is above the hanging wall of the fault and attributed to the locations of fault asperities and rupture directivity; the other is along the north-western margin of the Sichuan Basin and caused by both the directivity of fault rupture and the ampli-fication in the thick sediment basin. Rough topography above the rupture fault causes wave scattering, resulting in significantly larger peak ground motion on the apex of topographic relief than in the valley. Topography and scattering also reduce the wave energy in the forward direction of fault rupture but increase the PGV in other parts of the basin. These results suggest the need for a localized hazard as-sessment in places of rough topography that takes the topographic effects into account. Finally, had the earthquake started at the northeast end of the fault zone and ruptured to the southwest, Chengdu would have suffered a much stronger shaking than it experienced on 12 May, 2008.     

Comparing the adequacy of alternative ground motion intensity measures for the estimation of structural responses

Practical methods for the probability‐based seismic assessment of structures make use of estimates of demands produced by earthquakes of different intensities. The uncertainties associated with these estimates are highly dependent on the variable adopted as the intensity measure (IM, e.g., PGA, spectral acceleration, etc.). This generates the need to compare the efficiency of an originally adopted IMwith that of a new candidate. This implies comparing the dispersion of the demand measure (DM, e.g., maximum interstorey drift ratio, ductility demand, etc.) conditional to each of the two IMs. In order to obtain the demand estimates in a conventional way, a full set of dynamic response analyses should be performed for each IM under scrutiny, i.e., multiple records scaled at several fixed values of each IM. The procedure developed here serves to accelerate this comparison avoiding the effort required to evaluate the dynamic responses of the structure for all the ground motion time histories considered every time that a new IM is adopted. For this purpose, use is made of available results of analyses performed for a different (i.e., the original) IM. Two methods are proposed: the direct method involves performing a regression of the results obtained from the original analyses, taking the candidate IM as the independent variable. The indirect method involves rebuilding the probability density function of the DM given a defined value of the candidate IM by means of the total probability theorem, using the results of the original analyses and certain data relating the two IMs. The proposed methods have been tested by application to several SDOF systems with different periods and different cyclic‐response backbone curves. The conditions affecting their approximation are explored, and some criteria to improve them are identified. The procedure can also be used to determine the optimum value of a parameter to be used in a parameter‐based IM. Copyright © 2004 John Wiley & Sons, Ltd.     

面向地震烈度仪的现地地震动预测模型的构建与验证

利用初期P波预警参数构建现地地震动预测模型,使其在达到设定阈值时快速发出报警信息,是现地地震预警系统面临的一个关键问题,直接关系到发布信息的准确性和及时性。针对地震烈度仪基于微机电系统传感器记录到的数据质量较差,通过两次积分获取的位移存在较大偏差,会引起更多的误报和漏报,本文采用不同阶数(1—4阶)的巴特沃斯滤波器,分别构建了基于P波3 s和全P波段数据的位移幅值PD、速度幅值PV和加速度幅值PA与地震动峰值速度PGV和峰值加速度PGA的现地地震动预测模型,然后利用收集到的川滇示范预警网地震事件记录进行验证。结果表明,对于地震烈度仪微机电系统传感器的记录,采用1阶巴特沃斯滤波器处理、基于全P波段波形拟合获取到的PV与PGV的相关性和PA与PGA的相关性为两种最优现地地震动预测模型。具体应用时,应同时利用两种或两种以上的统计关系进行现地地震动预测,并将实际地震动观测值作为额外的判定条件,以降低误报率和漏报率。     

地震动空间变化随机描述及相干函数模型研究进展

本研究主要讨论地震动空间变化的随机描述.首先给出了基于密集地震台阵记录估计相干函数的方法,并对计算中需要关注的问题给出了相应的解释;然后对现有的经验和半经验相干函数模型的建立进行了详细的梳理,并对模型在工程应用中的适用性、有效性和局限性进行了讨论;最后通过对比分析不同相干函数模型对场址地震动空间相关性的模拟结果,对相干函数模型的选择提出了建议.     

Evaluation of the exact conditional spectrum and generalized conditional intensity measure methods for ground motion selection

Two existing, contemporary ground motion selection and modification procedures – (i) exact conditional spectrum (CS‐exact) and (ii) generalized conditional intensity measure (GCIM) – are evaluated in their ability to accurately estimate seismic demand hazard curves (SDHCs) of a given structure at a specified site. The amount of effort involved in implementing these procedures to compute a single SDHC is studied, and a case study is chosen where rigorous benchmark SDHCs can be determined for evaluation purposes. By comparing estimates from ground motion selection and modification procedures with the benchmark, we conclude that estimates from CS‐exact are unbiased in many of the cases considered. The estimates from GCIM are even more accurate, as they are unbiased for most – but not all – of the cases where estimates from CS‐exact are biased. We find that it is possible to obtain biased SDHCs from GCIM, even after employing a very diverse collection of intensity measures to select ground motions and implementing its bias‐checking feature, because it is usually difficult to identify intensity measures that are truly ‘sufficient’ for the response of a complex, multi‐degree‐of‐freedom system. Copyright © 2015 John Wiley & Sons, Ltd.     

Study on simulating strong ground motion by fractal stochastic method

The time history of strong ground motion can be synthesized by empirical Green's function (EGF) method.Firstly a large seismic event is discretized into a series of subevents; secondly recordings of earthquakes with proper size and spatial distribution are chosen as time history (EGF) of those subevents; finally the EGFs are summated to get the time history of ground motion caused by the large event.     

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.     

地震动强度对场地地震反应的影响

通过对场地地震反应的研究发现,地震动强度不同,同样的场地对地震动的影响也不同,得到的反应谱形状也不同。目前我国抗震设计规范中不同烈度下的设计反应谱形状完全一致,没有考虑地震动强弱对相同场地反应谱形状的影响。     

随机有限断层法合成地震动的研究与应用

目前很多研究者采用随机有限断层模型预测地震动并被证明是可行的.本文运用随机有限断层地震动叠加合成方法,模拟了1988年肃南5.7级地震,与实际记录进行对比分析,发现：用有限断层方法模拟得到的峰值加速度以及峰值加速度出现所对应的特征时刻与真实记录较为吻合;比较模拟的地震动反应谱和实际记录的加速度反应谱,总体上在工程感兴趣的频段内,有限断层方法拟合的结果基本能满足实际工作的需要.为进一步开拓该方法在工程应用中的前景,以兰州市柴家峡水电站为例,将此理论方法应用于缺乏强震记录地区的近场地震动估计中,模拟分析了马衔山北缘活动断裂发震时在坝址区产生的地震动特征,其近场合成结果与1125年兰州7.0级地震的烈度分布符合较好,可供工程抗震设计参考使用.     

Analytical investigations of seismic responses for reinforced concrete bridge columns subjected to strong near-fault ground motion

Strong near-fault ground motion, usually caused by the fault-rupture and characterized by a pulse-like velocity- wave form, often causes dramatic instantaneous seismic energy (Jadhav and Jangid 2006). Some reinforced concrete (RC) bridge columns, even those built according to ductile design principles, were damaged in the 1999 Chi-Chi earthquake. Thus, it is very important to evaluate the seismic response of a RC bridge column to improve its seismic design and prevent future damage. Nonlinear time history analysis using step-by-step integration is capable of tracing the dynamic response of a structure during the entire vibration period and is able to accommodate the pulsing wave form. However, the accuracy of the numerical results is very sensitive to the modeling of the nonlinear load-deformation relationship of the structural member. FEMA 273 and ATC-40 provide the modeling parameters for structural nonlinear analyses of RC beams and RC columns. They use three parameters to define the plastic rotation angles and a residual strength ratio to describe the nonlinear load- deformation relationship of an RC member. Structural nonlinear analyses are performed based on these parameters. This method provides a convenient way to obtain the nonlinear seismic responses of RC structures. However, the accuracy of the numerical solutions might be further improved. For this purpose, results from a previous study on modeling of the static pushover analyses for RC bridge columns (Sung et al. 2005) is adopted for the nonlinear time history analysis presented herein to evaluate the structural responses excited by a near-fault ground motion. To ensure the reliability of this approach, the numerical results were compared to experimental results. The results confirm that the proposed approach is valid.     

A ground motion selection procedure for enforcing hazard consistency and estimating seismic demand hazard curves

This paper develops a procedure to select unscaled ground motions for estimating seismic demand hazard curves (SDHCs) in performance‐based earthquake engineering. Currently, SDHCs are estimated from a probabilistic seismic demand analysis, where several ensembles of ground motions are selected and scaled to a user‐specified scalar conditioning intensity measure (IM). In contrast, the procedure developed herein provides a way to select a single ensemble of unscaled ground motions for estimating the SDHC. In the context of unscaled motions, the proposed procedure requires three inputs: (i) database of unscaled ground motions, (ii) I M , the vector of IMs for selecting ground motions, and (iii) sample size, n; in the context of scaled motions, two additional inputs are needed: (i) a maximum acceptable scale factor, SF_max, and (ii) a target fraction of scaled ground motions, γ. Using a recently developed approach for evaluating ground motion selection and modification procedures, the proposed procedure is evaluated for a variety of inputs and is demonstrated to provide accurate estimates of the SDHC when the vector of IMs chosen to select ground motions is sufficient for the response quantity of interest. Copyright © 2015 John Wiley & Sons, Ltd.     

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。     

保定市设计地震动参数的研究

本文根据保定市及周围地区的地震地质环境，在地震危险性分析的基础上，采用等效线性一维波动方程进行土层的地震反应分析。给出50年超越概率63％、10％、2％基岩和地面的水平向峰值加速度、反应谱（场址基本烈度Ⅶ度）和地震影响系数最大值。该结果为抗震设计提供了可靠依据，具有应用价值。