Modification of stochastic ground motion models for matching target intensity measures

Stochastic ground motion models produce synthetic time‐histories by modulating a white noise sequence through functions that address spectral and temporal properties of the excitation. The resultant ground motions can be then used in simulation‐based seismic risk assessment applications. This is established by relating the parameters of the aforementioned functions to earthquake and site characteristics through predictive relationships. An important concern related to the use of these models is the fact that through current approaches in selecting these predictive relationships, compatibility to the seismic hazard is not guaranteed. This work offers a computationally efficient framework for the modification of stochastic ground motion models to match target intensity measures (IMs) for a specific site and structure of interest. This is set as an optimization problem with a dual objective. The first objective minimizes the discrepancy between the target IMs and the predictions established through the stochastic ground motion model for a chosen earthquake scenario. The second objective constraints the deviation from the model characteristics suggested by existing predictive relationships, guaranteeing that the resultant ground motions not only match the target IMs but are also compatible with regional trends. A framework leveraging kriging surrogate modeling is formulated for performing the resultant multi‐objective optimization, and different computational aspects related to this optimization are discussed in detail. The illustrative implementation shows that the proposed framework can provide ground motions with high compatibility to target IMs with small only deviation from existing predictive relationships and discusses approaches for selecting a final compromise between these two competing objectives.     

Multi‐objective risk‐informed design of floor isolation systems

The design of floor isolation systems (FISs) for the protection of acceleration sensitive contents is examined considering multiple objectives, all quantified in terms of the probabilistic system performance. The competing objectives considered correspond to (i) maximization of the level of protection offered to the sensitive content (acceleration reduction) and (ii) minimization of the demand for the isolator displacement capacity and, more importantly, for the appropriate clearance to avoid collisions with surrounding objects (floor displacement reduction). Both of these objectives are probabilistically characterized utilizing a versatile, simulation‐based framework for quantifying seismic risk, addressing all important uncertainties related to the seismic hazard and the structural model. FIS performance is assessed through time‐history analysis, allowing for all important sources of nonlinearity to be directly addressed in the design framework. The seismic hazard is described through a stochastic ground motion model. For efficiently performing the multi‐objective optimization, an augmented surrogate modeling methodology is established, considering development of a single metamodel with respect to both the uncertain model parameters and the design variables for the FIS system. This surrogate model is then utilized to simultaneously support the probabilistic risk assessment and the design optimization to provide the Pareto front of dominant designs. Each of these designs establishes a different compromise between the considered risk‐related objectives offering a variety of potential options to the designer. Within the illustrative example, the efficiency of the established framework is exploited to compare three different FIS implementations, whereas the impact of structural uncertainties on the optimal design is also evaluated. Copyright © 2016 John Wiley & Sons, Ltd.     

Global sensitivity analysis for stochastic ground motion modeling in seismic-risk assessment

Seismic risk assessment requires adoption of appropriate models for the earthquake hazard, the structural system and for its performance, and quantification of the uncertainties involved in these models through appropriate probability distributions. Characterization of the seismic hazard comprises undoubtedly the most critical component of this process, the one associated with the largest amount of uncertainty. For applications involving dynamic analysis this hazard is frequently characterized through stochastic ground motion models. This paper discusses a novel, global sensitivity analysis for the seismic risk with emphasis on such a stochastic ground motion modeling. This analysis aims to identify the overall (i.e. global) importance of each of the uncertain model parameters, or of groups of them, towards the total risk. The methodology is based on definition of an auxiliary density (distribution) function, proportional to the integrand of the integral quantifying seismic risk, and on comparison of this density to the initial probability distribution for the model parameters of interest. Uncertainty in the rest of the model parameters is explicitly addressed through integration of their joint auxiliary distribution to calculate the corresponding marginal distributions. The relative information entropy is used to quantify the difference between the compared density functions and an efficient approach based on stochastic sampling is introduced for estimating this entropy for all quantities of interest. The framework is illustrated in an example that adopts a source-based stochastic ground motion model, and valuable insight is provided for its implementation within structural engineering applications.     

A simulation‐based framework for risk assessment and probabilistic sensitivity analysis of base‐isolated structures

A versatile, simulation‐based framework for risk assessment and probabilistic sensitivity analysis of base‐isolated structures is discussed in this work. A probabilistic foundation is used to address the various sources of uncertainties, either excitation or structural, and to characterize seismic risk. This risk is given, in this stochastic setting, by some statistics of the system response over the adopted probability models and stochastic simulation is implemented for its evaluation. An efficient, sampling‐based approach is also introduced for establishing a probabilistic sensitivity analysis to identify the importance of each of the uncertain model parameters in affecting the overall risk. This framework facilitates use of complex models for the structural system and the excitation. The adopted structural model explicitly addresses nonlinear characteristics of the isolators and of any supplemental dampers, and the effect of seismic pounding of the base to the surrounding retaining walls. An efficient stochastic ground motion model is also discussed for characterizing future near‐fault ground motions and relating them to the seismic hazard for the structural site. An illustrative example is presented that emphasizes the results from the novel probabilistic sensitivity analysis and their dependence on seismic pounding occurrences and on addition of supplemental dampers. Copyright © 2011 John Wiley & Sons, Ltd.     

A framework for validation of seismic response analyses using seismometer array recordings

A framework for the validation of computational models used to predict seismic response based on observations from seismometer arrays is presented. The framework explicitly accounts for the epistemic uncertainty related to the unknown characteristics of the ‘site’ (i.e. the problem under consideration) and constitutive model parameters. A mathematical framework which makes use of multiple prediction–observation pairs is used to improve the statistical significance of inferences regarding the accuracy and precision of the computational methodology and constitutive model. The benefits of such a formal validation framework include: (i) development of consistent methods for determination of constitutive model parameters; (ii) rigorous, objective, and unbiased assessment of the validity of various constitutive models and computational methodologies for various problem types and ground motion intensities; and (iii) an improved understanding of the uncertainties in computational model assumptions, constitutive models and their parameters, relative to other seismic response uncertainties such as ground motion variability. Details regarding the implementation of such a framework to achieve the aforementioned benefits are also addressed.     

Earthquake ground motion modeling of induced seismicity in the Groningen gas field

A physics‐based numerical approach is used to characterize earthquake ground motion due to induced seismicity in the Groningen gas field and to improve empirical ground motion models for seismic hazard and risk assessment. To this end, a large‐scale (20 km × 20 km) heterogeneous 3D seismic wave propagation model for the Groningen area is constructed, based on the significant bulk of available geological, geophysical, geotechnical, and seismological data. Results of physics‐based numerical simulations are validated against the ground motion recordings of the January 8, 2018, M_L 3.4 Zeerijp earthquake. Taking advantage of suitable models of slip time functions at the seismic source and of the detailed geophysical model, the numerical simulations are found to reproduce accurately the observed features of ground motions at epicentral distances less than 10 km, in a broad frequency range, up to about 8 Hz. A sensitivity analysis is also addressed to discuss the impact of 3D underground geological features, the stochastic variability of seismic velocities and the frequency dependence of the quality factor. Amongst others, results point out some key features related to 3D seismic wave propagation, such as the magnitude and distance dependence of site amplification functions, that may be relevant to the improvement of the empirical models for earthquake ground motion prediction.     

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.     

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.     

基于条件均值反应谱的特大地震强震记录的选取及调整方法

在PEER地震动数据库(PGMD)的基础上, 结合近几年国内外特大地震的地面运动记录, 建立了地面运动数据库, 同时根据日本M_W9.0特大地震获得的141组记录进行统计回归建立加速度反应谱衰减关系, 并采用条件均值反应谱法, 即设定地震与结构概率需求结合的方法选择地面运动. 选波实例表明, 当设定地震为特大地震时, 基于条件均值反应谱法选取地面运动记录时, 扩展数据库中大震记录并建立符合大震记录加速度反应谱的衰减关系是十分必要与迫切的. 该思路为进一步研究结构动态时程分析中地面运动记录选取问题及所选记录提供了依据.      

Efficient sampling and data reduction techniques for probabilistic seismic lifeline risk assessment

Probabilistic seismic risk assessment for spatially distributed lifelines is less straightforward than for individual structures. While procedures such as the ‘PEER framework’ have been developed for risk assessment of individual structures, these are not easily applicable to distributed lifeline systems, due to difficulties in describing ground‐motion intensity (e.g. spectral acceleration) over a region (in contrast to ground‐motion intensity at a single site, which is easily quantified using Probabilistic Seismic Hazard Analysis), and since the link between the ground‐motion intensities and lifeline performance is usually not available in closed form. As a result, Monte Carlo simulation (MCS) and its variants are well suited for characterizing ground motions and computing resulting losses to lifelines. This paper proposes a simulation‐based framework for developing a small but stochastically representative catalog of earthquake ground‐motion intensity maps that can be used for lifeline risk assessment. In this framework, Importance Sampling is used to preferentially sample ‘important’ ground‐motion intensity maps, and K‐Means Clustering is used to identify and combine redundant maps in order to obtain a small catalog. The effects of sampling and clustering are accounted for through a weighting on each remaining map, so that the resulting catalog is still a probabilistically correct representation. The feasibility of the proposed simulation framework is illustrated by using it to assess the seismic risk of a simplified model of the San Francisco Bay Area transportation network. A catalog of just 150 intensity maps is generated to represent hazard at 1038 sites from 10 regional fault segments causing earthquakes with magnitudes between five and eight. The risk estimates obtained using these maps are consistent with those obtained using conventional MCS utilizing many orders of magnitudes more ground‐motion intensity maps. Therefore, the proposed technique can be used to drastically reduce the computational expense of a simulation‐based risk assessment, without compromising the accuracy of the risk estimates. This will facilitate computationally intensive risk analysis of systems such as transportation networks. Finally, the study shows that the uncertainties in the ground‐motion intensities and the spatial correlations between ground‐motion intensities at various sites must be modeled in order to obtain unbiased estimates of lifeline risk. Copyright © 2010 John Wiley & Sons, Ltd.     

全非平稳地震作用的结构随机反应与可靠度分析

在平稳地震动过程的Clough-Penzien功率谱基础上,采用林家浩非均匀调制函数建立全非平稳地震动过程的演变功率谱。根据我国现行的《建筑抗震设计规范》进行全非平稳地震动演变功率谱的参数识别研究。应用非平稳随机过程模拟的谱表示-随机函数方法,生成建筑结构抗震设计所用地震动的代表性样本集合。通过代表性样本集合的二阶统计值及地震反应谱与目标值的拟合比较,验证本文方法的有效性。最后结合概率密度演化方法,进行以层间位移角为控制准则的结构随机地震反应分析与抗震可靠度计算。     

Effect of travelling waves on stochastic seismic response and dynamic reliability of a long-span bridge on soft soil

It is generally known that the variability of earthquake ground motion is mainly in time and space. To investigate the impact of this variability on the seismic performance of a long-span flexible structure, we discuss the seismic dynamic responses of a real bridge subjected to stochastic seismic ground motion. We incorporate the effect of wave passage by means of the method of probability density evolution based on dynamic time-history analysis from the perspective of stochastic dynamics. First, we introduce the theory of probability density evolution and a category of stochastic seismic model. We then conduct a series of deterministic seismic dynamic analyses of the bridge to establish the probability density equation. Eventually, we obtain the probability information at the level of the probability density function of the seismic response by solving the probability-density evolution equation. The results show that the impact of travelling waves on a long-span structure is related to the characteristics of the earthquake ground motion and the structure, and that travelling waves increase the variability of the seismic response.     

Generation of critical stochastic earthquakes

A stochastic critical excitation is defined as that excitation with a given variance that maximizes the variance in the dynamic response of a system. A non-stationary filtered shot noise is used to develop a stochastic critical excitation model of an earthquake ground motion process, and the response statistics for a linear system are determined in both time and frequency domains. The sensitivity of response to several assumed earthquake pulse arrival rate functions is examined. Responses to recorded strong ground motion and to stochastic critical excitations with the same total energy are compared to assess the degree of conservatism in the procedure. An application of the procedure to seismic qualification of equipment is presented.     

基于城市抗震弹塑性分析的我国主要城市建筑地震风险评估

全国尺度的城市建筑地震风险评估对城市防震减灾工作有着重要意义。本文根据全国人口普查和城市统计年鉴等给出的宏观指标建立城市建筑数据库,通过GEAR1方法(Global earthquake activity rate model 1)和第五代中国地震动参数区划图给出具体场地的地面运动强度,通过地面坡度与剪切波速的对应关系确定的场地类别来考虑地震动输入,采用城市抗震弹塑性分析方法建立建筑分析模型,通过地震经济损失风险指标和建筑严重破坏和倒塌风险作为风险评价指标,给出中国大陆主要城市建筑地震风险分布图。结果分析表明,本文方法可以基于可公开获取的数据预测全国不同城市的建筑震害风险;根据第五代地震动参数区划图给出的地面强度,地震经济损失高风险区主要是设防加速度0.3g以上地区;考虑城市人口、GDP因素后,中、东部城市因人口和财富密度较高,建筑地震风险增加明显;不同地震动选波对经济损失风险影响较小,而对倒塌风险影响较大。本文分析方法可以为城市建筑地震风险分析提供相关参考。     

地震动竖向分量对铁路房屋的地震响应性能影响

为了提高铁路房屋的抗震能力,分析地震动竖向分量对铁路房屋的地震响应性能,提出基于荷载—变形关系联合评估的地震动竖向分量对铁路房屋的地震响应评估模型。构建地震动竖向分量的力学响应评估模型,识别铁路房屋的地震屈服响应参数,采用荷载—变形关系和极限荷载结合的方法进行铁路房屋的地震屈服响应应力评估,分析地震动竖向分量对铁路房屋的响应。建立动量平衡方程和弯矩平衡方程,构建铁路房屋的地震响应的三阶段荷载—变形模式,实现地震动竖向分量对铁路房屋的地震响应性能评估模型的优化设计。测试结果表明,采用该模型能有效分析地震动竖向分量对铁路房屋的地震响应性能影响,Simulink仿真结果和有限元模拟结果的准确性较高,力学参数辨识性能优越,计算结果准确可靠。     

Life-cycle based design of mass dampers for the Chilean region and its application for the evaluation of the effectiveness of tuned liquid dampers with floating roof

The assessment of the effectiveness of mass dampers for the Chilean region within a multi-objective decision framework utilizing life-cycle performance criteria is considered in this paper. The implementation of this framework focuses here on the evaluation of the potential as a cost-effective protection device of a recently proposed liquid damper, called tuned liquid damper with floating roof (TLD-FR). The TLD-FR maintains the advantages of traditional tuned liquid dampers (TLDs), i.e. low cost, easy tuning, alternative use of water, while establishing a linear and generally more robust/predictable damper behavior (than TLDs) through the introduction of a floating roof. At the same time it suffers (like all other liquid dampers) from the fact that only a portion of the total mass contributes directly to the vibration suppression, reducing its potential effectiveness when compared to traditional tuned mass dampers. A life-cycle design approach is investigated here for assessing the compromise between these two features, i.e. reduced initial cost but also reduced effectiveness (and therefore higher cost from seismic losses), when evaluating the potential for TLD-FRs for the Chilean region. Leveraging the linear behavior of the TLD-FR a simple parameterization of the equations of motion is established, enabling the formulation of a design framework that beyond TLDs-FR is common for other type of linear mass dampers, something that supports a seamless comparison to them. This framework relies on a probabilistic characterization of the uncertainties impacting the seismic performance. Quantification of this performance through time-history analysis is considered and the seismic hazard is described by a stochastic ground motion model that is calibrated to offer hazard-compatibility with ground motion prediction equations available for Chile. Two different criteria related to life-cycle performance are utilized in the design optimization, in an effort to support a comprehensive comparison between the examined devices. The first one, representing overall direct benefits, is the total life-cycle cost of the system, composed of the upfront device cost and the anticipated seismic losses over the lifetime of the structure. The second criterion, incorporating risk-averse concepts into the decision making, is related to consequences (repair cost) with a specific probability of exceedance over the lifetime of the structure. A multi-objective optimization is established and stochastic simulation is used to estimate all required risk measures. As an illustrative example, the performance of different mass dampers placed on a 21-story building in the Santiago area is examined.