Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios

Probabilistic seismic demand models are a common and often essential step in generating analytical fragility curves for highway bridges. With these probabilistic models being traditionally conditioned on a single seismic intensity measure (IM), the degree of uncertainty in the models is dependent on the IM used. Selection of an optimal IM for conditioning these demand models is not a trivial matter and has been the focus of numerous studies. Unlike previous studies that consider a single structure for IM selection, this study evaluates optimal IMs for use when generating probabilistic seismic demand models for bridge portfolios such as would be found in HAZUS‐MH. Selection criteria such as efficiency, practicality, sufficiency, and hazard computability are considered in the selection process. A case study is performed considering the multi‐span simply supported steel girder bridge class. Probabilistic seismic demand models are generated considering variability in the geometric configurations and material properties, using two suites of ground motions—one synthetic and one recorded motion suite. Results show that of the 10 IMs considered, peak ground acceleration (PGA) and spectral acceleration at the fundamental period are the most optimal for the synthetic motions, and that cumulative absolute velocity is also a close contender when using recorded motions. However, when hazard computability is considered, PGA is selected as the IM of choice. Previous studies have shown that spectrally based quantities perform better than PGA for a given structure, but the findings of this study indicate that when a portfolio of bridges is considered, PGA should be used. Copyright © 2007 John Wiley & Sons, Ltd.     

A framework for the evaluation of ground motion selection and modification procedures

This study develops a framework to evaluate ground motion selection and modification (GMSM) procedures. The context is probabilistic seismic demand analysis, where response history analyses of a given structure, using ground motions determined by a GMSM procedure, are performed in order to estimate the seismic demand hazard curve (SDHC) for the structure at a given site. Currently, a GMSM procedure is evaluated in this context by comparing several resulting estimates of the SDHC, each derived from a different definition of the conditioning intensity measure (IM). Using a simple case study, we demonstrate that conclusions from such an approach are not always definitive; therefore, an alternative approach is desirable. In the alternative proposed herein, all estimates of the SDHC from GMSM procedures are compared against a benchmark SDHC, under a common set of ground motion information. This benchmark SDHC is determined by incorporating a prediction model for the seismic demand into the probabilistic seismic hazard analysis calculations. To develop an understanding of why one GMSM procedure may provide more accurate estimates of the SDHC than another procedure, we identify the role of ‘IM sufficiency’ in the relationship between (i) bias in the SDHC estimate and (ii) ‘hazard consistency’ of the corresponding ground motions obtained from a GMSM procedure. Finally, we provide examples of how misleading conclusions may potentially be obtained from erroneous implementations of the proposed framework. Copyright © 2014 John Wiley & Sons, Ltd.     

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。     

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.     

Ground motion selection for simulation‐based seismic hazard and structural reliability assessment

This paper examines four methods by which ground motions can be selected for dynamic seismic response analyses of engineered systems when the underlying seismic hazard is quantified via ground motion simulation rather than empirical ground motion prediction equations. Even with simulation‐based seismic hazard, a ground motion selection process is still required in order to extract a small number of time series from the much larger set developed as part of the hazard calculation. Four specific methods are presented for ground motion selection from simulation‐based seismic hazard analyses, and pros and cons of each are discussed via a simple and reproducible illustrative example. One of the four methods (method 1 ‘direct analysis’) provides a ‘benchmark’ result (i.e., using all simulated ground motions), enabling the consistency of the other three more efficient selection methods to be addressed. Method 2 (‘stratified sampling’) is a relatively simple way to achieve a significant reduction in the number of ground motions required through selecting subsets of ground motions binned based on an intensity measure, IM. Method 3 (‘simple multiple stripes’) has the benefit of being consistent with conventional seismic assessment practice using as‐recorded ground motions, but both methods 2 and 3 are strongly dependent on the efficiency of the conditioning IM to predict the seismic responses of interest. Method 4 (‘generalized conditional intensity measure‐based selection’) is consistent with ‘advanced’ selection methods used for as‐recorded ground motions and selects subsets of ground motions based on multiple IMs, thus overcoming this limitation in methods 2 and 3. Copyright © 2015 John Wiley & Sons, Ltd.     

Intensity measure conversion of fragility curves

In seismic risk assessment of structures, fragility functions are the probabilistic characterization of vulnerability at the component and/or structural level, expressing the probability of failure as a function of a ground motion intensity measure (IM). Fragility curves, in general, are structure- and site-specific, thus a comparison of fragility curves, then of vulnerability, is not straightforward across multiple structures. Also, it could be the case that hazard at a site of interest is not available for the IM originally considered in the fragility assessment. These situations require to convert fragility curves from an original IM to a target one. The present study addresses a hazard-consistent probabilistic framework for converting spectral acceleration-based IMs from an original IM to a target IM at a given site. In particular, three conversion cases, under different assumptions on the explanatory power of the involved IMs with respect to structural failure, are discussed: (a) a vector-valued IM consisting of the original and target IMs, magnitude, and source-to-site distance; (b) a vector-valued IM consisting of the original and target IMs; and (c) the original (scalar) IM only, assuming that structural response, given the IM, is statistically independent of the other ground motion variables. In this framework, the original fragility functions are characterized using the state-of-the-art methods in performance-based earthquake engineering, then the fragility curves as a function of the target IM are evaluated through applications of the probability calculus rules, ensuring consistency with the seismic hazard at the site of interest. The conversion strategy is illustrated through the applications to three-, six-, and nine-story Italian code-conforming reinforced concrete buildings designed for a high-hazard site in Italy. The study shows that, in most of the cases, the converted fragility curves have agreement with the reference curves directly developed in terms of the target IM. Cases in which least agreement was found are likely due to the models used to obtain the terms required by the conversion equations.     

Conditional spectrum‐based ground motion record selection using average spectral acceleration

The use of a seismic intensity measure (IM) is paramount in decoupling seismic hazard and structural response estimation when assessing the performance of structures. For this to be valid, the IM needs to be sufficient;that is, the engineering demand parameter (EDP) response should be independent of other ground motion characteristics when conditioned on the IM. Whenever non‐trivial dependence is found, such as in the case of the IM being the first‐mode spectral acceleration, ground motion selection must be employed to generate sets of ground motion records that are consistent vis‐à‐vis the hazard conditioned on the IM. Conditional spectrum record selection is such a method for choosing records that are consistent with the site‐dependent spectral shape conditioned on the first‐mode spectral acceleration. Based on a single structural period, however the result may be suboptimal, or insufficient, for EDPs influenced by different period values, for example, peak interstory drifts or peak floor accelerations at different floors, potentially requiring different record suites for each. Recently, the log‐average spectral acceleration over a period range, AvgSA, has emerged as an improved scalar IM for building response estimation whose hazard can be evaluated using existing ground motion prediction equations. Herein, we present a recasting of conditional spectrum record selection that is based on AvgSA over a period range as the conditioning IM. This procedure ensures increased efficiency and sufficiency in simultaneously estimating multiple EDPs by means of a single IM. Copyright © 2017 John Wiley & Sons, Ltd.     

超高层建筑设计地震动参数的研究

本文以沈阳市世纪华丰文化广场工程场地为例,在地震危险性分析的基础上,进行土层地震反应分析,对超高层建筑设计地震动参数的确定进行研究,为抗震设计提供可靠依据。     

Accounting for source location errors in the bayesian analysis of seismicity and seismic hazard

A method is presented for incorporating the uncertainties associated with hypocentral locations in the formulation of probabilistic models of the time and space distributions of the activity of potential seismic sources, as well as of the resulting seismic hazard functions at sites in their vicinity. For this purpose, a bayesian framework of analysis is adopted, where the probabilistic models considered are assumed to have known forms and uncertain parameters, the distribution of the latter being the result of an a priori assessment and its updating through the incorporation of the direct statistical information, including the uncertainty associated with the relations between the actual hypocentral locations and the reported data. This uncertainty is incorporated in the evaluation of the likelihood function of the parameters to be estimated for a given sample of recorded locations. For the purpose of illustration, the method proposed is applied to the modelling of the seismic sources near a site close to the southern coast of Mexico. The results of two alternate algorithms for the incorporation of location uncertainties are compared with those arising from neglecting those uncertainties. One of them makes use of Monte Carlo simulation, while the other is based on a closed-form analytical integration following the introduction of some simplifying assumptions. For the particular case studied, accounting for location uncertainties gives place to significant changes in the probabilistic models of the seismic sources. Deviations of the same order of magnitude can be ascribed to differences in the mathematical and/or numerical tools used in the uncertainty analysis. The resulting variability of the seismic hazard at the site of interest is less pronounced than that affecting the estimates of activity of individual seismic sources.     

Seismic hazard analysis for engineering sites based on the stochastic finite-fault method

Seismic hazard analyses are mainly performed using either deterministic or probabilistic methods. However, there are still some defects in these statistical model-based approaches for regional seismic risk assessment affected by the near-field of large earthquakes. Therefore, we established a deterministic seismic hazard analysis method that can characterize the entire process of ground motion propagation based on stochastic finite-fault simulation, and we chose the site of the Xiluodu dam to demonstrate the method. This method can characterize earthquake source properties more realistically than other methods and consider factors such as the path and site attenuation of seismic waves. It also has high computational efficiency and is convenient for engineering applications. We first analyzed the complexity of seismogenic structures in the Xiluodu dam site area, and then an evaluation system for ground motion parameters that considers various uncertainties is constructed based on a stochastic finite-fault simulation. Finally, we assessed the seismic hazard of the dam site area comprehensively. The proposed method was able to take into account the complexity of the seismogenic structures affecting the dam site and provide multi-level parameter evaluation results corresponding to different risk levels. These results can be used to construct a dam safety assessment system of an earthquake in advance that provides technical support for rapidly and accurately assessing the post-earthquake damage state of a dam, thus determining the influence of an earthquake on dam safety and mitigating the risk of potential secondary disasters.     

Seismic demand sensitivity of reinforced concrete shear‐wall building using FOSM method

The uncertainty in the seismic demand of a structure (referred to as the engineering demand parameter, EDP) needs to be properly characterized in performance‐based earthquake engineering. Uncertainties in the ground motion and in structural properties are responsible for EDP uncertainty. In this study, sensitivity of EDPs to major uncertain variables is investigated using the first‐order second‐moment method for a case study building. This method is shown to be simple and efficient for estimating the sensitivity of seismic demand. The EDP uncertainty induced by each uncertain variable is used to determine which variables are most significant. Results show that the uncertainties in ground motion are more significant for global EDPs, namely peak roof acceleration and displacement, and maximum inter‐storey drift ratio, than those in structural properties. Uncertainty in the intensity measure (IM) of ground motion is the dominant variable for uncertainties in local EDPs such as the curvature demand at critical cross‐sections. Conditional sensitivity of global and local EDPs given IM is also estimated. It is observed that the combined effect of uncertainties in structural properties is more significant than uncertainty in ground motion profile at lower IM levels, while the opposite is true at higher IM levels. Copyright © 2005 John Wiley & Sons, Ltd.     

Sensitivity of PSHA results to ground motion prediction relations and logic-tree weights

Epistemic uncertainty in ground motion prediction relations is recognized as an important factor to be considered in probabilistic seismic hazard analysis (PSHA), together with the aleatory variability that is incorporated directly into the hazard calculations through integration across the log-normal scatter in the ground motion relations. The epistemic uncertainty, which is revealed by the differences in median values of ground motion parameters obtained from relations derived for different regions, is accounted for by the inclusion of two or more ground motion prediction relations in a logic-tree formalism. The sensitivity of the hazard results to the relative weights assigned to the branches of the logic-tree, is explored through hazard analyses for two sites in Europe, in areas of high and moderate seismicity, respectively. The analyses reveal a strong influence of the ground motion models on the results of PSHA, particularly for low annual exceedance frequencies (long return periods) and higher confidence levels. The results also show, however, that as soon as four or more relations are included in the logic-tree, the relative weights, unless strongly biased towards one or two relations, do not significantly affect the hazard. The selection of appropriate prediction relations to include in the analysis, therefore, has a greater impact than the expert judgment applied in assigning relative weights to the branches of the logic-tree.     

Simulation of risk-consistent earthquake motion

A method to combine probabilistic seismic hazard analysis and stochastic earthquake motion models is presented. A set of parameters characterizing stochastic earthquake motion models is determined on a consistent probabilistic basis. The method proposed herein consists of two steps. First, the ground motion intensity is determined in the context of the conventional hazard curve technique. Next, other ground motion parameters such as duration, predominant frequency and spectral shape parameters are determined as conditional means corresponding to the annual probability of exceedance for the ground motion intensity. Some example applications are presented.     

Probabilistic seismic hazard assessment of Italy using kernel estimation methods

A representation of seismic hazard is proposed for Italy based on the zone-free approach developed by Woo (BSSA 86(2):353–362, 1996a), which is based on a kernel estimation method governed by concepts of fractal geometry and self-organized seismicity, not requiring the definition of seismogenic zoning. The purpose is to assess the influence of seismogenic zoning on the results obtained for the probabilistic seismic hazard analysis (PSHA) of Italy using the standard Cornell’s method. The hazard has been estimated for outcropping rock site conditions in terms of maps and uniform hazard spectra for a selected site, with 10 % probability of exceedance in 50 years. Both spectral acceleration and spectral displacement have been considered as ground motion parameters. Differences in the results of PSHA between the two methods are compared and discussed. The analysis shows that, in areas such as Italy, characterized by a reliable earthquake catalog and in which faults are generally not easily identifiable, a zone-free approach can be considered a valuable tool to address epistemic uncertainty within a logic tree framework.     

Vector-valued fragility functions for seismic risk evaluation

This article presents a method for the development of vector-valued fragility functions, which are a function of more than one intensity measure (IM, also known as ground-motion parameters) for use within seismic risk evaluation of buildings. As an example, a simple unreinforced masonry structure is modelled using state-of-the-art software and hundreds of nonlinear time-history analyses are conducted to compute the response of this structure to earthquake loading. Dozens of different IMs (e.g. peak ground acceleration and velocity, response spectral accelerations at various periods, Arias intensity and various duration and number of cycle measures) are considered to characterize the earthquake shaking. It is demonstrated through various statistical techniques (including Receiver Operating Characteristic analysis) that the use of more than one IM leads to a better prediction of the damage state of the building than just a single IM, which is the current practice. In addition, it is shown that the assumption of the lognormal distribution for the derivation of fragility functions leads to more robust functions than logistic, log-logistic or kernel regression. Finally, actual fragility surfaces using two pairs of IMs (one pair are uncorrelated while the other are correlated) are derived and compared to scalar-based fragility curves using only a single IM and a significant reduction in the uncertainty of the predicted damage level is observed. This type of fragility surface would be a key component of future risk evaluations that take account of recent developments in seismic hazard assessment, such as vector-valued probabilistic seismic hazard assessments.     

A critical examination of seismic response uncertainty analysis in earthquake engineering

The last decade of performance‐based earthquake engineering (PBEE) research has seen a rapidly increasing emphasis placed on the explicit quantification of uncertainties. This paper examines uncertainty consideration in input ground‐motion and numerical seismic response analyses as part of PBEE, with particular attention given to the physical consistency and completeness of uncertainty consideration. It is argued that the use of the commonly adopted incremental dynamic analysis leads to a biased representation of the seismic intensity and that when considering the number of ground motions to be used in seismic response analyses, attention should be given to both reducing parameter estimation uncertainty and also limiting ground‐motion selection bias. Research into uncertainties in system‐specific numerical seismic response analysis models to date has been largely restricted to the consideration of ‘low‐level’ constitutive model parameter uncertainties. However, ‘high‐level’ constitutive model and model methodology uncertainties are likely significant and therefore represent a key research area in the coming years. It is also argued that the common omission of high‐level seismic response analysis modelling uncertainties leads to a fallacy that ground‐motion uncertainty is more significant than numerical modelling uncertainty. The author's opinion of the role of uncertainty analysis in PBEE is also presented. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic hazard disaggregation in performance‐based earthquake engineering: occurrence or exceedance?

Seismic hazard disaggregation is commonly used as an aid in ground‐motion selection for the seismic response analysis of structures. This short communication investigates two different approaches to disaggregation related to the exceedance and occurrence of a particular intensity. The impact the different approaches might have on a subsequent structural analysis at a given intensity is explored through the calculation of conditional spectra. It is found that the exceedance approach results in conditional spectra that will be conservative when used as targets for ground‐motion selection. It is however argued that the use of the occurrence disaggregation is more consistent with the objectives of seismic response analyses in the context of performance‐based earthquake engineering. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic demand models for probabilistic risk analysis of near fault vertical ground motion effects on ordinary highway bridges

The influence of vertical ground motions on the seismic response of highway bridges is not very well understood. Recent studies suggest that vertical ground motions can substantially increase force and moment demands on bridge columns and girders and cannot be overlooked in seismic design of bridge structures. For an evaluation of vertical ground motion effects on the response of single‐bent two‐span highway bridges, a systematic study combining the critical engineering demand parameters (EDPs) and ground motion intensity measures (IMs) is required. Results of a parametric study examining a range of highway bridge configurations subjected to selected sets of horizontal and vertical ground motions are used to determine the structural parameters that are significantly amplified by the vertical excitations. The amplification in these parameters is modeled using simple equations that are functions of horizontal and vertical spectral accelerations at the corresponding horizontal and vertical fundamental periods of the bridge. This paper describes the derivation of seismic demand models developed for typical highway overcrossings by incorporating critical EDPs and combined effects of horizontal and vertical ground motion IMs depending on the type of the parameter and the period of the structure. These models may be used individually as risk‐based design tools to determine the probability of exceeding the critical levels of EDP for pre‐determined levels of ground shaking or may be included explicitly in probabilistic seismic risk assessments. Copyright © 2011 John Wiley & Sons, Ltd.     

基于衰减关系的城镇烈度发生概率快速估计

震后快速产出的震动烈度分布是地震应急救援非常有效的依据, 通常由烈度与地震动参数的经验关系给出. 有台站的场点, 地震动参数可以直接由台站数据给出确定性的结果; 而无台站的场点, 地震动参数只能由衰减关系给出估计值. 目前我国台站覆盖有限, 且难于实时获取, 快速生成的地震动参数主要依赖于地震动衰减关系, 再依据烈度与地震动参数的经验关系, 输出确定性的震动烈度分布. 由于衰减关系本身存在着不确定性, 将其估计值用于生成确定性的震动烈度分布是不准确的. 而且实践证明, 震动烈度与实际调查烈度存在差异. 鉴于此, 从衰减关系模型中的ε出发, 提出了场点(城镇)遭遇不同烈度的概率计算方法: 利用衰减关系的估计值与衰减关系的标准差, 构造峰值加速度(PGA)变化的对数正态分布, 然后以烈度分档对应的PGA范围, 计算震区各城镇遭遇不同烈度的概率及各城镇抗震设防烈度被超越的概率. 具体以1966年3月8日河北邢台M_S6.8地震为例, 说明了此方法的可行性, 认为以概率形式给出城镇可能遭遇的烈度在表述上更为合理, 并建议将场点(城镇)遭遇烈度的概率表达方法用于震害快速评估.