Introduction of conditional mean spectrum and conditional spectrum in the practice of seismic safety evaluation in China

This paper aims at implementing and introducing the use of conditional mean spectrum (CMS) and conditional spectrum (CS) as the main input parameters in the practice of seismic safety evaluation (SSE) in China, instead of the currently used uniform hazard spectrum (UHS). For this purpose, a procedure for M-R-epsilon seismic hazard deaggregation in China was first developed. For illustration purposes, two different typical sites in China, with one to two dominant seismic zones, were considered as examples to carry out seismic hazard deaggregation and illustrate the construction of CMS/CS. Two types of correlation coefficients were used to generate CMS and the results were compared over a vibration period range of interest. Ground motion records were selected from the NSMONS (2007–2015) and PEER NGA-West2 databases to correspond to the target CMS and CS. Hazard consistency of the spectral accelerations of the selected ground motion records was evaluated and validated by computing the annual exceedance probability rate of the response spectra and comparing the results to the hazard curve corresponding to each site of concern at different periods. The tools developed in this work and their illustrative application to specific case studies in China are a first step towards the adoption of CMS and CS into the practice of seismic safety evaluation in this country.     

Conditional spectrum‐based ground motion selection. Part II: Intensity‐based assessments and evaluation of alternative target spectra

In a companion paper, an overview and problem definition was presented for ground motion selection on the basis of the conditional spectrum (CS), to perform risk‐based assessments (which estimate the annual rate of exceeding a specified structural response amplitude) for a 20‐story reinforced concrete frame structure. Here, the methodology is repeated for intensity‐based assessments (which estimate structural response for ground motions with a specified intensity level) to determine the effect of conditioning period. Additionally, intensity‐based and risk‐based assessments are evaluated for two other possible target spectra, specifically the uniform hazard spectrum (UHS) and the conditional mean spectrum (CMS, without variability).It is demonstrated for the structure considered that the choice of conditioning period in the CS can substantially impact structural response estimates in an intensity‐based assessment. When used for intensity‐based assessments, the UHS typically results in equal or higher median estimates of structural response than the CS; the CMS results in similar median estimates of structural response compared with the CS but exhibits lower dispersion because of the omission of variability. The choice of target spectrum is then evaluated for risk‐based assessments, showing that the UHS results in overestimation of structural response hazard, whereas the CMS results in underestimation. Additional analyses are completed for other structures to confirm the generality of the conclusions here. These findings have potentially important implications both for the intensity‐based seismic assessments using the CS in future building codes and the risk‐based seismic assessments typically used in performance‐based earthquake engineering applications. Copyright © 2013 John Wiley & Sons, Ltd.     

Correlation in spectral accelerations for earthquakes in Europe

The shape of a uniform hazard spectrum has been criticized to be unrealistic for a site where the spectral ordinates of the uniform hazard spectrum at different periods are governed by different scenario events and conservative for long‐return‐period earthquake shaking. The conditional mean spectrum considering epsilon (CMS‐ε) takes into account the correlation of spectral demands (represented by values of ε) at different periods, to address these issues. This paper proposes new prediction models for the correlation coefficient of ε(T₁) and ε(T₂), a key component for developing a CMS, using Pan‐European earthquake records from a European ground motion database. Epsilon (ε) for each record is computed using the 2005 Ambraseys ground‐motion prediction equation. The model can be used to develop CMS for European sites, and it can be incorporated in the European seismic standards. Copyright © 2012 John Wiley & Sons, Ltd.     

Probabilistic versus deterministic seismic hazard analysis: an integrated approach for siting problems

A methodology is proposed to determine design earthquakes for site-specific studies such as the siting of critical structures (power plants, waste disposals, large dams, etc.), strategic structures (fire stations, military commands, hospitals, etc.), or for seismic microzoning studies, matching the results of probabilistic seismic hazard analyses. This goal is achieved by calculating the source contribution to hazard and the magnitude–distance deaggregation, showing that, varying the selected frequency and the level of hazard, the reference earthquakes are changed as a result. A procedure is then adopted to minimize the residuals between the uniform hazard spectrum (target motion) and the design earthquake spectrum, to provide a specific earthquake scenario encompassing all the frequencies of the target motion. Finally, some considerations on the use and the influence exerted by ground motion uncertainty (σ) on hazard deaggregation are outlined.     

Hazard-consistent response spectra in the Region of Murcia (Southeast Spain): comparison to earthquake-resistant provisions

Hazard-consistent ground-motion characterisations of three representative sites located in the Region of Murcia (southeast Spain) are presented. This is the area where the last three damaging events in Spain occurred and there is a significant amount of data for comparing them with seismic hazard estimates and earthquake-resistant provisions. Results of a probabilistic seismic hazard analysis are used to derive uniform hazard spectra (UHS) for the 475-year return period, on rock and soil conditions. Hazard deaggregation shows that the largest hazard contributions are due to small, local events for short-period target motions and to moderate, more distant events for long-period target motions. For each target motion and site considered, the associated specific response spectra (SRS) are obtained. It is shown that the combination of two SRS, for short- and long-period ground motions respectively, provides a good approximation to the UHS at each site. The UHS are compared to design response spectra contained in current Spanish and European seismic codes for the 475-year return period. For the three sites analysed, only the Eurocode 8 (EC8) type 2 spectrum captures the basic shape of the UHS (and not the EC8 type 1, as could be expected a priori). An alternative response spectrum, anchored at short- and long-period accelerations, is tested, providing a close match to the UHS spectra at the three sites. Results underline the important contribution of the frequent, low-to-moderate earthquakes that characterize the seismicity of this area to seismic hazard (at the 475-year return period).     

Scaling of ground motions and its implications to plan-asymmetric structures

Ground motions are often scaled to certain convenient target spectra in the response assessment of structures. While uniform hazard spectrum (UHS) is more widely used, conditional mean spectrum (CMS) is recently proposed as a more desirable target for scaling of real accelerograms. In this backdrop, the present study spectrally scales, using wavelets, a set of near-field and far-field ground motions to both the targets, viz., UHS and CMS. Relevance of a set of useful ground motion characteristics, viz., the peak ground acceleration-to-peak velocity ratio (a_max/v_max), predominant period (T_p), Arias intensity (I_a), Housner intensity (I_H), cumulative absolute velocity (CAV) and significant duration (T_d^⁎), is reviewed. Influence of ground motion scaling is discussed in terms of possible changes of such identified parameters. Seismic demand of horizontally irregular structures is assessed under both scaled and seed records recognizing strength dependent stiffness. Threshold of the scale factor, shown to have well-correlated with the change of ground motion characteristics, may be as high as ~10 to adequately estimate torsion-induced amplification in asymmetric system without any bias.     

Effect of ground motion selection methods on seismic collapse fragility of RC frame buildings

Variation in the seismic collapse fragility of reinforced concrete frame buildings predicted using different ground motion (GM) selection methods is investigated in this paper. To simulate the structural collapse, a fiber‐element modelling approach with path‐dependent cyclic nonlinear material models that account for concrete confinement and crushing, reinforcement buckling as well as low cycle fatigue is used. The adopted fiber analysis approach has been found to reliably predict the loss in vertical load carrying capacity of structural components in addition to the sidesway mode of collapse due to destabilizing P–Δ moments at large inelastic deflections. Multiple stripe analysis is performed by conducting response history analyses at various hazard levels to generate the collapse fragility curves. To select GMs at various hazard levels, two alternatives of uniform hazard spectrum (UHS), conditional mean spectrum (CMS) and generalized conditional intensity measure (GCIM) are used. Collapse analyses are repeated based on structural periods corresponding to initial un‐cracked stiffness and cracked stiffness of the frame members. A return period‐based intensity measure is then introduced and applied in estimating collapse fragility of frame buildings. In line with the results of previous research, it is shown that the choice of structural period significantly affects the collapse fragility predictions. Among the GM selection methods used in this study, GCIM and CMS methods predict similar collapse fragilities for the case study building investigated herein, and UHS provides the most conservative prediction of the collapse capacity, with approximately 40% smaller median collapse capacity compared to the CMS method. The results confirm that collapse probability prediction of buildings using UHS offers a higher level of conservatism in comparison to the other selection methods. Copyright © 2017 John Wiley & Sons, Ltd.     

Peak-over-threshold: Quantifying ground motion beyond design

In performance-based seismic design, as adopted by several building codes worldwide, the structural performance is verified against ground motions that have predetermined exceedance return periods at the site of interest. Such a return period is evaluated by means of probabilistic seismic hazard analysis (PSHA), and the corresponding ground motion is often represented by the uniform hazard spectrum (UHS). The structural performance for ground motions larger than those considered in this design approach is, typically, not explicitly controlled under the assumption that they are sufficiently rare. On one hand, this does not achieve uniform safety at sites characterized by different design ground motions corresponding to the same return period; on the other hand, exceedances of the design spectra are systematically observed over large areas, for example in Italy. The latter issue is because of the nature of UHS, the exceedance of which is likely-to-almost-certain when the construction site is in the epicentral area of moderate-to-high magnitude earthquakes (ie, the design spectrum may be not conservative at these locations), especially if PSHA is based on seismic source zones. The former is partially because of the systematic difference of ground motions for return periods larger than the design one at the different sites. Quantification of the expected ground motion given the exceedance of the design ground motions (ie, the recently introduced as the expected peak-over-threshold or POT) can be of help in quantitatively assessing these issues. In the study, a procedure to compute the POT distribution is derived first; second, POT spectra are introduced and used to help understanding why and how seismic structural reliability of code-conforming structures decreases as the seismic hazard of the site increases; third, expected and 95^th percentile POT maps are shown for Italy to discuss how much high hazard sites are exposed to much larger peak-over-threshold with respect to mid-hazard and low-hazard sites; finally the POT is discussed with respect to the slope of the hazard curve (in log-log scale) at the threshold, a known proxy for ground motion beyond design. All data presented in the maps are made available for the interested reader as a supplemental archive.     

Regional variation of spectral parameters for seismic design from broadband probabilistic seismic hazard analysis

The characterisation of the seismic hazard input is a critical element of any seismic design code, not only in terms of the absolute levels of ground motion considered but also of the shape of the design spectrum. In the case of Europe, future revisions of the seismic design provisions, both at a national and a pan‐European level, may implement considerable modifications to the existing provisions in light of recent seismic hazard models, such as the 2013 European Seismic Hazard Model. Constraint of the shape of the long‐period design spectrum from seismic hazard estimates on such a scale has not been possible, however, owing to the limited spectral period range of existing ground motion models. Building upon recent developments in ground motion modelling, the 2013 European Seismic Hazard Model is adapted here with a new ground motion logic tree to provide a broadband Probabilistic Seismic Hazard Analysis for rock sites across a spectral period range from 0.05 seconds to 10.0 seconds. The resulting uniform hazard spectra (UHS) are compared against existing results for European and broadband Probabilistic Seismic Hazard Analysis and against a proposed formulation of a generalised design spectrum in which controlling parameters can be optimised to best fit the uniform hazard spectra in order to demonstrate their variability on a European scale. Significant variations in the controlling parameters of the design spectrum are seen both across and within stable and active regions. These trends can help guide recalibrations of the code spectra in future revisions to seismic design codes, particularly for the longer‐period displacement spectrum.     

Spectral shape,epsilon and record selection

Selection of earthquake ground motions is considered with the goal of accurately estimating the response of a structure at a specified ground motion intensity, as measured by spectral acceleration at the first‐mode period of the structure, Sa(T₁). Consideration is given to the magnitude, distance and epsilon (ε) values of ground motions. First, it is seen that selecting records based on their ε values is more effective than selecting records based on magnitude and distance. Second, a method is discussed for finding the conditional response spectrum of a ground motion, given a level of Sa(T₁) and its associated mean (disaggregation‐based) causal magnitude, distance and ε value. Records can then be selected to match the mean of this target spectrum, and the same benefits are achieved as when records are selected based on ε. This mean target spectrum differs from a Uniform Hazard Spectrum, and it is argued that this new spectrum is a more appropriate target for record selection. When properly selecting records based on either spectral shape or ε, the reductions in bias and variance of resulting structural response estimates are comparable to the reductions achieved by using a vector‐valued measure of earthquake intensity. Copyright © 2006 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.     

The effect of amplitude scaling limits on conditional spectrum-based ground motion selection

Amplitude scaling is commonly used to select ground motions matching a target response spectrum. In this paper, the effect of scaling limits on ground motion selection, based on the conditional spectrum framework, is investigated. Target spectra are computed for four probabilistic seismic hazard cases in Western United States, and 16 ground motion suites are selected using different scaling limits (ie, 2, 5, 10, and 15). Comparison of spectral acceleration distributions of the selected ground motion suites demonstrates that the use of a scaling limit of 2 yields a relatively poor representation of the target spectra, because of the small limit leading to an insufficient number of available ground motions. It is also shown that increasing scaling limit results in selected ground motions with generally increased distributions of Arias intensity and significant duration Ds_5-75, implying that scaling limit consideration can significantly influence the cumulative and duration characteristics of selected ground motions. The ground motion suites selected are then used as input for slope displacement and structural dynamic analyses. Comparative results demonstrate that the consideration of scaling limits in ground motion selection has a notable influence on the distribution of the engineering demand parameters calculated (ie, slope displacement and interstory drift ratio). Finally, based on extensive analyses, a scaling limit range of 3 to 5 is recommended for general use when selecting ground motion records from the NGA-West2 database.     

Artificial ground motion compatible with specified peak velocity and target spectrum

In this paper, a method, which synthesizes the artificial ground motion compatible with the specified peak velocity as well as the target acceleration response spectrum, was proposed. In this method, firstly, an initial acceleration time history α8^（0） （t）, which satisfies the prescribed peak ground acceleration, the target spectral acceleration ST（ω, ζ）,and the specified intensity envelope, is generated by the traditional method that generates the requency domain; secondly,α8^（0） （t）is further modulated by superimposing narrow-band time histories upon it in the time domain to make its peak velocity, approach the target peak ground velocity, and at the same time to improve its fitting precision to the target spectrum. Numerical examples show that this algorithm boasts high calculation precisions.     

Artificial ground motion compatible with specified ground shaking peaks and target response spectrum

1 Introduction Time history analysis is usually needed not only for the seismic design of important structures, such as nuclear plants, large concrete dams and super high-rise buildings, but also for seismic performance based design. Performance-based design requires tha knowledge of the entire process of nonlinear seismic responses of structures be obtained, which depends on the ground motion time history as input for this analysis. However, because the observed strong-motion recordings are l…     

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.     

Assessing adequacy of spectrum‐matched ground motions for response history analysis

Response spectrum matching is commonly used to generate ground motions with response spectra matching a scenario target spectrum. There is some debate in the literature about whether spectrum‐matched motions lead to biased structural analysis results. Furthermore, there are no objective, quantitative criteria available for deciding whether a ground motion has been manipulated excessively by spectrum matching, and whether large modification may also lead to bias. This study investigates both of these issues by presenting the results of structural analysis using two reinforced concrete moment frame models and two earthquake scenarios, with suites of unmatched and matched ground motions. Through comparison with a robust benchmark, it is shown that no significant bias is introduced by spectrum matching. The period range and target damping values for matching are also investigated, and matching up to three times the fundamental period is shown to be beneficial in reducing dispersion in the results. Finally, these analyses were also used to investigate whether large changes in the ground motion lead to biased analysis results. Several potential measures of change are investigated, including those based on peak absolute ground motion, cumulative squared ground motion (absolute or normalized), and input energy into single‐degree‐of‐freedom systems. Although no systematic, statistically significant correlation is found for the analysis results in terms of any of these measures of change, tentative criteria are proposed, which may be used by analysts to aid in the decision of whether to accept or reject a spectrum‐matched motion. Copyright © 2012 John Wiley & Sons, Ltd.     

Incremental dynamic analysis of wood-frame houses in Canada: Effects of dominant earthquake scenarios on seismic fragility

Seismic fragility can be assessed by conducting incremental dynamic analysis (IDA). This study extends the current conditional mean spectrum (CMS)-based record selection approach for IDA by taking into account detailed seismic hazard information. The proposed method is applied to conventional wood-frame houses in Canada, across which dominant earthquake scenarios and associated hazard levels vary significantly. Effects due to different seismic environments, site conditions, CMS-based record selection methods, and house models are investigated by comparing various seismic fragility models. Moreover, relative impact of the key characteristics is evaluated in terms of seismic loss curve for a group of wood-frame houses. Importantly, a close examination of regional seismic hazard characteristics using seismic hazard curve and seismic deaggregation facilitates the deeper understanding of the impact of ground motion characteristics on seismic fragility. A comprehensive and systematic assessment of key uncertainties associated with seismic fragility is provided.     

Conditional spectrum‐based ground motion selection. Part I: Hazard consistency for risk‐based assessments

The conditional spectrum (CS, with mean and variability) is a target response spectrum that links nonlinear dynamic analysis back to probabilistic seismic hazard analysis for ground motion selection. The CS is computed on the basis of a specified conditioning period, whereas structures under consideration may be sensitive to response spectral amplitudes at multiple periods of excitation. Questions remain regarding the appropriate choice of conditioning period when utilizing the CS as the target spectrum. This paper focuses on risk‐based assessments, which estimate the annual rate of exceeding a specified structural response amplitude. Seismic hazard analysis, ground motion selection, and nonlinear dynamic analysis are performed, using the conditional spectra with varying conditioning periods, to assess the performance of a 20‐story reinforced concrete frame structure. It is shown here that risk‐based assessments are relatively insensitive to the choice of conditioning period when the ground motions are carefully selected to ensure hazard consistency. This observed insensitivity to the conditioning period comes from the fact that, when CS‐based ground motion selection is used, the distributions of response spectra of the selected ground motions are consistent with the site ground motion hazard curves at all relevant periods; this consistency with the site hazard curves is independent of the conditioning period. The importance of an exact CS (which incorporates multiple causal earthquakes and ground motion prediction models) to achieve the appropriate spectral variability at periods away from the conditioning period is also highlighted. The findings of this paper are expected theoretically but have not been empirically demonstrated previously. Copyright © 2013 John Wiley & Sons, Ltd.     

基于实测记录分析场地因素对海底地震动特性影响

目前基于海底实测记录的分析发现海底与陆地地震动特性存在明显差异,但难以进一步确定海底地震动特性的影响因素。在以往研究的基础上对比同次地震中相邻海底台站间地震动特性的差异,并分析造成差异的原因。以日本K-NET地震台网中6个海底强震台站及其相邻不同场地条件陆地台站监测的8次强震记录为研究对象,通过分析强震记录的峰值加速度、水平放大系数谱、竖向与水平反应谱的比谱等,对比分析不同海底台站地震动的特性,以及海底台站与相邻不同场地条件陆地台站地震动特性的差别。研究发现：（1）海底与陆地竖向地震动存在明显差异;（2）不同海底台站间地震动特性亦存在较大差异和明显的规律性,海底场地条件、地形等场地因素对海底地震动特性的影响较大;（3）海底水平向地震动反应谱的特征周期较大,谱特性介于陆地中硬土与软土场地间。