A generalized conditional intensity measure approach and holistic ground‐motion selection

A generalized conditional intensity measure (GCIM) approach is proposed for use in the holistic selection of ground motions for any form of seismic response analysis. The essence of the method is the construction of the multivariate distribution of any set of ground‐motion intensity measures conditioned on the occurrence of a specific ground‐motion intensity measure (commonly obtained from probabilistic seismic hazard analysis). The approach therefore allows any number of ground‐motion intensity measures identified as important in a particular seismic response problem to be considered. A holistic method of ground‐motion selection is also proposed based on the statistical comparison, for each intensity measure, of the empirical distribution of the ground‐motion suite with the ‘target’ GCIM distribution. A simple procedure to estimate the magnitude of potential bias in the results of seismic response analyses when the ground‐motion suite does not conform to the GCIM distribution is also demonstrated. The combination of these three features of the approach make it entirely holistic in that: any level of complexity in ground‐motion selection for any seismic response analysis can be exercised; users explicitly understand the simplifications made in the selected suite of ground motions; and an approximate estimate of any bias associated with such simplifications is obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Ground motion selection for scenario ruptures using the generalised conditional intensity measure (GCIM) method

In this paper, the generalised conditional intensity measure (GCIM) method is extended to ground motion selection for scenario earthquake ruptures. The selection algorithm is based on generating random realisations of the considered intensity measure (IM) distributions for a specific rupture scenario and then finding the prospective ground motions that best fit the realisations using an optimal amplitude scale factor. Using different rupture scenarios and site conditions, two important aspects of the GCIM methodology are scrutinised: (i) different weight vectors for the various IMs considered and (ii) quantifying the importance of replicate selections for ensembles with different numbers of desired ground motions. It is demonstrated that considering only spectral acceleration (SA) ordinates in the selection process, as is common in many conventional selection procedures, may result in selected motions with a biased representation for duration and cumulative ground motion effects. In contrast, considering IMs other than SA ordinates (in particular, significant duration, cumulative absolute velocity, and Arias intensity) results in ensembles with an appropriate representation of these IMs, without a practically significant effect on SA ordinates. The benefit of conducting replicate selections to obtain a suite of motions with an improved representation for the distribution of the considered IMs is demonstrated, and a minimum number of replicates are suggested for different ground motion ensemble sizes. Copyright © 2015 John Wiley & Sons, Ltd.     

Markov chain Monte Carlo ground‐motion selection algorithms for conditional intensity measure targets

Two new algorithms are presented for efficiently selecting suites of ground motions that match a target multivariate distribution or conditional intensity measure target. The first algorithm is a Markov chain Monte Carlo (MCMC) approach in which records are sequentially added to a selected set such that the joint probability density function (PDF) of the target distribution is progressively approximated by the discrete distribution of the selected records. The second algorithm derives from the concept of the acceptance ratio within MCMC but does not involve any sampling. The first method takes advantage of MCMC's ability to efficiently explore a sampling distribution through the implementation of a traditional MCMC algorithm. This method is shown to enable very good matches to multivariate targets to be obtained when the numbers of records to be selected is relatively large. A weaker performance for fewer records can be circumvented by the second method that uses greedy optimisation to impose additional constraints upon properties of the target distribution. A preselection approach based upon values of the multivariate PDF is proposed that enables near‐optimal record sets to be identified with a very close match to the target. Both methods are applied for a number response analyses associated with different sizes of record sets and rupture scenarios. Comparisons are made throughout with the Generalised Conditional Intensity Measure (GCIM) approach. The first method provides similar results to GCIM but with slightly worse performance for small record sets, while the second method outperforms method 1 and GCIM for all considered cases.     

Ground motion selection for seismic slope displacement analysis using a generalized intensity measure distribution method

Selecting ground motions based on the generalized intensity measure distribution (GIMD) approach has many appealing features, but it has not been fully verified in engineering practice. In this paper, several suites of ground motions, which have almost identical distributions of spectral acceleration (SA) ordinates but different distributions of non‐SA intensity measures, are selected using the GIMD‐based approach for a given earthquake scenario. The selected ground motion suites are used to compute the sliding displacements of various slopes. Comparisons of the resulting displacements demonstrate that selecting ground motions with biased distribution of some intensity measures (ie, Arias intensity) may yield systematic biases (up to 60% for some slope types). Therefore, compared to the ground motions selected based only on the distribution of SA ordinates, the ground motion suite selected by the GIMD‐based approach can better represent the various characteristics of earthquake loadings, resulting in generally unbiased estimation in specific engineering applications.     

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.     

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。     

基于易损性的基础隔震结构地震动选取方法研究

对基础隔震结构进行动力弹塑性时程分析时,地震记录的选择是关键.提出基于基础隔震结构弹塑性动力放大系数谱进行地震记录选取的方法:首先采用动力弹塑性时程分析方法对基础隔震结构的两自由度简化模型进行分析,得到结构的动力放大系数谱;然后采用谱匹配的方法选取地震记录,对一8层混凝土框架结构的基础隔震结构进行增量动力分析、地震易损...     

A vector‐valued ground motion intensity measure consisting of spectral acceleration and epsilon

The ‘strength’ of an earthquake ground motion is often quantified by an Intensity Measure (IM), such as peak ground acceleration or spectral acceleration at a given period. This IM is used to predict the response of a structure. In this paper an intensity measure consisting of two parameters, spectral acceleration and epsilon, is considered. The IM is termed a vector‐valued IM, as opposed to the single parameter, or scalar, IMs that are traditionally used. Epsilon (defined as a measure of the difference between the spectral acceleration of a record and the mean of a ground motion prediction equation at the given period) is found to have significant ability to predict structural response. It is shown that epsilon is an indicator of spectral shape, explaining why it is related to structural response. By incorporating this vector‐valued IM with a vector‐valued ground motion hazard, we can predict the mean annual frequency of exceeding a given value of maximum interstory drift ratio, or other such response measure. It is shown that neglecting the effect of epsilon when computing this drift hazard curve leads to conservative estimates of the response of the structure. These observations should perhaps affect record selection in the future. Copyright © 2005 John Wiley & Sons, Ltd.     

A vector-valued intensity measure for near-fault ground motions

Near-fault ground motions containing high energy and large amplitude velocity pulses may cause severe damage to structures. The most widely used intensity measure (IM) is the elastic spectral acceleration at the fundamental period of the structure (Sa(T₁)); however, Sa(T₁) is not a sufficient IM with respect to the effects of the pulse-like ground motions on structural response. For near-fault ground motions, including pulse-like and non–pulse-like time histories, we propose a vector-valued IM consisting of a new IM called instantaneous power (IP(T₁)) and the Sa(T₁). The IP(T₁) is defined as the maximum power of the bandpass-filtered velocity time series over a time interval of 0.5T₁. The IP(T₁) is period-dependent because the velocity time series is filtered over a period range (0.2T₁-3T₁). This allows the IP(T₁) to represent the power of the near-fault ground motions relevant to the response of the structure. Using two-dimensional models of the 2- and 9-story steel-frame buildings, we show that the proposed [Sa(T₁), IP(T₁)] vector IM gives more accurate estimates of the maximum inter-story drift and collapse capacity responses from near-fault ground motions than using the vector IM consisting of the Sa(T₁), the presence of the velocity pulse, and the period of the velocity pulse. Moreover, for the structures considered, for a given Sa(T₁), the IP(T₁) is more strongly correlated with structural damage from near-fault ground motions than the combination of the velocity pulse and pulse period.     

地震强度指标选择对长周期钢结构余震IDA分析的影响

结构在主震作用下发生损伤,由于刚度和强度退化导致结构周期的延长,再加上高阶周期的影响,在随后的余震对主震损伤结构抗震性能的影响分析中,基于弹性周期的传统谱加速度可能不适用,有必要对地震动强度指标的选择进行进一步研究。本文以9层Benchmark钢框架为研究对象,选取10种地震动强度指标,分别从离散性和相关性两个维度对比分析了其在余震IDA分析中的优劣性。研究结果表明:与最大层间位移角相比,最大残余层间位移角更能够准确地量化主震对结构造成的损伤;对于钢框架结构,基于一段周期的几何平均谱加速度的IM_Boj&Lev指标是最优的地震动强度指标,相对于S_a（T₁）离散性降低了30%左右,相关性提高了6%左右。     

概率性地震需求分析中地震动强度指标的比较与选择

以汶川地区典型钢筋混凝土简支梁桥为背景,在充分考虑模型参数不确定性的基础上建立一系列桥梁有限元模型样本。采用汶川地震实测地震动,对建立的有限元模型进行非线性动力时程分析,并记录每组分析中桥梁构件的地震峰值响应。采用主成分分析方法对桥梁构件的地震需求参数进行降维处理,计算桥梁结构综合地震需求响应。通过回归分析建立地震动强度与桥梁结构综合需求之间的概率性关系,并对不同地震动强度指标进行分析和比较。结果表明基于速度的地震动强度指标具有较好的有效性、适用性和完备性,可以进一步用于地震易损性分析和地震风险评估。     

Correlation study between ground motion intensity measure parameters and deformation demands for bilinear SDOF systems

The correlation between ground motion intensity measures （IM） and single-degree-of-freedom （SDOF） deformation demands is described in this study. Peak ground acceleration （APG）, peak ground velocity （VPG）, peak ground displacement （DPG）, spectral acceleration at the first-mode period of vibration [As（T1）] and ratio of VPG to APG are used as IM parameters, and the correlation is characterized by correlation coefficients p. The numerical results obtained by nonlinear dynamic analyses have shown good correlation between As（T1） or VPG and deformation demands. Furthermore, the effect of As（T1） and VPG as IM on the dispersion of the mean value of deformation demands is also investigated for SDOF systems with three different periods T=0.3 s, 1.0 s, 3.0 s respectively.     

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.     

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Mw 9.0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.     

Spatial variation and conditional simulation of seismic ground motion

Spatially varying ground motion (SVGM) may have influence on certain civil engineering structures with spatially extended superstructure and/or substructures. Conditional simulation of spatially varying ground motion (CSSVGM) may be viewed from two different perspectives. Most procedures available in the literature neglect the spatial variability in auto-spectral density (ASD) and estimate the SVGM through cross-spectral density (CSD) which was computed using the empirical coherency models. This paper proposes a coherency model that accounts for the spatial variability of ASD. A framework has been developed for the CSSVGM, through the mapping of both proposed coherency model and ASD over the footprint of an array. Current framework (existing in the literature) accounts for only the phase variability of SVGM while proposed framework accounts for both phase and amplitude variability. Ground motion generated from both perspectives is then assessed with the data recorded over SMART1 and LSST arrays. For the purpose of assessment, a definition of target spectrum based on the direction of arrival is explored. The effect of choice of coherency model on the simulated spatially varying ground motion is investigated first. Spectra resulting from both the perspectives are assessed against the target spectrum. An attempt has been made to predict the SVGM for a future event using a coherency model calibrated against a past event and an estimate of ASD of the seed ground motion. Finally, the effect of form of ASD (of a seed ground motion) on SVGM simulated is investigated by considering the ASD in different forms. Simulating SVGM through the mapping of both coherency model and ASD seems to be more appropriate than through CSD.     

基于假设检验的地震动强度(烈度)速报方法

地震发生后数分钟内,快速、可靠地判别出地震动强度(烈度)的空间分布,用以估计不同地区的受灾程度,可以为政府开展应急救援并合理分配救援力量提供决策依据,保证救援人员及时、准确地到达极震区并展开搜救,以减少生命财产损失。本文基于统计学中的假设检验方法,对历史震害资料进行统计,提出了一种利用强地震动参数判别地震动强度(烈度)的方法。比较结果表明,本方法所确定的地震动强度(烈度)与实际震害烈度对应较好,能较真实地反映实际震害情况。     

The effect of glaciation on the intensity of seismic ground motion

Seismicity is known to contribute to landscape denudation through its role in earthquake‐triggered slope failure; but little is known about how the intensity of seismic ground motions, and therefore triggering of slope failures, may change through time. Topography influences the intensity of seismic shaking – generally steep slopes amplify shaking more than flatter slopes – and because glacial erosion typically steepens and enlarges slopes, glaciation may increase the intensity of seismic shaking of some landforms. However, the effect of this may be limited until after glaciers retreat because valley ice or ice‐caps may damp seismic ground motions. Two‐dimensional numerical models (FLAC 6.0) were used to explore how edifice shape, rock stiffness and various levels of ice inundation affect edifice shaking intensity. The modelling confirmed that earthquake shaking is enhanced with steeper topography and at ridge crests but it showed for the first time that total inundation by ice may reduce shaking intensity at hill crests to about 20–50% of that experienced when no ice is present. The effect is diminished to about 80–95% if glacier ice level reduces to half of the mountain slope height. In general, ice cover reduced shaking most for the steepest‐sided edifices, for wave frequencies higher than 3 Hz, and when ice was thickest and the rock had shear stiffness well in excess of the stiffness of ice. If rock stiffness is low and shear‐wave velocity is similar to that of ice, the presence of ice may amplify the shaking of rock protruding above the ice surface. The modelling supports the idea that topographic amplification of earthquake shaking increases as a result of glacial erosion and deglaciation. It is possible that the effect of this is sufficient to have influenced the distribution of post‐glacial slope failures in glaciated seismically active areas. Copyright © 2012 John Wiley & Sons, Ltd.     

A probability-consistent method based on practical ground surface motion

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