Intensity measures for probabilistic assessment of non‐structural components acceleration demand

A fundamental issue in the framework of seismic probabilistic risk analysis is the choice of ground motion intensity measures (IMs). Based on the floor response spectrum method, the present contribution focuses on the ability of IMs to predict non‐structural components (NSCs) horizontal acceleration demand. A large panel of IMs is examined and a new IM, namely equipment relative average spectral acceleration (E‐ASA_R), is proposed for the purpose of NSCs acceleration demand prediction. The IMs efficiency and sufficiency comparisons are based on (i) the use of a large dataset of recorded earthquake ground motions; (ii) numerical analyses performed on three‐dimensional numerical models, representing actual structural wall and frame buildings; and (iii) systematic statistical analysis of the results. From the comparative study, the herein introduced E‐ASA_R shows high efficiency with respect to the estimation of maximum floor response spectra ordinates. Such efficiency is particularly remarkable in the case of structural wall buildings. Besides, the sufficiency and the simple formulation allowing the use of existing ground motion prediction models make the E‐ASA_R a promising IMs for seismic probabilistic risk assessment. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Intensity measures for the seismic response evaluation of buried steel pipelines under near-field pulse-like ground motions

Ground-motion Intensity Measures (IMs) are used to quantify the strength of ground motions and evaluate the response of structures. IMs act as a link between seismic demand and seismic hazard analysis and therefore, have a key role in performance-based earthquake engineering. Many studies have been carried out on the determination of suitable IMs in terms of efficiency, sufficiency and scaling robustness. The majority of these investigations focused on ordinary structures such as buildings and bridges, and only a few were about buried pipelines. In the current study, the optimal IMs for predicting the seismic demand of continuous buried steel pipelines under near-field pulse-like ground motion records is investigated. Incremental dynamic analysis is performed using twenty ground motion records. Using the results of the regression analysis, the optimality of 23 potential IMs are studied. It is concluded that specific energy density (SED) followed by \(\sqrt {VSI[{\omega _1}(PGD + RM{S_d})]} \) are the optimal IMs based on efficiency, sufficiency and scaling robustness for seismic response evaluation of buried pipelines under near-field ground motions.

     

Ductility‐dependent intensity measure that accounts for ground‐motion spectral shape and duration

The calculated nonlinear structural responses of a building can vary greatly, even if recorded ground motions are scaled to the same spectral acceleration at a building's fundamental period. To reduce the variation in structural response at a particular ground‐motion intensity, this paper proposes an intensity measure (IM_comb) that accounts for the combined effects of spectral acceleration, ground‐motion duration, and response spectrum shape. The intensity measure includes a new measure of spectral shape that integrates the spectrum over a period range that depends on the structure's ductility. The new IM is efficient, sufficient, scalable, transparent, and versatile. These features make it suitable for evaluating the intensities of measured and simulated ground motions. The efficiency and sufficiency of the new IM is demonstrated for the following: (i) elastic‐perfectly plastic single‐degree‐of‐freedom (SDOF) oscillators with a variety of ductility demands and periods; (ii) ductile and brittle deteriorating SDOF systems with a variety of periods; and (iii) collapse analysis for 30 previously designed frames. The efficiency is attributable to the inclusion of duration and to the ductility dependence of the spectral shape measure. For each of these systems, the transparency of the intensity measure made it possible to identify the sensitivity of structural response to the various characteristics of the ground motion. Spectral shape affected all structures, but in particular, ductile structures. Duration only affected structures with cyclic deterioration. Copyright © 2015 John Wiley & Sons, Ltd.     

Intensity measure selection for vulnerability studies of building classes

The selection of a scalar Intensity Measure (IM) for performing analytical vulnerability (loss) assessment across a building class is addressed. We investigate the ability of several IM choices to downgrade the effect of seismological parameters (sufficiency) as well as reduce the record‐to‐record variability (efficiency) for both highrise and lowrise sets of ‘index’ buildings. These characteristics are explored in unprecedented detail, employing comparisons and statistical significance testing at given levels of local engineering demand parameters (story drift ratios and peak floor accelerations) that relate to losses, instead of global variables such as the maximum interstory drift. Thus, a detailed limit‐state‐specific view is offered for the suitability of different scalar IMs for loss assessment. As expected, typical single‐period spectral values are found to introduce unwanted bias at high levels of scaling, both for a single as well as a class of buildings. On the other hand, the geometric mean of the spectral acceleration values estimated at several periods between the class‐average second‐mode and an elongated class‐average first‐mode period offers a practical choice that significantly reduces the spectral‐shape bias without requiring the development of new ground motion prediction equations. Given that record selection remains a site‐ and building‐specific process, such an improved IM can help achieve reliable estimates for building portfolios, as well as single structures, at no additional cost. Copyright © 2015 John Wiley & Sons, Ltd.     

Average spectral acceleration as an intensity measure for collapse risk assessment

This paper investigates the performance of spectral acceleration averaged over a period range (Sa_avg) as an intensity measure (IM) for estimating the collapse risk of structures subjected to earthquake loading. The performance of Sa_avg is evaluated using the following criteria: efficiency, sufficiency, the availability or ease of developing probabilistic seismic hazard information in terms of the IM and the variability of collapse risk estimates produced by the IM. Comparisons are also made between Sa_avg and the more traditional IM: spectral acceleration at the first‐mode period of the structure (Sa(T₁)). Though most previous studies have evaluated IMs using a relatively limited set of structures, this paper considers nearly 700 moment‐resisting frame and shear wall structures of various heights to compare the efficiency and sufficiency of the IMs. The collapse risk estimates produced by Sa_avg and Sa(T₁) are also compared, and the variability of the risk estimates is evaluated when different ground motion sets are used to assess the structural response. The results of this paper suggest that Sa_avg, when computed using an appropriate period range, is generally more efficient, more likely to be sufficient and provides more stable collapse risk estimates than Sa(T₁). Copyright © 2015 John Wiley & Sons, Ltd.     

Conditional spectrum bidirectional record selection for risk assessment of 3D structures using scalar and vector IMs

Several proposals are explored for the hazard and intensity measure (IM) consistent selection of bidirectional ground motions to assess the performance of 3D structural models. Recent studies have shown the necessity of selecting records that thoroughly represent the seismicity at the site of interest, as well as the usefulness of efficient IMs capable of estimating the response of buildings with low scatter. However, the advances realized are mostly geared towards the structural analysis of 2D models. Few are the combined record, and IM selection approaches suggested expressly for nonlinear dynamic analysis of 3D structural models, especially when plan asymmetry and torsion sensitivity come into play. Conditional spectrum selection is leveraged and expanded here to offer a suite of approaches based on both scalar and vector IMs that convey information from two orthogonal horizontal components of the ground motion. Applications on multiple 3D building models highlight the importance of (a) employing the same IM for both record selection and response assessment and (b) maintaining hazard consistency in both horizontal components, when using either a scalar or a vector IM. All tested approaches that respect these conditions can be viable, yet the one based on the geometric mean of multiple spectral ordinates from both components over a period range seems to hold the most promise for general use.     

Developing efficient scalar and vector intensity measures for IDA capacity estimation by incorporating elastic spectral shape information

Scalar and vector intensity measures are developed for the efficient estimation of limit‐state capacities through incremental dynamic analysis (IDA) by exploiting the elastic spectral shape of individual records. IDA is a powerful analysis method that involves subjecting a structural model to several ground motion records, each scaled to multiple levels of intensity (measured by the intensity measure or IM), thus producing curves of structural response parameterized by the IM on top of which limit‐states can be defined and corresponding capacities can be calculated. When traditional IMs are used, such as the peak ground acceleration or the first‐mode spectral acceleration, the IM‐values of the capacities can display large record‐to‐record variability, forcing the use of many records to achieve reliable results. By using single optimal spectral values as well as vectors and scalar combinations of them on three multistorey buildings significant dispersion reductions are realized. Furthermore, IDA is extended to vector IMs, resulting in intricate fractile IDA surfaces. The results reveal the most influential spectral regions/periods for each limit‐state and building, illustrating the evolution of such periods as the seismic intensity and the structural response increase towards global collapse. The ordinates of the elastic spectrum and the spectral shape of each individual record are found to significantly influence the seismic performance and they are shown to provide promising candidates for highly efficient IMs. Copyright © 2005 John Wiley & Sons, Ltd.     

Multi-criteria decision making for seismic intensity measure selection considering uncertainty

Seismic intensity measure (IM) selection is associated with consideration of multiple criteria, and there are uncertainties within the selection process. In this paper, a novel multi-criteria decision making (MCDM) approach by incorporating stochastic multi-criteria acceptability analysis (SMAA) with technique for order preference by similarity to ideal solution (TOPSIS) is proposed to solve the stochastic decision making problem of IM selection. TOPSIS provides an alternative rank function, and the SMAA is used to address the uncertainties within the IM selection. The performance criteria (e.g., efficiency, proficiency, practicality, sufficiency, and correlation) are evaluated for the investigated structural components, and the decision matrix is formulated based on the criteria of each IM alternative. Furthermore, the importance of the component to system reliability is quantified in a probabilistic manner using nonlinear time history analysis and serves as the weighting factors in MCDM stage. The holistic acceptability indices indicating the overall acceptability levels of IM alternatives are computed by the proposed approach. Additionally, the effects of different IMs (e.g., average spectral acceleration, peak ground velocity, and spectral acceleration) on probabilistic seismic loss and resilience are investigated to further support the IM selection. The proposed approach is illustrated on a highway bridge, and the results are presented.     

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.     

Optimal intensity measures for probabilistic seismic demand modeling of extended pile-shaft-supported bridges in liquefied and laterally spreading ground

Seismic intensity measures (IMs) perform a pivotal role in probabilistic seismic demand modeling. Many studies investigated appropriate IMs for structures without considering soil liquefaction potential. In particular, optimal IMs for probabilistic seismic demand modeling of bridges in liquefied and laterally spreading ground are not comprehensively studied. In this paper, a coupled-bridge-soil-foundation model is adopted to perform an in-depth investigation of optimal IMs among 26 IMs found in the literature. Uncertainties in structural and geotechnical material properties and geometric parameters of bridges are considered in the model to produce comprehensive scenarios. Metrics such as efficiency, practicality, proficiency, sufficiency and hazard computability are assessed for different demand parameters. Moreover, an information theory based approach is adopted to evaluate the relative sufficiency among the studied IMs. Results indicate the superiority of velocity-related IMs compared to acceleration, displacement and time-related ones. In particular, Housner spectrum intensity (HI), spectral acceleration at 2.0 s (S _a-20), peak ground velocity (PGV), cumulative absolute velocity (CAV) and its modified version (CAV ₅) are the optimal IMs. Conversely, Arias intensity (I _a ) and shaking intensity rate (SIR) which are measures often used in liquefaction evaluation or related structural demand assessment demonstrate very low correlations with the demand parameters. Besides, the geometric parameters do not evidently affect the choice of optimal IMs. In addition, the information theory based sufficiency ranking of IMs shows an identical result to that with the correlation measure based on coefficient of determination (R ²). This means that R ² can be used to preliminarily assess the relative sufficiency of IMs.     

钢筋混凝土高层建筑抗震时程分析选波方法比较研究

针对钢筋混凝土高层建筑抗震时程分析输入地震波选择问题,以《建筑抗震设计规范》（GB 50011-2016）设计谱为目标谱,将满足谱匹配原则的加权调幅选波方法与国内学者建议的其它输入地震波选择方法进行了对比研究。以3栋钢筋混凝土高层建筑（15层、30层和44层）为实例,针对8度罕遇地震作用和Ⅱ类场地条件,将上述方法建议的各7条地震波输入结构进行弹塑性时程分析。以结构最大层间位移角均值沿楼层分布为比较参数。结果表明:加权调幅法可用于钢筋混凝土高层建筑抗震时程分析,可以较好地降低结构地震反应均值的离散性。在8度罕遇地震作用条件下,以不同学者建议选择的地震波为输入,高层建筑时程分析结果仍呈现出较大的不同。     

Fractional order intensity measures for probabilistic seismic demand modeling applied to highway bridges

Probabilistic seismic analysis of structures involves the construction of seismic demand models, often stated as probabilistic models of structural response conditioned on a seismic intensity measure. The uncertainty introduced by the model is often a result of the chosen intensity measure. This paper introduces the concept of using fractional order intensity measures (IMs) in probabilistic seismic demand analysis and uses a single frame integral concrete box‐girder bridge class and a seismically designed multispan continuous steel girder bridge class as case studies. The fractional order IMs considered include peak ground response and spectral accelerations at 0.2 and 1.0 s considering a single degree of freedom system with fractional damping, , as well as a linear single degree of freedom system with fractional response, . The study reveals the advantage of fractional order IMs relative to conventional IMs such as peak ground acceleration, peak ground velocity, or spectral acceleration at 0.2 and 1.0 s. Metrics such as efficiency, sufficiency, practicality, and proficiency are measured to assess the optimal nature of fractional order IMs. The results indicate that the proposed fractional order IMs produce significant improvements in efficiency and proficiency, whereas maintaining practicality and sufficiency, and thus providing superior demand models that can be used in probabilistic seismic demand analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Rocking amplification and strong‐motion duration

This paper characterizes the ability of natural ground motions to induce rocking demands on rigid structures. In particular, focusing on rocking blocks of different size and slenderness subjected to a large number of historic earthquake records, the study unveils the predominant importance of the strong‐motion duration to rocking amplification (ie, peak rocking response without overturning). It proposes original dimensionless intensity measures (IMs), which capture the total duration (or total impulse accordingly) of the time intervals during which the ground motion is capable of triggering rocking motion. The results show that the proposed duration‐based IMs outperform all other examined (intensity, frequency, duration, and/or energy‐based) scalar IMs in terms of both “efficiency” and “sufficiency.” Further, the pertinent probabilistic seismic demand models offer a prediction of the peak rocking demand, which is adequately “universal” and of satisfactory accuracy. Lastly, the analysis shows that an IM that “efficiently” captures rocking amplification is not necessarily an “efficient” IM for predicting rocking overturning, which is dominated by the velocity characteristics (eg, peak velocity) of the ground motion.     

远场长周期地震下高层建筑的地震损伤模型研究

传统高层建筑地震损伤模型不能反映构件极限滞回耗能随累积幅值的改变情况,无法有效确定组合参数,离散性较大。为此,设计一种远场长周期地震下高层建筑的地震损伤模型。针对不同层次高层建筑结构,依据广义力-广义变形曲线,构建变形损伤模型。结合累积能量比、远场长周期地震瞬时输入能比构建能量损伤模型。从变形与能量两方面综合评价损伤,依据钢筋混凝土结构构建最大反应变形与耗损能量的线性组合地震损伤模型,并对其进行改进。实验选用ILA003、ILA048和TCU115三种长周期地震波,计算不同构件和高层建筑结构整体损伤结果,验证所提模型的可靠性。将所提模型应用于实际高层建筑中,发现其实用性强。     

地面运动强度参数对RC桥梁地震需求的影响

在基于性能的地震工程学(PBEE)中,建立概率地震需求模型(PSDM)时需要对桥梁结构的工程需求参数(EDP)进行概率估计。其中,强地面运动参数(IM)的选择对EDP的概率估计影响很大,因此需要正确选择IM。分别采用目前最广泛使用的结构第一模态周期弹性谱加速度(5%阻尼比)Sa(T1,5%)和峰值地面加速度PGA作为IM,选择实际地震波并进行合理的调值,对一座钢筋混凝土桥墩进行IDA分析,其计算结果表明:对于不同性质EDP的概率估计值,以PGA作为IM计算所得的结果明显偏于非保守,且离散度一般也更大。说明可以针对不同性质的EDP,根据地面运动强度的大小,选择不同的IM,通过合理的调值对EDP进行概率估计,可以更加精确、高效地建立PSDM。     

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.     

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.     

Methodology for estimating human perception to tremors in high-rise buildings

Human perception to tremors during earthquakes in high-rise buildings is usually associated with psychological discomfort such as fear and anxiety. This paper presents a methodology for estimating the level of perception to tremors for occupants living in high-rise buildings subjected to ground motion excitations. Unlike other approaches based on empirical or historical data, the proposed methodology performs a regression analysis using the analytical results of two generic models of 15 and 30 stories. The recorded ground motions in Singapore are collected and modified for structural response analyses. Simple predictive models are then developed to estimate the perception level to tremors based on a proposed ground motion intensity parameter—the average response spectrum intensity in the period range between 0.1 and 2.0 s. These models can be used to predict the percentage of occupants in high-rise buildings who may perceive the tremors at a given ground motion intensity. Furthermore, the models are validated with two recent tremor events reportedly felt in Singapore. It is found that the estimated results match reasonably well with the reports in the local newspapers and from the authorities. The proposed methodology is applicable to urban regions where people living in high-rise buildings might feel tremors during earthquakes.     

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.