Prediction of spatially distributed seismic demands in specific structures: Structural response to loss estimation

A companion paper has investigated the effects of intensity measure (IM) selection in the prediction of spatially distributed response in a multi‐degree‐of‐freedom structure. This paper extends from structural response prediction to performance assessment metrics such as probability of structural collapse; probability of exceeding a specified level of demand or direct repair cost; and the distribution of direct repair loss for a given level of ground motion. In addition, a method is proposed to account for the effect of varying seismological properties of ground motions on seismic demand that does not require different ground motion records to be used for each intensity level. Results illustrate that the conventional IM, spectral displacement at the first mode, S_de(T₁), produces higher risk estimates than alternative velocity‐based IM's, namely spectrum intensity, SI, and peak ground velocity, PGV, because of its high uncertainty in ground motion prediction and poor efficiency in predicting peak acceleration demands. Copyright © 2009 John Wiley & Sons, Ltd.     

基于性能的钢筋混凝土框架剪力墙结构地震易损性分析

以某典型的20层钢筋混凝土框架剪力墙结构作为研究对象,研究基于性能的RC框架剪力墙结构易损性分析方法。首先选择合适的地震动记录,以0.2g为步长进行调幅后,建立300个结构-地震动样本空间,并确定结构损伤指标和性能参数;然后应用增量动力分析方法计算结构的地震动力响应,选择基本周期加速度反应谱为地震动参数,以研究结构反应的不确定性,并深入分析地震动参数与结构地震需求参数的关系;在此基础上,建立该结构基于加速度反应谱的易损性曲线进行结构易损性分析与评估。结果表明：随着地震动强度的增大,IDA曲线由单调增加变为非单调增加,分位曲线（16%,50%和84%）可以准确地衡量结构的性能;框剪结构在地震作用下的抗震性能表现良好,随着地震强度的增长,各性能超越概率大小的增长速度是不同的。     

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.     

Critical response of structures to multicomponent earthquake excitation

This paper aims to develop an improved understanding of the critical response of structures to multicomponent seismic motion characterized by three uncorrelated components that are defined along its principal axes: two horizontal and the vertical component. An explicit formula, convenient for code applications, has been derived to calculate the critical value of structural response to the two principal horizontal components acting along any incident angle with respect to the structural axes, and the vertical component of ground motion. The critical response is defined as the largest value of response for all possible incident angles. The ratio r_cr/r_srss between the critical value of response and the SRSS response—corresponding to the principal components of ground acceleration applied along the structure axes—is shown to depend on three dimensionless parameters: the spectrum intensity ratio γ between the two principal components of horizontal ground motion characterized by design spectra A(T_n) and γA(T_n); the correlation coefficient α of responses r_x and r_y due to design spectrum A(T_n) applied in the x‐ and y‐directions, respectively; and β = r_y/r_x. It is demonstrated that the ratio r_cr/r_srss is bounded by 1 and . Thus the largest value of the ratio is , 1.26, 1.13 and 1.08 for γ = 0, 0.5, 0.75 and 0.85, respectively. This implies that the critical response never exceeds times the result of the SRSS analysis, and this ratio is about 1.13 for typical values of γ, say 0.75. The correlation coefficient α depends on the structural properties but is always bounded between −1 and 1. For a fixed value of γ, the ratio r_cr/r_srss is largest if β = 1 and α = ±1. The parametric variations presented for one‐storey buildings indicate that this condition can be satisfied by axial forces in columns of symmetric‐plan buildings or can be approximated by lateral displacements in resisting elements of unsymmetrical‐plan buildings. Copyright © 2000 John Wiley & Sons, Ltd.     

A ground motion selection procedure for enforcing hazard consistency and estimating seismic demand hazard curves

This paper develops a procedure to select unscaled ground motions for estimating seismic demand hazard curves (SDHCs) in performance‐based earthquake engineering. Currently, SDHCs are estimated from a probabilistic seismic demand analysis, where several ensembles of ground motions are selected and scaled to a user‐specified scalar conditioning intensity measure (IM). In contrast, the procedure developed herein provides a way to select a single ensemble of unscaled ground motions for estimating the SDHC. In the context of unscaled motions, the proposed procedure requires three inputs: (i) database of unscaled ground motions, (ii) I M , the vector of IMs for selecting ground motions, and (iii) sample size, n; in the context of scaled motions, two additional inputs are needed: (i) a maximum acceptable scale factor, SF_max, and (ii) a target fraction of scaled ground motions, γ. Using a recently developed approach for evaluating ground motion selection and modification procedures, the proposed procedure is evaluated for a variety of inputs and is demonstrated to provide accurate estimates of the SDHC when the vector of IMs chosen to select ground motions is sufficient for the response quantity of interest. Copyright © 2015 John Wiley & Sons, Ltd.     

Determination of first mode ground period and site-dependent design response spectrum for Taiwan High Speed Rail

The objective of this paper is to identify the first mode ground period T_g, at each interesting site along Taiwan High Speed Rail (THSR) route, and further, to determine the site-dependent design response spectrum for particular sites with T_g larger than 1 s. In this paper, a linear model of shear wave propagating in a multi-layered half-space is developed to identify the first mode ground period T_g of an interesting site on the basis of the field bore hole data. Furthermore, for each one of the strong ground motion observation stations within the Chiayi-Tainan area, the first mode ground period T_g was identified by either coda waves or pre-event ambient vibrations from the seismograms. In addition, the site-specific parameter C_v in defining the normalized response spectrum was also determined based on the observed strong ground motions at the specified observation station, and hence the empirical function between T_g and C_v can be regressed for this interesting area. Therefore, for a particular site along THSR route within the Chiayi-Tainan area, the site-specific parameter C_v can be determined from the regressed empirical function by the identified first mode ground period T_g, and further, used to develop the site-dependent design response spectrum.     

Near‐fault ground motions,and the response of elastic and inelastic single‐degree‐of‐freedom (SDOF) systems

In order to investigate the response of structures to near‐fault seismic excitations, the ground motion input should be properly characterized and parameterized in terms of simple, yet accurate and reliable, mathematical models whose input parameters have a clear physical interpretation and scale, to the extent possible, with earthquake magnitude. Such a mathematical model for the representation of the coherent (long‐period) ground motion components has been proposed by the authors in a previous study and is being exploited in this article for the investigation of the elastic and inelastic response of the single‐degree‐of‐freedom (SDOF) system to near‐fault seismic excitations. A parametric analysis of the dynamic response of the SDOF system as a function of the input parameters of the mathematical model is performed to gain insight regarding the near‐fault ground motion characteristics that significantly affect the elastic and inelastic structural performance. A parameter of the mathematical representation of near‐fault motions, referred to as ‘pulse duration’ (T_P), emerges as a key parameter of the problem under investigation. Specifically, T_P is employed to normalize the elastic and inelastic response spectra of actual near‐fault strong ground motion records. Such normalization makes feasible the specification of design spectra and reduction factors appropriate for near‐fault ground motions. The ‘pulse duration’ (T_P) is related to an important parameter of the rupture process referred to as ‘rise time’ (τ) which is controlled by the dimension of the sub‐events that compose the mainshock. Copyright © 2004 John Wiley & Sons, Ltd.     

复合外套型特高压交流CVT抗震与减震试验研究

为研究复合外套型电气设备的抗震性能与安装减震装置后的减震效果,对其进行特高压交流CVT地震模拟振动台试验研究,分析设备的动力特性与地震响应。白噪声试验结果表明试验设备安装减震器后其结构第一阶频率由1.07Hz略降低至1.04Hz,即减震装置对结构的整体刚度影响较小;人工波试验中原结构在地震动峰值加速度0.2g(PAG=0.2g)抗震试验中设备最大应力与位移响应为46.33 MPa与349.12mm,减震结构在PAG=0.5g抗震试验中,设备最大应力与位移响应为27.64 MPa与330.06mm,设备安装减震装置后抗震性能得到显著提升。试验研究结果可为复合材料电气设备抗震性能研究与减震装置应用提供参数数据。     

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.     

Site assessment and evaluation of spatial earthquake ground motion of Kyeongju

The earthquake hazard has been evaluated for 10 km×10 km area around Kyeongju. The ground motion potentials were determined based on equivalent linear analysis by using the data obtained from in situ and laboratory tests. In situ tests include 16 boring investigations, 4 crosshole, 12 downhole, 26 spectral analysis of surface waves tests, and in the laboratory, resonant column tests were performed. The peak ground accelerations range between 0.141g and 0.299g on collapse level earthquake and between 0.050g and 0.120g on operation level earthquake, respectively, showing the high potential of amplification in the deep alluvial layer in Kyeongju area. Distribution maps of site amplification for the peak acceleration, amplification factors (F_a and F_v) and dominant site period of Kyeongju are constructed using geographic information system tools. The amplification factor based on the Korean seismic design guide underestimated the motion in short range and overestimated the motion in mid-period range in Kyeongju. The importance of site-specific analysis and the need for the improved site characterization method are introduced.     

On the effective seismic input for non-linear soil-structure interaction systems

Two equivalent semi-discrete formulations are presented for the problem of the transient response of soil-structure interaction systems to seismic excitation, considering linear behaviour of the soil material and arbitrary non-linear structural properties. One formulation results in a direct method of analysis in which the motion in the structure and the entire soil medium, rendered finite by an artificial absorbing boundary, is determined simultaneously. The other represents a substructuring technique in which the structure and the soil are analysed separately. The forces induced in the discretized system by the incident seismic motion are obtained as part of the general formulation by using the free-field motion of the unaltered soil as the earthquake input. It is shown that these forces act within the soil region in the direct method, but only on the soil-structure interface in the substructure formulation. Both sets of forces, however, involve only the displacements and tractions acting on the fictitious surface in the unaltered (linear) soil which coincides with the soil-structure interface of the complete system. It is shown, further, that the free-field displacements alone define a minimal set of data for evaluating the seismic response of the structure, since the tractions and displacements on that surface are interrelated. In practice, the minimal set must be obtained by extrapolating the available information, as the free-field ground motion at a site is usually specified at a single reference point.     

Seismic response of large-span spatial structures under multi-support and multidimensional excitations including rotational components

To achieve rational and precise seismic response predictions of large span spatial structures(LSSSs),the inherent non-uniformity and multidimensionality characteristics of earthquake ground motions should be properly taken into consideration.However,due to the limitations of available earthquake stations to record seismic rotational components,the effects of rocking and torsional earthquake components are commonly neglected in the seismic analyses of LSSSs.In this study,a newly developed method to extract the rocking and torsion components at any point along the area of a deployed dense array from the translational earthquake recordings is applied to obtain the rotational seismic inputs for a LSSS.The numerical model of an actual LSSS,the Dalian International Conference Center(DICC),is developed to study the influences of multi-support and multidimensional excitations on the seismic responses of LSSSs.The numerical results reveal that the non-uniformity and multidimensionality of ground motion input can considerably affect the dynamic response of the DICC.The specific degree of influence on the overall and local structural displacements,deformations and forces are comprehensively investigated and discussed.     

The design of visco‐acoustic weighted L1‐error frequency–space wavefield extrapolators

Seismic imaging is an important step for imaging the subsurface structures of the Earth. One of the attractive domains for seismic imaging is explicit frequency–space (f – x) prestack depth migration. So far, this domain focused on migrating seismic data in acoustic media, but very little work assumed visco‐acoustic media. In reality, seismic exploration data amplitudes suffer from attenuation. To tackle the problem of attenuation, new operators are required, which compensates for it. We propose the weighted L ₁ ‐error minimisation technique to design visco‐acoustic f – x wavefield extrapolators. The L ₁ ‐error wavenumber responses provide superior extrapolator designs as compared with the previously designed equiripple L ₄ ‐norm and L_∞‐norm extrapolation wavenumber responses. To verify the new compensating designs, prestack depth migration is performed on the challenging Marmousi model dataset. A reference migrated section is obtained using non‐compensating f – x extrapolators on an acoustic dataset. Then, both compensating and non‐compensating extrapolators are applied to a visco‐acoustic dataset, and both migrated sections are then compared. The final images show that the proposed weighted L ₁ ‐error method enhances the resolution and results in practically stable images.     

Evaluation of combination rules for maximum response calculation in multicomponent seismic analysis

The existing rules for combining peak response to individual components of ground motion are evaluated. The response values r_e to two horizontal components of ground motion estimated by four multicomponent combination rules—SRSS‐, 30%‐, 40%‐ and simplified‐SRSS‐rules—are compared with the critical response, r_cr, obtained by the CQC3‐rule, which takes into account the direction of the principal ground components with respect to the structural axes and provides the largest response over all possible seismic incident angles. The following results are obtained in the first part of the paper and are valid for any elastic structure and any earthquake design response spectrum: For realistic values of the ratio γ of the design spectra for the two principal components of ground motion the SRSS‐rule estimate lies between 0.79r_cr and 1.00r_cr, the Simplified‐SRSS‐rule estimate lies between 1.00r_cr and 1.26r_cr, the 40%‐rule estimate lies between 0.99r_cr and 1.25r_cr, and the 30%‐rule estimate lies between 0.92r_cr and 1.16r_cr. None of the multicomponent combination rules account for the increase in response of systems if the vibration periods of the two modes that contribute most to the response to the x‐ and y‐components of ground motion are close to each other. Evaluated in the second part of the paper is the accuracy of the multicomponent combination rules in estimating the response of a range of one‐storey systems with (a) symmetrical plan and (b) unsymmetrical plan, and of two multistorey buildings. The SRSS‐rule underestimates the response by up to 16% and the other three rules overestimate it by up to 18%. Although these errors appear to be smaller than the many approximations inherent in structural design, they can be eliminated with very little additional computation by using an explicit formula for the critical response based on the CQC3 rule. Copyright © 2001 John Wiley & Sons, Ltd.     

Uniform-hazard response spectra—An alternative approach

An alternative method is presented for generating uniform-hazard response spectra making use of a seismic hazard curve expressing annual probability of exceedance as a function of Peak Ground Acceleration (PGA), a set of normalized (PGA = 1g) mean response spectra, and a coefficient-of-variation function for the random normalized spectral values in terms of period T. The practice of using mean + 1σ normalized response spectra, scaled to specified PGA levels, is discussed and associated mean return periods are evaluated.     

黄河阶地特征与地震动参数的相关性研究

在分析已有资料的基础上划分了兰州盆地与建设工程分布密切相关的T₀、T₁、T₂、T₃和T₄级黄河阶地,建立201个土层地震反应模型。通过一维等效线性化计算和反应谱分析,得出兰州盆地沉积阶地50年超越概率10%地表地震动参数,分析阶地高度和v_S≤500 m/s覆盖层厚度特征与地震动参数峰值加速度Am和加速度反应谱特征周期T_g的相关性。表明兰州盆地T₀~T₂阶地覆盖层厚度与50年超越概率10%A_m呈正相关,T₃及以上阶地覆盖层厚度对A_m增大有明显的减小作用。T_g值随T₀~T₃阶地覆盖层厚度的增加而变大,当覆盖层厚度进一步变大,T_g值不再同步增大,阶地覆盖层厚度对T_g的影响是有限的,阶地海拔高度与地表50年超越概率10%地震动参数没有关系。     

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.     

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 scaling methods for different site conditions and structure characteristics

Non‐linear dynamic time‐history analyses conducted as part of a performance‐based seismic design approach often require that the ground motion records are scaled to a specified level of seismic intensity. Recent research has demonstrated that certain ground motion scaling methods can introduce a large scatter in the estimated seismic demands. The resulting demand estimates may be biased, leading to designs with significant uncertainty and unknown margins of safety, unless a relatively large ensemble of ground motion records is used. This paper investigates the effectiveness of seven ground motion scaling methods in reducing the scatter in estimated peak lateral displacement demands. Non‐linear single‐degree‐of‐freedom systems and non‐linear multi‐degree‐of‐freedom systems are considered with different site conditions (site soil profile and epicentral distance) and structural characteristics (yield strength, period, and hysteretic behavior). It is shown that scaling methods that work well for ground motions representative of stiff soil and far‐field conditions lose their effectiveness for soft soil and near‐field conditions for a wide range of structural characteristics. Copyright © 2003 John Wiley & Sons, Ltd.     

Decentralized static output‐feedback H∞ controller design for buildings under seismic excitation

In this work, we present a new method in designing static output‐feedback H_∞ controllers suitable for vibrational control of buildings under seismic excitation. The method produces a Linear Matrix Inequality (LMI) formulation that allows obtaining static output‐feedback controllers with different information structure constraints by imposing a convenient zero–nonzero structure on the LMI variables. The application of the proposed methodology is illustrated by designing centralized and decentralized velocity‐feedback H_∞ controllers to mitigate the seismic response of a five‐story building. Copyright © 2011 John Wiley & Sons, Ltd.