Equating incremental dynamic analysis with static nonlinear analysis at near-field excitation

In an incremental dynamic analysis(IDA) using a set of ground motion records,nonlinear time history analysis needs to be performed on structures.It is well recognized that IDA calls for high computational efforts and the results are highly sensitive to selected ground motions.As a result,alternative static methods are needed.This study aims to introduce a new double-stage(N1- N2) static method to estimate capacity curves of MR frames.The technique is regulated to resemble IDA results with specific emphasis on near-field ground motions.Using an ensemble of 56 near-field earthquake records,required ID As have been carried out for SAC-Los Angeles 3-,9- and 20-story buildings and an additional 15-story building.The results of the proposed static method are compared with those from IDA,displacement-based adaptive procedure(DAP),and multimodal procedure(MMP).The results indicate that in addition to enhanced accuracy,very little time is required in the case of N1-N2 method.Thus,for the 3-story structure,the time required is less than 1 minute.The proposed N1-N2 method shows the best accuracy in terms of lateral mechanisms for the 15-story frame while for the other cases,the first mode load pattern leads to the best accuracy.     

结合Landsat ETM与实测光谱估测太湖叶绿素及悬浮物含量

实地测试太湖水体的反射光谱,实验室分析水样,运用相关分析法探求叶绿素、悬浮物的光谱特征波段,估测叶绿素和悬浮物含量;对比LandsatETM波段,运用不同的函数曲线对相应的波段组合进行回归拟合,建立相应的估测模型,选取精度最好的两个分别对太湖的叶绿素和悬浮物含量进行估测.结果表明:(1)对多光谱遥感而言,LandsatTM/ETM是定量获取叶绿素和悬浮物的较好的数据源,但不是最适合的数据源;(2)通过ETM3与叶绿素建立一定的函数关系来估测叶绿素含量具有较高的精度,其中利用算术组合ETM3/ETM1估测叶绿素的精度最高;(3)ETM4与悬浮物具有较高的相关度,其中利用算术组合ETM4/ETM1估测悬浮物含量的精度最高;(4)LandsatETM卫星影像中,不同尺寸的像元窗口影响水质参数的估测精度;对叶绿素估测而青,7×7或者5×5窗口比较适合,对悬浮物估测而言,一般不超过3×3.     

Cloud to IDA: Efficient fragility assessment with limited scaling

Incremental dynamic analysis (IDA) leads to curves expressed in terms of structural response versus intensity, commonly known as the IDA curves. It is known that implementation of IDA usually involves significant computational effort and most often significant scaling of the original records to various intensity levels. Employing as the performance variable the critical demand to capacity ratio (DCR) throughout the structure, which is equal to unity at the onset of the limit state, facilitates the identification of the intensity values at the onset of a desired limit state and hence the implementation of the IDA procedure. Employing the structural response to un‐scaled records and the corresponding regression‐based response predictions (a.k.a., the “Cloud Analysis”) helps in identifying the range of intensity values corresponding to demand to capacity ratio values in the vicinity of unity. The Cloud to IDA procedure for structural fragility assessment is proposed on the premise of exploiting the Cloud Analysis results to obtain the IDA curves both with minimum number of analyses and minimum amount of scaling. The transverse frame of a shear‐critical 7‐story older RC building in Van Nuys, CA, which is modeled in Opensees with fiber‐section considering the flexural‐shear‐axial interactions and the bar slip, is employed as a case study. It is demonstrated, by comparing the results to IDA and other state of the art non‐linear dynamic procedures based on no scaling or spectral‐shape‐compatible scaling, that the Cloud to IDA procedure leads to reliable results in terms of structural fragility and risk for the prescribed limit state.     

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.     

An improved capacity spectrum method for ATC‐40

In order to account for the non‐linear behavior of structures via non‐linear static procedure, the capacity spectrum method has been adopted by ATC‐40 for evaluation and retrofit of reinforced concrete buildings. For elastic‐perfectly‐plastic SDOF systems, the accuracy of the capacity spectrum method depends only on the acceleration response spectrum chosen to form the demand spectrum and the adopted model for calculating the equivalent viscous damping ratios. According to this method, the pseudo‐acceleration response spectrum (PS_a) is used to create the demand diagram. It is found that the ATC‐40 procedure, using its Type A hysteretic model, may be inaccurate especially for systems with damping ratios greater than 10% and periods longer than 0.15sec. In order to improve the accuracy of the capacity spectrum method, this study proposes to use the real absolute acceleration response spectrum (S0._a) instead of the PS_a to establish the demand diagram. The step‐by‐step procedure of the improved method and examples are implemented in this paper to illustrate the calculations of earthquake‐induced deformations. In addition, three selected models of equivalent viscous damping are also compared in this paper to assess the accuracy of the model used in the ATC‐40 procedure. Results show that the WJE damping model may be used by the capacity spectrum method to reasonably predict the inelastic displacements when the ductility demand (μ) of the structures is less than 4, whereas the damping model proposed by Kowalsky can be implemented when μ>4.0. Alternatively, the damping model proposed by Kowalsky may be used to calculate the equivalent viscous damping for the entire range of ductility. Copyright © 2003 John Wiley & Sons, Ltd.     

Approximate incremental dynamic analysis using the modal pushover analysis procedure

Incremental dynamic analysis (IDA)—a procedure developed for accurate estimation of seismic demand and capacity of structures—requires non‐linear response history analysis of the structure for an ensemble of ground motions, each scaled to many intensity levels, selected to cover the entire range of structural response—all the way from elastic behaviour to global dynamic instability. Recognizing that IDA of practical structures is computationally extremely demanding, an approximate procedure based on the modal pushover analysis procedure is developed. Presented are the IDA curves and limit state capacities for the SAC‐Los Angeles 3‐, 9‐, and 20‐storey buildings computed by the exact and approximate procedures for an ensemble of 20 ground motions. These results demonstrate that the MPA‐based approximate procedure reduces the computational effort by a factor of 30 (for the 9‐storey building), at the same time providing results to a useful degree of accuracy over the entire range of responses—all the way from elastic behaviour to global dynamic instability—provided a proper hysteretic model is selected for modal SDF systems. The accuracy of the approximate procedure does not deteriorate for 9‐ and 20‐storey buildings, although their dynamics is more complex, involving several ‘modes’ of vibration. For all three buildings, the accuracy of the MPA‐based approximate procedure is also satisfactory for estimating the structural capacities for the limit states of immediate occupancy, collapse prevention, and global dynamic instability. Copyright © 2006 John Wiley & Sons, Ltd.     

Extension of the CSM‐FEMA440 to plan‐asymmetric real building structures

The capacity spectrum method (CSM) has established itself as one of the most used Nonlinear Static Procedures for the seismic assessment of structures, since its introduction in 1975, when it was first presented by Freeman. More recently, this procedure was implemented in the ATC40 guidelines and lately improved in the FEMA‐440 report. The first step of work addressed by this paper relates to the comparison between the two features of the CSM. In the second part, an extension of the FEMA‐440CSM version is proposed for plan‐asymmetric real RC building structures. The case studies under analysis are the SPEAR building—an irregular 3D structure representing typical old three‐storey buildings in the Mediterranean region, from the early 1970s—and two real Turkish buildings with five and eight storeys. The CSM‐ATC40, the CSM‐FEMA440 and the proposed extended CSM‐FEMA440 method are applied and the results obtained duly compared with nonlinear dynamicit timehistory analyses. For the latter, semi‐artificial ground motions are used to define the seismic action. Copyright © 2010 John Wiley & Sons, Ltd.     

Incremental dynamic analysis and FEMA P695 seismic performance evaluation of a cold-formed steel–framed building with gravity framing and architectural sheathing

The objective of this paper is to present incremental dynamic analysis (IDA) and seismic performance evaluation results for a two-story cold-formed steel (CFS)–framed building. The archetype building was designed to current U.S. standards and then subjected to full-scale shake table tests under the U.S. National Science Foundation Network for Earthquake Engineering Simulation (NEES) program. Test results showed that the building's stiffness and capacity were considerably higher than expected and the building suffered only nonstructural damage even at excitations in excess of Maximum Considered Earthquake levels for a high seismic zone. For the archetype building, three-dimensional finite element models at different modeling fidelity levels were created using OpenSees. The models are subjected to IDA using the far-field ground motion records prescribed in Federal Emergency Management Agency (FEMA) P695. Seismic performance quantification following the FEMA P695 procedure shows that if the modeling fidelity only follows the state-of-the-practice, ie, only includes shear walls, unsafe collapse margin ratios are predicted. State-of-the-art models that account for participation from CFS gravity walls and architectural sheathing have overall performance that are consistent with testing, and IDA results indicate acceptable collapse margin ratios, predicated primarily on large system overstrength. Neglecting the lateral force resistance of the gravity system and nonstructural components, as done in current design, renders a safe design in the studied archetype, but largely divorced from actual system behavior. The modeling protocols established here provide a means to analyze a future suite of CFS-framed archetype buildings for developing further insight on the seismic response modification coefficients for CFS-framed buildings.     

Prediction of the median IDA curve by employing a limited number of ground motion records

A methodology has been proposed which can be used to reduce the number of ground motion records needed for the reliable prediction of the median seismic response of structures by means of incremental dynamic analysis (IDA). This methodology is presently limited to predictions of the median IDA curve only. The reduction in the number of ground motion records needed to predict the median IDA curve is achieved by introducing a precedence list of ground motion records. The determination of such a list is an optimization problem, which is solved in the paper by means of (1) a genetic algorithm and (2) a proposed simple procedure. The seismic response of a simple, computationally non‐demanding structural model has been used as input data for the optimization problem. The presented example is a three‐storey‐reinforced concrete building, subjected to two sets of ground motion records, one a free‐field set and the other a near‐field set. It is shown that the median IDA curves can be predicted with acceptable accuracy by employing only four ground motion records instead of the 24 or 30 records, which are the total number of ground motion records for the free‐field and near‐field sets, respectively. Copyright © 2007 John Wiley & Sons, Ltd.     

Apparent translational component for rotational ground motions

Even though the rotational ground motion may contribute significantly to the response of certain structures, their effects are generally ignored in seismic design, because of non-availability of appropriate instruments for direct recording of the rotational components. Like many others, a simplified framework was proposed by the authors elsewhere (Rodda and Basu in Int J Earthq Impact Eng 1(3):253–288, 2016) to extract the rotational motion as a temporal derivative of an apparent translational component (ATC) followed by scaling with an apparent velocity. ATC was defined such that its time derivative is closely correlated with the respective rotational motion. But the a priori knowledge of rotational motion is required in estimating the ATC for rocking component. An empirical procedure has been proposed here to bypass the requirement of rotational motion a priori. This paper also assesses the definition of ATC through examining the similitude between the time derivative of ATC and the respective rotational motion (benchmark) quantitatively. Similitude is assessed on smoothened response spectra (by Hamming window) of the time derivative of ATC and that of rotational motion. A new definition of spectral contrast angle (SCA) based on distance correlation has been proposed to assess the spectral similitude. To differentiate the similar from non-similar spectra, SCA corresponding to an acceptable degree of similarity is proposed by studying a large ensemble of ground motions from the PEER database. This similitude study is further extended using relative energy build up and energy spectra.     

钢框架结构地震响应与破坏过程的耐震时程分析

耐震时程法（ETM）是一种基于动力时程的结构抗震分析方法,其典型表征在于随着持续时间的增加,地震动强度逐渐增大。本文合成了基于中国抗震反应谱的耐震时程曲线,并以此作为输入,对一个8层3跨钢框架结构的抗震性能进行了分析和评估。采用增量动力分析方法（IDA）对结构在不同耐震持时下的整体响应进行了评估;以大震下天然地震动分析结果为标准,对比了结构在耐震时程曲线（ETA）作用下的塑性铰分布概率、形成顺序和延性分布。研究结果表明：耐震时程法能较好地预测钢框架结构的非线性动力响应及破坏过程,且分析次数少,这为钢框架结构的抗震性能快速分析与评估提供了一种新的手段。     

钢筋混凝土框架结构震后功能恢复能力的量化研究

震后功能恢复能力是指建筑物、社区或城市等遭受地震影响后实现功能恢复的能力。以一钢筋混凝土框架结构为对象,基于OpenSees有限元分析平台,对其进行增量动力分析,得到其对应于不同损伤状态的地震易损性曲线。进而基于单体建筑损失评估理论,评估该结构在不同强度水准地震动作用下的地震损失,包括直接经济损失和间接经济损失等。在此基础上,分别利用直线型、指数型以及三角函数型功能恢复模型,在不同强度水准地震动作用下,分别计算该结构的震后功能恢复能力。结果表明:随着地震动强度的增加,基于3种恢复模型计算得到的震后功能恢复能力都在下降,而且直线型和三角函数型恢复模型得到的恢复能力均比指数型的下降更快;在同一强度水准地震动作用下,基于指数型恢复模型计算得到的震后功能恢复能力均高于直线型和三角函数型恢复模型,即使在较强水准地震动作用下,根据指数型恢复模型得到的恢复能力依然较大。而在各个强度水准地震动作用下,基于直线型和三角函数型恢复模型得到的震后功能恢复能力非常接近。     

A web‐based methodology for the prediction of approximate IDA curves

A web‐based methodology for the prediction of approximate IDA curves, which consists of two independent processes, is proposed. The result of the first process is a response database of the SDOF model, whereas the second process involves the prediction of approximate IDA curves from the response database by using n‐dimensional linear interpolation. Such an approach enables user‐friendly prediction of the seismic response parameters with high accuracy. In order to demonstrate the capabilities of the proposed methodology, a web application for the prediction of the approximate 16th, 50th and 84th fractile responses of an RC structure was developed. For the presented case study, the response database was computed for a set of 30 ground motion records and the discrete values of six structural parameters. Very good agreement between the computed and the approximated IDA curves of the four‐storey RC building was observed. Copyright © 2012 John Wiley & Sons, Ltd.     

基于推覆分析的RC框架地震倒塌易损性预测

基于倒塌率的结构倒塌易损性分析是目前评价结构抗倒塌能力最合理的方法.但是,目前基于增量动力分析(IDA)的倒塌率分析方法,工作量和实施难度大,很难直接用于工程设计,因此有必要研究便于工程应用的新方法.本文基于18个典型多层RC框架结构的IDA倒塌率分析和静力推覆分析,发现RC框架在大震下的倒塌率及抗倒塌安全储备(CMR)与静力推覆得到的结构位移安全储备之间存在较好的相关关系.依据此关系,建议了保证大震倒塌率的推覆位移安全储备,并通过9个RC框架结构算例进行了验证.本文方法简单易行,可供规则多层RC框架结构抗倒塌设计参考.     

Collapse risk and residual drift performance of steel buildings using post-tensioned MRFs and viscous dampers in near-fault regions

The potential of post-tensioned self-centering moment-resisting frames (SC-MRFs) and viscous dampers to reduce the collapse risk and improve the residual drift performance of steel buildings in near-fault regions is evaluated. For this purpose, a prototype steel building is designed using different seismic-resistant frames, i.e.: moment-resisting frames (MRFs); MRFs with viscous dampers; SC-MRFs; and SC-MRFs with viscous dampers. The frames are modeled in OpenSees where material and geometrical nonlinearities are taken into account as well as stiffness and strength deterioration. A database of 91 near-fault, pulse-like ground motions with varying pulse periods is used to conduct incremental dynamic analysis (IDA), in which each ground motion is scaled until collapse occurs. The probability of collapse and the probability of exceeding different residual story drift threshold values are calculated as a function of the ground motion intensity and the period of the velocity pulse. The results of IDA are then combined with probabilistic seismic hazard analysis models that account for near-fault directivity to assess and compare the collapse risk and the residual drift performance of the frames. The paper highlights the benefit of combining the post-tensioning and supplemental viscous damping technologies in the near-source. In particular, the SC-MRF with viscous dampers is found to achieve significant reductions in collapse risk and probability of exceedance of residual story drift threshold values compared to the MRF.     

Empirical seismic vulnerability assessment of Icelandic buildings affected by the 2000 sequence of earthquakes

In June 2000, two Mw6.5 earthquakes occurred within a 4-day interval in the largest agricultural region of Iceland causing substantial damage and no loss of life. The distance between the earthquake epicentres and the fault rupture was approximately 15 km. Nearly 5000 low-rise residential buildings were affected, some of which were located between the faults and exposed to strong ground motion from both events. The post-earthquakes damage and repair costs for every residential building in the epicentral region were assessed for insurance purposes. The database is detailed and complete for the whole region and represents one of the best quality post-earthquake vulnerability datasets used for seismic loss estimation. Nonetheless, the construction of vulnerability curves from this database is hampered by the fact that the loss values represent the cumulative damage from two sequential earthquakes in some areas, and single earthquakes in others. A novel methodology based on beta regression is proposed here in order to define the geographical limits on areas where buildings sustained cumulative damage and predict the seismic losses for future sequence of events in each area. The results show that the average building loss in areas affected by a single event is below 10% of the building replacement value, whilst this increases to an average of 25% in areas affected by the two earthquakes. The proposed methodology can be used to empirically assess the vulnerability in other areas which experienced sequence of events such as Emilia-Romagna (Italy) in 2012.     

Modal pushover‐based scaling of earthquake records for nonlinear analysis of single‐story unsymmetric‐plan buildings

The modal pushover‐based scaling (MPS) procedure, currently restricted to symmetric‐plan buildings, is extended herein to unsymmetric‐plan buildings. The accuracy of the extended MPS procedure was evaluated for a large set of three‐degree‐of‐freedom unsymmetric‐plan structures with variable stiffness and strength. The structures were subjected to nonlinear response history analysis considering sets of seven records scaled according to the MPS procedure. Structural responses were compared against the benchmark values, defined as the median values of the engineering demand parameters due to 30 unscaled records. This evaluation of the MPS procedure has led to the following conclusions: (i) the MPS procedure provided accurate estimates of median engineering demand parameter values and reduced record‐to‐record variability of the responses; and (2) the MPS procedure is found to be much superior compared to the ASCE/SEI 7‐10 scaling procedure for three‐dimensional analysis of unsymmetric‐plan buildings. Copyright © 2013 John Wiley & Sons, Ltd.     

Mainshock-consistent ground motion record selection for aftershock sequences

In recent years, the additional risk posed to the built environment due to aftershock sequences and triggered events has been brought to attention, and several efforts have been directed towards developing fragility functions for structures in damaged conditions. Despite this rise of interest, a rather fundamental component for such tasks, namely that of aftershock ground motion record selection, has remained under-scrutinized. Herein, we propose a pragmatic procedure that can be applied for the selection of mainshock-aftershock ground motion pairs using consistent causal parameters and accounting for the correlation between their spectral accelerations. In addition, a structural analysis strategy that can be employed for the analytical derivation of damage-dependent fragility functions is outlined and presented through a case study. A more conventional back-to-back IDA analysis is also carried out in order to compare the derived damage-dependent fragility functions with the ones obtained with the proposed procedure. The results indicate that record selection remains a crucial factor even when assessing the structural vulnerability of damaged buildings, and should thus be treated cautiously.     

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.     

混凝土高层建筑结构地震破坏抗毁能力评估

提出基于构件性能的混凝土高层建筑结构地震破坏抗毁能力评估方法,采用强度与延性法分析混凝土高层建筑构件强度和变形,以对强震作用下混凝土高层建筑结构性能实施准确描述。基于建筑结构性能以及多条地震波情况下高层建筑结构倒塌极限状态的分析规范,采用IDA方法设置建筑结构抗倒塌能力系数,并依据该系数获取基于构件性能的混凝土高层建筑结构地震破坏抗毁能力评估流程,实现建筑结构地震破坏抗毁能力的准确评估。实验结果说明,所提方法实现了混凝土高层建筑结构地震破坏抗毁能力的准确评估。