Statistical insight into constant-ductility design using a non-stationary earthquake ground motion model

A recently developed earthquake ground motion model non-stationary in both intensity and frequency content is validated at the inelastic Single-Degree-Of-Freedom (SDOF) structural response level. For the purpose of this study, the earthquake model is calibrated for two actual earthquake records. The objective of a constant (or target) displacement ductility used in conventional earthquake-resistant design is examined from the statistical viewpoint using this non-stationary earthquake model. The non-linear hysteretic structural behaviour is modelled using several idealized hysteretic SDOF structural models. Ensemble-average inelastic response spectra corresponding to various inelastic SDOF response (or damage) parameters and conditioned on a constant displacement ductility response are derived from the two identified stochastic ground motion models. The effects of the type of hysteretic behaviour, the structural parameters, the target displacement ductility factor, and the ground motion model on the statistics of the inelastic response parameters are thoroughly investigated. The results of this parametric study shed further light on the proper interpretation and use of inelastic response or damage parameters in earthquake-resistant design in order to achieve the desirable objective of ‘constant-damage design’. © 1997 by John Wiley & Sons, Ltd.     

单自由度自复位体系设计能量谱研究

本文对具有旗帜型滞回模型的单自由度自复位体系提出了设计能量谱的构造方法,包括设计输入能量谱和设计滞回耗能比谱。首先按中国规范场地类别选取360条实际强震记录进行时程分析,对影响单自由度自复位体系输入能量谱和滞回耗能比谱的参数,包括地震波类型、滞回模型、阻尼比、延性系数等进行研究。在此基础上分别建议了设计输入能量谱和设计滞回耗能比谱及其曲线参数的确定方法,并与实际强震记录计算结果进行比较。结果表明结构滞回模型对能量谱影响明显;阻尼比和延性系数对输入能量谱的影响在整个周期范围内有显著差异,但均有明显的削峰作用。建议的两种设计能量谱综合考虑了结构参数、地震波参数和中国场地类别的影响,可以较好的拟合实际情况,并对弹塑性单自由度自复位体系在地震作用下的耗能需求做出较准确的估计。     

基于性能的基础隔震钢筋混凝土框剪结构的倒塌可靠度分析

利用基于性能的结构可靠度分析方法,对基础隔震钢筋混凝土框剪结构进行分析研究。选取20条实际地震动记录,以0.2g为步长对结构地震动参数PGA进行调幅后,建立了140个结构-地震动样本空间。选取上部结构的最大层间位移角、隔震层位移为量化指标,对每一个样本进行动力非线性时程分析后,将结构响应进行统计得到结构在各地震动强度下超越极限破坏状态的概率,将其绘制成基础隔震钢筋混凝土框剪结构的易损性曲线并利用整体可靠度方法分析结构发生倒塌的可靠度指标。该方法直观地反映了结构发生倒塌的概率,为结构的地震损失评估提供依据。     

Effect of earthquake ground motions on fragility curves of highway bridge piers based on numerical simulation

Fragility curves express the probability of structural damage due to earthquakes as a function of ground motion indices, e.g., PGA, PGV. Based on the actual damage data of highway bridges from the 1995 Hyogoken‐Nanbu (Kobe) earthquake, a set of empirical fragility curves was constructed. However, the type of structure, structural performance (static and dynamic) and variation of input ground motion were not considered to construct the empirical fragility curves. In this study, an analytical approach was adopted to construct fragility curves for highway bridge piers of specific bridges. A typical bridge structure was considered and its piers were designed according to the seismic design codes in Japan. Using the strong motion records from Japan and the United States, non‐linear dynamic response analyses were performed, and the damage indices for the bridge piers were obtained. Using the damage indices and ground motion indices, fragility curves for the bridge piers were constructed assuming a lognormal distribution. The analytical fragility curves were compared with the empirical ones. The proposed approach may be used in constructing the fragility curves for highway bridge structures. Copyright © 2001 John Wiley & Sons, Ltd.     

A simplified method of constructing fragility curves for highway bridges

Fragility curves are found to be useful tools for predicting the extent of probable damage. They show the probability of highway structure damage as a function of strong motion parameters, and they allow the estimation of a level of damage probability for a known ground motion index. In this study, an analytical approach was adopted to develop the fragility curves for highway bridges based on numerical simulation. Four typical RC bridge piers and two RC bridge structures were considered, of which one was a non‐isolated system and the other was an isolated system, and they were designed according to the seismic design code in Japan. From a total of 250 strong motion records, selected from Japan, the United States, and Taiwan, non‐linear time history analyses were performed, and the damage indices for the bridge structures were obtained. Using the damage indices and ground motion parameters, fragility curves for the four bridge piers and the two bridge structures were constructed assuming a lognormal distribution. It was found that there was a significant effect on the fragility curves due to the variation of structural parameters. The relationship between the fragility curve parameters and the over‐strength ratio of the structures was also obtained by performing a linear regression analysis. It was observed that the fragility curve parameters showed a strong correlation with the over‐strength ratio of the structures. Based on the observed correlation between the fragility curve parameters and the over‐strength ratio of the structures, a simplified method was developed to construct the fragility curves for highway bridges using 30 non‐isolated bridge models. The simplified method may be a very useful tool to construct the fragility curves for non‐isolated highway bridges in Japan, which fall within the same group and have similar characteristics. Copyright © 2003 John Wiley & Sons, Ltd.     

Elastic-plastic response spectra for different hysteretic rules

The general features of elastic-plastic response spectra for several accelerograms that are widely used for the design buildings in Japan were studied in terms of the effects of the different hysteretic models used in the analyses. Lare fluctuations existed in the spectra for both input ground motion and the different models. The models were classified according to their strain energy-absorbing capacities in three groups, within each of which the relevant nature of elastic-plastic responses of the structures were similar. Finally, empirical formulae with which to estimate two measures structural damage, the ductility factors and cumulative plastic displacement normalized by the yielding displacement, wer developed for each group of hysteretic models.     

Ground motion duration effects on nonlinear seismic response

The study presented in this paper addresses the question of which nonlinear demand measures are sensitive to ground motion duration by statistical analyses of several case studies. A number of single degree of freedom (SDOF) structures were selected considering: (1) four oscillation periods; (2) three evolutionary and non‐evolutionary hysteretic behaviours; (3) two target ductility levels. Effects of duration are investigated, by nonlinear dynamic analysis, with respect to six different demand indices ranging from displacement ductility ratio to equivalent number of cycles. Input is made of six real accelerogram sets representing three specific duration scenarios (small, moderate and large duration). For all considered demand quantities time‐history results are formally compared by statistical hypothesis test to asses the difference, if any, in the demand concerning different scenarios. Incremental dynamic analysis curves are used to evaluate duration effect as function of ground motion intensity (e.g. spectral acceleration corresponding to the SDOF's oscillation period). Duration impact on structural failure probability is evaluated by fragility curves. The results lead to the conclusion that duration content of ground motion is statistically insignificant to displacement ductility and cyclic ductility demand. The conclusions hold regardless of SDOF's period and hysteretic relationship investigated. Copyright © 2005 John Wiley & Sons, Ltd.     

Inelastic buildings with tuned mass dampers under moderate ground motions from distant earthquakes

The effectiveness of tuned mass dampers (TMD) in vibration control of buildings was investigated under moderate ground shaking caused by long‐distance earthquakes with frequency contents resembling the 1985 Mexico City (SCT) or the 1995 Bangkok ground motion. The elastic–perfectly plastic material behaviour was assumed for the main structure, with linear TMDs employed by virtue of their simplicity and robustness. The accumulated hysteretic energy dissipation affected by TMD was examined, and the ratio of the hysteretic energy absorption in the structure with TMD to that without it is proposed to be used, in conjunction with the peak displacement ratio, as a supplementary TMD performance index since it gives an indication of the accumulated damage induced in the inelastic structures. For the ground motions considered, TMD would be effective in reducing the hysteretic energy absorption demand in the critical storeys for buildings in the 1.8–2.8 s range. The consequence is reduction in damage of the buildings which would otherwise suffer heavy damage in the absence of TMD, resulting in economical restorability in the damage control limit state. This is of practical significance in view of the current trend toward performance‐based design. Copyright © 2001 John Wiley & Sons, Ltd.     

考虑场地类别与强震持时的滞回耗能谱的特征分析

基于力或位移的结构抗震设计方法大多无法反映地震动持时的影响,而能量设计方法则能较好地弥补其不足。按场地类别和强震持时,将302条Northridge地震记录分为15组,对地震记录的峰值进行规一化处理,采用钢筋混凝土退化三线型恢复力模型,对单自由度体系进行弹塑性时程分析,研究场地类别、强震持时、强度屈服水平以及结构周期等因素对滞回耗能的影响。结果表明:在给定地震记录的峰值和屈服强度水平下,结构的滞回耗能依赖于场地条件和强震持时等因素;滞回耗能随强震持时的增加而增大,随场地特征周期的增加而增大。通过非线性回归分析,建立了与峰值加速度、峰值速度、强震持时相对应的简化滞回耗能谱的计算公式。     

Neural networks for quick earthquake damage estimation

This paper proposes the use of neural networks to predict damage due to earthquakes from the indices of recorded ground motion. Since the relationship between ground motion indices and resulting damage is difficult to express in mathematical form, neural networks are conveniently applied for this problem. Simulated earthquake ground motions are used to have a well-distributed data set and the ductility factor from non-linear analysis of two single-degree-of-freedom structural models is used to represent the damage. A sensitivity analysis procedure is described to identify qualitatively the input parameters that have a greater influence on the damage. The result of the trained neural network is then verified by using several recorded earthquake ground motions. It is found that some instability in the prediction can occur. Instability occurs when input values exceed the range of the training data. The neural network model using PGA and SI as input give the best performance in the recall tests using actual earthquake ground motion, demonstrating the usefulness of neural network models for the quick estimation of damage through earthquake intensity monitoring.     

Statistical analysis of peaks and directivity of earthquake ground motion

Conversion factors are useful for attenuation and damage estimation relationships. These factors among different definitions of peaks (i.e. larger, average and resultant) for peak ground motion indices and acceleration response spectrum were investigated. A large number of horizontal acceleration records recorded at 76 free-field sites of the Japan Meteorological Agency were used in this study. Two orthogonal horizontal components were combined in the time domain to get the maximum resultant peak ground motion indices and acceleration response spectrum in the horizontal plane. From the analysis, the means of the larger/resultant ratio were found to be 0·934 for acceleration, 0·926 for velocity, and 0·913 for displacement. A similar decreasing trend was observed for the means of the average/resultant ratio of the ground motion indices and acceleration response spectrum. The directivity of peak ground motion indices was also examined. It was found that the peak ground motion is more likely to occur in the transverse direction than in other directions. This trend is more prominent in the long-period contents of ground motion.     

A damage-based definition of effective peak acceleration

This paper presents a rational basis for obtaining the Effective Peak Acceleration (EPA) of a given ground motion process. The proposed formulation considers the statistical variability in the ground motion, and is centred on the idea of explicitly linking EPA with expected cumulative damage in the structures due to the inelastic excursions. The structural behaviour has been modelled by a Single-Degree-Of-Freedom (SDOF) bilinear hysteretic oscillator. EPA is considered to be the expected PGA of a scaled ground motion process such that this oscillator undergoes a specified expected damage under the unscaled process if it is linearly designed for the scaled process. For estimation of the damage, the oscillator has been replaced by an equivalent linear oscillator through stochastic averaging. A parametric study has been carried out to investigate the dependence of EPA on several governing parameters, and it has been shown that despite the strong dependence of EPA on oscillator time period, it may be possible to obtain ‘period-averaged’ EPA values for several ground motion processes for engineering applications. © 1998 John Wiley & Sons, Ltd.     

单自由度体系的地震残余变形研究

结构在经受地震动作用后会发生变形和位移,其中在震动结束后不能恢复的这一部分,即为残余变形或永久变形。残余变形取决于结构本身的动力性能和输入地震波的特性以及场地条件等。残余变形能够提供震害评估的信息,同时也是震后加固修复的指标。对单自由度体系进行了研究,考察不同自振周期、阻尼比、延性水准、滞回特性以及输入地震动下的残余变形,得到其影响因素并分析其中机理,为以最大变形和累积耗能为依据的基于性能的抗震工程学提供了补充和新的思路。     

Consistent inelastic design spectra: Hysteretic and input energy

This is the second of two companion papers on inelastic design spectra (for strength, displacement, hysteretic and input energy) for systems with a prescribed ductility factor. All the spectra are consistent (interrelated and based on the same assumptions). This paper deals with two quantities related to cumulative damage: hysteretic and input energy. The input data for the procedure are the characteristics of the expected ground motion in terms of a smooth elastic pseudo-acceleration spectrum and the time integral of the square of the ground acceleration ∫a² dt. Simple, approximate expressions for two dimensionless parameters (the parameter γ and the hysteretic to input energy ratio E_HE_I) have been proposed. The parameter 7, which controls the reduction of the deformation capacity of structures due to low-cycle fatigue, depends on the natural period of the system, the prescribed ductility factor, the hysteretic behaviour and the ground motion characteristics. The ratio E_H/E_I is influenced by damping, the ductility factor and the hysteretic behaviour. Very good approximations to the inelastic spectra for hysteretic and input energy can be derived from the elastic spectrum using the spectra for the reduction factor R, proposed in the companion paper, and the proposed values for γ and E_H/E_I     

高层混合结构滞回耗能比的研究

基于结构层间弯曲屈服强度的概念,提出了高层混合结构滞回耗能比的简化计算公式,该公式综合体现了结构以及地震动特征参数对结构滞同耗能比的影响。研究表明,结构滞回耗能比随地震动的峰值速度与峰值加速度的比值的增大而增大;随着地震动幅值的增大,滞回耗能比也线性增加;对于短持时地震动,滞回耗能比与强震持时之间没有一定的规律性,但对于长持时地震动,结构滞回耗能比会随强震持时的增大而线性增加。随着结构弯曲屈服强度系数的增大,结构滞回耗能比呈凹函数下降,结构的自振周期越大,同一弯曲屈服强度系数对应的滞回耗能比越小;钢框架与混凝土剪力墙承载力比值的增加能够降低结构的滞回耗能比。     

Damage response of multistorey r/c buildings with different structural systems subjected to seismic motion of arbitrary orientation

In the present study the combined influence of seismic orientation and a number of parameters characterizing the structural system of Reinforced Concrete (R/C) buildings on the level of expected damages are examined. For the purposes of the above investigation eight medium‐rise buildings are designed on the basis of the current seismic codes. The structural characteristics examined are the ratio of the base shear received by the structural walls, the ratio of horizontal stiffness in two orthogonal directions and the structural eccentricity. Then, the buildings are analyzed by nonlinear time response analysis using 100 bidirectional earthquake ground motions. The two horizontal accelerograms of each ground motion are applied along horizontal orthogonal axes, forming 72 different angles with the structural axes. The structural damage is expressed in terms of the Park and Ang damage index. The results of the analyses revealed that the damage level of the buildings is strongly affected by the incident angle of the ground motion. The extent at which the orientation of the seismic records influences the damage response depends on the structural system and the distance of the record to the fault rupture. As a consequence, the common practice of applying the earthquake records along the structural axes can lead to significant underestimation of structural damage. Also, it was shown that the structural eccentricity can significantly differentiate the seismic damage level, as well as the impact of the earthquake orientation on the structural damage. Copyright © 2015 John Wiley & Sons, Ltd.     

A new approach of selecting real input ground motions for seismic design: The most unfavourable real seismic design ground motions

This paper presents a new way of selecting real input ground motions for seismic design and analysis of structures based on a comprehensive method for estimating the damage potential of ground motions, which takes into consideration of various ground motion parameters and structural seismic damage criteria in terms of strength, deformation, hysteretic energy and dual damage of Park & Ang damage index. The proposed comprehensive method fully involves the effects of the intensity, frequency content and duration of ground motions and the dynamic characteristics of structures. Then, the concept of the most unfavourable real seismic design ground motion is introduced. Based on the concept, the most unfavourable real seismic design ground motions for rock, stiff soil, medium soil and soft soil site conditions are selected in terms of three typical period ranges of structures. The selected real strong motion records are suitable for seismic analysis of important structures whose failure or collapse will be avoided at a higher level of confidence during the strong earthquake, as they can cause the greatest damage to structures and thereby result in the highest damage potential from an extended real ground motion database for a given site. In addition, this paper also presents the real input design ground motions with medium damage potential, which can be used for the seismic analysis of structures located at the area with low and moderate seismicity. The most unfavourable real seismic design ground motions are verified by analysing the seismic response of structures. It is concluded that the most unfavourable real seismic design ground motion approach can select the real ground motions that can result in the highest damage potential for a given structure and site condition, and the real ground motions can be mainly used for structures whose failure or collapse will be avoided at a higher level of confidence during the strong earthquake. Copyright © 2007 John Wiley & Sons, Ltd.     

Damage index based on stiffness degradation of low‐rise RC walls

Widely used damage indices, such as ductility and drift ratios, do not account for the influences of the duration of strong shaking, the cumulative inelastic deformation or energy dissipation in structures. In addition, the formulation and application of most damage indices have until now been based primarily on flexural modes of failure. However, evidence from earthquakes suggests that shear failure or combined shear‐flexure behavior is responsible for a large proportion of failures. Empirical considerations have been made in this paper for evaluating structural damage of low‐rise RC walls under earthquake ground motions by means of a new energy‐based low‐cycle fatigue damage index. The proposed empirical damage index is based on the results of an experimental program that comprised six shake table tests of RC solid walls and walls with openings; results of six companion walls tested under QS‐cyclic loading were used for comparison purposes. Variables studied were the wall geometry, type of concrete, web shear steel ratio, type of web shear reinforcement, and testing method. The index correlates the stiffness degradation and the destructiveness of the earthquake in terms of the duration and intensity of the ground motions. The stiffness degradation model considers simultaneously the increment of damage associated to the low‐cycle fatigue, energy dissipation, and the cumulative cyclic parameters, such as displacement demand and hysteretic energy dissipated. Copyright © 2014 John Wiley & Sons, Ltd.     

Generalized dynamic analysis of structural single rocking walls (SRWs)

The investigation of structural single rocking walls (SRWs) continues to gain interest as they produce self-centering lateral load responses with reduced structural damage. The simple rocking model with modifications has been shown to capture these responses accurately if the SRW and its underlying base are infinitely rigid. This paper advances previous rocking models by accounting for (1) the inelastic actions at or near the base of the SRW and (2) the flexural responses within the wall. Included in the proposed advancements are hysteretic and inherent viscous damping associated with these two deformation components so that the total dynamic responses of SRWs can be captured with good accuracy. A system of nonlinear equations of motion is developed, in which the rocking base is discretized into fibers using a zero-length element to locate the associated compressive deformations and damage. The flexural deformations of the rocking body are captured using an elastic term, while the impact events are modeled using impulse-momentum equations. Comparisons with experiments of structural precast concrete and masonry SRWs show that the proposed approach accurately estimates the dynamic responses of different SRWs with and without unbonded posttensioning, for various dynamic excitations and degrees of hysteretic action. Using the proposed approach, a numerical investigation employs different configurations of structural SRWs to quantify the various sources of energy loss, including hysteretic action and impact damping, during various horizontal ground motions.     

长周期地震动强度指标与SDOF体系残余变形相关性分析

为分析两类长周期地震动作用下如何选取合理的强度指标作为结构抗震设计的输入,从2011年东日本9.0级地震、2003年十胜冲8.0级地震和2016年熊本7.3级地震数据库中选取90条可靠的远场长周期地震动。从1994年美国北岭6.7级地震和1999年台湾集集7.6级地震数据库中选取60条近场长周期地震动,以SDOF体系为研究对象,讨论了阻尼比、屈服刚度折减系数和强度折减系数对残余变形与18个地震动强度指标的相关系数的影响,对比分析了两类长周期地震作用下相关系数之间的异同。研究结果表明:在考虑近场长周期地震动作用时,建议应根据结构周期的大小来选择合适的强度指标作为地震动的输入。远场长周期地震动作用下,以PGA、PGV和PGD为代表的强度指标与残余变形的相关程度均较高,PGV稳定性略好于PGA和PGD,建议PGV作为地震动输入的控制指标。残余变形相关系数受阻尼比、屈服刚度折减系数以及强度折减系数影响不大。