Seismic damage assessment based on different hysteretic rules

The inelastic response of a single-degree-of-freedom (SDOF) system to different sets of earthquake records was analysed to study the significance of ground motion characteristics on structural damage. Six non-linear models were used. The ductility ratio and hysteretic energy index were chosen as two important damage indices to measure the structural damage. The dispersion phenomenon exhibited by yield spectra due to input ground motion was reduced by incorporating the ground motion a/v ratio into the two damage indices. Finally, empirical formulae for estimating two measures of structural damage were developed for each hysteretic model.     

A NOTE ON DAMAGE-BASED INELASTIC SPECTRA

When a structure is subjected to moderate to severe ground motions, a few excursions of the response yield level may take place following the reductions usually enforced in the design forces. These excursions are associated with progressive damage in the structure. Thus, a choice of the design level has to be suitably based on the maximum damage to be allowed in the structure. In this paper, a stochastic technique of developing damage-based non-linear spectra has been proposed for the aseismic design of those structures which can be idealized through Single-Degree-Of-Freedom (SDOF) oscillators. The proposed technique has been illustrated by obtaining the non-linear spectra which can possibly be used for a damage-based design. Along with the spectra, allowable ductility demand which should be supplied through proper sizing and detailing of the members and is compatible with the damage has also been specified. The non-linear SDOF oscillators have been approximated for this purpose by equivalent linear oscillators using a new stochastic linearization technique. The proposed linearization technique has been validated through simulation results in the case of an idealized, non-hysteretic, Elasto-Plastic (EP) model.     

Ductility demand spectra for multiple near- and far-fault earthquakes

This study presents ductility demand spectra for single degree of freedom (SDOF) systems under multiple near- and far-fault seismic ground motions. The main innovation has to do with the quantification of the seismic sequence effect directly into ductility demands, a phenomenon which has not been studied in the past. Due to lack of real seismic sequences records, this paper examines only artificial sequences, where they have been generated by a rational and random combination of real single events. A statistical investigation of more than 120 millions dynamic inelastic analyses is conducted to obtain expressions for the ductility demands, in terms of the period of vibration, the viscous damping, the post-yield stiffness and the force reduction factor. It is found that due to the seismic sequence effect, it is certainly insufficient to consider only the ‘design earthquake’, since this traditional hypothesis leads to underestimated ductility demands and therefore to underestimated structural damage.     

Evaluation of site‐dependent constant‐damage design spectra for reinforced concrete structures

An investigation on the validity of the conventional design approach known as constant displacement ductility is carried out. The hysteretic behaviour described by the Modified Takeda model is taken to represent the characteristics of reinforced concrete structural systems. The results presented in the form of seismic damage spectra indicate that the conventional design approach may not be valid because cumulative damage is excessively high. The inelastic design spectra based on the constant‐damage concept are proposed in terms of simplified expressions. The expressions are derived from constant‐damage design spectra computed by non‐linear response analysis for SDOF systems subjected to ground motions recorded on rock sites, alluvium deposits, and soft‐soil sites. The proposed expressions, which are dependent on the local soil conditions, are functions of target seismic damage, displacement ductility ratio and period of vibration. The seismic damage of structures that have been designed based on this new design approach is also checked by a design‐and‐evaluation approach. The results are found to be satisfactory. Copyright © 2004 John Wiley & Sons, Ltd.     

Earthquake‐resistant structural design through energy demand and capacity

An energy‐based earthquake‐resistant structural design method is proposed. The proposed method uses specific input energy spectra, modal or time‐history analyses, and energy distribution among structural members. For a given member strength and stiffness, a relationship between the energy attributable to damage absorbed by a member and its cumulative ductility demand can be determined. Member strength, stiffness and energy capacity are design parameters which are simultaneously used in the design. The method can avoid soft‐storey design. The damage is measured based on a cumulative basis considering earthquake magnitude, frequency, and duration. Tests have been carried out to determine energy absorbing capacities of various structural components. More efforts are needed to make the energy‐based earthquake‐resistant structural design practical, but ssimple formulations for this method are possible. Copyright © 2007 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.     

剪切型结构的抗震强度折减系数研究

为了研究剪切型结构抗震强度需求的变化规律,本文基于单自由度体系的非线性时程分析,研究了不同场地条件下延性折减系数与位移延性系数和结构自振周期的关系;采用修正等效单自由度体系位移延性折减系数的方法,研究了剪切型多自由度体系的延性折减系数;以基于中国建筑抗震规范设计的代表不同抗震能力要求的RC框架结构为分析对象,通过静力弹塑性分析,研究了RC框架结构的体系超强能力。分析结果表明场地类别、位移延性水准和结构振动周期对单自由度体系的延性折减系数有显著的影响;多自由度体系的抗震延性折减系数明显比其相应的等效单自由度体系的抗震延性折减系数小;RC框架结构的超强系数一般随结构楼层数的增加而减小,随抗震设防烈度的增大而减小,内框架的超强系数比边框架的超强系数大。     

Nonlinear dynamic analysis of reinforced concrete shear wall structures

During strong ground motions, structural members made of reinforced concrete undergo cyclic deformations and experience permanent damage. Members may lose their initial stiffness as well as strength. Recently, Los Alamos National Laboratory has performed experiments on scale models of shear wall structures subjected to recorded earthquake signals. In general, the results indicated that the measured structural stiffnesses decreased with increased levels of excitation in the linear response region. Furthermore, a significant reduction in strength as well as in stiffness is also observed in the inelastic range. Since the in-structure floor response spectra which are used to design and qualify safety equipment have been based on calculated structural stiffness and frequencies, it is possible that certain safety equipment could experience greater seismic loads than were specified for qualification due to stiffness reduction.In this research, a hysteresis model based on the concept of accumulated damage has been developed to account for this stiffness degradation both in the linear and inelastic ranges. Single and three-degrees-of-freedom seismic Category I structures were analysed and compared with equivalent linear stiffness degradation models in terms of maximum displacement responses, permanent displacement, and floor response spectra. The results indicate significant differences in response between the hysteresis model and equivalent linear stiffness degradation model at PGA levels of greater than 0.8 g. The hysteresis model is used in the analysis of reinforced concrete shear-wall structures to obtain the in-structure response spectra. Results of both cumulative and one shot tests are compared.     

Inelastic seismic spectra including a damage criterion: A stochastic approach

In this paper, a stochastic approach for obtaining damage-based inelastic seismic spectra is proposed. The Park and Ang damage model, which includes displacement ductility and hysteretic energy, is adopted to take into account the cumulative damage phenomenon in structural systems under strong ground motions. Differently from previous studies in this field, damage-based seismic spectra are obtained by means of peak theory of stochastic processes. The following stochastic inelastic seismic spectra are constructed and then analyzed: damage-based displacement and acceleration inelastic spectra, damage-based response modification factor spectra, damage-based yield strength demand spectra and damage-based inelastic displacement ratio spectra.     

Inelastic response and design criteria of plan-wise asymmetric systems

The study of the torsional response of buildings in the inelastic range of behaviour is of great interest since the ability of structures to resist strong earthquakes mainly relies on their ductility and capacity for energy dissipation. Furthermore, an examination of the performance of structures during past earthquakes demonstrates that plan-asymmetric buildings suffered greater damage due to torsional response. The paper deals with this subject by analysing a model which idealizes a one-storey building with resisting elements oriented along two perpendicular directions. In addition to the parameters of the elastic behaviour, the inelastic system response depends on full yield capacity and plan-wise strength distribution. The influence of the criterion adopted for the design of resisting elements on local ductility demand and damage has been evaluated by parametric analysis. In particular, a comparison has been carried out between systems with equal design levels for all elements and systems with design levels dependent on the element location. For a given elastic behaviour and total capacity, the strength distributions in plan have been defined which minimize ductility demand and structural damage. Finally, based on these findings, responses from models designed according to several seismic codes have been compared.     

Optimum strength ratio of hysteretic damper

This paper deals with steel moment frames combined with hysteretic dampers. Specifically, it examines the strength of dampers required to minimize damage to moment frames under earthquake loading. The important structural variables are the ratio of the dampers' shear strength to the maximum resistance, termed β in this study, and the relative stiffness between the damper and the main frame, termed k. The equivalent viscous damping ratio of the entire structural system is affected by the quantities β and k and the ductility ratio of the main frame. The optimum dampers' strength ratio (β_opt), which maximizes the equivalent viscous damping ratio, was formulated as a function of k, and it was found that β_opt is independent of the ductility ratio of the main frame. Earthquake response analysis confirmed that damage to the main frame can be significantly reduced by hysteretic dampers and minimized at the value of β_opt. © 1998 John Wiley & Sons, Ltd.     

Seismic safety of low ductility structures used in Spain

The most important aspects of the design, seismic damage evaluation and safety assessment of structures with low ductility like waffle slabs buildings or flat beams framed buildings are examined in this work. These reinforced concrete structural typologies are the most used in Spain for new buildings but many seismic codes do not recommend them in seismic areas. Their expected seismic performance and safety are evaluated herein by means of incremental non linear structural analysis (pushover analysis) and incremental dynamic analysis which provides capacity curves allowing evaluating their seismic behavior. The seismic hazard is described by means of the reduced 5% damped elastic response spectrum of the Spanish seismic design code. The most important results of the study are the fragility curves calculated for the mentioned building types, which allow obtaining the probability of different damage states of the structures as well as damage probability matrices. The results, which show high vulnerability of the studied low ductility building classes, are compared with those corresponding to ductile framed structures.     

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.     

抗震结构的等效延性破坏准则及其子结构试验验证

基于试验结果与分析，本文提出了反映结构低周疲劳特性的“等效延性破坏准则”。将由结构非线性动力反应分析求得的、预计按本文所提破坏准则能引起柱破坏的三种不同位移反应时程，施加于三个柱试件，以验证所提准则的有效性与实用性。     

延性需求谱在基于性能的抗震设计中的应用

基于性能的抗震设计理论涉及如何简便而合理地确定结构在指定强度地震下的弹塑性位移需求。本文给出了利用延性需求谱求解结构位移需求的一般步骤:借助模态Pushover分析将多自由度体系分解为几个非线性单自由度体系,以考虑各阶振型的影响;利用延性需求谱计算对应模态的等效单自由度体系的延性及位移需求,并以一定方式组合转化为多自由度体系位移需求。最后,通过算例分析表明:利用延性需求谱求解结构位移需求是一种具有一定精度可为工程接受的简便方法,在基于性能的抗震设计中具有较好的应用前景。     

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。     

钢筋混凝土结构的屈服位移Chopra能力谱损伤分析与性能设计

本文提出了应用地震损伤指数评定结构抗震性能要求的方法。首先，建立了抗力谱曲线和结构损伤指数的关系，得到了反映不同设防水准损伤目标的结构地震务容许延性系数；其次，应用屈服位移Chopra能力谱法确定地震损伤延性系数；然后，提出了应用结构地震损伤延性系数和容许延性系数之间的关系来评定结构抗震性能的方法；最后，通过算例说明了本文方法实施的步骤。     

地震动输入能量衰减规律的研究

对所收集到的266条强震记录，将其按场地条件分类，计算了不同场地条件、不同延性系数下的“绝对”和“相对”输入能量反应谱，然后利用两步回归法，得出了不同场地条件下地震动“绝对”和“相对”两种输入能量的衰减规律，分析了场地条件、延性系数、震级及距离等参数对地震动能量谱的影响，并对两种输入能量衰减规律进行了比较。     

Constant-ductility strength demand spectra for seismic design of structures

In displacement-based seismic design, constant-ductility strength demand spectra （CDSDS） are very useful for preliminary design of new structures where the global displacement ductility capacity is known. The CDSDS can provide the required inelastic lateral strength of new structures from the required elastic lateral strength. Based on a statistical study of nonlinear time-history for an SDOF system, the mean CDSDS corresponding to four site conditions are presented and approximate expressions of the inelastic spectra are proposed, which are functions of the structural period and ductility level. The effects of site conditions, structural period, level of ductility, damping and post-yield stiffness of structures on CDSDS are also investigated. It is concluded that site conditions, ductility level and structural period have important effects on the CDSDS and damping, post-yield stiffness effects are rather complex and of minor importance. The damping, post-yield stiffness effects depend on both the level of ductility and the natural period of structures.     

Near-fault ground motions with prominent acceleration pulses： pulse characteristics and ductility demand

Major earthquakes of last 15 years (e.g., Northridge 1994, Kobe 1995 and Chi-Chi 1999) have shown that many near-fault ground motions possess prominent acceleration pulses. Some of the prominent ground acceleration pulses are related to large ground velocity pulses, others are caused by mechanisms that are totally different from those causing the velocity pulses or fling steps. Various efforts to model acceleration pulses have been reported in the literature. In this paper, research results from a recent study of acceleration pulse prominent ground motions and an analysis of structural damage induced by acceleration pulses are summarized. The main results of the study include: (1) temporal characteristics of acceleration pulses; (2) ductility demand spectrum of simple acceleration pulses with respect to equivalent classes of dynamic systems and pulse characteristic parameters; and (3) estimation of fundamental period change under the excitation of strong acceleration pulses. By using the acceleration pulse induced linear acceleration spectrum and the ductility demand spectrum, a simple procedure has been developed to estimate the ductility demand and the fundamental period change of a reinforced concrete (RC) structure under the impact of a strong acceleration pulse.