近断层区的输入能量设计谱及其在基于能量抗震设计中的应用

研究并确定输入能量设计谱是建立基于性能抗震设计和评估能量方法的必要基础。选取断层15km投影距离内的224条强震记录讨论场地类型和断层距等因素的影响,建议了近场地震的输入能量设计谱(EIDS),在与实际记录及日本等国已有抗震规范比较后表明,所建议的设计能量谱能较好地反映近断层区潜在能量需求,在此基础上形成了基于能量的桥梁结构抗震评估设计方法,并用3座实际RC桥墩进行算例验证证明了所建议方法的可行性,表明基于既有抗震规范设计的桥梁结构仍有必要进行考虑近断层效应的耗能能力验算。     

Design energy input spectra for moderate‐seismicity regions

This paper proposes energy input spectra applicable to seismic design of structures located in low‐to‐moderate‐seismicity regions. These spectra represent the load effect, in terms of input energy, of the most severe earthquake that the construction might encounter during its lifetime. The spectra have been derived through dynamic response analyses of over 100 ground motion records obtained from 48 earthquakes that have occurred in Spain. An empirical equation for estimating the energy input contributable to damage from the total input energy is also suggested. This equation takes into account both the damping and the degree of plastification of the structure. Finally, the proposed design energy input spectra are compared with the provisions of the current Spanish Seismic Code and with the response spectra of recent earthquakes that have occurred in Turkey and Taiwan. Copyright © 2002 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。     

Site-dependent design spectra and strength modification factors, based on records from Greece

Elastic and inelastic spectra are derived, based on a representative sample of acceleration records from Greece, carefully selected based on magnitude, distance and peak ground acceleration criteria, and grouped into three ground condition categories according to the 2004 Eurocode 8 (EC8) provisions. Using software developed in-house, elastic (pseudoacceleration, pseudovelocity and displacement), as well as inelastic (strength and displacement) spectra are computed for various critical damping ratios and ductility levels. After appropriate scaling, mean spectra are computed both irrespective of, as well as for each different, ground condition, and comparisons with EC8 provisions are made. As a further evaluation of the code spectra, three additional earthquake scenarios are considered representing ground-motion characteristics not reflected in the compiled dataset of records. Subsequently, modification factors for strength (q_μ) are derived from statistical analysis of constant ductility spectra, and corresponding empirical relationships, suitable for design purposes, are proposed.     

Incorporating low‐cycle fatigue model into duration‐dependent inelastic design spectra

Seismic performance of structures is related to the damage inflicted on the structure by the earthquake, which means that formulation of performance‐based design is inherently coupled with damage assessment of the structure. Although the potential for cumulative damage during a long‐duration earthquake is generally recognized, most design codes do not explicitly take into account the damage potential of such events. In this paper, the classical low‐cycle fatigue model commonly used for seismic damage assessment is cast in a framework suitable for incorporating cumulative damage into seismic design. The model, in conjunction with a seismic input energy spectrum, may be used to establish an energy‐based seismic design. In order to ensure satisfactory performance in a structure, the cyclic plastic strain energy capacity of the structure is designed to be larger than or equal to the portion of seismic input energy contributing to cumulative damage. The resulting design spectrum, which depends on the duration of the ground motion, indicates that the lateral strength of the structure must be increased in order to compensate for the increased damage due to an increased number of inelastic cycles that occur in a long‐duration ground motion. Examples of duration‐dependent inelastic design spectra are developed using parameters currently available for the low‐cycle fatigue model. The resulting spectra are also compared with spectra developed using a different cumulative damage model. Copyright © 2004 John Wiley & Sons, Ltd.     

Regional variation of spectral parameters for seismic design from broadband probabilistic seismic hazard analysis

The characterisation of the seismic hazard input is a critical element of any seismic design code, not only in terms of the absolute levels of ground motion considered but also of the shape of the design spectrum. In the case of Europe, future revisions of the seismic design provisions, both at a national and a pan‐European level, may implement considerable modifications to the existing provisions in light of recent seismic hazard models, such as the 2013 European Seismic Hazard Model. Constraint of the shape of the long‐period design spectrum from seismic hazard estimates on such a scale has not been possible, however, owing to the limited spectral period range of existing ground motion models. Building upon recent developments in ground motion modelling, the 2013 European Seismic Hazard Model is adapted here with a new ground motion logic tree to provide a broadband Probabilistic Seismic Hazard Analysis for rock sites across a spectral period range from 0.05 seconds to 10.0 seconds. The resulting uniform hazard spectra (UHS) are compared against existing results for European and broadband Probabilistic Seismic Hazard Analysis and against a proposed formulation of a generalised design spectrum in which controlling parameters can be optimised to best fit the uniform hazard spectra in order to demonstrate their variability on a European scale. Significant variations in the controlling parameters of the design spectrum are seen both across and within stable and active regions. These trends can help guide recalibrations of the code spectra in future revisions to seismic design codes, particularly for the longer‐period displacement spectrum.     

Levels of Probability of Exceedance for Current Code Spectra in China

Long-period acceleration spectra determined by seismic safety evaluation for project sites are generally lower than that given by relative code spectra. In this paper, we discuss the recurrence periods corresponding to the code spectra of different periods, by using ground motion attenuation laws for sites of types Ⅰand Ⅲ. We show the results that the longer the periods of code spectra are commonly the more conservative the seismic level is. As for the project examples in this paper, when the periods are longer than 3.7 or 5.2 seconds for sites of types Ⅰ or Ⅲ, the recurrence periods corresponding to the code spectra are longer than 5000 years. We suggest that some problems need to be further discussed, including the reliability of the present attenuation laws, the performance of those project structures that suffer long period seismic waves and have been designed according to the conservative codes, and the effects of ground motion parameters such as velocity and displacement on seismic design.     

一致概率谱衰减指数的取值方法探讨

在重大工程的地震安全性评价工作中,根据概率法地震危险性分析得到的一致概率反应谱,与建筑抗震设计规范给出的设计反应谱常常不一致,特别是在长周期部分,一致概率谱一般均低于相应的规范谱。为解决地震安全性评价得到的一致概率谱在抗震设计中的应用,本文通过比较、分析一致概率谱和规范谱,针对一致概率谱标定得到的衰减指数γ较规范谱明显偏大的特点,提出了一致概率谱衰减指数的取值方法。     

设计反应谱长周期区段的研究

本文利用近20年国内外大地震时获得的数字强震仪记录分析强震动的长周期分量特性,给出了不同场地上的平均加速度反应谱及其拟合曲线。结果表明,现行抗震设计规范中设计谱的特征周期和长周期谱值明显偏小。在此基础上提出了长周期设计反应谱的修正建议。文中还根据统计分析提出了不同阻尼比的反应谱修正公式。     

An alternative construction of normalized seismic design spectra for near-fault regions

This paper presents a methodology for constructing seismic design spectra in near-fault regions.By analyzing the characteristics of near-fault pulse-type ground motions,an equivalent pulse model is proposed,which can well represent the characteristics of the near-fault forward-directivity and fling-step pulse-type ground motions.The normalized horizontal seismic design spectra for near-fault regions are presented using recorded near-fault pulse-type ground motions and equivalent pulse-type ground motions,which are derived based on the equivalent pulse model coupled with ground motion parameter attenuation relations.The normalized vertical seismic design spectra for near-fault regions are obtained by scaling the corresponding horizontal spectra with the vertical-to-horizontal acceleration spectral ratios of near-fault pulse-type ground motions.The proposed seismic design spectra appear to have relatively small dispersion in a statistical sense.The seismic design spectra for both horizontal and vertical directions can provide alternative spectral shapes for seismic design codes.     

Introducing new design spectra derived from Italian recorded ground motions 1972 to 2017

The shape of design spectra, traditionally based on regions characterized by constant displacement, constant velocity, and constant acceleration, has been discussed from a conceptual point of view by Calvi (2018). In the same study, a formulation for the definition of the design spectra relying on four parameters was proposed. Predictive models are proposed herein to calculate these four parameters, conditional on magnitude and distance. These models were developed using a large number of recorded ground motions in Italy, and they allow defining combined spectral acceleration versus spectral displacement plots. Such design spectra are shown to reasonably interpolate the experimental data, resulting in acceleration and displacement demand that approximate the response spectra resulting from +1σ results obtained from recorded ground motions. While it is recognized that numerous additional parameter should be considered (eg, focal depth and fault distance, site amplification), it is also concluded that this approach to define the seismic demand is promising toward a rationalization of seismic design. A thorough application of the approach developed and preliminary tested in this work may result in a re‐visitation of seismic design approaches and, ultimately, in a more efficient use of the available resources.     

Merging energy‐based design criteria and reliability‐based methods: exploring a new concept

This paper examines the potential development of a probabilistic design methodology, considering hysteretic energy demand, within the framework of performance‐based seismic design of buildings. This article does not propose specific energy‐based criteria for design guidelines, but explores how such criteria can be treated from a probabilistic design perspective. Uniform hazard spectra for normalized hysteretic energy are constructed to characterize seismic demand at a specific site. These spectra, in combination with an equivalent systems methodology, are used to estimate hysteretic energy demand on real building structures. A design checking equation for a (hypothetical) probabilistic energy‐based performance criterion is developed by accounting for the randomness of the earthquake phenomenon, the uncertainties associated with the equivalent system analysis technique, and with the site soil factor. The developed design checking equation itself is deterministic, and requires no probabilistic analysis for use. The application of the proposed equation is demonstrated by applying it to a trial design of a three‐storey steel moment frame. The design checking equation represents a first step toward the development of a performance‐based seismic design procedure based on energy criterion, and additional works needed to fully implement this are discussed in brief at the end of the paper. Copyright © 2006 John Wiley & Sons, Ltd.     

An energy-based methodology for the assessment of seismic demand

A methodology for the assessment of the seismic energy demands imposed on structures is proposed. The research was carried out through two consecutive phases. Inelastic design input energy spectra for systems with a prescribed displacement ductility ratio were first developed. The study of the inelastic behavior of energy factors and the evaluation of the response modification in comparison with the elastic case were performed by introducing two new parameters, namely: (1) the Response Modification Factor of the earthquake input energy (R_E), representing the ratio of the elastic to inelastic input energy spectral values and (2) the ratio α of the area enclosed by the inelastic input energy spectrum in the range of periods between 0.05 and 4.0 s to the corresponding elastic value. The proposed design inelastic energy spectra, resulting from the study of a large set of strong motion records, were obtained as a function of ductility, soil type, source-to-site distance and magnitude.Subsequently, with reference to single degree of freedom systems, the spectra of the hysteretic to input energy ratio were evaluated, for different soil types and target ductility ratios. These spectra, defined to evaluate the hysteretic energy demand of structures, were described by a piecewise linear idealization that allows to distinguish three distinct regions as a function of the vibration period. In this manner, once the inelastic design input energy spectra were determined, the definition of the energy dissipated by means of inelastic deformations followed directly from the knowledge of hysteretic to input energy ratio.The design spectra of both input energy and hysteretic to input energy ratio were defined considering an elasto-plastic behavior. Nevertheless, other constitutive models were taken into account for comparison purposes.     

Testing the acceleration spectra given by China and USA seismic codes based on energy supply in near-fault region

For near-fault ground motion,there should be a remarkable impulsive energy supply. Therefore,it is essential to check the validity of actual seismic design codes with energy balance concept. Based on the relationship between the spectrum velocity and the input energy equivalent velocity with 5% damping ratio,the input energy spectra compatible with main China and USA seismic codes were derived,and the accuracy and applicability were veri-fied by using near-fault records. The recommended energy input design spectrum (EIDS) applicable to the distance of 0～15 km from fault was introduced to check the validity of modern seismic codes. Comparison tests show that the GB50011-2001 Code of China can just match the energy effect of near-fault ground motion to a certain extent only under seldom occurred earthquake with fortification intensity of 9 degree for site soil of Ⅲ and IV,indicating that the impact of near-fault effect has not been embodied in the current code acceleration spectrum. In order to make the design spectrum be applicable to near-fault region,it is necessary to adjust the spectrum platform pa-rameters. On the contrary,for distinct fault distance and site soil,the UBC97 Code of USA can match well with the energy supply of near-fault ground motion except for the site soil of hard rock (SA). Accordingly,correctness of the formula derivation in this paper is certified.     

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.     

Characteristics of response spectra for long-periods of main-shock recordings of the Chi-Chi earthquake

Current practice uses predictive models to extrapolate long-period response spectra based on far-field recordings in moderate and weak earthquakes. However, the spectra are not long enough and the data are often not reliable, which means that the seismic design code cannot accurately define seismic design requirements for long-period structures. The near-field recordings in the main-shock of the Chi-Chi earthquake have a large signal-to-noise ratio (SNR), which makes them suitable for studying the long-period acceleration response spectrum up to 20 sec. The acceleration response spectra from 246 stations within 120 km of the causative fault are statistically analyzed in this paper. The influence of distance and site conditions on long-period response spectrum is discussed, and the shapes of the amplification spectra are compared with the standard spectra specified in the seismic design code of China. Finally, suggestions for future revisions to the code are proposed.     

工程结构等延性地震抗力谱研究

研究结构的非弹性反应谱对改进现有的结构抗震设计、发展基于性态的抗震设计以及了解复杂地面运动特性与结构动力特性之间的关系具有重要的意义。利用大量的单自由度在强震记录作用下的弹塑性动力时程分析,对等延性地震抗力谱这一重要的非弹性反应谱进行了较为详尽的研究,给出了四类场地条件(基岩、硬土、一般土和软土)下的平均等延性地震抗力谱,总结了对工程结构的抗震设计和研究具有实际意义的规律和特征,并分析了场地条件、结构的延性系数以及周期等对等延性地震抗力谱的影响,提出了新的拟合公式,其成果可供抗震研究和设计直接应用。     

中、美主要抗震设计规范加速度谱的近断层地震动能量检验.

近场地震通常有显著的脉冲型高能输入,有必要从能量角度对现行抗震规范进行有效性检验,以探讨规范加速度设计谱能否体现近断层区域地震地面运动的能量耗散需求. 基于本文作者所建议的5%阻尼比下谱速度与输入能量等效速度之间关系,推导了与当前中、美主要抗震设计规范(GB50011-2001, UBC97)加速度谱相容的输入能量谱,并对其适用范围进行了讨论. 将其与基于实际近断层记录分组所得的输入能量设计谱进行对比表明, 我国GB50011-2001规范除软土场地的9度罕遇烈度外均难以体现近场地震的能量要求,有必要对设计谱平台高度进行调整;而美国UBC97规范则在除SA类场地之外的其它条件下均能较好地与15 km范围内的近场能量需求相吻合,从而也证明了本文推导方法的正确性.      

关于改进我国抗震设计反应谱的探讨

本文回顾了地震反应分析理论发展的三个阶段,指出反应谱理论仍然是许多国家现阶段抗震设计的理论依据,我国规范也主要采用反应谱法进行抗震设计分析。进一步讨论了反应谱与抗震设计反应谱的联系和区别。把我国《建筑抗震设计规范(GB50011—2001)》中有关地震影响系数分别与ISO 3010:2001(E)和美国的建筑抗震设计规范中的地震影响系数做了对比,发现我国规范有些地方考虑得还不够全面,还需要不断地完善。提出在抗震设计中运用地震动参数代替地震烈度来进行计算能更好地反映工程实际情况。     

Evaluation of reduction factors for high-damping design response spectra

High-damping response spectra are essential tools for the assessment and design methods based on the equivalent elastic structure concept. They are also often used for the analysis and design of structures with seismic isolation or energy dissipation systems. Many formulations of the reduction factors have been proposed and included in seismic codes to estimate high-damping response spectra from their 5% damping representation. They are reviewed in the present paper. The accuracy of each of them in estimating the maximum elastic response of structures with viscous damping ratios greater than 5% is assessed by comparing exact and approximate displacement response spectra for three different damping levels, namely 10, 20 and 30%, respectively. The comparison is referred to more than 120 ground motion records, relevant to earthquakes with magnitude between 6 and 8, epicentral distance ranging from 1 to 100 km and Peak Ground Accelerations (PGA’s) greater than 0.1 g. The comparison between exact and approximate response spectra is carried out for both single earthquakes and groups of earthquakes with similar magnitude and epicentral distance. The drawbacks of using the same damping reduction factor to estimate both maximum displacement response and design seismic forces are also addressed.