Damage-based inelastic response spectra for seismic design incorporating performance considerations

Modern seismic design allows a structure to develop inelastic response during moderate to severe earthquakes. The emerging performance-based design requires more clearly defined levels of inelastic response, or damage, to be targeted for different earthquake hazard levels. While there are a range of factors that could influence the level of damage and hence the performance, the design strength remains to be a fundamental design parameter that is inherently related to the structural performance. In this paper, the response reduction factor, which is a normalized form of the design strength, is investigated on a direct damage basis. The implications of the damage-based strength reduction factor (SRF), denoted as R_D factor, on multiple performance targets are discussed. A series of R_D spectra are generated from a large set of ground motions in different groupings to examine the effects of local site condition, earthquake magnitude and distance to rupture on the R_D spectra. The overall mean and standard deviation of the R_D spectra for different levels of damage are obtained, and simple empirical formulas are proposed.     

Constant‐ductility response spectra for sequential earthquake and tsunami loading

Simplified approaches for examining structural system response under sequential earthquake and tsunami loading are helpful for understanding response trends. To aid understanding, nonlinear (constant‐ductility) response spectra are developed for elastoplastic single degree of freedom systems subjected to seismic loads followed by hydrodynamic tsunami loads. The forcing function is composed of long‐duration earthquake motion concatenated with a range of tsunami hydrodynamic forces that are proportional to the pseudo‐spectral acceleration produced by the earthquake motion. The constant‐ductility spectra are thus constructed for scenarios where the loading imposed by one hazard is not dominant over the other. The spectra and basic intensity measures indicate that the amplification of response for sequential earthquake and tsunami loading over the earthquake only case is most significant for systems with long natural periods and high‐ductility capacity under seismic loading. Copyright © 2017 John Wiley & Sons, Ltd.     

Inelastic spectra to predict period elongation of structures under earthquake loading

Period lengthening, exhibited by structures when subjected to strong ground motions, constitutes an implicit proxy of structural inelasticity and associated damage. However, the reliable prediction of the inelastic period is tedious and a multi‐parametric task, which is related to both epistemic and aleatory uncertainty. Along these lines, the objective of this paper is to investigate and quantify the elongated fundamental period of reinforced concrete structures using inelastic response spectra defined on the basis of the period shift ratio (T_in/T_el). Nonlinear oscillators of varying yield strength (expressed by the force reduction factor, R_y), post‐yield stiffness (a_y) and hysteretic laws are examined for a large number of strong motions. Constant‐strength, inelastic spectra in terms of T_in/T_el are calculated to assess the extent of period elongation for various levels of structural inelasticity. Moreover, the influence that structural characteristics (R_y, a_y and degrading level) and strong‐motion parameters (epicentral distance, frequency content and duration) exert on period lengthening are studied. Determined by regression analyses of the data obtained, simplified equations are proposed for period lengthening as a function of R_y and T_el. These equations may be used in the framework of the earthquake record selection and scaling. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Sliding and overturning potential of Christchurch 2011 earthquake records

The 22 February 2011 M_w 6.3 earthquake produced a number of unique accelerograms in the city of Christchurch and the port of Lyttelton. Four of these records are analyzed in this paper. The two are from the Christchurch Catholic Cathedral College and Christchurch Hospital stations in the center of the city, which were placed on top of loose sandy soils that suffered softening due to liquefaction; one is from the Lyttelton station, Lyttelton Port Company, on a rock outcrop; and one is from the station at the Heathcote Valley Primary School, on stiff colluvial silts and sands near the edge of a steep and stiff sedimentary basin. The (elastic) response spectra are discussed and related to some salient characteristics of the motions. Symmetric and asymmetric sliding of a block resting through Coulomb friction on horizontal or inclined planes and rocking–overturning of rigid blocks, when excited at their base by these records, offer a strong indication of their ‘destructiveness potential’. The corresponding sliding and overturning spectra of the 2011 records are compared with those of some historic accelerograms to get an understanding of the severity of ground shaking that caused 170 deaths and heavy geotechnical and structural damage in the city of Christchurch. The possible role played by the unusually large vertical accelerations is also explored. Copyright © 2012 John Wiley & Sons, Ltd.     

双规准化地震动加速度反应谱研究

本文提出了双规准反应谱的概念。在统计了美国西部大量强震记录的基础上,分别研究了规准反应谱和双规准反应谱的特性,并进行了详细的对比分析。研究结果表明,双规准反应谱比通常的规准反应谱有更好的规律性,这不仅有利于认识地震动的特性,还可使基于场地的抗震设计反应谱大大简化,更便于广大工程设计人员应用。     

不同地震水准反应谱之间的关系和罕遇地震作用设计反应谱的确定

不同地震作用水准的设计反应谱长期以来一直采用各水准谱形完全一致的假定。这与地震危险性分析的一般结论不符。《建筑抗震设计规范》(GB50011-2001)对此作出了修订。本文基于设计反应谱的三参数标定模型推导了罕遇和多遇地震作用设计反应谱的关系，指出两者谱值之比在高频、中频和低频段分别对应于峰值加速度、速度和位移之比。引入地震动衰减规律进行了罕遇和多遇地震作用设计谱关系的近似估计，提出了基于多遇地震作用设计谱确定罕遇地震作用设计谱的调整方案，验证了现行规范将反应谱特征周期适当延长以得到罕遇地震作用设计谱的做法的合理性。     

地震动双规准速度反应谱研究

本文在统计了大量强震记录的基础上,分别研究了双规准加速度反应谱和双规准速度反应谱的特性,进行了对比分析,并分别得出了定量分析的结果。研究结果表明,双规准加速度反应谱在短周期段有很好的统一性,而双规准速度反应谱在长周期段的统一性较好,这种规律性对于认识地震动的特性、改进抗震设计反应谱具有重要的意义。     

摩擦摆隔震结构地震反应谱的计算分析

探讨了摩擦摆基底隔震结构的地震反应谱规律。采用上部结构-摩擦摆两质点模型并利用系统振动微分方程，计算绘制了设计参数(质量比、摩擦系数、滑道半径)不同取值下上部结构的绝对加速度、侧向位移和基底水平滑移反应谱。结果表明：摩擦摆系统对刚度较大的上部结构具有良好的隔震效果。摩擦系数对上部结构的加速度反应、层间水平侧移和系统滑移均有较大的影响，质量比的影响次之．而滑道半径仅对系统滑移有较为显著的作用。     

Study on elastic response of structures to near-fault ground motions through record decomposition

Accelerograms recorded near active faults have some important characteristics that make them different from those recorded in far-fault regions. High-frequency components in acceleration records and long-period velocity pulses are among notable specifications of such ground motions. In this paper, a moving average filtering with appropriate cut-off frequency has been used to decompose the near-fault ground motions into two components having different frequency contents: first, Pulse-Type Record (PTR) that possesses long-period pulses; second, the relatively high-frequency BackGround Record (BGR), which does not include large velocity pulses. Comparing the results with those extracted through wavelet analysis shows that moving average filter is an appropriate and efficient tool for near-fault records decomposition. The method is applied to decompose a suite of 91 selected near-fault records and the elastic response of structures is examined through their response to the decomposed parts. The results emphasizes that in contrast with ordinary far-fault earthquake records, response spectra of near-fault ground motions typically have two distinct local peaks, which are representatives of the high- and low-frequency components, i.e., BGR and PTR, respectively. Moreover, a threshold period is identified below which the response of structures is dominated by BGR while PTR controls the response of structures with periods longer than this period.     

土层结构对反应谱特征周期的影响

本文选取和构造了若干有工程意义的典型场地剖面,利用目前工程上广泛应用的场地地震反应分析的一维等效线性化波动方法,计算了在不同地震动输入下的不同场地剖面的地表加速度峰值和地表速度峰值。利用计算得到的地表加速度峰值和速度峰值计算了不同场地在不同地震动输入下的反应谱的特征周期。研究了不同土层结构对地表加速度反应谱特征周期的影响,获得了一些有意义的结果。     

土层结构对反应谱平台值的影响

本文利用目前工程上广泛应用的场地地震反应的一维等效线性化波动方法,计算了不同场地模型在三种不同强度的地震动输入下的地表加速度反应谱。为了研究不同的土层结构对反应谱平台值的影响,本文将计算得到的地表加速度反应谱拟合成建筑抗震设计规范规定的设计反应谱的形式,分析对比了不同的覆盖层厚度、软弱土层对反应谱平台值的影响,得到了一些有价值的研究成果。     

摩擦摆基础隔震结构多维地震反应分析

对摩擦摆基础隔震结构进行了单向、双向和三向地震反应对比分析,表明考虑双向水平地震动时摩擦摆基础隔震结构的支座位移增大,而结构的加速度和楼层剪力减小,其中对支座位移和结构加速度影响较大;考虑竖向地震动时摩擦摆基础隔震结构的支座位移略有减小,而结构的加速度和楼层剪力增大,其中对结构加速度影响较大.因而,在进行摩擦摆基础隔震结构地震反应分析时,应考虑多维地震动的影响.     

几条地震波的归一化时-频反应谱分析

时-频反应谱是地震动幅值、频谱和持时三要素构成的空间三维谱.基于此,本文提出归一化时-频反应谱定义与计算方法,计算三条典型地震波的归一化时-频反应谱,对比分析表明:不同地震记录的时-频反应谱的幅值在时间和周期两个轴上的分布差别很大,具有不同时-频反应谱的地震波可能对结构地震响应产生不同影响;对12层钢筋混凝土框架结构模型进行弹塑性时程分析,通过结构地震反应、结构损伤曲线与输入地震动的归一化时-频反应谱对比,发现结构最大反应并不一定是造成结构倒塌的直接原因,用结构弹性阶段反应最大值进行抗震设计存在一定局限性,从而证明归一化时-频反应谱可有效用来分析地震动特性和结构破坏机理.     

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。     

Response spectra for differential motion of columns paper II: Out-of-plane response

It is shown that the common response spectrum method for synchronous ground motion can be extended to make it applicable for earthquake response analyses of extended structures experiencing differential out-of-plane ground motion. A relative displacement spectrum for design of first-story columns SDC (T, T_T, ζ, ζ_T, τ, δ) is defined. In addition to the natural period of the out-of-plane response, T, and the corresponding fraction of critical damping, ζ, this spectrum also depends on the fundamental period of torsional vibrations, T_T, and the corresponding fraction of critical damping, ζ_T, on the “travel time,” τ (of the waves in the soil over a distance of about one-half the length of the structure), and on a dimensionless factor δ, describing the relative response of the first floor. The new spectrum, SDC, can be estimated by using the empirical scaling equations for relative displacement spectra, SD, and for peak ground velocity, v_max. For recorded strong-motion acceleration, and for symmetric buildings, the new spectrum can be computed from Duhamel's integrals of two uncoupled equations for dynamics equilibrium describing translation and rotation of a two-degree-of-freedom system. This representation is accurate when the energy of the strong-motion is carried by waves in the ground the wavelengths of which are one order of magnitude or more longer than the characteristic length of the structure.     

Analysis of ground motions at Treasure Island site during the 1989 Loma Prieta earthquake

Site response analyses and coherence studies were conducted at the Treasure Island site where surface motions were recorded during the Loma Prieta earthquake. The analyses were conducted using a nonlinear dynamic effective stress method which took into account the effects of the liquefaction that occured at the site. The rock motions recorded at nearby Yerba Buena Island were used as input motions. Computed and recorded ground motions transverse to the direction of wave propagation and associated response spectra were in good agreement. Agreement was also good in the radial direction, except in certain frequency bands higher than 1·25 Hz. Coherence studies showed that some of these discrepancies may be due to low coherence between the Treasure Island and Yerba Buena motions in these same frequency bands.     

Damaging properties of ground motions and prediction of maximum response of structures based on momentary energy response

Dynamic damaging potential of ground motions must be evaluated by the response behaviour of structures, and it is necessary to indicate what properties of ground motions are most appropriate for evaluation. For that purpose, the behaviour of energy input process and hysteretic energy dissipation are investigated in this study. It is found that the momentary input energy that is an index for the intensity of input energy is related to the characteristics of earthquakes such as cyclic or impulsive, and to the response displacement of structures immediately. On the basis of these results, a procedure is proposed to predict inelastic response displacement of structures by corresponding earthquake input energy to structural dissipated damping and hysteretic energy. In this procedure the earthquake response of structures is recognized as an input and dissipation process of energy, and therefore structural properties and damaging properties of ground motions can be taken into account more generally. Lastly, the studies of the pseudodynamic loading test of reinforced concrete structure specimens subjected to ground motions with different time duration are shown. The purpose of this test is to estimate the damaging properties of ground motions and the accuracy of the proposed prediction procedure. Copyright © 2002 John Wiley & Sons, Ltd.     

频率对K_0固结饱和粘土动力特性影响的试验分析

通过循环三轴试验,研究了k0固结饱和粘土在0.5 Hz、0.1 Hz与0.01 Hz循环应力作用下,循环强度与土样破坏时最终累积孔压的变化。结果表明,当循环频率从0.1 Hz减少至0.01 Hz时,若循环应力作用下三轴土样发生应力反向,k0固结饱和粘土循环强度大约降低3%左右;若没有应力反向,且当循环破坏次数从10变化至1 000时,循环强度的降低不超过1%,若循环破坏次数大于1 000时,循环频率的改变对循环强度基本没有影响。对于有应力反向情况,循环频率减小将导致最终累积孔压比增加;对于无应力反向情况,循环频率改变对最终累积孔压比的影响并不显著。循环频率对最终累积孔压比的影响与其对循环强度的影响一致。     

竖向地震动加速度反应谱特性

以33次地震中的地表地震动记录为数据基础,考虑场地条件、震级和距离的影响,分别对竖向地震动的加速度规准化反应谱和双规准化反应谱进行了研究。结果表明,规准反应谱明显受到场地条件、震级和震中距的影响,不同场地、距离和震级的平均规准反应谱之间差别显著;相比较而言,不依赖于场地、距离和震级的平均双规准反应谱之间却表现出良好的规律性和一致性。双规准反应谱的统一特性可以为竖向地震动设计谱的预测提供参考依据。