Correlation study between ground motion intensity measure parameters and deformation demands for bilinear SDOF systems

The correlation between ground motion intensity measures （IM） and single-degree-of-freedom （SDOF） deformation demands is described in this study. Peak ground acceleration （APG）, peak ground velocity （VPG）, peak ground displacement （DPG）, spectral acceleration at the first-mode period of vibration [As（T1）] and ratio of VPG to APG are used as IM parameters, and the correlation is characterized by correlation coefficients p. The numerical results obtained by nonlinear dynamic analyses have shown good correlation between As（T1） or VPG and deformation demands. Furthermore, the effect of As（T1） and VPG as IM on the dispersion of the mean value of deformation demands is also investigated for SDOF systems with three different periods T=0.3 s, 1.0 s, 3.0 s respectively.     

拟合反应谱峰加速度和峰速度的人造非平稳地震动

为满足重要工程对设计地震动的需要,文中研究了一种考虑场地附近天然地震记录数据相位非平稳特性、同时拟合S0A(T)、PGA和PGV的人造地震动技术,并以新疆玛纳斯县城区基岩场地为例,利用该区域强震记录提取的天然地震动非平稳相位,进行了非平稳人造地震动的合成。研究成果可为拟合反应谱人造地震动的工程应用提供参考。     

On the estimation of hysteretic energy demands for SDOF systems

Based on a statistical study of the dynamic response of single degree of freedom (SDOF) systems subjected to earthquake ground motions, a rule to estimate hysteretic energy demands is proposed. Expressions for elastic–perfectly plastic, stiffness degrading and pinching SDOF systems were obtained. The proposed rule does not explicitly depend on the period of the system; instead, it depends on the elastic pseudo‐acceleration and elastic velocity spectra. It is shown that the proposed rule can be applied to compute hysteretic energy demands for systems located at different soil conditions. In addition, information about scatter and bias of the proposed rule is also presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Artificial ground motion compatible with specified peak velocity and target spectrum

In this paper, a method, which synthesizes the artificial ground motion compatible with the specified peak velocity as well as the target acceleration response spectrum, was proposed. In this method, firstly, an initial acceleration time history α8^（0） （t）, which satisfies the prescribed peak ground acceleration, the target spectral acceleration ST（ω, ζ）,and the specified intensity envelope, is generated by the traditional method that generates the requency domain; secondly,α8^（0） （t）is further modulated by superimposing narrow-band time histories upon it in the time domain to make its peak velocity, approach the target peak ground velocity, and at the same time to improve its fitting precision to the target spectrum. Numerical examples show that this algorithm boasts high calculation precisions.     

The role of ground motion duration and pulse effects in the collapse of ductile systems

The seismic collapse capacity of ductile single-degree-of-freedom systems vulnerable to P-Δ effects is investigated by examining the respective influence of ground motion duration and acceleration pulses. The main objective is to provide simple relationships for predicting the duration-dependent collapse capacity of modern ductile systems. A novel procedure is proposed for modifying spectrally equivalent records, such that they are also equivalent in terms of pulses. The effect of duration is firstly assessed, without accounting for pulses, by assembling 101 pairs of long and short records with equivalent spectral response. The systems considered exhibit a trilinear backbone curve with an elastic, hardening and negative stiffness segment. The parameters investigated include the period, negative stiffness slope, ductility and strain hardening, for both bilinear and pinching hysteretic models. Incremental dynamic analysis is employed to determine collapse capacities and derive design collapse capacity spectra. It is shown that up to 60% reduction in collapse capacity can occur due to duration effects for flexible bilinear systems subjected to low levels of P-Δ. A comparative evaluation of intensity measures that account for spectral shape, duration or pulses, is also presented. The influence of pulses, quantified through incremental velocity, is then explicitly considered to modify the long records, such that their pulse distribution matches that of their short spectrally equivalent counterparts. The results show the need to account for pulse effects in order to achieve unbiased estimation of the role of duration in flexible ductile systems, as it can influence the duration-induced reduction in collapse capacity by more than 20%.     

近断层地震动速度、位移峰值衰减规律的研究

在全球范围内选取6．0≤Mw≤7．6、震源深度H≤20km且断层距df≤40km的地震动速度和位移峰值数据．进行分组统计分析,确定了PGV和PGD的近断层研究区域分别为20km和15km。认为两水平分量为2条独立数据,在各自研究区域分别得到由366条PGV和265条PGD数据组成的数据库;其中水平方向分为硬土和软土2类场地,竖向只考虑土层场地．利用作者前文已提出的近断层地震动衰减模型和最小二乘法进行数据拟合分析．得到PGV和PGD随断层距和震源深度变化的衰减曲面,分析了水平、竖向以及竖向与水平比值的衰减规律。     

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。     

Empirical evaluation of peak ground velocity and displacement as a function of elastic spectral ordinates for design

In the framework of the revision of Part 1 of Eurocode 8, this study aims at developing new empirical correlations to compute peak values of ground velocity (PGV) and displacement (PGD) as a function of elastic spectral ordinates for design. At variance with the expressions for PGV and PGD currently adopted in the Eurocode 8, based solely on the peak ground acceleration (PGA), in this paper reference is made to spectral ordinates of the short and intermediate period range, namely S_s, which is the constant acceleration spectral ordinate, and S₁, which is the spectral ordinate at 1 s. On the one hand, a relationship between PGV and the product (S_s?S₁) was found based on the regression analysis on a high‐quality strong‐motion dataset. On the other hand, the PGD was estimated by extrapolating to long periods the constant displacement branch of the elastic response spectrum, introducing a correlation between the corner period T_D and S₁. For this purpose, results of a long period probabilistic seismic hazard assessment study for Italy, encompassing low to high seismicity areas, were considered. Furthermore, verification of the proposed relationship against strong‐motion records was carried out, and differences justified in terms of the concept of uniform hazard spectrum.     

Direct use of PGV for estimating peak nonlinear oscillator displacements

A predictive model is presented for estimating the peak inelastic oscillator displacements (S_d,ie) from peak ground velocity (PGV). The proposed model accounts for the variation of S_d,ie for bilinear hysteretic behavior under constant ductility (µ) and normalized lateral strength ratio (R) associated with postyield stiffness ratios of α=0 and 5%. The regression coefficients are based on a ground‐motion database that contains dense‐to‐stiff soil site recordings at distances of up to 30 km from the causative fault. The moment magnitude ( M ) range of the database is 5.2? M ?7.6 and the ground motions do not exhibit pulse‐dominant signals. Confined to the limitations imposed by the ground‐motion database, the model can estimate S_d,ie by employing the PGV predictions obtained from the attenuation relationships (ground‐motion prediction equations). In this way, the influence of important seismological parameters can be incorporated to the variation of S_d,ie in a fairly rationale manner. This feature of the predictive model advocates its implementation in the probabilistic seismic hazard analysis that employs scalar ground‐motion intensity indices. Various case studies are presented to show the consistent estimations of S_d,ie by the proposed model. The error propagation in the S_d,ie estimations is also discussed when the proposed model is associated with attenuation relationships. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic response of self‐centring hysteretic SDOF systems

The seismic response of single‐degree‐of‐freedom (SDOF) systems incorporating flag‐shaped hysteretic structural behaviour, with self‐centring capability, is investigated numerically. For a SDOF system with a given initial period and strength level, the flag‐shaped hysteretic behaviour is fully defined by a post‐yielding stiffness parameter and an energy‐dissipation parameter. A comprehensive parametric study was conducted to determine the influence of these parameters on SDOF structural response, in terms of displacement ductility, absolute acceleration and absorbed energy. This parametric study was conducted using an ensemble of 20 historical earthquake records corresponding to ordinary ground motions having a probability of exceedence of 10% in 50 years, in California. The responses of the flag‐shaped hysteretic SDOF systems are compared against the responses of similar bilinear elasto‐plastic hysteretic SDOF systems. In this study the elasto‐plastic hysteretic SDOF systems are assigned parameters representative of steel moment resisting frames (MRFs) with post‐Northridge welded beam‐to‐column connections. In turn, the flag‐shaped hysteretic SDOF systems are representative of steel MRFs with newly proposed post‐tensioned energy‐dissipating connections. Building structures with initial periods ranging from 0.1 to 2.0s and having various strength levels are considered. It is shown that a flag‐shaped hysteretic SDOF system of equal or lesser strength can always be found to match or better the response of an elasto‐plastic hysteretic SDOF system in terms of displacement ductility and without incurring any residual drift from the seismic event. Copyright © 2002 John Wiley & Sons, Ltd.     

Study on equivalent velocity pulse of nearfault ground motions

Introduction By analyzing earthquake motions, we could find that earthquake motions near the causativefault have two characteristics. One is the remarkable directivity effect. The amplitude of thefault-normal component is larger than that of the fault-parallel one; the other is obvious pulse mo-tions. Bertero, et al (1977) studied the earthquake records of the 1971 San Fernando earthquake.They first pointed out that some ground motions recorded near the causative fault is characterizedb…     

地震有效峰值加速度与地震烈度相关性研究

利用2008年5月12日发生的汶川8·0级以及2008年8月30日凉山州会理县—攀枝花市间6·1级地震中获取的四川省境内的地震加速度记录数据,分析了有效峰值加速度（EPA）与加速度峰值（PGA）对比结果及加速度数据有效值与地震烈度的相关性。得出了有效峰值加速度（EPA）与烈度的相关性较之地震峰值加速度（PGA）与烈度的...     

利用数字强震仪记录实时仿真地动速度

本文首先讨论了计算单自由度系统相对速度递归公式所存在的问题,然后根据递归方程不变性和中心差分,得到了新的计算单自由度系统相对速度地震反应的递归公式,分析了新公式的误差精度。在此基础上,利用地震仪原理,提出了由加速度记录实时恢复地动速度的计算方法。     

近断层地震动加速度峰值衰减规律的研究

提出了近断层地面运动的衰减模型,对全球范围内6．0≤Mw≤7．6且震源深度均小于20km的636条地震动加速度峰值进行了统计分析,确定了本文研究的近断层区域为断层距25km,利用此范围内的440条记录进行了近断层加速度衰减规律的研究。水平地震记录分为硬土和软土两种场地类型,竖向地震记录只考虑土层场地,利用最小二乘法进行数据拟合分析,得到PGA随断层距和震源深度变化在不同震级处形成的衰减曲面,分析了近断层处水平、竖向的PGA以及竖向与水平PGA之比(V／H)的衰减规律。     

Kinematic soil-structure interaction effects on maximum inelastic displacement demands of SDOF systems

This paper presents a statistical study of the kinematic soil-foundation-structure interaction effects on the maximum inelastic deformation demands of structures. Discussed here is the inelastic displacement ratio defined as the maximum inelastic displacement demands of structures subjected to foundation input motions divide by those of structures subjected to free-field ground motions. The displacement ratio is computed for a wide period range of elasto-plastic single-degree-of-freedom (SDOF) systems with various levels of lateral strength ratios and with different sizes of foundations. Seventy-two earthquake ground motions recorded on firm soil with average shear wave velocities between 180 m/s and 360 m/s are adopted. The effects of period of vibration, level of lateral yielding strength and dimension of foundations are investigated. The results show that kinematic interaction will reduce the maximum inelastic displacement demands of structures, especially for systems with short periods of vibration, and the larger the foundation size the smaller the maximum inelastic displacement becomes. In addition, the inelastic displacement ratio is nearly not affected by the strength ratio of structures for systems with periods of vibration greater than about 0.3 s and with strength ratios smaller than about 3.0. Expressions obtained from nonlinear regression analyses are also proposed for estimating the effects of kinematic soil-foundation-structure interaction from the maximum deformation demand of the inelastic system subjected to free-field ground motions.     

Estimation of peak relative velocity and peak absolute acceleration of linear SDOF systems

In the seismic analysis and design of structures, the true velocity and absolute acceleration are usually approximated by their corresponding pseudo-values. This approach is simple and works well for structures with small damping (say, less than 15%). When the damping of a structure is enhanced for the purpose of response reduction, it may result in large analysis and design errors. Based on theory of random vibration and the established mechanism of seismic response spectra analysis, a method is developed (1) to predict the relative velocity spectra with any damping ratio level directly from the 5% standard pseudo-acceleration spectrum; and (2) to estimate the peak absolute acceleration. The accuracy of both is validated by using two selected ensembles of ground motion records.     

Effect of seismic super-shear rupture on the directivity of ground motion acceleration

The effect of seismic super-shear rupture on the directivity of ground motions using simulated accelerations of a vertical strike-slip fault model is the topic of this study. The discrete wave number/finite element method was adopted to calculate the ground motion in the horizontal layered half space. An analysis of peak ground acceleration （PGA） indicates that similar to the sub-shear situation, directivity also exists in the super-shear situation. However, there are some differences as tbllows： （1） The PGA of the fault-normal component decreases with super-shear velocity, and the areas that were significantly affected by directivity in the PGA field changed from a cone-shaped region in the forward direction in a sub-shear situation to a limited near-fault region in a super-shear situation. （2） The PGA of the fault-parallel and vertical component is not as sensitive as the fault-normal component to the increasing super-shear velocity. （3） The PGA of the fault-normal component is not always greater than the fault-parallel component when the rupture velocity exceeds the shear wave velocity.     

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。     

Non‐iterative equivalent linearization of inelastic SDOF systems for earthquakes in Japan and California

The seismic performance of existing structures can be assessed based on nonlinear static procedures, such as the Capacity Spectrum Method. This method essentially approximates peak responses of an inelastic single‐degree‐of‐freedom (SDOF) system using peak responses of an equivalent linear SDOF model. In this study, the equivalent linear models of inelastic SDOF systems are developed based on the constant strength approach, which does not require iteration for assessing the seismic performance of existing structures. To investigate the effects of earthquake type and seismic region on the equivalent linear models, four ground‐motion data sets—Japanese crustal/interface/inslab records and California crustal records—are compiled and used for nonlinear dynamic analysis. The analysis results indicate that: (1) the optimal equivalent linear model parameters (i.e. equivalent vibration period ratio and damping ratio) decrease with the natural vibration period, whereas they increase with the strength reduction factor; (2) the impacts of earthquake type and seismic region on the equivalent linear model parameters are not significant except for short vibration periods; and (3) the degradation and pinching effects affect the equivalent linear model parameters. We develop prediction equations for the optimal equivalent linear model parameters based on nonlinear least‐squares fitting, which improve and extend the current nonlinear static procedure for existing structures with degradation and pinching behavior. Copyright © 2010 John Wiley & Sons, Ltd.     

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.