Damping modification factors for SDOF systems subjected to near‐fault,far‐fault and artificial earthquakes

Damping modification factors (DMF) are used in modern seismic codes to adjust elastic response spectral values corresponding to 5% of viscous damping to other higher or lower damping levels. This paper presents a simple and effective procedure to estimate DMF for single‐degree‐of‐freedom systems. Empirical expressions are proposed for displacement, velocity and acceleration response spectra, where four types of soil conditions, from hard rock to soft soil are considered. This study also examines, for the first time, the influence of artificial earthquakes on DMF. Furthermore, natural near‐fault and far‐fault seismic ground motions are considered where it is testified that the fault distance has no impact on DMF. Finally, it confirms that, in contrast to the considerations of many seismic codes, DMF are strongly dependent on the period of structural vibration while there are significant problems of using the same modification factor to estimate maximum displacement, velocity and seismic forces. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic design spectra and mapping procedures using hazard analysis based directly on oscillator response

The calculation of design spectra for building sites threatened by seismic ground motion is approached by considering the maximum responses of linearly elastic oscillators as indicators of ground motion intensity. Attenuation functions describing the distribution of response as a function of earthquake magnitude and distance are derived using 68 components of recorded ground motion as data. With a seismic hazard analysis for several hypothetical building sites, the distributions of maximum oscillator responses to earthquakes of random magnitude and location are calculated, and spectra are drawn to indicate the maximum responses associated with specified probability levels. These spectra are compared to design spectra calculated from published methods of amplifying peak ground motion parameters. The latter spectra are found to be inconsistent in terms of risk for building sites very close and very far from faults. A ground motion parameter defined to be proportional to the maximum response of a 1 Hz, 2 per cent damped linearly elastic oscillator is investigated; this parameter, in conjunction with peak ground acceleration, is found to lead to risk-consistent design spectra. Through these two parameters, a design earthquake magnitude and design hypocentral distance are defined, for a specified building site and risk level. The use of these parameters in the seismic hazard mapping of a region is illustrated.     

镇江市地震台RZB型分量钻孔应变仪地震记录特征与地震参数相关性分析

选取镇江市地震台RZB型分量钻孔应变仪2014年5月至2018年3月记录的全球142次地震,探讨该应变仪地震记录能力,分析震级、震中距与最大振幅之间的关系,以及地震波传播方向与四分量中振幅最大分量方位的关系。结果发现：该应变仪可记录研究时段全球发生的所有8级以上地震,理论上震级越大,记录的地震震中距越大;震级相同,震中距越大,应变仪记录的地震波最大振幅越小,拟合曲线较为符合幂函数关系;震中距相近,震级越大,应变仪记录的地震波最大振幅也越大,拟合曲线较为符合幂函数关系。偶有数据点偏离拟合曲线较远,是因为：①地震震源较深;②应变量的最大值或最小值未被记录到,量取值非实际最大和最小振幅;③有时地震波形周期难以分辨。多数地震最大振幅所在分量方向与地震传播方向基本相同。     

Prediction of ground motion spectra on solidly frozen bedrock during large earthquakes

Two methods are discussed for determining changes in ground displacement spectra and the velocity and acceleration spectra derived from these when recorded on solidly frozen bedrock (T < ?3°C) versus epicentral distance and energy class. The first of these methods characterizes the entire epicenter field of earthquakes, while the second aims at studying possible differences between spectra in different source zones. We have found the maximum spectral level as a function of epicentral distance and energy class. The calculated spectra are compared with the available records of large earthquakes. The manner in which near and comparatively small earthquakes can be used to find ground motion spectra is shown for solidly frozen bedrock for earthquakes as large as the 15–17 energy class, as well, determination of the differences between the spectra of seismic signals due to earthquakes occurring in different source zones is performed. The results can be used both directly and for the zonation and prediction of seismic hazard within the zone of solidly frozen rock, and also for the case where the temperature regime of the frozen rock has been changed or disturbed.     

Evaluation of damping reduction factors for estimating elastic response of structures with high damping

The damping reduction factors are used in a few building codes in order to estimate the elastic response spectrum with high damping ratios from its 5%‐damped counterpart. At present, much research regarding this factor has been published. The purpose of this paper is to evaluate the accuracy of five different models of damping reduction factors. In addition, the damping reduction factors adopted in the recent U.S.A. seismic codes are also evaluated. Statistical studies are carried out according to a total of 216 earthquake ground motions recorded on firm sites in California. Considered here are elastic single‐degree‐of‐freedom (SDOF) systems with natural vibrating periods between 0.1 and 6.0 s. Mean ratios and dispersion of approximate to exact maximum elastic displacement demands corresponding to various damping reduction factors are computed as functions of the natural vibrating period and the viscous damping ratio. Copyright © 2005 John Wiley & Sons, Ltd.     

Engineering implications of the 1985 nahanni earthquakes

A series of strong ground motions was recorded during a set of earthquakes which occurred in the North Nahanni River area of the Northwest Territories of Canada in late 1985. The strongest of these motions were recorded within 10 km of the epicentre of a magnitude 6.9 event; peak accelerations were well above 1g and peak velocities exceeded 0.4 m/s. This paper describes a study of the engineering characteristics of the Nahanni strong motions, particularly as they affect the response of building structures. The response characteristics are analysed in terms of the response spectra and the unit velocity base shear coefficients for multi-degree-of-freedom elastic frame structures. An analysis of the strong motion durations of the records and several measures of intensity is also included. The characteristics of the Nahanni records are compared with those of typical strong seismic ground motions and an ensemble of epicentral region seismic motions recorded under similar conditions. Comparisons are also made with the equivalent parameters in the 1985 edition of the National Building Code of Canada. It is concluded that the Nahanni records are very strong seismic ground motion records with relatively unusual response characteristics, even when compared with those of other records obtained within the epicentral region. The impact of these characteristics on engineering design is most significant for low period structures in epicentral regions. The specifications of typical design codes do not adequately describe the response to such records for very low periods.     

新疆喀什原场地地震动频谱特性研究

2020年1月19日和2020年2月21日在新疆喀什地区先后发生M_S6.4和M_S5.1地震,针对新疆强震动台网收集到的128条强震动记录进行统计分析,研究2次地震记录的幅值及反应谱特性,并与两个现行规范设计反应谱进行对比,结果表明：(1)震级相同时,震中距越小加速度反应谱越大,且加速度反应谱衰减速度越慢;震中距相同时,震级越大加速度反应谱越大,且加速度反应谱衰减速度越慢;(2)震级越大加速度谱值、速度谱值、位移谱值越大;(3)M_S6.4、M_S5.1地震波加速度反应谱及其平均值曲线相近,与我国现行规范加速度反应谱相比差别很大。建议在新疆喀什地区采用基于当地强震记录的加速度反应谱进行结构抗震设计。     

A note on computing uniform risk spectra from intensity data on earthquake occurrences

Reliability of uniform risk Fourier and response spectra, derived from Modified Mercalli Intentsity data, on earthquake occurrences has been investigated by comparing these spectra with the corresponding spectra based on magnitude data. By treating the site intensity from ab earthquake, with given maximum intensity and epicentral distance, as a random variable, a Bayesian probability approach is suggested to compute the intensity spectra, in the present study. Examples of comparison of the intensity and the magnitude spectra for two typical sites in the highly seismic northeast Indian region have shown very good consistency and agreement between the two spectra. Thus, in the proposed approach, intensity data can be used to get quite reliable design spectra for regions where the history of instrumentally recorded data is not sufficient for engineering seismic risk analysis.     

四川地区强震前弱震空区的变化特征

本文使用四川台网地震目录全部资料,适当参考邻省地震目录,对于四川省从1970年下半年以来发生的15组5级以上地震(另有5组缺乏完整资料无法讨论),作 R-t 图、D-t 图寻找时间空区,并作相应的平面空区图.通过对比分析,发现6组6级以上和4组5级地震前震中附近出现空区现象.根据形成空区的变化过程可分为先扩(大)后缩(小)型和逐渐扩大的开放型两种类型.平面空区的位置和形状往往与构造展布有关.有5组5级震例,或因震前震中区小震不断,或因震中及其附近地区小震太少,看不出明显的空区.本文利用出现空区的10个震例,总结出空区参数与未来地震的震级的经验关系:M=5.50 lg Rmax-2.331.32 M=2.98 lgT+2.941.06 M=2.52lg(RmaxT)-0.510.96文中将上述结果与大竹政和的结果作了对比.空区不同变化形态可用金森博雄概括的突起点模式加以解释.      

Probabilistic estimation of maximum inelastic displacement demands for performance‐based design

A probabilistic approach to estimate maximum inelastic displacement demands of single‐degree‐of‐freedom (SDOF) systems is presented. By making use of the probability of exceedance of maximum inelastic displacement demands for given maximum elastic spectral displacement and the mean annual frequency of exceedance of elastic spectral ordinates, a simplified procedure is proposed to estimate mean annual frequencies of exceedance of maximum inelastic displacement demands. Simplifying assumptions are thoroughly examined and discussed. Using readily available elastic seismic hazard curves the procedure can be used to compute maximum inelastic displacement seismic hazard curves and uniform hazard spectra of maximum inelastic displacement demands. The resulting maximum inelastic displacement demand spectra provide a more rational way of establishing seismic demands for new and existing structures when performance‐based approaches are used. The proposed procedure is illustrated for elastoplastic SDOF systems having known‐lateral strength located in a region of high seismicity in California. Copyright © 2007 John Wiley & Sons, Ltd.     

Simplified non-linear seismic displacement demand prediction for low period structures

The prediction of non-linear seismic demand using linear elastic behavior for the determination of peak non-linear response is widely used for seismic design as well as for vulnerability assessment. Existing methods use either linear response based on initial period and damping ratio, eventually corrected with factors, or linear response based on increased equivalent period and damping ratio. Improvements to the original EC8 procedure for displacement demand prediction are proposed in this study. Both propositions may be graphically approximated, which is a significant advantage for practical application. A comparison with several other methods (equal displacement rule, EC8 procedure, secant stiffness and empirical equivalent period methods) is performed. The study is based on non-linear SDOF systems subjected to recorded earthquakes, modified to match design response spectra of different ground types, and focuses on the low frequency range that is of interest for most European buildings. All results are represented in the spectral displacement/fundamental period plane that highlights the predominant effect of the fundamental period on the displacement demand. This study shows that linearized methods perform well at low strength reduction factors but may strongly underestimate the displacement demand at strength reduction factors greater than 2. This underestimation is an important issue, especially for assessment of existing buildings, which are often related with low lateral strength. In such cases, the corresponding strength reduction factors are therefore much larger than 2. The new proposals significantly improve the reliability of displacement demand prediction for values of strength reduction factors greater than 2 compared to the original EC8 procedure. As a consequence, for the seismic assessment of existing structures, such as unreinforced masonry low-rise buildings, the current procedure of EC8 should be modified in order to provide accurate predictions of the displacement demand in the domain of the response spectrum plateau.     

Scaling of spectral displacement ordinates with damping ratios

The next generation of seismic design codes, especially those adopting the framework of performance‐based design, will include the option of design based on displacements rather than forces. For direct displacement‐based design using the substitute structure approach, the spectral ordinates of displacement need to be specified for a wide range of response periods and for several levels of damping. The code displacement spectra for damping values higher than the nominal value of 5% of critical will generally be obtained, as is the case in Eurocode 8 and other design codes, by applying scaling factors to the 5% damped ordinates. These scaling factors are defined as functions of the damping ratio and, in some cases, the response period, but are independent of the nature of the expected ground shaking. Using both predictive equations for spectral ordinates at several damping levels and stochastic simulations, it is shown that the scaling factors for different damping levels vary with magnitude and distance, reflecting a dependence of the scaling on the duration of shaking that increases with the damping ratio. The options for incorporating the influence of this factor into design code specifications of displacement response spectra are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

Seismic microzoning from synthetic ground motion earthquake scenarios parameters: The case study of the city of Catania (Italy)

The city of Catania (Italy) in the South-Eastern Sicily has been affected in past times by several destroying earthquakes with high values of estimated magnitude. The seismogenic area to the south of Volcano Etna, known as Iblean Area, is placed between the African and the Euro-Asiatic plates on the west of the Ibleo-Maltese escarpment, to the south of the Graben of the Sicilian channel and on the east of the overlapping front of Gela. Basing on the seismic history of Catania, the following earthquake scenarios have been considered: the “Val di Noto” earthquake of January 11, 1693 (with intensity X-XI on MCS scale, magnitude M_W=7.41 and epicentral distance of about 13 km); the “Etna” earthquake of February 20, 1818 (with intensity IX on MCS scale, magnitude M_W=6.23 and epicentral distance of about 10 km). The soil response analysis at the surface, in terms of time history and response spectra, has been obtained by 1-D equivalent linear models for about 1200 borings location available in the data-bank of the central area of Catania of about 50 km², using deterministic design scenario earthquakes as input at the conventional bedrock.Seismic microzoning maps of the city of Catania have been obtained in terms of different peak ground acceleration at the surface and in terms of amplification ratios for given values of frequency.     

Characterization of displacement demand for elastic and inelastic SDOF systems

The results of a research concerning the characterization of elastic and inelastic displacement spectral demand as a function of magnitude, source-to-site distance, and soil type are presented. The displacement spectra were computed for single degree of freedom systems subjected to a large set of strong ground motion records.In the elastic case, design displacement spectra, modeled in a simplified way with a bilinear shape in the period range 0–4 s, are then proposed for the estimation of the displacement demand to structures located on different local soil condition, at different distance from the causative fault, and for different levels of magnitude. In order to evaluate the reliability of the proposed design displacement spectra, probabilistic displacement spectra corresponding to different levels of probability of non-exceedance were also carried out.The inelastic displacement demand to elasto-plastic systems was analyzed through the ratio between inelastic and elastic spectral displacements. Simplified relationships of the inelastic displacement ratio are then proposed as a function of displacement ductility, soil condition and period of vibration. Finally, as a comparison, the inelastic displacement ratios were also estimated considering other constitutive models.     

Spectral analysis and design approach for high force‐to‐volume extrusion damper‐based structural energy dissipation

High force‐to‐volume extrusion damping devices can offer significant energy dissipation directly in structural connections and significantly reduce seismic response. Realistic force levels up to 400 kN have been obtained experimentally validating this overall concept. This paper develops spectral‐based design equations for their application. Response spectra analysis for multiple, probabilistically scaled earthquake suites are used to delineate the response reductions due to added extrusion damping. Representative statistics and damping reduction factors are utilized to characterize the modified response in a form suitable for current performance‐based design methods. Multiple equation regression analysis is used to characterize reduction factors in the constant acceleration, constant velocity, and constant displacement regions of the response spectra. With peak device forces of 10% of structural weight, peak damping reduction factors in the constant displacement region of the spectra are approximately 6.5 ×, 4.0 ×, and 2.8 × for the low, medium, and high suites, respectively. At T = 1 s, these values are approximately 3.6 ×, 1.8 ×, and 1.4 ×, respectively. The maximum systematic bias introduced by using empirical equations to approximate damping reduction factors in design analyses is within the range of +10 to ?20%. The seismic demand spectrum approach is shown to be conservative across a majority of the spectrum, except for large added damping between T = 0.8 and 3.5 s, where it slightly underestimates the demand up to a maximum of approximately 10%. Overall, the analysis shows that these devices have significant potential to reduce seismic response and damage at validated prototype device force levels. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Source study of two small earthquakes of Delhi, India, and estimation of ground motion from future moderate, local events

We study source characteristics of two small, local earthquakes which occurred in Delhi on 28 April 2001 (Mw3.4) and 18 March 2004 (Mw2.6). Both earthquakes were located in the heart of New Delhi, and were recorded in the epicentral region by digital accelerographs. The depths of the events are 15 km and 8 km, respectively. First motions and waveform modeling yield a normal-faulting mechanism with large strike-slip component. The strike of one of the nodal planes roughly agrees with NE–SW orientation of faults and lineaments mapped in the region. We use the recordings of the 2004 event as empirical Green’s functions to synthesize expected ground motions in the epicentral region of a Mw5.0 earthquake in Delhi. It is possible that such a local event may control the hazard in Delhi. Our computations show that a Mw5.0 earthquake would give rise to PGA of ~200 to 450 gal, the smaller values occurring at hard sites. The estimate of corresponding PGV is ~6 to 15 cm/s. The recommended response spectra, Sa, 5% damping, for Delhi, which falls in zone IV of the Indian seismic zoning map, may not be conservative enough at soft sites for a postulated Mw5.0 local earthquake.     

A new methodology to determine elastic displacement spectra in the near-fault region

The evaluation of the displacement demand especially at small distances from the causative fault, in the so-called near-source region, is a subject of particular interest for earthquake engineering design, in the light of the growing application of the displacement-based design philosophy. This study presents a new methodology to determine the elastic displacement spectra using a sample of near-fault records from small-to-moderate magnitude earthquakes, typical of the seismic activity in Europe. The displacement spectrum is developed using near-fault attenuation relationships available in literature for peak ground velocity that is less sensitive in the procedures applied to correct the accelerograms. Also, the distance from the causative fault and the type of directivity are taken into consideration. The prevailing period corresponds to the maxima of the displacement spectra for zero damping and is used to normalize the spectra, leading to significant decrease of the statistical dispersion. The average bi-normalized spectrum, in terms of the peak ground displacement d_g,max and the dominant period T_d-p, appears to be slightly affected by the soil category and earthquake magnitude. A correlation between the damping correction factor η and the normalized period T/T_d-p is detected and the applicability of several provisions of the current version of Eurocode 8 is examined, including characteristic periods and spectral amplitudes.     

适用于结构时程分析法的输入地震波

本文对建筑结构抗震设计时程法所需的输入地震波提出一种基于规范反应谱的、与设防烈度、场地条件、设计近震或远震、结构自振特性有关的选择原则和方法。按远、近震和四类场地标定了反应谱、延性谱和积累损伤谱。通过对六幢不同高度的剪切和弯曲型结构模型的弹塑性分析,表明离差很小。建议在进行结构时程法分析时,按地震加速度反应谱特定的分布规律选择4条加速度记录作为输入计算。两个实际的例子表明按上述方法计算的结果与按底部剪力法计算的结果基本相符。     

Response of vertical deformation on faults to remote strong earthquakes

Vertical coseismic deformation on non-causative fault caused by remote strong earthquakes(epicentral distance≥1500 km,MS≥7.0)are observed by fault-monitoring instruments of new type during recent two years.The monitor-ing result shows,delay time,maximum amplitude and duration of vertical deformation on the non-causative faulthave remarkable close relationship with earthquakes magnitude and epicentral distance.The delay time of verticalcoseismic deformation have positive linear relationship with epicentral distance.The velocity of coseismic defor-mation is 5.5 km/s,close to the velocity of surface wave in granite.The logarithms of maximum amplitude of co-seismic deformation and epicentral distance have remarkable linear relationship with magnitude.The greater themagnitude and the closer the epicentral distance are,the bigger the maximum amplitude of coseismic deformationon non-causative fault will be.Relative to the epicentral distance,the magnitude is the most important factor to theduration of coseismic vertical deformation on the non-causative fault.Stronger earthquake causes longer vibrationduration of coseismic deformation.The experiential equation of co-seismic deformation faults obtained by thiswork is significant on the coseismic deformation research.