Ground-Motion Prediction Equations (GMPEs) for inelastic displacement and ductility demands of constant-strength SDOF systems

The objective of this paper is to present ground-motion prediction equations for ductility demand and inelastic spectral displacement of constant-strength perfectly elasto-plastic single-degree-of-freedom (SDOF) oscillators. Empirical equations have been developed to compute the ductility demand as a function of two earthquake parameters; moment magnitude, and source-to-site distance; one site parameter, the ground type; and three oscillator parameters, an undamped natural period, critical damping ratio, and the mass-normalized yield strength. In addition, a comparative study of the proposed model with selected previous studies and recommendations of Eurocode 8 is presented. Proposed equations can easily be incorporated in existing probabilistic seismic hazard analysis (PSHA) software packages with the introduction of an additional parameter. This leads to hazard curves for inelastic spectral displacement, which can provide better estimates of target displacement for nonlinear static procedures and an efficient intensity measure for probabilistic seismic demand analysis (PSDA). Proposed equations will be useful in performance evaluation of existing structures.     

Hazard-consistent response spectra in the Region of Murcia (Southeast Spain): comparison to earthquake-resistant provisions

Hazard-consistent ground-motion characterisations of three representative sites located in the Region of Murcia (southeast Spain) are presented. This is the area where the last three damaging events in Spain occurred and there is a significant amount of data for comparing them with seismic hazard estimates and earthquake-resistant provisions. Results of a probabilistic seismic hazard analysis are used to derive uniform hazard spectra (UHS) for the 475-year return period, on rock and soil conditions. Hazard deaggregation shows that the largest hazard contributions are due to small, local events for short-period target motions and to moderate, more distant events for long-period target motions. For each target motion and site considered, the associated specific response spectra (SRS) are obtained. It is shown that the combination of two SRS, for short- and long-period ground motions respectively, provides a good approximation to the UHS at each site. The UHS are compared to design response spectra contained in current Spanish and European seismic codes for the 475-year return period. For the three sites analysed, only the Eurocode 8 (EC8) type 2 spectrum captures the basic shape of the UHS (and not the EC8 type 1, as could be expected a priori). An alternative response spectrum, anchored at short- and long-period accelerations, is tested, providing a close match to the UHS spectra at the three sites. Results underline the important contribution of the frequent, low-to-moderate earthquakes that characterize the seismicity of this area to seismic hazard (at the 475-year return period).     

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.     

Influence of the mean period of ground motion on the inelastic dynamic response of single and multi degree of freedom systems

This paper focuses on examining the effects of frequency content of the ground motion on the inelastic demands imposed on both single degree of freedom (SDF) and multi degree of freedom (MDF) steel‐framed systems. A detailed literature review is conducted to identify the indicator that best represents the frequency content of ground motion. The mean period (T_m) of ground motion is selected owing to its ability to distinguish between various spectral shapes of ground motion, and its relationship with magnitude, distance and site characteristics. Inelastic displacement demands on SDF systems for target ductility levels are first studied in the light of T_m, using a suite of 128 ground motion records. The study is then extended to MDF systems with the help of incremental dynamic analysis by employing the same ground motion ensemble to assess the influence of T_m on various engineering demand parameters. The results obtained indicate that, for SDF systems, the amplification of displacements occurs when the period ratio between elastic period (T_e) and T_m is lower than unity. For MDF systems, the results demonstrate that the influence of higher modes on the base shear and maximum storey drift profile becomes more pronounced, as T_m approaches the higher mode periods of the structure. These observations, for both SDF and MDF systems, tend to be more evident for higher levels of inelasticity. The significance of the results, with particular reference to European seismic design procedures, is highlighted. Copyright © 2010 John Wiley & Sons, Ltd.     

Broadband (0.05 to 20 s) prediction of displacement response spectra based on worldwide digital records

A new set of empirical equations for prediction of displacement response spectral ordinates from 20 Hz to T = 20 s is illustrated. The coefficients of the equations were obtained by regressing a dataset based on 1,155 tri-axial digital and 9 analog accelerometer records from 60 earthquakes worldwide. Long period disturbances in the accelerograms were evaluated and removed using a very recent method, aimed at preserving the long-period spectral content of the records. Analysis of variance has disclosed only little evidence for regional dependence of ground motions, while a carefully conducted evaluation of site effects resulted in clearly differentiated spectral amplification bands associated to the main ground types B, C, and D of Eurocode 8. Spectral ordinates for vibration periods >5 s were found to scale with magnitude quite consistently with theoretical scaling from Brune’s model. On the other hand, comparison of results with those yielded by recent prediction models in Europe and the United States (NGA), indicated that the latter may not be uniformly reliable at long periods. The proposed empirical equations are easily implemented in computer programs for seismic hazard assessment, being characterized by a simple functional form and a restricted number of predictor variables. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Acceleration response modification factors for nonstructural components attached to inelastic moment‐resisting frame structures

A statistical analysis of the peak acceleration demands for nonstructural components (NSCs) supported on a variety of stiff and flexible inelastic regular moment‐resisting frame structures with periods from 0.3 to 3.0 s exposed to 40 far‐field ground motions is presented. Peak component acceleration (PCA) demands were quantified based on the floor response spectrum (FRS) method without considering dynamic interaction effects. This study evaluated the main factors that influence the amplification or decrease of FRS values caused by inelasticity in the primary structure in three distinct spectral regions namely long‐period, fundamental‐period, and short‐period region. The amplification or decrease of peak elastic acceleration demands depends on the location of the NSC in the supporting structure, periods of the component and building, damping ratio of the component, and level of inelasticity of the supporting structure. While FRS values at the initial modal periods of the supporting structure are reduced due to inelastic action in the primary structure, the region between the modal periods experiences an increase in PCA demands. A parameter denoted as acceleration response modification factor (R_acc) was proposed to quantify this reduction/increase in PCA demands. Copyright © 2007 John Wiley & Sons, Ltd.     

Derivation of design soil coefficients (S) and response spectral shapes for Eurocode 8 using the European Strong-Motion Database

A revision is presently under way to upgrade the status of the `Designrecommendations for earthquake resistance of structures', commonlyreferred to as Eurocode 8 (or EC8). In order to improve the definition ofthe design elastic response spectra (ERS) as defined in the Eurocode 8 –Part 1 (Draft May 2001), the values of the soil amplification factors havebeen calculated for sites on sedimentary soils, both stiff (category B) andsoft (category C), with respect to rock sites (category A), such ascontemplated in EC8. The work was performed by a systematic study ofresponse spectra as a function of magnitude and site conditions, usingrecords from the European Strong-Motion Database.The results confirm the occurrence of systematic spectral amplification onsedimentary soils with respect to reference rock in a large set of Europeanstrong motion data. Such amplification has been quantified through ameasure derived from the Housner Spectrum Intensity definition.The values of the soil coefficients recommended in the current version ofEC 8 are shown to be realistic for category C, in the case of a moderateseismicity context. However the values for subsoil class B need to besignificantly increased both for the moderate and high seismicity context.     

Prediction of elastic displacement response spectra in Europe and the Middle East

Empirical equations are presented for the prediction of displacement response ordinates for damping ratios of 2, 5, 10, 20 and 30% of critical and for response periods up to 4s, using 532 accelerograms from the strong‐motion databank from Europe and the Middle East. The records were all re‐processed and only employed for regressions at periods within the usable range, defined as a fraction of the filter cut‐off and depending on the instrument type (digital or analogue), earthquake magnitude and site class. The equations can be applied to predict the geometric mean displacement and pseudo‐acceleration spectra for earthquakes with moment magnitudes ( M ) between 5 and 7.6, and for distances up to 100km. The equations also include style‐of‐faulting and site class as explanatory variables. The predictions obtained from these new equations suggest that earlier European equations for spectral displacements underestimate the ordinates at longer periods as a result of severe filtering and the use of the spectral ordinates at periods too close to the filter cut‐off. The results also confirm that the period defining the start of the constant displacement plateau in the Eurocode 8 (EC8) spectrum is excessively short at 2s. The results not only show that the scaling factor defined in EC8 for estimating the spectral ordinates at damping ratios different from 5% of critical are a good general approximation, but also that this scaling varies with magnitude and distance (reflecting the influence of duration) and also displays a mild dependence on response period. Copyright © 2007 John Wiley & Sons, Ltd.     

Seismic microzonation of Chania,Crete (Greece) based on SASW measurements and non-linear site response analyses

Following a brief overview of past applications of, and more recent advances on seismic microzonation, the results of a seismic microzonation study for the city of Chania, Greece, are presented. The study was based on V_s vs. depth profiles obtained at 19 sites of the urban area by performing SASW measurements. The spatial distribution of V_s values was utilized in estimating V_s30 values, depth to bedrock and the fundamental ground period variation across the area of the city as well as for conducting 1-D finite element non-linear inelastic site response analyses. The input earthquake excitations employed in the response analyses were based on the results of an available seismic hazard study for the Chania Area. The results of analyses were utilized for establishing the spatial distribution of rock motion amplification, the expected ground motions and spectral values in the area of the city. Contour maps providing values of the expected ground motion in the urban area are given which may become a practical tool in assessing the seismic risk and expected damage in the Chania area. The maps can also be used in the design of new earthquake resistant structures or the seismic retrofitting of existing ones. Finally, the results were utilized to demonstrate the inadequacy of using V_s,30 values for classifying the soil conditions in the Chania area.     

Empirical equations for the prediction of displacement spectrum intensity and its correlation with other intensity measures

Displacement spectrum intensity (DSI), defined as the integral of a ground motion's displacement response spectrum from 2.0 to 5.0 s, is proposed as an indicator of the severity of the long period content of a ground motion. It is demonstrated how the distribution of DSI can be predicted using existing ground motion prediction equations for (pseudo) spectral accelerations, which is necessary for it to be a useful intensity measure (IM) in either probabilistic or deterministic seismic hazard analysis. Empirical correlation equations between DSI and other common ground motion IMs are developed for active shallow crustal earthquakes using a dataset of ground motions from active shallow crustal earthquakes. The ability of DSI to account for near-source ground motions exhibiting forward directivity, potentially damaging far-source long-period ground motion, and its use with other spectrum intensity parameters to characterise short, medium, and long period severity of ground motions is discussed. The developed ground motion prediction and correlation equations enable DSI to be utilised in rigorous ground motion selection frameworks such as the generalised conditional intensity measure (GCIM) approach.     

平谷台地磁加卸载响应比与地震

将磁暴过程作为地球磁场对太阳风的加卸载响应,分析了平谷台１９９５年１月至１９９８年４月期间磁暴场的暴时扰日变化Ｄｓ（Ｚ）的响应比值Ｐ（Ｚ）的变化。发现Ｐ（Ｚ）高值与平谷台５５０ｋｍ,左右范围内ＭＳ≥５０的中强主震有较好的对应。     

黑龙江及周边地区中强地震前加卸载响应比特征分析

选取所研究区域地震能量的贝尼奥夫应变(相当于室内岩石实验中的声发射)作为响应,以黑龙江及其周边地区2005年以来14次ML 5.0以上地震作为震例,检验卸载响应比理论的预测效果,提取异常特征,初步总结该方法的时、空、强预测指标,发现具有一定的预报效能。     

Comparison of DSHA-based response spectrum with design response spectrum of building code of Pakistan (BCP-SP-2007) for a site in Muzaffargarh area,Pakistan

The building code of any country is considered to be a basic technical guidance document for the seismic design of structures. However, building codes are typically developed for the whole country, without considering site specific models that incorporate detailed site-specific data. Therefore, the adequacy of the design spectrum for building codes may sometimes be questionable. To study the sufficiency of the building codes of Pakistan (BCP-SP-2007), a deterministic seismic hazard analysis (DSHA) based spectrum was developed for a site in the Muzaffargarh area, Pakistan, using an updated earthquake catalogue, seismic source model, and a next generation attenuation model (NGA-WEST-2). Further, an International Building Code (IBC-2000) spectrum was developed for the study area to compare the results. The DSHA-based response spectrum resulted in a peak ground acceleration (PGA) value of 0.21 g for the Chaudwan fault. The evaluation of BCP-SP-2007 and IBC-2000 spectra provided a critical assessment for analyzing the associated margins. A comparison with the DSHA-based response spectrum showed that the BCP-SP-2007 design spectrum mostly overlapped with the DSHA spectrum unlike IBC-2000. However, special attention is needed for designing buildings in the study area when considering earthquake periods longer than 1 s, and the BCP-SP-2007 spectrum can be enhanced when considering a period range of 0.12–0.64 s. Finally, BCP-SP-2007 is based on a probabilistic approach and its comparison with deterministic results showed the significance of both methods in terms of design.     

The expert system for earthquake prediction (I)—the overall design and main structure

The Expert System For Earthquake Prediction (ESEP) is summarized in this paper. ESEP embraces three subsystems: long-middle term prediction system, annual prediction system and middle-short term prediction system. Each of the subsystems is composed of seven modules: the controlling module, the data base module, the expert knowledge base module, the method base module, the fact preparation module, the reasoning and decision-making module and the plotting and displaying module. The reasoning model ESEP/R and the knowledge expression model ESEP/K are set up in the ESEP, and new evidence combinations, CON (confine), W (weigh), and SYN (synthesize), have been proposed. The distinctive features of the ESEP are: (1) systemized; (2) several experts’ knowledge can be synthesized; (3) a large amount of data and experts’ experience is embraced; (4) four reasoning models and the synthetic decision-making technic are adopted; (5) several software environments are used; (6) modularization; and (7) possessing the friendly user interfaces. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 1–8, 1992.     

浅壳与上地幔地震竖向加速度谱阻尼修正系数模型

本文基于日本KiK-Net,K-Net台网及汶川地震中6 000余条浅壳与上地幔地震竖向加速度记录,分场地类型建立了包含阻尼比和谱周期两个参数的阻尼修正系数模型,用以调整无震级和震源距信息的设计谱。基于固定效应模型对阻尼修正系数对数值及阻尼比对数值的三次多项式进行线性回归得到模型表达式,基于随机效应模型对阻尼修正系数模型的残差及残差的标准差进行分离,分析震源、路径以及场地效应对模型误差的影响。研究结果表明:高阻尼长周期震源效应引起的残差大于其他效应引起的残差;场地效应引起的残差小于其他效应引起的残差。对模型残差的标准差及阻尼比对数值进行线性回归,回归方程易于计算模型残差的标准差。     

由加卸载响应比的时空变化预测中国大陆未来的地震趋势

利用加卸载响应比理论在１９９４年底对中国大一年左右尺度的地震趋势预测，总体上是符合实际情况的。在１９９５年还发展了基于高响应比区向未来震中延迁移、全聚的规律对地震的时空强参数进行预测的方法。并据此对云南孟连地震作了中期预测，该次地震的时空强参数都在预测范围内。     

Near‐fault ground motions,and the response of elastic and inelastic single‐degree‐of‐freedom (SDOF) systems

In order to investigate the response of structures to near‐fault seismic excitations, the ground motion input should be properly characterized and parameterized in terms of simple, yet accurate and reliable, mathematical models whose input parameters have a clear physical interpretation and scale, to the extent possible, with earthquake magnitude. Such a mathematical model for the representation of the coherent (long‐period) ground motion components has been proposed by the authors in a previous study and is being exploited in this article for the investigation of the elastic and inelastic response of the single‐degree‐of‐freedom (SDOF) system to near‐fault seismic excitations. A parametric analysis of the dynamic response of the SDOF system as a function of the input parameters of the mathematical model is performed to gain insight regarding the near‐fault ground motion characteristics that significantly affect the elastic and inelastic structural performance. A parameter of the mathematical representation of near‐fault motions, referred to as ‘pulse duration’ (T_P), emerges as a key parameter of the problem under investigation. Specifically, T_P is employed to normalize the elastic and inelastic response spectra of actual near‐fault strong ground motion records. Such normalization makes feasible the specification of design spectra and reduction factors appropriate for near‐fault ground motions. The ‘pulse duration’ (T_P) is related to an important parameter of the rupture process referred to as ‘rise time’ (τ) which is controlled by the dimension of the sub‐events that compose the mainshock. Copyright © 2004 John Wiley & Sons, Ltd.     

The spatial temporal evolution characteristics of the load／unload response ratio（LURR） and its implications for predicting the three elements of earthquakes

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