Design spectra including effect of rupture directivity in near-fault region

In order to propose a seismic design spectrum that includes the effect of rupture directivity in the near-fault region, this study investigates the application of equivalent pulses to the parameter attenuation relationships developed for near-fault, forward-directivity motions. Near-fault ground motions are represented by equivalent pulses with different waveforms defined by a small number of parameters （peak acceleration, A, and velocity V; and pulse period, Tv）. Dimensionless ratios between these parameters （e.g., ATv/V, VTv/D） and response spectral shapes and amplitudes are examined for different pulses to gain insight on their dependence on basic pulse waveforms. Ratios of ATv/V, VTv/D, and the ratio of pulse period to the period for peak spectral velocity （Tv-p） are utilized to quantify the difference between rock and soil sites for near-fault forward-directivity ground motions. The ATv/Vratio of recorded near-fault motions is substantially larger for rock sites than that for soil sites, while Tvp/Tv ratios are smaller at rock sites than at soil sites. Furthermore, using simple pulses and available predictive relationships for the pulse parameters, a preliminary model for the design acceleration response spectra for the near-fault region that includes the dependence on magnitude, rupture distance, and local site conditions are developed.     

Near-fault ground motion bi-normalized pseudo-velocity spectra and its applications

Ground motions with forward-directivity effect in the near-fault region are obviously different from ordinary far-field ground motions. Design spectral models for this kind of motions have been proposed by correlating sim-ple pulses with parameters attenuation relationships in a previous study of the authors. To further test the applica-bility of the established design spectral model, we analyze ground motion pseudo-velocity response spectra (PVS), normalized pseudo-velocity spectra (NPVS) and bi-normalized pseudo-velocity spectra (BNPVS) of 53 typical near-fault forward-directivity ground motions. It is found that BNPVS not only has more salient features to reflect the difference between soil and rock sites, but also has less scattering to reveal the nature of forward-directivity motions. And then, BNPVS is used for prediction of design spectra accounting for the influence of site conditions, and the constructed design spectra are compared with those spectra established previously. It is concluded that site condition can heavily affect ground motions, buildings on rock can be even more dangerous than those on soil sites, in particular for ordinary buildings with short to middle vibration periods. Finally, pulse models are also suggested for structural analyses in the near-fault region.     

Estimation of strong seismic ground motion for engineering use in Perth Western Australia

Probabilistic seismic hazard analysis (PSHA) was performed to determine two alternate magnitude-distance combinations for the 475 yr event, and the worst-case scenario event in Perth, Western Australia. Regional strong ground motion (SGM) time histories on rock sites are used to modify an eastern North America (ENA) seismic model to suit southwest Western Australian (SWWA) conditions. This model is then used to stochastically simulate a set of 475 yr design events and a set of worst-case scenario event for rock sites in the Perth metropolitan area (PMA). The simulated time histories are then used as input to typical soft soil sites in the PMA to estimate surface ground motions. The spectral accelerations of the ground motions on rock and soil sites are calculated and compared with the corresponding design spectra defined in current and previous Australian earthquake loading code. Discussions of the adequacy of the code spectra and the differences to ours, along with implications on structural response and damage are made.     

Response spectra for nuclear structures on rock sites considering the near-fault directivity effect

Near-fault ground motions, potentially with large amplitude and typical velocity pulses, may significantly impact the performance of a wide range of structures. The current study is aimed at evaluating the safety implications of the near-fault effect on nuclear power plant facilities designed according to the Chinese code. To this end, a set of nearfault ground motions at rock sites with typical forward-directivity effect is examined with special emphasis on several key parameters and response spectra. Spectral comparison of the selected records with the Chinese and other code design spectra was conducted. The bi-normalized response spectra in terms of different corner periods are utilized to derive nuclear design spectra. It is concluded that nuclear design spectra on rock sites derived from typical rupture directivity records are significantly influenced both by the earthquake magnitude and the rupture distance. The nuclear design spectra specified in the code needs to be adjusted to reflect the near-fault directivity effect of large earthquakes.     

Modeling of spatially correlated,site-reflected,and nonstationary ground motions compatible with response spectrum

Seismic risk analysis and mitigation of spatially extended structures require the synthesis of spatially varying ground motions in the response history analysis of these structures. These synthetic motions are usually desired to be spatially correlated, site reflected, nonstationary, and compatible with target design response spectra. In this paper, a method is presented for simulating spatially varying ground motions considering the nonstationarity, local site effects, and compatibility of response spectra. The scheme for generating spatially varying and response spectra compatible ground motions is first established for spatial locations on the ground surface with varying site conditions. The design response spectrum is introduced as the “power” spectrum at the base rock. The site amplification approach is then derived based on the deterministic wave propagation theory, by assuming that the base rock motions consist of out-of-plane SH wave or in-plane combined P and SV waves propagating into the site with assumed incident angles, from which tri-directional spatial ground motions can be generated. The phase difference spectrum is employed to model ground motions exhibiting nonstationarity in both frequency and time domains with different site conditions. The proposed scheme is demonstrated with numerical examples.     

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.     

Gaussian mixture–based equivalent linearization method (GM-ELM) for fragility analysis of structures under nonstationary excitations

Gaussian mixture–based equivalent linearization method (GM-ELM) is a recently developed stochastic dynamic analysis approach which approximates the random response of a nonlinear structure by collective responses of equivalent linear oscillators. The Gaussian mixture model is employed to achieve an equivalence in terms of the probability density function (PDF) through the superposition of the response PDFs of the equivalent linear system. This new concept of linearization helps achieve a high level of estimation accuracy for nonlinear responses, but has revealed some limitations: (1) dependency of the equivalent linear systems on ground motion intensity and (2) requirements for stationary condition. To overcome these technical challenges and promote applications of GM-ELM to earthquake engineering practice, an efficient GM-ELM-based fragility analysis method is proposed for nonstationary excitations. To this end, this paper develops the concept of universal equivalent linear system that can estimate the stochastic responses for a range of seismic intensities through an intensity-augmented version of GM-ELM. Moreover, the GM-ELM framework is extended to identify equivalent linear oscillators that could capture the temporal average behavior of nonstationary responses. The proposed extensions generalize expressions and philosophies of the existing response combination formulations of GM-ELM to facilitate efficient fragility analysis for nonstationary excitations. The proposed methods are demonstrated by numerical examples using realistic ground motions, including design code–conforming nonstationary ground motions.     

Side-effect of using response spectral amplification ratios for soft soil sites—Earthquake source-type dependent amplification ratios

Our previous studies show that site effects (amplification of rock motions), source and path effects are coupled when response spectra are used to characterize the amplification ratios for a soil site modelled as nonlinear or elastic. The coupling is referred to as a “side effect” of using response spectral amplification ratios. In the present study we use a suite of rock site records, well distributed with respect to magnitude and source distance, from crustal, subduction interface and slab earthquakes to evaluate the response spectral amplification ratio for soft soil sites. We compare these side-effects for ground motions generated by three types of earthquakes, and we find that, at periods much shorter or much longer than the natural period of a soil site modelled as elastic, the average amplification ratios with respect to rock site ground motions from three types of earthquakes are moderately different and are very similar for other spectral periods. These differences are not statistically significant because of the moderately large scatter of the amplification ratios. However, the extent of magnitude- and source-distance-dependence of amplification ratios differs significantly. After the effects of magnitude and source distance on the amplification ratios are accounted for, the differences in amplification ratios between crustal and subduction earthquake records are very large in some particular combinations of source distance and magnitude range. These findings may have potential impact in establishing design spectra for soft soil sites using strong motion attenuation models or numerical modelling.     

地震动功率谱与反应谱的转换关系

本文详细评述了现今常用的几种加速度反应谱与功率谱的转换关系。对于小阻尼单质点体系而言，考虑到输入地震动是一非平稳的随机过程，又由于其传递函数的窄频带滤波特性，它的加速度反应将是一窄频带的非平稳随机过程。对于峰值系数水平的超越不是独立的，而是成群超越。据此本文考虑非平稳效应和对峰值系数水平的成群效应，对前人的转换关系进行了修正，并基于随机振动理论，给出了对工程上常用的频率平稳、强度非平稳的地震;动模型的功率谱和反应谱的转换关系。此转换关系对于长、短持时的地震动记录和反应谱长、短周期部分以及不同阻尼比的反应谱都能给出精度较高的结果。     

Resonance and criticality measure of ground motions via probabilistic critical excitation method

Resonant characteristics of recorded ground motions are investigated and a new measure of criticality of ground motions is proposed. Four classes of recorded ground motions, i.e., (i) near fault motions (rock records), (ii) near fault motions (soil records), (iii) long duration motions (rock records) and (iv) long duration motions (soil records), are taken from Abrahamson N, Ashford S, Elgamal A, Kramer S, Seible F, Somerville P, Proc of First PEER Workshop on Characterization of Special Source Effects, 1998. It is shown that resonant characteristics of recorded ground motions can be captured appropriately by means of the probabilistic critical excitation method due to the present author regardless of the type of ground motions and the distance between the critical response and the actual one can be a new measure of criticality of ground motions. The time-averaged approximate treatment of nonstationary ground motions as stationary ones is shown to be adequate for structures with shorter natural periods subjected to long duration ground motions.     

Deterministic and probabilistic representation of near-field pulse-like ground motion

The response and damage assessment of engineering structures under near-field ground motions is currently of great interest. Near-field ground motion with directivity focusing or fling effects produces pulse-like ground motion that has characteristics different from those of ordinary records. This paper develops simple deterministic and probabilistic models for near-field pulse-like ground motions. These models belong to the class of engineering models that aim to replicate some of the gross features observed in near-field records. The ground velocity is expressed as a steady-state function or a stationary random process modulated by an envelope function. Both models account for the non-stationarity and the multiple pulses in the ground velocity. While the deterministic model is similar to some of the models developed earlier, the probabilistic model facilitates handling uncertainties in the ground motion and variability in the structure's properties. For instance, this model combined with structural reliability methods can be used for reliability assessment of structures under near-field random ground motion. The reduction of the structural response by adding supplemental dampers is also investigated.     

A study of response spectra for different geological conditions in Gujarat,India

In this study, the effect of ground geology on the acceleration response spectra is studied at 32 sites in Gujarat, India. The sites are grouped into Proterozoic, Mesozoic, Tertiary and Quaternary. The normalized acceleration response spectra at 5% damping of 407 strong ground motions (horizontal and vertical components) recorded at these sites varying in magnitude from 3.0 to 5.7 are determined. The study shows that the shape of the acceleration response spectra is influenced by the regional geology and local site conditions. The peak of maximum horizontal spectral amplification is between 0.03 and 0.05 s in Proterozoic formations, 0.06 and 0.10 s in Mesozoic formations, 0.06 and 0.08 s in Tertiary and 0.12 s in Quaternary formations. The maximum vertical spectral acceleration is at 0.025 s in Proterozoic, 0.07 s in Mesozoic, 0.05 s in Tertiary and 0.10 s in Quaternary formations. The average acceleration amplification factor in all the geological formations is between 2.5 and 3.0 both in horizontal and vertical components. It has been observed that acceleration response spectra at sites having same geological formations are also influenced by local site conditions. The study shows that the acceleration response spectrum in the current Indian code applicable for the entire country underestimates the seismic forces at hard-rock sites and overestimates at soft-soil sites. Using recorded strong motion data with Mw ranging from 3.5 to 5.7, an attenuation relationship is developed at six periods to predict geometric mean of horizontal spectral amplitudes for rock and soil sites. The spectral amplitudes predicted with the attenuation relationship match well with the observed one within statistical limits for hypocentral distances less than 200 km.     

基岩地震动的一个相干函数模型-走滑断层情形h

目前研究地震动空间变化的主要方法是利用密集台阵（如SMART1台阵等）的强震观测记录进行统计分析，由于地震动观测资料的不足，因而缺少基岩及不同场地类别地震动相干函数模型. 本文利用数值方法了模拟理论地震图，进而研究采用震源位错模型的基岩随机地震动的空间变化规律，并考虑震源破裂速度、子源个数、震源深度和介质传播速度等因素的影响. 其具体思路为:首先对应于每个样本，用有限差分数值模拟方法计算弹性半空间近场地震动场，而后对所有样本的计算结果进行统计，给出了一个走滑断层情形下的近场基岩表面及沿基岩竖直方向水平分量地震动的相干函数模型.      

A coherency function model of ground motion at base rock corresponding to strike-slip fault

IntroductionEarthquakedamagesurveyandresearchresultshavedemonstratedthatspatialdistributiondifferenceofgroundmotionisoneoftheimportantreasonswhichcausedlongstructure(eglongspanbridge,undergroundpipe)destroy.Thathowtoprovideareasonableinputofgroundmotionfieldforaseismicdesignoflongstructureisaurgentprobleminearthquakeengineeringfield.Atpresent,themethodtostudyspatialvariationofgroundmotionsisadoptingstatisticanalysisbasedondensearrayrecordssuchasSMART-1array,etc,togetcoherencyfunctionofground…     

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.     

Ground motion record simulation for structural analysis by consideration of spectral acceleration autocorrelation pattern

A novel approach is introduced to generate simulated ground motion records by considering spectral acceleration correlations at multiple periods. Most of the current reliable Ground Motion Record(GMR) simulation procedures use a seismological model including source, path and site characteristics. However, the response spectrum of simulated GMR is somewhat different when compared with the response spectrum based on recorded GMRs. More specifi cally, the correlation between the spectral values at multiple periods is a characteristic of a record which is usually different between simulated and recorded GMRs. As this correlation has a signifi cant infl uence on the structural response, it is needed to investigate the consistency of the simulated ground motions with actual records. This issue has been investigated in this study by incorporating an optimization algorithm within the Boore simulation technique. Eight seismological key parameters were optimized in order to achieve approximately the same correlation coeffi cients and spectral acceleration between two sets of real and simulated records. The results show that the acceleration response spectra of the synthetic ground motions also have good agreement with the real recorded response spectra by implementation of the proposed optimized values.     

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).     

Response spectral relationships for rock sites derived from the component attenuation model

The seismological model was developed initially from the fundamental relationship between earthquake ground motion properties and the seismic moment generated at the source of the earthquake. Following two decades of continuous seismological research in the United States, seismological models which realistically account for both the source and path effects on the seismic shear waves have been developed and their accuracy rigorously verified (particularly in the long and medium period ranges). An important finding from the seismological research by Atkinson and Boore and their co‐investigators is the similarity of the average frequency characteristics of seismic waves generated at the source between the seemingly very different seismic environments of Eastern and Western North America (ENA and WNA, respectively). A generic definition of the average source properties of earthquakes has therefore been postulated, referred to herein as the generic source model. Further, the generic ‘hard rock’ crustal model which is characteristic of ENA and the generic ‘rock’ crustal model characteristic of WNA have been developed to combine with the generic source model, hence enabling simulations to be made of the important path‐related modifications to ground motions arising from different types of crustal rock materials. It has been found that the anelastic contribution to whole path attenuation is consistent between the ENA and WNA models, for earthquake ground motions (response spectral velocities and displacements) in the near and medium fields, indicating that differences in the ENA and WNA motions arise principally from the other forms of path‐related modifications, namely the mid‐crust amplification and the combined effect of the upper‐crust amplification and attenuation, both of which are significant only for the generic WNA ‘rock’ earthquake ground motions. This paper aims to demonstrate the effective utilization of the latest seismological model, comprising the generic source and crustal models, to develop a response spectral attenuation model for direct engineering applications. The developed attenuation model also comprises a source factor and several crustal (wave‐path modification) component factors, and thus has also been termed herein the component attenuation model (CAM). Generic attenuation relationships in CAM, which embrace both ENA and WNA conditions, have been developed using stochastic simulations. The crustal classification of a region outside North America can be based upon regional seismological and geological information. CAM is particularly useful for areas where local strong motion data are lacking for satisfactory empirical modelling. In the companion paper entitled ‘response spectrum modelling for rock sites in low and moderate seismicity regions combining velocity, displacement and acceleration predictions’, the CAM procedure has been incorporated into a response spectrum model which can be used to effectively define the seismic hazard of bedrock sites in low and moderate seismicity regions. This paper and the companion paper constitute the basis of a long‐term objective of the authors, to develop and effectively utilize the seismological model for engineering applications worldwide.     

1999年台湾集集大地震强地面运动的模拟

利用有限断层模型对1999年台湾集集大地震所产生的近场强地面运动进行了数值模拟,尝试了将具有明确物理意义的震源动力模型的研究结果应用于描述震源过程。计算结果显示,基岩台或接近工程基岩台的计算模拟记录同观测记录符合得很好。进一步研究表明,当综合考虑场地效应对地震动影响时,模拟计算结果得到了明显的改善,同实际观测记录更为相符。本文的研究结果说明,为了科学合理地预测大地震所产生的强地面运动,应综合考虑影响地震所产生的地面运动的"三要素",即:震源过程、传播路径及场地效应。     

基于数值模拟的设定地震场地谱时程拟合方法

本文将确定性数值模拟方法与地震动预测方程相结合,提出了一种重大水电工程场址设定地震的地震动时程生成方法。该方法基于场址设定地震,首先采用地震动预测方程确定场址的场地相关反应谱;其次建立包含震源和场址的场地模型,通过确定性数值模拟方法生成场址地震动时程;最后对生成的场址地震动时程进行调整,使其反应谱与设计谱相一致,用于工程抗震分析。这一方法生成的地震动时程既考虑了震源机制、传播路径以及局部场地效应等物理背景,又与场地相关的设计地震反应谱保持一致,为重大工程抗震分析与评价提供了一种新的思路。