Semi‐empirical model for site effects on acceleration time histories at soft‐soil sites. Part 2: calibration

A previously developed simplified model of ground motion amplification is applied to the simulation of acceleration time histories at several soft‐soil sites in the Valley of Mexico, on the basis of the corresponding records on firm ground. The main objective is to assess the ability of the model to reproduce characteristics such as effective duration, frequency content and instantaneous intensity. The model is based on the identification of a number of parameters that characterize the complex firm‐ground to soft‐soil transfer function, and on the adjustment of these parameters in order to account for non‐linear soil behavior. Once the adjusted model parameters are introduced, the statistical properties of the simulated and the recorded ground motions agree reasonably well. For the sites and for the seismic events considered in this study, it is concluded that non‐linear soil behavior may have a significant effect on the amplification of ground motion. The non‐linear soil behavior significantly affects the effective ground motion duration for the components with the higher intensities, but it does not have any noticeable influence on the lengthening of the dominant ground period. Copyright © 2004 John Wiley & Sons, Ltd.     

Torsional response of symmetric buildings to incoherent and phase‐delayed earthquake ground motion

This paper studies the effect of coherency loss and wave passage on the seismic torsional response of three‐dimensional, multi‐storey, multi‐span, symmetric, linear elastic buildings. A model calibrated against statistical analyses of ground motion records in Mexico City is used for the coherency function. The structural response is assessed in terms of shear forces in structural elements. Incoherence and wave passage effects are found to be significant only for columns in the ground level of stiff systems. The increase of column shears in the ground level is much higher for soft than for firm soil conditions. For the torsionally stiff systems considered, it is found that incoherent and phase‐delayed ground motions do not induce a significant rotational response of the structure. The use of a code eccentricity to account for torsion due to ground motion spatial variation is assessed. On firm soil, the use of a base shear along with an accidental eccentricity results in highly overestimated shear forces; however, for soft soil conditions, code formulations may result in underestimated shear forces. Copyright © 2003 John Wiley & Sons, Ltd.     

地震波时变修正Kanai-Tajimi非平稳随机模型的建立

利用谐小波变换对实际强震记录的时变谱进行估计,并统计分析了远场3类不同场地上地震波的时变谱特征,分析发现对于硬场地上的远场地震波在时域内平稳段较短,下降段衰减较快,而在频域内则具有较大的中心频率和较宽的频带.利用均匀调制非平稳模型和时变修正Kanai-Tajimi非平稳模型模拟地震波的时变谱,把非线性函数的参数识别问题转化成求解无约束优化问题,利用拟牛顿迭代法求得最优解,得到3类不同场地上这两种模型的参数具体取值以及参数函数集的具体表达式.为了定量地确定模拟模型的精度,定义了误差函数,验证了所提时变谱参数识别方法的精度,给出了与建筑抗震规范相对应的不同场地不同烈度下多遇和罕遇地震的谱强度因子的大小.最后提出了利用求解时变线性微分方程组来合成非平稳地震波的方法.     

Influence of irregular topography and random soil properties on coherency loss of spatial seismic ground motions

Coherency functions are used to describe the spatial variation of seismic ground motions at multiple supports of long span structures. Many coherency function models have been proposed based on theoretical derivation or measured spatial ground motion time histories at dense seismographic arrays. Most of them are suitable for modelling spatial ground motions on flat‐lying alluvial sites. It has been found that these coherency functions are not appropriate for modelling spatial variations of ground motions at sites with irregular topography (Struct. Saf. 1991; 10 (1):1–13). This paper investigates the influence of layered irregular sites and random soil properties on coherency functions of spatial ground motions on ground surface. Ground motion time histories at different locations on ground surface of the irregular site are generated based on the combined spectral representation method and one‐dimensional wave propagation theory. Random soil properties, including shear modulus, density and damping ratio of each layer, are assumed to follow normal distributions, and are modelled by the independent one‐dimensional random fields in the vertical direction. Monte‐Carlo simulations are employed to model the effect of random variations of soil properties on the simulated surface ground motion time histories. The coherency function is estimated from the simulated ground motion time histories. Numerical examples are presented to illustrate the proposed method. Numerical results show that coherency function directly relates to the spectral ratio of two local sites, and the influence of randomly varying soil properties at a canyon site on coherency functions of spatial surface ground motions cannot be neglected. Copyright © 2010 John Wiley & Sons, Ltd.     

Estimating non‐linear site response by single period approximation

Site effects characterize the filtering mechanisms within the soil sedimentary layers overlying bedrock. In regions of high seismicity such as California where strong motion records are relatively abundant, site coefficients can be developed by regression of recorded ground shaking parameters. In regions of low‐to‐moderate seismicity or of high seismicity but with a paucity of recorded strong motion data, such empirical models cannot be obtained in the same way. This study describes the theoretical development of a simple, rational manual procedure to calculate site coefficients, based on a single period approximation (SPA), and to construct displacement response spectra (RSD) for soil sites. The proposed simplified model, which takes into account the non‐linear behaviour of soil that is dependent on the level of shaking, impedance contrast at the soil–bedrock interface and the plasticity of soil material, has been verified by comparison with results obtained from non‐linear shear wave analyses and data recorded during the 1994 Northridge earthquake. The proposed model is believed to be a convenient tool for calculating non‐linear site responses and constructing site‐specific response spectra, which has the potential of being incorporated into code provisions. Copyright © 2006 John Wiley & Sons, Ltd.     

Simulation of synthetic ground motions for specified earthquake and site characteristics

A method for generating a suite of synthetic ground motion time‐histories for specified earthquake and site characteristics defining a design scenario is presented. The method employs a parameterized stochastic model that is based on a modulated, filtered white‐noise process. The model parameters characterize the evolving intensity, predominant frequency, and bandwidth of the acceleration time‐history, and can be identified by matching the statistics of the model to the statistics of a target‐recorded accelerogram. Sample ‘observations’ of the parameters are obtained by fitting the model to a subset of the NGA database for far‐field strong ground motion records on firm ground. Using this sample, predictive equations are developed for the model parameters in terms of the faulting mechanism, earthquake magnitude, source‐to‐site distance, and the site shear‐wave velocity. For any specified set of these earthquake and site characteristics, sets of the model parameters are generated, which are in turn used in the stochastic model to generate the ensemble of synthetic ground motions. The resulting synthetic acceleration as well as corresponding velocity and displacement time‐histories capture the main features of real earthquake ground motions, including the intensity, duration, spectral content, and peak values. Furthermore, the statistics of their resulting elastic response spectra closely agree with both the median and the variability of response spectra of recorded ground motions, as reflected in the existing prediction equations based on the NGA database. The proposed method can be used in seismic design and analysis in conjunction with or instead of recorded ground motions. Copyright © 2010 John Wiley & Sons, Ltd.     

Site effect evaluation at Mexico City: Dominant period and relative amplification from strong motion and microtremor records

Site effects in Mexico City are discussed in terms of simple 1D, one-layer, linear models. The analysis is focussed on two parameters: dominant period and maximum amplification relative to a firm site within the city. The data used is a compilation of strong motion data and microtremor measurements. Strong motion data consist of digital acceleration records for nine events recorded by the Accelerographic Network of Mexico City. The authors analyzed spectral ratios of horizontal components of soft soil sites relative to an average of firm site observations for this data set. Dominant period, maximum relative amplification and an estimate of material damping were computed from the empirical transfer functions thus obtained. Microtremor data were compiled from measurement of different groups during the period 1985–1992. In all, 409 measurement points were analyzed. Values of dominant period obtained from microtremor measurements are in excellent agreement with those obtained from empirical transfer functions for strong motion data. The synthesis of results allows us to draw a detailed and robust map of dominant period for Mexico City. Based on this map, the authors propose some modifications to the current microzonation of Mexico City and evaluate a proposed model to account for site effects in this city.     

The effects of torsion and motion coupling in site response estimation

Soil amplification characteristics are investigated using data from the Chibaken‐Toho‐Oki earthquake and its aftershocks recorded at Chiba dense array in Japan. The frequency‐dependent amplification function of soil is calculated using uphole‐to‐downhole spectral ratio analysis, considering the horizontal components of shear wave. The identified spectral ratios consistently demonstrate the splitting of peaks in their resonance frequencies and low amplification values in comparison with a 1D model. The torsional behaviour and horizontal ground motion coupling are clarified as the reasons for these phenomena at the site. To prove the hypothesis, the torsional motion is directly evaluated using the data of the horizontal dense array in different depths at the site. The comparison between Fourier spectra of torsional motion and identified transfer functions reveals the peaks at the same frequencies. The wave equation including torsion and horizontal motion coupling is introduced and solved for the layered media by applying wave propagation theory. Using the developed model, the effects of torsional motion with horizontal motion coupling on soil transfer function are numerically examined. Splitting and low amplification at resonance frequencies are confirmed by the results of numerical analysis. Furthermore, the ground motion in two horizontal directions at the site is simulated using site geotechnical specification and optimizing the model parameters. The simulated and recorded motions demonstrate good agreement that is used to validate the hypothesis. In addition, the spectral density of torsional ground motions are compared with the calculated one and found to be well predicted by the model. Finally, the results are used to explain the overestimation of damping in back‐calculation of dynamic soil properties using vertical array data in small strain level. Copyright © 2003 John Wiley & Sons, Ltd.     

Modelling non‐linear ground response of non‐liquefiable soils

A non‐linear finite element (FE) model is presented to account for soil column effects on strong ground motion. A three‐dimensional bounding surface plasticity model with a vanishing elastic region, appropriate for non‐liquefiable soils, is formulated to accommodate the effects of plastic deformation right at the onset of loading. The elasto‐plastic constitutive model is cast within the framework of a FE soil column model, and is used to re‐analyse the downhole motion recorded by an array at a Large‐Scale Seismic Test (LSST) site in Lotung, Taiwan, during the earthquake of 20 May 1986; as well as the ground motion recorded at Gilroy 2 reference site during the Loma Prieta earthquake of 17 October 1989. Results of the analysis show maximum permanent shearing strains experienced by the soil column in the order of 0.15 per cent for the Lotung event and 0.8 per cent for the Loma Prieta earthquake, which correspond to modulus reduction factors of about 30 and 10 per cent respectively, implying strong non‐linear response of the soil deposit at the two sites. Copyright © 2000 John Wiley & Sons, Ltd.     

Ground motion scaling methods for different site conditions and structure characteristics

Non‐linear dynamic time‐history analyses conducted as part of a performance‐based seismic design approach often require that the ground motion records are scaled to a specified level of seismic intensity. Recent research has demonstrated that certain ground motion scaling methods can introduce a large scatter in the estimated seismic demands. The resulting demand estimates may be biased, leading to designs with significant uncertainty and unknown margins of safety, unless a relatively large ensemble of ground motion records is used. This paper investigates the effectiveness of seven ground motion scaling methods in reducing the scatter in estimated peak lateral displacement demands. Non‐linear single‐degree‐of‐freedom systems and non‐linear multi‐degree‐of‐freedom systems are considered with different site conditions (site soil profile and epicentral distance) and structural characteristics (yield strength, period, and hysteretic behavior). It is shown that scaling methods that work well for ground motions representative of stiff soil and far‐field conditions lose their effectiveness for soft soil and near‐field conditions for a wide range of structural characteristics. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic reliability functions for multistorey frame and wall‐frame systems

Seismic reliability functions of multistorey frame systems are expressed as values of Cornell's βindex in terms of two alternative measures of the earthquake intensity, normalized with respect to the yield displacement or to the deformation capacity of a simplified model of the global behaviour of the system obtained by pushover analysis. The safety margin is defined as the difference of the natural logarithms of the intensity that leads to collapse and that assumed to act on the system. The problem of defining a deformation capacity for a multistorey system is circumvented in this manner. The method proposed is illustrated through its application to several reinforced concrete rigid frames, including both column‐and‐beam and wall‐frame systems. Ground motion excitations are representative of those recorded at soft soil sites in the Valley of Mexico. A comparison is made of the reliability functions obtained on the basis of the gross section or the cracked section of reinforced concrete members. The results show that the reliability functions do not only depend on the expected values of the normalized intensity, but also on its dispersion, which is sensitive to the ratio of the fundamental period of the system to the dominant period of the ground motion. Some comments are presented about the establishment of reliability‐based seismic design criteria for generic systems. Copyright © 2006 John Wiley & Sons, Ltd.     

Ground‐shaking mapping for a scenario earthquake considering effects of geological conditions: a case study for the 1995 Hyogo‐ken Nanbu,Japan earthquake

In order to examine the applicability of ground‐shaking mapping techniques to a near‐field earthquake, a peak ground velocity map of the 1995 Hyogo‐ken Nanbu, Japan earthquake computed from seismic zoning methods that consider the effects of geological conditions is compared with the actual observed intensity map. When computing the ground‐shaking map, the site amplification at each site is calculated in terms of the average shear‐wave velocity of the ground estimated from the corresponding geomorphological conditions. This map shows a relatively good agreement with the observed intensity map. However, the computations provide smaller values for certain disastrous areas of the earthquake, where the effects on ground motion of a deep, irregular underground structure have been reported. The effect of such structures on site response is examined implementing 2D FEM analyses, thereby being also incorporated into the method. Results considering the effect of the irregular underground structure show better agreement with the observed intensity map. Copyright © 2002 John Wiley & Sons, Ltd.     

土层特性变异性对场地传递函数的影响

选取日本Kik-Net强震数据库中软（FKSH14）、硬（FKSH12）两类场地,建立场地概率模型。应用Monte Carlo技术随机生成50组场地剖面,分别计算场地的传递函数STF及STF标准差,讨论场地土层厚度、剪切波速,以及两者组合工况对场地传递函数的标准差的影响。结果显示：对于硬土场地,场地特征频率标准差相对于软土场地较大,且剪切波速变异性的影响略大于土层厚度变异性的,两者组合工况的影响最大;而对于软土场地,土层厚度、剪切波速变化工况下,场地特征频率的标准差相当,略低于两者组合工况;对于软、硬两类场地,土层厚度与剪切波速两者组合工况下的STF标准差略大于单一量变化工况,但3种工况下的场地STF标准差相差不明显;场地STF标准差在场地自振频率附近的频率段取值较大,极值点与场地STF的极值点相对应;基于实际地震记录的场地传递函数标准差高于模拟的结果,但是两者极值点对应的频率范围吻合。     

汶川地震远场地震动特征及其对长周期结构影响的分析

汶川8．0级大地震中,中国数字强震动台网获得了大量的数字强震动记录,这些记录特别是远场记录具有丰富的长周期地震动分量。本文根据东南强震动中心获取的区域数字强震动记录,分析汶川8．0级地震的远场地震动特征,研究了基岩场地及深厚软弱场地的长周期地震动及其差异;根据长周期结构的特点,选取建于深厚软弱场地上的江苏A050强震台的超长地震记录进行结构地震反应分析,研究汶川8．0级地震对远场长周期结构的影响,并结合实际震害特点,提出了长周期结构抗震及地震安全对策中一些值得注意和思考的问题。     

Detection of soil liquefaction from strong motion records

During the recent earthquakes in Japan and the U.S.A. a number of records from liquefied‐soil sites have been obtained. The ground motion parameters from these sites were studied and several methods for detection of liquefaction from seismic records were developed. The methods, however, focus mainly on the horizontal ground motion and may interpret as liquefaction‐induced some records from soft‐soil deposits or records with dominant surface waves, at which sites the phenomenon was not observed. Besides, not all of the available records from liquefied sites were processed. In this paper, after examination of the ability of different types of ground motion parameters to indicate alone soil liquefaction we propose a new liquefaction detection method that simultaneously analyses instantaneous frequency content of the horizontal and the vertical ground acceleration. We also compare performance of the proposed method with that of the other liquefaction detection methods. The computations are carried out using a common data set including records from liquefied and non‐liquefied sites. Results show that the frequency‐related parameters and the proposed method detect more efficiently the occurrence of liquefaction from the seismic records. Copyright © 2001 John Wiley & Sons, Ltd.     

Effect of peak ground velocity on deformation demands for SDOF systems

The effect of peak ground velocity (PGV) on single‐degree‐of‐freedom (SDOF) deformation demands and for certain ground‐motion features is described by using a total of 60 soil site records with source‐to‐site distances less than 23 km and moment magnitudes between 5.5 and 7.6. The observations based on these records indicate that PGV correlates well with the earthquake magnitude and provides useful information about the ground‐motion frequency content and strong‐motion duration that can play a role on the seismic demand of structures. The statistical results computed from non‐linear response history analyses of different hysteretic models highlight that PGV correlates better with the deformation demands with respect to other ground motion intensity measures. The choice of PGV as ground motion intensity decreases the dispersion due to record‐to‐record variability of SDOF deformation demands, particularly in the short period range. The central tendencies of deformation demands are sensitive to PGV and they may vary considerably as a function of the hysteretic model and structural period. The results provided in this study suggest a consideration of PGV as a stable candidate for ground motion intensity measure in simplified seismic assessment methods that are used to estimate structural performance for earthquake hazard analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

Influence of time‐varying frequency content in earthquake ground motions on seismic response of linear elastic systems

Earthquake ground motion records are nonstationary in both amplitude and frequency content. However, the latter nonstationarity is typically neglected mainly for the sake of mathematical simplicity. To study the stochastic effects of the time‐varying frequency content of earthquake ground motions on the seismic response of structural systems, a pair of closely related stochastic ground motion models is adopted here. The first model (referred to as ground motion model I) corresponds to a fully nonstationary stochastic earthquake ground motion model previously developed by the authors. The second model (referred to as ground motion model II) is nonstationary in amplitude only and is derived from the first model. Ground motion models I and II have the same mean‐square function and global frequency content but different features of time variation in the frequency content, in that no time variation of the frequency content exists in ground motion model II. New explicit closed‐form solutions are derived for the response of linear elastic SDOF and MDOF systems subjected to stochastic ground motion model II. New analytical solutions for the evolutionary cross‐correlation and cross‐PSD functions between the ground motion input and the structural response are also derived for linear systems subjected to ground motion model I. Comparative analytical results are presented to quantify the effects of the time‐varying frequency content of earthquake ground motions on the structural response of linear elastic systems. It is found that the time‐varying frequency content in the seismic input can have significant effects on the stochastic properties of system response. Copyright © 2016 John Wiley & Sons, Ltd.     

Ductility‐dependent intensity measure that accounts for ground‐motion spectral shape and duration

The calculated nonlinear structural responses of a building can vary greatly, even if recorded ground motions are scaled to the same spectral acceleration at a building's fundamental period. To reduce the variation in structural response at a particular ground‐motion intensity, this paper proposes an intensity measure (IM_comb) that accounts for the combined effects of spectral acceleration, ground‐motion duration, and response spectrum shape. The intensity measure includes a new measure of spectral shape that integrates the spectrum over a period range that depends on the structure's ductility. The new IM is efficient, sufficient, scalable, transparent, and versatile. These features make it suitable for evaluating the intensities of measured and simulated ground motions. The efficiency and sufficiency of the new IM is demonstrated for the following: (i) elastic‐perfectly plastic single‐degree‐of‐freedom (SDOF) oscillators with a variety of ductility demands and periods; (ii) ductile and brittle deteriorating SDOF systems with a variety of periods; and (iii) collapse analysis for 30 previously designed frames. The efficiency is attributable to the inclusion of duration and to the ductility dependence of the spectral shape measure. For each of these systems, the transparency of the intensity measure made it possible to identify the sensitivity of structural response to the various characteristics of the ground motion. Spectral shape affected all structures, but in particular, ductile structures. Duration only affected structures with cyclic deterioration. Copyright © 2015 John Wiley & Sons, Ltd.     

Tall building performance‐based seismic design using SCEC broadband platform site‐specific ground motion simulations

The scarcity of strong ground motion records presents a challenge for making reliable performance assessments of tall buildings whose seismic design is controlled by large‐magnitude and close‐distance earthquakes. This challenge can be addressed using broadband ground‐motion simulation methods to generate records with site‐specific characteristics of large‐magnitude events. In this paper, simulated site‐specific earthquake seismograms, developed through a related project that was organized through the Southern California Earthquake Center (SCEC) Ground Motion Simulation Validation (GMSV) Technical Activity Group, are used for nonlinear response history analyses of two archetype tall buildings for sites in San Francisco, Los Angeles, and San Bernardino. The SCEC GMSV team created the seismograms using the Broadband Platform (BBP) simulations for five site‐specific earthquake scenarios. The two buildings are evaluated using nonlinear dynamic analyses under comparable record suites selected from the simulated BBP catalog and recorded motions from the NGA‐West database. The collapse risks and structural response demands (maximum story drift ratio, peak floor acceleration, and maximum story shear) under the BBP and NGA suites are compared. In general, this study finds that use of the BBP simulations resolves concerns about estimation biases in structural response analysis which are caused by ground motion scaling, unrealistic spectral shapes, and overconservative spectral variations. While there are remaining concerns that strong coherence in some kinematic fault rupture models may lead to an overestimation of velocity pulse effects in the BBP simulations, the simulations are shown to generally yield realistic pulse‐like features of near‐fault ground motion records.     

Validation of (not‐historical) large‐event near‐fault ground‐motion simulations for use in civil engineering applications

Ground‐motion simulations generated from physics‐based wave propagation models are gaining increasing interest in the engineering community for their potential to inform the performance‐based design and assessment of infrastructure residing in active seismic areas. A key prerequisite before the ground‐motion simulations can be used with confidence for application in engineering domains is their comprehensive and rigorous investigation and validation. This article provides a four‐step methodology and acceptance criteria to assess the reliability of simulated ground motions of not historical events, which includes (1) the selection of a population of real records consistent with the simulated scenarios, (2) the comparison of the distribution of Intensity Measures (IMs) from the simulated records, real records, and Ground‐Motion Prediction Equations (GMPEs), (3) the comparison of the distribution of simple proxies for building response, and (4) the comparison of the distribution of Engineering Demand Parameters (EDPs) for a realistic model of a structure. Specific focus is laid on near‐field ground motions (<10km) from large earthquakes (M_w7), for which the database of real records for potential use in engineering applications is severely limited. The methodology is demonstrated through comparison of (2490) near‐field synthetic records with 5 Hz resolution generated from the Pitarka et al (2019) kinematic rupture model with a population of (38) pulse‐like near‐field real records from multiple events and, when applicable, with NGA‐W2 GMPEs. The proposed procedure provides an effective method for informing and advancing the science needed to generate realistic ground‐motion simulations, and for building confidence in their use in engineering domains.