Seismic demand models for probabilistic risk analysis of near fault vertical ground motion effects on ordinary highway bridges

The influence of vertical ground motions on the seismic response of highway bridges is not very well understood. Recent studies suggest that vertical ground motions can substantially increase force and moment demands on bridge columns and girders and cannot be overlooked in seismic design of bridge structures. For an evaluation of vertical ground motion effects on the response of single‐bent two‐span highway bridges, a systematic study combining the critical engineering demand parameters (EDPs) and ground motion intensity measures (IMs) is required. Results of a parametric study examining a range of highway bridge configurations subjected to selected sets of horizontal and vertical ground motions are used to determine the structural parameters that are significantly amplified by the vertical excitations. The amplification in these parameters is modeled using simple equations that are functions of horizontal and vertical spectral accelerations at the corresponding horizontal and vertical fundamental periods of the bridge. This paper describes the derivation of seismic demand models developed for typical highway overcrossings by incorporating critical EDPs and combined effects of horizontal and vertical ground motion IMs depending on the type of the parameter and the period of the structure. These models may be used individually as risk‐based design tools to determine the probability of exceeding the critical levels of EDP for pre‐determined levels of ground shaking or may be included explicitly in probabilistic seismic risk assessments. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic isolation of cable‐stayed bridges for near‐field ground motions

This study examines the efficacy of using seismic isolation to favorably influence the seismic response of cable‐stayed bridges subjected to near‐field earthquake ground motions. In near‐field earthquake ground motions, large amplitude spectral accelerations can occur at long periods where many cable‐stayed bridges have significant structural response modes. This combination of factors can result in large tower accelerations and base shears. In this study, lead–rubber bearing seismic isolators were modeled for three cable‐stayed bridges, and three cases of isolation were examined for each bridge. The nine isolated bridge configurations, plus three non‐isolated configurations as references, were subjected to near‐field earthquake ground motions using three‐dimensional time‐history analyses. Introduction of a small amount of isolation is shown to be very beneficial in reducing seismic accelerations and forces while at the same time producing only a modest increase in the structural displacements. There is a low marginal benefit to continue to increase the amount of isolation by further lengthening the period of the structure because structural forces and accelerations reduce at a diminishing rate whereas structural displacements increase substantially. In virtually all cases the base shears in the isolated bridges were reduced by at least 50several instances by up to 80individual near‐field records showed large variability from one record to the next, with coefficients of variation about the mean as large as 50assessing the characteristics of near‐field ground motion for use in isolation design of cable‐stayed bridges. Copyright © 2003 John Wiley & Sons, Ltd.     

断层走向对刚构桥地震反应的影响

我国西部部分连续刚构桥临近地震断层建设,在抗震分析时通常会忽略断层走向与桥梁纵桥向夹角对其地震反应的影响。利用Midas Civil软件建立4座墩高不同的大跨度连续刚构桥模型,选取10组近断层强震记录进行时程分析,研究断层走向对刚构桥地震反应(位移和弯矩反应)的影响。结果显示：在水平双向近断层地震动输入下,桥梁主墩及主梁纵桥向地震反应在断层走向与纵桥向夹角为75°～135°范围内最大,而横桥向最大地震反应则发生在夹角为0°～30°或120°～180°范围;在三向近断层地震动输入下,与仅考虑水平双向地震动输入下的桥梁地震反应相比,竖向地震动对主梁竖向弯矩响应的影响较大,特别是主墩和主梁的交界处,增大比例可达2倍及以上。就文章选取的4座桥梁算例,不考虑断层走向和桥梁纵桥向的夹角则存在低估桥梁地震反应的可能,低估误差在15%～40%左右。     

A comparative study between China and U.S. on seismic design philosophy and practice of a long span arch bridge

This paper presents the first of a series of case studies on the seismic design of long span bridges （cable-stayed bridges, suspension bridges and arch bridges） under a cooperative research project on seismic behavior and design of highway bridges between the State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University and the Multidisciplinary Center for Earthquake Engineering Research, University at Buffalo. The objective of this series of case studies is to examine the differences and similarities on the seismic design practice of long span bridges in China and the U.S., to identify research needs and to develop design guidelines beneficial to bridge engineers in both countries. Unlike short to medium span bridges, long span bridges are not included in most seismic design specifications, mainly because they are location dependent and structurally unique. In this paper, an available model of a steel tied half through arch bridge with a main span of 550m in China is discussed. Analysis is focused on comparisons of the seismic responses due to different ground motions. Seismic design criteria and seismic performance requirements for long span bridges in both countries were first introduced and compared, and then three near field earthquake records with large vertical components were selected as the excitations to examine the seismic behavior and seismic vulnerability of the bridge. Results show that （1） the selected near field ground motions cause larger responses to key components （critical sections） of the bridge （such as arch rib ends） with a maximum increase of more than twice those caused by the site specific ground motions; （2） piers, longitudinal girders and arch crowns are more vulnerable to vertical motions, especially their axial forces; and （3） large vertical components of near field ground motions may not significantly affect the bridge＇s internal forces provided that their peak acceleration spectra ordinates only appear at periods of less than 0.2s. However, they may have more influence on the longitudinal displacements of sliding bearings due to their large displacement spectra ordinates at the fundamental period of the bridge.     

Analytical solution for vertical site response analysis and its validation

Existing studies for site response analysis in geotechnical earthquake engineering have widely concentrated on the horizontal component of the ground motion. However, strong vertical ground motions have been repeatedly observed, resulting in significant vertical compression damage of engineering structures. Furthermore, for the seismic design of critical structures(e.g. large-scale dams and nuclear power plants), the ground motions in all three directions should be considered. Therefore, there is a need to investigate the site response subjected to the vertical component of the ground motion, especially for the seismic design of critical structures. Consequently, in this study, a numerical program for vertical site response analysis is proposed based on the commonly used analytical transfer function method. The proposed program is then validated against well-documented case studies obtained from the Japanese KiK-net(Kiban Kyoshin network) downhole array monitoring system. Results show that the response spectra at the ground surface are well predicted in the low frequency range(5 Hz), while discrepancies are observed in the high frequency range. However, the high frequency discrepancies do not significantly affect the overall prediction accuracy, as the overall seismic response of geotechnical structures are usually dominated by low frequency vibrations. Furthermore, the limitations in the analysis are also discussed.     

9.21台湾集集地震中场地类别对地震动若干特性的影响

对9．21台湾集集地震主震的404组强震记录按照不同震中距和场地类别进行分组，然后对加速度水平分量和垂直分量的持时、峰值加速度、包络线、反应谱及其均方差作了，统计分析。结果表明，场地条件对不同分量加速度某些特征的影响较为显著，断层方向对地震动水平特性也有一定的影响。该结果对地震危险性分析以及结构抗震验算有一定参考价值。此外，对地震动三分量包络线的研究为三维地震动模拟提供了一定参考。     

摩擦摆基础隔震结构多维地震反应分析

对摩擦摆基础隔震结构进行了单向、双向和三向地震反应对比分析,表明考虑双向水平地震动时摩擦摆基础隔震结构的支座位移增大,而结构的加速度和楼层剪力减小,其中对支座位移和结构加速度影响较大;考虑竖向地震动时摩擦摆基础隔震结构的支座位移略有减小,而结构的加速度和楼层剪力增大,其中对结构加速度影响较大.因而,在进行摩擦摆基础隔震结构地震反应分析时,应考虑多维地震动的影响.     

近断层地震动作用下风机塔地震反应分析

为了研究近断层地震动速度脉冲及强竖向地震动对风机塔地震响应的影响,以某陆上风电场1.5 MW风机塔为研究对象开展了结构在水平向脉冲型地震动、水平向非脉冲型地震动、水平与竖向地震动组合3种地震输入工况的时程分析。通过3种工况下塔顶位移时程、加速度时程、塔底剪力、弯矩及轴力的对比分析发现:近断层速度脉冲对结构塔顶水平位移、塔顶水平加速度、塔底剪力与弯矩均影响显著;竖向地震动会加大结构的塔顶竖向加速度响应及塔底轴力响应;随着竖向与水平加速度峰值比增大,塔顶竖向加速度响应增大,最大轴力随着峰值比增大而增大,最小轴力随着峰值比增大而减小。此外,增量动力分析表明,采用自接触的有限元模型可以更真实地预测风机塔的失稳破坏机制。     

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.     

Seismic response of a bridge–soil–foundation system under the combined effect of vertical and horizontal ground motions

Different levels of model sophistication have recently emerged to support seismic risk assessment of bridges, but mostly at the expense of neglecting the influence of vertical ground motions (VGMs). In this paper, the influence of VGMs on bridge seismic response is presented and the results are compared with the case of horizontal‐only excitations. An advanced finite element model that accounts for VGMs is first developed. Then, to investigate the effect of soil–structure interaction (SSI) including liquefaction potential, the same bridge with soil‐foundation and fixed boundary conditions is also analyzed. Results show that the inclusion of the VGMs has a significant influence on the seismic response, especially for the axial force in columns, normal force of bearings, and the vertical deck bending moments. However, VGMs do not have as much influence on the seismic demand of the pile cap displacements or pile maximum axial forces. Also, the significant fluctuation of the column axial force can reduce its shear and flexural capacity, and a heightened reversal of flexural effects may induce damage in the deck. In addition, relative to the fixed base case, SSI effects tend to reduce response quantities for certain ground motions while increasing demands for others. This phenomenon is explained as a function of the frequency content of the ground motions, the shift in natural vertical periods, and the VGM spectral accelerations at higher modes. Moreover, the mechanisms of liquefaction are isolated relative to SSI effects in nonliquefiable soils, revealing the influence of liquefaction on bridge response under VGMs. Copyright © 2012 John Wiley & Sons, Ltd.     

垂直向地震作用对节理岩体失稳破坏的影响

基于线弹性断裂力学理论分析了垂直向地震作用对节理岩体地震动力破坏的影响。在仅考虑峰值时,最不利的单向地震动加速度方向是水平倾向坡外,双向则依据破裂机制是拉剪或压剪,加速度分别是水平倾向坡外与向下或向上的组合。地震动的幅值、作用方向及双向地震动的组合都可使岩体的破坏机制发生转化,并且是突变的、不可逆的。较低峰值的双向地震动产生的应力强度因子可能大于较高峰值的单向地震动所产生的应力强度应子。在岩体节理分布特征和静态应力场一定的初始条件下,第一个导致岩体中产生破裂的地震动加速度幅值及其方向的组合唯一地决定了岩体不可逆破坏发展的方向、机制及最终的破坏特征,其复杂性远大于静力作用时的情况。对岩体地震动力破坏问题的认识应充分考虑垂直向地震动的重要影响。     

水平及竖向地震共同作用下双线隧道的响应分析

基于有效的土-结相互作用有限元数值模拟方法,利用有限元软件ABAQUS对水平及竖向地震共同作用下双线盾构隧道的地震响应进行分析研究。地震动输入选取近场地震Loma、ChiChi、Mammoth和WoLong的基岩水平及竖向加速度时程记录。结果表明,不同近场地震记录对隧道结构的作用不同,隧道的地震反应与场地性质及地震动的频谱特性密切相关。对比隧道在水平及竖向地震动共同作用下的响应与单向水平地震动作用下的响应,发现隧道的最大地震附加内力及其分布均发生较大的变化,在隧道结构抗震设计中需引起重视。另外,分析中还考虑了在双向地震动共同作用下,隧道间距、土-结接触面的摩擦系数、土-结相对刚度、输入的地震记录和竖向地震动相对强度对隧道地震响应的影响等,研究结果对隧道工程的抗震设计具有一定的参考价值。     

Hydrodynamic pressures and response of gravity dams to vertical earthquake component

Hydrodynamic pressures and structural response of concrete gravity dams, including dam-reservoir interaction, due to the vertical component of earthquake ground motions are investigated. The response of the dam is approximated by the deformations in the fundamental mode of vibration, and the effects of deformability of bed rock on hydrodynamic pressures are recognized in the analysis. Expressions for the complex frequency response functions for the dam displacement, dam acceleration and lateral hydrodynamic force are derived. These results along with the Fast Fourier Transform algorithm are utilized to compute the time-history of responses of dams of 100, 300 and 600 ft height, with full reservoir, for different values of elastic modulus of mass concrete: 3.0, 3.5, 4.0, 4.5 and 5.0 million psi, to the vertical component of El Centro, 1940, and Taft, 1952, ground motions. It is concluded that the hydrodynamic forces caused by vertical ground motion are affected substantially by damreservoir interaction and depend strongly on the modulus of elasticity of the dam. The dam response to the vertical component of ground motion is compared with that due to the horizontal component. It is concluded that because the vertical component of ground motion causes significant hydrodynamic forces in the horizontal direction on a vertical upstream face, responses to the vertical component of ground motion are of special importance in analysis of concrete gravity dams subjected to earthquakes.     

Engineering characteristics of near-fault vertical ground motions and their effect on the seismic response of bridges

A wide variety of near-fault strong ground motion records were collected from various tectonic environments worldwide and were used to study the peak value ratio and response spectrum ratio of the vertical to horizontal component of ground motion, focusing on the effect of earthquake magnitude, site conditions, pulse duration, and statistical component. The results show that both the peak value ratio and response spectrum ratio are larger than the 2/3 value prescribed in existing seismic codes, and the relationship between the vertical and horizontal ground motions is comparatively intricate. In addition, the effect of the near-fault ground motions on bridge performance is analyzed, considering both the material nonlinear characteristics and the P~? effect.     

Response to orthogonal components of ground motion and assessment of percentage combination rules

The effects of horizontal components of ground motion on the linear response of torsionally stiff and torsionally flexible systems, on soft and firm soil conditions, are examined. A one‐story, two‐way asymmetric structural system is used, subjected to uncorrelated ground motion components along their principal directions. Spectral densities for ground accelerations in firm and soft soils are modeled based on recorded data from large intensity Mexican earthquakes. It is shown that for firm soils, in general, these effects are important in the case of torsionally flexible systems that are stiff under translation, or for torsionally stiff systems that are flexible in translation. The percentage combination rules usually specified in seismic design codes are assessed against the dynamic response. Such combination rules can result in overly conservative design forces or underestimated design forces, particularly for torsionally flexible structures. Given the relative magnitude of the response to each ground motion component, it was found that using different percentage values in the combination rules has no significant effect on improving the estimation of the total response. Copyright © 2003 John Wiley & Sons, Ltd.     

A simplified multisupport response spectrum method

A simplified multisupport response spectrum method is presented.The structural response is a sum of two components of a structure with a first natural period less than 2 s.The first component is the pseudostatic response caused by the inconsistent motions of the structural supports,and the second is the structural dynamic response to ground motion accelerations.This method is formally consistent with the classical response spectrum method,and the effects of multisupport excitation are considered for any modal response spectrum or modal superposition.If the seismic inputs at each support are the same,the support displacements caused by the pseudostatic response become rigid body displacements.The response spectrum in the case of multisupport excitations then reduces to that for uniform excitations.In other words,this multisupport response spectrum method is a modification and extension of the existing response spectrum method under uniform excitation.Moreover,most of the coherency coefficients in this formulation are simplified by approximating the ground motion excitation as white noise.The results indicate that this simplification can reduce the calculation time while maintaining accuracy.Furthermore,the internal forces obtained by the multisupport response spectrum method are compared with those produced by the traditional response spectrum method in two case studies of existing long-span structures.Because the effects of inconsistent support displacements are not considered in the traditional response spectrum method,the values of internal forces near the supports are underestimated.These regions are important potential failure points and deserve special attention in the seismic design of reticulated structures.     

近断层竖向与水平向加速度反应谱比值特征

显著的竖向地震动是近断层地震动区别于远场地震动的重要特征之一,为更合理地确定竖向地震动作用,研究了近断层区域竖向地震动的反应谱特征及其与水平向反应谱比值的影响因素.首先,选取1952—1999年世界范围内震级在M5.4—7.6之间的18次地震的地震动记录,研究竖向地震加速度反应谱及其与水平向加速度反应谱比值特征;然后统计分析了断层距、场地条件、震级以及断层机制对竖向与水平向加速度反应谱比的影响.结果表明,一般情况下竖向加速度具有更丰富的短周期分量,并且竖向加速度反应谱衰减较慢;断层距在20km以内的近断层区域、软弱土层场地、中等震级地震和逆断层大震级中长周期范围等条件下,具有较大的竖向与水平向加速度反应谱比值;在近断层区域的结构抗震设计中应充分考虑竖向地震动的影响.     

地形效应影响下地震动参数与斜坡稳定性的相关性研究

地形对地震动的影响比较复杂, 考虑地形放大效应的地震滑坡稳定性分析需要选择合适的地震动参数. 本文使用自贡地形影响台阵记录到的2008年汶川M_S8.0地震主震加速度记录, 分析了地震动峰值加速度、 阿里亚斯烈度以及90%能量持时随地形高度的变化, 探讨了地形效应作用下峰值加速度和阿里亚斯烈度与地震动作用下斜坡稳定性的相关性. 结果表明: ① 地形场地对峰值加速度和阿里亚斯烈度均有显著的放大效应. 地形放大效应较为复杂, 其整体上随台站高度的增加而增大, 水平向的放大效应大于竖直向. 水平向峰值加速度的放大系数为1.1—1.8, 阿里亚斯烈度的放大系数为1.2—3.3; 竖直向相应放大系数分别为1.1—1.3和1.2—1.7. ② 地形对地震动持时也有一定的放大效应, 但不同高度、 不同分量的放大效应没有显著差异, 其放大系数均约为1.3. ③ 阿里亚斯烈度和峰值加速度均能很好地表征地形对地震动的影响, 与地震动对斜坡稳定性的影响具有很强的相关性. 与峰值加速度相比, 阿里亚斯烈度综合了地震动的多方面特征, 可以更好地表征地形对地震动的影响, 与地震动作用下斜坡稳定性的相关性更强.      

Dynamic behavior of a smart device on a surface subjected to earthquake motion

This paper leverages concepts from an existing model to simulate the planar response of a smart device subjected to friction forces induced by an underlying moving plane. An interpolation technique is used to enhance detection of transition points (between sticking and sliding states), which must be accurately identified because of the frequency of their occurrence during seismic motion. The behavior of a smart device on an unconstrained table or desk, which is itself on a moving floor, is introduced and discussed. After validation of the results using experimental data, the revised model is used to study the sliding potential of smart devices on a surface during strong seismic events. Sliding spectra associated with selected ground motions are presented and extended to incorporate the effect of vertical accelerations with the purpose of assessing their influence. It is shown that vertical accelerations have a minimal effect on the sliding behavior of smart devices and that a “probability of exceeding the slip limit” curve can be developed to relate the probability of sticking to a demand parameter that represents the ground motion.     

Bidirectional loading hybrid tests of square cross‐sections of steel bridge piers

Steel rectangular section columns with stiffened plates are commonly used for elevated highway bridges in the urban areas of Japan. The seismic design of bridge piers is usually performed by dynamic analysis in the horizontal direction using various independent directional seismic acceleration data. However, this simple treatment does not reflect the effect of bilateral loading as a structural response to inelastic interaction. In this study, unidirectional and bidirectional loading hybrid tests were conducted to examine the seismic response and performance of square cross‐sections of steel bridge piers subjected to bidirectional seismic accelerations. Comparison of the results of unidirectional and bidirectional loading tests revealed that the maximum load is the same as the average of unidirectional loading in the NS and EW directions; however, the maximum response displacement and residual displacement increase in proportion with hard to soft ground types. Moreover, a modified seismic design is proposed considering these bidirectional loading effects. Copyright © 2012 John Wiley & Sons, Ltd.