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.     

Estimation of seismic drift demands for frame structures

A process is outlined and evaluated for the estimation of seismic roof and storey drift demands for frame structures from the spectral displacement demand at the first mode period of the structure. The spectral displacement demand is related to the roof drift demand for the multi‐degree‐of‐freedom (MDOF) structure using three modification factors, accounting for MDOF effects, inelasticity effects, and P‐delta effects. Median values and measures of dispersion for the factors are obtained from elastic and inelastic time history analyses of nine steel moment resisting frame structures subjected to sets of ground motions representative of different hazard levels. The roof drift demand is related to the storey drift demands, with the results being strongly dependent on the number of stories and the ground motion characteristics. The relationships proposed in this paper should prove useful in the conceptual design phase, in estimating deformation demands for performance assessment, and in improving basic understanding of seismic behaviour. Copyright © 2000 John Wiley & Sons, Ltd.     

Influence of earthquake ground‐motion duration on damage estimation: application to steel moment resisting frames

This paper presents an analytical study evaluating the influence of ground motion duration on structural damage of 3‐story, 9‐story, and 20‐story SAC steel moment resisting frame buildings designed for downtown Seattle, WA, USA, using pre‐Northridge codes. Two‐dimensional nonlinear finite element models of the buildings are used to estimate the damage induced by the ground motions. A set of 44 ground motions is used to study the combined effect of spectral acceleration and ground motion significant duration on drift and damage measures. In addition, 10 spectrally equivalent short‐duration shallow crustal ground motions and long‐duration subduction zone records are selected to isolate duration effect and assess its effect on the response. For each ground motion pair, incremental dynamic analyses are performed at at least 20 intensity levels and response measures such as peak interstory drift ratio and energy dissipated are tracked. These response measures are combined into two damage metrics that account for the ductility and energy dissipation. Results indicate that the duration of the ground motion influences, above all, the combined damage measures, although some effect on drift‐based response measures is also observed for larger levels of drift. These results indicate that because the current assessment methodologies do not capture the effects of ground motion duration, both performance‐based and code‐based assessment methodologies should be revised to consider damage measures that are sensitive to duration. Copyright © 2016 John Wiley & Sons, Ltd     

Spatial seismic modeling of base‐isolated buildings pounding against moat walls: effects of ground motion directionality and mass eccentricity

Structural impact between adjacent buildings may induce local and, in some extreme cases, severe damage, especially in the case of seismically isolated buildings. This study parametrically investigates in the three‐dimensional domain the effect of pounding on the peak response of base‐isolated buildings, which are simulated as nonlinear three‐dimensional multi‐degree‐of‐freedom systems. Firstly, it is shown that considering unidirectional, instead of bidirectional, excitations may lead to underestimation of the base drift demands. Subsequently, the peak responses of seismically isolated buildings utilizing lead rubber bearings are studied while varying important parameters, such as the incidence angle of seismic excitations, the available seismic clearance, and mass eccentricities, under the action of bidirectional horizontal excitations. A large number of numerical simulations are performed using a specially developed software that implements an efficient approach to model impacts, taking into account arbitrary locations of contact points. It is found that the peak interstory drift ratio is significantly influenced by the directionality of the ground motion. Therefore, the seismic performance of structures should ideally be assessed examining the peak structural response while bidirectional ground motions are imposed at various incident angles. Furthermore, it is also observed that the interstory drift ratios increase while decreasing the available gap size, up to a certain value. Finally, the parametric analyses indicate that the effects of impact are more severe for structures with mass eccentricities, and in which case, the estimation of the critical incidence angle becomes more laborious. Copyright © 2016 John Wiley & Sons, Ltd.     

The effect of amplitude scaling limits on conditional spectrum-based ground motion selection

Amplitude scaling is commonly used to select ground motions matching a target response spectrum. In this paper, the effect of scaling limits on ground motion selection, based on the conditional spectrum framework, is investigated. Target spectra are computed for four probabilistic seismic hazard cases in Western United States, and 16 ground motion suites are selected using different scaling limits (ie, 2, 5, 10, and 15). Comparison of spectral acceleration distributions of the selected ground motion suites demonstrates that the use of a scaling limit of 2 yields a relatively poor representation of the target spectra, because of the small limit leading to an insufficient number of available ground motions. It is also shown that increasing scaling limit results in selected ground motions with generally increased distributions of Arias intensity and significant duration Ds_5-75, implying that scaling limit consideration can significantly influence the cumulative and duration characteristics of selected ground motions. The ground motion suites selected are then used as input for slope displacement and structural dynamic analyses. Comparative results demonstrate that the consideration of scaling limits in ground motion selection has a notable influence on the distribution of the engineering demand parameters calculated (ie, slope displacement and interstory drift ratio). Finally, based on extensive analyses, a scaling limit range of 3 to 5 is recommended for general use when selecting ground motion records from the NGA-West2 database.     

Effect of soil parameter uncertainty on seismic demand of low-rise steel buildings on dense silty sand

Focusing on low-rise steel buildings supported by shallow isolated foundations on dense silty sand, this study demonstrates the effect of uncertainty in soil parameters on seismic response of structures. Considering a set of 20 ground motions representing 10% in 50 years hazard level and concentrating on peak base moment, base shear and interstory drift as the demand variables of interest, it is found that uncertainty in soil parameters may result in significant response variability of the structures, especially when vertical factor of safety is low and the structure is relatively stiff. Uncertainty in friction angle results in significant variability of the peak base moment and base shear, while peak interstory drift ratio is found to be virtually unaffected by uncertainty in soil parameters. It is also found that a linear soil–structure-interaction (SSI) model will not be able to predict such response variability under these set of ground motions.     

Prediction of spatially distributed seismic demands in specific structures: Ground motion and structural response

The efficacy of various ground motion intensity measures (IMs) in the prediction of spatially distributed seismic demands (engineering demand parameters, (EDPs)) within a structure is investigated. This has direct implications to building‐specific seismic loss estimation, where the seismic demand on different components is dependent on the location of the component in the structure. Several common IMs are investigated in terms of their ability to predict the spatially distributed demands in a 10‐storey office building, which is measured in terms of maximum interstorey drift ratios and maximum floor accelerations. It is found that the ability of an IM to efficiently predict a specific EDP depends on the similarity between the frequency range of the ground motion that controls the IM and that of the EDP. An IMs predictability has a direct effect on the median response demands for ground motions scaled to a specified probability of exceedance from a ground motion hazard curve. All of the IMs investigated were found to be insufficient with respect to at least one of magnitude, source‐to‐site distance, or epsilon when predicting all peak interstorey drifts and peak floor accelerations in a 10‐storey reinforced concrete frame structure. Careful ground motion selection and/or seismic demand modification is therefore required to predict such a spatially distributed demands without significant bias. Copyright © 2009 John Wiley & Sons, Ltd.     

A method for computing interstory drift spectra with consideration of gravity effects

Vertical loads such as gravity may have an important influence on the seismic response of buildings. In this paper, the continuous shear-beam model is extended to study the seismic demand of shear buildings with consideration of the gravity load effect under near-field ground motions. An analytical solution of the free motion equation of as gravity shear beam model is provided in terms of a Bessel series. A method for computing interstory drift spectra is proposed. The interstory drift spectra for two near-field records with distinct pulses are presented to illustrate the effects of gravity and the damping ratio. The interstory drift spectra are also used to analyze the spectral characteristics of near fault ground motion during the 2008 Wenchuan earthquake. The effects of the gravity load ratio, damping ratio and higher modes are investigated and discussed.     

A new approach of selecting real input ground motions for seismic design: The most unfavourable real seismic design ground motions

This paper presents a new way of selecting real input ground motions for seismic design and analysis of structures based on a comprehensive method for estimating the damage potential of ground motions, which takes into consideration of various ground motion parameters and structural seismic damage criteria in terms of strength, deformation, hysteretic energy and dual damage of Park & Ang damage index. The proposed comprehensive method fully involves the effects of the intensity, frequency content and duration of ground motions and the dynamic characteristics of structures. Then, the concept of the most unfavourable real seismic design ground motion is introduced. Based on the concept, the most unfavourable real seismic design ground motions for rock, stiff soil, medium soil and soft soil site conditions are selected in terms of three typical period ranges of structures. The selected real strong motion records are suitable for seismic analysis of important structures whose failure or collapse will be avoided at a higher level of confidence during the strong earthquake, as they can cause the greatest damage to structures and thereby result in the highest damage potential from an extended real ground motion database for a given site. In addition, this paper also presents the real input design ground motions with medium damage potential, which can be used for the seismic analysis of structures located at the area with low and moderate seismicity. The most unfavourable real seismic design ground motions are verified by analysing the seismic response of structures. It is concluded that the most unfavourable real seismic design ground motion approach can select the real ground motions that can result in the highest damage potential for a given structure and site condition, and the real ground motions can be mainly used for structures whose failure or collapse will be avoided at a higher level of confidence during the strong earthquake. Copyright © 2007 John Wiley & Sons, Ltd.     

A measure of the capacity of earthquake ground motions to damage structures

Even though a number of parameters have been proposed in the literature for measuring the capacity of earthquake ground motions to damage structures, most of them are not consistent with building damage observed during earthquakes. In this study, a parameter for measuring seismic damage capacity is proposed. It uses the energy dissipated by a structure in inelastic deformations and a structural overall drift, and it is evaluated for three typical ground motions recorded in severe earthquakes. By using this parameter, consistent results with building damage observed in these earthquakes are obtained, which indicate the importance of displacement control for minimizing seismic damage.     

Seismic demand sensitivity of reinforced concrete shear‐wall building using FOSM method

The uncertainty in the seismic demand of a structure (referred to as the engineering demand parameter, EDP) needs to be properly characterized in performance‐based earthquake engineering. Uncertainties in the ground motion and in structural properties are responsible for EDP uncertainty. In this study, sensitivity of EDPs to major uncertain variables is investigated using the first‐order second‐moment method for a case study building. This method is shown to be simple and efficient for estimating the sensitivity of seismic demand. The EDP uncertainty induced by each uncertain variable is used to determine which variables are most significant. Results show that the uncertainties in ground motion are more significant for global EDPs, namely peak roof acceleration and displacement, and maximum inter‐storey drift ratio, than those in structural properties. Uncertainty in the intensity measure (IM) of ground motion is the dominant variable for uncertainties in local EDPs such as the curvature demand at critical cross‐sections. Conditional sensitivity of global and local EDPs given IM is also estimated. It is observed that the combined effect of uncertainties in structural properties is more significant than uncertainty in ground motion profile at lower IM levels, while the opposite is true at higher IM levels. Copyright © 2005 John Wiley & Sons, Ltd.     

脉冲型地震动作用下隔震结构动力响应的影响参数研究

通过对隔震结构进行非线性动力响应分析,分别研究地震动参数和支座参数对结构地震响应的影响。首先,建立铅芯橡胶支座基础隔震结构的非线性运动方程;然后,以人工合成脉冲型地震动作为输入,运用MATLAB进行编程并求解结构在脉冲型地震动作用下的地震响应;最后,分别研究速度脉冲周期、支座屈服力、屈服后与屈服前的刚度比对隔震支座最大位移和上部结构层间位移的影响。研究结果表明,脉冲周期对结构地震响应影响很大,在进行隔震设计时应使结构自振周期远离脉冲周期;支座刚度比对结构地震响应影响较大,在进行支座选型时应重点关注;支座屈服力对支座位移的影响显著,屈服力越大,支座位移越小。     

长短周期地震波作用下钢框架结构的响应特性对比分析

作为一种特殊的地震动,长周期地震动对结构的危害已引起国内外学者的关注。选取10条KiK-net、K-NET台网中典型的长周期地震动,以及10条国内外的短周期地震动,对比分析两者时程特征和反应谱特征的差异。将所选长、短周期地震动输入钢框架结构模型;通过非线性时程分析,研究钢框架结构在长、短周期地震动作用下的响应差异。结果表明：短周期地震动的平均地面峰值加速度是长周期地震动的3.26倍,而平均地面峰值位移比长周期地震动低10.89%;短周期地震动作用下,钢框架结构顶点加速度响应平均值是长周期地震动的5.16倍,结构顶点位移响应平均值仅比长周期地震动多0.91%;长周期地震动作用下,钢框架结构层间位移角响应较大,结构底部受影响范围更广。对于长周期地震动隐患地区的高层钢框架结构,应对长、短周期震害分别进行考虑;对于中、长周期钢框架结构,建议选用峰值位移作为抗震分析指标。     

近断层脉冲型地震动作用下高层摩擦摆基础隔震结构的减震性能研究

近断层地震动中长周期、短持时和高能量的加速度脉冲将对高层摩擦摆基础隔震结构的减震性能产生不利影响,考虑土-结构相互作用（SSI效应）后的隔震结构将产生动力耦合效应,可能进一步放大隔震结构地震响应。为此,通过一幢框架-核心筒高层摩擦摆基础隔震结构的非线性地震响应分析,考察近断层脉冲型地震动作用下框架-核心筒摩擦摆基础隔震结构的层间位移角、楼层加速度和隔震层变形等响应规律,揭示隔震体系的损伤机理。基于集总参数SR （sway-rocking）模型,分析不同场地类别与不同地震动类型对隔震体系动力响应影响规律。结果表明:高层摩擦摆基础隔震结构在近断层脉冲型地震动作用下的减震效果相比普通地震动减震效果变差,楼层剪力、层间位移角和隔震层变形等超越普通地震动作用下的1.5倍;对于Ⅲ和Ⅳ类场地类别,考虑SSI效应使隔震结构的地震响应进一步放大,弹塑性层间位移角随着土质变软增大尤为明显。     

Response of tall buildings to base rocking induced by Rayleigh waves

By now, it is well known that long‐period surface waves can induce resonant response in high‐rise buildings, in particular those located in sedimentary basins. Rayleigh wave passage has been reported to induce rocking motion at the base of the buildings which can increase displacement demands significantly. However, the building behavior to base rocking has not been extensively studied because commercially available instruments do not record rotational components of ground motion, and thus, rocking time histories have not been available to the analysts. In a recent study, we proposed an effective method for estimating the rocking associated with Rayleigh waves, which takes into account their frequency‐dependent phase velocities. In the present work, we select a number of recorded seismic motions which include surface waves on sedimentary basins from recent well‐recorded earthquake events. Then, we proceed to identify and extract the recorded surface waves by using the technique mentioned above. Using realistic soil‐structure analytical models that have been proposed in the published literature for high‐rise buildings, we study their response to Rayleigh waves as they respond to both translational and rocking motions. Of particular interest is to compare the response of such structures with and without the presence of rotational motions due to surface waves. Using the roof displacement and the building interstory drift as response quantities, our results indicate that demands are controlled by rotational (rocking) motions associated with Rayleigh waves.     

Conditional spectrum‐based ground motion record selection using average spectral acceleration

The use of a seismic intensity measure (IM) is paramount in decoupling seismic hazard and structural response estimation when assessing the performance of structures. For this to be valid, the IM needs to be sufficient;that is, the engineering demand parameter (EDP) response should be independent of other ground motion characteristics when conditioned on the IM. Whenever non‐trivial dependence is found, such as in the case of the IM being the first‐mode spectral acceleration, ground motion selection must be employed to generate sets of ground motion records that are consistent vis‐à‐vis the hazard conditioned on the IM. Conditional spectrum record selection is such a method for choosing records that are consistent with the site‐dependent spectral shape conditioned on the first‐mode spectral acceleration. Based on a single structural period, however the result may be suboptimal, or insufficient, for EDPs influenced by different period values, for example, peak interstory drifts or peak floor accelerations at different floors, potentially requiring different record suites for each. Recently, the log‐average spectral acceleration over a period range, AvgSA, has emerged as an improved scalar IM for building response estimation whose hazard can be evaluated using existing ground motion prediction equations. Herein, we present a recasting of conditional spectrum record selection that is based on AvgSA over a period range as the conditioning IM. This procedure ensures increased efficiency and sufficiency in simultaneously estimating multiple EDPs by means of a single IM. Copyright © 2017 John Wiley & Sons, Ltd.     

Generalized force vectors for multi‐mode pushover analysis of torsionally coupled systems

A generalized multi‐mode pushover analysis procedure was developed for estimating the maximum inelastic seismic response of symmetrical plan structures under earthquake ground excitations. Pushover analyses are conducted with story‐specific generalized force vectors in this procedure, with contributions from all effective modes. Generalized pushover analysis procedure is extended to three‐dimensional torsionally coupled systems in the presented study. Generalized force distributions are expressed as the combination of modal forces to simulate the instantaneous force distribution acting on the system when the interstory drift at a story reaches its maximum value during seismic response. Modal contributions to the generalized force vectors are calculated by a modal scaling rule, which is based on the complete quadratic combination. Generalized forces are applied to the mass centers of each story incrementally for producing nonlinear static response. Maximum response quantities are obtained when the individual frames attain their own target interstory drift values in each story. The developed procedure is tested on an eight‐story frame under 15 ground motions, and assessed by comparing the results obtained from nonlinear time history analysis. The method is successful in predicting the torsionally coupled inelastic response of frames responding to large interstory drift demands. Copyright © 2014 John Wiley & Sons, Ltd.     

近断层地震动下设置BRB的双向减隔震桥梁地震反应

在近断层地震动下桥梁结构将发生较大反应,减隔震设计是减轻地震损伤的重要手段。提出了在桥梁双柱墩横桥向设置防屈曲支撑(BRB),在纵桥向设置铅芯橡胶支座(LRB)的双向减隔震体系。利用Midas Civil软件建立3种不同减隔震方式的桥梁结构模型:LRB仅单向,LRB双向与LRB联合BRB,运用非线性时程分析方法计算了桥墩反应(墩顶侧移角、残余位移角和曲率延性)、LRB支座变形和BRB的耗能特性等。结果表明:在近断层地震动输入下联合设置LRB和BRB的双向减隔震桥梁减震效果明显,相比其它2种方式,能有效降低墩柱的塑性变形及起到保护桥墩的作用。在横桥向,桥墩最大侧移角、残余位移角和最大曲率延性系数都显著降低。     

基于MPA方法的结构滞回耗能计算

在能量反应分析中,滞回耗能是最具明确工程意义的而又便于工程应用的能量指标,可用以衡量结构的塑性累积损伤。然而,以往研究中,在计算多自由度体系的滞回耗能时,通常采用时程分析法,计算比较烦杂,不利于工程实际的应用。因此,本文提出了一种采用模态pushover分析（MPA）计算多层结构滞回耗能的简便方法,并通过两个高层结构算例,验证了该方法的精度。结果表明：基于模态pushover分析的结构滞回耗能计算方法精度良好,结果可靠;对于框架结构,可以直接采用第一阶模态（倒三角）加载模式对结构进行pushover分析计算,对于高层框架剪力墙结构,必须组合高阶模态的滞回耗能计算结果。     

Seismic responses of bridges with rocking column-foundation: A dimensionless regression analysis

Rocking column-foundation system is a new design concept for bridges that can reduce overall seismic damage, minimize construction and repair time, and achieve lower cost in general. However, such system involves complex dynamic responses due to impacts and highly nonlinear rocking behavior. This study presents a dimensionless regression analysis to estimate the rocking and shaking responses of the flexible column-foundation system under near-fault ground motions. First, the transient drift and rocking responses of the system are solved numerically using previously established analytical models. Subsequently, the peak column drifts and uplift angles are derived as functions of ground motion characteristics and the geometric and dynamic parameters of column-foundation system in regressed dimensionless forms. The proposed response models are further examined by validating against the numerical simulations for several as-built bridge cases. It is shown that the proposed model not only physically quantifies the influences of prominent parameters, but also consistently reflects the complex dynamics of the system. The seismic demands of rocking column-foundation system can be realistically predicted directly from structural and ground motion characteristics. This can significantly benefit the design of bridges incorporating this new design concept.