Analysis of the observed seismic response of a highway bridge

Strong-motion accelerograms obtained on the San Juan Bautista 156/101 Separation Bridge during the 6 August 1979 Coyote Lake, California, earthquake are used to examine the response of this multiple-span bridge to moderate levels of earthquake loading. Although the bridge was not damaged, the records are of significant engineering interest as they are the first to be recorded on a highway bridge structure in North America. A technique of system identification is used to determine optimal modal parameters for linear models which can closely replicate the observed time-domain seismic response of the bridge. Time variations in frequency and damping in the horizontal response are identified using a moving-window analysis. A three-dimensional finite element model is developed to study the bridge response in detail. The first two horizontal modal frequencies computed from this model are in excellent agreement with information obtained during the system identification analysis provided the finite element model's expansion joints are locked, preventing relative translational motions from occurring across the joints. Locking is confirmed by the observed seismic deformations of the structure in the fundamental mode. Fundamental vertical frequencies of the individual spans, predicted by the finite element model, are in very good agreement with ambient vibration test data.     

Structural identification of Egnatia Odos bridges based on ambient and earthquake induced vibrations

The dynamic characteristics of two representative R/C bridges on Egnatia Odos motorway in Greece are estimated based on low amplitude ambient and earthquake-induced vibrations. The present work outlines the instrumentation details, algorithms for computing modal characteristics (modal frequencies, damping ratios and modeshapes), modal-based finite element model (FEM) updating methods for estimating structural parameters, and numerical results for the modal and structural dynamic characteristics of the two bridges based on ambient and earthquake induced vibrations. Transverse, bending and longitudinal modes are reliably identified and stiffness-related properties of the piers, deck and elastomeric bearings of the FEMs of the two bridges are estimated. Results provide qualitative and quantitative information on the dynamic behavior of the bridge systems and their components under low-amplitude vibrations. Modeling assumptions are discussed based on the differences in the characteristics identified from ambient and earthquake vibration measurements. The sources of the differences observed between the identified modal and structural characteristics of the bridges and those predicted by FEMs used for design are investigated and properly justified.     

基于响应面的预应力混凝土桥动力有限元模型研究

建立了基于正交实验的响应面模型和精细有限元模型,并将其用于中华大桥的有限元模型修正,通过实测动力数据对修正后的有限元模型计算结果进行了验证。基于修正后的有限元模型,分析了预应力对预应力钢筋混凝土桥梁模态信息（频率和振型）的影响,以及单元类型对桥梁模态频率的影响。结果表明,修正后的有限元模型能够比较准确地反映桥梁实际结构的动力特性,基于响应面模型和遗传算法的修正方法可有效地用于大桥的健康监测和状态评估;预应力对预应力钢筋混凝土桥梁模态信息的影响较小,建模时可不予精确考虑;对于由多根预应力混凝土梁组成的桥梁体系,采用实体单元分析较好。     

Ambient vibration testing of two masonry monuments in Cyprus

The current study investigates the dynamic characteristics of two historical monuments in Cyprus, the St. Nicholas Cathedral in Famagusta and the St. Mamas Church in Morphou. The testing was performed using the ambient vibration survey approach and the output-only method for both structures, to obtain the frequencies and mode shapes of the lower modes. These results contributed in the updating of the finite element models and in the planning of the monitoring strategy that was implemented for these structures, as well as the study for their seismic vulnerability. Comparisons are made between the measured and finite element model dynamic characteristics, and conclusions are drawn.     

Dynamic testing and system identification of a multi-span highway bridge

A simple and effective procedure for conducting the free vibration test on highway bridges is presented. The impulsive force in each direction is generated by a loaded truck that either stops suddenly or falls down from a rigid block. The feasibility of the procedure is demonstrated in identification of the dynamic properties, i.e. the vibration frequencies, mode shapes, and damping ratios, of a three-span box-girder concrete bridge using the Ibrahim Time-Domain (ITD) technique. Up to 14 modes have been identified for the present case. For the purpose of verification, ambient vibration tests were also carried out, with the data processed by the random decrement (Randomdec) technique to yield the free vibration response, followed by the ITD technique. The dynamic properties identified from the two types of test correlate very well with each other, indicating the validity of each procedure described herein. Although many more modes can be identified from the free vibration test because of the higher quality of data produced, the easiness and general applicability of the ambient vibration test can still be appreciated. A comparison of the experimental results with those by the finite element method indicated a lesser degree of correlation, implying that the finite element model adopted in design requires further refinement, say, through a more realistic evaluation of the boundary conditions, geometric and material properties of the bridge. Copyright © 1999 John Wiley & Sons Ltd.     

超大跨度斜拉桥考虑行波效应的地震动随机响应研究

斜拉桥地震反应不同于其它桥型,具有明显的空间耦合效应.利用有限元理论对苏通长江公路大桥的空间抗震性能进行分析,重点研究行波效应对结构响应的影响,并与一致激励计算的结果进行比较,为大跨度斜拉桥抗震分析采用随机方法提供了一定的参考依据.研究结果表明,行波效应对斜拉桥结构内力有显著的影响,大跨度斜拉桥抗震性能分析必须考虑行波效应.而行波效应的影响与结构自身动力特性、视波速、构件位置及研究响应类型(位移与内力)相关.     

独塔刚构体系斜拉桥地震反应分析

基于非线性有限元理论,以某独塔双索面刚构体系斜拉桥为例建立了动力空间有限元模型,对该桥的动力特性进行了研究。在此基础上通过三角级数拟合规范反应谱的方法,合成了适用于结构分析的人造地震波,并以此和两条实际地震记录作为输入地震动,应用时程分析法对比分析了一致激励和行波激励下的结构地震反应。研究结果表明,在考虑纵向+竖向组合作用时,独塔双索面斜拉桥的内力和位移反应比纵向分量单独作用时更为显著;行波效应可以明显减小结构的位移反应,对结构抗震来讲是有利的。以上结论将为此类桥梁的设计和发展提供一定的理论依据。     

立交桥曲线箱梁动力分析模型

提出了1种双脊骨空间有限元模型,用来模拟和分析立交桥曲线箱梁的固有振动特性和动力反应。将曲线箱梁分别看作是由空间梁或壳组成的空间结构,并分别采用分段空间直梁模型、壳元模型和实体元模型进行模拟,分析相同曲线箱梁的振动特性和地震时程反应,通过与双脊骨模型的计算结果的比较验证双脊骨模型的可靠性。初步研究了在相同曲率半径下不同跨度的曲线箱梁的固有振动特性,分析了双脊骨模型的脊骨间距、横向连接间距等参数对模型计算结果的影响。研究结果可为曲线梁桥抗震性能和地震反应分析提供参考。     

地震作用下高速铁路车-线-桥耦合系统动力响应分析

地震激励对高速车辆-简支箱梁桥系统动力响应的影响关系到高速铁路运营安全。基于车辆-轨道耦合动力学和列车-轨道-桥梁动力相互作用理论,运用有限元和多体动力学方法,建立高速铁路桥梁区段车辆-轨道-桥梁耦合系统动力学模型,分析在人工地震波作用下高速铁路车-线-桥耦合系统动力响应。结果表明:地震激励对轨道板、支撑层和桥梁的横向振动特性的影响大于对垂向振动特性的影响,桥梁结构对地震激励的敏感程度大于轨道结构;车辆运行速度对系统垂向振动特性的影响大于对横向振动特性的影响。研究结论可为地震荷载作用下高速铁路安全运营提供理论依据。     

Modal identification of structures from ambient vibration,free vibration,and seismic response data via a subspace approach

This work presents a unified procedure for determining the natural frequencies, modal damping ratios and modal shapes of a structure from its ambient vibration, free vibration and earthquake response data. To evaluate the coefficient matrices of a state‐space model, the proposed procedure applies a subspace approach cooperating with an instrumental variable concept. The dynamic characteristics of a structure are determined from the coefficient matrices. The feasibility of the procedure is demonstrated through processing an in situ ambient vibration measurement of a five‐storey steel frame, an impulse response measurement of a three‐span continuous bridge, and simulated earthquake responses of five‐storey steel frames from shaking table tests. The excellent agreement of the results obtained herein with those published previously confirms the feasibility of the present procedure. Copyright © 2001 John Wiley & Sons, Ltd.     

Correlating measured and simulated dynamic responses of a tall building to long‐distance earthquakes

For almost a decade, a 66‐storey, 280m tall building in Singapore has been instrumented to monitor its dynamic responses to wind and seismic excitations. The dynamic characteristics of the tall building have been investigated via both the finite element method and the experimental modal analysis. The properties of the finite element model have been shown to correlate well with those derived from the data recorded during the ambient vibration tests. During the study period, 21 sets of earthquake ground motions have been recorded at the building site. The basement motions may be divided into three categories based on their predominant frequency components with respect to the building's fundamental frequency. The calibrated three‐dimensional finite element model is employed to simulate the seismic response of the tall building. Correlation analysis of the time histories between the recorded data and the simulated results has been carried out. The correlation analysis results show that the simulated dynamic response time histories match well with those of the recorded dynamic responses at the roof level. The results also show that the simulated maximum response at the roof level is close to the peak response recorded during the earthquakes. Copyright © 2004 John Wiley & Sons, Ltd.     

Enhancing resilience of highway bridges through seismic retrofit

The present study evaluates seismic resilience of highway bridges that are important components of highway transportation systems. To mitigate losses incurred from bridge damage during seismic events, bridge retrofit strategies are selected such that the retrofit not only enhances bridge seismic performance but also improves resilience of the system consisting of these bridges. To obtain results specific to a bridge, a reinforced concrete bridge in the Los Angeles region is analyzed. This bridge was severely damaged during the Northridge earthquake because of shear failure of one bridge pier. Seismic vulnerability model of the bridge is developed through finite element analysis under a suite of time histories that represent regional seismic hazard. Obtained bridge vulnerability model is combined with appropriate loss and recovery models to calculate seismic resilience of the bridge. Impact of retrofit on seismic resilience is observed by applying suitable retrofit strategy to the bridge assuming its undamaged condition prior to the Northridge event. Difference in resilience observed before and after bridge retrofit signified the effectiveness of seismic retrofit. The applied retrofit technique is also found to be cost‐effective through a cost‐benefit analysis. First order second moment reliability analysis is performed, and a tornado diagram is developed to identify major uncertain input parameters to which seismic resilience is most sensitive. Statistical analysis of resilience obtained through random sampling of major uncertain input parameters revealed that the uncertain nature of seismic resilience can be characterized with a normal distribution, the standard deviation of which represents the uncertainty in seismic resilience. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic analysis of the fatih sultan mehmet (second Bosporus) suspension bridge

Theoretical dynamic characteristics of the Fatih Bridge in terms of natural frequencies and mode shapes of free vibration were obtained using a range of finite element models. Based on this free-vibration data, separate analyses of the asynchronous response of the bridge to earthquake excitation in three orthogonal axes with different speeds of wave propagation, and of stochastic response to vertical excitation were used to estimate levels of dynamic response due to seismic loading. Fatih is the third of three modern European long-span box-girder suspension bridges that have been investigated and the relationship of the different design features and the dynamic responses of this type of bridge is reviewed. The main conclusion is that where seismic response is an important consideration, the effects of asynchronous excitation can be significant and must be considered.     

Parameter identification of framed structures using an improved finite element model‐updating method—Part II: application to experimental data

In this study, we determine an updated finite element model of a reinforced concrete building—which was damaged from shaking during 1994 Northridge earthquake—using forced‐vibration test data and a novel model‐updating technique. Developed and verified in the companion paper (viz. BVLSrc, Earthquake Eng. Struct. Dyn. 2006; this issue), this iterative technique incorporates novel sensitivity‐based relative constraints to avoid ill conditioning that results from spatial incompleteness of measured data. We used frequency response functions and natural frequencies as input for the model‐updating problem. These data were extracted from measurements obtained during a white‐noise excitation applied at the roof of the building using a linear inertial shaker. Flexural stiffness values of properly grouped structural members, modal damping ratios, and translational and rotational mass values were chosen as the updating parameters, so that the converged results had direct physical interpretations, and thus, comparisons with common parameters used in seismic design and evaluation of buildings could be made. We investigated the veracity of the updated finite element model by comparing the predicted and measured dynamic responses under a second, and different type of forced (sine‐sweep) vibration, test. These results indicate that the updated model replicates the dynamic behaviour of the building reasonably well. Furthermore, the updated stiffness factors appear to be well correlated with the observed building damage patterns (i.e. their location and severity). Copyright © 2006 John Wiley & Sons, Ltd.     

Dynamic characteristics of a base isolated building from ambient vibration measurements and low level earthquake shaking

Ambient vibration tests were conducted on a base-isolated apartment building in Takamatsu, Japan, to determine the mode shapes and the associated natural frequencies and damping ratios at very low levels of excitation. The latest developments in signal analysis for modal decomposition are used to analyze the ambient response data. A finite element model of the building and isolators was calibrated and refined using the experimental results from the ambient vibration tests. This model was then used to simulate the recorded response of the building under excitation from a small earthquake. The finite element model, calibrated by ambient vibration data and the low level of earthquake shaking, provides the starting point for modelling the non-linear response of the building when subjected to strong shaking.     

Seismic response analysis of road vehicle-bridge system for continuous rigid frame bridges with high piers

The objective of this study is to investigate the effects of earthquakes on road vehicle-bridge coupling vibration systems. A two-axle highway freight vehicle is treated as a 13 degree-of-freedom system composed of several rigid bodies, which are connected by a series of springs and dampers. The framework of the earthquake-vehicle-bridge dynamic analysis system is then established using an earthquake as the external excitation. The equivalent lateral contact force serves as the judgment criteria for sideslip accidents according to reliability theory. The entire process of the vehicle crossing the bridge is considered for a very high pier continuous rigid frame bridge. The response characteristics of the vehicle and the bridge are discussed in terms of various parameters such as earthquake ground motion, PGA value of the earthquake, incident angle, pier height, vehicle speed and mass. It is found that seismic excitation is the most influential factor in the responses of the vehicle-bridge system and that the safety of vehicles crossing the bridge is seriously impacted by the dual excitations of earthquake and bridge vibration.     

Seismic analysis and design of rigid bridge abutments considering rotation and sliding incorporating non-linear soil behavior

A two-dimensional (2D) finite element analytical model is developed to analyze the seismic response of rigid highway bridge abutments, retaining and founded on dry sand. A well verified finite element code named FLEX is used for this purpose. The proposed model has the following characteristics: (1) The soil (dry sand in this study) is modeled by a 2D finite element grid; (2) The bridge abutment is molded as a rigid substructure; (3) The strength and deformation of the soil are modeled using the viscous cap constitutive model. This model consists of a failure surface and hardening cap together with an associated flow rule. The cap surface is activated for the soil under the wall to represent compaction during wall rocking. In addition, viscoelastic behavior is provided for representing the hysteretic-like damping of soil during dynamic loading; (4) Interface elements are used between the wall and the soil (at the backface of the wall and under its base) to allow for sliding and for debonding/recontact behavior; (5) The finite element grid is truncated by using an absorbing boundary approximation. Using this boundary at both sides of the grid simulates the horizontal radiation of energy scattered from the wall and the excavation. Shear beams are placed adjacent to the lateral boundaries from each side which give the far-field ground motion, for comparison with those computed adjacent to the boundaries. The analytical model is verified comparing predictions to results from dynamic centrifuge tests, with satisfactory agreement. The proposed model is used to study the dynamic response of an 8.0 m high and 3.0 m wide rigid bridge abutment (proportioned using the traditional approach to design) for different sinusoidal and earthquake acceleration input motions. The results from the analysis show that outward tilting of rigid bridge abutments is the dominant mode of response during dynamic shaking and that these abutments end up with a permanent outward tilt at the end of shaking. The results from all the analyzed cases of the 8.0 m high gravity retaining wall together with those from the analysis of the tilting wall centrifuge tests are discussed and used for proposing a practical method for evaluating the seismic response of rigid abutments during earthquakes.     

考虑竖向地震作用的拱式廊桥的地震响应分析

本文以某大型商业拱式廊桥工程实例为依托,利用有限元软件分别建立了整桥模型和不考虑上部建筑结构的桥梁模型以及不考虑下部桥梁结构的建筑模型,并计算了各自的自振动力特性,在此基础上通过反应谱方法分析了同时考虑水平地震作用和竖向地震作用的廊桥主拱圈和上部建筑结构柱的地震响应以及不同模型计算结果的差异,以此研究桥梁结构与建筑结构的耦合作用,为廊桥的抗震设计或分析提供一定的参考依据。     

Rapid evaluation and damage assessment of instrumented highway bridges

This study focuses on the use of strong motion data recorded during earthquakes and aftershocks to provide a preliminary assessment of the structural integrity and possible damage in bridges. A system identification technique is used to determine dynamical characteristics and high‐fidelity first‐order linear models of a bridge from low level earthquake excitations. A finite element model is developed and updated using a genetic algorithm optimization scheme to match the frequencies identified and to simulate data from a damaging earthquake for the bridge. Here, two criteria are used to determine the state of the structure. The first criteria uses the error between the data recorded or simulated by the calibrated nonlinear finite element model and the data predicted by the linear model. The second criteria compares relative displacements of the structure with displacement thresholds identified using a pushover analysis. The use of this technique can provide an almost immediate, yet reliable, assessment of the structural health of an instrumented bridge after a seismic event. Copyright © 2011 John Wiley & Sons, Ltd.