Seismic damage of highway bridges during the 2008 Wenchuan earthquake

Many highway bridges were severely damaged or completely collapsed during the 2008 Wenchuan earthquake.A field investigation was carried out in the strongly affected areas and over 320 bridges were examined. Damage to some representative highway bridges is briefly described and a preliminary analysis of the probable causes of the damage is presented in this paper. The most common damage included shear-flexural failure of the pier columns, expansion joint failure, shear key failure, and girder sliding in the transversal or longitudinal directions due to weak connections between girder and bearings. Lessons learned from this earthquake are described and recommendations related to the design of curved and skewed bridges, design of bearings and devices to prevent girder collapse, and ductility of bridge piers are presented.Suggestions for future seismic design and retrofitting techniques for bridges in moderate to severe earthquake areas are also proposed.     

Post‐earthquake bridge repair cost and repair time estimation methodology

While structural engineers have traditionally focused on individual components (bridges, for example) of transportation networks for design, retrofit, and analysis, it has become increasingly apparent that the economic costs to society after extreme earthquake events are caused at least as much from indirect costs as direct costs due to individual structures. This paper describes an improved methodology for developing probabilistic estimates of repair costs and repair times that can be used for evaluating the performance of new bridge design options and existing bridges in preparation for the next major earthquake. The proposed approach in this paper is an improvement on previous bridge loss modeling studies—it is based on the local linearization of the dependence between repair quantities and damage states so that the resulting model follows a linear relationship between damage states and repair points. The methodology uses the concept of performance groups (PGs) that account for damage and repair of individual bridge components and subassemblies. The method is validated using two simple examples that compare the proposed method to simulation and previous methods based on loss models using a power–law relationship between repair quantities and damage. In addition, an illustration of the method is provided for a complete study on the performance of a common five‐span overpass bridge structure in California. Intensity‐dependent repair cost ratios (RCRs) and repair times are calculated using the proposed approach, as well as plots that show the disaggregation of repair cost by repair quantity and by PG. This provides the decision maker with a higher fidelity of data when evaluating the contribution of different bridge components to the performance of the bridge system, where performance is evaluated in terms of repair costs and repair times rather than traditional engineering quantities such as displacements and stresses. Copyright © 2009 John Wiley & Sons, Ltd.     

Design formulations for supplemental viscous dampers to highway bridges

Design formulas for supplemental viscous dampers to building structures are readily available in FEMA provisions and MCEER research reports. However, for the design of supplemental viscous dampers corresponding to a desired system damping ratio of highway bridges, there exist, if any, few design guidelines. This is particularly true if the bridge components such as elastomeric bearings, piers and abutment possess different damping ratios, stiffnesses, and lumped masses. In this paper, the design formulas for supplemental viscous dampers to highway bridges have been derived based on the concept of ‘composite damping ratio’. The design formulas can be used to determine the damping coefficients of the dampers corresponding to a desired system damping ratio of the bridge in which different component damping ratios may be assumed for the elastomeric bearings, piers and abutments. The proposed design formulas are numerically validated by comparing the seismic responses of a three‐span bridge equipped with viscous dampers with those of the same bridge without viscous dampers but with an assigned inherent system damping ratio equal to the target system damping ratio. Copyright © 2005 John Wiley & Sons, Ltd.     

Performance-based earthquake assessment of bridge systems including ground-foundation interaction

Performance-based earthquake engineering (PBEE) assessment studies on highway bridges can only address post-earthquake repair fully when considering the response of the bridge-foundation-ground and the consequences of damage and repair to all system components. In this paper, nonlinear time history analysis of coupled bridge-foundation-ground systems is coupled with a PBEE framework to investigate a typical highway overpass bridge founded on different soil profiles. The prototype bridges are typical reinforced concrete highway overpass bridges with single-column bents founded on four sites of varying stiffness and strength profiles ranging from rigid rock to weak upper soil strata. Probabilistic repair cost and time response quantities are used to contrast performance of the four scenarios. Intensity-dependent repairs, repair hazard curves, and repairs disaggregated by performance groups indicate contributions to system repair for each scenario. A sensitivity study is presented that demonstrates the most important parameters to be the damage state and repair quantities related to the foundations and abutments.     

Probabilistic seismic loss assessment of aging bridges using a component‐level cost estimation approach

Deteriorating highway bridges in the United States and worldwide have demonstrated susceptibility to damage in earthquake events, with considerable economic consequences due to repair or replacement. Current seismic loss assessment approaches for these critical elements of the transportation network neglect the effects of aging and degradation on the loss estimate. However, the continued aging and deterioration of bridge infrastructure could not only increase susceptibility to seismic damage, but also have a significant impact on these economic losses. Furthermore, the contribution of individual aging components to system‐level losses, correlations between these components, and uncertainty modeling in the risk assessment and repair modeling are all crucial considerations to enhance the accuracy and confidence in bridge loss estimates. In this paper, a new methodology for seismic loss assessment of aging bridges is introduced based on the non‐homogeneous Poisson process. Statistical moments of seismic losses can be efficiently estimated, such as the expected value and variance. The approach is unique in its account for time‐varying seismic vulnerability, uncertainty in component repair, and the contribution of multiple correlated aging components. A representative case study is presented with two fundamentally distinct highway bridges to demonstrate the effects of corrosion deterioration of different bridge components on the seismic losses. Using the proposed model, a sensitivity study is also conducted to assess the effect of parameter variations on the expected seismic losses. The results reveal that the seismic losses estimated by explicitly considering the effects of deterioration of bridge components is significantly higher than that found by assuming time‐invariant structural reliability. Copyright © 2011 John Wiley & Sons, Ltd.     

A simplified method of constructing fragility curves for highway bridges

Fragility curves are found to be useful tools for predicting the extent of probable damage. They show the probability of highway structure damage as a function of strong motion parameters, and they allow the estimation of a level of damage probability for a known ground motion index. In this study, an analytical approach was adopted to develop the fragility curves for highway bridges based on numerical simulation. Four typical RC bridge piers and two RC bridge structures were considered, of which one was a non‐isolated system and the other was an isolated system, and they were designed according to the seismic design code in Japan. From a total of 250 strong motion records, selected from Japan, the United States, and Taiwan, non‐linear time history analyses were performed, and the damage indices for the bridge structures were obtained. Using the damage indices and ground motion parameters, fragility curves for the four bridge piers and the two bridge structures were constructed assuming a lognormal distribution. It was found that there was a significant effect on the fragility curves due to the variation of structural parameters. The relationship between the fragility curve parameters and the over‐strength ratio of the structures was also obtained by performing a linear regression analysis. It was observed that the fragility curve parameters showed a strong correlation with the over‐strength ratio of the structures. Based on the observed correlation between the fragility curve parameters and the over‐strength ratio of the structures, a simplified method was developed to construct the fragility curves for highway bridges using 30 non‐isolated bridge models. The simplified method may be a very useful tool to construct the fragility curves for non‐isolated highway bridges in Japan, which fall within the same group and have similar characteristics. Copyright © 2003 John Wiley & Sons, Ltd.     

在役公路梁式桥综合震害等级预测研究

为客观预测在役公路梁式桥综合震害状况,考虑在役桥梁在运营期存在的病害问题,从压力和承压两方面建立在役公路梁式桥综合震害预测评价指标体系。以桥梁作为承灾体,建立在役公路梁式桥综合震害物元可拓模型,运用熵权法进行赋权,确定桥梁的综合震害状况。以一座在役梁式桥为例,运用上述模型确定算例的综合震害状况。研究结果表明,该桥的综合震害等级为Ⅲ级,破坏等级中等,且根据结果分析影响桥梁震害程度的主要影响因素;该模型通过对多个指标关联系数的综合分析来评价在役梁式桥的综合震害等级,极大地提高了该模型评估的准确率及可靠性,为桥梁震害等级的预测提供一定的参考,对提升桥梁综合抗震能力具有积极意义。     

Quasi‐static and pseudo‐dynamic testing of unbonded post‐tensioned rocking bridge piers with external replaceable dissipaters

It has been well documented that following a major earthquake a substantial percentage of economic loss results from downtime of essential lifelines in and out of major urban centres. This has thus led to an improvement of both performance‐based seismic design philosophies and to the development of cost‐effective seismic structural systems capable of guaranteeing a high level of protection, low structural damage and reduced downtime after a design‐level seismic event. An example of such technology is the development of unbonded post‐tensioned techniques in combination with rocking–dissipating connections. In this contribution, further advances in the development of high‐performance seismic‐resistant bridge piers are achieved through the experimental validation of unbonded post‐tensioned bridge piers with external, fully replaceable, mild steel hysteretic dissipaters. The experimental response of three 1 : 3 scale unbonded, post‐tensioned cantilever bridge piers, subjected to quasi‐static and pseudo‐dynamic loading protocols, are presented and compared with an equivalently reinforced monolithic benchmark. Minimal physical damage is observed for the post‐tensioned systems, which exhibit very stable energy dissipation and re‐centring properties. Furthermore, the external dissipaters can be easily replaced if severely damaged under a major (higher than expected) earthquake event. Thus, negligible residual deformations, limited repair costs and downtime can be achieved for critical lifeline components. Satisfactory analytical–experimental comparisons are also presented as a further confirmation of the reliability of the design procedure and of the modelling techniques. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic zoning for initial‐ and total‐cost minimization

We consider two design criteria to study seismic zoning. In the first, codes require that structures be designed for some specified values. Zoning is then optimal when it minimizes the expected present value of the initial costs of all structures to be built in the region being zoned. In the second criterion, it is designed so that the present value of the total cost is minimized, including initial and maintenance costs as well as losses due to damage and failure. We will call these criteria zoning for the initial‐ and total‐cost minimization, respectively. It is shown that under certain conditions, the boundaries coincide with isoparametric curves and the problem may be solved in one dimension. We also deal with problems not reducible to a single dimension. Different methods are proposed to solve the various kinds of problems. The work ends with some illustrative examples. Copyright © 2000 John Wiley & Sons, Ltd.     

Effect of cumulative seismic damage and corrosion on the life‐cycle cost of reinforced concrete bridges

Bridge design should take into account not only safety and functionality, but also the cost effectiveness of investments throughout a bridge life‐cycle. This paper presents a probabilistic approach to compute the life‐cycle cost (LCC) of corroding reinforced concrete (RC) bridges in earthquake‐prone regions. The approach is developed by combining cumulative seismic damage and damage associated with corrosion due to environmental conditions. Cumulative seismic damage is obtained from a low‐cycle fatigue analysis. Chloride‐induced corrosion of steel reinforcement is computed based on Fick's second law of diffusion. The proposed methodology accounts for the uncertainties in the ground motion parameters, the distance from the source, the seismic demand on the bridge, and the corrosion initiation time. The statistics of the accumulated damage and the cost of repairs throughout the bridge life‐cycle are obtained by Monte‐Carlo simulation. As an illustration of the proposed approach, the effects of design parameters on the LCC of an example RC bridge are studied. The results are valuable in better estimating the condition of existing bridges and, therefore, can help to schedule inspection and maintenance programs. In addition, by taking into consideration the two deterioration processes over a bridge life‐cycle, it is possible to estimate the optimal design parameters by minimizing, for example, the expected cost throughout the life of the structure. A comparison between the effects of the two deterioration processes shows that, in seismic regions, the cumulative seismic damage affects the reliability of bridges over time more than the corrosion even for corrosive environments. Copyright © 2008 John Wiley & Sons, Ltd.     

A probabilistic approach for the prediction of seismic resilience of bridges

This paper proposes a probabilistic approach for the pre‐event assessment of seismic resilience of bridges, including uncertainties associated with expected damage, restoration process, and rebuilding/rehabilitation costs. A fragility analysis performs the probabilistic evaluation of the level of damage (none, slight, moderate, extensive, and complete) induced on bridges by a seismic event. Then, a probabilistic six‐parameter sinusoidal‐based function describes the bridge functionality over time. Depending on the level of regional seismic hazard, the level of performance that decision makers plan to achieve, the allowable economic impact, and the available budget for post‐event rehabilitation activities, a wide spectrum of scenarios are provided. Possible restoration strategies accounting for the desired level of resilience and direct and indirect costs are investigated by performing a Monte Carlo simulation based on Latin hypercube sampling. Sensitivity analyses show how the recovery parameters affect the resilience assessment and seismic impact. Finally, the proposed approach is applied to an existing highway bridge located along a segment of I‐15, between the cities of Corona and Murrieta, in California. Copyright © 2013 John Wiley & Sons, Ltd.     

斜交连续刚构桥桥墩地震易损性分析

以美国西部地区某斜交公路连续刚构桥为研究对象，研究其不等高墩易损性差异以及斜交角的改变对桥墩地震易损性的影响。考虑桥梁结构参数和地震动的不确定性，选取100条地震动，沿纵桥向输入，生成"结构-地震动"样本库，以地震动峰值加速度（PGA）为强度指标（IM），利用OpenSees软件对结构进行非线性时程分析得到桥墩动力响应，而后以桥墩曲率延性比衡量桥梁破坏状态，在确定桥墩损伤指标的基础上，采用可靠度理论得到各桥墩的地震易损性曲线，判断桥墩的损伤模式、损伤特点。在此基础上，改变桥梁斜交角度进行易损性分析，得到斜交角变化对桥墩地震易损性的影响。研究表明：该桥最矮墩发生损伤的概率大于其他桥墩，桥墩最先进入塑性的是墩顶和墩底区域；不同斜交角对桥墩的地震响应影响显著，各墩损伤破坏排序与斜交桥结构构造特点有关，同一排架墩的两侧墩柱易损性呈现与角度变化趋势相反的排列，损伤越严重，趋势越明显；对于此不等高的斜交刚构桥，最矮墩为其抗震薄弱环节，斜交角越大，越应该关注钝角处矮墩的损伤情况，并提高其设计标准，在进行斜交刚构桥抗震设计中应予以重视。     

Influence of uncertain boundary conditions and model structure on flood inundation predictions

In this study, the GLUE methodology is applied to establish the sensitivity of flood inundation predictions to uncertainty of the upstream boundary condition and bridges within the modelled region. An understanding of such uncertainties is essential to improve flood forecasting and floodplain mapping. The model has been evaluated on a large data set. This paper shows uncertainty of the upstream boundary can have significant impact on the model results, exceeding the importance of model parameter uncertainty in some areas. However, this depends on the hydraulic conditions in the reach e.g. internal boundary conditions and, for example, the amount of backwater within the modelled region. The type of bridge implementation can have local effects, which is strongly influenced by the bridge geometry (in this case the area of the culvert). However, the type of bridge will not merely influence the model performance within the region of the structure, but also other evaluation criteria such as the travel time. This also highlights the difficulties in establishing which parameters have to be more closely examined in order to achieve better fits. In this study no parameter set or model implementation that fulfils all evaluation criteria could be established. We propose four different approaches to this problem: closer investigation of anomalies; introduction of local parameters; increasing the size of acceptable error bounds; and resorting to local model evaluation. Moreover, we show that it can be advantageous to decouple the classification into behavioural and non-behavioural model data/parameter sets from the calculation of uncertainty bounds.     

不规则公路桥梁地震动参数快速评估技术研究

快速评估不规则公路桥梁的地震动参数为桥梁地震响应分析、桥梁安全性设计提供科学依据。研究一种快速、有效的不规则公路桥梁地震动参数评估技术,以C形不规则公路桥梁为原型设计振动台与公路桥梁模型,选取Imperial Valley波作为地震动输入,采用加速度传感器、位移传感器采集桥梁加速度与位移数据;结合已知地震动数据计算地震动持续时长参数,优化衰减模型获取精确的地表峰值加速度参数。分析地表峰值加速度与其他地震动参数关系可知,地表峰值加速度与损坏概率成正比,桥梁结构发生损坏的概率在50%以下;震级越大、震中距越小、地表峰值加速度越大。     

Multiobjective optimization for performance‐based seismic design of steel moment frame structures

The performance‐based seismic design of steel special moment‐resisting frame (SMRF) structures is formulated as a multiobjective optimization problem, in which conflicting design criteria that respectively reflect the present capital investment and the future seismic risk are treated simultaneously as separate objectives other than stringent constraints. Specifically, the initial construction expenses are accounted for by the steel material weight as well as by the number of different standard steel section types, the latter roughly quantifying the degree of design complexity related additional construction cost; the seismic risk is considered in terms of maximum interstory drift demands at two hazard levels with exceedance probabilities being 50% and 2% in 50 years, respectively. The present formulation allows structural engineers to find an optimized design solution by explicitly striving for a desirable compromise between the initial investment and seismic performance. Member sizing for code‐compliant design of a planar five‐story four‐bay SMRF is presented as an application example using the proposed procedure that is automated by a multiobjective genetic algorithm. Copyright © 2004 John Wiley & Sons, Ltd.     

Effect of earthquake ground motions on fragility curves of highway bridge piers based on numerical simulation

Fragility curves express the probability of structural damage due to earthquakes as a function of ground motion indices, e.g., PGA, PGV. Based on the actual damage data of highway bridges from the 1995 Hyogoken‐Nanbu (Kobe) earthquake, a set of empirical fragility curves was constructed. However, the type of structure, structural performance (static and dynamic) and variation of input ground motion were not considered to construct the empirical fragility curves. In this study, an analytical approach was adopted to construct fragility curves for highway bridge piers of specific bridges. A typical bridge structure was considered and its piers were designed according to the seismic design codes in Japan. Using the strong motion records from Japan and the United States, non‐linear dynamic response analyses were performed, and the damage indices for the bridge piers were obtained. Using the damage indices and ground motion indices, fragility curves for the bridge piers were constructed assuming a lognormal distribution. The analytical fragility curves were compared with the empirical ones. The proposed approach may be used in constructing the fragility curves for highway bridge structures. Copyright © 2001 John Wiley & Sons, Ltd.     

桃夭门大桥基岩长周期设计反应谱

文中结合舟山市桃夭门大桥抗震设计在长周期频段的需要,研究分析了桃夭门大桥场地基本地震地质环境特点和长周期地面运动谱的研究现状,从强震记录长周期分量信息特点出发,以强震记录为基础,选用了11个有代表性的M≥65的强震,共72条强震地面运动记录,参照核法规HAF0101(1)特定场地谱的确定方法,通过统计分析建立了以均值反应谱为基础的长周期反应谱     

Digital mapping of riverine waterway hydrodynamic and geomorphic features

This paper proposes an innovative, non‐intrusive method for mapping waterway characteristics in riverine areas. The technique uses photogrammetry to provide quantitative information about the dry area in the vicinity of the waterways (banks and floodplain) and image processing algorithms to characterize the flow. Riverside images of a riverine area are decomposed into quasi‐planar areas and ortho‐rectified and re‐assembled to obtain a panoramic ortho‐view of the area of interest. Morphological features of interest (such as river bank positions, flood plain edges, mud deposits, vegetation and erosion patterns) are then identified on the ortho‐view and mapped digitally. Image sequences of the river flow are recorded, allowing a surface velocity analysis to be obtained through Large Scale Particle Image Velocimetry (LSPIV). Finally, the mapped elements and the surface velocities are displayed together in a GIS‐like visualization. Through the presentation of a case study of a flood event at a culvert site, this paper demonstrates the capability of the technique to monitor characteristics of waterways over time. The method is inexpen‐sive (a conventional video or digital camera can be used), fast and requires minimum preparation. It can be applied in such important river‐related research areas as morphodynamic and sediment transport studies. It also fosters an improved understand‐ing of the coupling between the river and its banks, which is essential for river restoration and eco‐habitat studies. The present methodology is readily available for implementation in routine bridge inspections, fitted with an easy‐to‐use graphical interface. Copyright © 2009 John Wiley & Sons, Ltd.     

Life‐cycle cost analysis based on a renewal model of earthquake occurrences

A decision methodology for the management of seismic risk of a single building is presented. The decision criterion aims at minimizing the expected life‐cycle cost, including the initial cost of the design and the expected cost of damage due to future earthquakes. The expected life‐cycle cost of each design alternative is formulated using a renewal model for the occurrence of earthquakes in a seismic source, which accounts for the temporal dependence between the occurrence of ‘characteristic’ earthquakes. The formulation involves the expected damage cost from an earthquake of specified magnitude in a given source. This term is estimated by simulating the processes of fault rupture, elastic wave propagation, surface soil amplification, dynamic structural response and generation of damage costs. As an example, the methodology is applied to an actual office building in Tokyo. A simple decision problem between two design alternatives is set: a bare steel moment frame, and the same frame equipped with oil dampers. Through this case study, the installation of the oil dampers is demonstrated to be effective in reducing the life‐cycle cost of the building under consideration. Copyright © 2004 John Wiley & Sons, Ltd.     

Post‐earthquake functionality of highway overpass bridges

Bridges are crucial to the transportation network in a region struck by an earthquake. Collapse of a bridge determines if a road is passable. Ability of a bridge to carry traffic load after an earthquake determines the weight and speed of vehicles that can cross it. Extent of system and component structural damage in bridges determines the cost and time required for repair. Today, post‐earthquake bridge evaluation is qualitative rather than quantitative. The research presented in this paper aims to provide a quantitative engineering basis for quick and reliable evaluation of the ability of a typical highway overpass bridge to function after an earthquake. The Pacific Earthquake Engineering Research (PEER) Center's probabilistic performance‐based evaluation approach provides the framework for post‐earthquake bridge evaluation. An analytical study was performed that linked engineering demand parameters to earthquake intensity measures. The PEER structural performance database and reliability analysis tools were then used to link demand parameters to damage measures. Finally, decision variables were developed to describe three limit states, repair cost, traffic function, and collapse, in terms of induced damage. This paper presents the analytical models used to evaluate post‐earthquake bridge function, decision variables and their correlation to the considered limit states, and fragility curves that represent the probability of exceeding a bridge function limit state given an earthquake intensity. Copyright © 2005 John Wiley & Sons, Ltd.