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Practical Approach to Fragility Analysis of Bridges  [cached]
Yasamin Rafie Nazari,Khosrow Bargi
Research Journal of Applied Sciences, Engineering and Technology , 2012,
Abstract: Damages during past earthquakes reveal seismic vulnerability of bridge structures and the necessity of probabilistic approach toward seismic performance evaluation of bridges and its interpretation in terms of decision variables such as repair cost, downtime and life loss. This Procedure involves hazard analysis, structural analysis, damage analysis and loss analysis. The purpose of present study is reviewing different methods developed to derive fragility curves for damage analysis of bridges and demonstrating a simple procedure for fragility analysis using Microsoft Office Excel worksheet to reach probability of occurring predefined level of damage due to different levels of seismic demand parameters. The input of this procedure is the intensity of ground motion and the output is an appropriate estimate of the expected damage. Different observed damages of the bridges are discussed and compared the practical definition of damage states. Different methods of fragility analyses are discussed and a practical step by step example is illustrated.
Seismic Performances of Mountainous Continuous Rigid Frame Solid and Hollow Pier Railway Bridges  [PDF]
Akhil Subedi, Gopal S. Bhandari, Paribesh Parajuli
Open Journal of Civil Engineering (OJCE) , 2018, DOI: 10.4236/ojce.2018.84035
Abstract: This paper focuses on the seismic performance of mountainous railway bridges having different pier type i.e. rectangular hollow piers and solid piers. The piers used were of same materials and inertial properties. For this, 3-D FEM models of these bridges were created by ANSYS 15.0. For seismic assessment, Response Spectrum and Dynamic Time-History Analysis methods were adopted. Different types of earthquake waves used were Elcentro, Wenchuan and Nepal earthquakes, all normalized to 0.3 g Peak Ground Acceleration (PGA). The study concluded that even though the hollow pier bridges are susceptible to large displacements, its dealing with internal forces is remarkable compared to solid pier bridges.
Seismic performance of RC pier with reinforcement corrosion

ZHAO Jianfeng
, LI Hongyi, LIU Suwen

- , 2017, DOI: 10.6040/j.issn.1672-3961.0.2016.356
Abstract: 摘要: 为研究氯离子侵蚀效应引起的钢筋锈蚀对在役桥墩抗震性能的影响,以圆柱形桥墩为例,通过概率方法确定钢筋初始锈蚀时间、锈蚀速率,进而建立钢筋直径及屈服强度的退化模型;采用ABAQUS软件建立非线性动力分析模型,针对单方面考虑纵筋锈蚀或箍筋锈蚀以及同时考虑两者锈蚀3种情况,分析材料劣化引起桥墩抗震性能的变化。结果表明:同时考虑箍筋、纵筋锈蚀比只考虑纵筋锈蚀时桥墩的抗震性能退化明显;纵筋锈蚀严重影响钢筋混凝土桥墩的抗弯性能;箍筋锈蚀严重影响RC(reinforced concrete)桥墩的延性性能。
Abstract: In order to study the seismic performance of the reinforced concrete bridge piers in service, which was affected by the reinforcement corrosion due to the chloride ion corrosion, a cylindrical pier was taken as an example. By means of probability method, the initial corrosion time and the corrosion rate were determined, the deterioration models of the diameter and the yield strength of steel were established. The nonlinear dynamic analysis model was made by ABAQUS software and three analysis cases as consisting of stirrup corrosion, longitudinal reinforcement corrosion and the combination corrosion of deterioration, were investigated to study the seismic performance of reinforced concrete piers caused by material deterioration. The results showed that compared with only considering the corrosion situation of longitudinal reinforcement in the past, the deterioration of seismic performance was more serious when the stirrups and longitudinal reinforcement corrosion were both considered, the ductility performance of the bridge pier was affected seriously by the stirrup corrosion and the bending performance of the bridge pier was affected seriously by the longitudinal reinforcement corrosion
Seismic fragility analysis of bridges using fuzzy-stochastic method

JING Chongwen
, YI Weijian, PANG Yutao

- , 2016,
Abstract: 目前,大多数易损性分析方法采用的损伤等级的取值都是确定的,然而,在实际的工程中,结构损伤域的边界不明确,具有一定的模糊性。为此,本文在传统易损性分析的基础上,结合模糊数学与传统可靠度计算方法,考虑模糊准则下的结构易损性。并以一座单塔斜拉桥为例,建立结构的概率地震需求模型,分析考虑模糊准则与不考虑模糊准则2种情况下,4个关键部位的易损性曲线。研究结果表明:在考虑模糊准则与不考虑模糊准则2种情况下的结构的地震易损概率明显不同,因而,有必要在地震风险评估中考虑模糊失效准则的影响。
At present, the value of different damage levels is costant in most fragility analysis. However, in actual projects, the boundary of structural damage domains is actually not explicit, and have the characteristic of fuzziness. Therefore, this paper proposes a fuzzy-stochastic method to analyze seismic vulnerabilities of highway bridges on the basis of traditional fragility theory. The fuzzy-stochastic method combines the fuzzy mathematics and the traditional reliability method. The details of this method are illustrated by taking a single pylon cable-stayed bridge as an example. The probabilistic seismic demand model is established to calculate the probability of bridge components, and fragility curves of four key sections in two different cases of are compared to study the influence of the fuzzy rules on the fragility curves. It is found that the fuzzy rules has a significant influence on structure vulnerabilitis and should be taken into account in the potential earthquakes risk assessment
Generalized Fragility Relationships with Local Site Conditions for Probabilistic Performance-based Seismic Risk Assessment of Bridge Inventories  [cached]
Lau D.T.,Vishnukanthan K.,Waller C.L.,Sivathayalan S.
Civil Engineering Dimension , 2012,
Abstract: The current practice of detailed seismic risk assessment cannot be easily applied to all the bridges in a large transportation networks due to limited resources. This paper presents a new approach for seismic risk assessment of large bridge inventories in a city or national bridge network based on the framework of probabilistic performance based seismic risk assessment. To account for the influences of local site effects, a procedure to generate site-specific hazard curves that includes seismic hazard microzonation information has been developed for seismic risk assessment of bridge inventories. Simulated ground motions compatible with the site specific seismic hazard are used as input excitations in nonlinear time history analysis of representative bridges for calibration. A normalizing procedure to obtain generalized fragility relationships in terms of structural characteristic parameters of bridge span and size and longitudinal and transverse reinforcement ratios is presented. The seismic risk of bridges in a large inventory can then be easily evaluated using the normalized fragility relationships without the requirement of carrying out detailed nonlinear time history analysis.
Dynamic Reliability Analysis on Pounding of High-Pier Bridges Subjected to Stochastic Seismic Excitations

贾宏宇, 杜修力, 罗楠, 张金, 郑史雄, 张克跃
JIA Hongyu
, DU Xiuli, LUO Nan, ZHANG Jin, ZHENG Shixiong, ZHANG Keyue

- , 2018, DOI: 10.3969/j.issn.0258-2724.2018.01.011
Abstract: 为了研究不同地震动强度作用下高墩桥梁的碰撞可靠度的不同,在频域范围内提出了一种以虚拟激励法为基础的动力可靠度计算方法,依托某高墩大跨度桥梁为工程背景,分析了高墩桥梁在不同地震强度下的碰撞可靠度.选择反应谱的水平加速度作为地震强度衡量指标,且将不同强度指标的反应谱转化为相应的功率谱;利用虚拟激励法求解随机振动方程,得到结构响应的均值与均方差值,再基于Davenport理论获得结构峰值响应的期望和标准差;根据首次超越理论计算梁体碰撞可靠度.研究表明:地震动加速度小于0.22g时,梁体之间不发生碰撞,动力可靠度为1.0;加速度大于0.22g时,梁体碰撞动力可靠度下降明显,即在强震作用下,梁体发生碰撞.
:A dynamic reliability analysis based on the pseudo-excitation method in the frequency domain was proposed to investigate the pounding reliability of high-pier bridges subjected to seismic excitations with different ground motion intensity levels. A high-pier bridge was selected as the numerical example and the pounding reliability of the high-pier bridge was computed for each ground motion intensity level. The horizontal acceleration response spectrum was chosen as the seismic intensity measure and the response spectra for different intensity measures were converted into the corresponding power spectra. Next, the stochastic vibration equation was solved using the pseudo-excitation method to determine the mean and mean square deviation of the structural dynamic responses. The expected values and standard deviation of the structural peak responses were obtained using Davenport's theory. Finally, the pounding reliability between the adjacent beams of the high-pier bridge was determined using the first passage theory. The results indicate that pounding will not occur between the adjacent decks and the pounding reliability is 1.0 when the ground acceleration is less than 0.22g. In addition, there is an obvious decrease in the pounding reliability such that the structure collides under the strong ground motions when the ground acceleration is more than 0.22g
Influence of Pile-Soil Interaction on the Seismic Fragility and Post-earthquake Traffic Capacity of an Isolated Bridge

- , 2018, DOI: 10.3969/j.issn.1000-0844.2018.04.721
Abstract: 为确定桩土作用对一座位于Ⅲ类场地上的110 m三跨连续梁桥地震易损性曲线和震后通行能力的影响,首先建立墩底固结和考虑桩土作用2种有限元模型,选取50条实测的、符合工程场地条件的不同强度地震波作为输入,分别以桥墩墩顶和支座最大位移为目标响应,计算得到转角延性比和支座剪应变值,进而构建桥墩和支座的易损性曲线;然后通过宽界限法建立桥梁系统的地震易损性曲线,提出新的平均损伤水平值计算公式并结合易损性曲线评估该连续梁桥的震后通行能力。分析结果表明,同一地震强度下考虑桩土作用时的桥墩位移峰值比墩底固结情况大,更符合实际情况;对于桥梁构件易损性曲线而言,考虑桩土作用时支座破坏超越概率最大,但与墩底固结情况相比相差不大;采用桥梁系统地震易损性曲线评价桥梁交通流量变化更加合理,固结模型的震后交通流量评估Ⅲ类场地情况时不可忽略桩土作用对桥梁地震易损性的影响。
To determine the influence of pile-soil interaction on the seismic fragility curves and post-earthquake traffic capacity of a 110 m-long, three-span continuous girder bridge, two diffe-rent finite element models that consider fixed pier bottoms and the pile-soil interaction were constructed. Then, 50 seismic waves with different intensities were selected as excitation. The ducti-lity ratio of the rotation angle and the shear strain of the bearing were calculated with the maximum displacements of the pier top and bearing as the target responses. Subsequently, the seismic fragility curves of the entire bridge were established through the wide-bound method, and a new formula for the calculation of average damage level was developed to estimate the post-earthquake traffic capacity of the girder bridge. Analytical results demonstrate that under the same seismic intensity, the peak displacement of the pier under pile-soil interaction is larger than that estimated by the consolidation model, which better agrees with the practical situation. With respect to the fragility curves of bridge components, the maximum damage exceedance probability of the bearing occurs when the pile-soil interaction is considered, but is not large different from the situation of fixed pier bottoms. Changes in traffic flow can be reasonably evaluated by using the seismic fragility curves of the entire bridge system. However, the traffic capacity assessment given by the consolidation model is unsafe. This result implies that the influence of pile-soil interaction on the seismic fragility of bridges cannot be ignored in class-Ⅲ sites.
Seismic Fragility of Irregular Continuous Rigid Frame Bridge

董俊, 单德山, 张二华, 马腾
, SHAN Deshan, ZHANG Erhua, MA Teng

- , 2015,
Abstract: 摘要: 为探讨非规则桥梁的抗震性能,建立了典型非规则公路桥梁的地震易损性理论模型.考虑桥梁结构参数和地震动的不确定性,抽样生成桥梁地震易损性分析模型样本库.用OpenSees软件对模型样本库进行非线性动力时程分析,以获得结构动力响应.在研究桥墩反弯点时程曲线和桥墩曲率包络线分布特征的基础上确定桥梁构件的损伤指标.采用概率地震需求分析方法获得桥梁各构件易损性曲线,并基于一阶可靠度理论获得桥梁系统的易损性曲线.结果表明:在地震作用下,非规则桥梁支座最容易损伤破坏,桥梁系统的易损性明显高于桥梁构件的易损性;易损性曲线可用于评估非规则桥梁的抗震性能,为震后桥梁损伤识别提供依据.
Abstract: To investigate the seismic performances of irregular bridges, a seismic vulnerability model for a typical irregular highway bridge was created. By considering the uncertainties of an earthquake and bridge parameters, a model sample database was generated by adopting the sampling method to carry out the seismic vulnerability analysis of a bridge. To obtain the structural dynamic responses, a nonlinear time-history analysis was carried out for the sample database by using the software OpenSees. On the basis of the research on the distribution characteristics of time-history curves of inflection point and the curvature envelope of each pier, pier and bearing damage indexes were determined. The fragility curves of dangerous bridge members were generated by using the probabilistic seismic demand analysis approach, and the first-order reliability theory was employed to generate the fragility curve of a bridge system. The research results show that bearings are easy to damage to an irregular bridge subject to an earthquake action. Compared with its members, an irregular bridge system has a high failure probability. The fragility curves obtained can be used to evaluate the seismic performances of an irregular bridge and provide an evidence for post-earthquake damage identification
Probabilistic seismic demand models and fragility estimates for multi-span simply supported railway box girder bridges

- , 2017, DOI: 10.11835/j.issn.1674-4764.2017.06.002
Abstract: 基于已建成高速铁路桥结构类型统计数据,以典型预应力混凝土简支箱梁桥为对象进行易损性研究。考虑5个不确定性参数,基于拉丁超立方抽样的反复试验法建立桥梁样本。采用"装箱法"选择地震动记录,与桥梁样本配对后进行非线性时程分析得到结构响应。定义各构件的损伤状态,通过对构件需求能力比进行二次回归建立桥梁各构件的概率地震需求模型,并生成构件易损性曲线,运用二阶单一边界法生成全桥易损性曲线。结果表明:二次回归分析产生的概率需求模型比线性回归方法更可靠;在地震作用下,此类桥梁构件中的墩柱、活动支座较易损伤,二阶单一边界法能较好地评估全桥系统易损性,在应用上二阶单一边界法比一阶上下边界法简洁方便。
For the proposes of fragility analysis, a typical configuration of multi-span simply supported concrete box girder bridges are selected as analytical object from the statistics of as-built high-speed railway bridges in China. A set of bridge samples, in which five uncertain parameters are considered, are established using the trial and error method based on the Latin hypercube sampling. A portfolio of recorded ground motions divided into bins are assembled, and matched with bridge samples. Then nonlinear time history analyses are performed to capture the responses of structure. Damage states of bridge components are defined, and probabilistic seismic demand models are formulated by quadratic regression analysis for the ratios of the capacity and demand. Fragility curves of bridge components are developed consequently and the fragility of bridge system is evaluated using a single estimate for the second order bounds method. The results show that PSDMs formulated by quadratic regression are better than that by traditional linear regression. The expansion bearing and the column piers of this bridge type are fragile under earthquake excitation. A single estimate for the second order bounds method is preferable to evaluate the fragility of bridge system, and is easier to use than the first order bounds method.
Fragility Analysis of Large-Span Continuous Rigid Bridge Considering Wave Passage Effectt

陈志伟, 蒲黔辉, 李晰, 陈志强, 贾宏宇
CHEN Zhiwei
, PU Qianhui, LI Xi, CHEN Zhiqiang, JIA Hongyu

- , 2017, DOI: 10.3969/j.issn.0258-2724.2017.01.004
Abstract: 为了分析地震动的行波效应对山区大跨连续刚构桥易损性的影响,以西南地区某高墩大跨连续刚构桥为研究对象,采用谱兼容的方法选取了20条地震记录对桥梁结构进行了一致激励和多点激励下的增量动力分析,并得到其易损性曲线.研究结果表明:墩高越高,桥墩相对位移越大,最高墩的相对位移为矮墩的1.03~2.81倍,但矮墩发生损伤的概率要大于高墩,在抗震设计中应得到重视;与一致激励相比较,考虑行波效应时,矮墩发生轻微损伤和中等损伤的概率降低,高墩发生轻微损伤和中等损伤的概率增大,但行波效应会同时增加矮墩和高墩发生严重损伤的概率,因此在高墩桥的抗震设计中,特别是在高烈度地区,应考虑行波效应对桥梁结构的影响.
: To study wave passage effect on the fragility of the large-span continuous rigid bridge (LSCRB) in mountainous area, an actual LSCRB in southwest area was chosen as the study object. Twenty earthquake records were selected using the spectra-compatible method. Then, incremental dynamic analysis (IDA) of the bridge structure was conducted under uniform excitations and non-uniform excitations to obtain the fragility curves. The analysis results show that the relative displacements of the piers increase with the height of piers, and the relative displacement of the highest pier is around 1.03-2.81 times that of low pier, but the seismic design of low piers should be paid more attention because the damage probability of low piers is greater than that of high piers. Compared with the case under uniform excitations, the wave passage effect may reduce the probabilities of slight and moderate damages of low piers, and increase those of high piers. Furthermore the probability of extensive damage may be increased by the wave passage effect both for the low and high piers. As a result, in the seismic design of the high-pier bridges, it is necessary to consider the effect of wave passage on bridge structure, especially for the high-intensity zones
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