Performance-based seismic fragility analysis of retaining walls based on the probability density evolution method

Seismic fragility analysis is an efficient way to study the seismic behaviour and performance of structures under the excitation of earthquakes of varying intensity, and an essential part of the seismic risk assessment of structures. A recently developed dynamic reliability methodology, the probability density evolution method (PDEM), is proposed for the dynamic reliability and seismic fragility analysis of a retaining wall. The PDEM can obtain an instantaneous probability density function of the seismic responses and easily acquire the seismic reliability of the structural system. An important advantage of the PDEM is its high efficiency relative to that of the Monte Carlo simulation method, which is often used in the reliability and fragility analysis of structures. The present study uses a typical gravity retaining wall to illustrate stochastic seismic responses and fragility curves that can be obtained by the PDEM. The combined uncertainties of the seismic force and soil properties are explicitly and systematically modelled by stochastic ground motions and random variables respectively. The performance of the retaining wall is analysed for different acceptable levels of backfill settlement. Additionally, seismic fragility curves are constructed without assuming the distribution of the seismic response.     

Nonlinear Static Procedure for Seismic Vulnerability Assessment of Bridges

Abstract:   The impact of an earthquake event on the performance of a highway transportation network depends on the extent of damage sustained by its individual components, particularly bridges. Seismic damageability of bridges expressed in the form of fragility curves can easily be incorporated into the scheme of risk analysis of a highway network under the seismic hazard. In this context, this article focuses on a nonlinear static method of developing fragility curves for a typical type of concrete bridge in California. The method makes use of the capacity spectrum method (CSM) for identification of spectral displacement, which is converted to rotations at bridge column ends. To check the reliability of this current analytical procedure, developed fragility curves are compared with those obtained by nonlinear time history analysis. Results indicate that analytically developed fragility curves obtained from nonlinear static and time history analyses are consistent.     

System loss assessment of bridge networks accounting for multi-hazard interactions

This paper details an integrated method for the multi-hazard risk assessment of road infrastructure systems exposed to potential earthquake and flood events. A harmonisation effort is required to reconcile bridge fragility models and damage scales from different hazard types: this is achieved by the derivation of probabilistic functionality curves, which express the probability of reaching or exceeding a loss level given the seismic intensity measure. Such probabilistic tools are essential for the loss assessment of infrastructure systems, since they directly provide the functionality losses instead of the physical damage states. Multi-hazard interactions at the vulnerability level are ensured by the functionality loss curves, which result from the assembly of hazard-specific fragility curves for local damage mechanisms. At the hazard level, the potential overlap between earthquake and flood events is represented by a time window during which the effects of one hazard type on the infrastructure may still be present: the value of this temporal parameter is based on the repair duration estimates provided by the functionality loss curves. The proposed framework is implemented through Bayesian Networks, thus enabling the propagation of uncertainties and the computation of joint probabilities. The procedure is demonstrated on a bridge example and a hypothetical road network.     

Seismic partitioned fragility analysis for high‐rise RC chimney considering multidimensional ground motion

In order to identify the vulnerable parts and areas of the high‐rise reinforced concrete chimney, this paper presents an effective method, which called partitioned fragility analysis. One 240‐m‐high reinforced concrete chimney was selected as the practical project, and its analytical model was created with ABAQUS software. The selected high‐rise chimney structure was divided into 17 parts, and then the damage probability of each part in different damage states was obtained with the fragility analysis considering multidimensional ground motions. Twenty ground motion records were taken from the Next Generation Attenuation database as the input motions, and the peak ground acceleration was selected as the intensity measure. The response of the chimney structure under multidimensional ground motions was obtained based on incremental dynamic analysis. The maximum strains of concrete and steel bars were defined as the damage limit states of the chimney structure. The fragility curves and surfaces obtained from this analysis showed that the vulnerable areas of the chimney structure appear at 0–20 m, 90–130 m, and 150–200 m along the height of the chimney respectively. Based analytical results, these vulnerable parts can be retrofitted to enhance the seismic resistance of existing chimney structures. And the partitioned fragility analysis method can also be used to improve the design of new chimney structures.     

Fragility-based assessment of typical mid-rise and low-rise RC buildings in Turkey

This paper focuses on the seismic fragility assessment of typical low-rise and mid-rise reinforced concrete (RC) buildings in Turkey by considering Düzce Damage database, which was compiled after the two devastating earthquakes in 1999 that affected the Marmara region. A set of fragility curves is developed by making use of the building characteristics in the database. The generated fragility curve set is referred as “reference” since it forms the basis of a parametric study. Then the influence of sampling techniques, sample size, type of hysteresis model and limit state definitions on the fragility curves is investigated. The results revealed that the uncertainty in capacity and degradation characteristics have a significant influence whereas the other investigated parameters do not seem to have an important role on the final fragility functions. In the last part of the study, the damage observed in Düzce buildings after 1999 earthquakes is estimated by using the generated fragility curves for low-rise and mid-rise RC frame buildings. Estimated damage distributions seem to be comparable with the actual damage data.     

An expert judgement approach to determining the physical vulnerability of roads to debris flow

The physical vulnerability of roads to debris flow may be expressed through fragility functions that relate flow volume to damage probabilities. Fragility relationships are essential components of quantitative risk assessments as they allow for the estimation of risk within a consequence-based framework. To the best of the authors’ knowledge, this is the first time that fragility curves have been produced in order to provide the conditional probability for a road to be in, or to exceed, a certain damage state for a given debris flow volume. Preliminary assessments were undertaken by means of a detailed questionnaire. A total of 47 returns were received from experts in 17 countries: 32 % academia, 51 % the commercial sector and 17 % governments. Fragility curves have been defined for three damage states (limited damage, serious damage and destroyed) for each of low-speed and high-speed roads in order to cover the typical characteristics of roads vulnerable to debris flow. The probability of any given damage state being reached or exceeded by a debris flow of a given volume (10–100,000 m³) was derived from the mean of the responses received. Inevitably there was a degree of scatter in the results, and the treatment of such variation, or ‘experimental errors’, was crucial to understanding the data and developing the fragility curves. Fragility curves are quantitative expressions of vulnerability. The method adopted is based upon qualitative, expert judgment of quantitative probabilities. In addition to an assessment of the probabilities of given damage states being exceeded, respondents to the questionnaire were polled as to their level of experience and confidence in their ability to provide a valid and coherent set of answers to the questions posed. The development of the fragility curves and their validation are described in the paper.     

Seismic performance of viaducts with probabilistic method

Due to the uncertainty of both ground motions and structural capacity, it is necessary to consider the seismic performance of viaduct structures using the probabilistic method. The risk is quantified by a procedure on the basis of a numerical determination of the fragility curves. A group of ground motions, Large Magnitude-Short Distance Bin (LMSR-N), selected specially due to its response spectra, is accorded well with the corresponding spectra of the Chinese code for seismic design. The characteristic values of the curvature ductility factors for the serviceability and the damage control limit states are obtained, and two equations for estimating the characteristic values of the curvature ductility factors are developed through regression analysis. Then, the serviceability and damage control limit states were proposed. Three damage states were constituted according the results of the experiment by Pacific Earthquake Engineering Research (PEER) Center. The analytical fragility curves were obtained specifically, using both Capacity Spectrum Method (CSM) (non-linear static) analysis and Ineremental Dynamic Method (IDM) (non-linear dynamic) analysis, respectively, in this paper. The structural fragility curves developed by CSM method can help make the structural analysis simple and quick, avoiding the implementation of the dynamic response history analysis (RHA). Although the dynamic RHA requires a lot of complicated analysis for the structure, the results from RHA are reliable and accurate. Fragility curves are powerful tools for use in performance-based seismic bridge design.     

基于响应面法的LRB基础隔震结构地震易损性分析

提出了一种基于响应面法的LRB基础隔震结构地震易损性分析方法,考虑了LRB基础隔震结构中各子结构之间(即上部结构和LRB隔震支座)地震需求的相关性。分析中考虑地震动与LRB基础隔震结构物理参数的不确定性,以均匀设计法建立地震动-LRB基础隔震结构样本,通过对有限元模型进行非线性时程分析,分别建立各子结构响应均值、方差及其相关系数与不确定参数之间的响应面模型。在此基础上,采用蒙特卡罗模拟得到LRB基础隔震结构在不同性能水准下的地震易损性曲线。分析结果表明,所建立的响应面模型精度高、结构可靠,减小了复杂有限元模型非线性时程分析计算的工作量,有效提高了LRB基础隔震结构地震易损性分析的时效性。为了准确建立LRB基础隔震结构的地震易损性曲线,应考虑各子结构地震响应需求之间的相关性。     

Seismic fragility assessment of a tall reinforced concrete chimney

In China, a considerable proportion of reinforced concrete (RC) industrial chimneys in operation was designed and constructed in accordance with less rigorous outdated seismic criteria during the end of 19th and early 20th century. However, few research works have been reported till date on a realistic overall assessment of the seismic performance of these existing aging RC chimney structures. Therefore, in this study, fragilities of existing RC chimney were studied. For this purpose, an existing 240 m tall RC chimney was selected and structurally modeled with a lumped mass beam (stick) model by means of the OpenSees analysis program. In order to capture the uncertainties in ground motion realizations, a series of 21 ground motions are selected from the Next Generation Attenuation database as the input motions. To develop the analytical fragility curves, nonlinear incremental dynamic analysis of the studied RC chimney was then carried out using the selected input motions, which were normalized to different excitation levels. The section curvature ductility ratio was considered as the damage index. Based on material strain and sectional analysis, four limit states (LSs) were defined for five damage state. The seismic responses of the all sections were utilized to evaluate the likelihood of exceeding the LSs. Then the peak ground acceleration (PGA)‐based seismic fragility curves of the structure were constructed assuming a lognormal distribution. Finally, under the light of these fragility curves, the damage risks in existing RC chimney were discussed. The analytical results indicated that for design level earthquake of PGA = 0.1 g (g is the gravitational acceleration) and the maximum considered earthquake of PGA = 0.22 g, the probabilities of exceeding the light damage state were around 1.5% and 44%, respectively, while the exceedance probabilities corresponding to moderate, extensive and complete damage states were approximately zero in both cases. On the other hand, fragility analysis revealed that the RC chimney structure had considerable ductility capacity and was capable to withstand a strong earthquake with some structural damages. Copyright © 2014 John Wiley & Sons, Ltd.     

Fragility analysis of track-on steel-plate-girder railway bridges in Korea

More than 40% of the bridges in conventional Korean railway lines are track-on steel-plate-girder (TOSPG) bridges. They are characterized by a superstructure consisting of railway tracks sitting directly on steel plate girders without any ballast system. Most of these bridges have been designed with little or no consideration given to seismic loading. In this paper, seismic fragility curves of TOSPG bridges in Korea are developed. Fragility curves are developed first for the components, by using the probabilistic seismic demand model. The developed component fragility curves show that the bearings are the most vulnerable components of the TOSPG bridges against seismic loading. On the other hand, the piers are much less vulnerable, although they contain no reinforcing bars. This is because the superstructure mass is very light, and therefore horizontal loading transferred from the superstructure to the piers is minimal. A generic damage measure is introduced for measuring the system-level damage of structures out of the component-level damages. The system fragility curves are then developed, using the generic damage measure. Finally, representation of seismic risk in terms of expected seismic losses is demonstrated. This demonstration shows how the fragility analysis is utilized for risk assessment and support in decision-making.     

Direct displacement-based assessment with nonlinear soil–structure interaction for multi-span reinforced concrete bridges

A practical and readily implementable seismic assessment procedure for multi-span reinforced concrete bridges is introduced in this paper. The procedure is based on an existing direct displacement-based assessment (DDBA) approach, and accounts for nonlinear dynamic soil–structure interaction (NLSSI) effects. Several simplified bridge structures lying on shallow foundations have been used as application examples. The validation has been done by comparing DDBA+NLSSI with the results of finite-element nonlinear time-history simulations by means of incremental dynamic analysis. Moreover, the influence of NLSSI on the assessment procedure has been evaluated by considering the same bridges with fixed base and with NLSSI effects. In spite of its simplicity that presently prevents its use for complex bridge structures, the proposed procedure is found to provide fast and reliable results, useful to give a first-level screening on a large set of bridges for highlighting the most critical situations, as well as to carry out fast parametric analyses to produce fragility curves in the framework of performance-based vulnerability/risk assessment.     

基于变形的土石坝地震易损性分析

地震易损性分析是地震风险分析的重要组成部分,可以预测结构在遭受不同等级地震荷载作用下发生各级破损的概率。土石坝在地震作用下易发生不同程度的破坏,对其进行易损性分析可以为土石坝地震风险分析及评价提供有效途径。考虑土石坝材料参数及地震动输入不确定性因素的影响,提出了基于变形的土石坝地震易损性分析方法。采用正交设计法选取材料参数样本组合,分别施加不同地震峰值加速度进行地震反应分析,基于坝顶相对沉陷破损评价指标,给出了大坝的易损性曲线。以云鹏心墙土石坝为例进行了地震易损性分析,得到大坝不同震损等级的风险概率,对土石坝地震风险评估和抗震设计优化、维修加固决策等具有重要意义和应用价值。     

Drift-based and dual-parameter fragility curves for concentrically braced frames in seismic regions

This paper discusses the development of drift-based and dual-parameter fragility curves for steel braces as part of concentrically braced frames designed in seismic regions. The experimental results from 24 different research programs are compiled into a database for this effort. Drift-based fragility curves are developed for three damage states of steel braces subjected to cyclic loading associated with brace flexural buckling, local buckling and brace strength loss due to fracture. The effects of material variability, brace cross sectional shape and loading protocol on the drift-based fragility curves are investigated. The effect of global and local slenderness ratios on the fracture ductility of various shapes of steel braces is examined through dual-parameter fragility curves that relate these geometric ratios with the expected story drift ratios that each of the three pre-described damage states occur. The proposed fragility curves can be employed for rapid assessment of the seismic vulnerability of concentrically braced frames.     

Performance of Buildings under Earthquakes in Barcelona, Spain

Abstract:   The seismic risk of the buildings of Barcelona, Spain, is analyzed by using a method based on the capacity spectrum. The seismic hazard in the area of the city is described by means of the reduced 5% damped elastic response spectrum. Obtaining fragility curves for the most important building types of an urban center requires an important amount of information about the structures and the use of nonlinear structural analysis tools. The information on the buildings of Barcelona was obtained by collecting, arranging, improving, and completing the database of the housing and current buildings. The buildings existing in Barcelona are mainly of two types: unreinforced masonry structures and reinforced concrete buildings with waffled slab floors. In addition, the Arc-View software was used to create a GIS tool for managing the collected information to develop seismic risk scenarios. This study shows that the vulnerability of the buildings is significant and therefore, in spite of the medium to low seismic hazard in the area of the city, the expected seismic risk is considerable.     

钢筋混凝土框架结构的损伤状态相关余震易损性分析

一次主震过后通常伴有多次余震发生,由于主、余震间隔时间较短,主震损伤结构通常要遭受进一步的余震作用.为了评估震损结构的余震安全,提出了一种损伤状态相关的余震易损性分析方法.该方法采用有限次整体调幅的主余震序列作为输入,利用Park-Ang指数描述结构在主余震序列作用下的主震损伤和累积损伤,基于logistic回归方法生...     

Drift-based fragility assessment of confined masonry walls in seismic zones

The paper presents drift-based fragility curves developed for confined masonry (CM) walls, which are the main structural components for the lateral load-resisting systems employed in housing dwellings in Latin-America. Drift-based fragility curves were developed for two key damage states associated with the structural performance and repairability of CM walls, from experimental results of 118 confined masonry specimens tested under lateral cyclic loading, during research programs carried out in Mexico, Chile, Peru, Venezuela and Colombia. In particular, four sources of uncertainty, due to specimen-to-specimen, finite-sample, measured diagonal compression strength of the masonry and wall height-to-length aspect ratio were included. These fragility curves are very useful for assessing the seismic vulnerability of CM structures, and for estimating the earthquake-induced economic losses employing recently proposed methodologies based on aggregating the estimated damage at the component level for a specific structure.     

基于试验的大跨异形钢连廊连体结构地震易损性分析

为研究大跨异形钢连廊连体结构的地震易损性,以某实际工程为研究背景,首先分别定义连体结构中的框架剪力墙结构、橡胶支座端和预埋锚固端的极限状态与损伤指标,并采用有限元软件SAP2000建立分析模型。其次,根据结构所在的场地条件,选取了24条地震动记录,并对结构进行三向地震激励下的增量动力分析。在此基础上,以最大层间位移角、橡胶支座的剪切应变和预埋锚固端的损伤因子作为结构地震需求参数,以地面峰值加速度作为地震动强度参数,根据增量动力分析的结果,得到大跨异形钢连廊连体结构的地震易损性曲线。最后,采用振动台试验对易损性分析结果进行验证。结果表明：在8度罕遇地震时,主楼、附楼I、橡胶支座端及角钢预埋锚固端发生毁坏的超越概率分别为0.8%、0.3%、0及47.7%,整体结构发生毁坏的超越概率上界为48.4%,下界为47.7%。这说明用局部结构的地震易损性来评价整体结构的地震易损性是偏于不安全的。易损性分析结果也显示连体结构易发生损坏的部位依次是预埋锚固端、主楼、附楼I和橡胶支座端,这与振动台试验结果相同。建议在设计中加强连体结构的锚固端,保证其可靠连接。     

A proposed structural design method considering fluid viscous damper degradations

The purpose of this study is to perform a seismic assessment of the moment resistant steel structures enhanced with viscous dampers where the dampers are degraded due to possible leak of viscous fluid. This paper proposes a design procedure based on corrected response spectrums as a result of seismic assessments based on nonlinear time series analyses on three‐, five‐, and seven‐story steel frame structures denoted as “generic structures.” The proposed design procedure is a seismic displacement‐based design methodology for buildings with viscous dampers as passive energy dissipation systems. Prior literature on these types of structures often overlook the viscous dampers degradation due to the fluid leak. In this paper, in order to study these effects, a target displacement is specified at first and the lateral forces and required stiffness are obtained. The effectiveness of the proposed procedure is verified with the collapse fragility curves of the generic structures according to the ASCE 7‐10 and displacement‐based design methodology. The results show that the structures designed based on proposed procedure demonstrate acceptable performance with degrading dampers.     

Seismic fragility analysis of a buried gas pipeline based on nonlinear time-history analysis

Seismic fragility analysis was performed for API X65, a type of buried gas pipeline that is widely used in Korea. For this purpose, nonlinear time-history analyses were carried out using 15 different analytical models of the pipeline, which represent variations of modeling parameters. The nonlinear Winkler approach was adopted to simulate the soil-pipeline interaction during an earthquake loading. A set of 12 recorded ground motions were selected for the time-history analyses and scaled to represent a range of earthquake intensity levels. Then, fragility functions were developed with respect to the damage states, which are defined in terms of the maximum axial strain of the pipeline. The parameters under consideration for subsequent seismic fragility analyses are the soil conditions, boundary conditions, burial depth, and type of pipeline. Comparative analyses revealed that the first three parameters, most notably the soil conditions, influence the fragility curves, but the last parameter negligibly affects the fragility curves. It is concluded in short that this study is promising to give a useful insight for a rapid seismic performance evaluation of a buried gas pipeline based on nonlinear and fragility analyses.     

Procedure for determining the seismic vulnerability of an irregular isolated bridge

A seismic vulnerability procedure, based on the capacity/demand ratio approach, is applied to an irregular isolated bridge. Special features are incorporated in both, demand estimation and capacity evaluation. The seismic demand is represented by an average pseudo-acceleration spectrum derived from 159 earthquake accelerograms recorded in the region where the bridge is located. The capacity spectrum method is adopted for estimating the structural expected performance for several limit states. The capacity curve derived from a static non-linear procedure is obtained by means of a lateral load pattern that follows the displacement configuration, previously assessed by the use of time history analyses of the bridge supported on non-linear isolator bearings. Based on a moment–curvature analysis of the pier's sections, the maximum curvature ductility was established for each of the four defined performance limit states. Finally, probability density functions of the bridge capacity and demand were assessed and fragility curves were proposed aimed at determining the expected behaviour of the bridge as function of peak ground acceleration (PGA) of the typical strong motions recorded in the area.