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.     

Developing fragility curves for a pile-supported wharf

This study proposes a procedure for developing seismic fragility curves for a pile-supported wharf. A typical pile-supported wharf, as commonly used in the ports of Taiwan, is chosen for demonstration. For a structural model of the wharf, the deck is modeled by shell elements and the Winkler model is used for the pile–soil system, in which the piles and soils are represented by beam elements and springs, respectively. A pushover analysis with lateral loads distributed according to the fundamental modal shape of the wharf structure is conducted to deduce the capacity curve of the wharf. The procedure for developing fragility curves can be explicitly performed using the spreadsheet platform in Microsoft EXCEL. First, quantitative criteria for damage states are established from the sequence of development of plastic zones. Then a nonlinear static procedure called the Spectrum Capacity Method (CSM) is used to efficiently construct a response matrix of the wharf to 24 earthquake events with differing levels of peak ground acceleration (PGA). Based on the damage criteria and the response matrix, the fragility curves of the wharf can be thus constructed through simple statistical analysis. Shifted lognormal cumulative distribution functions are also employed to better approximate the fragility curves for practical applications.     

Dynamic soil–structure interaction analysis via coupled finite-element–boundary-element method

In this paper, a study on the transient response of an elastic structure embedded in a homogeneous, isotropic and linearly elastic half-plane is presented. Transient dynamic and seismic forces are considered in the analysis. The numerical method employed is the coupled Finite-Element–Boundary-Element technique (FE–BE). The finite element method (FEM) is used for discretization of the near field and the boundary element method (BEM) is employed to model the semi-infinite far field. These two methods are coupled through equilibrium and compatibility conditions at the soil–structure interface. Effects of non-zero initial conditions due to the pre-dynamic loads and/or self-weight of the structure are included in the transient boundary element formulation. Hence, it is possible to analyse practical cases (such as dam–foundation systems) involving initial conditions due to the pre-seismic loads such as water pressure and self-weight of the dam. As an application of the proposed formulation, a gravity dam has been analysed and the results for different foundation stiffness are presented. The results of the analysis indicate the importance of including the foundation stiffness and thus the dam–foundation interaction.     

基于性能的钢筋混凝土框架剪力墙结构地震易损性分析

以某典型的20层钢筋混凝土框架剪力墙结构作为研究对象,研究基于性能的RC框架剪力墙结构易损性分析方法。首先选择合适的地震动记录,以0.2g为步长进行调幅后,建立300个结构-地震动样本空间,并确定结构损伤指标和性能参数;然后应用增量动力分析方法计算结构的地震动力响应,选择基本周期加速度反应谱为地震动参数,以研究结构反应的不确定性,并深入分析地震动参数与结构地震需求参数的关系;在此基础上,建立该结构基于加速度反应谱的易损性曲线进行结构易损性分析与评估。结果表明：随着地震动强度的增大,IDA曲线由单调增加变为非单调增加,分位曲线（16%,50%和84%）可以准确地衡量结构的性能;框剪结构在地震作用下的抗震性能表现良好,随着地震强度的增长,各性能超越概率大小的增长速度是不同的。     

Fragility curves for reinforced concrete structures in Skopje (Macedonia) region

A method for the development of earthquake intensity–damage relations, given as fragility curves and damage probability matrices is proposed in this paper. The proposed method is applied on reinforced-concrete frame-wall structures. Two sets of fragility curves and damage probability matrices are developed. The first one is for reinforced-concrete frame structures lower than 10 stories. For this purpose, a six-story frame structure is used. The other set is defined for reinforced-concrete frame-wall structures higher than 10 stories. A 16-story frame-wall structure was chosen as a sample. The sample structures were designed according to Macedonian design code. The conditions of the local seismic hazard were the subject of special concern for the development of earthquake intensity–damage relations. Because of the limited number of real time histories from the Skopje region, a set of 240 synthetic time histories were generated. Geological dates from the Skopje region were used. Response of the sample structures under earthquake excitation was defined performing nonlinear dynamic analysis. Modeling of the nonlinear behavior of the structural elements was completed according to state-of-the-art methods in this field. A modified Park and Ang damage model was chosen as a measure of the structure's response to earthquake excitation. Five damage states were defined to express the condition of damage. As a result of the analytical research, the values of the global damage index corresponding to each damage state were determined. Using the dates from the nonlinear dynamic analysis of the sample structures under all 240 synthetic time histories, the two sets of fragility curves and damage probability matrices were defined.     

Development of seismic fragility surfaces for reinforced concrete buildings by means of nonlinear time‐history analysis

Fragility curves are generally developed using a single parameter to relate the level of shaking to the expected structural damage. The main goal of this work is to use several parameters to characterize the earthquake ground motion. The fragility curves will, therefore, become surfaces when the ground motion is represented by two parameters. To this end, the roles of various strong‐motion parameters on the induced damage in the structure are compared through nonlinear time‐history numerical calculations. A robust structural model that can be used to perform numerous nonlinear dynamic calculations, with an acceptable cost, is adopted. The developed model is based on the use of structural elements with concentrated nonlinear damage mechanics and plasticity‐type behavior. The relations between numerous ground‐motion parameters, characterizing different aspects of the shaking, and the computed damage are analyzed and discussed. Natural and synthetic accelerograms were chosen/computed based on a consideration of the magnitude‐distance ranges of design earthquakes. A complete methodology for building fragility surfaces based on the damage calculation through nonlinear numerical analysis of multi‐degree‐of‐freedom systems is proposed. The fragility surfaces are built to represent the probability that a given damage level is reached (or exceeded) for any given level of ground motion characterized by the two chosen parameters. The results show that an increase from one to two ground‐motion parameters leads to a significant reduction in the scatter in the fragility analysis and allows the uncertainties related to the effect of the second ground‐motion parameter to be accounted for within risk assessments. Copyright © 2009 John Wiley & Sons, Ltd.     

Earthquake motion input and its dissemination via the Internet

Objectives of this task are to conduct research on seismic hazards, and to provide relevant input on the expected levels of these hazards to other tasks. Other tasks requiring this input include those dealing with inventory, fragility curves, rehabilitation strategies and demonstration projects. The corresponding input is provided in various formats depending on the intended use: as peak ground motion parameters and/or response spectral values for a given magnitude, epicentral distance and site conditions; or as time histories for scenario earthquakes that are selected based on the disaggregated seismic hazard mapped by the U.S. Geological Survey and are incorporated in building codes. The user community for this research is both academic researchers and practicing engineers who may use the seismic input generated by the synthesis techniques that are developed under this task for a variety of applications. These include ground motions for scenario earthquakes, for developing fragility curves and in specifying ground motion input for critical facilities (such as hospitals) located in the eastern U.S. Supported in part by the Earthquake Engineering Research Centers Program of the National Science Foundation under Award Number EEC-9701471 to the Multidisciplinary Center for Earthquake Engineering Research.     

Seismic fragility assessment of highway bridges using support vector machines

Seismic fragility curves provide a powerful tool to assess the reliability of structures. However, conventional fragility analysis of structures comprising a large number of components requires enormous computational efforts. In this paper, the application of probabilistic support vector machines (PSVM) for the system fragility analysis of existing structures is proposed. It is demonstrated that support vector machine based fragility curves provide accurate predictions compared to rigorous methodologies such as component based fragilities developed by Monte Carlo simulations. The proposed method is applied to an existing bridge structure in order to develop fragility curves for serviceability and collapse limit states. In addition, the efficiency of using the PSVM method in the application of vector-valued ground motion intensity measures (IM) as well as traditional single-valued IM are investigated. The results obtained from an incremental dynamic analysis of the structure are used to train PSVMs. The application of PSVM in binary and multi-class classifications is used for the fragility analysis and reliability assessment of the bridge structure.     

Intensity measure conversion of fragility curves

In seismic risk assessment of structures, fragility functions are the probabilistic characterization of vulnerability at the component and/or structural level, expressing the probability of failure as a function of a ground motion intensity measure (IM). Fragility curves, in general, are structure- and site-specific, thus a comparison of fragility curves, then of vulnerability, is not straightforward across multiple structures. Also, it could be the case that hazard at a site of interest is not available for the IM originally considered in the fragility assessment. These situations require to convert fragility curves from an original IM to a target one. The present study addresses a hazard-consistent probabilistic framework for converting spectral acceleration-based IMs from an original IM to a target IM at a given site. In particular, three conversion cases, under different assumptions on the explanatory power of the involved IMs with respect to structural failure, are discussed: (a) a vector-valued IM consisting of the original and target IMs, magnitude, and source-to-site distance; (b) a vector-valued IM consisting of the original and target IMs; and (c) the original (scalar) IM only, assuming that structural response, given the IM, is statistically independent of the other ground motion variables. In this framework, the original fragility functions are characterized using the state-of-the-art methods in performance-based earthquake engineering, then the fragility curves as a function of the target IM are evaluated through applications of the probability calculus rules, ensuring consistency with the seismic hazard at the site of interest. The conversion strategy is illustrated through the applications to three-, six-, and nine-story Italian code-conforming reinforced concrete buildings designed for a high-hazard site in Italy. The study shows that, in most of the cases, the converted fragility curves have agreement with the reference curves directly developed in terms of the target IM. Cases in which least agreement was found are likely due to the models used to obtain the terms required by the conversion equations.     

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.     

Vulnerability of ordinary moment resistant concrete frames

The effects of structural modeling (bar slip in lap splice), ground motion selection process (epsilon effect) and size of a structure (number of bays and stories) on the fragility of reinforced concrete ordinary moment resisting frames are investigated. An analytical model is developed to account for bar slip in lap splice, which exhibits good correlation with existing experimental data. Then, incremental dynamic analysis is used to derive the fragility curves for four model structures. The model structures simulate frames with a different number of bays and stories. Finally, the fragility curves are corrected for the epsilon effect. The results show that slip in the lap splice can significantly increase the failure probability, especially for the collapse prevention limit state. At the same time, it is found that spectral shape has a significant impact on the fragility curves. It is also found that accounting for or ignoring bar slip or epsilon effects increases the probability of failure for larger structures. This indicates an unconservative bias in the safety of larger structures.     

Convex model-based calculation of robust seismic fragility curves of isolated continuous girder bridge

The convex model approach is applied to derive the robust seismic fragility curves of a five-span isolated continuous girder bridge with lead rubber bearings (LRB) in China. The uncertainty of structure parameters (the yield force and the post-yield stiffness of LRB, the yield strength of steel bars, etc.) are considered in the convex model, and the uncertainty of earthquake ground motions is also taken into account by selecting 40 earthquake excitations of peak ground acceleration magnitudes ranging from 0.125 to 1.126 g. A 3-D finite element model is employed using the software package OpenSees by considering the nonlinearity in the bridge piers and the isolation bearings. Section ductility of piers and shearing strain isolation bearings are treated as damage indices. The cloud method and convex model approach are used to construct the seismic fragility curves of the bridge components (LRB and bridge piers) and the bridge system, respectively. The numerical results indicate that seismic fragility of the bridge system and bridge components will be underestimated without considering the uncertainty of structural parameters. Therefore, the failure probability P _f,max had better be served as the seismic fragility, especially, the fragility of the bridge system is largely dictated by the fragility of LRB. Finally, the probabilistic seismic performance evaluation of the bridge is carried out according to the structural seismic risk estimate method.     

Development of fragility functions for geotechnical constructions: Application to cantilever retaining walls

Fragility curves constitute an emerging tool for the seismic risk assessment of all constructions at risk. They describe the probability of a structure being damaged beyond a specific damage state for various levels of ground shaking. They are usually represented as two-parameter (median and log-standard deviation) cumulative lognormal distributions. In this paper a numerical approach is proposed for the construction of fragility curves for geotechnical constructions. The methodology is applied to cantilever bridge abutments on surface foundation often used in road and railway networks. The response of the abutment to increasing levels of seismic intensity is evaluated using a 2D nonlinear FE model, with an elasto-plastic criterion to simulate the soil behavior. A calibration procedure is followed in order to account for the dependency of both the stiffness and the damping on the soil strain level. The effect of soil conditions and ground motion characteristics on the global soil and structural response is taken into account considering different typical soil profiles and seismic input motions. The objective is to assess the vulnerability of the road network as regards the performance of the bridge abutments; therefore, the level of damage, is described in terms of the range of settlement that is observed on the backfill. The effect of backfill material to the overall response of the abutment wall is also examined. The fragility curves are estimated based on the evolution of damage with increasing earthquake intensity. The proposed approach allows the evaluation of new fragility curves considering the distinctive features of the structure geometry, the input motion and the soil properties as well as the associated uncertainties. The proposed fragility curves are verified based on observed damage during the 2007 Niigata-Chuetsu Oki earthquake.     

Fragility curves for reinforced concrete buildings to seismically triggered slow-moving slides

Probabilistic fragility functions have been developed for low-rise, reinforced concrete buildings subjected to earthquake triggered slow-moving slides, applying a recently published methodology by the same authors [5] (Fotopoulou and Pitilakis, 2012). We performed an extensive numerical parametric study considering different idealized slope configurations, soil and geological settings, as well as distances of the structure to the slope's crest and foundation typologies. Various features of the structural damage are explored, highlighting trends on the building's behavior to the permanent co-seismic slope deformations. The proposed generalized probabilistic fragility curves have been developed as a function of the expected outcrop peak ground acceleration (PGA) as provided by modern seismic codes, i.e. EC8, or the induced permanent slope ground displacements (PGD) for different slope angles, water table level and soil type, foundation typology and seismic design code. Detailed sensitivity analyses of the above parameters, reveal their relative importance for the vulnerability analysis and the quantitative risk assessment of low-rise RC buildings subjected to earthquake triggered slow-moving slides.     

An earthquake-source-based metric for seismic fragility analysis

The seismic fragility of a system is the probability that the system enters a damage state under seismic ground motions with specified characteristics. Plots of the seismic fragilities with respect to scalar ground motion intensity measures are called fragility curves. Recent studies show that fragility curves may not be satisfactory measures for structural seismic performance, since scalar intensity measures cannot comprehensively characterize site seismicity. The limitations of traditional seismic intensity measures, e.g., peak ground acceleration or pseudo-spectral acceleration, are shown and discussed in detail. A bivariate vector with coordinates moment magnitude m and source-to-site distance r is proposed as an alternative seismic intensity measure. Implicitly, fragility surfaces in the (m, r)-space could be used as graphical representations of seismic fragility. Unlike fragility curves, which are functions of scalar intensity measures, fragility surfaces are characterized by two earthquake-hazard parameters, (m, r). The calculation of fragility surfaces may be computationally expensive for complex systems. Thus, as solutions to this issue, a bi-variate log-normal parametric model and an efficient calculation method, based on stochastic-reduced-order models, for fragility surfaces are proposed.     

Seismic fragility assessment of existing sub-standard low strength reinforced concrete structures

An analytical seismic fragility assessment framework is presented for the existing low strength reinforced concrete structures more common in the building stock of the developing countries.For realistic modelling of such substandard structures,low strength concrete stress-strain and bond-slip capacity models are included in calibrating material models.Key capacity parameters are generated stochastically to produce building population and cyclic pushover analysis is carried out to capture inelastic behaviour.Secant period values are evaluated corresponding to each displacement step on the capacity curves and used as seismic demand.A modified capacity demand diagram method is adopted for the degrading structures,which is further used to evaluate peak ground acceleration from back analysis considering each point on the capacity curve as performance point.For developing fragility curves,the mean values of peak ground acceleration are evaluated corresponding to each performance point on the series of capacity curves.A suitable probability distribution function is adopted for the secant period scatter at different mean peak ground acceleration values and probability of exceedance of limit states is evaluated.A suitable regression function is used for developing fragility curves and regression coefficients are proposed for different confidence levels.Fragility curves are presented for a low rise pre-seismic code reinforced concrete structure typical of developing countries.     

Seismic collapse capacity of basic inelastic structures vulnerable to the P‐delta effect

The collapse capacity of earthquake‐excited inelastic nondeteriorating SDOF systems, which are vulnerable to the destabilizing effect of gravity loads (P‐delta effect), is evaluated. In this paper, the collapse capacity of the system subjected to a ground motion is defined as spectral acceleration at its initial structural period, at which the structure becomes unstable. Characteristic structural parameters, which affect the collapse capacity, are identified. Ground motion records of the ATC 63 far‐field set characterize severe earthquake excitation. In extensive incremental dynamic analyses studies, the impact of these parameters and of aleatory uncertainties on the collapse capacity is assessed and quantified. Median and percentile collapse capacities are plotted against the initial structural period leading to collapse capacity spectra. Nonlinear regression analyses are applied to derive analytical expressions of the design collapse capacity spectra and collapse fragility curves. The ultimate objective is to provide collapse capacity spectra for easy application and yet sufficient accurate assessment of the dynamic stability of flexible multistory buildings. Copyright © 2011 John Wiley & Sons, Ltd.     

近场地震作用下考虑二阶效应的混凝土框架抗震分析

利用钢筋混凝土柱的试验结果,验证OpenSees程序用于钢筋混凝土结构非线性分析的可行性。以此为基础,对钢筋混凝土框架结构在远场地震、近场非脉冲地震与近场脉冲地震作用的性能进行非线性时程分析,研究框架结构在三类地震作用下的反应以及二阶效应对结构反应的影响。针对近场脉冲地震对结构进行增量动力分析(IDA)和易损性分析,分别得到结构的IDA曲线、易损性曲线和近场脉冲地震作用下二阶效应对结构抗震性能的影响。分析结果表明,在三类地震作用下,近场脉冲地震导致的二阶效应对结构抗震性能的影响最为显著,结构抗震设计中宜考虑二阶效应的影响。     

地震和风耦合作用下上海中心大厦结构易损性研究

随着城市人口的增加,越来越多的超高层建筑在中国各大城市涌现,在其全寿命周期内不可避免的会遭受风甚至地震等多灾害的作用。以上海中心大厦为分析模型,根据其场地条件,采用Benowitez在2015年提出的1种基于随机波的模型方法模拟不同高度处具有空间相关性的脉动风荷载时程。通过对Perform 3D有限元软件建立的上海中心大厦模型进行非线性动力时程分析,研究地震和风耦合作用下对于结构性能的影响,并基于多灾害需求生成结构在地震和风耦合作用下的易损性曲面来研究结构的抗振可靠度。结果表明:结构的响应和易损性随着风速和PGA的增大而显著增大;随着风速的增大结构的响应和易损性均有增大的趋势,但随着地震动的增大,风荷载对结构响应和易损性影响逐步减小。