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Seismic fragility analysis of reinforced concrete continuous span bridges with irregular configuration
Abstract
A set of fragility curves of a class of reinforced concrete bridges with different degrees of irregularity has been generated. Eighteen bridge configurations have been identified, from regular to so-called highly irregular models. The geometric irregularity in this class of bridges is assumed to vary with the height of the piers. Using non-linear analytical models and an appropriate suite of 60 ground motions, analytical fragility curves have been generated for the individual piers of each of these 18 bridge models. Discussions have been made about the imposition of the displacement ductility demand of the piers versus the earthquake intensity as well as the bridge regularity. Comparison of the fragility curves shows that the most vulnerable bridges are the irregular bridges and high damage probability is expected for the short piers of this class of bridges. It was found that the fragility curves may be used for categorisation of regular and irregular bridges.
... As a short definition, seismic fragility gives the probability that a structure or structural component will reach or exceed a specific level of damage during earthquakes of certain intensity. Therefore, fragility curves may be used to make probabilistic estimates of different damages during ground motion [21]. ...
... For this reason, nonlinear time history analysis [22,23] is usually used. There are many works that have used this method to perform seismic fragility analysis [21,[24][25][26][27][28][29]. ...
... These acceleration time histories consist of three groups (each of which includes 20 records) with 2%, 10% and 50% probabilities of exceedance over 50 years. These time histories have been used in several researches for the development of fragility curves [21,26]. It should be noted that in order to properly represent the specified probability levels these sixty ground motions should be used together, and not individually. ...
Seismic vulnerability assessment for steel X-braced and chevron-braced RC frames has been
performed via development of analytical fragility curves. Several parameters including the
height of the frame, the P-Δ effect, the fraction of base shear for which the bracing system
has been designed and type of bracing system have been investigated. Definition of damage
states based on the descriptions as provided by HAZUS which gives the limit states and the
associated inter-storey drift limits for RC buildings has been used. The results of fragility
curves show that strengthening the concrete frames by internal steel bracing can reduce the
probability of damage and this reduction is higher when chevron bracing system is used.
... Seismic fragility functions for various types of bridges have been developed in several studies [1][2][3][4][5][6][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Seismic demands on various structural components have been considered as EDPs when developing the fragility functions [11][12][13][14][15]. ...
... Seismic demands on various structural components have been considered as EDPs when developing the fragility functions [11][12][13][14][15]. However, the majority of previous studies have focused on a single component, such as column failure [16][17][18][19][20][21][22][23]. Nielson and DesRoches examined the effects of column curvature and bearing displacement on the fragility of bridges in the eastern US [24]. ...
Reinforced concrete (RC) bridges with multi-column bents are the most common bridges in Iran. There were no special requirements for design of the cap beam–column joints prior to introduction of the seismic codes and thus many existing bridges have poor joint details. Cyclic tests conducted on old multi-column bridge bents have resulted in extensive damage to the joints with little or no damage to the cap beam or columns. In these tests, exterior joints have been damaged more severely than interior joints. The main objective of this research is to develop fragility functions for a typical RC bridge with deficient joint detailing. Nonlinear incremental dynamic analyses (IDA) are performed on finite element model of the bridge to develop the fragility functions at four performance levels. The model for the bridge bent includes nonlinear spring elements with proper characteristics simulating the hysteretic responses of the interior and exterior joints. The parameters defining the hysteretic characteristics of these springs are derived by comparing the analytical and experimental hysteretic responses of the test specimens. The fragility assessment of the bridge is carried out at component level assuming a probabilistic log-normal distribution of the responses. The fragility of the bridge system is generated using Joint Probabilistic Seismic Demand Model (JPSDM). The analytical results indicate the bridge system fragility is highly influenced by the fragility of the exterior and interior joints.
... Jiang et al. studied the probabilistic seismic damage characteristics of deepwater continuous rigid frame bridge, which took the influence of pile-soil dynamic interaction and hydrodynamic effect into account for the submerged parts [8]. Akbari investigated the seismic fragility of continuous rigid frame bridge by modifying the design parameters of pier height [9]. Based on the time-varying law of the seismic sequence of main aftershocks, Liang et al. discussed time-varying seismic fragility of an offshore bridge with continuous rigid frame bridge in service period [10]. ...
... According to the Guidelines for Seismic Design of Highway Bridges JTG/T B02-012008, the seismic hazard analysis of the design site is carried out [29]. e maximum acceleration response spectrum of horizontal design at the bridge location is calculated by equation (9), and the relative parameters and results are shown in Table 6 and Table 7. ...
Earthquakes can cause serious damage to traffic infrastructures, among which the impact on bridge structure is the most important. Therefore, in order to assess bridges serviceability, it is important to master their damage mechanism and to analyze its probability of occurrence under a given seismic action. Various uncertainties, like the location of epicentre of future earthquakes and their magnitudes, make this task quite challenging. We are also required to consider different earthquake scenarios and the damaged states of bridge components associated with those earthquakes. To suppress these difficulties, this study proposed a new method of performance-based seismic fragility and risk assessment for bridges. The proposed method included three steps: (1) performance-based seismic fragility estimation of a five-span continuous rigid frame bridge, (2) seismic hazard analysis for locations of the bridge, and (3) seismic risk analysis of the bridge. The proposed method that considered the performance of the bridge and the uncertainty in the location of the earthquake epicentre and magnitudes can provide valuable references for seismic-resistant design of multispan continuous rigid frame bridges in the future.
... The drift is defined as the horizontal displacement of the loading point divided by the distance from the loading point to the base of the column. The target performance at each level of deformation is described based on the recommendation by Akbari [35]. The drift limits for RC piers at slight, moderate, extensive, and collapse damages are 0.7%, 1.5%, 2.5%, and 5%, respectively. ...
... The damage states are quantitatively measured by the drift of the columns under cyclic loading. The drift limits for the columns at slight, moderate, extensive, and collapse damage states are 0.7%, 1.5%, 2.5%, and 5%, respectively [35]. As the output of each simulation, five different response quantities depicted in Fig. 7 are monitored by examining the cyclic response at different drift limits. ...
Through the use of ultra-high performance fiber reinforced concrete (UHPFRC) tubes in an RC bridge pier, the pier can substantially reduce seismic damages during earthquakes compared to the conventional RC piers. The seismic behavior of such a novel bridge pier is affected by various design factors. This study aims at identifying the significant levels of each main factor and their interactions which affect the cyclic response of UHPFRC tube-confined pier. A fractional factorial design methodology is used to statistically estimate the effects of different main factors and their interactions. 3D finite element models of the UHPFRC tube-confined columns are first generated and validated by using experimental results. Then, a sensitivity study is conducted considering ten potential material and geometry-related factors. Five response variables, i.e. the initial stiffness, load-carrying capacity, residual drift, hysteretic energy dissipation, and equivalent viscous damping, for the UHPFRC tube-confined column are examined. From the parametric study, the significant factors including the main factors and their interactions are determined for each response variable. According to the sensitivity analysis results, predictive equations are proposed to predict the response quantities for other UHPFRC tube-confined columns with the same column cross-section through regression analysis. Results demonstrate that the longitudinal steel reinforcement ratio, axial load ratio, and aspect ratio have large effects (with total contributions greater than 40%) on all the response variables.
... Highway bridges are one of the essential structures in a transportation network. Irregular bridges with piers of unequal height are more susceptible to damage compared to regular bridges (Akbari, 2012) Probabilistic analyses have been widely performed on highway bridges to evaluate vulnerability of . The results obtained from fragility studies provide valuable knowledge for seismic hazard analysis. ...
... Highway bridges are one of the essential structures in a transportation network. Irregular bridges with (Akbari, 2012). Probabilistic analyses have been widely performed on highway bridges to evaluate vulnerability of . ...
... It was suggested that the highest probability of damage is related to the shortest piers. In addition, irregular bridges are more vulnerable than the regular ones [5]. In a study implemented by Abbasi et al. [6] on a set of typical irregular bridges, fragility curves were generated to assess four levels of irregularity, ranging from regular to highly irregular. ...
... Fig. 10 illustrates the fragility curves of the bridge models assuming θ = 45°. As it was expected [5,8], probability of damage to the fixed-base models is increased in irregular bridges such that BM5 is the most vulnerable model, while BM1 has the least likelihood of complete failure among the investigated models. Not only for θ = 45°but for all the seven incident angles studied, the same results are obtained. ...
Highway bridges with piers of unequal height crossing irregular topographical surfaces have potential complexities in terms of component vulnerability evaluations. This paper investigates the seismic behavior of a five-span concrete girder bridge with three coefficients of pier height and two different types of irregular configurations. Moreover, soil-structure interaction is taken into account by modeling a typical deep foundation, including piles and the surrounding soil, in order to examine the effect of pier base flexibility compared to the equivalent fixed-base model. For this purpose, incremental dynamic analyses are performed on the three-dimensional analytical finite element models using a set of ground motion pairs each rotated about the vertical axis of bridge producing seven angles of seismic incidence. The results obtained from the dynamic analyses and fragility assessment of the selected bridge models illustrate that substructure irregularity, support condition of piers, and directionality of seismic excitations are three interdependent factors in vulnerability assessment of highway bridges. Variation in each of the above-mentioned factors leads to change in the fragility characteristics of a bridge at global system failure mode or individual component limit states.
... With respect to the bridges dynamic behaviour in the longitudinal direction (Tables 2 and 3), it is noticeable that when isolation is included the displacements on top of the piles reduced on the average of 50% for the bridges with piers height of 10 m whereas for bridges with slender piers (H=30 m) the displacements increased up to 50% for soil type I whereas for soil type II the increases are up to 4%, showing the isolation effectiveness on medium stiffness soils. The pier angular distortions for a seismic demand corresponding to the service limit state (Tr=50 years) show values lower equal to 0.006 for the non-isolated bridges that correspond to negligible or light damage states; when including the isolation systems, the piers' angular distortions decreased in all cases to values that do not generate damage on them [10]. For a seismic scenario equivalent to the failure limit state, the piers distortion demands show that bridges without an isolation systems could achieve from moderate to severe damage states, states that could be classified as light when accounting for an isolation device [10]. ...
... The pier angular distortions for a seismic demand corresponding to the service limit state (Tr=50 years) show values lower equal to 0.006 for the non-isolated bridges that correspond to negligible or light damage states; when including the isolation systems, the piers' angular distortions decreased in all cases to values that do not generate damage on them [10]. For a seismic scenario equivalent to the failure limit state, the piers distortion demands show that bridges without an isolation systems could achieve from moderate to severe damage states, states that could be classified as light when accounting for an isolation device [10]. These results show the isolation effectiveness in preventing severe damage on the piers, considered as the most vulnerable element for a bridge system. ...
... The height irregularity of bridges produces force demand concentrations in short piers and it is responsible of seismic damages observed in different countries. The substructures composed by piers with different heights conduct to strong lateral stiffness irregularities and several studies relate it with the observed seismic damages of bridges in China, Japan, New Zealand, Chile and other countries [2,[8][9][10]13,16,17,27]. Despite that many countries have an important number of medium length span bridges with irregularity in the piers' height, there are limited number of studies quantifying the irregular configuration and the influence of the soil type. ...
... The influence of soil-structure interaction in the displacement and force demands of irregular bridges have been analyzed by Kappos [14], and the importance of the strength of pier cross sections in irregular bridges is discussed in [26]. In addition of the pier stiffness to characterize irregular bridges, the use of fragility curves is proposed by Akbari [2]. Irregular bridges usually have out of phase deck movements which eventually cause unseating problems: this topic in an irregular bridge is discussed by Thakkar [23]. ...
... The height irregularity of bridges produces force demand concentrations in short piers and it is responsible of seismic damages observed in different countries. The substructures composed by piers with different heights conduct to strong lateral stiffness irregularities and several studies relate it with the observed seismic damages of bridges in China, Japan, New Zealand, Chile and other countries [2,[8][9][10]13,16,17,27]. Despite that many countries have an important number of medium length span bridges with irregularity in the piers' height, there are limited number of studies quantifying the irregular configuration and the influence of the soil type. ...
... The influence of soil-structure interaction in the displacement and force demands of irregular bridges have been analyzed by Kappos [14], and the importance of the strength of pier cross sections in irregular bridges is discussed in [26]. In addition of the pier stiffness to characterize irregular bridges, the use of fragility curves is proposed by Akbari [2]. Irregular bridges usually have out of phase deck movements which eventually cause unseating problems: this topic in an irregular bridge is discussed by Thakkar [23]. ...
This paper presents the parametric study of irregular RC bridge structures subjected to strong seismic records. We determine the expected damages and the concentration demands on short piers of bridges with columns of unequal height located on soft and rigid soil sites. Medium length span bridges are analyzed using the most common structural configurations built in many countries with several height pier configurations. The structures were subjected to strong seismic ground motions recorded on soft and hard soils of earthquakes generated at subduction seismic sources. The parameters of interest in the study are the strength and stiffness characteristics of the substructure and the influence of the dynamic characteristics of the seismic records. The parameter combinations produced more than three hundred 3D non-linear time history analyses conducted with the Perform-3D software. Based on the evaluation of damages indexes, we determine the pier expected damages and the importance of the soil type, on the behavior of irregular pier bridge substructures. It is also quantified the impact of the pier configuration in the global behavior of the bridges and the influence of the shortest pier in the expected damages of the other piers. In most of the cases, the piers adjacent to the tallest piers of the bridge were the elements more affected by the irregularity.
... Ref. [34] assessed regular and irregular configurations of continuous span single-column-bent RC bridges by generating fragility curves. In this study the pier height was considered as the only parameter affecting geometric irregularity and other parameters were not considered. ...
... Several studies are available in the literature on the seismic performance of irregular RC bridges (Hu & Guo, 2020;Sajed & Tehrani, 2020;Soltanieh, Memarpour, & Kilanehei, 2019). The findings of previous studies confirm the higher vulnerability of irregular bridges compared to regular bridges (Akbari, 2012). Afsar Dizaj, Salami, and Kashani (2022a) investigated the influence of bridge layout on the seismic vulnerability of irregular multi-span RC bridges. ...
This paper investigates the seismic fragility of ageing irregular multi-span RC bridges. Different irregularity sources are considered, including (i) substructure stiffness irregularity arising from the unequal-height piers, (ii) substructure stiffness irregularity arising from the spatially variable (asymmetrical) corrosion damage of piers, and (iii) irregular distribution of effective tributary masses on piers of varying heights. To this end, a three-dimensional nonlinear finite element model is developed for multi-span RC bridges and verified against a large-scale shake table test results of a two-span concrete bridge specimen available in the literature. Nonlinear pushover, incremental dynamic, and seismic fragility analyses are performed on three groups of two-span RC bridges with different configurations. Moreover, a time-dependent dimensionless local damage index is employed to evaluate the failure sequence and collapse probability of selected bridge layouts. The analysis results of the three studied irregularity sources show the considerable significance of spatially variable corrosion of bridge piers and substructure irregularity on the failure sequence of piers and seismic fragility of multi-span RC bridges. Furthermore, analysis outcomes show that uneven corrosion of piers triggers unbalanced distribution of seismic ductility demands and irregular seismic response of equal-height multi-span RC bridges.
... The irregularity associated with the substructure of such bridges results in unbalanced seismic demand in piers of varied stiffnesses, where the stiffer piers attract greater seismic inertia forces and ductility demands. A significant deal of research has been dedicated to investigating the seismic behaviour of irregular multi-span RC bridges [21][22][23][24][25][26][27][28][29][30]. The state-of-theart studies on the seismic performance and irregularity criteria of concrete bridges are comprehensively reviewed by Akbari and Maalek [23]. ...
This paper investigates the seismic performance and vulnerability of multi-span Reinforced Concrete (RC) bridges with unequal height piers exposed to varied corrosion damage scenarios. An advanced three-dimensional nonlinear finite element modelling technique is developed and verified with available experimental results of a reference shake table test on a large-scale RC bridge. In addition to the pristine state of the reference bridge, various hypothetical corrosion scenarios, including the symmetrical and asymmetrical corrosion of piers, are considered. Several nonlinear analyses, including the pushover and Incremental Dynamic Analysis (IDA) approach, are performed to evaluate the seismic behaviour and vulnerability of hypothetical RC bridge specimens. The influence of symmetrical and asymmetrical corrosion of piers on nonlinear dynamic behaviour and failure mechanism (both in the global and local scales) of studied bridges are then discussed. Finally, the IDA results are used to develop time-dependent fragility curves. The analyses show that seismic vulnerability of a deteriorated irregular multi-span RC bridge crucially depends on the corrosion scenario of its piers, where the unbalanced distribution of seismic ductility demand might be regulated/intensified by different corrosion scenarios. Moreover, some corrosion scenarios resulted in near-synchronised failure of unequal height piers.
... The outcome of previous studies shows that multispan RC bridges with substructure irregularity are more vulnerable than regular bridges. Moreover, the vulnerability of irregular RC bridges increases significantly as their altitudinal irregularly increases [27][28]. Gomez-Soberon et al. [26] analysed the seismic performance of several highway bridges with various irregularity conditions. ...
This paper investigates the nonlinear dynamic behaviour and failure probability of multi-span Reinforced Concrete (RC) bridges supported on piers of unequal heights. To this end, a three-dimensional nonlinear finite element model of RC bridges with substructure irregularity is developed. The model is verified against an available experimental data of a large-scale shake table test results of a benchmark irregular two-span RC bridge. Six hypothetical two-span irregular RC bridges with piers varied in height, and various superstructure mass-distribution conditions (equal and unequal) and a regular bridge layout (as a reference) are considered. Through Incremental Dynamic Analyses (IDAs), the seismic performance of selected bridge layouts is investigated at both local and global scales. Finally, the influence of bridge layout on seismic vulnerability of piers of varying heights is analysed. Results show that the unbalanced seismic displacement demand and failure probability of different bents of a multi-span irregular RC bridge significantly depend on the height of piers and their arrangement. Therefore, the typical presumption of shorter piers having a higher failure probability due to their higher seismic force absorption is not always the most possible failure mechanism.
... Previous studies have found that the height of irregular bridge piers has a great impact on its seismic fragility [55]. Therefore, in order to investigate the influence of pier height, the seismic fragility curves of pier 1, pier 2, and pier 3 at room temperature and in Maduo are compared in Fig. 12. ...
Lead rubber bearings (LRBs) have been widely used as seismic isolators for bridges, owing to their outstanding working performance and wide applicability. However, the mechanical behavior of the main constituents of LRBs (rubber and lead) is sensitive to temperature variations. The objective of this study is to investigate the influence of regional temperature uncertainty on the seismic fragility of LRB-isolated bridges by combining joint seismic fragility and a (back propagation) BP neural network. In this study, a typical continuous beam bridge that is seismically isolated and uses LRBs is assumed to be located in three regions at different latitudes in China. Using the finite elements models of the bridge and incorporating the thermal–mechanical behavior of LRBs, concrete, and steel at different temperatures, the seismic responses of the piers and the bearings are derived by nonlinear dynamic analysis that is used to develop the statistical relationship between the regional temperature and the bridge’s seismic demand via a BP neural network. Then, the well-trained networks are applied to predict the seismic responses of the piers and the bearings at different temperatures in the three selected regions. Finally, the joint seismic fragility methodology is used to establish and compare the seismic fragility at component level and that at bridge system level in the considered regions. Analysis results show that regional temperature variations may have a notable effect on the component-level fragility as well as the bridge-level fragility.
... Also, they compared the maximum ductility demands obtained using elastic and inelastic analyses to study the influence of the irregularity on the seismic response [12,13]. Akbari studied the displacement ductility demands of the irregular bridge piers versus the earthquake intensity using analytical fragility curves [14]. Levi performed an experimental analysis on a two-fifths scale curved steel plate girder bridge subjected to earthquake simulations. ...
In this paper, the seismic behavior of a total of 84 reinforced concrete bridges, including 12 straight and 72 curved bridges was studied. The bridges were designed and detailed according to the American Association of State Highway and Transportation Officials (AASHTO) regulations. To evaluate the accuracy of the seismic response predictions obtained using elastic analyses, as suggested by AASHTO, both linear and nonlinear time history analyses were performed and the results were compared. In addition, to investigate the accuracy of the code provisions regarding the limitations on the bridge subtended angle for the use of equivalent straight bridges, the results obtained for the curved bridges were compared with those obtained for the equivalent straight bridges. Furthermore, the effects of different types of irregularity on the predicted displacement demands from equivalent straight bridges were investigated. To study the effects of different types of irregularity on the results, different irregular arrangements of spans, various column heights, different abutment conditions, and different subtended angles were considered. Also the effect of combination of different types of irregularity was investigated by considering bridges with different configurations. The results indicated that the deviation of the results obtained from the linear and nonlinear analyses is significant, particularly in the transverse direction of the bridges with irregularity in columns height for different subtended angles. Also, it was shown that in bridges with restrained abutments, unlike the bridges with unrestrained (i.e., free) abutments, the equivalent straight bridges cannot be used in lieu of the curved bridges, since the differences between the results from the two models are significant and become larger with increasing the subtended angle of the bridges. It was shown that some modeling assumptions widely used for seismic analysis of bridge structures can be unrealistic and may lead to inaccurate predictions. It was shown that the AASHTO specifications regarding the use of elastic analysis for some irregular bridges and the limitations on the subtended angle for the use of equivalent straight bridges need to be reevaluated.
... Rotational ductility as EDP was adopted in a number of studies [4,79,80] after transforming the column drift limits evaluated [77] (Table 9.). To define limits for the qualitative definitions as per [72], rotational ductility was utilized (Table 9.) [81]. ...
The seismic assessment of bridges has been on ever-increasing demand owing to the crippling consequences of earthquakes on the integrity of the transportation networks of which the bridges are the most sensitive elements. It has been widely accepted that a priori assessment of vulnerability of a bridge to seismic damage helps towards critical pre-earthquake safety decisions regarding replacement or setting up appropriate retrofit strategy for the bridge with an objective of minimizing life and socio-economic losses during future earthquakes. This paper reviews the past studies on vulnerability assessment of various existing bridge types and configurations through the generation of analytical fragility curves and summarizes the various steps involved in different methodologies. Generation of fragility function is one of the key components of seismic vulnerability assessment. Past studies reveal that realistic fragility estimates are obtained through detailed analysis of bridge-foundation-soil system, reliable definition and quantification of damage states and identification of an optimal earthquake intensity measure corresponding to the particular bridge structural configuration and site-specific earthquake hazard.
... However, in the present research, the effects of abutments are neglected in structural modeling because this paper is intended to focus on different subjects including directivity of records, different averaging methods and the use of 2D and 3D analysis. It is noted that similar abutment conditions have been used in many studies (e.g., [1,[35][36][37][38][39][40]). [41] except that the design spectrum given in the 2010 National Building Code of Canada (NBCC) [42] was adopted. ...
Inelastic dynamic analyses were carried out using 3D and 2D models to predict the mean seismic response of four-span reinforced concrete (RC) bridges considering directionality effects. Two averaging methods, including an advanced method considering displacement direction, were used for the prediction of the mean responses to account for different incident angles of ground motion records. A method was developed to predict the variability of the mean displacement predictions due to variability in the incident angles of the records for different averaging methods. When the concepts of averaging in different directions were used, significantly different predictions were obtained for the directionality effects. The accuracy of the results obtained using 2D and 3D analyses with and without the application of the combination rules for the prediction of the mean seismic demands considering the incident angle of the records was investigated. The predictions from different methods to account for the records incident angles were evaluated probabilistically. Recommendations were made for the use of the combination rules to account for the directivity effects of the records and to predict the actual maximum displacement, referred to as the maximum radial displacement.
... They founded that the ductility demand of the shorter column of the irregular bridge B213 was remarkably larger than that of the regular bridge. This irregular bridge then has been widely used as a benchmark reference bridge (Akbari, 2012;Ghassemieh et al., 2018;Kappos et al., 2002;Maalek et al., 2009), therefore in this study is called "reference bridge". ...
... They compared maximum seismic demands of the regular and irregular models and concluded that the seismic displacement demand is significantly affected by the heights of the piers. Akbari (2012) generated analytical fragility curves for a class of highway bridges with continuous span and different degrees of irregularity. It has been concluded that the short piers and the irregular models are more vulnerable to seismic excitations. ...
The effects of earthquake incidence angle on the seismic fragility of highway bridges of unequal pier heights are investigated. A variety of configurations from regular to so-called highly irregular models are considered. In order to accurately quantify the uncertainties in the modeling process, the most influential sources related to the material properties, earthquake characteristics and structural geome-tries are considered in the nonlinear simulation. Several three-dimensional bridge models are simulated in OpenSees platform, and a set of strong ground motion records are employed in a series of nonlinear time history analyses of the bridge models. Different incidence angle of the records have been used to investigate the response of the models and to extract the most critical engineering demand parameters. The system and component fragility parameters are developed and compared for different values of the excitation angles for all the bridge models. Given the wide range of variables used here, a conversion coefficient is proposed to convert the bridge response for different incidence angles to critical response. ARTICLE HISTORY
... The resulting plot of the fragility model, termed fragility curve, has been widely used to date. Besides its traditional and extensive use in Earthquake Engineering for performance-based assessment of building structures (Ellingwood et al., 2007;Kappos and Panagopoulos, 2010;Kirc xil and Polat, 2006) or bridge structures (Akbari, 2012;Billah and Alam, 2015;Nielson and DesRoches, 2007;Shinozuka et al., 2000;Zhong et al., 2012), fragility analysis has been employed in assessing structural performance due to other types of hazards. These efforts, to name a few, include the vulnerability of structures due to tsunami (Koshimura et al., 2009), flooding (Van de Lindt and Taggart, 2009), wind (Lee and Rosowsky, 2005) and technological hazards such as blast (Olmati et al., 2014). ...
Fragility analysis is often employed to evaluate the vulnerability of structures subject to strong earthquakes, and in recent years, it further becomes one of the basic components for assessing the seismic resilience of civil structures and infrastructure systems. For river-crossing bridges that are exposed to both strong earthquakes and flooding events, a significant risk to bridge structures is the conjunct effects of seismic excitation and bridge scour. However, how to consider scour as a secondary hazard in performing fragility analysis and how to achieve balance among physical complexity, simplification and analytical rigour are not fully addressed in the literature. Extended from the traditional fragility modelling and incremental dynamic seismic analysis, a scour-dependent empirical fragility modelling approach is proposed in this article. In the proposed model, the model parameters are associated with scour depths in terms of quadratic polynomials, which provide great flexibility to consider the complex effects of bridge scour. Numerical analysis based on a simple two-span bridge model with pile foundations demonstrates the effectiveness and accuracy of the proposed approach. The fragility surface generated in this work can be used to assess the seismic resilience of scoured bridge under earthquake loads.
... In the irregular bridge structure with unequal pier heights, the seismic demands for each pier are usually different, while the shortest pier being subjected to maximum demand (Bi & Hao, 2011;Frankie, 2013). Fragility curves of 18 different bridge configurations with different pier height are generated by Akbari (2012), and it is figured out that the shortest-piers of the irregular bridge are extensively damaged while the higher-piers remain elastic under the action of high-intensity earthquake based on the capacity/demand ratio approach. Jara, Galván, and Olmos (2013) proposed a seismic vulnerability procedure for an irregular isolated bridge, and the impacts of two earthquake sources with different fault characteristics are discussed for the first isolated bridge with varied substructure height from 46.05 m to 70.75 m in Mexico (Jara, Madrigal, Jara, & Olmos, 2013). ...
In this paper, probabilistic seismic demand analysis is adopted to investigate the seismic fragility of a certain typical irregular highway bridge in the Chinese western mountainous areas. Considering the uncertainties of ground motion and structural parameters, the sample library for seismic fragility analysis is constructed aided by Latin hypercube sampling method, and the nonlinear time history analysis for each sample is implemented to achieve the structural dynamic response under the seismic excitation. Moreover, the curvature ductility ratio and the relative displacement are regarded as the damage indexes for pier and bearing, respectively. Furthermore, the fragility nephograms for the whole piers and fragility curves for various critical sections with different damage states are obtained based on a lognormal distribution assumption and the reliability theory. Finally, the bridge system fragility curves are generated through the first-order reliability analysis method. Fragility curves obtained from the above proposed technique can be used to evaluate the seismic performance of irregular bridges, and it can lay a basis for post-earthquake damage assessment.
... Damage to bridges in different countries have been identified with force demand concentrations on certain piers of substructures composed by columns with different lengths causing an irregular lateral stiffness distribution. There are several studies of irregular bridges Fig. 1 Bridge irregularity type I supported on traditional elastomeric bearings that show the effects of the irregular pier heights in the seismic behavior of the system (Akbari 2010;Kappos and Panagopoulos 2002;Isakovic and Fischinger 2006). This study was motivated by the increasing use of isolation systems in bridges with these characteristics and the importance of quantifying the influence of the isolation parameters for improving the seismic response of bridges with height irregularities. ...
Bridge structures are usually built on irregular topographical surfaces which create substructures with different pier heights and non uniform stiffness distribution. Three irregularity types of typical reinforced concrete (RC) medium length bridges located in a high seismicity zone of Mexico, were analyzed aimed at determining the best strength and stiffness parameters of an isolation system. The isolation system is composed by lead rubber bearings (LRB) located on each pile and abutment. The variation of the bridge characteristics and the isolation parameters produced 169 models that were subjected to ten seismic records representative of the subduction zone in the Pacific Coast of Mexico. A total of 1690 nonlinear time history analyses (NLTHA) were carried out in longitudinal and transverse directions of the structures. The maximum pier drifts, bending moments and shear forces demands were analyzed to identify the best isolation properties for reducing the concentration of damage in one or two elements and for improving the structural behavior of irregular bridges. Additionally, the analysis of the seismic response of the bridges supported on traditional neoprene bearings was carried out.
This article is a parametric study of 315 reinforced concrete bridges including 45 straight and 270 curved bridges for different geometrical conditions in different layouts, which were stimulated by earthquake near-field records. Past experiences show that irregular bridges with skew angles exhibit more critical behavior when exposed to near-field records. For this reason, in current research the effect of parameters such as skew angle (α), degree of the curvature (β) and irregularity obtained for different ratios of the height of the middle columns of the bridge in three different layouts on the seismic performance of the bridge has been investigated by performing non-linear time history analysis. Bridges in all modeling types are designed according to AASHTO standard criteria. The results of different modeling types are compared with the base model (regular bridge without curvature and zero skew angle). The results show that the seismic behavior of the bridge is strongly influenced by the skew angle of the bridge deck and bridge curvature. It was also observed that the rate of impact of changes in the skew angle of the bridge compared to the changes in the curvature of the bridge and irregularity is more noticeable to change the seismic responses of the bridge. If it is necessary to build curved bridges, in order to avoid the occurrence of torsional breakage in the bridge columns, it is recommended that the curvature angle should be considered equal to 40 degrees at most, and even if possible, it is recommended to avoid building bridges with skew angle of more than 30 degrees.
This study aimed to understand the seismic performance of a typical reinforced concrete (RC) bridge considering number of aftershocks following a major earthquake. The primary objectives of this research are to compare the performance of RC bridge comparing mainshock only fragility and mainshock aftershocks sequence fragility and also evaluate the performance after a major earthquake and its aftershocks. Real suite of mainshock aftershock sequences were applied to perform Incremental dynamic analysis (IDA) in a nonlinear model of typical RC bridge in Nepal using Opensees and damage classification was done using Park-Ang damage index. Fragility curves and fragility surfaces were constructed using the probabilistic seismic demand model (PSDM) form IDA analysis. The results shows that there is underestimation of bridge fragility using only mainshock data for computing fragility curves. Also, the expected seismic performance of the bridge after a major earthquake and its aftershocks were computed using fragility surface with the concept of multi-hazard analysis.
This study presents a sampling-based reliability sensitivity analysis to identify the random variables that are most influential on the seismic reliability of a corroded reinforced concrete (RC) bridge bent. To this end, a nonlinear finite element (FE) model of a scaled RC bent is developed, which accounts for the corrosion initiation and pitting corrosion models, as well impact of corrosion on the cover concrete, core concrete, reinforcing bars, and bond-slip behavior considering underlying uncertainties. Ground motion records are selected using conditional spectrum (CS) method. Pushover analysis is conducted on RC bent in discrete time points to evaluate the corrosion-dependent drift limit for different damage states. Seismic reliability analysis of the RC bent is conducted using Monte Carlo sampling (MCS) method in different damage states and time points. Results indicate the severe decrease in the seismic reliability index of the RC bent after 30 years of exposure to chloride, especially in the higher damage states. Finally, importance vectors are developed based on sensitivity analyses. The obtained results demonstrate that the importance of underlying random variables depends on the corrosion level and intended damage state. The obtained importance vectors show that the random variable related to the seismic input is the most influential variable on the seismic reliability of the corroded RC bent. It is also found that variables related to corrosion initiation time contribute the most to the seismic reliability of the RC bent in the first 15 years, while in the last 15 years the structural variables are the important ones.
This paper aims to evaluate the seismic vulnerability of a RC bridge pier using analytical approach that involves numerical modelling of structure, nonlinear analyses on the model and preparation of damage ranks for different damage states. In addition, simplified method to develop fragility curves for a typical highway bridge pier using nonlinear modelling at element and material levels has been discussed in this study. An existing two-span PSC box girder bridge has been chosen to carry out the analysis. Beam with hinges model for element modelling, reinforcing steel and concrete 01 models have been adopted for steel and concrete materials, respectively. Nonlinear static analysis and time history analyses were carried out to evaluate the capacity of pier, and corresponding responses of pier were studied under different ground motion intensities. By assuming log-normal distribution, fragility curves were constructed in longitudinal and transverse directions. In longitudinal direction, the probability of exceeding slight, moderate and extensive damage states is 73.9%, 65.2% and 58.5%, respectively, at 2.5 g (g = 9.81 m/s2) peak ground acceleration (PGA) and the probability of collapse at 2.5 g is 50%. In transverse direction, the probability of exceeding slight, moderate and extensive damage states is 91.7%, 98.2% and 80.75%, respectively, at PGA 3 g, and the probability of collapse is 59.8% in this direction. This simplified method discussed in the present study is useful to construct fragility curves for bridges in India which fall in the same group and similar characteristics. Fragility curves are particularly useful in assessing the seismic vulnerability of bridge piers in highly seismic-prone areas of India where seismic retrofit of bridges and pre-earthquake planning are becoming more prevalent.
Concrete bridge piers reinforced with conventional steel bars experience large permanent (residual) deformation that may lead to uneconomical repair or demotion of bridges due to their non-functionality post strong seismic event. Thus, sufficiently ductile materials are required to reinforce concrete bridge piers in the plastic hinge zone in order to limit their permanent damage and deformation post-earthquake event. Previous studies showed that partial replacement of conventional steel reinforcement bars with superelastic shape memory alloy (SMA) bars in the plastic hinge zone of concrete bridge piers has the capacity to limit the residual deformation owing to the superior self-centering properties of SMA bars. In this study, the efficacy of hybrid SMA/steel reinforcement for hollow section concrete bridge piers under combined reverse cyclic and constant axial loading is numerically investigated for the first time. The responses of the piers were evaluated in terms of different performance indices including hysteretic characteristics, residual deformation, energy dissipation capacity, and self-centering capacity. A sensitivity analysis was used to explore the main effects of key design parameters and their interactions on each performance index at four damage states, namely, complete, extensive, moderate, and slight damage states. The results of this study demonstrate the effectiveness of hybrid SMA/steel reinforcement for enhancing the seismic behavior of hollow section concrete bridge piers.
Seismic response of 9 regular and irregular four-span RC bridges with different configurations was studied using elastic and inelastic time history analyses. The influence of using different approaches for applying the ground motion records, considering the interaction of the orthogonal horizontal components of the ground motion records and their incident angles, was investigated. For this purpose, the records were applied to the structural models using three different methods and the results were compared. To investigate the influence of the directivity of the records on the mean seismic response, the records were applied at 19 different incident angles. The use of the 100–30 combination rule for prediction of the maximum response was also investigated. In addition, the results from linear and nonlinear analyses were compared and the maximum ductility demands and drift ratios were predicted. The results indicated that as the irregularity of the bridges increased, the seismic response became more coupled in the two principal directions and also became more sensitive to the incident angle of the records. It was also shown that when the mean seismic response was considered, the results were less sensitive to the incident angle compared to the case that the response from the individual records was considered.
This paper investigates the effects of the nonlinear behaviour of isolation pads on the seismic capacity of bridges to identify the parameters of base isolation systems that can be used to improve seismic performance of bridges. A parametric study was conducted by designing a set of bridges for three different soil types and varying the number of spans, span lengths, and pier heights. The seismic responses (acceleration, displacement and pier seismic forces) were evaluated for two structural models. The first model corresponded to the bridges supported on elastomeric bearings with linear elastic behaviour and the second model simulated a base isolated bridge that accounts for the nonlinear behaviour of the system. The seismic demand was represented with a group of twelve real accelerograms recorded on the subduction zone on the Pacific Coast of Mexico. The nonlinear responses under different damage scenarios for the bridges included in the presented study were estimated. These results allow determining the seismic capacity of the bridges with and without base isolation. Results show clearly the importance of considering the nonlinear behaviour on the seismic performance of bridges and the influence of base isolation on the seismic vulnerability of medium size bridges.
With the continuous improvement and development of highways and railways in western China, a large number of continuous rigid frame bridges have been built. In order to explore the response mechanism of tall pier and long-span continuous rigid frame bridges under earthquake, this study takes Wolonggou Bridge as the research object. The fragility under the action of horizontal and vertical earthquakes is studied in detail by the method of theoretical and numerical simulation. The results show that the damage of the pier exceeds the maximum probability under the action of longitudinal and transverse earthquakes. Under the longitudinal earthquake, the damage probability of the pier bottom is greater than that of the top. Under the transverse earthquake, the highest probability of damage occurs near the bottom of the pier.
Bridges are commonly used lifelines; they play an important role in the economic activity of a city or a region and their role can be crucial in a case of a seismic event since they allow the arrival of the first aid. Reinforced concrete (RC) bridges are worldwide used type view their durability, flexibility and economical cost. In fact, their behavior under seismic loading was the aim of various studies. In the present study the effect of two structural parameters i.e. the height and the type of piers of reinforced concrete bridges on seismic response is investigated. For that reason, different multi-span continuous girder bridges models with various geometrical parameters are considered. Then, non-linear dynamic analyses are performed based on two types of piers which are: multiple columns bent and wall piers with varying heights. In this approach, a serie of 40 ground motions records varying from weak to strong events selected from Building Research Institute (BRI) strong motion database are used including uncertainty in the soil and seismic characteristics. Modelling results put most emphasis on the modal periods and responses of the top pier displacements, they show the influence of the considered parameters on the behavior of such structures and their impact on the strength of reinforced concrete bridges.
This paper presents an up-to-date state-of-the-art review on the behaviour of irregular bridges under seismic excitation. Although several characteristics and definitions may be applicable to the regularity of bridge structures, almost all the published literature referencing the term ‘irregular bridge’ focuses on a specific class of straight reinforced concrete (RC) bridge with unequal pier heights as the main source of irregularity along the bridge length. Several successive as well as interrupted research works on the subject have been reported during the last two decades. Among significant developments under continuous progress in this field, two main advancements can be recognised: (a) the development of displacement-based design methodology; (b) further understanding of the higher modes effects, which reflects the adequacy of different analysis methods for irregular bridges. However, a review of the literature reveals that works being actively conducted on this subject are still inadequate and hence deserve further attentions in future researches to gaining a better awareness of the seismic performance of irregular bridges, in order to provide simply applicable and more definitive guidelines for actual design purposes.
Curved bridges provide a vital benefit to the nation's infrastructure system by allowing for accessibility and ease of transition in irregular highway layouts. Curved bridges using straight prestressed concrete I-girders with curved decking can fulfill this need. A number of such bridges have been constructed both in seismically and nonseismically active zones. This paper determines the seismic vulnerability sensitivity of the bridges with vastly different configurations via use of conventional fragility-assessment techniques. Experimental design established a statistical setting using core variables to produce a wide variety of hypothetical bridges to represent both as-built and proposed bridge configurations. Each bridge was designed following the strength and serviceability limit states stipulated by current bridge design specifications. As part of the sensitivity analysis, nonlinear time history analyses (NLTHAs) using numerous synthetic ground motions were performed to establish seismic demands on critical bridge components. Using probabilistic seismic demand models (PSDMs), component and system-level fragility curves were generated. The resulting fragility data were scrutinized to explore the effects of the different design parameters on seismic vulnerability of the bridges. The results indicate that the shorter-span bridges with a tighter radius of curvature are less sensitive to seismic excitations than those with straighter decking, indicating that a span length-to-radius of curvature ratio (S/R) for both single and multispan bridges is statistically determined to be the most influential parameter.
Based on recent findings, the main span of the Vincent Thomas suspension bridge crosses directly over the Palos Verdes fault, which has the capacity to produce a devastating earthquake. In spring 2000, the bridge underwent a major retrofit using visco-elastic dampers. This study focuses on seismic vulnerability of the retrofitted bridge. Three-dimensional member-based detailed and panel-based simplified finite element models of the bridge are developed. In order to show the appropriateness of these models, eigenproperties of the bridge are evaluated and compared with the system identification results obtained using ambient vibration data. In addition, a model validation is performed by simulating the dynamic response during the 1994 Northridge earthquake and comparing with the measured response. Finally, considering a set of strong ground motions in the Los Angeles area, nonlinear time history analyses are performed and the ductility demands of critical sections are presented in terms of fragility curves. The study shows that a ground motion with peak ground acceleration of 0.9 g or greater will result in plastic hinge formation at one or more locations with a probability of exceedance of 50%. Also, it is found that the effect of dampers is minimal for low to moderate earthquakes and high for strong earthquakes.
Safety and serviceability of highway bridges, during and after an earthquake, is a prerequisite to ensure continuous transport facilities, emergency and evacuation routes. Recently, fragility curves have emerged as important decision support tools to identify the potential seismic risk and consequences during and after an earthquake. There has been a substantial increase in interest among researchers in the topic of seismic fragility assessment of highway bridges as evidenced by the growing number of published literature. Advanced computational techniques and available resources have led to the development of different methodologies for fragility assessment. This study presents a review of the different methodologies developed for seismic fragility assessment of highway bridges along with their features, limitations and applications. This study presents a review of available methodologies and identifies opportunities for future development. This study mainly focuses on the key features of different methods and applications rather than penetrating down to a critique of the associated analysis procedure or mathematical framework. It synthesises the existing information on fragility analysis, presents it in concise and useful tables, and explains different applications for different purposes, which would motivate decision-makers and stake holders to extend the application of fragility curves for more informed decision-making.
The optimal decisions to maintain or improve the reliability and functionality of structures and infrastructure systems can only be achieved through proper integrated management planning in a life-cycle comprehensive framework. Structure and Infrastructure Engineering (SIE) is an international journal dedicated to recent advances inmaintenance, management, and life-cycle performance of a wide range of infrastructures. The purpose of this article is to provide a brief review of the recent research accomplishments in the field of design, maintenance, life-cycle management, and optimisation of structures and infrastructures reported in papers published in SIE during the period 2005–2011. The papers are categorised under main topics and very briefly discussed.
Cyclic response of a class of reinforced concrete bridges with different degrees of irregularity in longitudinal direction has been investigated. Eighteen bridge configurations have been identified from regular to the so-called highly irregular models. The geometric irregularity in this class of bridges is assumed to vary with the height of the piers. Using non-linear fibre-based analytical models, the cyclic response curves have been generated for theindividual piers of each of these 18 bridge models. Discussions have been made about the imposition of the displacement ductility demand of the piers versus the bridge regularity. Comparison of the cyclic response curves shows that the most vulnerable bridges are the irregular ones, and a high level of damage and ductility demand is expected for the short piers of this class of bridges.
Six large-scale (1:2.5) bridge specimens have been constructed and are being tested pseudodynamically at the ELSA laboratory. The tests are being conducted in the framework of the activities of the integrated European programme of the pre-normative research in support of Eurocode 8 involving eighteen research institutions from the European Union. The results obtained for the first part of the testing (regular and irregular bridges with different reinforcement arrangements) as well for a cyclic test of a squat pier are presented.
Fragility curves for expressway structures in Japan were proposed based on actual damage data from the 1995 Hyogoken-Nanbu (Kobe) Earthquake. First, spatial distributions of strong motion indices, e.g., the peak ground acceleration, the peak ground velocity, the JMA seismic intensity, were estimated using Kriging technique, in which attenuation relations of these indices are considered as trend components. The actual damage data for expressway structures in Japan were compared with these estimated ground motion indices and then fragility curves were constructed assuming log-normal distributions. The proposed fragility curves may be used in damage estimation of expressway structures in Japan due to earthquakes.
This paper presents a formal probabilistic framework for seismic design and assessment of structures and its application to steel moment-resisting frame buildings. This is the probabilistic basis for the 2000 SAC Federal Emergency Management Agency ~FEMA! steel moment frame guidelines. The framework is based on realizing a performance objective expressed as the probability of exceeding a specified performance level. Performance levels are quantified as expressions relating generic structural variables ''demand'' and ''capacity'' that are described by nonlinear, dynamic displacements of the structure. Common probabilistic analysis tools are used to convolve both the randomness and uncertainty characteristics of ground motion intensity, structural ''demand,'' and structural system ''capacity'' in order to derive an expression for the probability of achieving the specified performance level. Stemming from this probabilistic framework, a safety-checking format of the conventional ''load and resistance factor'' kind is developed with load and resistance terms being replaced by the more generic terms ''demand'' and ''capacity,'' respectively. This framework also allows for a format based on quantitative confidence statements regarding the likelihood of the performance objective being met. This format has been adopted in the SAC/FEMA guidelines.
Seismic fragility relationships, including the soil–structure interaction (SSI) of a common bridge configuration in central and eastern USA, are derived in this study. Four different modelling methods are adopted to represent abutments and foundations of the bridge, namely, (a) fixed abutments and foundations, (b) lumped springs developed from conventional pile analysis of piles at abutments and foundations, (c) lumped springs developed from three-dimensional finite element (3D FE) analysis of abutments and foundations and (d) 3D FE models. Seismic demand on the bridge components is estimated from inelastic response history analysis of the SSI systems. Finally, fragility curves of the components and bridge system are derived. The four different SSI approaches result in different seismic fragility. The implication of this work is that careful consideration is necessary when selecting an analytical representation of a soil and foundation system to obtain reliable earthquake impact assessment. In addition, it is found that abutment bearings are the most critical components for the studied bridge configuration.
A structure is considered to be irregular in this paper if its response is influenced considerably by higher modes. Herein, the effects of the higher modes on the geometric regularity of single-column-bent viaducts have been investigated by comparing modal parameters resulting from the elastic eigenvalue modal analysis with transverse displacements obtained from static modal pushover analyses. A class of bridges with equal span lengths, but with different pier heights has been considered in this study. For a better identification of the modal behaviour of this class of bridges, several regularity indices are discussed. Some of these indices were used previously in model updating, model validation and the determination of modal correlations in the field of experimental vibration analysis (modal testing) of mechanical and structural systems. Certain modifications have been applied to previous works in order to improve bridge regularity indices. New indices have also been proposed for the attainment of a more realistic representation of the structural particulars of such bridges to be consistent with the analytical methods addressed in the AASHTO Specifications, for practical design purposes. The results calculated with the aid of various indices are reported and compared.
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.
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.
Traditional pushover analysis is performed subjecting the structure to monotonically increasing lateral forces with invariant distribution until a target displacement is reached; both the force distribution and target displacement are hence based on the assumption that the response is controlled by a fundamental mode, that remains unchanged throughout.
However, such invariant force distributions cannot account for the redistribution of inertia forces caused by structural yielding and the associated changes in the vibration properties, including the increase of higher‐mode participation. In order to overcome such drawbacks, but still keep the simplicity of using single‐run pushover analysis, as opposed to multiple‐analyses schemes, adaptive pushover techniques have recently been proposed.
In order to investigate the effectiveness of such new pushover schemes in assessing bridges subjected to seismic action, so far object of only limited scrutiny, an analytical parametric study, conducted on a suite of continuous multi‐span bridges, is carried out. The study seems to show that, with respect to conventional pushover methods, these novel single‐run approaches can lead to the attainment of improved predictions. Copyright © 2007 John Wiley & Sons, Ltd.
The trend of isolating highway bridges is on the rise after the recent large earthquakes in Japan, the United States, and other countries. Recent investigation shows that isolated systems perform well against seismic forces as the substructures of such systems experience less lateral forces due to energy dissipation of the isolation device. Hence, it is anticipated that there might be an effect on fragility curves of highway bridges due to isolation. In this study, 30 isolated bridge models were considered (and they were designed according to the seismic design code of highway bridges in Japan) to have a wider range of the variation of structural parameters, e.g. pier heights, weights, and over-strength ratio of structures. Then, fragility curves were developed by following a simplified procedure using 250 strong motion records, which were selected from 5 earthquake events that occurred in Japan, the USA, and Taiwan. It is observed that the level of damage probability for the isolated system is less than that of the non-isolated one for a lower level of pier height. However, having the same over-strength ratio of the structures, the level of damage probability for the isolated system is found to be higher for a higher level of pier height compared to the one of the non-isolated system. The proposed simple approach may conveniently be used in constructing fragility curves for a class of isolated bridge structures in Japan that have similar characteristics.
A set of fragility curves for the bridges commonly found in the Central and Southeastern United States (CSUS) is presented. Using the results of an inventory analysis of the typical bridges in the CSUS, four typical bridge types are identified. Using nonlinear analytical models, and a suite of synthetic ground motions, analytical fragility curves are developed for the four bridge types. The fragility curves were first generated for the individual components of each of the bridge types and then, they were combined into fragility curves that represent the entire bridge system using first-order reliability principles. The fragility curves show that the peak ground acceleration for a 50% probability of exceeding slight damage ranges from approximately 0.19 to 0.24 g for the four bridge types. Comparison of the fragility curves shows that the most vulnerable bridge types are the multi-span simply supported and multi-span continuous steel-girder bridges. The least vulnerable bridge is the multi-span continuous pre-stressed concrete-girder bridge. The developed fragility curves can be used for economic loss estimation as well as a basis for assigning retrofit prioritization for bridges. This is particularly useful in the Central and Southeastern United States where seismic retrofit of bridges is becoming more prevalent.
Past earthquakes, such as the 1971 San Fernando earthquake, the 1994 Northridge earthquake, the 1995 Great Hanshin earthquake in Japan, and the 1999 Chi-Chi earthquake in Taiwan, have demonstrated that bridges are vulnerable to earthquakes. The seismic vulnerability of highway bridges is usually expressed in the form of fragility curves, which display the conditional probability that the structural demand (structural response) caused by various levels of ground shaking exceeds the structural capacity defined by a damage state. Fragility curves of structures can be generated empirically and analytically. Empirical fragility curves are usually developed based on the damage reports from past earthquakes, while analytical fragility curves are developed from seismic response analysis of structures and the resulting fragility curves are verified with actual earthquake data, if available. Since earthquake damage data are very scarce in the central and eastern United States, the analytical method is the only feasible approach to develop fragility curves for structures in this region. This report presents an analytical method for the development of fragility curves of highway bridges. In this method, uncertainties in the parameters used in modeling ground motion, site conditions, and bridges are identified and quantified to establish a set of earthquake-site-bridge samples. A nonlinear time history response analysis is performed for each earthquake-sitebridge sample to establish the probabilistic characteristics of structural demand as a function of a ground shaking parameter, for example, spectral acceleration or peak ground acceleration. Furthermore, bridge damage states are defined and the probabilistic characteristics of structural capacity corresponding to each damage state are established. Then, the conditional probabilities that structural demand exceeds structural capacity are computed and the results are displayed as fragility curves. The advantage of this approach is that the assessment of uncertainties in the modeling parameters can be easily verified and refined. To illustrate the proposed method, the method is applied to a continuous concrete bridge commonly found in the highway systems affected by the New Madrid seismic zone. National Science Foundation EEC-9701785
Several definitions have been used concerning structural regularity. A structure is considered here as regular, if its responses obtained from different well recognized analysis methods do not show significant differences. In this paper, the effects of the inclusion of higher modes on the response of a class of reinforced concrete viaducts with different degrees of irregularity have been investigated. The seismic responses of continuous span single-column-bent viaducts have been studied through the comparison of the results obtained from different pushover-based analysis methods. Commonly used single and multi-mode pushover-based analysis methods have been utilized and their corresponding results have been compared with the results obtained from simpler methods such as the so-called uniform load procedure, as well as the more sophisticated inelastic time history analysis methods. For the class of the bridges under consideration, those configurations for which the effects of the higher modes are considerable have been identified and categorized as irregular, for which the minimum analysis requirements have been indicated in order to achieve a reliable bridge response. In contrast, the conditions in which a configuration may be classified as regular have been demonstrated and the adequacy of the simplified methods for the analysis of such models has been examined. The regularity issue has been discussed initially based on an expression developed by other researchers. Another index has also been introduced here for the attainment of a more realistic representation of the structural particulars of such bridges consist with the analysis methods specified in the AASHTO Specifications.
A stress‐strain model is developed for concrete subjected to uniaxial compressive loading and confined by transverse reinforcement. The concrete section may contain any general type of confining steel: either spiral or circular hoops; or rectangular hoops with or without supplementary cross ties. These cross ties can have either equal or unequal confining stresses along each of the transverse axes. A single equation is used for the stress‐strain equation. The model allows for cyclic loading and includes the effect of strain rate. The influence of various types of confinement is taken into account by defining an effective lateral confining stress, which is dependent on the configuration of the transverse and longitudinal reinforcement. An energy balance approach is used to predict the longitudinal compressive strain in the concrete corresponding to first fracture of the transverse reinforcement by equating the strain energy capacity of the transverse reinforcement to the strain energy stored in the concrete as a result of the confinement.
This paper presents a statistical analysis of structural fragility curves. Both empirical and analytical fragility curves are considered. The empirical fragility curves are developed utilizing bridge damage data obtained from the 1995 Hyogo-ken Nanbu (Kobe) earthquake. The analytical fragility curves are constructed on the basis of the nonlinear dynamic analysis. Two-parameter lognormal distribution functions are used to represent the fragility curves with the parameters estimated by the maximum likelihood method. This paper also presents methods of testing the goodness of fit of the fragility curves and estimating the confidence intervals of the two parameters (median and log-standard deviation) of the distribution. An analytical interpretation of randomness and uncertainty associated with the median is provided.
A model for evaluating structural damage in reinforced concrete structures under earthquake ground motions is proposed. Damage is expressed as a linear function of the maximum deformation and the effect of repeated cyclic loading. Available static (monotonic) and dynamic (cyclic) test data were analyzed to evaluate the statistics of the appropriate parameters of the proposed damage model. The uncertainty in the ultimate structural capacity was also examined.
This paper presents a procedure for the evaluation of the expected seismic damage to bridges and highway systems in Memphis and Shelby County, Tenn. Data pertinent to 452 bridges and major arterial routes were collected and implemented as a geographic information system database. The bridges were classified into several bridge types using a bridge classification system modified from the NBIS/Federal Highway Administration coding guidelines. The bridge damage states considered are no/minor damage, repairable damage, and significant damage. The fragility curves corresponding to these damage states were established for various bridge types. Given an earthquake with a moment magnitude of 7.0 occurring at Marked Tree, Ark., the intensity of ground shaking and liquefaction-induced permanent ground deformation in Memphis and Shelby County were estimated, and then the expected damage to bridges and highway systems was determined. The results can be used to prioritize bridges for retrofitting, to prepare a pre-earthquake preparedness plan, to develop a postearthquake emergency response plan, and to assess the regional economic impact from the damage to highway transportation systems.
This paper describes an analytical method to construct fragility curves for highway bridge piers considering both structural parameters and variation of input ground motion. A typical bridge structure was considered and its piers were designed using the seismic design codes in Japan. Based on PGA and PGV, earthquake records were selected from the 1995 Hyogoken-Nanbu earthquake. Using the records as input ground motion, nonlinear dynamic response analyses were performed and the damage indices for the RC bridge piers were obtained. Using the damage indices and ground motion indices, fragility curves for the bridge piers were constructed. The fragility curves constructed following this approach were then compared with the empirical fragility curves.
The latest developments of a methodology developed by the authors and their co-workers for estimating direct losses from earthquakes in reinforced concrete (R/C) buildings are presented; they concern the derivation of capacity curves and vulnerability (fragility) curves in terms of peak ground acceleration (PGA), as well as spectral displacement, for all types of R/C buildings that are common in Greece. The vulnerability assessment methodology is based on the hybrid approach, which combines statistical data with appropriately processed results from nonlinear dynamic or static analyses that permit interpolation and (under certain conditions) extrapolation of statistical data to PGAs and/or spectral displacements for which no data is available. A detailed discussion of the limitations of the hybrid approach is provided, along with a proposal for improving the quality of results by applying a weighting technique to both the analytical and the statistical input data.
The influence of the higher modes and their consideration in the pushover analysis of reinforced concrete single column bent viaducts with different degree of irregularity is discussed. Typical multimode pushover-based methods (modal pushover analysis, modal adaptive non-linear static procedure and incremental response spectrum analysis) are addressed and compared with a single mode procedure (N2) and inelastic time history analysis.
If in the transverse direction the substructure of the viaduct is flexible in comparison with the superstructure, the influence of higher modes is small (the structure is regular) and single mode procedure works well. This typically occurs when the columns are high or considerably damaged. Conversely, for the analysis of irregular structures having short and slightly damaged columns, the multimode methods are needed. In most cases, all the analysed multimode pushover-based methods have given the results comparable with time history analysis, with the exception of cases where torsional sensitivity is varying during the response. All the methods have limitations (discussed in detail in the paper), which should be fully recognized by the user. Copyright
Bridge fragility curves, which express the probability of a bridge reaching a certain damage state for a given ground motion parameter, play an important role in the overall seismic risk assessment of a transportation network. Current analytical methodologies for generating bridge fragility curves do not adequately account for all major contributing bridge components. Studies have shown that for some bridge types, neglecting to account for all of these components can lead to a misrepresentation of the bridges' overall fragilities.
In this study, an expanded methodology for the generation of analytical fragility curves for highway bridges is presented. This methodology considers the contribution of the major components of the bridge, such as the columns, bearings and abutments, to its overall bridge system fragility. In particular, this methodology utilizes probability tools to directly estimate the bridge system fragility from the individual component fragilities. This is illustrated using a bridge whose construction and configuration are typical to the Central and Southeastern United States and the results are presented and discussed herein. This study shows that the bridge as a system is more fragile than any one of the individual components. Assuming that the columns represent the entire bridge system can result in errors as large as 50% at higher damage states. This provides support to the assertion that multiple bridge components should be considered in the development of bridge fragility curves. The findings also show that estimation of the bridge fragilities by their first‐order bounds could result in errors of up to 40%. Copyright © 2006 John Wiley & Sons, Ltd.
It is widely recognized that nonlinear time-history analysis constitutes the most accurate way to simulate the response of
structures subjected to strong levels of seismic excitation. This analytical method is based on sound underlying principles
and has the capability to reproduce the intrinsic inelastic dynamic behavior of structures. Nonetheless, comparisons with
experimental results from large-scale testing of structures are still needed, in order to ensure adequate levels of confidence
in this numerical methodology. The fiber modelling approach employed in the current endeavor inherently accounts for geometric
nonlinearities and material inelasticity, without a need for calibration of plastic hinges mechanisms, typical in concentrated
plasticity models. The resulting combination of analysis accuracy and modelling simplicity, allows thus to overcome the perhaps
not fully justifiable sense of complexity associated to nonlinear dynamic analysis. The fiber-based modelling approach is
employed in the framework of a finite element program downloaded from the Internet for seismic response analysis of framed
structures. The reliability and accuracy of the program are demonstrated by numerically reproducing pseudo-dynamic tests on
a four span continuous deck concrete bridge. Modelling assumptions are discussed, together with their implications on numerical
results of the nonlinear time-history analyses, which were found to be in good agreement with experimental results.
This work investigates the effect of a modelling approach, also including the interaction phenomenon between supporting ground and the pier plus deck system, on the seismic response of reinforced concrete (R/C) bridges with irregular configuration, as well as its ramifications on the design of the piers. The focus is on a four span highway bridge with piers of unequal height crossing a mountain valley. The bridge and its foundation system, including the surrounding soil, are modelled by finite elements plus the spring/dashpot/added mass discrete parameter system. A hierarchy of finite element meshes is developed, starting with shell elements, and ending with linear elements whose performance as far as dynamic loads are concerned is gauged to be completely satisfactory. Moreover, two basic types of foundations are examined, namely spread footings versus pile groups. Following a preliminary design of the bridge, a series of time history analyses of the combined deck–pier–foundation system are performed, the results of which are used in assessing the influence of foundation compliance on the superstructure. Furthermore, the influence of key construction details such as pier–to–deck connection on the dynamic displacement and force fields that develop, is also examined. Finally, a series of recommendations are given on when and how to account for the influence of the ground in the design of the piers.
This study represents results of fragility curve development for two (2) sample bridges typical in southern California, strengthened for seismic retrofit by means of steel jacketing of bridge columns. Monte Carlo simulation is performed to study nonlinear dynamic responses of the bridges before and after retrofit. Fragility curves in this study are represented by lognormal distribution functions with two parameters and developed as a function of PGA. The improvement in the fragility due to the retrofit is quantified by comparing fragility curves of the bridge before and after retrofit. In order to formulate the problem of fragility enhancement, the quantification is made by comparing the median values of the fragility curves before and after the retrofit. Under the hypothesis that this quantification also applies to empirical fragility curves developed on the basis of Northridge earthquake damage, the enhanced version of the empirical curves is developed.
This study presents a probability density function (PDF) interpolation technique for the evaluation of seismic fragility curves as a function of the return period. Seismic fragility curves have been developed in terms of various seismic intensities, such as the peak ground acceleration (PGA), peak ground velocity and pseudovelocity spectrum. However, of these seismic intensity measures, the return period of design earthquakes is more useful, as seismic hazard curves are generally represented with the return period of design earthquakes; seismic design codes also require consideration of the return period of the design earthquake spectrum for a specific site. Therefore, this paper focuses on the evaluation of seismic fragility curves as a function of the return period. Seismic fragility curves based on the return period are compared with those based on the PGA as an example bridge. The seismic fragility curves developed in this study make more intuitive sense for the design, retrofit and performance evaluation of bridges.
Seismic Fragility Analysis of Highway Bridges
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Seismic analysis and retrofit of mid-America bridges. Thesis (PhD) Department of Civil and Environ-mental Engineering, Georgia Institute of Technology Seismic fragility of typical bridges in moderate seismic zones
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Earthquake hazard reduction in existing reinforced concrete buildings and concrete frame buildings with masonry infills
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Seismic design and retrofitting of bridges SeismoStruct – a computer program for static and dynamic non-linear analysis of framed structures
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Influence of regularity on the seismic response of RC bridges. 2nd international workshop on seismic design and retrofitting of RC bridges
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Calvi, G.M., Elnashai, A.S., and Pavese, A., 1994. Influence of regularity on the seismic response of RC bridges. In: 2nd international workshop on seismic design and retro-fitting of RC bridges, 8–13 August, Queenstown, New Zealand, 80–89.
Seismic fragility and risk management of highway bridges in New York State. Thesis (PhD). The City University of
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Ying, P., 2007. Seismic fragility and risk management of highway bridges in New York State. Thesis (PhD). The City University of New York, New York. Structure and Infrastructure Engineering
Evaluation of bridge damage data from the Loma Prieta and
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Seismic Fragility Analysis of Highway Bridges. Center-to-center project workshop on earthquake engineering frontiers in transportation systems
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Develop suites of time histories project task: 5.4.1”. Draft report of joint venture steel project phase 2
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