SEISMIC FRAGILITY CURVES FOR SYSTEM AND INDIVIDUAL COMPONENTS OF MULTI-FRAME CONCRETE BOX-GIRDER BRIDGES

Transcription

1 0 0 SEISMIC FRAGILITY CURVES FOR SYSTEM AND INDIVIDUAL COMPONENTS OF MULTI-FRAME CONCRETE BOX-GIRDER BRIDGES Mohammad Abbasi PhD candidate, University of Nevada, Reno Dept. of Civil and Environmental Engineering. MS 0, Reno, NV mabbasi@nevada.unr.edu Mohamed A. Moustafa, Corresponding Author Assistant Professor, University of Nevada, Reno Dept. of Civil and Environmental Engineering. MS 0, Reno, NV Tel: --; Fax: --0; mmoustafa@unr.edu Word count:, words text + 0 tables/figures x 0 words (each) =, words Revised version submission date: November, 0

2 Abbasi, Moustafa 0 0 ABSTRACT Multi-frame reinforced concrete box-girder bridges are one of the most common bridge classes in California. The use of in-span hinges distinguishes multi-frame bridges from others and provides benefits of accommodating thermal expansion/contraction, creep, and post-tensioning while reducing additional forces in the bridge superstructure. However, some adverse conditions can be expected during earthquakes such as pounding of adjacent frames and deck unseating. To further investigate its seismic performance and risks, this study focused on developing system and individual components seismic fragility curves for four-span multi-frame reinforced concrete boxgirder bridges. Sources of variability and uncertainties associated with the ground motions and the structural geometries and materials were considered for a comprehensive assessment. In total, 00 analytical models were developed using OpenSees and randomly paired with a suite of 00 selected ground motions to perform nonlinear time history analysis. The system fragility curves were developed for four different damage states to be readily used for risk assessment and planning of new construction. Moreover, individual components fragility curves were developed and compared to provide a tool for prioritization and informed seismic retrofit decisions for existing bridges of this class. Keywords: Fragility curves; multi-frame box-girder bridges; nonlinear time history analysis.

3 Abbasi, Moustafa INTRODUCTION Fragility curves are conditional probability statements that give the likelihood that a structure will meet or exceed a specified level of damage for a given ground motion intensity measure (). Peak ground acceleration (PGA) is typically the considered intensity measure and conditioning parameter. Fragility curves provide a powerful tool for seismic assessment of structures by including different sources of uncertainties such as uncertainty in ground motions, geometry, or material. Fragility analysis can be more reliable than deterministic procedures as it is not limited to specified parameters and is more appropriate for evaluating, controlling and decreasing seismic risk. Thus, fragility analysis became vital for multiple applications such as rapid initial estimation of loss, supporting design strategies, retrofit prioritization for structural components, and optimizing design guidelines for safety, cost, and functionality. Such advantages of fragility analysis led to the development of several fragility curves for various bridge types and configurations. Previous studies (,,) developed analytical fragility curves for bridges in the Central and Southeastern United States (CSUS) and under ground motions with spatial variation (). Kim and Shinozuka () conducted fragility analysis to measure retrofit efficiency of bridges before and after piers steel jacketing. Karim and Yamazaki () examined the effects of base isolation on the fragility of highway bridges. Other studies (,,0) developed fragility curves for as-built (with and without seismic detailing) and retrofit bridge types in CSUS. Most of the CSUS fragility curves are not appropriate for susceptibility evaluation of bridges in California (CA) because of differences in bridge types, configurations, and design aspects, and there is no consensus between CSUS and CA bridge experts on the definition of limit states to support local risk evaluation and decision-making requirements. Thus, several studies were dedicated to developing fragility curves for CA bridges, but many of them were bridge specific (e.g.,). Bridge-specific fragility curves ignore the variability and uncertainties in bridge configurations and design parameters, which is desired for meaningful seismic reliability and performance evaluation (,). This study attempts to fill a knowledge gap by considering several sources of uncertainties to perform fragility analysis for a common CA bridge type that has not been thoroughly considered in previous studies. California bridges are categorized under thirteen main types. Multi-span reinforced concrete boxgirder bridges account for the bulk of the overall inventory. This is % of the state bridge inventory based on the regional database assembled by California Department of transportation (Caltrans). These consist of single and multiple frame bridges, with about % of the box-girder bridges having at least one in-span hinge that separates the bridge into two adjacent frames. The objective of this study is to develop system fragility curves and compare individual bridge components fragilities for CA four-span multi-frame RC box-girder bridges. For a thorough and advanced assessment, uncertainties associated with the earthquake, structural geometries, and materials are considered and nonlinear time history analysis (NTHA) is performed on D prototype bridges modeled in OpenSees (). The system fragility curves are developed considering the contribution of the columns and deck seating at the abutment and the in-span hinge as primary components, while other components such as elastomeric bearing pads, abutments, shear keys, and foundation as secondary components (-). PROBABILISTIC FRAGILITY FUNCTIONS The primary fragility statement offers the probability that the actual seismic demand on the structure reaches or exceeds the capacity which is dependent on the value of seismic intensity

4 Abbasi, Moustafa 0 measure (IM). Both the demand and capacity (resistance) are assumed to follow a log-normal distribution (,0,). Component fragility can be obtained using Equation : IM β β where, D and C are demand and capacity, SD and SC are the median values of the demand and the capacity, and βd IM and βc are the logarithmic standard deviation of the demand and the capacity, and Φ(.) is the standard normal cumulative distribution function. The estimation of the seismic demand (SD and βd IM) and capacity limit states (SC and βc) parameters is discussed next. Probabilistic Seismic Demand Models The relationship between the median demand and IM can be expressed as a power function () as shown in Equation : () where a and b are regression coefficients. The values of a and b can be determined by a linear regression of the demand-im pairs in the transformed space. The dispersion of the demand as a function of IM can be estimated based on Equation : () ln ln () 0 0 Thus, the fragility for any component of bridge can be determined by assigning a probability distribution for demand as a function of IM, typically expressed as probabilistic seismic demand model (PSDM), and combining it with the capacity distribution. According to Nielson and DesRoches (0), the estimation of system fragility curves is simplified by developing joint probabilistic seismic demand models (JPSDMs), realizing that the demands on the various components have some level of correlation during a given earthquake. The JPSDMs is developed by evaluating the demands placed on each component (marginal distribution) via regression analysis akin to the PSDMs. The correlation coefficients between the component demands are provided through applying the results of the NTHA. The resulting covariance matrix is then collected. Accordingly, the probability of system failure can be calculated by Monte Carlo simulation to compare JPSDM and component capacities. This procedure is repeated for various levels of IM in the different damage states. Finally, the lognormal parameters of the bridge system fragility can be evaluated by a regression analysis. Limit State Capacities Definition of the component capacities is one of controversial steps in the fragility formulation. Typically, component limit states are determined based on experimental studies on the various bridge components and thorough input from design and bridge maintenance groups. For this study, the bridge system and different components limit states were selected based on the study by Ramanathan () and in accordance to the qualitative damage state descriptions (Table a) presented in FEMA loss assessment package HAZUS-MH (). A lognormal distribution is assumed for individual components damage/limit states and characterized by representative values for the median, SC, and dispersion, βc, as summarized in Table b. Discrete damage states are defined for each component, which corresponds to significant changes in component and overall

5 Abbasi, Moustafa 0 0 global system performance. However, a continuous range of damage exists between the discrete states to enable the closed-form computation of the component fragility curves. According to some previous studies (e.g.,), the system fragility curves are developed by categorizing the components into primary and secondary members. Only the primary members play a major role in the vertical stability and load carrying capacity of the bridge. In this study, columns and deck seating at abutments and in-span hinges are considered to be the primary components. Other components, such as the elastomeric bearing pads, abutments, shear keys, and foundation, are less likely to affect the overall stability of the bridge and considered secondary components. Four damage criteria (DC) are considered in this study. These are: slight, moderate, extensive, and complete damage states, and are designated as DC, DC, DC, and DC, respectively. Primary components contribute to all four damage states, while secondary components contribute only to the slight and moderate damage states (Table ). TABLE Component damage criteria and limit states a. Damage state qualitative descriptions DC Aesthetic damage Primary DC Repairable minor functional damage Components DC Repairable major functional damage DC Component replacement Secondary DC Aesthetic damage/repairable minor functional damage Components DC Repairable major functional damage/component replacement Bridge Components b. Quantitative limit states DC DC DC DC Sc βc Sc βc Sc βc Sc βc Primary Column (µф ƾ ) Deck seating* (mm) Abut-p (mm) n/a n/a n/a n/a Abut-a (mm) n/a n/a n/a n/a Brg-Long&Trans # (mm) n/a n/a n/a n/a Secondary Shear key n/a n/a n/a n/a Foundation-dis (mm) n/a n/a n/a n/a Foundation-rot (rad) n/a n/a n/a n/a Deck-t (mm) n/a n/a n/a n/a ƾ Curvature ductility * Deck seating = Deck seating in the both the abutments and the in-span hinge Abut-p = Abutment passive deformation Abut-a = Abutment active deformation # Brg-Long &Trans = Elastomeric bearing deformation in the longitudinal and transverse directions Deck-t = Deck transverse displacement at both the in-span hinge and abutments BRIDGE CASE STUDY Bridge Description This paper considers a four-span multi-frame concrete box girder bridge with one in-span hinge, which is schematically shown in Figure. In this bridge class, the columns and the superstructure are monolithic via an integral bent cap. Elastomeric bearing pads are used at the seat-type abutments and the in-span hinge; the locations that exhibit the risk of increased pounding and deck unseating. It is noted that four spans are not the typical case for CA multi-frame bridges. However,

6 Abbasi, Moustafa 0 0 it is still representative of the key feature of multi-frame bridges, which is the relative motion between the different bridge frames. Based on the work done by Wang (), relative displacements of two adjacent frames of a multi-frame bridge can be developed by two parameters. The first is a dynamic component resulting from the inertia effects and vibration variation between the two adjacent frames, which is affected by factors such as the stiffness and the yield strengths of the frames, and impact on closing the joints. The second parameter is a pseudo static component due to the time delay between the vibrations of the adjacent frames, which is dominated by the out-ofphase vibration of the frames. Different bridge geometry and design parameters (e.g. spans, number of columns per bent, column diameter) are some of the variables and sources of uncertainties considered to cover different bridge cases. Each bent column is supported on a pile cap and a group of piles. Bridge design details are attributed to the early Caltrans classification period before () as shown for some components in Table a. The correlation between span lengths, column heights, number of columns per bent, and deck widths was defined according to previous studies (e.g.,,,) after generating 0 specified deck widths (Table b) by Latin-hypercube sampling (LHS) technique (). LHS is commonly adopted for variance reduction and provides an effective scheme to cover the probability space of the random variables when compared to pure random sampling using naïve Monte Carlo Simulation (). The selected geometries (Table ) are based on extensive review of bridge plans in California and is consistent with the national bridge inventory database (). Other bridge parameters and random variables are discussed in the next subsections. Abutment L L 0.L 0.L L Joint Seal Elastomeric bearing pad H H In-Span hinge H Frame Frame Piles (a) Longitudinal direction < Deck width < < Deck width < 0 (b) Cross-section FIGURE Schematic view of a representative prototype bridge.

7 Abbasi, Moustafa TABLE Bridge geometries and specifications considered in this study a. Selected component specifications Bridge seismic Column transverse Bearing Abutment Shear key Piles type design era reinforcement thickness seat width strength Pre- #@00 mm Cast in place mm 0 mm % b. Representative bridge geometry Case Number Span length [m] Deck width [m] Column height [m] # of Columns Bridges Analytical Modeling The analytical fragility curves are generated using NTHA of D analytical finite element models developed using OpenSees (), which involves geometrical and material nonlinearities. Nonlinear beam column elements with fiber-sections and distributed plasticity were assigned to the columns to capture their nonlinear hysteretic behavior. Rigid links were used to connect the column tops to the bent cap and the deck longitudinal elements. This study considered older bridge details, i.e. before capacity-protected superstructure design was introduced. However, the deck and bent cap from different design eras can still be assumed to remain essentially elastic during an earthquake based on previous studies (,,,,). Thus, linear/elastic beam-column elements with lumped mass were used to represent the bent cap, longitudinal deck elements, and dummy transverse deck rigid elements. The elements connections at the expansion joints and at the seattype abutment were represented using bi-linear sliding bearings and modeled by elastic-perfectly plastic springs. To account for the potential pounding at the abutments and in-span hinge locations, impact elements were considered (,) and modeled using a bilinear model developed by Muthukumar (0). Nonlinear springs were used to model the behavior of the abutments in both the transverse and longitudinal directions. In order to capture the response of the abutment back wall soil in passive response, the hyperbolic soil model recommended by Shamsabadi and Yan () was applied and added to the pile contributions. Since non-integral abutments are considered, tensile behavior of the abutment springs would have only a slight contribution from the piles. The effect of wing walls decreases as the width of the abutment increases (), and accordingly, the transverse resistance is assumed to be provided solely by the pile. A trilinear behavior is used to model the abutment piles response in the longitudinal and transverse direction based on the recommendations of Choi (). Since this study aims at developing fragility curves that are applicable across a wide geographic area, a range of soil profiles from soft to medium and stiff are considered. In order to determine the stiffness of translational springs, the foundation systems and the different soil profiles were modeled in LPILE (). Multi-column bents supported on piles are pinned at the base and therefore have no rotational stiffness. Translational springs are modeled using simple linear springs

8 Abbasi, Moustafa and were assigned to zero length elements at the base of the columns. For shear keys, a multilinear models based on the work done by Megally et al. () was considered. Shear keys are located at the seat-type abutments to limit movement along transverse direction. Figure illustrates the aforementioned OpenSees model features. 0 0 FIGURE Schematic representation of a typical D analytical OpenSees bridge model. Ground Motion Selection and Modeling Uncertainties The uncertainties in the various bridge modeling and analysis parameters include ground motions, geometric and material properties. Modeling parameters can significantly affect the fragility analysis accuracy, so detailed and extensive uncertainty treatment is addressed in this paper. A proper set of earthquakes is a critical step in the development of fragility curves. These records should contain a vast collection of different seismic intensities, earthquake magnitudes, and epicentral distance to better characterize the hazard uncertainties at the region of interest. For this study, a suite of 00 ground motions was adopted from Baker et al. () for the Pacific Earthquake Engineering Research Center (PEER) Transportation Research program. The set comprises 0 ground motions with strong velocity pulses, which is characteristic of sites experiencing near-fault directivity effects as in California. All the ground motions pertain to shallow crustal earthquakes with magnitude ranging from. to.. The incidence angle for each set of orthogonal horizontal component of ground motions and bridge sample is treated as a random variable and the vertical component of ground motions is ignored. This study focuses on a class of bridges rather than an individual bridge, so the intensity measure (IM) of choice is PGA (). When a proper suite of ground motions is chosen, a bridge model must be sampled. The probabilistic sampling of the bridge models allows for incorporating uncertainties such as those associated with material and geometric properties. In case of geometry, each bridge sub-class was produced by Latin-hypercube sampling. Other modeling parameters uncertainties included material strength, deck gap, mass, damping, and load direction, and were taken into account using

9 Abbasi, Moustafa Quasi-Monte Carlo sampling (). Quasi-Monte Carlo sampling is a technique used to sample random variables governed by probability density functions. It uses quasi-random (also known as low-discrepancy) sequences instead of random or pseudorandom sequences and, in turn, is more accurate than other sampling techniques. Table summarizes some of the uncertainties modeling parameters and their relevant probability distributions. Note that λ, μ are mean and ζ, σ are dispersion values in lognormal and normal distributions, respectively, while l and u are the lower and upper limits in uniform distribution, respectively. TABLE Random variables and distributions incorporated in the bridge modeling Modeling parameter Probability Distribution parameters distribution Ref. Steel yield strength [MPa] Lognormal λ =. ζ = 0.0 () Concrete unconfined strength [MPa] Normal μ =. σ =. () Elastomeric bearing shear modulus [MPa] Uniform l = 0. u =.0 () Coefficient of friction Lognormal λ = -0. ζ = 0. (,0) Piles translational stiffness [kn/mm/pile] Lognormal λ =. or. ζ = 0. Piles axial stiffness [kn/mm/pile] Lognormal λ =.0 or. ζ = 0. () Abutment passive initial stiffness [kn/mm/m] Uniform l =. u = () Damping Normal μ = 0.0 σ =. (,) Abutment gap [mm] Normal μ = 0. σ = () Mass Uniform l = 0. u =. () Loading direction [radians] Uniform l = 0 u = π () FRAGILITY ANALYSIS This study aims at developing system fragility curves in addition to all individual component fragility curves across each damage state for a four-span multi-frame RC box-girder bridge. For each of the selected 0 geometric configurations (Table ), 0 bridge model realizations were generated by changing the modeling parameters (Table ) using statistical sampling on their relevant distributions. This resulted in a total of 00 prototype bridges, which were randomly paired with the selected 00 ground motions. A full nonlinear time history analysis was performed for each of the 00 ground motion/bridge pairs. The highest demand placed on each bridge component was recorded. The bridge components considered in this study are the columns, abutments, bearings, shear keys, foundation, and deck seating at the abutment and the in-span hinge. A regression analysis of the obtained analysis data was used to evaluate the probabilistic seismic demand parameters (Equations and ). For brevity, only a sample of the regression analysis of the resulting seismic demands for two of the primary bridge components: columns and deck seating at the abutment is shown in Figures a and b, respectively. However, the probabilistic seismic demand parameters for all the components are summarized in Table for completeness. The table lists the regression coefficients (a and b), the dispersion (σ and also referred to as βd IM), and R that indicates accuracy of the regression. Based on the fragility analysis of different cases, the overall system fragility curves for the multiframe bridge were developed for the four damage states defined in the previous section. This study also developed component fragility curves across each damage state. The system and component fragility curves for the different considered damage states are shown in Figures and, respectively. Each fragility curve represents a lognormal distribution that is characterized by the median () and dispersion (logarithmic standard deviation, ) values, which are summarized in Table for the system and all individual components. A simple technique to compare differences

10 Abbasi, Moustafa 0 in the fragility curves is to evaluate the relative change in the median value of the fragility curves. A positive change indicates a less vulnerable structure while a negative change indicates a more vulnerable structure. TABLE Probabilistic Seismic Demand Parameters Components a b σ R column Abutment passive Abutment active Bearing- Transverse- Abutment Bearing- Longitudinal- Abutment Shear key Deck seating-abutment Foundation -displacement Foundation -rotation Deck- Transverse-Abutment Bearing- Longitudinal- Hinge Bearing- Transverse-Hinge Deck seating-hinge (a) (b) FIGURE Seismic demands for: (a) columns; (b) deck seating at the abutments P[LS PGA] Slight Moderate Extensive Complete PGA (g) FIGURE Multi-frame reinforced concrete box-girder bridge system fragility curves for different damage states.

11 Abbasi, Moustafa TABLE System and component fragility parameters Components DC DC DC DC ζ ζ ζ Overall System Column Deck seating-abutment Deck seating-hinge Abutment passive n/a n/a n/a n/a Abutment active n/a n/a n/a n/a * Bearing- T - Abutment n/a n/a n/a n/a * Bearing- L - Abutment n/a n/a n/a n/a * Bearing- T - Hinge n/a n/a n/a n/a * Bearing- L - Hinge n/a n/a n/a n/a Shear key n/a n/a n/a n/a Foundation -displacement n/a n/a n/a n/a Foundation -rotation n/a n/a n/a n/a * Deck- T - Abutment n/a n/a n/a n/a * Deck- T - Hinge n/a n/a n/a n/a *L-Abutment/ Hinge = Displacement along the longitudinal in the Abutment/ In-Span Hinge *T-Abutment/ Hinge = Displacement along the Transverse in the Abutment/ In-Span Hinge The system fragility curves for the four damage states are presented in Figure and then compared with individual component fragilities in Figure. In particular, Figures a and b show the fragility curves for slight and moderate damage states, respectively, for all primary and secondary components along with the overall system. Figures c and d show the fragility curves for the extensive and complete damage states, respectively, but only for the primary bridge components (columns and deck seating at the abutments and in-span hinges) and overall system. Figure a indicates that the deck seating at the abutments and also the bearing at the abutments along the longitudinal direction are the most seismically vulnerable components of this bridge type at the slight damage state. In addition, the bearing of the in-span hinges and abutments along the transverse direction and the columns are the next susceptible components at the slight damage state. The figure also illustrates that the shear keys and deck seating at the in-span hinges show higher fragility than the deck displacement along the transverse direction at the abutment points. The abutments in passive performance are narrowly less fragile than its counterpart in active performance. The figure finally shows that the lowest fragility at the slight damage state is expected for the deck displacement at the in-span hinge in the transverse direction along with the foundation displacement. For the moderate damage state shown in Figure b, the columns followed by the deck seating and bearing at the abutments in the transverse direction are the components with the highest fragility, i.e. high probability of exceedance at lower PGA levels. Shear keys and the bearing at the abutments in the longitudinal direction show approximately the same fragility. Based on Figure b, the bearing at the in-span hinges in the transverse direction is more fragile, i.e. at higher risk, than the deck displacement in the transverse direction at the abutments for moderate damage state. The figure also indicates that the deck seating at the in-span hinge is among the less fragile components. Unlike the slight damage state, a significant difference between the passive and active performance of the abutments is observed for the moderate damage state. The foundation rotation, foundation displacement, and the deck displacement at the in-span hinge in the transverse direction feature the minimum seismic fragility among all the bridge component at the moderate damage state.

12 Abbasi, Moustafa (a) (b) 0 (c) (d) FIGURE Component fragility curves for: (a) slight; (b) moderate; (c) extensive; and (d) complete damage states. For the extensive and complete damage states, only the primary bridge components were considered for the fragility analysis as discussed before. This is because the secondary components are less likely to lead to a complete failure of the bridge. According to Figures c and d, the columns are the most critical components at the extensive and complete damage states. This agrees with the current design philosophy and guidelines where the columns are designed with large ductility to accommodate seismic damage while the reminder of the bridge is capacity protected. However, the fragility curves in Figures c and d show that there is still a high risk for deck unseating at the abutment and much lesser risk for unseating at the in-span hinges. Therefore, deck seating conditions at the abutment should receive higher priority over the in-span hinge in terms of seismic repair and/or retrofit decisions. While abutment unseating was not demonstrated in previous CA earthquakes, it still poses a risk and high seismic vulnerability. This risk was possible to capture using the adopted probabilistic study with all uncertainties considerations, which was not likely to be captured using deterministic studies for a specific structure under a specific earthquake. It is also noted that the risk of deck unseating at abutments is consistent with Caltrans

13 Abbasi, Moustafa seismic design practices evolution over three significant design eras separated by the historic San Fernando and Loma Prieta earthquakes. In this regard, abutment seat widths chronologically increased from the - in. range (pre- era) to - in. (-0 era) and then to - in. or even larger in the post 0 design era. It is also noted that many of the bridge design details incorporated in this study are attributed to the pre- classification (Caltrans, ), which represents limited seismic details. This is to provide assessment tool for retrofit prioritization of older multi-frame bridges along with overall system fragilities to inform new bridge design. Developing fragility curves for multi-frame bridges that are designed based on the post Loma Prieta and Northridge era can be a good subject for a future study. The fragility curves developed herein are mainly applicable for multi-frame boxgirder bridges rather than single-frame bridges. For single-frame bridge fragility curves in California, the reader is referred to HAZUS () but should be alerted that a possible drawback of HAZUZ fragility curves is that it considered only the vulnerability of the columns to represent the overall system. SUMMARY AND CONCLUSIONS In this study, the fragility curves for multi-frame reinforced concrete box-girder bridges were developed. These curves were generated using nonlinear time history analysis of 00 different D bridge models paired randomly with 00 ground motions, which considered bridge material and geometric variability along with ground motions uncertainties. The fragility analysis considered the vulnerability of multiple bridge components such as columns, deck seating at the abutment and in-span hinge, elastomeric bearing pads, abutments, shear keys, and foundation. Thus, individual components fragility curved were also developed. All system and component fragility curves were developed for four different damage states that varied from slight to complete damage. The system fragility curves can be readily used for seismic risk assessment along with planning, design improvement, and financial loss estimation for new bridge construction. Moreover, the developed component fragility curves can be beneficial in informing seismic retrofit prioritization and decisions for existing multi-frame box-girder bridges. REFERENCES. Padgett, J.E., and R. DesRoches. Bridge Functionality Relationships for Improved Seismic Risk Assessment of Transportation Network. Earthquake Spectra, (), 00, -0.. Hwang, H., J. Liu, and Y. Chiu. Seismic Fragility Analysis of Highway Bridges. Center for Earthquake Research and Information, University of Memphis, TN, Choi, E. Seismic analysis and retrofit of Mid-America bridges. PhD Thesis, Georgia Institute of Technology, 00.. Choi, A., R. DesRoches, and B.G. Nielson. Seismic Fragility of Typical Bridges in Moderate Seismic Zones. Engineering Structure, (), 00, -.. Kim, S.H., and M.Q. Feng. Fragility analysis of bridges under ground motion with spatial variation. Int. J. Non-Linear Mech.,, 00, 0-.. Kim, S.H., and M. Shinozuka. Development of fragility curves of bridges retrofitted by column jacketing. Probabilistic Engineering Mechanics,, 00, 0-.. Karim, K.R., and F. Yamazaki. Effect of isolation on fragility curves of highway bridges based on simplified approach. Soil. Dyn. Curves Earthquake Eng.,, 00, -.. Nielson, B.G., and R. DesRoches. Analytical Seismic Fragility Curves for Typical Bridges in the Central and Southeastern United States. Earthquake Spectra,, 00, -.

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