Analytical Fragility Curves for Ordinary Highway Bridges in Turkey

Analytical Fragility Curves for OrdinaryHighway Bridges in Turkey

Ozgur Avs�ar,a) Ahmet Yakut,b) and Alp Canerb)

This study focuses on the development of analytical fragility curves for theordinary highway bridges constructed after the 1990s. Four major bridge classeswere employed based on skew angle, number of columns per bent, and spannumber (only multispan bridges). Nonlinear response-history analyses (NRHA)were conducted for each bridge sample using a detailed 3-D analytical modelsubjected to earthquake ground motions of varying seismic intensities. Acomponent-based approach that uses several engineering demand parameterswas employed to determine the seismic response of critical bridge components.Corresponding damage limit states were defined either in terms of membercapacities or excessive bearing displacements. Lognormal fragility curves wereobtained by curve fitting the point estimates of the probability of exceeding eachspecified damage limit state for each major bridge class. Bridges with largerskew angles or single-column bents were found to be the most seismicallyvulnerable. [DOI: 10.1193/1.3651349]

INTRODUCTION

Recent studies have indicated that the probability of a large earthquake in different partsof Turkey is quite high (Stein et al. 1997, Parsons et al. 2000). This prediction has led tosignificant research in seismic risk analyses with the purpose of determining the vulnerabil-ity of structures so that the expected losses can be mitigated. Bridges are one of the mostimportant components of highways and are among the critical structures considered in seis-mic risk analyses. Although comprehensive research has been performed in Turkey focus-ing on the development of fragility curves for buildings, no such studies have been carriedout for bridges. Fragility curves for ordinary highway bridges in Turkey are necessary toassess their seismic risk and vulnerability. A fragility curve, which is a fundamental compo-nent of seismic risk assessment methodology, is a probabilistic tool used to assess potentialseismic damage to highway bridges at a given seismic hazard level. As given in Equation 1,a fragility function simply depicts the probability that the seismic demand imposed on thestructure (D) is greater than or equal to the capacity of the structure (CLS) for the investi-gated limit state (LS). This probability statement is conditional on the selected seismic inten-sity measure (IM) representing the level of seismic action for a specific damage limit state.

PðLSjIMÞ ¼ P ðD � CLSÞjIM½ � (1)

Analytical fragility curves are employed for assessing the seismic performance of highwaybridges when neither the actual bridge damage data nor an expert opinion is available. In

a) Anadolu University, Department of Civil Engineering, _Iki Eylul Kampusu 26555 Eskis�ehir, Turkeyb) Middle East Technical University, Department of Civil Engineering, 06531 Ankara, Turkey

971

Earthquake Spectra, Volume 27, No. 4, pages 971–996, November 2011; VC 2011, Earthquake Engineering Research Institute

this method, analytical models of the bridge are formed and ground motions with variousintensity levels are considered to simulate bridge damage by executing numerous analyses.Fragility curves are highly sensitive to the choices made for the analysis method, structuralidealization, seismic hazard, and damage limit state definitions (Kwon and Elnashai 2006,Padgett and DesRoches 2007).

The choice of analysis procedure and the associated structural idealization of highwaybridges directly influence the analysis results, as well as the bridge damage data necessaryfor the development of analytical fragility curves. The elastic spectral method is the simplestand the least time-consuming approach for the generation of analytical fragility curves.Using this method, Hwang et al. (2000) developed fragility curves for the major bridges inMemphis, Tenn. The nonlinear static method is an alternative approach, often referred to asthe capacity spectrum method. This method has been utilized by various researchers to de-velop analytical fragility curves for bridges (Dutta and Mander 1998, Mander and Basoz1999, Shinozuka et al. 2000b, Monti and Nistico 2002, Banerjee and Shinozuka 2007).Nonlinear response-history analysis (NRHA) is believed to be the most rigorous method ofestimating the inelastic seismic demands of structures. Although the NRHA method hasbeen identified as the most time-consuming and computationally demanding, fragilitycurves developed using this procedure are believed to have better reliability than the onesdeveloped using the above-mentioned analytical procedures (Shinozuka et al. 2000b). Thismethod has been utilized in different ways by various researchers to develop fragility curves(Hwang et al. 2001, Karim and Yamazaki 2003, Choi et al. 2004, Mackie and Stojadinovic2007, Padgett and DesRoches 2009).

In the past, the seismic vulnerability assessments and loss estimates due to earthquakedamage for highway bridges in Turkey have been performed using studies and codes devel-oped for other regions of the world, especially the United States and Japan. In order to performreliable seismic vulnerability assessments of Turkey’s highway bridges, it is very important tohave bridge fragility curves representing the general attributes of the country’s highway bridgestructures, as well as the seismic source characteristics of the bridge sites in Turkey. The mainobjective of this study is to generate fragility curves for the ordinary highway bridges in Tur-key constructed after the 1990s in order to assess their seismic vulnerability. The bridges inves-tigated are dominated by multispan, simply supported bridges with cast-in-place continuousdecks. A comprehensive and original combination of modeling, analysis, damage limit statedefinition, and the quantification of seismic vulnerability procedures has been used. Descrip-tions of each component of the whole procedure used are explained in the following sections,along with the properties and classification of the bridge types investigated.

PROPERTIES AND CLASSIFICATION OF BRIDGES

A general understanding of ordinary highway bridges in Turkey constructed after the1990s, in terms of their structural attributes as well as their seismic behavior, is essential forthe generation of their analytical fragility curves. When the total number of bridges is con-sidered, analyzing each bridge in the inventory individually and obtaining its fragility curveis neither feasible nor practical. For this reason the bridges in this study have been groupedinto four classes based on their basic structural attributes. The seismic response of thebridges within the same class is expected to be similar.

O. AVS�AR, A. YAKUT, AND A. CANER972

In order to make a representative classification, a group of 52 bridges reflecting the gen-eral characteristics of the ordinary highway bridges constructed after the 1990s in differentparts of Turkey was selected (Avs�ar 2009, Sevgili and Caner 2009). Schematic drawings ofa sample bridge and the components that constitute the general attributes of the bridges areshown in Figure 1. The group of bridges investigated can be defined as ordinary standardbridges according to Caltrans (2006). The bridge superstructure is supported by steel shimelastomeric bearings, which are placed on the abutments and bent cap beams. Elastomericbearings are commonly used between the superstructure and substructure of bridges as iso-lating devices and are composed of a rubber pad and internally placed thin steel reinforcingplates. There is no dowel or connecting device between the elastomeric bearings and eitherthe superstructure or substructure. Since these elastomeric pads are simply placed betweentwo concrete surfaces, friction force is the only resisting force that holds the elastomericpads in their position. Ideally, during an earthquake the bearings deform elastically beforethe friction force is exceeded and the superstructure keeps its original position. However, ifthe friction force is exceeded the superstructure slides on the elastomeric bearings andunseating takes place. Shear keys are the sacrificial bridge components; they are designed toact as a structural fuse in a bridge system to protect the substructure components and foun-dation systems during severe earthquakes. Since their aspect ratio is relatively low, they ex-perience shear failure when pounding takes place between them and the superstructure.

All the bridges in the inventory are multiple simple-span composite structures that uti-lize prestressed concrete girders and continuous cast-in-place reinforced concrete (RC)decks. C40 concrete class (the characteristic strength is 40 MPa) is used for the prestressedgirders and C25 is used for the rest of the RC components of the associated bridges. Thequality of reinforcement steel is S420 (minimum yield strength¼ 420 MPa) for all RCmembers. A minimum longitudinal reinforcement ratio of 1% is satisfied for the RC

Figure 1. General properties of the ordinary highway bridges.

ANALYTICAL FRAGILITY CURVES FOR ORDINARY HIGHWAY BRIDGES IN TURKEY 973

columns, as per the American Association of State Highway and Transportation Officials(AASHTO) standards (AASHTO 1996). The bridges have a seat-type abutment system andmultiple- or single-column bents. Most of the bridges are straight, and the curve angle ofthe curved bridges is negligible, so all the bridges in the inventory are assumed to bestraight.

Histograms of the most important structural attributes were obtained and some of them,such as skew angle, span number, maximum span length, and number of columns per bent,are presented in Figure 2.

MAJOR BRIDGE CLASSES

Based on examination of the data available from past earthquake reports and previousstudies, span number, bent column number, and skew angle were designated as the primarystructural attributes for the associated bridge inventory data. The rest of the structural attrib-utes are considered to be secondary structural attributes. Depending on the number of spans,bridges can generally be classified as multispan (MS) or single-span (SS) (Basoz and Kire-midjian 1997, FEMA 2003, Nielson and DesRoches 2007). SS bridges are considered to beless vulnerable than MS bridges to seismic forces (AASHTO 2007, FHWA 1995) and thusare not included in this study. As in previous studies (Basoz and Kiremidjian 1997, FEMA2003), the bridges are classified according to column bent number depending on whetherthey have a single-column bent or multiple-column bent. Skew angle is considered to have

Figure 2. Statistical distributions of several structural attributes of highway bridges.


a major effect on the performance of bridges (FHWA 1995, Basoz and Kiremidjian 1997,Pamuk et al. 2005). The bridges in this study are classified into two groups according totheir skew angle: those with a negligible skew angle and those with a significant skewangle. In order to specify the two bridge types, a limiting skew angle value is required.There is no definite limiting skew angle value, but it can vary between 20� and 30� accord-ing to codes and previous studies (Caltrans 2006, FHWA 1995, Pezeshk et al. 1993,AASHTO 1996). In this study, the limit for skew angle was taken as 30�, which is the me-dian value of the bridge inventory employed. Four major bridge classes were determinedbased on the primary structural attributes mentioned above (Table 1).

BRIDGE SAMPLING

As in previous studies (Shinozuka et al. 2000a, Hwang et al. 2001, Choi et al. 2004), for eachmajor bridge class ten bridge samples were generated considering the secondary structural attrib-utes of the bridges. Material variability was not considered during the bridge sampling because ofthe negligible variation of the material properties in the selected representative bridges.

Bridge samples were generated by utilizing the Latin hypercube sampling (LHS) method,which utilizes a constrained sampling approach instead of randomly selected samples (Ayyuband Lai 1989). Following this method, instead of selecting each secondary structural attributerandomly, a statistical distribution of the structural attributes was taken into account duringselection. The probability distribution and the corresponding distribution parameters of thestructural attributes used during the sampling process are given in Table 2. For bridge sampling,two different superstructure types were considered: those with closely spaced prestressed girdersand those with widely spaced prestressed girders, as shown in Figure 1. Three different sub-structure types with a varying number of columns per bent were identified; and these three sub-structure types were also identified based on the column and cap beam sections used. In order toprevent the generation of bridge samples with unreasonable combinations of structural parame-ters, each generated sample was checked and compared to the existing bridges in the inventorydata. In such a circumstance, the structural properties of the generated unreasonable bridge sam-ple were modified to obtain as realistic a combination of structural properties as possible.

MODELING

Comprehensive 3-D analytical models for each of the bridge component were devel-oped using the OpenSees (PEER 2005) platform, as shown schematically in Figure 3. Themass and stiffness proportional Rayleigh damping coefficients were determined for theresponse-history analysis of the bridges considering the first two modal periods assuming a

Table 1. Major bridge classes

No. Bridge Classes Abbreviation

1 Multispan, multiple column, skew less than 30� MS_MC_SL30

2 Multispan, multiple column, skew greater than 30� MS_MC_SG30

3 Multispan, single column, skew less than 30� MS_SC_SL30

4 Multispan, single column, skew greater than 30� MS_SC_SG30


Table 2. Structural attributes employed for generating bridge samples

Parameters

Modelling Parameter Probability Distribution 1 2

Span Length [m] Normal mean¼ 23.8 St.Dev.¼ 6.10

Col Height [m] Normal mean¼ 6.73 St.Dev.¼ 2.04

Skewness [�] Uniform lower¼ 0� upper¼ 60�

Span No. Discrete 2-3-4-5

Superstructure Type Discrete Type 1-2

Substructure Type Discrete Type 1-2-3

Figure 3. Detailed 3-D analytical model of the bridge and its components.


5% viscous damping ratio. Additional hysteretic damping was developed through the yield-ing of bridge components such as bent columns and cap beams, which are known to experi-ence inelastic deformations. P-delta effects were taken into account in the analyses in orderto capture the increase in the bent column seismic demands. Superstructure was modeledusing standard prismatic elastic beam elements and assumed to remain in the elastic rangeper Caltrans (2006). Nonlinear modeling of the bent columns and cap beams was achievedby using fiber-based nonlinear elements to represent the distributed plasticity along themember length. Each fiber on the RC section was represented by a uniaxial stress-strainrelationship for reinforcement steel, unconfined concrete, and confined concrete. The rein-forcement steel was modeled by a bilinear steel material model with kinematic hardening.The Kent-Scott-Park (Kent and Park 1971, Scott et al. 1982) material model was employedfor the confined and unconfined concrete. The effects of abutments and backfill soil on thebridge system was modeled using the approach presented in the Caltrans (2006) provisions.

As discussed previously, in the ordinary highway bridges in Turkey, elastomeric bearingsare simply placed in between the superstructure and substructure components, without anydowel or connecting device. Therefore, the only resisting force holding the elastomeric bear-ing in place against lateral loads is the friction force between the rubber and concrete surfaces.Horizontal force on the bearing increases in proportion to the bearing’s seismic displacementuntil the friction force between the bearing and the concrete pedestal is exceeded. After thispoint, it is assumed that no additional horizontal force is carried by the bearings, so the forceremains constant. The ultimate shear capacity due to friction depends on the level of axialload on the elastomeric bearings and the dynamic coefficient of friction between the concretesurface and bearings, which is specified as 0.40 by Caltrans (2006). The behavior of the elas-tomeric bearings is characterized by an elastic-perfectly plastic model.

The superstructure and substructure components of the highway bridges are not continu-ous in the longitudinal and transverse directions and there exists joints with a certain gap inbetween. The opening and closing of expansion joints between bridge components introdu-ces nonlinearities and discontinuities that affect the load path and hence the dynamicresponse of bridges. Upon the closure of joints, pounding takes place between the adjoiningbridge components, which is modeled by pounding elements. The behavior of the poundingelement, which is effective when it is under compression, is represented by the force-deformation relationship schematically shown in Figure 4.

The contact force-based model was employed in the analytical model by linear springswith the parameters dg, Kg, and Fy. These parameters depend on whether the pounding isin the longitudinal or transverse direction. In longitudinal direction, pounding can take placebetween the superstructure and the abutment backwall when the 50 mm gap distance (dg) isclosed. Whereas in the transverse direction, pounding can take place between the super-structure and the shear keys at the bents or abutments when the 25 mm gap distance (dg) isclosed. Since the superstructure stiffness and capacity is much greater than the stiffness andcapacity of the abutment backwall or shear keys, stiffness (Kg) and the capacity (Fy) of thepounding element is obtained from the abutment backwall and shear keys for the longitudi-nal and the transverse pounding elements, respectively.

In the model for a bridge with skew, the substructure is aligned with respect to the trans-verse direction of the bridge. Therefore the skew angle is used to model the bent and


abutment alignment with respect to superstructure axis. All the springs in the analyticalmodel behave uniaxially and they are uncoupled. These springs are effective when they areforced in their predefined spring direction. Gap springs have been defined at each super-structure girder end node. This gap model represents the pounding in either the longitudinaldirection (pounding between the superstructure and abutment) or the transverse direction(pounding between the superstructure and substructure shear keys). Since these springs areuniaxial members, they become effective when they are forced in their predefined directionunder ground motion, which can be specified as unidirectional or bidirectional.

GROUND MOTION DATA AND INTENSITY MEASURE

The seismic hazard level of earthquake ground motions can be represented by differentground motion intensity measures (IMs). The essential point in selecting the appropriate IMis that it should have a certain level of correlation with the seismic damage of highwaybridges. The most commonly utilized IM for bridge fragility curves is peak ground accelera-tion (PGA), and to a lesser degree peak ground velocity (PGV). These values can beobtained from ground motion records and are independent of structural properties. Spectralaccelerations at certain periods have also been employed in previous studies (FEMA 2003,Nielson and DesRoches 2006). Only considering a single spectral acceleration can lead tounrealistic acceleration values due to higher mode effects and period elongation due toinelastic response. Moreover, fragility curves are developed for a group of bridges whosefundamental periods are not unique among the representative bridge samples. Therefore,instead of dealing with a single period value, considering a period range over the responsespectra of the ground motions is more reasonable. For this reason as a third IM, accelerationspectrum intensity (ASI) calculated from Equation 2 was employed (Von Thun et al. 1988,Yakut and Yılmaz 2008). Ti and Tf are defined as the initial and final periods and SA repre-sents the 5% damped response spectrum. According to the modal analysis results of thesample bridges of major bridge classes employed herein, the values of Ti¼ 0.40 s and

Figure 4. Analytical model for pounding element.


Tf¼ 1.10 s were used for the ordinary highway bridges in Turkey (Avs�ar 2009). Ti¼ 0.40 swas obtained from the modal analysis results to account for the pre-yield fundamental pe-riod of the bridge samples as well as their higher mode periods. Tf ¼ 1.10 s was selected toaccount for the post-yield period of the bridge samples. Tf¼ 1.10s was calculated by averag-ing the elongated periods of the bridge samples after performing NRHA.

ASI ¼ðTf

T i

SAðT ; nÞdT (2)

GROUND MOTION SELECTION

A ground motion set that contains a total of 25 ground motions recorded in Turkey andin other regions having similar faulting mechanisms and seismic potential was compiledwithout applying any scaling to represent the record-to-record variability. Moreover, groundmotion records having two horizontal orthogonal components were selected. Some of theimportant features of the earthquakes selected and several of the IM parameters of theground motions are given in Table 3. The response spectra of all the selected groundmotions and their mean are presented in Figure 5.

METHODOLOGY USED FOR FRAGILITY CURVES

A specific methodology that relies on a component-based evaluation of the bridge mod-els using NRHA was implemented. The following steps outline the methodology:

1) Obtain 3-D model of each sample bridge and determine the response quantities foreach component under each ground motion record.

2) Define the damage limit states and corresponding demand parameters for allcomponents.

3) Determine the performance level of each component by comparing componentdemands from NRHA results with component damage limits expressed in terms ofengineering demand parameters (EDPs). The EDPs employed in this study are: col-umn and cap beam curvature, shear in both principal axes, and deck displacement.

4) Evaluate the global performance level of each bridge model for the given groundmotion record.

5) Determine the exceedance probabilities of each specified damage limit state foreach ground motion.

6) Plot the selected IM of the ground motion against the probability of exceedance foreach damage limit state and major bridge class in order to obtain the fragility points.

7) Determine the fragility curves for each damage limit state and major bridge class bycurve fitting the jaggedly varying fragility points through lognormal distributionfunctions characterized by median and dispersion.

A thorough discussion of the underlying concepts these steps rely on is given next.

DAMAGE LIMIT STATE DEFINITIONS

A limit state can be defined as the ultimate point beyond which a bridge structure canno longer satisfy the specified performance level. The three damage limit states identified in


this study were termed serviceability (LS-1), damage control (LS-2), and collapse preven-tion (LS-3); these are similar to the ones presented in TEC (2007).

Serviceability corresponds to the system’s yield point, beyond which the structure expe-riences inelastic deformations. Damage control represents the extent of bridge damage after

Table 3. Some important parameters of the selected 25 earthquake ground motions

# EarthquakeStation/

Component MwD

(km)ASI(g*s)

PGA(g)

PGV(cm/s)

1 Parkfield, 2004 Parkfield, CA - Gold Hill3W; CSMIP station

36420

6.0 3.9 0.140 0.532 18.7

2 Landers, 1992 23559 Barstow 7.3 36.1 0.157 0.133 23.8

3 Parkfield, 1966 1438 Temblor pre-1969 6.1 9.9 0.161 0.312 18.0

4 Parkfield, 2004 Parkfield, CA - Cholame2E; CSMIP station 36230

6.0 14.5 0.172 0.469 22.5

5 Landers, 1992 33083 Boron Fire Station 7.3 90.6 0.178 0.103 11.1

6 Coyote Lake, 1979 57217 Coyote Lake Dam(SW Abut)

5.7 3.2 0.187 0.209 14.8

7 Duzce, 1999 375 Lamont 375 7.1 8.2 0.249 0.706 27.2

8 Morgan Hill, 1984 57383 Gilroy Array #6 6.2 11.8 0.252 0.255 20.5

9 Parkfield, 2004 Parkfield, CA - Cholame3E; CSMIP station 36450

6.0 14.8 0.260 0.620 25.2

10 Landers, 1992 5071 Morongo Valley 7.3 19.3 0.270 0.162 18.3

11 Parkfield, 2004 Parkfield, CA - FaultZone 7; CSMIP station

36431

6.0 1.7 0.271 0.241 19.5

12 Westmorland, 1981 5051 Parachute Test Site 5.8 24.1 0.282 0.194 32.3

13 Denizli, 1976 Denizli Directorate ofMeteorology

5.0 67.6 0.283 0.300 19.3

14 Bingol, 2003 Bingol Dir. of PublicWorks and Settlement

6.1 4.9 0.284 0.396 28.4

15 Landers, 1992 24 Lucerne 7.3 1.1 0.305 0.752 55.8

16 Coyote Lake, 1979 57383 Gilroy Array #6 5.7 3.1 0.346 0.370 34.7

17 Morgan Hill, 1984 1652 Anderson Dam(Downstream)

6.2 2.6 0.364 0.350 26.4

18 Victoria, 1980 6604 Cerro Prieto 6.4 34.8 0.383 0.604 25.1

19 Landers, 1992 23 Coolwater 7.3 2.1 0.416 0.344 32.9

20 Landers, 1992 22170 Joshua Tree 7.3 11.6 0.425 0.279 34.5

21 Superstition Hills, 1987 286 Superstition Mtn. 6.7 4.3 0.528 0.781 37.0

22 Superstition Hills, 1987 5051 Parachute Test Site 6.7 0.7 0.549 0.414 70.1

23 Parkfield, 2004 Coalinga, CA - SlackCanyon; Hidden Valley

6.0 32.1 0.552 0.271 36.4

24 Morgan Hill, 1984 57217 Coyote Lake Dam(SW Abut)

6.2 0.1 0.819 0.961 64.6

25 Kobe, 1995 0 KJMA 6.9 0.6 1.169 0.701 77.7


which repair of the bridge may not be economically feasible. And finally, collapse preven-tion is the ultimate capacity of the structure, beyond which the structural system is no longerstable and partial or total collapse may occur. Since a component-based approach wasemployed, the damage limit states for each major bridge component were required. Thesedamage limit states were specified in terms of deformations for the local and globalresponse parameters, which are known as engineering demand parameters (EDPs). There-fore, capacity limits for each component EDP were determined for each of the three damagelimit states.

For columns and cap beams, curvature and shear capacity were considered to be theirEDPs. The section yield point determined from the bilinear moment-curvature curve corre-sponded to the serviceability damage limit state, at which point the columns and cap beamshad some minor repairable cracks. The damage control limit state was defined as section cur-vature, at which point spalling of the concrete cover occurred (Priestley et al. 1996) but themembers could be repaired without traffic closures. The ultimate curvature capacity of the col-umn and cap beam sections was considered to be the collapse prevention damage limit state,at which point significant repair was required, with traffic limited to service use with someexceptions for emergency use. The ultimate curvature capacity of the cap beams was specifiedas the ultimate point obtained from moment-curvature analysis. The ultimate curvature of thecap beams corresponded to the point at which the reinforcement steel or confined concreteextreme fiber had reached its ultimate strain value or when the moment capacity at themoment-curvature curve had decreased to 80% of its maximum attained moment capacity(Priestley et al. 1996). The ultimate curvature capacity of the columns was determined usingan empirical equation, which was proposed by Erduran and Yakut (2004) for the column dis-placement ductility capacity based on the results of previous column experiments. Displace-ment ductility capacity, with a relevant plastic hinge length assumption for a cantilever col-umn, was employed to obtain the ultimate curvature capacity of the columns (Avs�ar 2009).

Figure 5. Response spectra of the selected 25 ground motions.


Shear failure is a brittle type of failure that occurs without the bridge exhibiting anysign of damage before its failure. Member failure takes place suddenly when the shearcapacity of the RC sections is exceeded by the seismic shear demand. Therefore, only thecollapse prevention limit state was defined for the shear capacity of columns and cap beams.This limit state was calculated using the following equation, proposed by Priestley et al.(1996).

Vs ¼ kffiffiffifc

pAe þ

AswfyD0

scot hþ P tan a; (3)

where k is expressed as a factor defining the relationship between the ductility and strengthof the concrete shear-resisting mechanism. A constant value of 0.29 MPa is assumed for thecalculations, which corresponds to the initial shear strength of the RC members. The vari-able fc represents the compressive strength of unconfined concrete. The variable Ae repre-sents the effective shear area of a cross-section that is equal to 0.8Agross. The variable Asw

represents the area of the transverse reinforcement in the direction of the applied shearforce, while fy is the yield strength of the transverse reinforcement. The variable D0 is thecore dimension in the direction of the applied shear force, s represents the spacing of thetransverse reinforcement, and h is the angle of the critical inclined flexure shear cracking tothe member axis, which is assumed to be 30�. The variable a is the angle formed betweenthe column axis and the strut from the point of load application to the center of the flexuralcompression zone at the critical section of the column plastic hinge. The variable P is theaxial force, which is obtained from the gravity analysis of the bridge.

The qualitative damage limit states described by the Federal Highway Administration(FHWA 1995) for superstructure bearing displacements were employed. In this study, thedisplacement capacity of the bearings, beyond which the friction force is exceeded by theseismic forces, was accepted as the ultimate bearing displacement defining the serviceabilitylimit state. The limiting friction force is a function of the friction coefficient, the axial loadon the bearing, and the lateral stiffness of the bearing. During extreme seismic events,superstructure girders may experience large horizontal displacements and fall over the ped-estal to rest directly on the cap beams. This could cause excessive damage to the asphalt,disturbing traffic flow and affecting the functionality of the bridge. The damage controllimit state was defined as displacement of this severity (Figure 6).

Finally, when superstructure displacement exceeds the available seat length provided bythe cap beams, the superstructure will fall over the bent and total collapse will occur. Thissituation was defined as the collapse prevention limit state (Figure 6). The conditions underwhich this limit state occurs depend on the dimensions of the cap beams and the abutmentwidth, which provides seat for the superstructure. A detailed discussion of the damage limitsfor each EDP and the major bridge classes can be found in Avs�ar (2009).

DETERMINATION OF COMPONENT AND BRIDGE DAMAGE LIMIT STATES

The maximum response of the bridge components was calculated by taking the absolutemaximum of the response time history of each defined EDP. It should be noted that eachbridge model was subjected to two horizontal orthogonal components of the selectedground motion records in the analysis. The seismic damage limit state of the bridge


components under each ground motion was determined by comparing the correspondingthreshold values of the damage limit states and the maximum seismic response of the bridgecomponents. For columns and cap beams, the maximum curvature obtained from the analy-sis was compared with the corresponding capacity determined for each damage limit state.Additionally, maximum shear force demand was compared with shear capacity to determinewhether the collapse damage limit state was exceeded or not. Similarly, the computed maxi-mum deck displacement was compared using the values associated with each damage limitstate.

Since no specific method exists for determining the relationship of overall bridge dam-age to the damage limit state of its components, a simple assumption was made for identify-ing the damage limit state of the bridges as a whole. If any of the bridge componentsattained or exceeded a damage limit state, the overall bridge system was assumed to be inthe same damage limit state, regardless of the damage limit states of the rest of the bridgecomponents. This method assumes a series system for the bridges in the study. It is a con-servative approach for determining overall bridge damage because the correlation betweenthe damage limit states of the bridge components and their influence on the overall bridgedamage is not taken into account.

An example of a damage limit state assessment of a sample bridge is presented in Table 4.In the table, the parameters are given according to their section local axis in terms of 33 (strongaxis) and 22 (weak axis). K and V represent the curvature and shear for the RC members,respectively. If the bridge component has reached or exceeded a certain damage limit state,then the score of the bridge component for that limit state is assumed to be 1, otherwise it is 0.According to the assumptions made in identifying the bridge damage limit state, if any of thebridge components have a score of 1, then the whole bridge is assumed to be in that damagelimit state. That is, the damage limit state of the whole bridge is dictated by the damage limitstate of the most severely damaged component.

Figure 6. Damage control and collapse prevention limit states for superstructure displacement.


DETERMINATION OF BRIDGE FRAGILITY

The damage limit states of each bridge sample in the four major bridge classes wereidentified under the selected ground motions. For a selected ground motion record with acertain IM value, the number of bridge samples that reached or exceeded a specified damagelimit state was obtained. The IMs were calculated by taking the geometric mean of the twohorizontal components of the ground motions. The ratio of the number of sample bridgesthat reached or exceeded the specified damage limit state to the total number of samplebridges gives the probability of exceeding the corresponding limit state of the bridge classfor the investigated earthquake. After performing the same assessment for each earthquakeground motion in the set and for the three specified damage limit states, the probability ofexceeding the damage limit states was obtained for each earthquake, and consequently for

Table 4. Determination of the damage limit state of the bridges

Serviceability Limit State (LS-1)

EQ#Intensity Measure(ASI, PGV, PGA) Col. K33 Col. K22 Cap K33

DeckDisp. OverAll

EQ-1 IM-i 1 1 0 1 1

EQ-2 IM-i 0 1 1 1 1

– – – – – – –

– – – – – – –

EQ-N IM-i 1 0 1 1 1

Damage Control Limit State (LS-2)

EQ#Intensity Measure(ASI, PGV, PGA) Col. K33 Col. K22 Cap K33

DeckDisp. OverAll

EQ-1 IM-i 1 0 0 0 1

EQ-2 IM-i 0 0 0 0 0

– – – – – – –

– – – – – – –

EQ-N IM-i 0 0 1 0 1

Collapse Prevention Limit State (LS-3)

EQ#Intensity Measure(ASI, PGV, PGA)

Col.K33

Col.K22

CapK33

Col.V2

Col.V3

CapV2

DeckDisp. OverAll

EQ-1 IM-i 1 0 0 1 0 0 0 1

EQ-2 IM-i 0 0 0 0 0 0 0 0

– – – – – – – – – –

– – – – – – – – – –

EQ-N IM-i 0 0 0 0 0 0 0 0

0¼NOT Attained the Specified Damage Limit State1¼Attained the Specified Damage Limit State


each IM. Since fragility curves were developed for bridge classes, an evaluation of theresults of the bridge samples was made for each bridge class separately.

When earthquake ground motions are represented with an appropriate seismic IM, thedistribution of exceeding probabilities with respect to the selected IM can be obtained, asshown in Figure 7. In this graph the x-axis is the seismic IM of the ground motion and they-axis is the probability of exceedance of a certain damage limit state. In seismic loss esti-mation studies, continuous functions of fragility curves are more convenient in the calcula-tions than jaggedly varying fragility points. Therefore, a mathematical expression was uti-lized to characterize the jaggedly varying exceedance probability points to achieve smoothfragility curves for specific damage limit states and bridge classes. A representative sketchis shown in Figure 7, which illustrates a function that is the best fit for the exceedance prob-ability points.

As in the most recent studies (FEMA 2003, Karim and Yamazaki 2003, Elnashai et al.2004, Nielson and DesRoches 2007, Banerjee and Shinozuka 2007), fragility curves for allbridge classes are modeled as lognormally-distributed functions that give the probability ofreaching or exceeding different damage limit states for a given level of ground motion.Each fragility curve is characterized by a median value and an associated dispersion factor(lognormal standard deviation) of ground motion, which is represented by seismic IMs.

FRAGILITY CURVES FOR MAJOR BRIDGE CLASSES

Fragility functions for each bridge class were developed for the various IMs (ASI, PGV,and PGA) by employing the above-mentioned procedure. The median and dispersion valuesof the cumulative lognormal probability distribution functions that were utilized to developfragility curves were determined for each damage limit state for each bridge classes, and fordifferent IMs (Table 5). The median and dispersion values of the cumulative lognormalprobability distribution function were determined by employing the least-squares techniqueto the exceedance probability points. In addition, to investigate the correlation between theexceedance probability points and the developed fragility curves, the coefficient of determi-nation (R2) was computed for each individual fragility curve. When the coefficient of

Figure 7. Schematic representation of a fragility curve.


determination values calculated for each IM were investigated, it was found that ASI hasthe highest R2 value and PGA has the lowest. This implies that fragility curves developedusing ASI have a better correlation with the corresponding exceedance probability points ascompared to the other IMs. PGA has the least correlation with the probability of exceedingdata points. This result is consistent with the correlation of the bridge damage limit stateand the IM.

In Figures 8, 9, and 10, fragility curves of four bridge classes are shown for ASI, PGV,and PGA, respectively. The three curves in each figure represent the probability of exceed-ing the limit states LS-1 (serviceability), LS-2 (damage control), and LS-3 (collapse preven-tion), from left to right. These curves are grouped separately in Figure 11 for the three

Table 5. Fragility curve parameters of the bridge classes

MS_ MC_SL30

LS-1: Serviceability LS-2: Damage Control LS-3: Collapse Prevention

Intensity Measure Median Disp. R2 Median Disp. R2 Median Disp. R2

ASI (g*s) 0.121 0.401 0.758 0.592 0.290 0.748 0.693 0.308 0.902

PGV (cm/s) 11.238 0.454 0.299 59.678 0.573 0.569 72.287 0.628 0.619

PGA (g) 0.117 0.400 0.121 0.693 0.280 0.296 0.869 0.316 0.361

MS_MC_SG30



ASI (g*s) 0.137 0.366 0.843 0.497 0.272 0.777 0.623 0.309 0.721

PGV (cm/s) 10.914 0.423 0.235 49.109 0.532 0.501 62.887 0.570 0.469

PGA (g) 0.094 0.500 0.128 0.583 0.350 0.176 0.756 0.380 0.205

MS_SC_SL30



ASI (g*s) 0.133 0.381 0.779 0.438 0.389 0.846 0.593 0.368 0.937

PGV (cm/s) 11.083 0.354 0.307 44.434 0.486 0.602 57.340 0.529 0.643

PGA (g) 0.110 0.450 0.131 0.577 0.400 0.144 0.741 0.480 0.207

MS_SC_SG30



ASI (g*s) 0.123 0.346 0.804 0.347 0.400 0.826 0.508 0.385 0.900

PGV (cm/s) 10.090 0.386 0.323 33.049 0.444 0.655 47.656 0.535 0.740

PGA (g) 0.100 0.420 0.124 0.482 0.360 0.223 0.613 0.400 0.218


damage limit states and three IMs to compare the effect of different bridge classes on thefragility curves.

Bridge classes with larger skew angles are more vulnerable to seismic effects than thosewith small skew angles. The fragility curve for bridges with a skew greater than 30� (ClassSG30, as described above) shows that they have a higher probability of exceeding LS-2 andLS-3 than bridges with a skew angle of less than 30� (Class SL30). This outcome is consistentwith the response of the bridges observed in the Loma Prieta and Northridge earthquakes(Buckle 1994, Basoz and Kiremidjian 1997). In various codes and research studies such asBuckle (1994), FHWA (1995), Basoz and Kiremidjian (1997), and Pamuk et al. (2005), skewangle is considered to be a major factor in the performance of bridges and it is agreed thatbridges with a large skew are more vulnerable to seismic effects. The number of bent columnsalso has a considerable effect on fragility curves. Single-column bents are found to be morevulnerable compared to multiple column bents. This finding is in accordance with the per-formance of bridges during the Loma Prieta and Northridge earthquakes. As discussed byBasoz and Kiremidjian (1997), bridges with single-column bents performed poorly duringthese earthquakes. They stated that the substructure bent column number plays an importantrole in determining the damage level bridges are expected to experience.

The effects of skew and bent type on fragility curves depend on the ground motion IM.For instance, as seen in Figure 11, the difference between the fragility curves for lower and

Figure 8. Fragility curves for different damage limit states (ASI).


higher IM values is negligible, whereas in the intermediate IM values the difference is morepronounced. The values of the utilized IMs corresponding to the same level of damage stateexceedance probability related to each other at a certain level. The relative relationshipbetween the three IMs considering the damage limit state exceeding probability depends onthe major bridge types employed in the study. A thorough discussion of the ground motionIMs employed here can be found in Avsar and Yakut (2010).

The difference between the fragility curves of all the bridge classes for the serviceabilitydamage limit state is negligible regardless of the IM considered. Reaching or exceeding theserviceability damage limit state mostly occurs when the superstructure displacement exceedsthe specified displacement limit, at which point the friction force between the bearings andconcrete surfaces can no longer hold the elastomeric bearings in place. A single fragility curvecan be utilized for all bridge classes for the serviceability limit state. This finding is in agree-ment with the fragility curves found in FEMA’s HAZUS-MH MR1: Technical Manual. In thistechnical manual, a modification factor is employed for the skew of the bridges to determinethe fragility curves for the moderate, extensive, and complete damage limit states. Whereas,for the slight damage limit state no modification factor is considered. In other words, the skewangle does not impact the determination of fragility curves for the slight damage limit state.

The fragility curves for the damage control (LS-2) and collapse prevention (LS-3) dam-age limit states were mostly dominated by the column and cap beam curvature demands.

Figure 9. Fragility curves for different damage limit states (PGV).


The main reason for exceeding the column and cap beam curvature capacities for these twodamage limit states was the transfer of high shear forces from superstructure to the substruc-ture by the shear keys. The shear keys of the existing bridges investigated were designed tobe rigid in order to transfer a considerable amount of the seismic force of an earthquake tothe substructure when pounding occurs in the transverse direction.

The difference between the fragility curves for the damage limit states LS-2 and LS-3 isrelatively small. One of the main reasons for this small difference is the acceptance criteriadefinitions of the corresponding damage limit states, especially for the bridges with multiple-column bents. The other reason is the difference in the number of EDPs defined for the LS-2and LS-3 damage limit states. Any shear damage to the bridge components is specified onlyfor the collapse prevention damage limit state. Therefore, the number of EDPs defined for thecollapse prevention damage limit state is more than the others. The columns and cap beamsof several of the bridge samples experienced shear failure. This increased the probability ofexceedance for the collapse prevention damage limit state, which caused there to be a smallerdifference between the fragility curves for the LS-2 and LS-3 damage limit states.

CASE STUDY: FRAGILITY-BASED ASSESSMENT OF A SELECTED BRIDGEDATABASE

A seismic risk assessment of a sample of existing highway bridges around the MarmaraRegion (in the northeastern part of Turkey) was performed using the fragility curves

Figure 10. Fragility curves for different damage limit states (PGA).


developed. In this application, a deterministic approach was applied for the seismic hazardassessment of the bridge sites. One hundred and five bridges were selected for the casestudy, each of which were classified into the four major specified bridge categories. Asshown in Figure 12, the bridge class MS_MC_SL30 (multispan, multi-column bridges witha skew angle of less than 30�) dominated the sample.

In the deterministic seismic hazard assessment for the bridge sites, a scenario earthquake(Mw 7.4) along the Marmara Sea Segment of the North Anatolian Fault was considered(Yucemen et al. 2006). Ground motion seismic IMs of ASI, PGV, and PGA were calculatedconsidering the relevant attenuation relationships. The attenuation relationship found inBoore et al. (1997) was employed for the calculation of ASI and PGA, and the relationshipfound in Akkar and Bommer (2007) was employed for the calculation of PGV.

The data pertinent to the bridges were collected into a database using the geographic in-formation system (GIS) software, ArcView (ESRI 1999).

The damage limit states of the bridges in the database were calculated using the associ-ated fragility curves developed herein. The important task was to determine the bridge per-formance level using the calculated probabilities for each damage limit state. A similar pro-cedure presented by Hwang et al. (2000) was employed for the estimation of bridge seismic

Figure 11. Fragility curves for different damage limit states and IMs (ASI, PGV, PGA).


damage. If the discrete probability of any damage limit state was greater than 50%, then thebridge was expected to sustain the corresponding damage. Otherwise, three damage limitstates having the highest probabilities were taken into consideration. In this case theexpected damage limit state for the bridge was determined by considering the average ofthe three damage limit states. To illustrate this condition, consider a bridge sample whosediscrete probabilities in each damage limit state are 5%, 30%, 40%, and 25% for the damagelimit states slight/no, moderate, significant, and collapse, respectively. Since none of thedamage limit state probabilities is greater than 50%, the damage limit states moderate,

Figure 13. Bridge damage distribution for Marmara Scenario earthquake (Mw 7.4).

Figure 12. Bridge type distribution among 105 sample bridges.


significant, and collapse are taken into consideration due to their higher probability com-pared to the slight/no damage limit state. The average of the three damage limit states isconsidered to be significant damage, which is between the moderate and collapse damagelimit states. Therefore, the damage limit state of the sample bridge is determined to be sig-nificant. Here, averaging is not a numerical calculation, rather it is a subjective assignmentof a damage limit state that is the intermediate of the three damage limit states that havehigher discrete probabilities.

The damage distribution of the bridges is presented in Figure 13. As can be seen in thisfigure, under the conditions of the Marmara Scenario earthquake (Mw 7.4), most of thebridges were in the slight/no damage limit state and some were in the moderate damagelimit state according to ASI- and PGA-based fragility curves, and vice versa for PGV-basedfragility curves. Very few bridges, those that were very close to the fault segments, were inthe significant or collapse limit state with respect to both ASI- and PGV-based curves. Thedamage limit state distributions and locations of the 105 sample bridges due to the MarmaraScenario earthquake are presented for ASI-based fragility curves in Figure 14.

CONCLUSIONS

In this study, analytical fragility curves were developed for the ordinary highwaybridges in Turkey constructed after the 1990s to be used in the assessment of their seismicvulnerability. The following conclusions have been drawn according to the results obtainedin this study.

• The most significant contribution of this study is the development of fragilitycurves for certain bridge classes common in the highway transportation system inTurkey. They can be used to determine the seismic risk associated with existing or-dinary highway bridges in Turkey.

Figure 14. Scenario earthquake damage distribution (ASI).


• The fragility curves of the highway bridges were developed for three damage limitstates. The fragility curve for the serviceability damage limit state was mostly gov-erned by the relative displacement of the superstructure. Whereas, the curvaturedemands of the columns and cap beams dominated the fragility curves for the dam-age control and collapse prevention damage limit states. The fragility curves devel-oped were the first of their kind for Turkish highway bridges in terms of themethodology applied as well as the acceptance criteria employed in the calculationprocedure.

• When fragility curves for the major bridge classes were investigated, it was foundthat the bridges with skew and single-column bents exhibited higher vulnerabilitycompared to those without skew and with multiple-column bents. This result is inline with past earthquake experiences.

• Among the investigated ground motion IMs (ASI, PGV, and PGA), ASI and PGVappeared to have a better correlation with the seismic damage sustained by bridgecomponents because these fragility curves were more reliable. Therefore, the fragil-ity curves generated based on ASI or PGV were found to be more realistic whenestimating the damage limit state of the bridges.

• The difference between the fragility curves of all the bridge classes for the service-ability damage limit state (LS-1) was almost invariant, regardless of the IM consid-ered. The effects of bridge skew angle or bent column number on the fragilitycurve for the serviceability limit state were found to be insignificant. Therefore, itwas determined that a single fragility curve can be utilized for all bridge classes forthe serviceability damage limit state.

• When the horizontal component of the seismic force is greater than the frictionforce, which is the case even at lower ground motion intensities, the “walk-out”phenomenon takes place and the superstructure starts to move. This can cause per-manent displacement of the superstructure, affecting the functionality of the bridge.Therefore, the proposed fragility curves for the serviceability damage limit stateresult in a higher probability of exceedance values.

ACKNOWLEDGMENTS

The authors would like to thank the anonymous reviewers for their constructivecomments.

REFERENCES

American Association of State Highway and Transportation Officials (AASHTO), 1996.AASHTO Guide Specifications for LRFD Seismic Bridge Design, 16th ed., Washington, D.C.

American Association of State Highway and Transportation Officials (AASHTO), 2007. Stand-ard Specifications for Highway Bridges, Subcommittee for Seismic Effects on Bridges,Washington, D.C.

Akkar, S., and Bommer, J. J., 2007. Empirical prediction equations for peak ground velocityfrom strong-motion records from Europe and Middle East, Bulletin of Seismological Societyof America 97, 511–530.


http://dx.doi.org/10.1785/0120060141

http://dx.doi.org/10.1785/0120060141

Avs�ar, O., 2009. Fragility Based Seismic Vulnerability Assessment of Ordinary HighwayBridges in Turkey, PhD thesis, Dept. of Civil Engineering, Middle East Technical University,Ankara, Turkey.

Avsar, O., and Yakut, A., 2010. Evaluation of ground motion intensity measures for the fragilitycurves of ordinary highway bridges in Turkey, 9th US National and 10th Canadian Confer-ence on Earthquake Engineering: Reaching Beyond Borders, Paper No. 380, 25–29 July,Toronto, Canada.

Ayyub, B. M., and Lai, K.–L., 1989. Structural reliability assessment using Latin hypercubesampling, in Proceedings, 5th International Conference on Structural Safety and Reliability(ICOSSAR), American Society of Civil Engineers (ASCE), San Francisco, CA, 1177–1184,

Banerjee, S., and Shinozuka, M., 2007. Nonlinear static procedure for seismic vulnerabilityassessment of bridges, Computer-Aided Civil and Infrastructure 22, 293–305.

Basoz, N., and Kiremidjian, A. S., 1997. Evaluation of Bridge Damage Data from The LomaPrieta and Northridge, CA Earthquakes, Tech. Rep. 127 and Tech. Rep. MCEER-98-004,John A. Blume Earthquake Engineering Center, Stanford, CA.

Boore, D. M., Joyner, W. B., and Fumal, T. E., 1997. Equations for estimating horizontalresponse spectra and peak acceleration from western North American earthquakes: A Sum-mary of Recent Work, Seismological Research Letters 68, 128–153.

Buckle, I. G., 1994. The Northridge, California Earthquake of January 17, 1994: Performanceof Highway Bridges, Tech. Rep. NCEER-94-0008, National Center for Earthquake Engineer-ing Research, Buffalo, NY.

California Department of Transportation (Caltrans), 2006. Seismic Design Criteria, Version 1.4,Sacramento, CA.

Choi, E., DesRoches, R., and Nielson, B., 2004. Seismic fragility of typical bridges in moderateseismic zones, Engineering Structures 26, 187–199.

Dutta, A., and Mander, J. B., 1998. Seismic fragility analysis of highway bridges, Proc. ofINCEDE–MCEER Ctr-Ctr Workshop on Earthquake Engineering Frontiers in Transporta-tion Systems, 22–23 June, Tokyo, Japan.

Elnashai, A. S., Borzi, B., and Vlachos, S., 2004. Deformation–based vulnerability functions forRC bridges, Structural Engineering and Mechanics 17, 215–244.

Environmental Systems Research Institute, Inc. (ESRI), 1999. ArcView GIS 3.2, geographic in-formation system software, available at www.esri.com.

Erduran, E., and Yakut, A., 2004. Drift based damage functions for reinforced concrete col-umns, Computers and Structures 82, 121–130.

Federal Emergency Management Agency (FEMA), 2003. HAZUS-MH MR1: Technical Manual,Vol. Earthquake Model, Washington, D.C.

Federal Highway Administration (FHWA), 1995. Seismic Retrofitting Manual for HighwayBridges, Report No. FHWA-RD-94-052, McLean, VA.

Hwang, H., Liu, J. B., and Chiu, Y. H., 2001. Seismic Fragility Analysis of Highway Bridges,Report No. MAEC RR-4, Center for Earthquake Research Information, University of Mem-phis, TN.

Hwang, H., Jernigan, J. B., and Lin, Y., 2000. Evaluation of seismic damage to Memphisbridges and highway systems, Journal of Bridge Engineering 5, 322–330.

Karim, K. R., and Yamazaki, F., 2003. A simplified method of constructing fragility curves forhighway bridges, Earthquake Engineering and Structural Dynamics 32, 1603–1626.


http://dx.doi.org/10.1111/j.1467-8667.2007.00486.x

http://dx.doi.org/10.1016/j.engstruct.2003.09.006

www.esri.com

http://dx.doi.org/10.1016/j.compstruc.2003.10.003

http://dx.doi.org/10.1061/(ASCE)1084-0702(2000)5:4(322)

http://dx.doi.org/10.1002/eqe.v32:10

Kent, D. C., and Park, R., 1971. Flexural members with confined concrete, Journal the Struc-tural Division 97, 1969–1990.

Kwon, O. S., and Elnashai, A. S., 2006. The effect of material and ground motion uncertaintyon the seismic vulnerability curves of RC structure, Engineering Structures 28, 289–303.

Mackie, K. R., and Stojadinovic, B., 2007. R-factor parameterized bridge damage fragilitycurves, Journal of Bridge Engineering 12, 500–510.

Mander, J. B., and Basoz, N., 1999. Seismic fragility curve theory for highway bridges, in Pro-ceedings, 5th US Conference on Lifeline Earthquake Engineering, American Society of CivilEngineers, Reston, VA, 31–40.

Monti, G., and Nistico, N., 2002. Simple probability-based assessment of bridges under scenarioearthquakes, Journal of Bridge Engineering 7, 104–114.

Nielson, B. G., and DesRoches, R., 2006. Effect of using PGA versus Sa on the uncertainty inprobabilistic seismic demand models of highway bridges, 8th National Conference on Earth-quake Engineering, 18–21 April 2006, San Francisco, CA.

Nielson, B. G., and DesRoches, R., 2007. Analytical seismic fragility curves for typical bridgesin the Central and Southeastern United States, Earthquake Spectra 23, 615–633.

Pamuk, A., Kalkan, E., and Ling, H. I., 2005. Structural and geotechnical impacts of surfacerupture on highway structures during recent earthquakes in Turkey, Soil Dynamics andEarthquake Engineering 25, 581–589.

Pacific Earthquake Engineering Research Center (PEER), 2005. Open System for EarthquakeEngineering Simulation (OpenSees), Version 1.7.3, http://opensees.berkeley.edu.

Padgett, J. E., and DesRoches, R., 2009. Retrofitted bridge fragility analysis for typical classesof multispan bridges, Earthquake Spectra 25, 117–141.

Padgett, J. E., and DesRoches, R., 2007. Sensitivity of seismic response and fragility to parame-ter uncertainity, Journal of Structural Engineering 133, 1710–1718.

Parsons, T., Toda, S., Stein, R. S., Barka, A., and Dieterich, J. H., 2000. Heightened odds of largeearthquakes near Istanbul: An interaction-based probability calculation, Science 288, 661–665.

Pezeshk, S., Chang, T. S., Yiak, K. C., and Kung, H. T., 1993. Seismic vulnerability evaluationof bridges in Memphis and Shelby Country, Tennessee, Earthquake Spectra 9, 803–816.

Priestley, M. J. N., Seible, F., and Calvi, G. M., 1996. Seismic Design and Retrofit of Bridges,John Wiley & Sons, Inc., New York, NY, 686 pp.

Scott, B. D., Park, R., and Priestley, M. J. N., 1982. Stress-strain behavior of concrete confinedby overlapping hoops at low and high strain rates, ACI Structural Journal 79, 13–27.

Sevgili, G., and Caner, A., 2009. Improved seismic response of multisimple-span skewedbridges retrofitted with link slabs, Journal of Bridge Engineering 14, 452–259.

Shinozuka, M., Feng, M. Q., Lee, J., and Naganuma, T., 2000a. Statistical analysis of fragilitycurves, Journal of Engineering Mechanics 126, 1224–1231.

Shinozuka, M., Feng, M. Q., Kim, H. K., and Kim, S. H., 2000b. Nonlinear static procedure forfragility curve development, Journal of Engineering Mechanics 126, 1287–1295.

Stein, R. S., Barka, A. A., and Dieterich, J. H., 1997. Progressive failure on the North Anatolianfault since 1939 by earthquake stress triggering, Geophysical Journal International 128,594–604.

Turkish Earthquake Code (TEC), 2007. Specification for Structures to be Built in DisasterAreas, Ministry of Public Works and Settlement, Government of the Republic of Turkey,Ankara.


http://dx.doi.org/10.1016/j.engstruct.2005.07.010



http://dx.doi.org/10.1193/1.2756815

http://dx.doi.org/10.1016/j.soildyn.2004.11.011

http://dx.doi.org/10.1016/j.soildyn.2004.11.011

http://opensees.berkeley.edu

http://dx.doi.org/10.1193/1.3049405


http://dx.doi.org/10.1126/science.288.5466.661

http://dx.doi.org/10.1193/1.1585741




http://dx.doi.org/10.1111/j.1365-246X.1997.tb05321.x

Von Thun, J. L., Rochim, L. H., Scott, G. A., and Wilson, J. A., 1988. Earthquake groundmotions for design and analysis of dams, Earthquake Engineering and Soil Dynamics II -Recent Advances in Ground-Motion Evaluation, Geotechnical Special Publication 20,463–481.

Yakut, A., and Yılmaz, H., 2008. Correlation of deformation demands with ground motionintensity, Journal of Structural Engineering 134, 1818–1828.

Yucemen, M. S., Kocyigit, A., Yakut, A., and Gencoglu, S., 2006. Guidelines for the Develop-ment of Seismic Hazard Maps, Technical report prepared for the General Directorate ofDisaster Affairs, Government of the Republic of Turkey, Ankara.

(Received 4 May 2010; accepted 27 December 2010)



Analytical Fragility Curves for Ordinary Highway Bridges in Turkey

Documents

Transcript of Analytical Fragility Curves for Ordinary Highway Bridges in Turkey