Retroﬁtted Bridge Fragility Analysis for Typical Classes ... · Retroﬁtted Bridge Fragility Analysis for Typical Classes of Multispan Bridges Jamie E. Padgett,a) M.EERI, and Reginald

Retrofitted Bridge Fragility Analysisfor Typical Classes of Multispan Bridges

Jamie E. Padgett,a)M.EERI, and Reginald DesRoches,b)

M.EERI

Retrofitted bridge fragility curves provide a powerful tool for assessing theeffect of retrofit measures on the seismic performance of different bridge typesunder a range of loading levels. Traditional methods for retrofit assessmenttypically evaluate the effectiveness of retrofit based on the performance ofindividual components. However, the use of fragility curves for retrofittedbridges has the ability to capture the impact of retrofit on the bridge systemvulnerability. Using three-dimensional nonlinear analysis, fragility curves aredeveloped for four common classes of multispan bridges and five retrofitmethods. The results show that the effectiveness of retrofit is a function ofbridge type and damage state. General conclusions of the influence of thedifferent retrofit measures on the fragility of each class of typical bridges in theCentral and Southeastern United States, as well as the fragility parameters, arepresented. The results from this work can be used to enhance regional seismicrisk assessment and can form the basis for retrofit cost-benefit studies.�DOI: 10.1193/1.3049405�

INTRODUCTION

Bridges may be susceptible to damage during an earthquake event, particularly ifthey were designed without adequate seismic detailing. However, the likelihood of ex-periencing various levels of damage is best described probabilistically since there is un-certainty in a number of contributing factors, ranging from the characteristics of theseismic event to the detailing and response of the bridge to its ability to sustain demandsbefore suffering damage. This potential for failure is traditionally characterized throughthe development of bridge fragility curves. The use of bridge fragilities has been moti-vated by the importance of these tools in regional seismic risk assessment and loss es-timation packages such as HAZUS-MH (FEMA 2005), REDARS (Cho et al. 2006), orMAEViz (MAEC 2007). Moreover, these types of applications for large inventories ofbridges have necessitated the development of fragility curves for typical classes ofbridges (Dutta and Mander 1998, Choi et al. 2004, FEMA 2005, Nielson and DesRoches2007b). The focus thus far has been to assess the vulnerability of common classes ofbridges in their existing (as-built) condition, which has helped to reveal the most com-mon and potentially vulnerable bridges found in the Central and Southeastern UnitedStates (CSUS).

a) Assistant Professor, Department of Civil and Environmental Engineering, Rice University, 6100 Main Street,MS-318, Houston, TX USA 77005

b) Professor and Associate Chair, School of Civil and Environmental Engineering, Georgia Institute of
Technology, Atlanta, GA USA 30332-0355
117Earthquake Spectra, Volume 25, No. 1, pages 117–141, February 2009; © 2009, Earthquake Engineering Research Institute

118 J. E. PADGETT AND R. DESROCHES

Many bridges across the U.S. either have been or are currently being considered forseismic retrofit in an effort to minimize the potential damage to bridges and to alleviateindirect effects of post-event transportation network closure, such as indirect economiclosses, business disruption, or inhibition of emergency response efforts. Bridges in theCSUS may be prime candidates for seismic retrofit, as many of them were designed withlittle or no seismic consideration. There is, however, a lack of understanding of the im-pact of these retrofits on the bridge fragility. To date, few studies have evaluated the fra-gility of retrofitted bridges (Shinozuka et al. 2002, Kim and Shinozuka 2004, Cimellaroand Domaneschi 2006). Those that have been performed have not utilized a methodol-ogy appropriate for bridge system fragility assessment, nor have they considered a rangeof retrofit measures as is necessary for evaluating the performance for classes of CSUSretrofitted bridges.

The development of fragility curves for bridge types common to the CSUS, with arange of different retrofit measures, provides timely information for decision makers inthat region. Many states are in the early stages of establishing seismic retrofit programs,evaluating bridge vulnerability, and identifying retrofit strategies. Few studies have pro-vided insight into the relative performance of different retrofit measures for bridgescommon to the region, and the use of retrofitted bridge fragility curves offers a quanti-tative measure of the relative benefits of retrofits in terms of reducing the potential forbridge damage. This paper focuses on the development of fragility curves for commonclasses of CSUS bridges with a range of different retrofit measures, encompassing re-sponse modification, partial replacement, and capacity enhancement approaches. The re-sulting fragility curves offer guidance on selecting appropriate retrofits for the bridgesfound in the region and provide key tools for incorporation in regional SRA packagesfor assessing the effects of different mitigation strategies.

REVIEW OF RETROFIT IN THE CSUS

Bridge retrofit activities are at a more mature stage in such West Coast states as Cali-fornia, motivated by past earthquake events like the 1971 San Fernando earthquake.Awareness of the potential seismic hazard in the Central and Southeastern U.S. has morerecently increased and has motivated seismic retrofit activities in some CSUS states. TheCentral U.S. Earthquake Consortium (CUSEC) collaborated with the U.S. Department ofTransportation to prepare a monograph that helps to increase the awareness of the earth-quake risk to transportation systems in the Central U.S. (CUSEC 2000), focusing on thevulnerable regions of Arkansas, Illinois, Indiana, Kentucky, Mississippi, Missouri, andTennessee. They discuss and encourage mitigation efforts, including the development oradoption of sufficient design criteria and bridge retrofit programs that implement tech-nologies that are new and innovative in the CSUS community. Additionally, the authorsof this paper have conducted a review of the state-of-practice in seismic retrofit for theregion, with a focus on highlighting the common approaches (Padgett 2007).

Protection of a number of different bridge components using a range of measureshave been considered or adopted in the region. A subset of retrofit measures are identi-fied for assessment in this paper based on typical practice in the CSUS and/or havingbeen identified as potentially viable retrofit measures for CSUS bridge types based on

RETROFITTED BRIDGE FRAGILITY ANALYSIS FOR TYPICAL CLASSES OF MULTISPAN BRIDGES 119

past studies (Chai et al. 1991, Saiidi et al. 2001, DesRoches et al. 2003, DesRoches et al.2004b, Maleki 2004). Characteristic CSUS bridge deficiencies have been recognized asinadequately detailed columns with limited ductility capacity and low shear strength,brittle steel bearings, short seat widths, and inadequately reinforced pile caps, amongothers (DesRoches et al. 2004a). As such, general column retrofits often include sometype of encasement to improve the shear or flexural strength, flexural confinement andductility capacity, or lap splice performance. Steel jackets, such as those shown in Figure1a from Tennessee, are a common measure that will be included in this study. Isolationis another potential approach to limit the forces transferred to the substructure and re-place existing seismically vulnerable bearings. Figure 1b shows an application of elas-tomeric isolation bearings in Illinois. Avoiding unseating and collapse of bridge spans isa primary concern for most CSUS states, which seek to promote life safety and avoidcomplete bridge damage. The use of restrainer cables (Figure 1c in Kentucky) and seatextenders (Figure 1d) are both common retrofit measures across several states in theCSUS. Some retrofit measures that specifically target lateral restraint or limit excessivetransverse motion have been used. Typically, these take the form of concrete shear keys(Figure 1e), though steel keeper brackets or transverse bumpers are also used. The fiveretrofit measures identified above will be evaluated as a part of this work and cover arange of common bridge retrofits. Note that this list is not fully comprehensive, as othermeasures such as shock transmission units, FRP column wraps, other types of isolationbearings, etc., have already been used in practice in the CSUS and may be considered infuture projects.

Figure 1. CSUS bridge retrofits: (a) steel jackets in TN, (b) elastomeric isolation bearings in IL,(c) restrainer cables in KY, (d) seat extenders in TN, and (e) shear keys in TN.


Little technical support has been offered to date for evaluating the impact of the vari-ous retrofit measures on the seismic performance of bridges in the CSUS region or inselecting measures appropriate for these bridges. There is a strong need for a compara-tive assessment of the viability of various retrofit strategies for typical CSUS bridges. Inaddition to posing a discussion of the array of different retrofit options that are availablefor bridges, the recent edition of the Seismic Retrofitting Manual for Highway Bridges(FHWA 2006) has noted the potential application of fragility curves for assessing bridgevulnerability, prioritizing bridges for retrofit, and performing seismic risk assessments.Building on this philosophy, fragility curves for retrofitted CSUS bridge classes also of-fer an approach for selecting appropriate measures for further detailed assessment. Oneadvantage of this approach is the ability to capture the impact of retrofit on the bridgesystem vulnerability. Most of the retrofit measures noted above tend to target a particularresponse quantity, such as the restrainers that aim to reduce deck displacements andbearing deformations. However, there may be inadvertent affects on other componentssuch as the columns or abutments. This is a particularly important consideration in theCSUS because of the number of different deficiencies that may be present in a singlenonseismically designed bridge class, or may be impacted by the common retrofit mea-sures in either a positive or negative fashion.

SEISMIC FRAGILTY METHODOLOGY FOR RETROFITTEDBRIDGE CLASSES

Seismic fragility curves are conditional probability statements of damage that de-pend on the intensity of the ground motion, while fragility curves for retrofitted bridgesoffer a means of comparing the influence of various retrofit measures on the potentialdamage. The intention of this paper is to develop fragility curves for typical classes ofretrofitted bridges found in the CSUS. These curves are not intended for bridge-specificapplication but instead reflect the vulnerability of a general portfolio of structures andindicate the relative effectiveness of different retrofit measures on the bridge class. Onlya brief overview of the fragility methodology is provided in this paper, while further de-tails on the approach can be found elsewhere (Padgett and DesRoches 2007b).

Following from the basic definition of a fragility, as presented in Equation 1, theseismic demand �D� placed on the structure is assessed relative to its capacity �C� in theevaluation of the conditional probability of failure:

Pf = P�D � C�IM� �1�

where IM is the intensity measure of the ground motion. This indicates the need to es-timate both the seismic demand and capacity to evaluate the fragility for general classesof bridges as addressed in this paper. In the methodology applied, the fragility is evalu-ated both at the component (bearing, column, abutment) and bridge system level, in or-der to assess the source of retrofit contribution to system fragility shift. Three-dimensional, nonlinear time history analysis is used to evaluate the parameters of aprobabilistic demand model. Prior to establishing demand models, statistical samples ofthe bridge must be generated. Random samples of various modeling parameters arecombined with the eight geometric bridge samples to give 96 bridge models. Examples


of the modeling parameters that are varied and the probability distributions used tomodel them are shown in Appendix A. Latin-hypercube sampling is used to generatethese bridge models. This sampling is performed to account for the uncertainty in thebridge inventory as it applies to geometery, material properties, component behaviorsand damping.

Peak component responses from the time history analyses are monitored along witha measure of ground motion intensity, selected as peak ground acceleration (PGA). Inthis case, the PGA is measured as the geometric mean of the peak ground accelerationof the two component motions. This intensity measure was selected from a study of tenIMs in which PGA was found to be an effective predictor of the demand for bridge port-folios, while limiting the uncertainty introduced in the model, among other ideal char-acteristics (Padgett et al. 2008). Following the work by Cornell et al. (2002), the medianvalue of the seismic demand placed on a given component �SD� is assumed to follow apower law function, which in the lognormally transformed state is of the form:

ln�SD� = ln�a� + b ln�IM� �2�

where a and b can be estimated from a regression analysis. The dispersion of the de-mand, �D�IM, conditioned upon the IM is also estimated in the regression analysis. Com-parison of the probabilistic seismic demand models (PSDMs) for different CSUS bridgetypes and retrofit measures are presented below.

Capacity estimates for both as-built and retrofitted components are considered,which correspond to qualitative damage states (DS) termed slight, moderate, extensive,and complete damage. The capacities for each component have been derived using theresults from past experimental testing and the results of an expert opinion survey(Padgett and DesRoches 2007a), such that each limit state is associated with a particularlevel of anticipated bridge functionality. For example, slight damage corresponds todamage for which the bridge is anticipated to be fully open within a day, while extensivedamage corresponds to bridge closure for the first 30 days. Details on the derivation ofthe lognormal probabilistic models of component capacities can be found elsewhere forthe as-built components (Nielson 2005) and retrofitted components (Padgett 2007).However, the extensive table of limit state capacity models (in terms of a median, Sc, andlognormal standard deviation, �c) for each damage state and bridge component in itsretrofitted or as-built condition can be found in Appendix B.

Comparing the demand and capacity models allows for evaluation of the bridge com-ponent fragility, with and without retrofit. Given lognormal probability models for boththe capacity �C� and demand �D�, the conditional failure probability in Equation 1 maybe solved in closed form for each component as shown in Eqn. 3:

P�D � C�PGA� = P�C − D � 0�PGA� = �� ln�SD/Sc��D�IM

2 + �c2� �3�

where � is the standard normal cumulative distribution function, and the ground motionintensity measure has been taken as PGA.


Beyond evaluation of the impact of retrofit on component vulnerability, which offersinsight on the relative impact of retrofit on different components in the system, assess-ment of bridge system fragility is necessary to fully evaluate the effect of a particularmeasure on the bridge performance. While as-built or retrofitted bridge fragility workfor California-type bridges have focused on column vulnerability (Karim and Yamazaki2001, Kim and Shinozuka 2004, Mackie and Stojadinovic 2004), past studies by Nielsonand DesRoches (2007a) have indicated the potential to underestimate system fragilityfor CSUS bridges if other components are neglected. As such, the system fragility foreach class of CSUS retrofitted bridges is evaluated through a Monte Carlo simulationdirectly from the demand and capacity estimates. Correlation between the demandsplaced on various components is assessed to define a joint probability distribution fordemand, and the demand model is integrated across all failure domains (as defined bythe limit state capacity estimates). The instance of any bridge component being at orbeyond a particular limit state constitutes the bridge system being at or beyond that limitstate as well (given a series system approximation). These system failure probabilitiesare evaluated across the range of intensity measures through the Monte Carlo simula-tion, and the parameters for the lognormal distribution representing the system fragility(median and dispersion) are estimated through a regression analysis. This allows for as-sessment of the conditional probability of achieving various qualitative damage statesfor the retrofitted bridge system.

CSUS RETROFITTED BRIDGE CLASSES AND ANALYTICALBRIDGE MODELS

CLASSES OF RETROFITTED BRIDGES CONSIDERED

Recent evaluation of the bridge inventory in the 11 states in the Central and South-eastern U.S. has revealed that nearly 90% of the CSUS inventory is comprised of ninetypical bridge classes (Nielson and DesRoches 2007b). The four most common and mostvulnerable bridge classes have been identified for retrofit evaluation as a part of thiswork. These bridge types (listed in order of their relative vulnerability) include the mul-tispan continuous (MSC) steel girder, multispan simply supported (MSSS) steel girder,MSC concrete girder, and MSSS concrete girder. The details and geometry consideredfor the bridges are based on past studies that have examined bridge plans from over 150bridges (Choi 2002) and presented typical representative configurations for MSSS andMSC steel and concrete girder bridges found in the CSUS. For each bridge class, eightrepresentative geometries have been identified (Nielson 2005) and used in this work inorder to capture geometric variability in the class, e.g., span length, column height, anddeck width; however, other parameters of the bridges are considered as random variablesas discussed later in the paper.

The bridges examined in this study have characteristically nonseismic detailing, suchas multicolumn bents having approximately a 1% longitudinal reinforcement ratio in thecolumns with widely spaced transverse ties providing limited confinement, and high-type steel fixed and expansion (rocker) bearings for the steel bridges. Many of the detailscan be attributed to the median construction period of the bridges, which were found torange from the 1960s to the early 1980s (Nielson and DesRoches 2007b). The bridges


are characteristically non-skewed bridges, as found by Nielson (2005) to be typical ofthe CSUS inventory, and the most common number of spans was found to be three.

The five retrofit measures evaluated in this study for each bridge class are listed inTable 1 along with two common combinations of superstructure retrofits. These mea-sures include steel jackets, elastomeric isolation bearings, steel restrainer cables, seat ex-tenders, and shear keys. Assumptions are made as to the design approach and character-istics of each class of retrofit, while some uncertainties in the future realization of theseretrofits are also considered. As such, the results are relevant for the following set ofassumptions based on a review of the current state of retrofit practice in the region(Padgett 2007), though the methodology could be applied for other conditions:

• Full height circular column jackets are considered, as it is common practice inthe region.

• The restrainer cables are designed to carry half of the weight of the superstruc-ture.

• Transverse keeper plates are provided in the detailing for the elastomeric isola-tion bearings. The bearings are designed to produce a two- to threefold increasein the fundamental period in the longitudinal direction.

• The concrete shear keys are designed to limit the force transferred to the col-umns to approximately half of the columns’ shear strength.

• The seat extenders are assumed to provide an additional 152 mm of support be-yond the bent beam.

With characteristics of the common bridge types and retrofit measures to be evalu-ated for the CSUS, the methodology presented above is applied for all bridge types andretrofit measures in order to better understand the impact on bridge fragility. Compari-sons are made at intermediate stages between the as-built and retrofitted bridges classesto identify sources of fragility impact stemming from demand shift, capacity enhance-ment, or component vulnerability. The modeling scheme used in the analytical fragilitymethod for the classes of retrofitted bridges is presented below.

Table 1. Retrofit measures considered

Retrofit Abbreviation

Steel column jacket Steel jacketElastomeric isolation bearing Elasto brgSteel restrainer cables RestrainerSeat extenders Seat extenderTransverse shear keys Shear keyRestrainer cables and shear keys RC & SKSeat extenders and shear keys SE & SK


FINITE ELEMENT BRIDGE MODELS

Three-dimensional nonlinear analytical models are created using the OpenSEESplatform to develop the fragility curves (McKenna and Fenves 2005). The compositeslab and girders are modeled using linear elastic models, since the deck is expected toremain elastic. Pounding between the decks is modeled using a multilinear pounding el-ement (Muthukumar and DesRoches 2005, Muthukumar and DesRoches 2006). Thebearings are modeled using nonlinear inelastic elements that represent the stiffness andstrength degradation observed during experimental tests (Choi 2002). Discretized fibersections are used for the circular columns and beam-column elements are used for theconcrete bent beams. The pile foundations are modeled with simplified linear transla-tional and rotational springs. The active, passive, and transverse responses of the abut-ments are represented by nonlinear inelastic springs.

A similar level of fidelity is used to model the retrofitted components of the bridge.The elastomeric bearings are modeled using bilinear springs in the longitudinal andtransverse directions. The restrainer cables are modeled using tension-only springs witha gap representing the initial slack in the cables. The steel jackets are modeled by alter-ing the column section model. Material models for the concrete fibers have an increasedcompressive strength and ultimate strain due to the jacket. The elastic modulus is alsoincreased to reflect the increase in stiffness due to jacketing.

INTERMEDIATE RESULTS AND COMPARISONS

COMPERISON OF PROBABILISTIC SEISMIC DEMAND MODLES

Probabilistic seismic demand models are constructed using the results of nonlineartime history analysis with 48 ground motions from Wen and Wu (2001) and 48 groundmotions from Rix and Fernandez (2004). The three-dimensional analytical models foreach bridge type consider the potential nonlinear behavior of a number of componentsranging from the bearings, to columns, to abutments as noted above. It is noted that foreach type of retrofitted bridge up to 18 variable parameters (i.e., bearing stiffness, re-strainer slack, gap between deck, etc.) with defined probabilistic models were consid-ered. The use of a preliminary screening study permitted a considerable reduction in thenumber of parameters sampled upon to an average of four variables in addition to con-sidering eight base geometries in simulating the 96 bridge models for each PSDM. Ingeneral, variation in the gross geometric properties, the angle of loading with the two-component ground motions, and a handful of analytical modeling parameters were con-sidered for each bridge type and retrofit measure based on their significant influence onthe seismic response. If the variable was found to be significant for any bridge or retrofittype and subsequently used in the Latin Hypercube sampling for at least one retrofittedbridge class PSDM, it is listed in Appendix A.


Retrofit Measure

The PSDMs reveal the impact of a given retrofit measure on the seismic demandplaced on each component of a particular class of retrofitted bridges. The componentdemands considered in this work include column curvature ductility demands, fixedbearing deformations in the longitudinal and transverse directions, expansion bearingdeformations in the longitudinal and transverse directions, and abutment deformations inpassive, active, and transverse action. In general, the results reveal that some retrofitmeasures reduce the demand placed on a component (i.e., the targeted response quan-tity) yet may increase the demand placed on another component. Alternatively, the de-mand on some bridge components may not be affected at all. The findings are unique foreach retrofit measure considered.

Taking the MSC steel girder bridge class as an example, the impact of two differentretrofit measures on the demand models is compared in Table 2. Recall that the param-eters listed represent the regression parameters from Equation 2 along with the disper-sion. From the table it is evident that the elastomeric bearings reduce the median valueof the demands placed on the columns, exhibited by the reduction in parameters affect-ing both the intercept �ln�a�� and slope �b� of the regression model. In addition, theyresult in a slight reduction in the dispersion in the demand ��D�IM�. On the other hand,the use of elastomeric isolation bearings yields an increase in the median value of thepassive abutment demands. Different retrofits have different relative effects on the com-ponent demands. The restrainer cables are shown to result in a slight reduction in themedian of the demand placed on the columns and the longitudinal bearing deformations.However, they result in a considerable increase in the demand model for the abutmentdeformation in active action, increasing parameters that effect the median and dispersionassociated with that component. As anticipated, the restrainers have a negligible effecton the PSDM for transverse bearing deformation.

Table 2. Sample PSDMs for two different retrofits of the MSC steel girder bridge class

As-BuiltElastomeric

BearingsRestrainer

Cables

Component Response ln�a� b �D�IM ln�a� b �D�IM ln�a� b �D�IM

column ductility 1.92 1.71 0.88 0.89 1.38 0.74 1.62 1.60 0.88fixed bearing deformation-Long. 2.08 1.59 1.00 5.62 1.15 0.69 1.44 1.38 0.90fixed bearing deformation-Trans. 2.97 1.82 1.23 3.19 0.31 0.24 2.93 1.79 1.19expansion bearing deformation-Long. 5.80 1.46 0.73 5.62 1.15 0.69 5.45 1.34 0.65expansion bearing deformation-Trans. 4.44 1.94 0.99 3.19 0.31 0.24 4.41 1.93 0.98abutment deformation-Passive 3.72 2.29 1.83 4.29 2.37 1.71 2.80 1.97 1.76abutment deformation-Active 0.35 0.62 0.59 0.92 0.66 0.54 3.95 1.83 1.30abutment deformation-Trans. 2.38 0.87 0.49 4.00 1.64 1.10 2.43 0.89 0.52


Bridge Type

The relative demands placed on bridge components vary by bridge type, as does theinfluence of different retrofit measures on those demand models. As an example, Figure2a shows the regression lines from the demand models for active abutment deformationsfor the MSC and MSSS steel girder bridges. Shown relative to the as-built demands(solid lines) are the median demand models for the bridge retrofit with restrainer cables.The plot reveals that the initial demands placed on the as-built abutments were quitedifferent, with higher initial demands placed on the MSSS bridge. However, it is shownthat the restrainer cables have a larger impact on the MSC bridge’s abutment demandsthan the MSSS bridge, leading to a considerable shift in the regression line for the me-dian value of the demand relative to the as-built. For this particular example, the largerinertial mass of the MSC bridge as compared with the MSSS bridge that is transferredthrough the cable forces is a causative factor for the larger increase in abutmentdeformations.

Figure 2b shows another example comparing the transverse fixed bearing deforma-tions for two different classes of continuous bridges in the as-built state and retrofit withshear keys. While the results are more subtly revealed in this case, the shear key retrofithas more of an impact on reducing the fixed bearing deformations (at higher PGAs) forthe steel bridge than its concrete counterpart. This is attributed to the relative weight,bearing types, and configurations of the bridges. The comparisons shown focus primarilyon the fact that the retrofits dissimilarly impact the median value of the demand for dif-ferent bridge types. In many cases, the retrofits have a dissimilar impact on the disper-sion in the demand for various bridge types. For example, the use of elastomeric isola-tion bearings leads to a 54% reduction in the dispersion in active abutment deformationsin the MSC concrete girder bridge, but has only an 8% reduction in the MSC steel girderbridge. The retrofit impacts on the component demands are most meaningful when com-

(a) (b)

Figure 2. Comparison of the resulting PSDM regression for the median value of the (a) activeabutment and (b) transverse fixed bearing deformations for different bridge types and retrofitmeasures.


pared relative to the actual capacity of the component. However, insight gained from thedemand models as exemplified above reveals the root of the component fragility shift.

COMPARISON OF COMPONENT FRAGILITY

Retrofit Measure

Evaluation of the component fragility curves offers a means to assess whether theretrofit measures have an impact on the probability of damage of the component con-sidering both the impact of retrofit on the bridge’s demand and capacity. Additionally,these retrofitted component fragility curves provide an explanation for why a given ret-rofit measure has an impact on the bridge system fragility. As concluded from the de-mand analysis in the previous section, different retrofit measures have a dissimilar im-pact on the fragility of a component for a given bridge type and damage state. If thecomponent is already a highly vulnerable component in the bridge, the relative ability ofdifferent retrofit measures to reduce that fragility is an important contributing factor toits ability to improve the system.

Figure 3 shows the fragility curves for the moderate damage state of three compo-nents in the MSC steel girder bridge with several retrofit measures relative to the as-builtbridge. These plots reveal that for a given bridge type and damage state, the impact of aretrofit measure can vary dramatically from one component to another. For example, therestrainer cables are shown to have a slight positive impact on the columns, no impact onthe expansion bearings in the transverse direction, and a negative impact on the abut-ments in active action. The relative effectiveness of different retrofits for a particularcomponent is also evident. The elastomeric bearings have a large impact in reducingtransverse bearing vulnerability (by replacing existing steel bearings with isolation bear-ings), the shear keys result in a notable reduction, yet the restrainers and steel jacketshave virtually no effect on this component.

Bridge Type

The effectiveness of a given retrofit in reducing component vulnerability is also afunction of the bridge type common to the CSUS. An example of this is shown in Figure4, comparing the impact of shear keys on the moderate damage state fragility of thefixed bearings in the transverse direction. The retrofit has a considerable impact on thebearings in the MSC steel girder bridge, but has a negligible impact on the MSSS steelgirder bridge. Differences in bearing and bridge configuration are contributing factors tothis finding, where the abutment helps to restrain the entire bridge deck of the continu-ous bridge and reduce bearing deformations when a transfer mechanism is provided bythe shear keys. The fact that different retrofit measures are more effective in reducingcomponent vulnerability for some bridge types follows intuition, given that the dynamiccharacteristics of each bridge class are unique. These include, among other properties,differences in typical geometries, bearing types, and construction materials, which havean effect on the natural frequencies and nonlinear dynamic response.


(a) (b)

(c)

Figure 3. Moderate damage component fragilities with various retrofit measures for the MSCsteel girder bridge: (a) columns, (b) expansion bearings in the transverse direction, and (c) abut-
ments in active action.
Figure 4. Comparison of the impact of Shear Keys on the moderate damage state of fixed bear-
ings in the Continuous and Simply Supported steel girder bridge classes.


Damage State

A given retrofit measure may be more effective in reducing the potential for a par-ticular level of component damage. Some measures may be more effective at the lowerdamage states and others at the extensive or complete damage state. A primary exampleof this is the seat extenders, which only affect the longitudinal bearing vulnerability atthe complete damage state. This is due to their influence in shifting the bearing capacitylimit states for complete damage due to increased support length. While the seat extend-ers have the same effect regardless of bridge type, the relative effectiveness of a particu-lar retrofit on component vulnerability tends to vary by bridge type. The MSSS steelgirder bridge is used as an example to examine how the effectiveness of different retro-fits differs by damage state for the longitudinal vulnerability of the expansion bearings.As shown in Figure 5, the seat extenders have no impact on the slight damage state butconsiderably reduce the component vulnerability at the complete damage state. For thisbridge type, the restrainer cables have a very limited impact on the slight damage state,because of the low levels of deformation that lead to slight bearing damage and the rela-tive slack in the cables. However, their effectiveness is increased by the higher damagestate, where they are more effective in avoiding complete damage of the bearings for theMSSS steel girder bridge.

Figure 5. Comparison of the effectiveness of different retrofits on component vulnerability as afunction of damage state.


BRIDGE SYSTEM FRAGILITY RESULTS

RETROFITTED BRIDGE SYSTEM FRAGILITY

The culmination of this work evaluates the impact of retrofit on bridge system vul-nerability. Applying the methodology above, the bridge system fragility curves are de-rived for each CSUS bridge type and retrofit measure. These fragility curves are alsoestimated as lognormal distributions of the form

P�DS�PGA� = �� ln�PGA� − ln�medsys��sys

� �4�

where medsys is the median value of the system fragility (in units of g PGA), and �sys isthe dispersion, or logarithmic standard deviation, of the system fragility. These param-eters are estimated by a regression analysis of the failure probability estimates from theintegration across all potential failure domains. The fragility statement gives the prob-ability of entering a particular damage state, DS, for the bridge system (i.e., slight, mod-erate, extensive, or complete), based on the system failure model and limit states previ-ously discussed where each capacity estimate corresponds to a particular damage state.The parameters for the retrofitted bridge system fragility curves developed are shown inTables 3–6 for the four CSUS bridge classes. A discussion on the relative effectivenessof retrofits for different bridge types and damage states will follow in a later section.

MODIFICATION FACTORS

Previous research has proposed factors for scaling the median PGA value of an as-built bridge to account for a particular retrofit measure. Work by Kim and Shinozuka(2004) has presented an enhancement curve used to scale the median of the fragility oftypical California-type multiframe concrete bridges, based on analysis of two represen-tative structures. These were used to assess the impact of jacketing on the bridge fragil-ity curves developed through empirical data. While it is shown in the tables above thatsome retrofit measures evaluated for CSUS bridges can also affect the dispersion for the

Table 3. MSSS steel girder retrofitted bridge fragility curves

Slight Moderate Extensive Complete

Retrofit Condition medsys �sys medsys �sys medsys �sys medsys �sys

As-Built 0.25 0.45 0.47 0.40 0.60 0.44 0.91 0.50Steel Jackets 0.26 0.44 0.50 0.38 0.65 0.42 1.03 0.50Elastomeric Isolation Bearings 0.39 0.61 0.62 0.59 0.83 0.63 1.27 0.64Restrainer Cables 0.26 0.45 0.48 0.39 0.63 0.42 1.02 0.49Seat Extenders 0.25 0.46 0.47 0.40 0.61 0.44 1.15 0.49Shear Keys 0.25 0.46 0.46 0.41 0.59 0.44 0.89 0.50Restrainer Cables & Shear Keys 0.25 0.45 0.48 0.40 0.63 0.42 1.00 0.49Seat Extenders & Shear Keys 0.25 0.45 0.46 0.40 0.60 0.44 1.13 0.49


Table 4. MSC steel girder retrofitted bridge fragility curves




Table 5. MSSS concrete girder retrofitted bridge fragility curves




Table 6. MSC concrete girder retrofitted bridge fragility curves





fragility estimate, shifts in the median value are often indications of the most notablechanges in vulnerability. Presented herein are modification factors (retrofitted/as-builtmedian) that reveal the relative shift in the median value due to various retrofit measures(Tables 7 and 8). These modification factors can be applied as scalars to the medianPGA for as-built fragility curves to indicate the impact of retrofit. Care should be usedsuch that they are applied to similar classes and assumptions of bridge characteristicsand would be appropriate for use in conjunction with such fragility curves as those de-veloped by Nielson and DesRoches (2007b). Additionally, these modification factorspresent the opportunity to assess retrofit for refined sets of fragility curves developed inthe future, or empirical fragility curves should sufficient data allow for their develop-ment for these bridge types. However, a note of caution is provided that this does notfully capture the impact of retrofit in terms of altering the dispersion, for which Tables3–6 indicate a limited potential, particularly when using isolation bearings.

Table 7. Modification factors for median PGA of the steel girder bridgeclasses.

MSSS Steel MSC Steel

Retrofit Measure S M E C S M E C

Steel Jackets 1.06 1.06 1.07 1.13 1.04 1.14 1.14 1.18Elastomeric Isolation Bearings 1.57 1.00 1.37 1.39 1.37 1.00 1.27 1.61Restrainer Cables 1.03 1.03 1.04 1.11 1.03 1.05 1.11 1.17Seat Extenders 1.00 1.00 1.00 1.26 0.99 1.01 1.00 1.21Shear Keys 0.99 0.98 0.98 0.97 1.08 1.14 1.13 1.09Restrainers & Shear Keys 1.02 1.02 1.04 1.09 1.09 1.17 1.21 1.21Seat Extenders & Shear Keys 0.99 0.98 0.99 1.23 1.09 1.15 1.15 1.41

* Note: S=Slight; M=Moderate; E=Extensive; C=Complete

Table 8. Modification factors for median PGA of the concrete girderbridge classes.

MSSS Concrete MSC Concrete

Retrofit Measure S M E C S M E C

Steel Jackets 1.05 1.30 1.33 1.41 1.03 1.16 1.17 1.20Elastomeric Isolation Bearings 1.62 1.00 1.05 1.17 2.94 1.31 1.21 1.17Restrainer Cables 1.01 1.07 1.10 1.13 1.04 0.96 1.01 1.05Seat Extenders 0.99 1.03 1.02 1.32 1.01 1.00 1.00 1.31Shear Keys 1.04 0.97 0.92 0.87 1.01 0.98 0.99 1.01Restrainers & Shear Keys 1.06 1.03 1.06 1.07 1.04 0.96 1.04 1.12Seat Extenders & Shear Keys 1.04 1.01 0.95 1.22 1.01 0.97 0.99 1.37

*
Note: S=Slight; M=Moderate; E=Extensive; C=Complete


DISCUSSION

Plots of the fragility curves for the MSC concrete girder bridge are shown in Figure6 to illustrate the relative vulnerability of the as-built and retrofitted bridge system overa range of earthquake intensities and damage states. Additionally, a comparison of themedian PGA values for this class and the other three retrofitted bridge classes consid-ered is shown in Figure 7. The figures facilitate comparison of the relative effectivenessof different retrofit measures for the various bridge classes typical to the Central andSoutheastern U.S. and for damage states ranging from slight to complete.

MSSS STEEL

Evaluation of the fragilities (and median PGAs as shown in Figure 7) for the MSSSsteel girder bridge indicate that for the slight through extensive damage state, the elas-tomeric isolation bearing retrofit is the only measure that has a considerable impact onthe system vulnerability. This is due to the fact that the steel fixed bearings followed by

Figure 6. Fragility curves for the MSSS concrete girder bridge class, comparing the as-builtand retrofitted bridge fragility for each damage state.


the expansion bearings tended to dominate the bridge vulnerability at the lower damagestates. By replacing the vulnerable steel bearings with isolation bearings, the fragility issignificantly reduced. At these damage states, the other retrofit measures are not particu-larly effective in reducing the system vulnerability, primarily because of the vulnerabil-ity of the steel bearings. The restrainer cables have little impact at the lower damagestates because of the low levels of displacement required to induce damage in the fixedbearings and relative slack in the cables, and for the higher damage states were not par-ticularly effective in limiting deformations because of cable yielding. The findings areconsistent with the results of the component fragility for expansion bearing deforma-tions as previously discussed and presented in Figure 5. For the complete damage state,the seat extenders are effective due to the increase in the limit state capacity for com-plete damage, and the important contribution that the bearings in this bridge have on thesystem fragility.

Figure 7. Comparison of as-built and retrofitted median fragility values for each damage statefor the (a) MSSS steel, (b) MSC steel, (c) MSSS concrete, and (d) MSC concrete girderbridges.


MSC STEEL

The MSC steel girder bridge is the most vulnerable bridge type in the CSUS inven-tory (Nielson and DesRoches 2007b). The steel bearings in this bridge are still a primaryconcern, however; the fixed bearings above the columns are not as vulnerable as the ex-pansion bearings at the far ends of the continuous bridge deck, due to the large expan-sion joint at the deck ends. In addition, larger demands are placed on the columns of thisbridge because of the inertial loads of the continuous deck acting in unison. The elas-tomeric bearings, therefore, are effective in replacing the more vulnerable steel expan-sion bearings. However, because all the bearings act similarly in order to isolate the su-perstructure from the substructure, the demands are fairly high, causing them to beslightly more vulnerable than the original fixed bearings (which are not required to de-form considerably).

The expansion bearings are also vulnerable to damage in the transverse direction,which is part of the explanation for the synergistic improvement of the performance ofthe MSC steel girder bridge with seat extenders and shear keys. While the steel jacketshave a significant impact on reducing the column vulnerability, their inability to affectother components results in limited improvement for the bridge system fragility. The re-strainer cables offer a slight improvement in the vulnerability of the expansion bearings.However, the cables transfer large forces to the abutments, increasing the systemvulnerability.

MSSS CONCRETE

Figure 6 shows the relative vulnerability of the as-built and retrofitted MSSS con-crete girder bridge. This concrete girder bridge has considerably fewer vulnerable bear-ings than its steel counterpart, yet has a larger mass. The relative vulnerability of variouscomponents in this as-built bridge varies considerably depending on the damage state.This helps to explain why different retrofits have a varying effect at the different damagestates. For example, at the slight damage state, the longitudinal fixed and expansionbearings, as well as the abutments in active action, are the most susceptible to damage.Hence, the elastomeric bearings are particularly effective because they both replace thebearings and reduce the active demands placed on the abutments. Beyond the limit ofmoderate damage, the columns tend to become more vulnerable and the steel jacketingbecomes particularly effective. The elastomeric bearings are not as effective beyond theslight damage state as one might have expected, because of the increased vulnerability ofthe abutments in the transverse direction due to pounding of the heavier deck against thewingwall. It is also interesting to note that the use of shear keys actually increases thesystem vulnerability at the higher damage states. This is because the bearings of thebridge are not particularly susceptible to the higher levels of damage in the transversedirection, so there is negligible positive effect realized. Instead the shear keys actuallyresult in more vulnerable columns due to the inertial loads transferred when the bridgeis excited in the transverse direction.


MSC CONCRETE

It is evident from the plot in Figure 7 that the elastomeric bearings are very effectiveat the slight damage state for the MSC concrete girder bridge, although no other mea-sures impact the system fragility. The steel jackets are effective in reducing the columnvulnerability at the slight damage state, but the other vulnerable components are not im-proved. The slight improvement in transverse bearing vulnerability (though not a par-ticularly vulnerable component) using the shear keys is offset by the increased vulner-ability of the transverse demands on the abutments. As seen with the MSSS concretegirder bridge, the steel jackets tend to be more effective at limiting the higher levels ofdamage where the columns contribute more to the vulnerability (i.e., 20% increase incomplete damage state median value). The restrainer cables, however, are not effectivefor this bridge because their effectiveness on improving bearing performance is limitedby the yielding of the cables induced by the large inertial loads. Additionally, any posi-tive benefit they have is negated by the negative impact on the abutments in active ac-tion. Like the other bridge types, the seat extenders become effective at the completedamage state because they virtually remove any contribution of the bearings to the sys-tem’s potential for complete damage.

GENERAL FINDINGS FOR BRIDGE RETROFIT

The results from the previous section illustrate that the effectiveness of different ret-rofit measures is a function of both the bridge type and damage state being considered.However, there are several observations which can be made that could assist decisionmakers regarding bridge retrofit.

In general, none of the retrofit measures are particularly effective in reducing theprobability of having slight damage in the bridges, except for the elastomeric bearings.This is due to the fact that the slight damage state tends to be controlled by the vulner-able bearings connecting the piers to the bridge deck, as is the case for both the steelgirder bridges and the concrete girder bridges. Given the infrequent nature of earth-quakes in the CSUS, and the short time needed to restore full functionality for bridges inthe slight damage state, it is not likely that avoiding slight damage would be a preferredtarget performance goal for retrofit selection.

Seat extenders are generally among the most effective measures for reducing thelikelihood of complete damage in most of the bridge types evaluated. By extending theseat support length, unseating as a mode of failure is eliminated, thereby significantlyreducing the vulnerability of the bridge to the complete damage state. Seat extendersalso tend to be a cost-effective measure, making their use particularly attractive. Thecombined use of the seat extenders and shear keys is more effective for the continuousbridges than the simply supported bridges, due to the ability to help resist the transversedisplacements induced by the large inertial mass as well as the unseating potential. Thiscommon combination of superstructure retrofits may also be a highly viable approachfor the continuous bridges found in this region, should avoiding complete damage be thetarget objective.

For the moderate and extensive damage states, the effectiveness of different retrofit


measures varied by bridge type. The retrofit measures that addressed the most vulnerablecomponents of that bridge tend to be the most effective in reducing the overall bridgesystem vulnerability. For the concrete girder bridges, where the columns are a dominantcontributor to the fragility, the steel jackets are relatively effective, while for the steelgirder bridges supported on steel bearings, isolation tends to be the preferred approach.

CONCLUSIONS

This paper presents fragility curves developed for a range of retrofit measures con-sidered for four common bridge classes in the Central and Southeastern United States.The retrofits addressed include steel jackets, elastomeric isolation bearings, restrainercables, shear keys, seat extenders, and common combinations of the above. The meth-odology for assessing the fragility of the retrofitted bridges includes the use of three-dimensionsal nonlinear analytical models and time history analyis, extensive uncertaintytreatment, and incorporation of the impact of retrofit on multiple vulnerable componentsfor system fragility estimation. Through the process, the impact of retrofit on the proba-bilistic seismic demand models, component capacities, component and system vulner-ability is evaluated.

The intermediate analyses building up to the system fragility estimate offer key in-sight as to how different retrofit measures influence the demand placed on various com-ponents in the syste, and how they affect the fragility of the components when comparedto their capacity. It is found that some retrofits may have the negative effect of actuallyincreasing the demands placed on certain components as observed in the PSDMs,though they tend to improve the response of the targeted component. For example, formany of the bridge types, the elastomeric bearings increase the abutment vulnerability inpassive action, or the restrainers increase the active vulnerability. The ultimate impact ofthe retrofit measure on the system fragility is a function of the relative vulnerability ofthe various components in the system and the influence of the retrofit on shifting thosevulnerabilities. The effectiveness of the retrofit measure in improving system fragilitydepends upon which bridge type and damage state is being considered. In general, forthe slight damage state, the only retrofit measure that is effective in all bridge types isthe use of elastomeric bearings. This is because the slight damage state is controlled bydamage to the vulnerable bearings in steel girder and concrete girder bridges. Con-versely, for the complete damage state, seat extenders tend to be among the most effec-tive measure for most bridge types, since it essentially significantly reduces the likeli-hood of failure due to unseating.

The lognormal parameters defining the retrofitted bridge system fragility are pre-sented in this work for comparison of different retrofit measures and in a form such thatthey can be easily incorporated into seismic risk assessment packages for the CSUS re-gion. Additionally, modification factors are computed from the results for application toappropriate related as-built fragilities in order to scale the median PGA and estimate theimpact of retrofit. The proposed fragility curves presented provide the opportunity fordecision makers to compare and select suitable retrofit measures for the bridges commonto the CSUS region and serve as key tools for advanced analyses such as regional riskassessment or probabilistic cost-benefit analyses.


ACKNOWLEDGMENTS

This study has been supported by the Earthquake Engineering Research Centers pro-gram of the National Science Foundation under Award Number EEC-9701785 (Mid-America Earthquake Center).

APPENDIX A

Table 9 lists the probability distributions that were used in generating bridge modelsfor the probabilistic seismic demand analysis. Only parameters that were found to havea statistically significant impact on the response for at least one bridge type and retrofitmeasure are listed.

Table 9. Probability models for uncertain parameters considered in analysis that were signifi-cant for at least one bridge type and retrofit measure (Note: a total of 34 parameters wereconsidered)

Modeling Parameter Distribution Parameters UnitsSignificant for Retrofit

of Bridge Class**

loading direction Uniform 0 2� rad all

damping ratio Normal µ=0.045 �=0.0125 MSSS-S, MSC-S, MSC-C

fixed bearing stiffness (ratio) Uniform 0.5 1.5 MSSS-S, MSC-S

fixed bearing COF Lognormal �=0.21 �=0.5 MSSS-S

mass of deck (ratio) Uniform 0.9 1.1 MSSS-S, MSSS-C

active abutment stiffness Uniform 2.2 6.6 kN/mm/m all

foundation rotational stiffness Uniform 3.03*105 9.09*105 kN-m/rad MSSS-S, MSSS-C

deck-abutment gap (MSC-S) Normal µ=76.2 �=24.1 mm MSC-S

deck-abutment gap (MSC-C) Normal µ=38.1 �=4.32 mm MSC-C

deck-deck gap (MSSS-S) Normal µ=25.4 �=4.32 mm MSSS-S

pad shear modulus Uniform 0.66 2.07 MPa MSC-S

pad COF Normal �=ln�med� �=0.1 MSSS-C

concrete strength Normal µ=33.8 �=4.3 MPa MSSS-C

steel strength Lognormal �=6.13 �=0.08 MPa MSSS-C

restrainer cable length Uniform 1.52 3.05 m MSSS-S

restrainer cable slack Uniform 0 19.1 mm MSC-S, MSSS-C

effective EB stiffness (MSSS-S) Uniform 420.3 840.6 N/mm MSSS-S

effective EB stiffness (MSSS-C) Uniform 175.1 245.2 N/mm MSSS-C

gap to EB keeper Uniform 6.4 19.1 mm MSSS-S, MSC-C

SJ % increase in column stiffness Uniform 20 40 MSSS-S

gap between column and SJ Uniform 12.7 25.4 mm MSC-S, MSC-S

gap to shear key Uniform 6.4 19.1 mm MSC-S

* Note: MSSS=multispan simply supported; MSC=multispan continuous; S=steel; C=concrete; COF=coefficient of friction; EB=elastomeric isolation bearing; SJ=steel jacket** Note: bridge class is listed if the parameter is significant for at least one of the retrofitted bridge types within

that class


APPENDIX B

Table 10 presents the limit state capacities for as-built and retrofitted componentsused in the fragility analysis.

Table 10. Limit state capacities for as-built (Nielson and DesRoches 2007b) and retrofitted(Padgett 2007) components


As-Built Component Sc �c Sc �c Sc �c Sc �c

Concrete Column �µ�� 1.29 0.59 2.1 0.51 3.52 0.64 5.24 0.65Steel Bearing Fixed-Long (mm) 6.00 0.25 20.0 0.25 40.0 0.47 187 0.65Steel Bearing Fixed-Tran (mm) 6.00 0.25 20.0 0.25 40.0 0.47 187 0.65Steel Bearing Rocker-Long (mm) 37.40 0.60 104.0 0.55 136.0 0.59 187 0.65Steel Bearing Rocker-Tran (mm) 6.00 0.25 20.0 0.25 40.0 0.47 187 0.65Elastomeric Bearing Fixed-Long (mm) 28.90 0.60 104.0 0.55 136.0 0.59 187 0.65Elastomeric Bearing Fixed-Tran (mm) 28.80 0.79 90.90 0.68 142.0 0.73 195 0.66Elastomeric Bearing Expan-Long (mm) 28.90 0.60 104.0 0.55 136.0 0.59 187 0.65Elastomeric Bearing Expan-Tran (mm) 28.80 0.79 90.9 0.68 142.0 0.73 195 0.66Abutment-Passive (mm) 37 0.46 146 0.46 N/A N/A N/A N/AAbutment-Active (mm) 9.8 0.70 37.9 0.90 77.2 0.85 N/A N/AAbutment-Tran (mm) 9.8 0.70 37.9 0.90 77.2 0.85 N/A N/A


Retrofitted Component Sc �c Sc �c Sc �c Sc �c

Elastomeric Isolation BearingsMSSS Steel Bridge-Long (mm) 76.2 0.60 114.3 0.55 152.4 0.59 266.7 0.65MSSS Steel Bridge-Trans (mm) 76.2 0.79 114.3 0.68 152.4 0.73 266.7 0.66MSC Steel Bridge-Long (mm) 82.6 0.60 123.8 0.55 165.1 0.59 289.1 0.65MSC Steel Bridge-Trans (mm) 82.6 0.79 123.8 0.68 165.1 0.73 289.1 0.66MSSS Conc Bridge-Long (mm) 146.0 0.60 219.1 0.55 292.1 0.59 511.2 0.65MSSS Conc Bridge-Trans (mm) 146.0 0.79 219.1 0.68 292.1 0.73 511.2 0.66MSC Conc Bridge-Long (mm) 139.7 0.60 209.6 0.55 279.4 0.59 489.0 0.65MSC Conc Bridge-Trans (mm) 139.7 0.79 209.6 0.68 279.4 0.73 489.0 0.66

Steel Jacketed Column �µ�� 9.35 0.59 17.71 0.51 26.06 0.64 30.24 0.65Steel Bearing Fixed-Long w/SE (mm) 6.0 0.25 20.0 0.25 40.0 0.47 339.0 0.65Steel Bearing Rocker-Long w/SE (mm) 37.4 0.6 104.2 0.55 136.1 0.59 339.0 0.65Elastomeric Bearing Fixed-Long w/SE (mm) 28.9 0.6 104.2 0.55 136.1 0.59 339.0 0.65Elastomeric Bearing Expan-Long w/SE (mm) 28.9 0.6 104.2 0.55 136.1 0.59 339.0 0.65

*
Note: SE=seat extender


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(Received 20 September 2007; accepted 24 July 2008�

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