bridge vulnerablity curves

8/10/2019 Bridge Vulnerablity Curves

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EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS Earthquake Engng Struct. Dyn. 2008; 37 :11571174Published online 11 April 2008 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.801

Methodology for the development of analytical fragility curves forretrotted bridges

Jamie E. Padgett 1, , and Reginald DesRoches 2

1 Department of Civil and Environmental Engineering , Rice University , MS-318 , 6100 Main St. , Houston ,TX 77005 , U.S.A.

2School of Civil and Environmental Engineering , Georgia Institute of Technology , Atlanta , GA, U.S.A.

SUMMARYFragility curves for retrotted bridges indicate the inuence of various retrot measures on the probabilityof achieving specied levels of damage. This paper presents an analytical methodology for developingfragility curves for classes of retrotted bridge systems. The approach captures the impact of retrot onthe vulnerability of multiple components, which to date has not been adequately addressed, and results ina comparison of the system fragility before and after the application of different retrot measures. Detailspresented include analytical modeling, uncertainty treatment, impact of retrot on demand models, capacityestimates, and component and system fragility curves. The ndings indicate the importance of evaluatingthe impact of retrot not only on the targeted response quantity and component vulnerability but also onthe overall bridge fragility. As illustrated by the case study of a retrotted multi-span continuous (MSC)concrete girder bridge class, a given retrot measure may have a positive impact on some components,yet no impact or a negative impact on other critical components. Consideration of the fragility basedonly on individual retrotted components, without regard for the system, may lead to over-estimation or

under-estimation of the impact on the bridge fragility. The proposed methodology provides an opportunityto effectively compare the fragility of the MSC concrete bridge retrot with a range of different retrotmeasures. The most effective retrot in reducing probable damage for a given intensity is a function of the damage state of interest. Copyright q 2008 John Wiley & Sons, Ltd.

Received 27 August 2007; Revised 19 January 2008; Accepted 23 January 2008

KEY WORDS : seismic; fragility; bridges; retrot; reliability; concrete

Correspondence to: Jamie E. Padgett, Department of Civil and Environmental Engineering, Rice University, MS-318,6100 Main St., Houston, TX 77005, U.S.A.

E-mail: [email protected]

Contract / grant sponsor: National Science Foundation; contract / grant number: EEC-9701785

Copyright q 2008 John Wiley & Sons, Ltd.


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1160 J. E. PADGETT AND R. DESROCHES

2.2. Limit state capacities

Limit states capacities, or capacity estimates for short, are dened as a measure of the capacity of the bridge component to withstand the demands placed upon it during seismic excitation. These

models are often dened based on expert judgment, experimental data, analytical methods, orcombinations thereof. The as-built capacity estimates used as a part of this methodology are thosepresented by Nielson [24 ] and will be discussed in further detail in the following sections. As manyother studies have assumed, the limit states capacities follow a lognormal distribution [19, 25, 26 ].This provides ease of convolution with the lognormally distributed demands, where a closed-formsolution for the fragility is also in lognormal form as shown in the following equation:

Fragility =ln( S d / S c)

2 D | IM + 2C (4)

where S c is the median value of the structural capacity (for the limit state) and C is its associatedlogarithmic standard deviation of structural capacity. The details associated with estimating theseparameters will be presented throughout the paper.

2.3. Component and system fragility

The formulation presented above illustrates the fragility for a single representative componentand demand parameter. In the proposed methodology, it has been deemed that multiple criticalcomponent vulnerabilities can be affected by a given retrot measure. Therefore, a number of different component fragilities are captured and can be evaluated as shown in Equation (4). Thecomponents responses considered range from those associated with the columns to abutments tobearings, as listed in Table I. As discussed in Section 3, the fragility methodology considers three-dimensional analytical models and seismic response; hence, the response parameters evaluatedinclude both longitudinal and transverse actions.

The component fragilities offer valuable insight as to the relative vulnerability of different bridgecomponents and the impact of retrot on their susceptibility to damage. However, the ultimategoal of the fragility analysis is to evaluate the impact of retrot on the bridge system fragility. As aresult, a systems level approach to evaluating the retrotted bridge vulnerability is also conductedby considering the fragility for a particular damage state as the union of probabilities of eachof the components being in that same state. This system failure denition is associated with theassumption that damage to any component may inhibit the functionality of the bridge systeman

Table I. Component demands considered when evaluating fragility and retrot impact.

Component demand parameter Abbreviation

Column curvature ductility demand Longitudinal expansion bearing deformation Exp LongTransverse expansion bearing deformation Exp TranLongitudinal xed bearing deformation Fxd LongTransverse xed bearing deformation Fxd TranActive abutment deformation Ab ActPassive abutment deformation Ab PassTransverse abutment deformation Ab Tran

Copyright q 2008 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2008; 37 :11571174DOI: 10.1002/eqe


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DEVELOPMENT OF ANALYTICAL FRAGILITY CURVES 1161

idealization that is strengthened by the fact that associated limit states for each component implya loss of anticipated trafc carrying capacity to the bridge. To accomplish this estimate of bridgesystem level fragility, Nielson and DesRoches [20 ] proposed the use of joint probabilistic seismicdemand model (JPSDM). A similar approach is used in this work for estimating the demand onvarious components and impact of retrot on the JPSDM.

The JPSDM is developed by assessing the demands placed on each component (marginal distribu-tion) through a regression analysis as previously discussed. This is performed in the logarithmicallytransformed state, noting that Equation (2) can be rewritten as

ln( S d) = ln(a ) + b ln(IM ) (5)

The covariance matrix is developed through estimation of the correlation coefcients between thetransformed demands placed on the various retrotted components in order to fully characterizethe conditional joint normal distribution. A Monte Carlo simulation is used to compare realizationsof the demand (using the JPSDM dened by a conditional joint normal distribution) and capacityto calculate the probability of system failure across a range of IMs and for each damage state.Specically, system failure analysis by integration of the JPSDM over all failure domains [27 ] isaccomplished by sampling upon the demand model and the capacity model for a particular IM(peak ground acceleration (PGA) in this work). Exceedance of the capacity sample by the demandis tracked through an indicator function, and the probability of exceedance for the IM of interest isestimated directly. This procedure is repeated for each level of IM for slight, moderate, extensive,and complete damages. A regression analysis is used to estimate the lognormal parameters, whichcharacterize the retrotted bridge system fragility. Further details can be found elsewhere [20, 28 ].The advantage of this approach is the ability to capture the impact of retrot on multiple vulnerablecomponents that are critical to the bridges seismic performance when estimating the bridge systemvulnerability.

2.4. Description of case study retrotted bridge class

The methodology presented above for fragility development for retrotted bridges will be illus-trated along with further details on key aspects of the approach. These include uncertainty treat-ment, analytical modeling, inuence of retrot on the demand model and capacity estimates, andretrotted component fragilities, among others. A particular class of retrotted bridges will serveas a case studythe MSC concrete girder bridge class. This is a common bridge type found in theCentral and Southeastern U.S. (CSUS). Details considered for the bridges are based on previousstudies making inferences from the national bridge inventory database [29 ] and a thorough reviewof bridge plans for the region [30, 31 ].

These are typically zero-skew, non-seismically designed bridges having three spans and multiple-column bents. The reinforced concrete columns have limited reinforcement (i.e. roughly 1% longi-

tudinal steel and widely spaced transverse ties). Alternating xed and expansion elastomeric padswith steel dowels serve as the bridge bearings, and continuity is provided between the deck andgirders of the three spans. Eight representative congurations of the MSC concrete girder bridgeclass were identied by Nielson [24 ] and are listed in Table II. These will be used to representthe range of geometries of bridges in the class, as they were developed based on the populationdistributions of the CSUS bridge inventory and generated using the Latin hypercube samplingtechnique. An example of MSC concrete girder bridge conguration is shown in Figure 1.



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Table II. Sample representative bridge geometries for the MSC concrete girder bridge class [24 ].

Bridge no. n Mid-span length (m) Deck width (m) Column height (m)

1 39.6 21 .2 4.002 22.6 12 .8 3.933 18.9 10 .8 6.294 21.0 8 .00 3.195 26.2 13 .1 4.206 10.4 14 .1 3.647 14.5 8 .70 4.468 15.2 9 .80 5.93

2.4 m

5.0 m

1.6 m n m u l o C

t h g i e H

n

m 1 . 1

0.9 m

1 . 2

m

5.0 m

Pier

Girders @ 1.83 m o.c.1.1 mDeck Width n

Deck

17.8 cm

Mid Span Length n 12.2 m 12.2 m

Sample Bridge Geometry

Figure 1. Generic geometry of the multi-span continuous concrete girder bridge.

The retrot measures addressed as a part of this study include steel restrainer cables (RCs), steelcolumn jackets (SJ), elastomeric isolation bearings (EB), seat extenders (SEs), transverse shearkeys (SKs), and combinations of the above. The measures considered are common in the CSUSbridge retrots or those which have been identied as potentially viable to address the decienciesof the bridges in the region [28 ].

3. ANALYTICAL MODELING AND SIMULATION

3.1. Ground motion suite

In the absence of recorded strong motions for the CSUS, two suites of synthetic ground motionsare used as a part of this study. Wen and Wu [32 ] simulated ground motions for three cities in Mid-America (Memphis, TN; Carbondale, IL; and St. Louis, MO) for seismic performance assessment



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of structures, such that the median of the response spectra for the suite matches the uniform hazardresponse spectra for 10 and 2% probability of exceedance in 50 years. More recently, Rix andFernandez [33 ] developed a suite of scenario-based synthetic ground motions for Memphis, TN,that will also be used in this work. These scenario ground motions were developed based onstochastic methods, considering non-linear site response, and the inuence of the deep soil columnof the upper Mississippi embayment. Twenty ground motions were simulated for each of the 11different magnitudedistance pairs.

Forty-eight ground motions from Wen and Wu [32 ] and 48 ground motions from Rix andFernandez [33 ] are used in this study for the development of the PSDMs and fragility estima-tion. The ability of these suites to capture such inherent uncertainties as the earthquake source,wave propagation, and soil conditions dictates the ability of the fragility curve development proce-dure to propagate these aleatoric uncertainties. The developers of each suite of motions havegiven due attention to considering such uncertainties, yet with varying levels of delity or modelsimplemented. For example, Wen and Wu [32 ] have considered uncertainty in such parametersas magnitude, epicentral location, focal depth, fault size, path attenuation, and soil amplication,whereas soil prole has been generically dened for three different sites in the region. For theRix and Fernandez motions [33 ], which are scenario events with deterministic magnitudedistancepairs, care was taken to capture uncertainties in the source, path, and site in the development of theFourier amplitude spectrum, whereas the phase spectrum contains Gaussian white noise. Furtherdetails on the uncertainty modeling approaches adopted by each can be found in their respectiveworks. The development of the fragility curves produced in this work has also attempted to acknowl-edge and capture the epistemic uncertainties associated with different ground motion modelingapproaches by utilizing both suites of synthetic motions. The reduced ground motion suites usedin this work were identied by Nielson and DesRoches [30 ] for fragility analysis, consistingof a range of PGA and spectral acceleration values and representative of CSUS ground motioncharacteristics.

3.2. Analytical bridge models

Three-dimensional non-linear analytical models are developed in OpenSees [34 ] for use in thefragility analysis. A separate set of 96 models (note, the 96 models corresponds to the 96 groundmotions) is generated for the as-built and each class of retrotted bridges. Although each of the 96different three-dimensional models has slight variations in its properties and base geometry (seediscussion below regarding uncertainty treatment), the general modeling approach is consistent.The composite slab and girders are modeled with linear elastic beamcolumn elements, since thesuperstructure is expected to remain elastic under seismic excitation. Pounding between the deck and abutments is captured with a bi-linear contact element following the recommendations of Muthukumar [35 ]. The bearing models are dictated by the stiffness of the elastomer, sliding of the bearing, and stiffness and yield of the steel dowels, following the analytical modeling of Choi

[31 ] and Nielson [24 ]. Discretized ber sections applied to beamcolumn elements are used forthe both the circular columns and concrete bent beams, and the pile foundations are modeled withsimplied linear translational and rotational springs. The active, passive, and transverse responsesof the abutments are represented by non-linear inelastic springs. Further details on the assumptionsand analytical models themselves can be found elsewhere [24, 28 ].

Like the as-built bridge itself, properties of the retrot change for each bridge sample andgenerated analytical model. This is due to the variation in bridge geometry, which affects the



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Figure 2. Analytical modeling approach for retrotted components.

anticipated retrot design, as well as uncertainties in the realization of the retrot properties(i.e. realized strength of steel in jacketed column). However, each retrot measure has a typicalmodeling scheme, which is shown in Figure 2. The restrainer cables are modeled using non-lineartension-only elements with a gap representing the initial slack in the cable. Bi-linear springs inthe longitudinal and transverse directions simulate the forcedisplacement of typical laminatedelastomeric bearings. Keeper plates are common details for these bearings and are captured in themodel by stiff springs in the transverse direction, engaging after the gap is closed. Similarly, thereinforced concrete shear keys engage only in the transverse direction after overcoming an initialgap, with the Coulomb friction models dening their behavior. The steel jackets are reected inthe analytical model by altering the column section model. Material models for the concrete bers

are affected by having an increased compressive strength and ultimate strain due to the jacket, anda slight increase in elastic modulus to reect the increase in stiffness due to jacketing. In general,although the analytical model is somewhat affected by the use of steel jacketing, the primaryimpact of the retrot is to increase the column ductility capacity. The seat extenders do not requireunique analytical modeling; however, their effect on the fragility of the bridge will be to increasethe limit state capacity for collapse due to excess longitudinal displacement. The impact of thevarious retrots on the limit state capacities will be discussed in a later section.

3.3. Uncertainty treatment

One of the primary intentions of a fragility analysis is to capture the uncertainties inherent ina seismic performance assessment and quantify probabilistically the potential for damage. These

sources stem from uncertainties in the ground motion characteristics, bridge modeling parameters(such as bearing stiffness, concrete strength, restrainer cable slack), or variations in gross geometricproperties. The evaluation of general classes of retrotted bridges yields this added complexitywhere there may be variation in the span length, column height, and deck width. In general,these uncertainties tend to affect the demand estimate, and uncertainties in the capacity of variouscomponents are considered by use of a probabilistic model for the capacity estimate, as opposedto a deterministic limit.



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Table III. Most signicant modeling parameters identied from screening study of 23 parameters, alongwith the probabilistic model used for developing bridge samples in fragility analysis.

Signicance for retrot typeModeling

parameter Probabilistic model Units AB RC EB SJ SKLoading direction U (0, 2 ) rad x x x x xActive abutment stiffness U (3.5, 10 .5) kN/ mm / pile x x x xDeck-abutment gap N ( = 38 .1, = 5.84) mm x x x xDamping ratio N ( = 0.045 , = 0.0125 ) Ratio xKeeper gap U (6.4, 19 .1) mm x

Note : AB, as-built; RC, restrainer cable; EB, elastomeric bearing; SJ, steel jacket; SK, shear key; U , uniformdistribution; N , normal distribution.

A recent study [36 ] has performed detailed analysis of the sensitivity of the seismic responseand fragility to various sources of uncertainty and produced a set of recommendations on the most

important parameters to consider. These results have been adopted in this work. Uncertainty in theground motions is captured by the use of the two ground motion suites previously discussed, andthe angle of incidence of the two-component ground motion and the bridge is treated as a randomvariable. Variation in the gross geometric properties, a critical consideration, is accounted for bythe use of the eight geometric samples presented in Table II. Only the most critical analyticalmodeling parameters identied in a prior screening study [28 ] are treated as variables in developingpermutations of the bridge models. The screening study evaluated the statistical signicance of roughly 1516 different modeling parameters for the different MSC concrete retrotted bridges,including uncertainties in the retrot properties themselves. The parameters that most signicantlyaffect the bridge response differ for each retrot measure, but, in general, the use of the screeningstudy reduces the number of parameters that needs to be treated probabilistically from 15 to 3 or 4for the MSC concrete bridge class. Although probabilistic models for the 23 as-built and retrot

modeling parameters were developed in all, only those identied for use in the demand modelsampling are presented in Table III. The loading direction dened by a uniform distribution isassumed to have equal likelihood of intersecting the bridge at any direction. Based on a review of the current state of practice, gaps to the keeper plate provided at the elastomeric isolation bearingsrange from 6.4 to 19.1 mm and are modeled with a uniform distribution recognizing the uncertaintyin the realized value, yet given the limited further information available to fully characterize aprobabilistic model. The distributions for active abutment stiffness (uniform), deck-abutment gap(normal), and damping ratio (normal) presented in Nielson [24 ] based on a review past studies of typical damping values in bridges, and CSUS bridge characteristics, are adopted herein. Furtherdetails of the screening can be found elsewhere [28 ].

4. DEMAND AND CAPACITY ESTIMATES

4.1. Probabilistic seismic demand models

PSDMs are constructed from the peak component responses of the 96 simulations for the variousretrotted bridge classes using the outlined methodology. PGA is used as the intensity measure fordeveloping the relationships based on the conclusions of a recent study that identied the measure



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Figure 3. Comparison of the PSDMs for select components of the MSC concrete bridgeas-built and retrot with shear keys.

as an appropriate IM for CSUS bridge classes [37 ]. In many cases, the retrot measure alters thedemand model for different components.

Figure 3 shows the PSDMs for transverse abutment deformations and xed bearing deformationsfor the bridge retrot with shear keys. The regression line for the as-built bridge is plottedrelative to the retrotted bridge to indicate the shift in the demand resulting from its adoption. Asillustrated in this example, the bearing demands are decreased, whereas the abutment demands areincreased for the same level of ground shaking. This trend is consistent with the ndings of a priordeterministic evaluation of the three-dimensional seismic response of these types of retrottedbridges [28 ]. In some cases, the retrots affect both the median of the demand (Equation (5)) andthe dispersion. For example, Figure 3 indicates that the use of shear keys reduces the logarithmicstandard deviation associated with the transverse xed bearing demands from 0.62 for the as-built

bridge to 0.38. Results for the different retrot measures reveal a similar trend where the demandsmay be increased, decreased, or unaffected in terms of the median or dispersion. In addition tothe marginals for the JPSDM, correlation matrices are also constructed for each retrotted bridgetype, although most retrots only have a slight impact on the correlation between the componentdemands for the MSC concrete bridge.

4.2. Limit state capacity estimates

The damage states used in this study are qualitatively described as slight, moderate, extensive, andcomplete damages. Estimates of the limit state capacities for each component and damage stateare selected in an effort to maintain consistency across the various bridge components. Achievinga particular damage state for one component should have a similar impact on the functional

performance of the entire bridge system as achieving the damage state for another component.This objective, which is more thoroughly discussed in Padgett and DesRoches [36 ], is consideredin the construction of capacity estimates used in the development of bridge fragility curves in thiswork.

4.2.1. As-built components. The limit state capacities used for the as-built components are thoseproposed by Nielson and DesRoches [24, 30 ]. Physics-based limit state capacities were rened



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Table IV. Capacity estimates for as-built components adapted from Nielson and DesRoches [30].

Slight Moderate Extensive Complete

As-built component S c C S c C S c C S c C

Concrete column ( ) 1.29 0.59 2 .10 0.51 3 .52 0.64 5 .24 0.65Elastomeric bearing expan-long (mm) 28 .9 0.60 104 0.55 136 0.59 187 0.65Elastomeric bearing expan-tran (mm) 28 .8 0.79 90 .9 0.68 142 0.73 195 0.66Elastomeric bearing xed-long (mm) 28 .9 0.60 104 0.55 136 0.59 187 0.65Elastomeric bearing xed-tran (mm) 28 .8 0.79 90 .9 0.68 142 0.73 195 0.66Abutment-passive (mm) 37 .0 0.46 146 0.46 N / A N / A N / A N / AAbutment-active (mm) 9 .80 0.70 37 .9 0.90 77 .2 0.85 N / A N / AAbutment-tran (mm) 9 .80 0.70 37 .9 0.90 77 .2 0.85 N / A N / A

through a Bayesian updating process to incorporate the results of a survey on the limits inspectorsplace on damage before altering the bridge functionality [36 ]. Capacity estimates for a range of bridge components relevant for the case study MSC concrete bridge class are considered, as shownin Table IV. It is noted that some of the capacity estimates are listed as N / A for the componentsand damage states that the survey results indicated large amounts of damage could occur withoutleading to signicant long term impacts on the functionality of the bridge. These components,therefore, do not contribute to the system fragility for that particular damage state.

4.2.2. Retrotted components. It has been previously illustrated that various retrots affect theseismic response and demand of the bridge. However, the use of retrot may also alter the capacityof some components, including the retrotted component itself. For example, new limit statecapacities must be dened for the steel-jacketed columns or elastomeric isolation bearings. Thecapacity estimates for these components are dened with an effort to maintain the functional

implications of each damage state and at limits where visual damage may be apparent to inspectors.The median values of the retrotted component limit state capacities are assigned in most casesbased on past experimental tests of the retrots. With little additional information on the dispersionabout the median, judgment is often used along with knowledge of the uncertainty in the capacityof the as-built component.

Limit state capacities for slight through complete damage for the steel-jacketed columns areassessed based on tests of steel-jacketed circular columns by Chai et al. [38 ] and Priestley et al.[39 ]. For example, the moderate damage corresponds approximately to the point when yielding of the jacket and visual bulging may occur, whereas complete damage corresponds to the estimatedultimate curvature ductility demand of a typical jacketed column. Although the elastomeric isolationbearings replace more vulnerable as-built bearings, there are still limits on their displacementcapacities. Inferences are made as to the limit on shear strain and displacement capacities based

on past testing [4043 ]. For example, slight damage is approximated as the point at which testsof typical CSUS bearings and pedestals have revealed potential yielding of the anchor bolts andcracking of the pedestals; extensive damage corresponds to an anticipated yielding of the steelshims, which would require replacement following the event. Although the seat extenders do notaffect the demand placed on the bridge, they do alter the limit state capacity for the completedamage state by increasing the capacity to sustain deck displacements and bearing deformationsbefore unseating occurs. The shear keys and restrainer cables do not affect the limit state capacities,



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0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

PGA (g)

] A

G P | t h g i l S [ P

Slight Damage: Expansion Bearing-Long

As-BuiltSeat ExtenderRestrainerSteel JacketElasto BrgShear Key

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

PGA (g)

] A G P | t h g i l S [ P

Slight Damage: Abutment-Passive

As-BuiltSeat ExtenderRestrainerSteel JacketElastomer Isolation BrgShear Key

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

PGA (g)

] A G

P | t h g i l S [ P

Slight Damage: Fixed Bearing-Trans

As-BuiltSeat ExtenderRestrainerSteel Jacket

Elasto BrgShear Key

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

PGA (g)

] A G

P | t h g i l S [ P

Slight Damage: Abutment-Trans

As-BuiltSeat ExtenderRestrainerSteel Jacket

Elasto BrgShear Key

Figure 4. Slight damage state fragility curves for the expansion bearings in the longitudinal direction,abutments in passive action, xed bearings in the transverse direction, and abutments in the transverse

direction for the as-built bridge relative to the retrotted bridge.

This reveals the importance of considering a retrots impact on multiple components when devel-oping system fragility curves, as proposed in the presented methodology herein.

5.2. Fragility curves for case study bridge class

The insight gained from the component fragility curves leads to a need to evaluate the overall systemvulnerability and impact of retrot. The system fragility curves are developed by considering thecontribution of multiple vulnerable components through the methodology proposed in Section 2.Fragility curves depicting the overall bridge vulnerability and relative impact of various retrots onthe performance of the bridge system are presented for the case study MSC concrete bridge class.The fragility curves for slight through complete damage for the bridge retrot with steel column jackets, elastomeric isolation bearings, restrainer cables, shear keys, or seat extenders relative to

the as-built bridge are shown in Figure 6. Although combinations of retrot are often performed,this study does not evaluate the effect of combinations of retrot measures on the overall systemfragility. Future work will assess the effects of combinations on further reducing the vulnerabilityof bridges.

From Figure 6 it is evident that different retrot measures appear to be more effective fordifferent damage states in terms of reducing the probability of damage for a given PGA. Forexample, the elastomeric bearings reduce the system vulnerability for the slight damage state,



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0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

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1

PGA (g)


Slight Damage: As-Built Component Fragility

ColumnFxd-LongFxd-TranExp-LongExp-TranAb-PassAb-ActAb-Tran

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

PGA(g)

] A G P | e t a r e d o M [ P

Moderate Damage: As-Built Component Fragility

ColumnFxd-LongFxd-TranExp-LongExp-TranAb-PassAb-ActAb-Tran

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

PGA (g)

] A G P | e v i s n e t x E [ P

Extensive Damage: As-Built Component Fragility

ColumnFxd-LongFxd-TranExp-LongExp-Tran

Ab-PassAb-ActAb-Tran

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

PGA(g)

] A G P | e t e l p m o C [ P

Complete Damage: As-Built Component Fragility

ColumnFxd-LongFxd-TranExp-Long

Exp-TranAb-PassAb-ActAb-Tran

Figure 5. Comparison of component vulnerabilities for the four damage states before retrotting the MSCconcrete bridge. (Refer to Table I for abbreviation denitions.)

whereas the seat extenders are more effective for the complete damage state. Again, this is a result

of the inuence of the retrot measures on the seismic capacity and demand placed on variouscomponents, which was evident when viewing the component fragility curves. The median values(PGA) of the fragility curves for the different retrot measures normalized by the as-built fragilityare plotted in Figure 7. It is noted that this does not account for changes in dispersion which maybe important considerations, along with other factors such as cost, constructability, etc. However, alarger normalized median value is indicative of a retrot measure that results in a larger reductionin system vulnerability.

The importance of developing system level retrotted bridge fragility curves is again recognized.For example, if the impact of restrainers on the longitudinal vulnerability of the expansion bearingswere the only consideration made, the fragility would be assumed to be improved by 25% atthe moderate damage state on the basis of median value shift. However, by assessing the systemvulnerability, it is observed that the actual fragility is only improved by 1% relative to the as-built

bridge because of the contribution of other components such as the xed bearings, abutments,etc. On the other hand, evaluating the impact of retrotting with elastomeric isolation bearingsbased solely on reduced demands on the substructure would lead to a 42% under-estimation of the system improvement at the extensive damage state. This is because of the contribution of improved bearing fragility in addition to the columns, among other items. Hence, the importanceof capturing not only the enhanced performance of the targeted seismic response quantity andcomponent vulnerability but also system level impact of bridge retrot is emphasized.



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0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

PGA (g)


Slight Damage

As-BuiltSeat ExtenderRestrainerSteel JacketElastomeric Isolation BrgShear Key

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

PGA (g)

] A G P | e t a r e d o M [ P

Moderate Damage


0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

PGA (g)

] A G P | e

v i s n e t x E [ P

Extensive Damage


0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

PGA (g)

] A G P | e t e l p m o C [ P

Complete Damage


Figure 6. Fragility curves for retrotted MSC concrete bridge.

Figure 7. Comparison of median value of the fragility for various retrot measures normalized by theas-built median value PGA. (Note: The normalized median for elastomeric isolation bearings at the slight

damage state is off of the scale at 2.9.)



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6. CONCLUSIONS

This work has presented an approach to developing systems level fragility curves for retrottedbridge classes through an analytical methodology. Emphasis is placed on capturing the impact of retrot on multiple key components when assessing the bridge fragility in its retrotted condition.Although seismic retrot measures tend to be targeted at individual component response quantities,this study has shown that the fragility of other components may be indirectly affected in either apositive or a negative way. Alternatively, there may be additional sources of vulnerability, whichare not addressed by a given retrot scheme, yet should be captured when assessing the bridgefragility. This is accomplished by the development of joint PSDMs and capacity estimates whichcapture the inuence of retrot on both the dynamic response and limit state capacities for thesystem. Component level fragility curves may be developed for illustration purposes to evaluate theimpact of a particular retrot on the columns, bearings, or abutments; however, retrotted bridgesystem fragility curves may be directly evaluated.

A case study bridge class, the MSC concrete girder bridge, retrot with ve different measures isused to exemplify the methodology and recommended implementation details, including analyticalmodeling, uncertainty treatment, limit state capacities, etc. The retrot measures considered includesteel column jackets, elastomeric isolation bearings, restrainer cables, shear keys, and seat extenders.Three-dimensional analytical models are utilized and subjected to two-component synthetic groundmotions. Preliminary screening studies are used to identify the most critical variable modelingparameters for treatment in bridge sample simulation. The impact of retrot on PSDMs wasillustrated to note the shift in demand resulting from the use of different retrot measures, andlimit state capacities for retrotted components were proposed. The results reveal that the mosteffective retrot measure in reducing probable damage is a function of the damage state of interest.Additionally, the potential to over-estimate or under-estimate system fragility by only evaluatingthe impact of retrot on the targeted component was revealed.

ACKNOWLEDGEMENTS

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

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