2003---seismic retrofitting of highway bridges in illinois using friction pendulum seismic isolation...

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Engineering Structures 25 (2003) 1139–1156 www.elsevier.com/locate/engstruct Seismic retrofitting of highway bridges in Illinois using friction pendulum seismic isolation bearings and modeling procedures M. Dicleli a,, M.Y. Mansour b a Department of Civil Engineering and Construction, Bradley University, Peoria, Il 61625-0114, USA b Department of Civil Engineering, University of British Columbia, Vancouver, BC, Canada Received 15 November 2002; received in revised form 24 February 2003; accepted 26 February 2003 Abstract In this paper, the economical and structural efficiency of friction pendulum bearings (FPB) for retrofitting typical seismically vulnerable bridges in the State of Illinois is studied. For this purpose, a bridge was carefully selected by the Illinois Department of Transportation (IDOT) to represent typical seismically vulnerable bridges commonly used in the State of Illinois. A comprehensive structural model of the bridge was first constructed for seismic analysis. An iterative multi-mode response spectrum (MMRS) analysis of the bridge was then conducted to account for the nonlinear behavior of the bridge components and soil–bridge interaction. The calculated seismic demands were compared with the estimated capacities of the bridge components to determine those that need to be retrofitted. It was found that the bearings, wingwalls and pier foundations of the considered typical bridge need to be retrofitted. A conventional retrofitting strategy was developed for the bridge and the cost of retrofit was estimated. Next, the bridge was further studied to develop appropriate techniques for upgrading its seismic capacity using FPB to eliminate the need for seismic retrofitting of its vulnerable substructure components. It was observed that the use of FPB mitigated the seismic forces and eliminated the need for retrofitting of the substructure components of the bridge. An average retrofitting cost using FPB was calculated and found to be less than the cost of conventional retrofitting considered in this study. Thus, FPB may successfully be used for economi- cal seismic retrofitting of typical bridges in the State of Illinois or in regions of low to moderate risk of seismic activity. 2003 Elsevier Science Ltd. All rights reserved. Keywords: Bridge; Friction pendulum bearing; Seismic isolation; Soil–structure interaction; Nonlinear analysis; Seismic retrofitting; Cost 1. Introduction According to United States Geological Survey [1], the Central United States is a region of moderate to high risk of seismic activity and it is anticipated that the prob- ability of a Richter magnitude 6–7 earthquake occurring in Central United States within the next 50 years is higher than 90%. Recognizing the threat of seismic activity, in the early 1990s, Illinois Department of Trans- portation (IDOT) made a statewide assessment of the seismic vulnerabilities of its over 6000 highway bridges. Many of these bridges were found to be vulnerable as they were built in the late 1960s and early 1970s during Corresponding author. Tel.: +1-309-677-2942; fax: +1-309-677- 2867. E-mail address: [email protected] (M. Dicleli). 0141-0296/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0141-0296(03)00062-2 a rapid expansion of the highway system and before there were any seismic design regulations in American Association of State Highway Transportation Officials (AASHTO) [2] bridge design specifications. The assess- ment of the vulnerability of these bridges identified deficiencies [3] that are; brittle fixed steel bearings, rocker bearings with stability problem, short seat widths, columns with insufficient transverse reinforcement and lap splices and foundations with inadequate lateral and bearing resistance. Conventional seismic retrofitting methods [4–9] may be used to mitigate the risk that currently exists for seis- mically vulnerable bridges in Illinois. Some of these methods are; replacing old steel bearings with modern conventional bearings such as elastomeric, pot or spheri- cal bearings, widening the pier cap and abutment seat to accommodate seismic lateral movements of the super- structure, strengthening and enhancing the ductility

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Page 1: 2003---Seismic Retrofitting of Highway Bridges in Illinois Using Friction Pendulum Seismic Isolation Bearings and Modeling Procedures

Engineering Structures 25 (2003) 1139–1156www.elsevier.com/locate/engstruct

Seismic retrofitting of highway bridges in Illinois using frictionpendulum seismic isolation bearings and modeling procedures

M. Dicleli a,∗, M.Y. Mansourb

a Department of Civil Engineering and Construction, Bradley University, Peoria, Il 61625-0114, USAb Department of Civil Engineering, University of British Columbia, Vancouver, BC, Canada

Received 15 November 2002; received in revised form 24 February 2003; accepted 26 February 2003

Abstract

In this paper, the economical and structural efficiency of friction pendulum bearings (FPB) for retrofitting typical seismicallyvulnerable bridges in the State of Illinois is studied. For this purpose, a bridge was carefully selected by the Illinois Departmentof Transportation (IDOT) to represent typical seismically vulnerable bridges commonly used in the State of Illinois. A comprehensivestructural model of the bridge was first constructed for seismic analysis. An iterative multi-mode response spectrum (MMRS)analysis of the bridge was then conducted to account for the nonlinear behavior of the bridge components and soil–bridge interaction.The calculated seismic demands were compared with the estimated capacities of the bridge components to determine those thatneed to be retrofitted. It was found that the bearings, wingwalls and pier foundations of the considered typical bridge need tobe retrofitted.

A conventional retrofitting strategy was developed for the bridge and the cost of retrofit was estimated. Next, the bridge wasfurther studied to develop appropriate techniques for upgrading its seismic capacity using FPB to eliminate the need for seismicretrofitting of its vulnerable substructure components. It was observed that the use of FPB mitigated the seismic forces and eliminatedthe need for retrofitting of the substructure components of the bridge. An average retrofitting cost using FPB was calculated andfound to be less than the cost of conventional retrofitting considered in this study. Thus, FPB may successfully be used for economi-cal seismic retrofitting of typical bridges in the State of Illinois or in regions of low to moderate risk of seismic activity. 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Bridge; Friction pendulum bearing; Seismic isolation; Soil–structure interaction; Nonlinear analysis; Seismic retrofitting; Cost

1. Introduction

According to United States Geological Survey[1], theCentral United States is a region of moderate to highrisk of seismic activity and it is anticipated that the prob-ability of a Richter magnitude 6–7 earthquake occurringin Central United States within the next 50 years ishigher than 90%. Recognizing the threat of seismicactivity, in the early 1990s, Illinois Department of Trans-portation (IDOT) made a statewide assessment of theseismic vulnerabilities of its over 6000 highway bridges.Many of these bridges were found to be vulnerable asthey were built in the late 1960s and early 1970s during

∗ Corresponding author. Tel.:+1-309-677-2942; fax:+1-309-677-2867.

E-mail address: [email protected] (M. Dicleli).

0141-0296/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0141-0296(03)00062-2

a rapid expansion of the highway system and beforethere were any seismic design regulations in AmericanAssociation of State Highway Transportation Officials(AASHTO) [2] bridge design specifications. The assess-ment of the vulnerability of these bridges identifieddeficiencies[3] that are; brittle fixed steel bearings,rocker bearings with stability problem, short seat widths,columns with insufficient transverse reinforcement andlap splices and foundations with inadequate lateral andbearing resistance.

Conventional seismic retrofitting methods[4–9] maybe used to mitigate the risk that currently exists for seis-mically vulnerable bridges in Illinois. Some of thesemethods are; replacing old steel bearings with modernconventional bearings such as elastomeric, pot or spheri-cal bearings, widening the pier cap and abutment seat toaccommodate seismic lateral movements of the super-structure, strengthening and enhancing the ductility

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1140 M. Dicleli, M.Y. Mansour / Engineering Structures 25 (2003) 1139–1156

capacity of the columns using concrete and steel jackets,advanced composite fiber reinforced polymer or pre-stressed wire wrapping and increasing the size of thefootings, the number of piles and providing dead mananchors to improve the lateral resistance of the footings.However, most of these retrofitting methods are expens-ive and difficult to implement. Furthermore, retrofittinga component of the bridge may overstress some othercomponents and result in additional retrofitting cost.Mobilization and traffic control during substructureretrofitting over an extended period of time constitutesan additional hidden cost that need to be considered.Thus, an economical and innovative method for mitigat-ing the seismic forces on the bridges in Illinois byresponse modification may provide an efficient solutionto the above problems. This may be achieved by replac-ing the already vulnerable existing bearings by frictionpendulum bearing (FPB) to reduce the seismic forces inthe bridge substructures and eliminate the need for theircostly retrofitting.

In this paper, the economical and structural efficiencyof FPB for retrofitting typical seismically vulnerablebridges in the State of Illinois is studied. For this pur-pose, a bridge was carefully selected by IDOT to rep-resent typical seismically vulnerable bridges in the Stateof Illinois. Iterative multi-mode response spectrum(MMRS) analysis of the bridge is conducted consideringthe nonlinear behavior of the bridge components andsoil–bridge interaction effects to assess its seismic vul-nerability. A conventional retrofitting strategy is thendeveloped for the seismically vulnerable components ofthe bridge and the cost of retrofit is estimated. Next, thebridge is further studied to develop appropriate tech-niques for upgrading its seismic capacity using FPB toeliminate the need for retrofitting of its vulnerablecomponents. Finally an average retrofitting cost usingFPB is calculated and compared with the cost of conven-tional retrofitting to assess the economical efficiencyof FPB.

2. Friction pendulum bearings

FPBs are sliding-based seismic isolators, which areinstalled between the superstructure and the substructurein application to bridges. The elevation of a typical FPB[10] is shown in Fig. 1. The main components of theFPB are; a stainless steel concave spherical plate, anarticulated slider and a housing plate. The side of thearticulated slider in contact with the concave sphericalsurface is coated with a low-friction composite material.The other side of the slider is coated with stainless steeland sits in a spherical cavity coated with low-frictioncomposite material.

FPB uses the characteristic of a pendulum motion tolengthen the natural period of the isolated structure, thus,

deflects the earthquake input energy to mitigate the seis-mic forces. A pendulum motion for the supported struc-ture is achieved as the articulated slider rides on the con-cave surface as illustrated in Fig. 1. The movement ofthe slider generates a friction force that results in hyster-etic energy dissipation and further mitigation of the seis-mic forces. This force is equal to the product of thedynamic friction coefficient, m, and the weight, W, actingon the bearing. The tangential component of the weightof the bridge also acts as a restoring force opposing theseismic forces as shown in Fig. 1. The force–displace-ment hysteresis loop [11] of the FPB is illustrated in Fig.1 and is defined by the following equation [10]:

F � mW sgn(V) �WR

D (1)

where R is the radius of the concave surface, D is theisolator displacement and V is the isolator velocity. W/Rin Eq. (1) represents the lateral stiffness produced by thetangential component of the weight.

AASHTO’s Guide specifications for seismic isolationdesign [12] recommends various seismic analysismethods based on linear elastic and nonlinear theories.Methods based on linear elastic theories are commonlyused for the analysis of seismic isolated bridges. Sincethe behavior of FPB is nonlinear in nature, equivalentlinear elastic properties need to be defined for the elasticanalysis of bridges with such bearings. The linear elasticproperties of the FPB can be expressed in terms of anequivalent linear stiffness and an equivalent viscousdamping to account for the effect of the hysteretic energydissipation of the bearings. The equivalent linear stiff-ness, ke, is illustrated graphically in Fig. 1. It is obtainedby dividing the design horizontal bearing force, Fd,which is produced by design earthquake loading, by thecorresponding design bearing displacement, Dd. Thus,

ke �mWDd

�WR

(2)

The equivalent viscous damping ratio, ze, which pro-duces the same amount of viscous energy dissipation foreach cyclic motion of the bearing, is obtained from thefollowing equation [12,13]

ze �hysteretic energy dissipated

2πkeD2d

(3)

Substituting the area under the hysteresis loop of Fig.1 representing the hysteretic energy dissipated and theequivalent elastic bearing stiffness, as given by Eq. (2),in the above equation, the equivalent viscous dampingratio is expressed as

ze �2π� mm � (Dd /R)� (4)

A response spectrum obtained for a viscous damping

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1141M. Dicleli, M.Y. Mansour / Engineering Structures 25 (2003) 1139–1156

Fig. 1. Details, operation and force–displacement hysteresis of friction pendulum bearing.

equal to that produced by the bearings is then used inthe analyzes to account for the hysteretic energy dissi-pated by the bearings.

3. Description of the bridge

The bridge is located on route 24 in Johnson County,in Illinois and was constructed in 1970 to carry thewestbound lane traffic over a roadway. The bridge hasthree spans carrying two traffic lanes and a slab-on-pre-stressed-concrete-girder deck as shown in Fig. 2. The

Fig. 2. Bridge elevation, plan and deck cross-section (all dimensionsare in mm).

bridge deck is continuous from one abutment to the otherand is supported by two multi-column piers in between.The expansion joint widths at the north and south abut-ments are 38.1 and 25.4 mm, respectively. The strengthof concrete used in the prestressed concrete girders is34.5 MPa. The strengths of concrete and the steelreinforcement used for the rest of the bridge are 24 and275 MPa, respectively.

3.1. Bearings

Laminated elastomeric bearings with 203 × 356 ×67 mm3 dimensions are provided underneath each girderat both abutments and pier 1, whereas plain elastomericbearing pads with 152 × 356 × 13 mm3 dimensions areprovided at pier 2. The thin bearing pads at pier 2 areassumed to provide fixed support conditions, thus,allowing the rest of the superstructure to expand or con-tract on both sides of pier 2 under temperature variations.Both piers support two sets of girders from each adjacentspan and therefore accommodate two sets of bearings.

3.2. Substructures

The piers of the bridge are reinforced concrete multi-column bents typically used in Illinois bridges. The geo-metric details of piers 1 and 2 are presented in Fig. 3(a).

Both abutments are seat type as illustrated in Fig. 3(b).The abutment and the wingwalls are directly supportedon nine HP200X54 steel end-bearing piles, seven ofwhich are placed underneath the abutment. The H pilesare made of 248 MPa steel. The average length of thepiles is 4.2 m at the north and 6.2 m at the south abut-ments. Three of the abutment piles are battered with aslope of 1:6. A circular reinforced concrete encasementof 457 mm diameter is provided for the upper 914 mmlength of the abutment piles for corrosion protection.

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1142 M. Dicleli, M.Y. Mansour / Engineering Structures 25 (2003) 1139–1156

Fig. 3. Bridge abutments and piers.

3.3. Site properties

The site soil is composed of layers of stiff silty clayextending down to the hard sandstone. The base of thenorth abutment is placed approximately at the naturalground level. The south abutment is placed approxi-mately 1.7 m above the natural ground level. The fillmaterial above the ground level is medium moist siltyclay. The footings of piers 1 and 2 are placed respect-ively at 4.7 and 3.4 m below the natural ground surface.The standard penetration and unconfined compressivestrength test results at each substructure location wereprovided by IDOT and are presented elsewhere [14].

4. Types of analyzes conducted

First, a static analysis of the bridge is conducted todetermine the effect of the dead loads on the seismiccapacity and performance of bridge components. Next,a preliminary seismic analysis of the bridge is performedto obtain information about the expected level of nonlin-ear seismic behavior of the structural components. Theanalysis results revealed that (i) the pier columns maycrack but not to reach their ultimate capacities, (ii) thelongitudinal displacement of the bridge superstructure isexpected to be smaller than the expansion joint widths,thus no impacting between the superstructure and back-wall is anticipated, (iii) the piles’ initial elastic lateralload limit may be exceeded, (iv) flexural yielding of the

wingwalls are expected, and (v) sliding may occur at theabutment–backfill interface in the transverse direction.Following this, iterative MMRS analyzes of the bridgeare conducted considering the effects of the observednonlinear behavior and soil–bridge interaction. The nor-malized acceleration response spectrum of AASHTO [2]is used in the analyzes. For the bridge site, the zonalacceleration ratio is obtained as 0.14. For the site’s stiffsoil (AASHTO soil type II), the site coefficient isobtained as 1.20.

5. Structural model

A 3D structural model of the bridge is built and ana-lyzed using the program sap2000 [15]. The structuralmodel is capable of simulating the nonlinear behaviorof the structural components and soil–bridge interactioneffects when used in combination with iterative MMRSanalyzes. In the model, equivalent elastic stiffnessproperties are used for the components exhibiting non-linear behavior. These stiffness properties are updated ateach iteration step to simulate the nonlinear behavior ofthe components.

5.1. Superstructure modeling

The bridge superstructure is modeled using 3D beamelements. Full composite action between the slab and thegirders is assumed in the model [16,17]. The superstruc-ture is divided into a number of segments and its mass(13.40 ton/m) is lumped at each nodal point connectingthe segments. Each mass is assigned four dynamicdegrees of freedom (DOF); translations in the X and Ydirections and rotations about the X and Z axes as shownin Fig. 4. Detailed information about the selection ofdynamic DOF is presented elsewhere [14]. All six staticDOF were used in the analysis. The large in-plane trans-lational stiffness of the bridge deck is modeled as atransverse rigid bar [14] connected to the deck at thesubstructure locations as illustrated in Fig. 4.

5.2. Bearings modeling

As the stiffness of elastomeric bearings is temperaturedependent, an effective shear stiffness, Kb =1.35x(Kmin), is used for the elastomeric bearings [18],where Kmin is the shear stiffness of the bearing at 20°C. For the laminated elastomeric bearings at pier 1, theeffective shear stiffness is obtained as 1512 kN/m fromthe manufacturer’s catalog [19]. For the plain elasto-meric bearings at pier 2, the effective shear stiffness isobtained as 3517 kN/m using the following equation

Kb � 1.35GbAb

hb

(5)

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1143M. Dicleli, M.Y. Mansour / Engineering Structures 25 (2003) 1139–1156

Fig. 4. Structural model of the bridge at the piers and abutments.

where Gb is the shear modulus of the bearing materialat 20 °C (1830 kPa), Ab the plan area of the bearings(152 × 356 mm2), and hb is the bearing thickness (13mm).

The bearings are idealized as 3D beam elements con-nected between the superstructure and the substructuresat girder locations. Pin connection is assumed at thejoints linking the bearings to the substructures as shownin Fig. 4. Detailed information about bearings’ modelingis presented elsewhere [14].

5.3. Substructures modeling

The pies are modeled using 3D beam elements asillustrated in Fig. 4. The tributary masses of the pierelements are lumped at the joints connecting them. Thebeam–columns joints are modeled as rigid beamelements. The columns are connected to a horizontalrigid bar at their lower end to simulate the interactionbetween their axial deformation and wall’s flexuralrotation assuming that the cross-section of the wallalways remains plane. A 3D beam element representing

the wall is then connected between this horizontal rigidbar and a vertical rigid bar representing the pier’s rigidfooting. The length of the vertical rigid bar is set equalto the footing depth to estimate accurately the effect ofseismic forces transferred to the soil [20]. The interac-tion between the pier footing and the soil is modeledusing three translational and three rotational springs. Thecalculations of the stiffness of the springs are describedin the subsequent sections.

The abutments are modeled using a grid 3D beamelements as illustrated in Fig. 4. The vertical beamelements are placed at the pile locations. The horizontalbeam elements are placed at the top and bottom of theabutment and at the intersection of abutment back-walland breast wall. The tributary masses of the abutmentand wingwalls are lumped to each node and are assignedtranslational dynamic DOF in three orthogonal direc-tions of the bridge. The soil–bridge interaction at theabutment may have a significant effect on the dynamicresponse characteristics of particularly shorter bridges[21] and is included in the model using boundary springsattached at the interface nodes between the abutment,backfill and the piles as shown in Fig. 4.

6. Procedures for modeling soil–bridge interaction

The importance of including the flexibility andstrength of supports at abutments and piers in seismicanalysis of highway bridges is well recognized by vari-ous researchers [22–26] and transportation agencies[2,27–29]. Thus, the effect of soil–bridge interaction isincluded in the analysis of the bridge considered in thisstudy using boundary springs at the interface nodesbetween the bridge and the soil. In the following subsec-tions the procedures followed to model soil–bridge inter-action effects at the abutments and piers are described.

6.1. Modeling spread footings–soil interaction at piers1 and 2

The soil–footing interaction effect at the piers isincluded in the model using three translational and threerotational uncoupled boundary springs connected at theinterface nodes of soil and rectangular spread footings.The method proposed by Dorby and Gazetas [26] isemployed in the calculation of the stiffness of the bound-ary springs for the vertical, horizontal, rocking and tor-sional modes. For the vertical mode, the stiffness of theboundary spring is expressed as

KZ � SZ

LfG1�n

(6)

For the horizontal mode in X and Y directions

KY � SY

LfG2�n

(7)

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1144 M. Dicleli, M.Y. Mansour / Engineering Structures 25 (2003) 1139–1156

KX � SY

LfG2�n

�0.105LfG0.75�n �1�

Bf

Lf� (8)

For the rocking mode about the X and Y axes

KqX � SqXG

1�n(IqX)0.75�Bf

Lf��0.25

(9)

KqY � SqYG

1�n(IqY)0.75 (10)

For the torsional mode

KqZ � SqZG(IZ)0.75 (11)

In the above equations, Bf and Lf are respectively theshort and long dimensions of the footing, Iqx and Iqy arethe moment of inertia of the footing about the local Xand Y axes, J is the polar moment of inertia of the foot-ing, G and n are the equivalent shear modulus of elas-ticity and Poisson’s ratio of the soil taking into accountthe effect of cyclic loading and SX, SY, SqX, SqY, St, areconstants that depend on the dimensions of the footingas defined by Dorby and Gazetas [26].

For the site soil, first the initial shear modulus of elas-ticity, Gmax, (the initial slope of the backbone curve inthe stress–strain diagram of the soil) is obtained usingthe following equation [28]

Gmax � 11,700N0.8 (12)

where N represents the standard penetration test blowsper foot and Gmax is expressed in kPa. Next, the effectof the cyclic loading on the foundation soil is incorpor-ated in the analysis using an equivalent shear modulus,G, obtained by reducing Gmax using a reduction factorof 0.8 as recommended by Federal Highway Adminis-tration (FHWA) [29] considering the seismicity of thesite. Furthermore, a Poisson ratio of 0.45 is used for thesite soil [29]. The stiffness of the boundary springs arealso modified to account for the effect of the embedmentdepth of the footing [29]. More detailed informationabout the modeling procedure is presented elsewhere[14]. The stiffnesses of the boundary springs at the baseof both piers are presented in Table 1.

Table 1Stiffness of boundary springs at pier footings and abutment piles

Substructure KX (kN/m) KY (kN/m) KZ (kN/m) KqX (kN m/rad) KqY (kN m/rad) KqZ (kN m/rad)

Pier 1 footing 8.62 × 106 10.28 × 106 10.04 × 106 292 × 106 40.4 × 106 729 × 106

Pier 2 footing 4.60 × 106 5.52 × 106 5.36 × 106 156 ×106 21.6 × 106 532 × 106

North abutment vertical piles 2750 2500 324762 0 0 0North abutment battered piles 25725 2500 315915 0 0 0South abutment vertical piles 3600 2700 220000 0 0 0South abutment battered piles 12375 2700 214000 0 0 0

6.2. Modeling pile–soil interaction at abutments

The flexibility of the pile foundations at both abut-ments is modeled using a vertical and two horizontalboundary springs at the pile–abutment interface nodes asshown in Fig. 4. The formulation of spring stiffnesses isexplained below.

6.2.1. Stiffness of horizontal boundary springsA two-step procedure is adopted to include the lateral

pile–soil interaction effects in the seismic analyzes ofthe bridge. In the first step, a 2D structural model of thepile–soil system without the bridge is constructed usingthe program sap2000 [15]. Modeling details is presentedelsewhere [14]. Static pushover analyzes of the modelare conducted to determine the nonlinear lateral force–displacement relationship at the top of the pile (interfacenode). These analyzes are performed until failure isobserved either in the piles or the soil. The soil failureis assumed when a very small increase in the lateral loadtransferred by the pile causes an additional large soildeformation. Pile failure is assumed when the pilereaches its ultimate flexural capacity. The static pushoveranalyzes results for the piles at the north and south abut-ments of the bridge are presented in Fig. 5(a) and (b),respectively. In the second step, the horizontal boundarysprings connected at the pile–abutment interface nodesare assigned an equivalent linear stiffness obtained fromthe lateral force–displacement curves of the piles illus-trated in Fig. 5(a) and (b). The equivalent linear stiffnessis defined as the secant slope of the line from the originof the curve to the point representing pile’s seismic lat-eral load on the curve. Since the seismic lateral load onthe pile is not initially known to calculate this slope, firstan initial equivalent linear stiffness is assumed for thehorizontal boundary springs. Next, MMRS analysis ofthe bridge is conducted and the force in the horizontalboundary springs is calculated. Using the nonlinear lat-eral force–displacement curve of the piles, the secantstiffness is then calculated as the slope of the line con-necting the origin to the point of the calculated boundaryspring force on the curve. The boundary spring is thenassigned the calculated secant stiffness and a second

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Fig. 5. Static pushover analysis results for the piles at north and south abutments.

MMRS analysis is conducted. The iteration is continueduntil the difference between the load obtained in the cur-rent and previous steps is negligible.

6.2.2. Stiffness of vertical boundary springsAn elastic vertical force–deformation behavior is con-

sidered adequate for defining the vertical or axial flexi-bility of the piles [28]. For the steel H piles bearing onhard sandstone, their vertical stiffness is assumed to beindependent of the soil properties and equal to their axialstiffness [14,30]. The stiffness of the boundary springsin three orthogonal directions at the pile locations istabulated in Table 1.

6.3. Modeling soil–abutment interaction

6.3.1. Longitudinal direction responseGenerally, procedures such as those specified by

CALTRANS [27] and FHWA [28], to model backfill–abutment interaction are more biased towards accountingfor the behavior of the abutment–backfill system undertranslational mode. Furthermore, some of these methodsare specific to the type of the abutment they aredeveloped for and use soil properties that are difficultto estimate accurately. Thus, an alternative procedure isdeveloped as part of this study to model the interactionbetween the abutment and backfill.

In the longitudinal direction, a series of translationalsprings are attached to the nodes of only one of the abut-ments to model the passive resistance of the backfill asshown in Fig. 4. No springs are attached to the otherabutment since under seismic loading in the longitudinaldirection only one abutment is pushed towards the back-fill while the other is pulled away. Thus, two separatestructural models are built with springs attached to thenorth abutment only and to the south abutment only toobtain the seismic response of the bridge.

Using the relationship defined by Clough and Duncan[31] for the variation of the earth pressure coefficientas a function of the abutment movement, the horizontal

subgrade constant, ksh, for the backfill is obtained as afunction of the depth, z, from the abutment top as fol-lows [14]

ksh � �14500H �z (13)

where H is the abutment height. The stiffness of theboundary springs at the abutment–backfill interfacenodes are then calculated by multiplying ksh by the areatributary to the node.

6.3.2. Transverse direction responseTranslational springs are attached to the nodes of only

one of the wingwalls at each abutment to simulate theeffect of the backfill’s passive resistance in the trans-verse direction as illustrated in Fig. 4. The stiffness ofthese springs is again calculated by multiplying ksh bythe area tributary to the node on the wingwall. Nosprings are attached to the leading wingwalls since theyare displaced away from the backfill. Translationalsprings are also attached at each node of the abutmentto model the shear stiffness of the backfill until slidingbetween the abutment and backfill occurs. Althoughcomplicated methods are available to define the shearforce–deformation behavior of backfill [32], a simpleelastic approach is developed to calculate the shear stiff-ness of the backfill as follows [14]

Ksb �GBH

Lw

(14)

where Lw is the length of the wingwall, B the width ofthe abutment and G is the equivalent shear modulus ofthe backfill. The stiffness of the transverse boundarysprings at the abutment is obtained by equally distribut-ing the calculated shear stiffness to the interface nodes.

7. Iterative analysis procedure

The iterative MMRS analysis procedures to simulatethe nonlinear behavior of the bridge components that

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1146 M. Dicleli, M.Y. Mansour / Engineering Structures 25 (2003) 1139–1156

were identified by the preliminary seismic analysis ofthe bridge are defined in the following subsections.

7.1. Cracking of substructure members

The effect cracking in the pier columns is included inthe analysis using cracked moments of inertia. An iterat-ive analysis procedure is followed for an accurate esti-mation of the cracked moments of inertia of the piercolumns. This procedure requires the nonlinear moment–deflection diagrams of the columns, which are obtainedusing the column analysis program cola [33]. The col-umns are idealized as cantilevers with an equivalentlength measured from the support to their point ofinflection. First, the nonlinear top deflections, �c, of thecantilever columns are obtained from their moment–deflection curves using the columns’ preliminary seismicmoments calculated earlier. These deflections are thenset equal to the elastic top deflection of the idealizedcantilever columns to obtain their cracked moment ofinertia, Icr, as [14]

Icr �Mcsh2

c

3Ec�c(15)

where Mcs is the column’s seismic moment, hc the lengthof the idealized cantilever and Ec is the elastic modulusof concrete. The analysis of the bridge is then repeatedusing the calculated cracked moments of inertia and newseismic moments are obtained. Using the new seismicmoments, the moment–deflection curves and Eq. (15),more improved cracked moments of inertia are obtainedas defined before. The iteration is continued until thecracked moments of inertia obtained in the current iter-ation step are equal to those obtained in the previousstep.

7.2. Friction between abutment and backfill

The lateral earth pressure produced by the backfillexerts a normal force on the abutment. This normal forcemultiplied by the friction coefficient between the backfilland the concrete abutment surface produces a frictionresistance. As the bridge tries to move in the transversedirection, this friction resistance is mobilized and slidingoccurs between the abutment and backfill. This slidingbehavior is considered in the analysis [14]. First, MMRSanalysis of the bridge is conducted and the forces in thesprings defining the shear stiffness of the backfill areobtained. The sum of the spring forces is then calculatedand compared with the friction resistance at the abut-ment–backfill interface to check if sliding will occur. Toinclude the effect of the sliding behavior on the bridgeresponse, two different analyzes are conducted. First, thesprings defining the shear stiffness of the backfill areremoved from the model and MMRS analysis of the

bridge is repeated. Then, the calculated friction force isequally distributed to the abutment nodes in oppositedirection to that of the seismic forces and static analysisof the bridge is conducted. Finally, the results from theMMRS and static analyzes are combined to incorporatethe effect of sliding in the bridge response.

7.3. Dynamic and static backfill pressure at theabutments

At the abutment pushed towards the backfill, the totalearth pressure is taken as the sum of the static at-restearth pressure and the additional pressure arising fromthe longitudinal displacement of the abutment underseismic forces [28,29]. At the abutment pulled awayfrom the backfill, the generated active earth pressure iscalculated using Mononobe–Okabe method [28,29]. Theresults from the MMRS analyzes of the bridge are com-bined with the static analyzes results under the afore-mentioned at-rest and active earth pressures to incorpor-ate the total effect of the backfill pressures in theanalysis. The analysis is repeated for the movement ofthe bridge in the opposite direction. The maximum ofthe results obtained from the two analyzes is consideredfor assessing the seismic vulnerability of the bridge.

7.4. Yielding of wingwalls

The flexural yielding of the wingwalls is consideredunder transverse direction seismic loading. First, MMRSanalysis of the bridge is conducted to obtain the seis-mically induced moment in the wingwall. This momentis then compared with wingwall’s ultimate flexuralcapacity to determine whether flexural yielding hasoccurred. To incorporate wingwall’s flexural yielding inthe analysis, first the backfill passive resistance that pro-duces a moment equal to the ultimate flexural capacityof the wingwall is calculated. This is done by multiply-ing the calculated forces in the wingwall springs by theratio of the wingwall’s ultimate flexural capacity to theseismically induced moment in the wingwall. Then, thesprings are removed from the wingwall and MMRSanalysis of the bridge is conducted. Next, the calculatedpassive resistance is distributed to the wingwall nodesin opposite direction to that of the seismic forces andstatic analysis of the bridge is conducted. Lastly, theresults from the MMRS and static analyzes are combinedto incorporate the yielding of the wingwall in the analy-sis.

8. Analysis results

8.1. Mode shapes and periods of vibration

A total of 100 modes of vibration are considered inthe seismic analysis of the bridge to accomplish full par-

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ticipation of the structure mass including the mass of thesubstructures. Fig. 6(a) and (b) display the shapes of thefirst two vibration modes of the bridge. The fundamentalperiod of the bridge is 0.584 s and corresponds to itsmodal vibration in the longitudinal direction. Thesecond, third and fourth modal periods of the bridge are0.541, 0.395 and 0.308 s, respectively. The periods forthe first 20 modes vary between 0.584 and 0.049 s. Thecumulative percentages of modal mass participation forthe first 20 modes in the longitudinal and transversedirections are 84.13 and 80.54%, respectively. As notedfrom Fig. 6(b), the transverse direction mode is coupledwith the torsional mode of the bridge. The torsionalrotation occurs about pier 2 due to the larger stiffness ofthe bearings. Consequently, larger seismically inducedforces are anticipated at the north abutment due to theeffect of the torsion.

8.2. Maximum bearing forces and displacements

Table 2 displays the bearing lateral forces and dis-placements. The bearings at pier 2 attract the largest seis-mically induced forces due to their larger lateral stiff-ness. The bearing relative displacements at allsubstructure locations are almost identical due to large

Fig. 6. Bridge first and second modes of vibrations.

in-plane stiffness of the deck in the longitudinal directionand is equal to 24.1 mm. The displacements are less thanthe width of the expansion joint. Therefore, the super-structure is not anticipated to impact the abutmentback-wall.

8.3. Seismic forces in substructures

Table 3, in conjunction with Fig. 7, presents the sub-structure reactions for the abutment piles and base of thepier foundations. The total seismic force acting on thestructure is 1594 kN in the longitudinal and 1776 kN inthe transverse direction. The seismic force in the trans-verse direction includes the contribution of friction andpassive resistance of the backfill and the embankmentsoil and in the longitudinal direction includes the effectof static and dynamic backfill pressures. The piers carry67% of the total seismic force. At the abutments, themaximum longitudinal direction lateral force is 99 kNfor the battered piles and 28 kN for the vertical piles.The battered piles helped to reduce the lateral seismicforce and displacement demand on all other abutmentpiles. Table 4 presents the seismically induced forces inthe wingwalls and abutments, whereas Tables 5 and 6present the seismically induced forces in pier 1 and 2members, respectively.

9. Capacities of structure components

9.1. Capacity of elastomeric bearings

The displacement capacity of elastomeric bearings islimited to 50% of the bearing height as per AASHTO[2] and is calculated as 33 mm for the bearings at bothabutments and pier 1 and as 12.5 mm for those at pier2. This limitation is imposed to prevent delamination ofthe bearings or rollover at the bearing edges. Moreover,walking of the bearings under seismic loads is not antici-pated since the friction coefficient between the bearingpads and the concrete is much larger than the ratio ofthe seismically induced forces to unfactored dead loads.

9.2. Capacity of pier elements

Careful examination of the structural drawings of thebridge revealed that the transverse spiral reinforcementfor the pier columns is not extended sufficiently into thecap beam and footing in compliance with AASHTO [2].Additionally, within the potential plastic hinge zones,full welding or mechanical connection is required for thesplices in spiral reinforcement. For the pier columns, thesplices are only overlapped by 305 mm. Consequently,if the spalling of concrete cover occurs during a seismicevent, the spiral may unwind and the columns may loosetheir transverse confinement. AASHTO [2] requires that

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Table 2Bearing seismic lateral displacements and forces

Location Longitudinal direction Transverse direction

Force (kN) Displacement (m) Force (kN) Displacement (m)

Top Bottom Top Bottom

North abutment 38 0.02584 0.00171 31 0.03290 0.01537Pier 1 56 0.02597 0.00753 76 0.02602 0.00111Pier 2 97 0.02574 0.01184 106 0.01660 0.00142South abutment 38 0.02584 0.00171 12 0.01300 0.00701

Table 3Seismic substructure reactions (at foundation base for piers)

Substructure Longitudinal direction Transverse direction

Axial (kN) Shear (kN) Moment (kN m) Axial (kN) Shear (kN) Moment (kN m)

North abutment piles 1 10 99 0 0 362 11 24 0 11 36 03 12 99 0 22 36 04 16 24 0 37 36 05 �64 21 0 13 39 0

Pier 1 17 407 2075 0 510 30672 44 651 3354 0 671 4089

South abutment piles 1 10 96 0 0 14 02 11 28 0 4 14 03 12 96 0 7 14 04 16 28 0 13 14 05 �64 21 0 14 16 0

Fig. 7. Pile numbers at the abutments in reference to Tables 3 and 9.

splices in longitudinal reinforcement shall be providedaway from the location of potential plastic flexuralhinges at the column ends. For the pier columns, thesplices are provided at their lower ends contradictingAASHTO [2] requirements. Additionally, AASHTOrequires a minimum splice length of 60 times the bardiameter (2100 mm in this case) for the longitudinalreinforcement in the pier columns. This is much largerthan the provided splice length of 787 mm. Thus, ductilebehavior of the columns is not expected due to the inad-equate detailing of their reinforcement.

The shear and flexural capacities of the columns arecalculated considering the deficiencies in their reinforce-ment detailing. The flexural and shear capacities of thepier columns varies between 703 and 801 kNm andbetween 670 and 833 kN, respectively based on the levelof factored axial load applied on the columns.

9.3. Capacity of abutment components

The ultimate shear and flexural capacities of abutmentcomponents are calculated based on AASHTO [2] bridgedesign specifications. The ultimate flexural capacities of

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Table 4Seismic forces in abutment and wingwalls

Location Longitudinal direction Transverse direction

Shear (kN/m) Moment (kN m/m) Shear (kN/m) Moment (kNm/m)

North abutment Wingwall N/A N/A 68 110Back-wall 6 8 N/A N/ABreast-wall 26 15 N/A N/A

South abutment Wingwall N/A N/A 68 106Back-wall 6 8 N/A N/ABreast-wall 26 15 N/A N/A

Table 5Seismic forces in pier 1 members

Location Member end Longitudinal direction Transverse direction

Axial force (kN) Shear (kN) Moment (kN m) Axial Force (kN) Shear (kN) Moment (kN m)

Cap 1 Left 0 57 0 0 0 0Right 0 57 26 74 47 41

Cap 2 Left 0 57 26 74 184 136Right 0 57 26 74 98 95

Column 1 Top 4.2 123 55 126 150 189Bottom 4.2 123 372 126 150 200

Column 2 Top 4 122 56 0 150 189Bottom 4 122 370 0 150 200

Wall Top 12 378 1112 0 456 1795Bottom 12 378 1844 0 456 2685

Table 6Seismic forces in pier 2 members

Location Member end Longitudinal direction Transverse direction

Axial Force (kN) Shear (kN) Moment (kN m) Axial Force (kN) Shear (kN) Moment (kN m)

Cap 1 Left 0 0 0 0 0 0Right 0 97 43 98 32 28

Cap 2 Left 0 97 43 98 223 216Right 0 97 43 98 100 141

Column 1 Top 13 205 95 175 199 221Bottom 13 205 573 175 199 243

Column 2 Top 14 206 95 0 205 231Bottom 14 206 574 0 205 248

Wall Top 40 626 1724 0 608 2251Bottom 40 626 2958 0 607 3440

the wingwall and back-wall are calculated as 57 and 89kNm/m, respectively and their shear capacities are calcu-lated as 180 and 307 kN/m, respectively.

9.4. Capacity of abutment piles

For the calculation of the lateral capacities of the abut-ment piles, the bridge is assumed to remain serviceable

after a potential earthquake. Accordingly, the lateral dis-placements of the piles need to be limited to 38 mm perAASHTO [2] bridge design specifications. The lateralcapacities of the abutment piles corresponding to a dis-placement of 38 mm are obtained from the lateral force–deformation curves presented in Fig. 5(a) and (b).Accordingly, the lateral capacity of a typical north abut-ment pile is obtained as 82 kN for the strong and 68 kN

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for the weak axis bending. For a typical south abutmentpile, it is obtained as 95 kN for the strong and 75 kNfor the weak axis bending.

The pile’s axial compression capacity is obtained as845 kN based on pile driving data provided by IDOT.The vertical uplift capacities of the piles at the northand south abutments are calculated as 80 and 200 kN,respectively using the Alpha Method [34].

9.5. Structural and geotechnical capacities of pierfoundations

Careful examination of the structural drawings of thebridge revealed that the reinforcement in the footings ofthe piers is not detailed in compliance with AASHTO[2] bridge design specifications. The bottom reinforce-ment is not bent up at the faces of the footings to providesufficient development length for the steel bars to reachtheir full yield strength, and no reinforcement is pro-vided at the footing top to resist the tensile stresses intro-duced by the reversed seismic loading. Thus, ductilebehavior of the pier footings is not expected. Based onthe provided reinforcement detail, the ultimate shear andflexural capacities of the footings are calculated as 423kN/m and 120 kNm/m.

The ultimate bearing resistances of the soil at thefoundations of piers 1 and 2 are calculated as 1200 and1100 kPa, respectively [14]. AASHTO [2] limits theeccentricity of the applied vertical loads to one forth ofthe dimension in the direction of interest to prevent over-turning of the footing and/or bearing failure of the foun-dation soil. The eccentricity limits for the pier foun-dations in the longitudinal and transverse directions ofthe bridge are thus calculated as 571 and 2400 mm,respectively. The sliding resistance of the pier foun-dations is calculated as 1500 kN following the procedurerecommended by AASHTO [2].

10. Capacity/demand (C/D) ratios for vulnerablecomponents

The factored elastic seismic demands for each bridgecomponent are calculated following the procedures out-lined by AASHTO [2]. AASHTO [2] allows the designand evaluation of properly detailed ductile structuralmembers using a seismic force smaller than that obtainedfrom elastic seismic analysis of the bridge. However, forthe members of the bridge considered in this study, thecalculated elastic seismic demands are directly used toevaluate their seismic vulnerability since a ductilebehavior is not expected due to poor reinforcementdetailing. The capacity demand ratios for the vulnerablebridge components are presented below.

The seismically induced displacements at pier 2 bear-ings are found to be larger than their 12.5 mm displace-

ment capacity. The C/D ratio for the displacement of thebearings at pier 2 is calculated as 0.82.

Under transverse direction earthquake loading, thepassive resistance of the backfill is found to induce trans-verse seismic moments in the wingwalls in excess oftheir ultimate flexural capacities. The C/D ratio for thewingwalls is calculated as 0.52.

The seismically induced moments at the foundationsof both piers resulted in vertical load eccentricities inexcess of the maximum limits specified by AASHTO[2]. The C/D ratios for the eccentricities at pier 1 and 2foundations are calculated as 0.62 and 0.39, respectively.Thus, overturning of the piers and/or bearing failure oftheir foundation is anticipated.

11. Conventional seismic retrofitting

11.1. Bearing replacement

Although the seismically induced displacementexceeds the displacement capacity of the bearings at pier2, it is anticipated that the failure of such shallow bear-ings may not cause a major damage. Thus, any repairmay be done after the occurrence of a major earthquake.

11.2. Wingwall retrofit

The wingwalls at both abutments need to be retrofittedto enhance their flexural capacities for bending in thetransverse direction. Although, failure of the wingwallsis not expected to result in any structural failure otherthan settlements under the approach slab, their retrofit isrecommended due to their low estimated retrofitting cost.The retrofitting of wingwalls includes the addition of cle-ats at the joints between the wingwalls and the abutmentto enhance their flexural capacities as shown in Fig. 8(a).

11.3. Foundation retrofit at piers 1 and 2

The widths of the footings at piers 1 and 2 need tobe increased from 2286 to 3800 and 4800 mm, respect-ively to obtain a vertical load eccentricity smaller than25% of the footing width as specified by AASHTO [2].This will ensure the stability of the piers. Increasing thefooting width results in larger seismically induced flex-ural moments in the footing at the face of the wall.Therefore, the flexural capacities of the footings at boththe piers need to be increased. For this purpose, thedepths of the footings at piers 1 and 2 are increased from610 to 1100 and 1200 mm, respectively. This involvescasting of an overlay of reinforced concrete doweled tothe existing footing, as shown in Fig. 8(b). The dowelsbetween the new and existing concrete should be capableof transferring the shear stress on the interface. The dow-els are designed using a shear friction approach and a

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Fig. 8. Retrofit details for wingwalls and pier foundations.

coefficient of friction of 1.0. This assumes that the sur-face of the existing footing has been roughened prior tocasting the new concrete. Additional steel is provided atthe interface of the existing and new concrete overlay tominimize the footing depth requirement at pier 2 and toincrease the flexural strength without the need for addingextra reinforcement at the bottom of the footing. Thiswas not required at pier 1. In seismically active zones,it is recommended to provide reinforcement at the topof the footings to accommodate for seismic momentreversal [2]. Accordingly, minimum reinforcement isprovided at the top of both footings. The walls at bothpiers needs to be drilled to ensure the placement of theadditional transverse layers of steel, while for the bottomtransverse layer of reinforcement, holes need to bedrilled in the existing footings to overlap the new steelbars with the existing steel bars.

11.4. Conventional retrofitting cost

Details for the conventional retrofitting cost of thebridge are presented in Table 7. The ranges of unit pricesare provided by IDOT. The total cost of retrofitting thebridge ranges from US$111,273 to US$161,670. Mobil-ization and traffic control cost is not included in the cost

estimate. More details about the cost estimate is pro-vided elsewhere [14].

12. Seismic retrofitting of the bridge using FPB

12.1. Structural model with FPB

The structural model used for the detailed seismicanalysis of the bridge is slightly modified to incorporatethe FPB instead of the elastomeric bearings—the FPBare also modeled using 3D vertical beam elements. Theequivalent linear stiffness (Eq. (2)) of the FPB is usedto estimate the stiffness properties of the beam elements.However, an iterative analysis procedure is performedas the equivalent bearing stiffness and hysteretic damp-ing is function of the bearing displacement. The iterativeanalysis procedure is described in detail below.

12.2. Iterative analysis procedure

An iterative MMRS analysis technique is used toobtain the isolation bearing displacements and otherstructural responses. First, a maximum displacement, Dd,is assumed for the FPB. The assumed displacement, thebearing reactions due to the self-weight of the bridge, thefriction coefficient (4%) and the radius, R (1020 mm), ofthe bearings are substituted in Eq. (2) to calculate theequivalent stiffness for each bearing. The calculatedequivalent stiffness is then used to obtain the stiffnessof the beam elements used in the model. The equivalentviscous damping ratio is also calculated by substitutingthe bearing properties and the assumed displacement inEq. (4). The AASHTO [2] design response spectrumused in the analyzes is obtained for 5% viscous dampingratio. Therefore, it needs to be modified to incorporatethe effect of the 30% equivalent viscous damping gener-ated by the isolation system. For this purpose, the ampli-tudes of the design response spectrum corresponding tothe periods of the modes involving the movement of theisolation system are reduced by dividing them by adamping factor. The damping factor is obtained fromAASHTO guide specifications for seismic isolationdesign [12] and is equal to 1.0 for 5% and 1.7 for 30%damping. For the modes not involving the movement ofthe isolation system 5% structural damping is used. TheMMRS analysis of the bridge is then conducted usingthe modified design spectrum and new bearing displace-ments are obtained. The obtained displacements arecompared with the initially assumed bearing displace-ments. If the difference is smaller than an assumed levelof accuracy, the iteration is stopped; otherwise, the iter-ation is continued with the new displacements until thedesired convergence is achieved.

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Table 7Cost estimate for the conventional retrofit scheme

Item Unit Cost range (in US$) Quantity Total cost range (in US$)

Soil excavation cu yd 25–30 311 7775–9330New concrete cu yd 1000–1500 92 92,000–138,000Concrete removal cu yd 1000–1500 5.0 5000–7500Shear dowels Pound 0.95–1.00 540 513–540Reinforcing bars Pound 0.95–1.00 6300 5985–6300Total cost 111,273–161,670

12.3. Analysis results using FPB

12.3.1. Mode shapes and periods of vibrationA total of 100 modes of vibration are considered in

the seismic analysis of the bridge with FPB. The firsttwo modes of vibrations are those mainly involving theisolation system. The rest are the nonisolated modes ofvibration with 53% mass contribution, which is the totalmass of the substructure elements. The fundamental per-iod of the bridge is 1.423 s and corresponds to the modalvibration of the structure in the longitudinal direction,while the second period of vibration is 1.395 s and corre-sponds to the modal vibration of the structure in thetransverse direction. Fig. 9(a) and (b) display the shapes

Fig. 9. Bridge first and second modes of vibrations with friction pen-dulum bearings.

of the first two vibration modes of the isolated bridge inthe longitudinal and transverse directions, respectively.

12.3.2. FPB forces and displacementsTable 8 displays the maximum bearing lateral forces

and displacements. The bearings at pier 1 have largerseismically induced forces due to the larger dead loadreactions that produce larger friction forces. The bearingdisplacements at all substructure locations are almostidentical and equal to 50 mm due to the large in-planestiffness of the bridge deck relative to the equivalentstiffness of the FPB. This displacement is larger than thewidth of the expansion joints at both abutments. Thus,the superstructure is expected to impact the abutmentback-walls.

12.3.3. Seismic forces in substructuresTable 9, in conjunction with Fig. 7, displays the sub-

structure reactions at the piles and base of the pier foun-dations. The seismically induced forces in the abutmentsand wingwalls are displayed in Table 10 and those forthe members at piers 1 and 2 are displayed in Tables 11and 12, respectively. The FPB eliminated the in-planetorsional rotation of the bridge and resulted in a moreuniform distribution of seismic forces among substruc-tures as observed from Tables 9 to 12. The forces aregenerally reduced by a factor ranging between 3 and 4due to the presence of FPB when compared to those ofthe same bridge with elastomeric bearings. This is aresult of energy dissipation and lower equivalent linearstiffness of FPB compared to that of the elastomericbearings and even other rubber-based seismic isolationsystems for this particular application. The lower equiv-alent linear stiffness expressed in Eq. (2) mainly resultsfrom the relatively smaller weight of the only 32.4 mlong bridge superstructure transferred to the FPB.

12.4. C/D ratios

The C/D ratios for the previously determined vulner-able structural members are now all larger than 1.0 afterreplacing the existing bearings with FPB. The C/D ratiosfor the north and south abutment wingwalls in flexureare 1.84 and 2.11, respectively. The C/D ratios for the

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Table 8FPB seismic lateral displacements and forces

Location Longitudinal direction Transverse direction

Lateral force (kN) Displacement (m) Lateral force (kN) Displacement (m)

Top Bottom Top Bottom

North abutment 7 0.05203 0.00124 7 0.04969 0.00248Pier 1 28 0.05195 0.00373 28 0.04972 0.0004.7Pier 2 27 0.05196 0.00339 27 0.04969 0.00040South abutment 5 0.05204 0.00301 5 0.04976 0.00272

Table 9Seismic substructure reactions of the bridge with FPB (at foundation base for piers)

Substructure Longitudinal direction Transverse direction

Axial force (kN) Shear force (kN) Moment (kN m) Axial force (kN) Shear force (kN) Moment (kN m)

North abutment piles 1 14 36 0 0 72 14 11 0 2 7 03 15 36 0 3 7 04 21 11 0 5 7 05 �58 8 0 5 9 0

Pier 1 1.7 260 1088 0 292 12892 2.3 262 1018 0 244 1179

South abutment piles 1 14 36 0 0 7 02 14 11 0 2 7 03 15 36 0 3 7 04 21 11 0 5 7 05 �58 8 0 5 9 0

Table 10Seismic forces in abutment and wingwalls of the bridge with FPB

Location Longitudinal direction Transverse direction

Shear (kN/m) Moment (kN m/m) Shear (kN/m) Moment (kN m/m)

North abutment Wingwall N/A N/A 24 31Back-wall 2.2 2.9 N/A N/ABreast-wall 9.4 5.4 N/A N/A

South abutment Wingwall N/A N/A 20 27Back-wall 2.2 2.9 N/A N/ABreast-wall 9.4 5.4 N/A N/A

vertical load eccentricities at piers 1 and 2 are 1.08 and1.13, respectively. Thus, the use of FPB effectively miti-gated the seismically induced forces such that seismicretrofitting of the pier foundations and wingwalls is nomore required. However, since the calculated 50-mmbearing displacement under seismic excitation exceedsthe expansion joint widths, the bridge superstructure isexpected to impact the abutment back-walls. The conse-quences of this need to be addressed before a decisionis made to use FPB for seismic retrofitting.

12.5. Effect of superstructure impacting the back-wall

For the back-wall to fail in shear, the magnitude ofthe impact force must be at least equal to the shearcapacity of the back-wall plus the force required formobilizing the passive resistance of the soil behind theback-wall only. This force is calculated [14] as 3970 kN.Thus, a force equal to 3970 kN may potentially be trans-ferred to the breast wall and the piles. The sum of thelateral capacities of the abutment piles and passive resist-

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Table 11Seismic forces in pier 1 members of the bridge with FPB

Location Member end Longitudinal direction Transverse direction

Axial force (kN) Shear (kN) Moment (kN m) Axial force (kN) Shear (kN) Moment (kN m)

Cap 1 Left 0 28 0 0 0 0Right 0 28 10 29 23 20

Cap 2 Left 0 28 10 29 80 58Right 0 28 10 29 44 41

Column 1 Top 1 65 29 61 66 83Bottom 1 65 195 61 66 88

Column 2 Top 1 65 29 0 66 83Bottom 1 65 195 0 66 88

Wall Top 3 215 586 0 210 776Bottom 3 215 983 0 210 1163

Table 12Seismic forces in pier 2 members of the bridge with FPB

Location Member end Longitudinal direction Transverse direction

Axial force (kN) Shear (kN) Moment (kN m) Axial force (kN) Shear (kN) Moment (kN m)

Cap 1 Left 0 27 0 0 0 0Right 0 27 10 27 15 13

Cap 2 Left 0 27 10 27 60 60Right 0 27 10 27 28 40

Column 1 Top 1 63 29 75 61 68Bottom 1 63 174 75 61 76

Column 2 Top 1 63 29 0 63 67Bottom 1 63 174 0 63 74

Wall Top 3 205 525 0 190 700Bottom 3 205 910 0 190 1058

ance of the portion of the backfill behind the breast wallis 1407 kN. This is smaller than the anticipated 3970 kNforce transferred by the back-wall. Therefore, damageto the abutment piles may occur. This damage may beprevented if the back-wall is modified to fail in shear,for instance by providing a knock-off device [7]. Essen-tially, in seismic design of bridges, it is recommended[7] to use such a mode of damage as a ‘ fuse’ as it ismuch easier to repair the upper portion of the abutmentafter a seismic event. Therefore, either the abutment mayneed to be modified to fail in shear by providing aknock-off device or the expansion joints may be widenedto accommodate the required displacements if the back-wall damage is not desired.

12.6. Retrofitting scheme and cost

The isolated bridge must be free to move in any hori-zontal direction for the seismic isolation system to per-form as desired. Considering a maximum thermal move-ment of 10 mm in each end of the bridge, the minimumrequired expansion joint width at the abutments is calcu-

lated as 60 mm. Thus, the width of the expansion jointat the north and south abutments needs to be increasedby 22 and 35 mm, respectively. Furthermore, the mini-mum required displacement capacity of the bearingsincluding a tolerance for thermal movements needs tobe 60 mm. The elevations of existing bearing pedestalsalso need adjustment to prepare the bridge for the instal-lation of FPB.

Details for the cost estimate are presented in Table 13.The retrofitting cost includes expansion joint widening,jacking and removing the bearings, adjusting the elev-ation of bearing pedestals and erection and cost of FPB.The lower profile of FPB compared to most other iso-lation bearings required only minor modifications toadjust the bearing seat elevations. The estimated rangeof cost for the seismic retrofitting of the bridge usingFPB is calculated as US$107,515–US$133,170. This isonly 88% of the cost of conventional retrofitting. Thishas a considerable impact on the state economy con-sidering the large number of bridges that require seismicretrofitting. Furthermore, retrofitting with FPB requiresshorter construction time than that required for conven-

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Table 13Retrofitting cost of the bridge with FPB

Item Unit Cost range (in US$) Quantity Total cost range (in US$)

Concrete removal cu yd 1000–1500 5 5000–7500Concrete superstructures cu yd 1000–1500 5 5000–7500Reinforcing bars Pound 0.95–1.00 900 855–900Steel plates Pounds 2.00–3.00 1500 3000–6000Preformed joint seal Foot 60–70 81 4860–5670Jack and remove bearings Each 800–1200 24 19,200–28,800Bearing erection Each 200–500 24 4800–12,000Bearing cost Each 2700 24 64,800Total cost 107,515–133,170

tional retrofitting. Additionally, a complete detour of thetraffic for roadways under the bridges may not berequired when retrofitting with FPB. Consequently,retrofitting with FPB may become much more economi-cal when the additional cost of construction time andcost of traffic mobilization is considered.

13. Conclusions

The economical and structural efficiency of FPB forretrofitting typical seismically vulnerable bridges in theState of Illinois is investigated by studying a bridge,which was carefully selected by IDOT to represent typi-cal seismically vulnerable bridges commonly used in theState of Illinois. The following observations are made:

� FPB eliminated the in-plane torsional rotation of thebridge and resulted in a more uniform distribution ofseismic forces among substructures.

� A three to four times reduction in the seismicallyinduced forces in the structure components is achi-eved with the FPB. This is a result of: (i) energy dissi-pation and (ii) lower equivalent linear stiffness ofFPB compared to that of the elastomeric bearings andeven other rubber-based seismic isolation bearings forthis particular application. The lower equivalent linearstiffness mainly results from the relatively smallerweight of the only 32.4 m long bridge superstructuretransferred to the FPB.

� Thus, FPB effectively mitigated the seismic forcesand eliminated the need for costly retrofitting of thebridge substructure components. Furthermore, the lowprofile of FPB required only minor modifications toadjust the bearing seat elevations. However, FPBresulted in large superstructure displacements inexcess of the expansion joint widths. This requiredeither providing knock-off devices at the abutmentsor increasing the widths of the expansion joints toeliminate the possibility of the superstructure impact-ing the abutment back-wall and a potential damage tothe abutment piles.

� An average retrofitting cost using FPB is calculatedas only 88% of that using conventional retrofittingmethod. This has a considerable impact on the stateeconomy considering the large number of bridges thatrequire seismic retrofitting. It is worth mentioning thatretrofitting with FPB may require shorter constructiontime than that required for conventional retrofittingand may cause less interruption to the traffic over andunder the bridge. Consequently, retrofitting with FPBmay become much more economical when theadditional cost of construction time and cost of trafficmobilization is considered. Thus, FPB may be effec-tively used to retrofit typical bridges in the State ofIllinois or in regions of low to moderate risk of seis-mic activity.

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