Seismic Investigation of Steel Pile Bents:II. Retrofit and Vulnerability AnalysisAyman A. Shama,a) M.EERI, John B. Mander,b) M.EERI, and Stuart S. Chenc)

This paper is the second of a two-part study on the seismic vulnerabilityof deck bridges supported on steel pile bents. A conceptual elastic cap/elasto-plastic steel pile retrofit strategy is proposed in this part with the aim ofstrengthening the connection and ensuring plastification takes place only inthe steel pile. An experimental program was carried out to assess the retrofitstrategy. On the basis of the experimental results for existing as well as ret-rofitted connections, a seismic vulnerability analysis for bridges supported bysteel pile bents was performed. Fragility curves for such structures were de-veloped using a simplified fundamental mechanics-based approach. Thestudy showed that the retrofitted connections exhibited superior energy ab-sorptions with respect to the existing connections. Fragility curves also dem-onstrated the effectiveness of the retrofit strategy proposed.[DOI: 10.1193/1.1468250]

INTRODUCTION

Substructures consisting of steel pile bents have been widely used in the constructionof highway bridges throughout the United States. But the majority of these bridges werebuilt two to three decades ago, when design of structures for current high seismic loadswas not required. The experimental study performed on specimens simulating as-builtsubstructures indicated that the pile-to-pile cap connection, a connection primarily de-signed for vertical loading, is susceptible to damage from cyclic lateral loading (Shamaet al. 2002). Therefore, in zones of moderate to high seismicity it is required to performany properly designed seismic strengthening for this class of connection and hence im-proving the performance of bridges supported by such substructures during a potentialearthquake.

Two basic approaches are available for the retrofit of these substructures. The firstapproach is to reduce the seismic forces that can be developed in the cap beam duringseismic events. This approach can be achieved by connecting the bent piles with a linkbeam as shown in Figure 1. The location of the link beam can be adapted so that thefinal moment at the connection will be less than both the nominal moment capacity ofthe concrete beam and the plastic moment capacity of the steel H-pile. The merit of thismethod is that it can be accomplished without traffic disruption. The approach has been

a) Parsons Transportation Group Inc., 110 William Street, New York, NY 10038b) Department of Civil Engineering, University of Canterbury, New Zealandc) Department of Civil, Structural and Environmental Engineering, State University of New York at Buffalo, Buf-

falo, NY 14260

143Earthquake Spectra, Volume 18, No. 1, pages 143160, February 2002; 2002, Earthquake Engineering Research Institute

144 A. A. SHAMA, J. B. MANDER, AND S. S. CHENused in California in the retrofit of Santa Monica Viaducts (Priestley et al. 1997). Thismethod will not be explored further here and is out the scope of the present study.

The second approach is to increase the cap beam strength to the level required forshifting the plastic hinge location to the steel pile rather than the concrete cap. Hence,ensure better ductile connection that can possess large deformation capability and permitmuch more dissipation of seismic energy.

A conceptual elastic cap/elasto-plastic pile retrofit strategy, consistent with the sec-ond approach, is adopted in the present research. This paper first sets forth the seismicretrofit strategy and then goes on to present and compare the test results. The study isconcluded with seismic vulnerability analysis for highway bridges supported by suchsubstructures.

RETROFIT METHODOLOGY

A simplified stress distribution shown in Figure 2 is adopted to evaluate the addi-tional retrofit depth required. It is assumed in this mechanism that the stress block forcecouple Cm will resist the external applied moment to the connection. Therefore, thestress block force Cm can be evaluated as

Cm50.5abfc8bflemb (1)in which, a and b are stress block factors; fc85compressive strength of concrete; bf5width of the steel pile section; and lemb5embedment of steel pile into the concrete capbeam. The lever arm can be determined as

jd5lemb~120.5b! (2)

Figure 1. Retrofit strategies for steel pile bents: (a) link beam, and (b) cap beam strengthening.

SEISMIC INVESTIGATION OF STEEL PILE BENTS: RETROFIT AND VULNERABILITY ANALYSIS 145By assuming b51 (Shama et al. 2002), then jd can be taken as 0.5 lemb . The momentstrength of the connection can now be determined as

Mj5fCmjd (3)where f5strength reduction factor. Substitute Equations 1 and 2 in Equation 3, there-fore

Mj50.25fabfc8bflemb2 (4)if ab is taken as 0.36, i.e., moderate damage, and f50.90, further simplification forEquation 4 leads to

Mj50.08fc8bflemb2 (5)To ensure that plastic hinges will not occur at cap beam, the following condition

should be satisfied:

Mj>Mpo (6)

where Mpo is the overstrength plastic moment capacity of the steel H-pile section. There-fore

0.08fc8bf lemb2 >Mpo (7)and hence

lemb>A12.5Mpofc8bf (8)Further simplifications of Equation 8 can lead to the following expression for the

total embedment depth:

Figure 2. Mechanism adopted for connection retrofit.

146 A. A. SHAMA, J. B. MANDER, AND S. S. CHENlembdp

>3.5AS fsufc8 DS tfdpD (9)where fsu5the ultimate stress of the steelpile section; tf5flange thickness of the steelpile section; dp5depth of the steel pile section. The additional embedment depth re-quired is

lad5lemb2lab (10)

where lab5the embedment depth for the as-built structure.

Additional design considerations are required to account for the effects of reversedcyclic loading. Under cyclic loading a gap is expected to occur at the pile flange-concrete interface. If the opening of that gap is not controlled, it may affect the hystereticresponse of the connection, and hence its energy absorption. It is, therefore, necessary toprovide sufficient horizontal reinforcing bars crossing the pile-concrete interface. Thissteel is chosen such that its area has a yield force equal to the plastic shear capacity ofthe pile section. Thus, the area of steel required is

As5Vp

ffyh (11)

where Vp5the shear capacity of the pile section, fyh5the yield stress of reinforcing re-bars. Horizontal stirrups are provided to counteract shear forces. Shear forces are as-sumed to provide a strut and tie actions. Concrete struts are assumed to act at 457 todeliver the required shear force to a number of stirrups n. The force in each hoop can bedetermined as

Vst50.50Vp

n(12)

Each stirrup is assumed to carry a force of Avfyh , where Av is the area of one stirrup,therefore:

Av5Vstfyh (13)

CONSTRUCTION OF RETROFIT

The embedment depth of the retrofitted specimen was determined using Equation 9.For a 35 MPa concrete and 315 MPa steel and using the dimensions of the HP 10342steel pile section, the total embedment depth was determined as 625 mm. The originalspecimen had an embedment depth5300 mm. Therefore it was decided to use another300 mm for the overlay depth.

The longitudinal reinforcement required to close the anticipated gap between thesteel section and the concrete cap beam during cyclic loading is determined according toEquation 11:

SEISMIC INVESTIGATION OF STEEL PILE BENTS: RETROFIT AND VULNERABILITY ANALYSIS 147As5VP

ffyh 50.6FydPtw

ffyh 50.63315.23246310.54

0.85341351397 mm2.

Therefore 4 25-mm-diameter rebars (4 #8, As51963 mm2) were used.

The size and number of stirrups that resist the shear force was determined by assum-ing four stirrups will resist the shear force. Therefore, according to Equation 12

Vst50.50Vp

n5

0.5030.63315.23246310.54

431000561.02 kN

Substitute in Equation 13 Av5Vst /fyh 5 61.023103/413 5148 mm2; therefore 12-mm-diameter double-leg stirrups (As5226 mm

2) were used.

To ensure joint confinement, additional transverse reinforcement (9.5-mm-diameter137 galvanized wire rope) was added to the HP 10342 steel pile along the overlaylength, with a spiral pitch of 50 mm. To facilitate the top-down pouring of concrete in anactual bridge, it was decided to increase the width of the pile cap by 100 mm on eachside. The additional width is required for practical purposes where the pile cap will be inan inverted position in an actual scenario, and that extension of the width will facilitatethe concrete placing and compaction in the field. Additional reinforcement was providedin the form of #4 rebars (13-mm diameter) every 150 mm for the longitudinal direction.Diagonal 13-mm-diameter stirrups were used to improve joint shear resistance. The restof the stirrups were three-sided (U-shaped) #4 rebars. The retrofit construction was per-formed without drilling big holes in the cap beam. Instead, seven 16-mm diameter (7 #5)bars were provided as spacers along each of the two longitudinal sides of the cap beamand attached to it by galvanized straps. The straps were fixed to the cap beam by6 mm325 mm39.5 mm sleeve concrete anchors. Figure 3 illustrates the reinforcing de-tails for the pile bent retrofit at the connections.

SCOPE OF THE EXPERIMENTAL PROGRAM

The specimens were tested in displacement control under incremental cyclic loading.Two cycles of drift at levels ranged from 60.5% to 66%. The quasi-static displacementfunction was sinusoidal with a one-minute period per cycle. Table 1 summarizes theaxial loads and drift information for each specimen tested in the retrofit study.

SPECIMEN ReS1

This specimen was tested without any axial load with two reversed cycles at driftamplitude of 60.5%, 61%, 62%, 63%, 64%, and concluded with 26 cycles at 65%.The complete hysteretic response of the specimen is shown in Figure 4. Yielding of thepile section first occurred just prior to the 2% drift level, characterized by some diagonalstriations on the whitewashed flanges. Local buckling was initiated at the second cycleof 3% drift and continued to grow as the drift amplitude increased.

Strain hardening was observed on the first cycle at 3% drift was attained. Beyond the4% drift level, strength degradation of the steel material occurred as a result of the localbuckling. The specimen was exposed to a continued cycles of constant amplitude testing

148 A. A. SHAMA, J. B. MANDER, AND S. S. CHENat 5% drift, through which strength degradation of the specimen continued. Finally onthe 26th cycle, a visible horizontal fatigue crack was observed at the flange subjected tocompression when the lateral actuator is pushing.

Figure 3. Reinforcement details for retrofitted connections.

Table 1. Test program for retrofitted specimens

Spec.ID

GravityLoad(kN)

LateralActuatorAngle u

Vertical Axial LoadControl (kN)

Total AxialLoad (kN)

Max.Drift

No. ofCycles at

Max. Drift

ReS1 0 0 0 0 5% 29ReS2 150 0 150 150 6% 15ReS3 120 24 12011.43 Pda 12012.01 V 5% 3V5Pda cosu Pda5force in diagonal actuator

SEISMIC INVESTIGATION OF STEEL PILE BENTS: RETROFIT AND VULNERABILITY ANALYSIS 149Based on the crack initiation, and crack growth mechanism, it is evident that the fail-ure of that specimen was due to low cycle fatigue. A photograph portraying such failureis shown in Figure 5.

SPECIMEN ReS2

Specimen ReS2 was tested under a constant axial load of 150 kN with two reversedcycles at drift amplitude of 60.5%, 61%, 62%, 63%, 64%, 65% and concludedwith 15 cycles at 66%. Figure 6 presents the force-deformation results.

Figure 4. Specimen ReS1: lateral load displacement.

Figure 5. Connection ReS1 after test.

150 A. A. SHAMA, J. B. MANDER, AND S. S. CHENThis specimen exhibited inelastic behavior prior to 2% drift and experienced workhardening in the pile steel material through both the 3% drift and the 4% drift cycles.Local buckling of the steel pile flanges started to occur, along a 250-mm distance abovethe cap beam concrete surface, during the second cycle at 4% drift. Strength degradationof the steel pile followed and was observable at the beginning of the 5% drift.

It was decided to perform a constant cyclic high-amplitude test phase at the 6% driftlevel up to the fatigue failure of the specimen. A horizontal crack occurred at the com-pression flange after the 12th cycle was completed. The flaw continued to grow, propa-gating vertically both sides of the flange as well as horizontally in the web and fractureof the specimen was visible at the end of the 15th cycle. At that point the test wasstopped.

SPECIMEN ReS3

Specimen ReS3 was tested under variable axial load with two reversed cycles at eachdrift amplitude of 60.5%, 61%, 62%, 63%, and 64% concluding with 3 cycles at65%. This specimen also satisfied the main objective of the conceptual elastic cap/elastic-plastic pile retrofit strategy proposed in this study. The specimen behaved in anelastic manner prior to 2% drift. Yielding of the flanges in an area 250 mm above theadded concrete surface was noticed through both the 2% and the 3% drifts and diagonalyield lines were visible on the whitewashed flanges. Strain hardening of the steel mate-rial also occurred during both the 2% and 3% drifts. Local buckling was initiated duringthe second cycle at 3% drift. This local buckling became more pronounced during the4% drift and was characterized by observable strength degradation in force displacementloops (see Figure 7). Due to shortcomings of the test setup, the test of pile specimenReS3 was not continued to reach the failure of the steel.

Figure 6. Specimen ReS2: lateral load displacement.

SEISMIC INVESTIGATION OF STEEL PILE BENTS: RETROFIT AND VULNERABILITY ANALYSIS 151EVALUATION OF DAMPING

Effective damping (jeff) in a structure can be viewed as a combination of equivalentviscous damping jeq , and viscous damping inherent in the structure j0 assumed 0.05 forsteel pile bents. The most common method for defining the equivalent damping jeq is toequate the energy dissipated in a response cycle of the actual structure to that of anequivalent viscous system as (Chopra 1995):

jeq51

4p

EDEso

(14)

where ED5energy dissipated by damping, and Eso5maximum strain energy. For a bi-linear representation of cyclic loops ED is evaluated as

ED54DyDmax~K02Kef f! (15)

in which, Dy5yield displacement, Dmax5maximum displacement, K05initial stiffness,and Kef f5the secant stiffness which can be written in terms of ductility ratiom(5Dmax /Dy) as

Kef f5K0Sa1 ~12a!m D (16)where a5post-yield stiffness ratio. The maximum strain energy can be quantified as

Eso5Kef fDmax

2

2(17)

Assuming an overall bilinear response, as shown in Figure 8, the effective dampingdue to hysteresis can be determined by substituting Equations 15 through 17 in Equation14 and rearranging, the theoretical equivalent viscous damping can be quantified as

Figure 7. Specimen ReS3: lateral load displacement.

152 A. A. SHAMA, J. B. MANDER, AND S. S. CHENjeq52h

p

~12a!S12 1mD~12a1ma!

(18)

where h5energy absorption efficiency factor defined as

h5EcycleEEPP

(19)

where EEPP5the energy absorbed by a 100% perfect elasto-plastic system, defined ac-cording to the following relationship:

EEPP5~Fn11Fn

2!~xp11xp

2! (20)

where Fn15the nominal capacity of the system in the push direction; Fn

25the corre-sponding value in the pull direction; xp

15the plastic component of the displacement inthe push direction; and xp

25the corresponding value in the pull direction.

In the present study elastic-perfect plastic behavior will be assumed and Equation 18is simplified to

jeq52h

p S12 1mD (21)The hysteretic energy absorbed by the system per cycle is given by

Ecycle5(i51

n SFi1Fi212 D~xi2xi21! (22)where Fi5force in i-th step; and xi5displacement of the same step.

The experimental equivalent viscous damping is defined according to the 1994 Uni-form Building Code as

jeq51

2p

EcycleFmaxDmax

(23)

Figure 8. Bilinear representation of cyclic loops.

SEISMIC INVESTIGATION OF STEEL PILE BENTS: RETROFIT AND VULNERABILITY ANALYSIS 153where Fmax5average of the maximum strength in the forward and reverse loading di-rections, and Dmax can be evaluated as the average of the maximum displacement in bothloading directions.

Figure 9 presents experimental results where the equivalent viscous damping is plot-ted against the ductility amplitude for both as-built and retrofitted pile bents. The the-oretical relationships according to Equation 21 are also plotted in the figures. Based onthe experimental results values of h50.47 and h50.75 are suggested for both existingand retrofitted structures.

SEISMIC VULNERABILITY OF BRIDGES SUPPORTED ON PILE BENTS

In light of the foregoing experimental findings for existing (Shama et al. 2002) aswell as retrofitted structures, the seismic vulnerability of deck bridges supported by steelpile bents was investigated. NIBS (1997) defines a total of five damage states for high-way system components. These are (1) none, (2) slight/minor, (3) moderate, (4) exten-sive, and (5) complete. The quasi-static reversed cyclic loading experiments presented inthis study captured these damage states, summarized in Table 2.

EXPECTED SEISMIC STRUCTURAL RESISTANCE

The seismic demand of a bridge structure can be represented in terms of a designcode-like response spectrum; that is the seismic demand can be quantified by the lesserof

Cd52.5A

BS(24)

and

Cd5SA

Tef fBL(25)

where Cd5base shear demand; A5peak ground acceleration at the site; S5soil type fac-

Figure 9. Evaluation of energy absorption efficiency factor for pile bents before and after ret-rofit.

Table 2. Damage states for bridges supported by steel pile bents

154 A. A. SHAMA, J. B. MANDER, AND S. S. CHENtor; Tef f5effective period of vibration and BL , BS are spectral reduction factors used tomodify the elastic response spectrum for high damping, i.e., when the structure respondsin the inelastic range to account for hysteretic damping resulting from nonlinear effects.Based on regression analysis on the values given by Newmark and Hall (1992), Chengand Mander (1997) suggested the following relationships for the spectral reduction fac-tors as

Bs5S jef f0.05D0.5

and BL5S jef f0.05D0.3

(26)

It is assumed here that the peak response of the nonlinear structure to be equal to thedisplacement of a substitute SDOF system with an effective period (Teff) given by

Tef f52pAMK52pAW/g

Fy /D52pA D

Ccg(27)

where D5maximum displacement response; Cc5Fy /W5base shear capacity, in whichFy5yield force of the pile bent; and W5tributary weight. Same as the capacity spec-trum method, it is assumed that the intersection of the capacity and appropriatelydamped demand curve at a point represents the inelastic displacement of the structure.

Substructure Status Bending Axis Damage State* Drift Limit

Nonretrofitted Strong Axis Pre-Yield 0.01Slight Damagea1 0.02

Moderate Damagea2 0.03Extensive Damagea3 0.04Complete Damagea4 0.05

Weak Axis Pre-Yield 0.01Slight Damagea1 0.02

Moderate Damagea5 0.04Extensive Damagea6 0.06Complete Damagea4 0.07

Retrofitted Strong Axis Pre-Yield 0.01Slight Damagea1 0.02

Moderate Damagea5 0.04Extensive Damagea6 0.06

a1Inelastic action on the steel pile section occura2Shear cracks occurs in the concrete cap beama3Damage is mainly concentrated in the cap beam with concrete spallinga4Cap beam failure and slipping of the steel pile out of the socketa5First occurrence of local buckling in the flanges of the steel pile sectiona6Local buckling more pronounced in the steel pile flanges*Damage states are based on HP 10342 steel piles. Pile cap width and depth are 700 mm and 600 mm, respec-

tively.

SEISMIC INVESTIGATION OF STEEL PILE BENTS: RETROFIT AND VULNERABILITY ANALYSIS 155Therefore, replacing the base shear demand in Equations 24 and 25 with the structuralbase shear capacity and rearranging, the peak ground acceleration can be determined bytaking the greater of

A50.4CcBs (28)

or

A52p

SACCD

gBL (29)

For deck bridges supported by flexible steel pile bents, Equation 29 invariably governs.

Analysis of Bridge Capacity

It will be assumed here that the piles within a cap are either oriented to deform alongits strong or weak axis. In other words, no combination of the two cases is permissiblewithin the cap. Consider the pile bent shown in Figure 10 subjected to a lateral force.Assuming an admissible bent plastic mechanism shown in the same figure, the externaland internal virtual work can be equated as follows:

EWD5IWD (30)

CcWupH5LnMpup (31)

where up5plastic rotation; H5distance between the plastic hinges, i.e., distance fromthe bottom surface of the cap beam to the second plastic hinge within the soil; n5number of piles in the bent; L5a fixity factor denoting L51 for fixed-pinned behav-ior and L5(11r) for fixed-fixed, where r5pile-to-cap connection efficiency defined as

r5MjMP

(32)

Figure 10. Potential plastic mechanisms for pile bents.

156 A. A. SHAMA, J. B. MANDER, AND S. S. CHENwhere Mj5moment capacity of the concrete-pile connection (joint); and Mp5fyZp5nominal moment capacity of the pile.

From Equation 31 it is possible to solve for the base shear capacity coefficient as

Cc5~11r!nMp

WH(33)

By assuming that the tributary load W is shared equally between the n piles such thateach of them carries an axial load P, the total tributary load can be expressed as

W5nP (34)

Substituting Equation 34 into 33 one obtains

Cc5~11r!Mp

PH (35)

For small axial load, the plastic moment capacity of a steel H-pile for strong axis bend-ing can be approximated as

Mp5fy tf bf dp (36)where fy5yield stress of the steel pile section; tf5flange thickness of the steel pile; bf5flange width of the steel pile. Similarly for weak axis bending:

Mp5fy tf bf2

2(37)

The applied axial load on each pile can be expressed in terms of the axial yield load:

P5cPy2c fy bf tf (38)where c5ratio of the axial applied load to the axial yield load. Also in terms of tributaryweight:

P5wBL

n(39)

where w5the unit weight of the bridge deck, B5the deck width, and L5the deck spanlength. Thus

c5PPy

5wBL

2nfy bf tf (40)

By substituting Equations 36 and 38 into Equation 35, one can obtain an expression forthe base shear capacity coefficient of the strong axis bending pile:

Cc5~11r!dp

2cH(41)

SEISMIC INVESTIGATION OF STEEL PILE BENTS: RETROFIT AND VULNERABILITY ANALYSIS 157By substituting Equation 41 into Equation 29 one can obtain an expression for the ex-pected peak ground acceleration:

A52p

SA~11r!dpui

2cgBL (42)

in which ui5Di /H5the ith drift damage state.

Similarly for weak axis bending, by substituting Equations 37 and 38 into Equation35, an expression for the base shear capacity of weak axis bending pile bents is obtainedas follows:

Cc5~11r!bf

4cH(43)

By substituting Equation 43 into Equation 29 one can obtain an expression for the ex-pected peak ground acceleration for the motion along the weak axis bending of piles as

A52p

SA~11r!bfui

4cgBL (44)

FRAGILITY CURVE THEORY

As shown by Equations 42 and 44, it is possible to deterministically predict, for agiven bridge, the level of ground motion necessary to attain a target level of a damagestate. However, there are lots of uncertainties associated with both the capacity and thedemand. The uncertainty in the demand arises from the fact that the code specified spec-trum was established as a result of statistical analysis for a broad range of response spec-tra of actual ground motions occurred in different locations having similar soil condi-tions. At the site where the bridge is located, one can expect a series of seismic eventswith associated response spectra that may follow, or not, the ensemble used to establishthe general code specified spectrum at this particular site. The uncertainty in capacity isdue to different sources, such as (1) variability of structural material properties, (2) in-elastic energy absorption and damping, and (3) dispersion in calculating response due toapproximations in modeling. Therefore, there are several parameters, which invariablyhave a measure of both randomness and uncertainty associated with them, entering theproblem. An increasingly popular way of characterizing the probabilistic nature of thephenomena concerned is through the use of fragility curves.

By assuming that the structural capacity and seismic demand are random variablesthat conform to either a normal or lognormal distribution, then following the centrallimit theorem it can be shown that the composite performance outcome will be lognor-mally distributed. Such a distribution only requires knowledge of a median value and asuitable value of the logarithmic standard deviation (Kennedy et al. 1980) and can berepresented by the function

F~Sa!5FFln~Sa /A!bc G (45)

where F (.)=standard normal cumulative distribution function; Sa5spectral accelerationamplitude for a period of T51 s; A5the median (expected value) peak ground accelera-

158 A. A. SHAMA, J. B. MANDER, AND S. S. CHENtion for the given drift limit to be attained, as deterministically assessed by Equations 42and 44; and bc5composite lognormal standard deviation which combines aspects of un-certainty and randomness for both capacity and demand. Based on earlier studies onvariations in concrete and steel properties (Julian 1955; Shalon and Reintz 1955; Mirzaet al. 1979a, 1979b) and uncertainties arising from the paucity of data leading to sim-plifications and assumptions (Jernigan 1996), Dutta and Mander (1999) quantified thelogarithmic standard deviation bp corresponding to capacity as 0.20. In another study,Pekcan (1998) used peak acceleration response of various SDOF systems subjected to awide range of ground motions on various types of soils in an attempt to identify therandomness associated with the demand. His findings indicated that the random re-sponse due to the disparities of the ground motion input resembles a lognormal distri-bution bd . He proposed a value of 0.55 for the long period ranges of the idealized spec-tra given by Equation 25. Therefore the composite lognormal standard deviation bc canbe obtained from the square root of the sum of squares (SRSS) of bp and bd as 0.6.Basoz and Mander (1999) validated this value against experiential fragility curves ob-tained from data gathered from the 1994 Northridge and 1989 Loma Prieta earthquakes.

FRAGILITY CURVE APPLICATION TO STEEL PILE BRIDGES

The following assumptions have been made in the analysis:

The bridge is supported on steel pile bents with section HP 10342. Conse-quently, dp and bf are taken as 246 mm and 256 mm, respectively.

The unit weight of the concrete decks is w57 kPa, with representative spanlength and width of L58 m and B514 m.

The number of piles in a bent is taken as n55. The median compressive strength of the deck concrete fc8525 MPa. The median yield stress of the steel pile bents fy5320 MPa.

Based on the above assumptions, the ratio of the axial applied load to the axial yieldload c was determined according to Equation 40 as 0.095.

Table 3 presents the different values for the parameters used in determining the ex-pected peak ground acceleration of existing, as well as retrofitted structures, for differ-ent damage states.

Fragility curves are displayed in Figure 11 for two damage states namely moderatedamage (DS53) and onset of irreparable (extensive) damage (DS54) for both the ex-isting and retrofitted structures. It is shown that bridges retrofitted according to the ret-rofit strategy proposed in this study are less prone to damage than existing structures. Asan example, at spectral acceleration of 0.6 g, 28% of the nonretrofitted bridges will ex-hibit irreparable damage, whereas only 5% of the retrofitted bridges will experiencesuch damage.

SEISMIC INVESTIGATION OF STEEL PILE BENTS: RETROFIT AND VULNERABILITY ANALYSIS 159CONCLUSIONS

A conceptual elastic cap/elasto-plastic steel pile retrofit strategy was proposed in thisstudy with the intent of strengthening the steel pile bents to cap beam connections thatbehaved poorly when tested under cyclic lateral loading. The retrofitted connectionswere tested under same loading conditions as of the as-built connections and showeda superior performance in terms of energy absorption and ductility. In light of the ex-perimental results for existing as well as retrofitted connections, a seismic vulnerabilityanalysis for bridges supported by steel pile bents was performed. Theoretical fragilitycurves concluded this analysis provided some insight into the major factors that lead tobridge damage and /or collapse. Fragility curves also demonstrated the effectiveness ofthe retrofit strategy proposed in this study for pile-supported bridges.

ACKNOWLEDGMENTS

This research was carried out in the Department of Civil, Structural and Environ-mental Engineering at the State University of New York at Buffalo. Financial support isgratefully acknowledged from the Multidisciplinary Center for Earthquake EngineeringResearch through contract with the Federal Highway Administration. The authors wishto thank anonymous reviewers whose suggestions and comments led to great enhance-ments in the clarification of the material presented.

Table 3. Expected peak ground motions for existing and retrofitted structures

DS

Connectionefficiency Drift

Spectral reductionfactors

BL

Expected peak groundacceleration

Ai (g)

Pre-Ret. Post-Ret. Pre-Ret. Post-Ret. Pre-Ret. Post-Ret. Pre-Ret. Post-Ret.

1 1 1 0.01 0.01 1.00 1 0.32 0.322 0.80 1 0.02 0.02 1.50 1.69 0.66 0.773 0.40 1 0.03 0.04 1.60 1.88 0.75 1.204 0.30 1 0.04 0.06 1.67 1.93 0.85 1.535 0.10 1 0.05 0.07 1.69 1.95 0.90 1.66

Figure 11. Fragility curves for existing and retrofitted bridge piles for two damage states.

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(Received 4 January 2001; accepted 21 November 2001)