Influence of Pier Stiffness Degradation on Soil-Structure Interaction in Base-Isolated Bridges

rovides ancontinuousretical load-en-r belief ofness alsoSI. Aratio of pier

ffness;

Influence of Pier Stiffness Degradation on Soil-StructureInteraction in Base-Isolated Bridges

Muhammad Tariq Amin Chaudhary P.E., M.ASCE1

Abstract: Identification of system parameters by recorded accelerographs on base-isolated bridges during earthquakes popportunity to investigate the performance of such bridges. Stiffness degradation in reinforced concrete piers of four multispanbase-isolated bridges in Japan during eighteen earthquakes is examined by using system identification results and theodisplacement curves of reinforced concrete piers. Soil-structure interaction~SSI! effect identified in these bridges is found to be indepdent of free field acceleration and weakly dependent on dynamic soil properties. This apparent contradiction with the populastrong SSI in weaker soil prompted to consider the fact that with increasing seismic intensity, similar degradation in pier stifftakes place and it is the ratio of pier and foundation stiffness (kc /kh) which should be examined to determine the influence of Srelatively strong relationship between these variables supports the hypothesis that SSI is more strongly related to the stiffnessand foundation than dynamic soil properties.

DOI: 10.1061/~ASCE!1084-0702~2004!9:3~287!

CE Database subject headings: Bridges, piers; Concrete, reinforced; Soil-structure interaction; Base isolation; StiEarthquakes.

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Introduction

Bridge piers made of reinforced concrete are in widespreaddue to their robustness, stiffness, aesthetics, and cost effeness. Integrity of a bridge during an earthquake depends laon the performance of its piers. Past performance records rthat piers have been the most vulnerable component of a bduring seismic excitations~Priestley et al. 1996!. In order to reduce seismic demand on bridge piers, base isolation of the sstructure has been proposed and implemented in some brFew of the base-isolated bridges have been instrumentedstrong motion accelerometers to quantitatively investigate aperformance of such bridges during earthquakes~Chaudhary1999; Lee et al. 2001; Chaudhary et al. 2002!.

A base-isolated bridge is a nonclassically damped systedamping is nonproportionally distributed in its components.clusion of soil-structure interaction~SSI! pushes the system futher into the nonclassically damped paradigm. Effect of SSthe response of conventional bridges on shallow foundationbeen theoretically and experimentally evaluated in the~Levine and Scott 1989; Spyrakos 1990; Giuseppe et al. 2Saadeghvaziri et al. 2000!. Most of these studies focusedelaborate modeling of soil/foundation system and less attewas devoted to proper modeling of piers. Consequently, theence of SSI on the strength requirements of structural compois somewhat exaggerated. Vlassis and Spyrakos~2001! have theoretically investigated the influence of SSI on seismically isol

1203-1905 Normandy Rd., La Salle ON, Canada N9H 1P9. [email protected]

Note. Discussion open until October 1, 2004. Separate discusmust be submitted for individual papers. To extend the closing daone month, a written request must be filed with the ASCE ManaEditor. The manuscript for this paper was submitted for review andsible publication on May 1, 2002; approved on March 3, 2003. This pis part of theJournal of Bridge Engineering, Vol. 9, No. 3, May 1, 2004
©ASCE, ISSN 1084-0702/2004/3-287–296/$18.00.
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.

bridges on shallow foundations with the critical assumptioelastic piers and super-structure elements. Ciampoli and~1995!, however, considered the inelastic behavior of bridgeand concluded that the SSI does not significantly influenceinelastic seismic demand of piers.

The focus of this study is on identification of stiffness dedation in reinforced concrete piers of base-isolated bridges dseismic excitation and its influence on SSI. Seismic accelerdata from 18 earthquakes recorded on four base-isolated bin Japan is used to investigate this phenomenon. A two-stagtem identification methodology~Chaudhary 1999; Chaudhaet al. 2000! for nonclassically damped systems is employereliably identify the modal~frequencyv r , damping ratioj r andcomplex mode participation factorsl pr and mpr) and structura~massM, damping coefficientC, and stiffnessK! parameters othese bridges. Stiffness degradation in reinforced concrete~RC!piers and foundations of the bridges is analytically investigand analytical and identified substructure stiffness valuescompared to give confidence in the system identification meSSI is characterized by the variation in the substructure stifcompared to the fixed base structure. Influence of peak gracceleration, dynamic soil shear strain, soil shear moduluspier stiffness and wave parameter on SSI is investigated andclusions are summarized regarding the most influencing paeter.

Description of Bridges

A brief description of the four bridges investigated in this studpresented in this section while details can be found in Chaud~1999!. All bridges included in this study are base isolated inlongitudinal bridge direction and side stoppers are installeprevent appreciable movement in the transverse direction
though the superstructure is base isolated, the substructure was
URNAL OF BRIDGE ENGINEERING © ASCE / MAY/JUNE 2004 / 287

cialtruc-the

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designed for the full seismic force without taking the benefieffect of base isolation into account for these pioneering stures. Possibility of liquefaction at the site is low according tosoil classification of Japanese Highway Bridge Code 1998~JapanRoad Association 1998!.

Matsunohama Viaduct bridges, shown in Figs. 1~a and b!, arelocated on the Bay shore route of the Hanshin ExpresswOsaka. Both bridges are four-span continuous bridges. Mathama Viaduct Bridge A has a steel I-girder super-structure wis supported on laminated rubber bearing~RB! on the interiopiers and Teflon sliding bearings at the end piers. Whereatwo noncomposite steel box girders of Bridge B are supportelead RBs~LRBs! on the interior piers and pivot roller bearingsthe end piers. Both bridges are supported by reinforced consingle or two column piers founded in deep pile caps. Foutions of these bridges consist of 1.2 m diameter cast-in-situpiles used in different group configurations in a strata whichsists of diluvial deposits of sand, clay and gravel. Figs. 2~a and b!depicts the standard penetration test data and logs of bore ho

Fig. 1. Longitudinal ele

the vicinity of the instrumented piers of Bridge A and Bridge B,

288 / JOURNAL OF BRIDGE ENGINEERING © ASCE / MAY/JUNE 2004

respectively.Onneto bridge; located in Nemuro City, Eastern Hokka

consists of three, four-span continuous steel plate girder brand a Nielsen-type Lohse girder bridge. The west approachbridge, depicted in Fig. 1~c! is base isolated with lead rubbbearings and instrumented at Pier P-3. All piers of the bridgwall type while pile foundations comprising of 600 mm diamsteel pipe piles are used for all interior piers and abutments efor the piers supporting the Lohse girder which is comprisespread footings over a mudstone layer. Soil properties arouninstrumented pier are presented in Fig. 2~c!.

Yama-age bridge, located at Karasuyama in Tochigi preture, is schematically shown in Fig. 1~d!. It is a six-span continuous prestressed concrete twin cell box girder bridge and islated with high damping rubber bearings. The abutments ainverted T-type, closed abutments and piers are of reinforcedcrete wall type with rectangular section. The foundations osubstructures are of spread type footing founded in slate; a

n of base-isolated bridges
vatio
metamorphic rock or gravel layer as shown in Fig. 2~d!.

ac-cap,pilepile

ductandccel-verse

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gesrded.

tionationfreeake atd in

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Instrumentation and Strong Motion Records

One pier of each bridge is instrumented with strong motioncelerometers at three common locations, viz. free field, pierand girder while one additional accelerometer is placed at thecap location in Matsunohama Viaduct bridges and under thetip in the Onneto bridge. Pier P23 of Matsunohama ViaBridge A, Pier P32 of Bridge B, Pier P3 of the Onneto bridge,Pier P5 of the Yama-age bridge are the instrumented piers. Aerations were recorded along the longitudinal and the transbridge directions in the horizontal plane and in the up-down

Fig. 2. Ground profile in v

rection in the vertical plane for all bridges at all instrumented

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locations except for girder location in Matsunohama bridwhere accelerations in the transverse direction were not recoAs all bridges are isolated in the longitudinal bridge direconly, therefore system identification and performance evaluis carried out along this direction. A summary of maximumfield and pier cap acceleration recorded during each earthquthese bridges in the longitudinal bridge direction is presenteTable 1.

System Identification MethodologyA two-stage system identification~SI! methodology developed b

of instrumented bridge piers
icinity
Chaudhary~1999! and Chaudhary et al.~2000! is used to infer the


s. Areas

oughthe

tify-

stage

dal

l.y do-ri-itation

modal and structural parameters of the bridge systembrief description of this methodology is presented herein whethe reader is referred to the cited references for a thoranalytical development of the procedure. First stage oftwo-stage system identification methodology consists of idening the complex modal parameters inr modes~frequenciesf r ;damping ratiosj r ; and complex mode participation factorscpr)of the base-isolated bridge system. Whereas in the secondstructural parameters~i.e., mass@M#, stiffness@K#, and damping

Fig. 3. Flowc

Table 1. Summary of Recorded Acceleration at Four Bridges

Bridge Earthquake Date~dd-mm-yy

Matsunohama Bridge A Main shock 17-01-199Aftershock 1 17-01-1995Aftershock 2 17-01-1995Aftershock 3 17-01-1995Aftershock 4 17-01-1995

Matsunohama Bridge B Main shock 17-01-199Aftershock 1 17-01-1995Aftershock 2 17-01-1995Aftershock 3 17-01-1995Aftershock 4 17-01-1995

Onneto bridge On-1 31-08-1994On-2 9-10-1994On-3 21-01-1995On-4 29-04-1995

Yama-age bridge Yama-1 4-10-1994

Yama-2 17-02-1996Yama-3 20-02-1997Yama-4 12-05-1997


,

coefficient @C#! are found based on the identified moparameters.

Stage I—Identification of Complex Modal Parameters

It has been shown by Chaudhary~1999! and Chaudhary et a~2000! that theoretical absolute acceleration, in the frequencmain, at locationp of a N degree of freedom linear, time invaant, viscously damped system subjected to earthquake excz̈, is given as follows:

f methodology

Maximum acceleration~m/s2!

Pier deflection~mm!Free field Pier cap

1.50 2.26 21.440.20 0.22 1.180.13 0.41 1.000.059 0.09 0.040.21 0.27 1.34

1.36 2.01 6.360.20 0.16 0.300.18 0.28 0.320.04 0.03 0.170.13 0.17 0.541.91 1.13 7.07

0.47 0.39 2.380.44 0.28 1.110.26 0.23 1.02

0.09 0.37 0.63

0.29 0.68 1.420.10 0.36 0.280.12 0.27 0.63

hart o

!

5

5

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pa-heion

-

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pro-then

Ap~v!5S 11(r 51

N 2v2l prv rj r22v2v rmprA12j r212iv3l pr

v r22v212ivv rj r

D3Z~v! (1)

wherev r , j r , l pr , andmpr are the, to be identified,r th modafrequency, damping ratio, and real and imaginary parts of etive mode participation factor, respectively, whileZ(v)5Fouriertransform of recorded input accelerationz̈ and i 5A21.

System identification entails the determination of modalrametersv r , j r , l pr , and mpr such that the error between tmeasured accelerationA and theoretically predicted acceleratAp is minimized over a frequency band;v i to v f . That is, aminimization of the error functionJ given by the following equation is sought:

J5(v

v f

~@Re~A2Ap!#21@ Im~A2Ap!#2! (2)

Fig. 4. Cross section and

i

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where Re~.! and Im~.! refer to the real and imaginary parts,spectively.

Stage II—Identification of Structural Parameters

In the second stage, parameters of the structural model~i.e., @M#,@K#, and @C#! are inferred based on the identified modal pareters by employing a global search scheme. Judicious estimastructural parameters based on the physical dimensions anderties of the bridge components are made to reduce the sspace and to bound the solution within a physically probableues. To ensure that the solution stays around physically povalues, mass of the superstructure is assumed to be knowhigh certainty and is kept constant during the global searchcedure. Thorough search of this multidimensional space is

r layout in instrumented piers
reba
conducted such that the following error functionE is minimized:


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ands sub-e are

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nteds, se-tion

E5(r 51

R S Uv rm2v r

s

v rm U1Uj r

m2j rs

j rm U D (3)

Eq. ~3! represents the sum of normalized error in the identmodal model’s and structural model’s frequencies and damratios, respectively, for the modes included in the system idfication process. Superscriptsm and s refers to parametersmodal and structural models, respectively.

Application of Two-Stage System IdentificationMethod

Assumptions made while analytically modeling the bridges instudy are:~i! Equivalent linear models are used to representlinear response of isolation system, reinforced concrete piersoil-pile system,~ii ! effect of incoherence of support motioneach bridge pier is ignored,~iii ! response recorded at the instmented pier is representative of all piers in the bridge, and~iv!design material properties are representative of the prototyp

Due to limited instrumentation, the dynamic behavior ofbridges is studied by lumped mass models. The identified syparameters in modal and structural domains are reliable as amatch is achieved between the recorded and computed resp~Chaudhary 1999; Chaudhary et al. 2000, 2001, 2002!. The pro-cedure adopted to study the influence of various parameteSSI in these bridges is outlined in Fig. 3 and explained infollowing sections.

Stiffness of Reinforced Concrete Piers

Geometric Dimensions and Material Properties

Geometric dimensions, material properties and reinforcemenout of each column are found from the as built construction dings. Fig. 4 depicts the geometry and rebar layout of the inmented pier of each bridge while this information for other pis presented in Chaudhary~1999!. Concrete having design compressive strength (f c8) of 26.7 MPa is used for the MatsunohaViaduct bridges~Bridge A and Bridge B! while design compressive strength of concrete used in piers of Onneto and Yam

Fig. 5. ~a! Relationship between lateral load and pier

bridges is 20.6 MPa. Deformed rebars used in these piers have


s

yield stress of 311 MPa, ultimate stress of 466 MPa, strain astart of strain hardening 7 mm/mm, and ultimate strain ofmm/mm.

Stiffness of Reinforced Concrete Piers

Equivalent linear stiffness of a properly instrumented pier duan earthquake can be found as secant stiffness from the theoload versus deflection curves and the actual maximum recdeflection. The procedure consists of finding:~1! Actual recordeddeflection of pier;~2! moment curvature relationship of reinforcconcrete section~s!; and~3! load-deflection relationship of pier.brief description of these steps is given in the following.

1. Computation of Recorded Pier Deflection: Deflection offree end of the piers is determined from accelerographspile cap~or free field! and the pier cap locations. Displaments are calculated by integrating the observed acceleresponse after passing it through a 0.5–25 Hz bandfilter. As only one pier was instrumented in each bridtherefore it is assumed that the deflection of other piethe bridge is also the same. Maximum recorded deflecof the free end of pier are summarized in Table 1.

2. Moment-Curvature Relationship: Moment-curvatureshear strain versus shear stress relationships for sectionjected to combined axial load, moment, and shear forcfound by computer programRESPONSE-2000~Bentz 2000!.

3. Load-Deflection Relationship: Deflection at the free endcantilever pier is determined by integrating the theorecurvatures and shear strains over the entire height of thfor a particular value of lateral loadP. Knowing the curvature distribution, flexural deflection at a location is foundthe second moment-area theorem. Contribution of sheaformation is found by summing, over the entire pier heithe product of shear strain at a section and its height frombase.

Degradation in Pier Stiffness

Fig. 5~a! depicts the load-deflection curves of the instrumepiers of each bridge. Using the recorded pier displacementcant stiffness of each bridge pier is found from load-deflec

eflection and~b! stiffness degradation as function of pier drift
cap d
curves of respective pier. Degradation in pier stiffness is evalu-

itialshiprift,pier

lumn

stepters

soily andtible

se-duct

de-d forer the

ated as the ratio of pier stiffness at the current level to the instiffness. Fig. 5~b! presents the stiffness degradation relationfor all piers of the four bridges as a function of column dwhich is defined as the ratio of recorded pier deflection andheight. Itis observed that stiffness does not degrade till a codrift of 0.015% whereas substantial reduction~up to 45%! can beseen for moderate level of drift~0.12%! during the relativelystronger seismic excitation.

Computation of Foundation Impedance

Computation of dynamic impedance of foundations is a two-procedure:~a! Determination of representative soil parame

Fig. 6. Pile group la

and ~b! computation of dynamic impedance of foundation.

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Representative Soil Parameters

For calculating foundation impedance, it is important to useparameters that are representative of the site stratigraphlevel of ground shaking. In order to obtain shear strain compasoil shear wave velocities (Vs), dynamic soil shear modulai (Gs),and soil damping ratios (bs), one-dimensional site responanalysis programSHAKE91~Idris and Sun 1992! is used. A deconvolution analysis is performed for Matsunohama Viabridges using the recorded free field motions and the profilescribed by the bore holes, while a direct analysis is performeOnneto bridge by using the record placed in mudstone, und

for instrumented piers
yout
pile tip. Site response analysis for Yama-age bridge is not carried


undare

com-nda-

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unda-

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y the

tions

nessFig.pier

beiden

idgess is

pro-thanhese

fore

otldent

f free

lus-

h thellows:

thesheare SSIcel-indexncen thebe inr SSI

out as the level of seismic excitation is quite low and the groconditions are firm. Therefore, initial values of soil parametersadopted for this bridge for all earthquakes.

Dynamic Foundation Impedance

Dynamic foundation impedance is a frequency dependentplex quantity, whose real and imaginary parts represent foution stiffness and damping respectively. Prakash et al.~1996!, ob-served that the variation of stiffness with respect to frequenvery nominal for practical applications to problems in earthquengineering. Hence, frequency dependence of dynamic fotion stiffness is ignored in this study.

Pile group layout for the instrumented piers of MastunohBridges A and B and Onneto bridge are depicted in Fig. 6. Hzontal and rocking pile group impedance for the Matsunohbridges is computed by the procedure outlined by DobryGazetas~1998! for friction piles. On the other hand, impedanceend bearing pile groups of Onneto bridge are computed bthin layer element method using computer programTLEM ~Kona-gai 1998!. Yama-age bridge has spread footing type foundawhose stiffness is computed by analytical expressions~Gazeta1991!.

Identification of Soil-Structure Interaction

SSI is identified by comparing the identified substructure stiffwith the fixed-base stiffness for all bridges and is depicted in7. Fixed-base stiffness is given by the stiffness of the RCalone as foundation stiffness is taken to be infinite. It canobserved that fixed base stiffness is almost the same as thetified stiffness for Matsunohama Bridge A and Yama-age brduring all earthquakes. On the other hand, fixed-base stiffne

Fig. 7. Comparison of identifi

almost twice the identified value for Matsunohama Bridge B and


-

Onneto bridge. This comparison indicates that SSI is morenounced in Matsunohama Bridge B and Onneto bridgeBridge A and Yama-age bridge. Factors influencing SSI in tbridges are examined in the next section.

Identified stiffness is more than the fixed base stiffnessBridge A and Yama-age bridge~except for main shock of BridgA!, which may be due to:~1! Partial fixity at pier tops that is nconsidered while analytically modeling the piers;~2! residuaerror in the identification process;~3! material overstrength, an~4! in case of Yama-age bridge, the contribution of abutmbackfill ~Chaudhary et al. 2001!.

Factors Influencing Soil-Structure Interaction

This section examines the dependence of SSI on intensity ofield acceleration, soil shear strain («s), soil shear modulus (Gs),shear wave velocity (Vs), degradation in soil shear modu(G/Go), and wave parameter~a!. SSI effect is illustrated by comparing the system-identified characteristics of the bridges witfixed base system. Consequently SSI index is defined as fo

SSI–Index5~ksub!fixed–base

~ksub! identified(4)

Fig. 8 graphically summarizes the relationship betweenSSI index and free field acceleration, soil shear strain, soilmodulus, and shear wave velocity. It can be observed that thindex is virtually independent of the intensity of free field aceration and soil shear strain. On the other hand, the SSIreduces with increase inGs andVs and shows a weak dependeon these parameters. Relatively weaker correlation betweeSSI index and these important soil parameters appears tocontradiction with the code stipulations that suggest strongeeffect in weaker soils.

Next, the correlation of the SSI index with degradation inGs

d fixed base substructure stiffness
ed an
and the wave parameter is examined in Fig. 9. Although soil shear

t thisave

ture-ve-

rrela-

n thewavendrentution

tor ofnessdeeprgertionsoil

ess

alcan

or

andy

r

modulus is reduced by about 30–40% in some cases buparameter does not correlate well with the SSI index. The wparameter (a5VsT/H) has been extensively used in the literafor SSI studies~Ciampoli and Pinto 1995!. It correlates foundation properties with that of the structure through shear wavelocity (Vs), fundamental fixed base period~T!, and height~H! ofstructure. It is observed that the SSI index shows a weak cotion with these parameters too.

The reason for a weak correlation of the SSI index withGs ,Vs , andG/Go seems to be the focus of these parameters osoil side of the SSI phenomenon. On the other hand, theparameter~a! tries to combine the contributions of both soil astructure. Its weak correlation with the SSI index in the curstudy seems to be due to its failure to incorporate the contrib

Fig. 8. Correlation of soil-structure interaction index with~a! free fiwave velocity

Fig. 9. Relationship of soil-structure in

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of foundation stiffness. This parameter may be a good indicaSSI for structures founded on shallow foundations with stiffcomparable to that of piers but it cannot be reliably used forpile foundations that usually have stiffness considerably lathan that of the supporting piers. The focus of soil’s contribuin SSI has thus to be shifted from dynamic properties of(Gs ,Vs) to stiffness of foundation. Overall foundation stiffncomprises of two components: Sway (kh) and rocking (kr). As kr

is an order of magnitude larger thankh , therefore in the serisystem of foundation stiffness, the total foundation stiffnessbe approximated askh without causing any significant err~Chaudhary 1999!.

Fig. 10 presents the relationship between the SSI indexratio of pier and foundation stiffness (kc /kh) and a relativel

celeration;~b! soil shear strain;~c! soil shear modulus; and~d! shea

ion index withG/Go and wave parametera

eld ac

teract


s the.86.clu--ased. But

tiff-stiffth-sub-SSI,ighernd

e SSIeto

nd B

glysnds.

ges

rop-stiff-g theon-

tion. Thes of

ted in

f re-ngi-

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rub-

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rds.’’

-,

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iers.’’

ew

rntally,

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i

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strong correlation between these variables is observed, avalue of correlation coefficient for linear regression is 0Physical interpretation of this fact is explained as follows. Insion of SSI decreases substructure stiffnessksub as pier and foundation stiffness constitute a serial spring system. With increseismic excitation, pier and foundation stiffness are reducedreduction in the overall sub-structure stiffness (ksub) is dominatedby reduction in the component having numerically smaller sness value. Smallkc /kh value represents slender piers andfoundation making the pier a ‘‘weak link.’’ Thus during an earquake, the pier is mostly responsible for reduction in overallstructure stiffness and contribution of foundation; and henceis small. On the other hand, stocky piers are represented by hkc /kh value in which foundation also becomes a ‘‘weak link’’ aconsequently the SSI effect increases. This explains why theffect is pronounced at Matsunohama Bridge ‘‘B’’ and Onnbridge despite the fact that ground conditions at Bridges A aare similar and at Onneto bridge it is even more firm.

It is thus concluded that contribution of SSI is more stronrelated to the ratiokc /kh than just Gs or Vs in these bridgebecause this parameter (kc /kh) takes into account the type aconfiguration of pier and foundation as well as soil propertie

Conclusions

1. Substantial reduction in stiffness~up to 45%! of RC piers isobserved for moderate levels of drift~0.12%!. This reductionin stiffness influences the SSI contribution in the bridincluded in this study.

2. SSI cannot be properly characterized by dynamic soil perties alone in pile-supported bridges and foundationness shall be included in the parameter characterizinsoil’s contribution, as stiffness of bridge foundations is csiderably higher than the pier stiffness.

3. It is proposed that the ratio of pier and horizontal foundastiffness be used to characterize SSI effects in bridgesresults presented herein are in line with the conclusionthe theoretical study of Ciampoli and Pinto~1995!. Morefield data is needed to substantiate the argument presenthis paper before its adoption in design codes.

Fig. 10. Soil-structure interaction index as function ofkc /kh


References

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Chaudhary, M. T. A.~1999!. ‘‘Evaluation of seismic performance of baisolated bridges based on earthquake records.’’ PhD disserDept. of Civil Engineering, Univ. of Tokyo, Japan.

Chaudhary, M. T. A., Abe, M., and Fujino, Y.~2001!. ‘‘Performanceevaluation of base-isolated Yama-age bridge with high dampingber bearings using recorded seismic data.’’Eng. Struct.,23~8!, 902–910.

Chaudhary, M. T. A., Abe, M., and Fujino, Y.~2002!. ‘‘Role of structuradetails in altering the expected seismic response of base-isbridges.’’Mech. Syst. Signal Process.,16~2–3!, 413–428.

Chaudhary, M. T. A., Abe, M., Fujino, Y., and Yoshida, J.~2000!. ‘‘Sys-tem identification of two base-isolated bridges using seismic recoJ. Struct. Eng.,126~10!, 1187–1195.

Ciampoli, M., and Pinto, P. E.~1995!. ‘‘Effects of soil-structure interaction on inelastic seismic response of bridge piers.’’J. Struct. Eng.121~5!, 806–814.

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Gazetas, G.~1991!. ‘‘Foundation vibrations.’’Foundation engineerinhandbook, Y. Fang, ed., Van Nostrand Reinhold Co., New York.

Giuseppe, D. C., Mauro, D., and Domenico, L.~2000!. ‘‘Influence ofsoil-structure interaction on the seismic response of bridge pProc., 12th World Conf. on Earthquake Engineering, New ZealandNational Society for Earthquake Engineering, Auckland, NZealand. Paper No. 438.

Idriss, I. M., and Sun, J. I.~1992!. ‘‘SHAKE91: A computer program foconducting equivalent linear seismic response analyses of horizolayered soil deposits.’’User’s guide, Univ. of California, Davis, Calif.1–13.

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Lee, G. C., Kitane, Y., and Buckle, I. G.~2001!. ‘‘Literature review of theobserved performance of seismically isolated bridges.’’ResearchProgress Accomplishments 2000-2001, Multidisciplinary Center foEarthquake Engineering Research, Buffalo, New York, 51–62.

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Prakash, S., Kumar, S., and Sreeram, K.~1996!. ‘‘Pile-soil-pile interac-tion effects under earthquake loadings.’’Proc., 11th World Conf. oEarthquake Engineering, Acapulco, Mexico, Sociedad MexicanaIngenieria Sismica~Mexican Society for Earthquake Engineerin!,Elsevier Science, New York, Paper No. 359.

Priestley, M. J., Calvi, G. M., and Seible, S.~1996!. Seismic design anretrofit of bridges, Wiley, New York.

Saadeghvaziri, M. A., Yazdani-Motlagh, A. R., and Rashidi, S.~2000!.‘‘Effects of soil-structure interaction on longitudinal seismic respoof MSSS bridges.’’Soil Dyn. Earthquake Eng.,20~1–4!, 231–242.

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Influence of Pier Stiffness Degradation on Soil-Structure Interaction in Base-Isolated Bridges

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