A comparative study on aseismic performances of base isolation...

Engineering Structures 24 (2002) 1001–1013www.elsevier.com/locate/engstruct

A comparative study on aseismic performances of base isolationsystems for multi-span continuous bridge

Kyu-Sik Park, Hyung-Jo Jung, In-Won Lee∗

Structural Dynamics & Vibration Control Lab, Department of Civil Engineering, Korea Advanced Institute of Science and Technology, 373-1Guseong-dong, Yuseong-gu, Daejeon 305-701, South Korea

Received 9 October 2000; received in revised form 21 January 2002; accepted 4 February 2002

Abstract

Various base isolation systems (BISs) such as the pure-friction, laminated rubber bearing, lead rubber bearing, resilient-frictionbase isolator and electricite´ de France systems, which have been used or are considered to have considerable potential for wideapplications, are systematically compared and discussed for aseismic performances of multi-span continuous bridge in this study.Sensitivity analyses of the bridge employed the devices are carried out to choose the appropriate design parameters of variousdevices. It is possible to recommend the appropriate ranges of the natural period and the friction coefficient of the various BISs.Therefore, the recommended ranges of the design parameters are presented in this study. The design parameters such as the firstnatural period of the isolated bridge and the friction coefficient of the bearing are determined by the reciprocal relationship betweenthe peak deck displacement and the peak overturning moment of the bridge in the recommended ranges, and then the relativeeffectiveness of the bearings is described for the selected design parameters under the different ground motions. The peak responsesof the bridge with the friction-type bearing are less sensitive to substantial variations in the frequency range and the intensity ofthe ground excitation than those with the rubber-type bearing due to characteristics of the friction element within the range of thisstudy. 2002 Elsevier Science Ltd. All rights reserved.

Keywords:Base isolation system; Bridge structure; Aseismic performance; Sensitivity analysis; Design parameter; Comparative study

1. Introduction

Many aseismic construction designs and technologieshave been developed over the years in attempt to miti-gate the effects of earthquakes on buildings, bridges andpotentially vulnerable contents. The design method usingbase isolation systems (BISs) is a relatively recent, andevolving technology of this kind. The seismic isolationdiffers fundamentally from the conventional seismicdesign approaches in the method by which the periodlengthening (detuning) and hysteretic energy-dissipatingmechanisms are provided, as well as in the philosophyof how the earthquake attack is withstood. In the conven-tional approaches, it is accepted that considerable earth-quake forces and energy will be transmitted to the struc-ture from the ground. In the seismic isolation, however,

∗ Corresponding author. Tel.:+82-42-869-3618; fax:+82-42-864-3658.

E-mail addresses: [email protected] (K.-S. Park);[email protected] (H.-J. Jung); [email protected] (I.-W. Lee).

0141-0296/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.PII: S0141-0296 (02)00020-2

the fundamental aim is to substantially reduce the trans-mission of the earthquake forces and energy into thestructure. Therefore, the seismic isolation is an innov-ative aseismic design approach aimed at protecting struc-tures against damage from the earthquake by limiting theearthquake attack rather than resisting it.

The seismic isolation consists essentially of the instal-lation of mechanisms, which decouple the structureand/or its contents from potentially damaging earthquakeinduced ground or support motions. This decoupling isachieved by increasing the flexibility of the system,together with providing appropriate damping. Althoughit is a relatively recent technology, the seismic isolationhas been well evaluated and reviewed [7–9,22]; has beenthe subject of international workshops [12–14]; isincluded in the programs of international, regional andnational conferences on earthquake engineering [15–18];and has been proposed for specialized applications [21].In these many researches, it is widely accepted that theseismic isolation is very effective to mitigate the influ-ence of earthquakes on structures. However, there are

1002 K.-S. Park et al. / Engineering Structures 24 (2002) 1001–1013

few comparative studies on aseismic performances ofvarious BISs for the critical design parameters. Further-more, most of previous studies are focused on buildings[3,9–11]. On the other hand, there are few studies onbridges in spite that BISs are widely used for them.

To evaluate aseismic performances of BISs and suit-able earthquake-resistance design of the bridge, the sen-sitivity analysis for variations in the design parametersof devices is required. Therefore, a comparative studyon aseismic performances of different BISs for multi-span continuous bridge is accomplished in this paper.Various BISs such as the pure-friction (P-F), laminatedrubber bearing (RB) , lead rubber bearing (LRB), resili-ent-friction base isolator (R-FBI) and electricite deFrance (EDF) systems are considered. Sensitivity analy-ses for variations in the first natural period of the isolatedbridge and the friction coefficient of the bearing are alsoperformed under the different ground motions. The rec-ommended ranges of the design parameters are presentedin this study. The two design parameters, the first naturalperiod of the isolated bridge and the friction coefficientof the bearing, are determined by the reciprocal relation-ship between the peak deck displacement and the peakoverturning moment of the bridge. The peak responsesof the bridge with BISs are obtained, and then the rela-tive effectiveness of different BISs is evaluated for theselected design parameters of devices.

2. Aseismic BISs

A variety of the seismic isolation and energy-dissi-pation devices has been developed over the years all overthe world. The components in BISs are speciallydesigned, distinct from the structural member, andinstalled at or near the base of the structure. In bridges,however, where the aim is to protect relatively low-masspiers and their foundations, they are more commonlybetween the top of the piers and the superstructure. Thebasic features of such devices consist of the horizontalflexibility and the energy dissipative capacity. The mostimportant feature of the seismic isolation is that itsincreased flexibility lengthens the natural period of thestructure. Because the period is increased beyond thatof the earthquake, the resonance and near-resonance areavoided and the seismic acceleration response isreduced. However, the increased period and consequentincreased flexibility also affects the horizontal seismicdisplacement of the structure. These excessive displace-ments are counteracted by the introduction of increaseddamping and/or energy-dissipation. Because of thesecharacteristics of BISs, they can attenuate the harmfulhorizontal acceleration transmitted to the superstructureand reduce the sectional force of the substructure. Theseismic isolation concept for the protection of structuresfrom earthquakes has been proposed in various forms at

numerous times this century. Here, various leading BISs,which have been used or are considered to have con-siderable potential for wide applications, are brieflydescribed. Various systems have used RBs (elastomericbearings) with and without lead plugs, damping beingprovided either by the use of high-loss rubber or neo-prene materials in the construction of bearings or byauxiliary viscous dampers. There have been a numberof applications of friction sliding systems, both with andwithout provision of the elastic centering action.

2.1. The P-F system [5,8,9]

The P-F or sliding-joint system is classified as thesimplest device because it uses only the stick-slip mech-anism. A schematic diagram of the P-F system is shownin Fig. 1(a). When there is a sliding in the friction plates,the P-F system limits a maximum acceleration trans-mitted from the substructure to a certain value accordingto the friction coefficient. However, there may be anexcessive deflection or a residual deformation in the fric-tion surface after the seismic event, because the P-F sys-tem has no recovering force. Furthermore when the P-Fsystem does not slide, it acts as a fixed one. In this case,the P-F system cannot provide a certain amount of pro-tection. Because of these reasons, the friction element isused with RBs instead using alone. Nevertheless, the P-F system may be used economically in the simple orsmall-scale structure.

Whenever the structure sticks to the P-F system, thenon-sliding condition

xb(t) � 0 (1)

holds as long as

|Mxg(t) � �Nn � 1

mnan| � mMg (2)

where xb(t) is the displacement of base raft relative tothe ground, M is total mass on the device, xg(t) is thehorizontal ground acceleration, mn, an are mass andacceleration of the nth degree of freedom, m is the Cou-lomb friction coefficient and g is the acceleration ofgravity, respectively. As soon as the stick conditiongiven by Eq. (2) fails, a sliding will occur and the equ-ation of motion is stated as

Mxg(t) � mMgsgn[xb(t)] � �Nn � 1

mnan � �Mxg(t) (3)

Here, sgn[xb(t)] indicates the sign according to the direc-tion of velocity of the device.

2.2. The RB system [2,6,8,9,20]

Another method of seismically isolating structures isby mounting them on RBs. These bearings are fully

1003K.-S. Park et al. / Engineering Structures 24 (2002) 1001–1013

Fig. 1. Schematic diagram of BISs.

developed as commercial products whose main appli-cation has been for bridges. More recently, their use hasbeen extended to the seismic isolation of buildings andother structures. The RB system consists of alternatinglayers of rubber and steel with the rubber being vulcan-ized to the steel plates for the horizontal flexibility andthe vertical stiffness. The dominant feature of this deviceis the parallel action of spring and dashpot as shownschematically in Fig. 1(b). Because the damping capacityof the RB system is relatively small, it mainly shifts thenatural period of the isolated structure to avoid the detri-mental earthquake energy.The equation of motion isstated as

Mxb(t) � Cbxb(t) � Kbxb(t) � �Nn � 1

mnan � (4)

�Mxg(t)

where Cb and Kb are damping and stiffness coefficientsof the RB system, respectively.

2.3. The LRB system [8,9,20]

The RB system may not be able to resist the requireddisplacements for the seismic isolation. A lead-pluginsert provides hysteretic energy-dissipation, therefore,the damping required for a successful seismic isolationsystem can be incorporated in a single compact compo-nent with the RB system. Thus, one device is able tosupport the structure vertically, to provide the horizontalflexibility together with the restoring force, and to pro-vide the required hysteretic damping.

To determine properties of the LRB system, the bilin-ear model of characteristic curve is used. The effectivestiffness coefficient, Keff, is obtained with reference to

shear force versus displacement hysteresis loop shownin Fig. 2. In general, the concept of this effective valueis a gross approximation, but it works surprisinglywell [20].

The equation of motion, which uses the effective andequivalent values, is stated as

Mxb(t) � Ceqxb(t) � Keffxb(t) � �Nn � 1

mnan � (5)

�Mxg(t)

Here, Ceq is the linearized equivalent damping coef-ficient given by Eq. (6) and xeq is the linearized equival-ent damping ratio given by Eq. (7), respectively.

Ceq � 2xeq�MKeff (6)

Fig. 2. Characteristic curve of the LRB system: bilinear model.


xeq � �E / (2πKeffD2D) (7)

where �E is the total dissipated energy that is area of thecharacteristic curve and DD is the design displacement,respectively. In this study, the peak deformation of theRB system is used as a design displacement of a LRBunit. When the bilinear isolator has a high degree of non-linearty, the seismic responses of higher modes are oftenmuch greater than the responses which occur with theabove equivalent linear modes.

2.4. The R-FBI system [8,9,11]

The R-FBI system makes use of the parallel action ofresiliency of rubber and the friction of Teflon coatedplates. Similar to the P-F system, it does not slide belowthe frictional resistance. Unlike the P-F system, however,it has an additional resistance to an increase of deflectionand a recovering force by rubber after sliding.

Initially, when the bearing starts from rest or when-ever the friction plates are sticking to each other throughthe frictional force, the non-sliding condition given byEq. (1) holds as long as

|Mxg(t) � Kbxb(t) � �Nn � 1

mnan| � mMg (8)

As the ground acceleration is increased, the stick con-dition given by Eq. (8) fails and a sliding in the frictionplates will occur. Then, the equation of motion is givenby Eq. (9).

Mxb(t) � Cbxb(t) � mMgsgn[xb(t)] � Kbxb(t) (9)

� �Nn � 1

mnan � �Mxg(t)

2.5. The EDF system [8,9,19]

The EDF system consists of the elastomeric bearingand the friction plates in series. During a low-intensityearthquake, therefore, it behaves as a RB unit and returnsto its original position after the seismic event. Howeverwhen the frictional resistance is exceeded, a sliding willoccur and the EDF system may have a residual defor-mation in the friction surface during a high-intensityearthquake. Owing to the slip in the friction plates, theEDF system limits a maximum acceleration like a P-F unit.

Whenever the frictional resistance is not exceeded, theequations of motion are governed by

Mxb2(t) � Cbxb2(t) � Kbxb2(t) � �Nn � 1

mnan � (10a)

�Mxg(t)

xb1(t) � xb2(t),xb1(t) � xb2(t) (10b)

and hold as long as

|M[xg(t) � xb2(t)] � �Nn � 1

mnan| � mMg (11)

As soon as this condition fails, a sliding will occur andthe equations of motion are stated as

Cbxb1(t) � Kbxb1(t) � mMgsgn[xb2(t)�xb1(t)] (12a)

Mxb2(t) � mMgsgn[xb2(t)�xb1(t)] � �Nn � 1

mnan (12b)

� �Mxg(t)

In these equations, xb1(t) is the deflection experienced byNeoprene pad and xb2(t) is the displacement of the baseraft relative to the ground as shown in Fig. 1(e).

3. Sensitivity analysis

3.1. Analysis model

For the sensitivity analysis of various aseismic BISs,the Dong-Jin Bridge (Fig. 3, Table 1) is used. It is acontinuous bridge with 15 spans and has been con-structed in the western coast expressway in Korea. Thespan length of the bridge is 725 m and the width of thesuperstructure is 12.15 m. The longitudinal slope is0.03%. The schematic diagram of the Dong-Jin Bridgeis shown in Fig. 3. The superstructure and the substruc-ture are modeled by beam elements. Since, general pre-stressed concrete bridge has structural damping ratios of2–3%, Rayleigh damping with x � 2% is used in themodeling of the Dong-Jin Bridge.

The calculation of several design properties is themost important in the modeling of BISs. The horizontaland vertical translational stiffness of devices are calcu-lated by Eqs. (13) and (14) [4].

ktrans �GrAr

tr(13a)

kvert �ErAr

tr(13b)

kht � nktrans (14a)

kvt � nkvert (14b)

Here, ktrans, kvert are the horizontal and vertical trans-lational stiffness of each bearing, Gr, Er are the shearmodulus and Young’s modulus of rubber, Ar, tr are areaand rubber thickness of each bearing, and kht, kvt are totalhorizontal and vertical translational stiffness for n bear-ings, respectively. The rotational stiffness of bearingsabout the vertical axis is found by adding the individualbearing contribution when a unit rotation is applied to


Fig. 3. Schematic diagram of the Dong-Jin Bridge.

Table 1Pier length (H2) of the Dong-Jin Bridge

Pier No. P1 P2 P3 P4 P5 P6 P7

H2 (m) 0.94 1.09 1.21 1.33 1.46 1.57 1.98

Pier No. P8 P9 P10 P11 P12 P13 P14

H2 (m) 2.13 2.08 2.13 2.32 2.36 2.40 2.48

the entire group [4]. As shown in Fig. 4, it is assumedthat bearings are connected with a rigid link that trans-mits forces from the individual bearing to the pointwhere the moment, which produces the unit rotation, isapplied. It is calculated that the horizontal force actingon each pad and the moment about the centerline pro-duced by the force at each bearing by Eq. (15)

Vi � ktransqdi (15a)

Mi � Vidi (15b)

where di is the distance from the center of the superstruc-ture to the ith bearing. The spring constant for rotationis calculated by summing the moments and dividingby rotation

Fig. 4. Rotation and deflection of the bearing pad.

kvr �

2�n

i � 1

Mi

q� 2ktrans �n

i � 1

d2i (16)

Rotation has been released about an axis parallel to thestrong direction of pier because the stiffness in thisdirection is considered negligible [4]. The damping coef-ficient of bearings is calculated by Eq. (17)

cht � 2x�mkht (17)

where x is the damping ratio of rubber. Generally, thedamping ratio of rubber is 10% and this value is usedin this study.

3.2. Sensitivity analysis

For the sensitivity analysis on variations in the designparameters of devices, a number of different earthquakeexcitations are used. Among several major earthquakeexcitations, El Centro (N00W component, 1940), SanFernando (S16E component, 1971) and Mexico City(N90W component, 1985) earthquakes are used as theground acceleration. These earthquake records have avariety of peak ground acceleration (PGA) and covervarious forms of the frequency range as shown in Figs.


Fig. 5. Time histories of the historical earthquakes.

5 and 6. The El Centro accelerogram is typical of thoseto be expected on the ground of moderate flexibility dur-ing a major earthquake. It must also be recognized thatoccasionally earthquakes give their strongest excitationat long periods. The likelihood of these types of motionsoccurring at a particular site can sometimes be foreseen,such as with deep deposits of soft soil which may ampl-ify low-frequency earthquake motions, the old lake bedzone of Mexico City being the best known example.

Fig. 6. Fourier spectrums of the historical earthquakes.

Mexico City earthquake has considerable energy at lowfrequencies of about 0.5 Hz. Therefore, this earthquakeis used to evaluate performances of BISs in the severeinput excitation condition.

The commercial finite element analysis program, auto-matic dynamic incremental nonlinear analysis (ADINA)[1], developed by K.J. Bathe is used for the numericalanalysis. The method of nonlinear time history analysisis used instead of the response spectrum analysis andthe relative effectiveness of different BISs according tovariations in the design parameters is studied.

The most important parameters that control perform-ances of aseismic devices are the natural period of theisolated structure and the friction coefficient of thedevice. Aseismic performances of bearings are influ-enced by the natural period and the friction coefficientaccording to the frequency range and PGA of the inputground motions. To obtain variations in the natural per-iod of the isolated bridge, the size of the bearing ischanged and it leads to variations in the spring constantsand damping coefficient of the bearing as shown Eqs.(13)–(17).

The natural period of the isolated structure should belong enough to avoid the frequency range on whichearthquake energy concentrates and is short enough toresist the ambient vibration such as traffic or windinduced one. The friction coefficient of the bearingshould be large enough to resist the ambient vibrationand small enough to have an additional aseismic effectby sliding in the friction plates of the device. Consider-ing these reasons and manufacturing conditions ofdevices, the first natural period of the isolated bridge ischanged from 1.0 to 6.0 s with interval 1.0 s and thefriction coefficient of the bearing is changed from 0.02to 0.30 with interval 0.04 in this sensitivity analysis.

The main seismic attack on most structures is the setof horizontal inertial forces acting on the structuralmasses, these forces being generated as a result of hori-zontal ground accelerations. For most structures, verticalseismic loads are relatively unimportant in comparisonwith horizontal seismic loads. Therefore, in this studythe structure is excited in the horizontal (longitudinal)direction. The responses of the bridge with aseismicdevices have similar trend at abutment and pier becausebearings installed at them have the same properties ingeneral. Therefore, the peak responses of the center pier(pier 7) in the longitudinal direction are calculated andcompared. The peak deck displacement and the peakoverturning moment are obtained to check the ser-viceability and the design sectional force.

3.2.1. Variations in the first natural period of theisolated bridge

One of the most important features of BISs is to shiftthe natural period of the isolated structure to longer onein order to avoid the dominant frequency range of the


earthquake ground excitations. Therefore, parameterssuch as spring constants of the bearing must be selectedvery carefully to achieve this goal. In this section, there-fore, the sensitivity of the peak responses to variationsin the first natural period of the bridge with aseismicbearings, T1, is analyzed. Variations of the peakresponses of the isolated bridge according to the firstnatural period are shown in Figs. 7–9.

Fig. 7 shows that the peak responses of bridge withthe rubber-type bearing, such as the RB and LRB sys-tems, have similar trend to the response spectrum of eachearthquake because of the linearity of the device. As awhole, the peak deck displacement is increased as thefirst natural period is increased whereas the peak over-turning moment is decreased because the horizontalflexibility of the bridge is increased. Most of the deckdisplacement is the deformation of the device, thereforethe deformation of pier is negligible as the first naturalperiod is increased. The peak overturning moment isdecreased a little when the first natural period is longerthan 4.0 s. The peak responses of the bridge subjected toMexico City earthquake are amplified in the first naturalperiod of about 2.0–3.0 s because earthquake energy isdominant in this range therefore the resonance isoccurred. For Mexico City earthquake, flexible mount-ings with moderate damping increase rather thandecrease the structural response. The provision of highdamping as part of the isolation system gives animportant defense against the unexpected occurrence ofsuch motions. This concept is presented well in Fig. 7(b),due to the additional energy dissipative capacity of acentral lead core the peak responses of the bridge with

Fig. 7. Variations of the peak responses with the first natural period:rubber-type bearing.

Fig. 8. Variations of the peak responses with the first natural period:R-FBI system.

Fig. 9. Variations of the peak responses with the first natural period:EDF system.


the LRB system are much reduced when compared witha RB unit.

For the R-FBI and EDF systems, the natural periodand the friction coefficient are the important design para-meters simultaneously. Fig. 8 shows the peak responsesof the bridge with the R-FBI system versus the first natu-ral period of the isolated bridge according to the frictioncoefficient of the device. It is observed that the peakresponses of the bridge are similar to the response spec-trum of each earthquake for the small value of frictioncoefficient. As the friction coefficient is increased, thepeak responses are not sensitive to variations in the firstnatural period due to characteristics of friction elements.In the friction-type bearing which uses the frictionelements in parallel i.e., the R-FBI system, insensi-tiveness to the natural period may be obvious becausethe natural period is relatively not an important designparameter. The maximum peak deck displacement ofthree earthquakes is more reduced when compared withthe rubber-type bearing due to the frictional resistanceof friction elements.

In Fig. 9, the peak responses of the bridge with theEDF system show similar trend to those with the rubber-type bearing as the friction coefficient is increased. Ifthere is no sliding in the friction plates, the responses ofthe bridge are the same as those with a RB unit. How-ever, the peak deck displacement is larger when com-pared with the rubber-type bearing due to the sliding ofthe friction plates.

3.2.2. Variations in the friction coefficient of BISFor the friction-type bearing, such as the P-F, R-FBI,

EDF systems, the friction coefficient is more importantdesign parameter than the natural period. In this section,therefore, the sensitivity of the peak responses to vari-ations in the friction coefficient of the bearing, m, is dis-cussed. Variations of the peak responses of the isolatedbridge according to the friction coefficient of the bearingare shown in Figs. 10–12.

It is observed that an increase of friction coefficientof the P-F system, generally, leads to a decrease of thepeak deck displacement whereas it leads to an increaseof the peak overturning moment because of influence ofthe superstructure. The most portion of displacement isthe sliding deformation of the P-F system and the defor-mation of pier is negligible. As the friction coefficientis increased, a sliding seldom occurs in the P-F system,therefore the deformation of pier is increased. The P-Fsystem subjected to El Centro earthquake slides less than1 cm for m�0.18 and sliding dose not occur for m�0.18 about Mexico City earthquake as shown in Fig. 10.The P-F system has an excessive deformation when thevalue of friction coefficient is small and a residual defor-mation because there is no recovering force as shownFigs. 10 and 17.

For the R-FBI and EDF systems, the sensitivity of the

Fig. 10. Variations of the peak responses with the friction coefficient:P-F system.

Fig. 11. Variations of the peak responses with the friction coefficient:R-FBI system.


Fig. 12. Variations of the peak responses with the friction coefficient:EDF system.

peak responses to variations in the friction coefficient ofthe bearing according to the first natural period of theisolated bridge is obtained. Fig. 11 shows the peakresponses of the bridge with the R-FBI system versusthe friction coefficient according to the first natural per-iod. The R-FBI system subjected to El Centro earthquakeslides less than 1 cm for m�0.22(T1 � 1.0 s) and m�0.18(T1�2.0 s) and these results are similar to those ofa P-F unit. However, the R-FBI system gives anadditional resistance to an increase of deflection by theparallel action of stiffness and damping. Thus, the peakdeck displacement is smaller than that with a P-F unitwhereas the peak overturning moment is similar. ForMexico City earthquake, the R-FBI system does notslide for m�0.18(T1 � 1.06.0 s). It is observed that thepeak responses of the bridge are similar to those with aP-F unit. However, the peak overturning moment isdecreased as the friction coefficient is increased forT1 � 2.0 s opposite to the rubber-type bearing. This iswhy an increase of friction coefficient for T1 � 2.0 sreduces the resonance of the isolated bridge and the R-FBI system still provides a certain amount of protection.

Fig. 12 shows the peak responses of the bridge withthe EDF system versus the friction coefficient accordingto the first natural period. The EDF system subjected toEl Centro earthquake does not slide for m � 0.30(T1 �1.0 s), m�0.14(T1 � 2.0 s), m�0.10(T1 � 3.0 s), m�

Fig. 17. Residual deformation of the P-F and EDF systems.

0.06(T1 � 4.0 and 5.0 s) and m�0.10(T1 � 6.0 s). ForMexico City earthquake, sliding does not occur form � 0.30(T1 � 3.0 s), m�0.10(T1 � 4.0 s) and m�0.06(T1 � 5.0 and 6.0 s). For San Fernando earthquake,sliding does not occur for m�0.22(T1 � 3.0 s), m�0.14(T1 � 4.0 and 5.0 s) and m�0.10(T1 � 6.0 s). Whenthere is no sliding in the upper plate of the EDF system,it behaves like the rubber-type bearing and the peakresponses of the bridge remain constant for variations inthe friction coefficient. For Mexico City earthquake,when the first natural period is 2.0 s, the peak responsesof the bridge are amplified like those with the rubber-type bearing.

Figs. 13 and 14 present the peak responses of thebridge with the R-FBI and EDF systems according tothe first natural period and the friction coefficient simul-taneously.

It is impossible to elect the optimal values of the natu-ral period and the friction coefficient for the variousBISs, because the optimal design parameters varydepending on the various design conditions such as soiltype, structure type and possible input ground motion. Itis possible, however, to recommend the appropriateranges of the natural period and the friction coefficient.Therefore, within the range of the above sensitivityanalyses of the design parameters, it is recommended


Fig. 13. Variations of the peak responses with the design parameters: R-FBI system (left column-peak deck displacement: cm, right column-peakoverturning moment: ×107Nm).

using the first natural period shorter than 4.0 s to avoidan excessive deck displacement with suitable over-turning moment. Furthermore, the use of adequate fric-tion element is effective in reducing deck displacement.It is recommended using the friction coefficient smallerthan 0.18. If the value of friction coefficient is large than0.18, there is little advantage of reducing deck displace-ment whereas overturning moment is monotonouslyincreased.

3.2.3. Comparative study for different earthquakeswith the selected design parameters

Practical BISs must trade off between the extent offorce isolation and acceptable relative displacementsacross the isolation system during the earthquakemotion. The design parameters determined by thereciprocal relationship between the peak deck displace-

ment and the peak overturning moment of the bridge isused for comparisons and analyses of aseismic perform-ances of various BISs with the fixed design parametersinstead of the conventionally recommended ones [9].San Fernando earthquake has a general feature in theresponse spectrum and it is possible to examine thecharacteristic of sliding of the friction-type bearingowing to relatively large intensity of the ground motion.The first natural period of the isolated bridge and thefriction coefficient of the device are determined by usingsensitivity analysis results of San Fernando earthquake.Importance of the deck displacement or the overturningmoment is different according to various design con-ditions such as soil type, structure type and possibleinput ground motion. Therefore, the design parametersof the device are determined by following procedure inthis paper.


Fig. 14. Variations of the peak responses with the design parameters: EDF system (left column-peak deck displacement: cm, right column-peakoverturning moment: ×106Nm).

First, it is calculated that the ratio of the peak deckdisplacement and the peak overturning moment to aver-age value according to the first natural period and thefriction coefficient, respectively. To consider the influ-ence of small values of results, the average value is usedinstead of a maximum one.

Dratio �D

Daverage(18a)

Mratio �M

Maverage

(18b)

The curves of aDratio and (1�a)Mratio are plotted in Fig.15, for example. The a is a factor that indicates the rela-tive importance of the peak deck displacement. The avaries from 0 to 1 and a � 0.5, which means sameimportance of the peak deck displacement and the peak

overturning moment, is used in this study. One can con-sider a different relative importance of the peak deckdisplacement and the peak overturning moment using thefactor a according to various design conditions as shownin Fig. 15. Finally, the crossing point of two curves isselected as the design first natural period of the isolatedbridge and/or the friction coefficient of the device. Asshown in Fig. 15, if a is increased from a1 to a2, thenthe selected first natural period is decreased from Tselect1

to Tselect2, whereas the selected friction coefficient isincreased from mselect1 to mselect2. Therefore, the peak deckdisplacement will be decreased with Tselect2 and/ormselect2. Table 2 shows the selected first natural periodand the friction coefficient determined by above pro-cedure.

The peak responses of the bridge with various BISs,which are designed by the selected parameters of Table


Fig. 15. Selection of values of the design parameters.

Table 2The selected values of the design parameters

BIS The first natural Friction coefficientperiod (s)

RB system 3.0 N/ALRB system 3.0 N/AP-F system N/A 0.14R-FBI system 3.0 0.14EDF system 4.0 0.10

2, are shown in Fig. 16. As shown in the figure, theperformance of BISs varies depending on the inputground motions. While the peak deck displacement withthe friction-type bearing is generally smaller than thatwith the rubber-type bearing, the peak overturningmoment is larger due to the friction element. The P-Fsystem has a residual deformation after the seismic eventas shown in Fig. 17, because it does not have therecovering force. The EDF system has a residual defor-mation due to the sliding in the friction plates for SanFernando earthquake like a P-F unit as shown in Fig. 17.

In Figs. 7–14, 16, the peak responses of the bridgewith the friction-type bearing are less sensitive to sub-stantial variations in the frequency range and intensityof earthquake excitation due to characteristics of thestick-slip mechanism compared to those with the rubber-type bearing.

4. Conclusions

Comprehensive sensitivity analyses of several leadingBISs such as the P-F, RB, LRB, R-FBI and EDF sys-

Fig. 16. Aseismic performances of various BISs for the selectedvalues of the design parameters.

tems, are presented. The bridge with BISs must tradeoff between the extent of force isolation and acceptablerelative displacements across the isolation system duringthe earthquake motion. The recommended ranges of thetwo design parameters such as the first natural period ofthe isolated bridge and the friction coefficient of thebearing are presented in this study. The two design para-meters are determined by reciprocal relationship betweenthe peak deck displacement and the peak overturningmoment. Comparisons and analyses on aseismic per-formances of different BISs for the selected design para-meters are presented. Based on these results, the follow-ing conclusions may be drawn.

The peak deck displacement is increased as the firstnatural period of the isolated bridge is increased and asthe friction coefficient of the device is decreased. Con-trary to the peak deck displacement, the peak overturningmoment is increased as the first natural period isdecreased and as the friction coefficient is increased.

Several design parameters of the bearing are influ-enced by various design conditions such as soil type,structure type and possible input ground motion. There-fore, it is important that adequate design parametersdetermined by the sensitivity analysis of the bridge withBISs are used in the design of the device instead of theconventionally recommended ones. It is shown withinthe range of these sensitivity analyses on variations inthe design parameters of the bearing and a comparativestudy on aseismic performances of various BISs with theselected design parameters that the peak responses of thebridge with the friction-type bearing are less sensitiveto substantial variations in the frequency range and the


intensity of earthquake excitation when compared tothose with the rubber-type bearing because of character-istics of friction elements.

Within the range of the parametric study of this paper,it is recommended using the first natural period shorterthan 4.0 s to avoid excessive deck displacement withsuitable overturning moment. Furthermore, the use ofadequate friction element is effective in reducing deckdisplacement and it is recommended using the frictioncoefficient smaller than 0.18. If the value of frictioncoefficient is larger than 0.18, there is little advantageof reducing deck displacement whereas overturningmoment is monotonously increased.

Acknowledgements

This research was supported by the National ResearchLaboratory (NRL) program for Aseismic Control ofStructures. The financial support is gratefully acknowl-edged.

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