Correlation of Earthquake Ground Motion andthe Response of Seismically Isolated Bridges

Mario Rinke ∗

Abstract—The seismic response of bridges seismi-cally isolated by lead-rubber bearings (LRB) to earth-quake excitations of different magnitudes is presentedin this thesis. The force-deformation behavior of LRBis considered as bilinear. The specific purpose of thestudy is to assess the effect of seismic isolation on thepeak response of bridges subjected to different baseaccelerations ranging from 0.05g to 0.5g in the hori-zontal direction transversal to the bridge axis. Thusa certain level of efficiency can be shown in respectof the particular bearing modification. Furthermore,the effect of superstructure stiffness (i.e. pier stiff-ness, pier layout) on the isolator efficiency is inves-tigated in depth. The seismic response in the finiteelement model of the continuous span isolated bridgesis obtained by solving the governing equations of mo-tion in the incremental form using an iterative step-by-step method. To study the effectiveness of LRB,the seismic response of isolated bridges is also com-pared with the response of corresponding nonisolatedbridges (i.e. bridges without isolation devices). Theimportant parameters included are the flexibility ofthe substructure and the ground acceleration. Theresults show that specific design of the isolation de-vice has a significant effect on the seismic responseof the isolated bridges. The efficiency of LRB in thebridges subjected to low seismic activity is consider-ably smaller due to the lead mostly remaining in theelastic range. The LRB can in this case thereforenot contribute hysteretic damping which is, however,the great benefit of LRB from the design point ofview. Stiffer structures tend to improve the isolatorefficiency and show better performance in case of lowdamping.

Keywords: seismic isolation, lead-rubber bearing, iso-

lator efficiency

1 Introduction

The control of structures to improve their performanceduring earthquakes was first proposed more than a cen-tury ago. But it has only been in the last 30 years thatstructures have been successfully designed and built us-ing earthquake protective systems. Today these systemsrange from simple passive devices to fully active sys-

∗Design engineer at Whitbybird Ltd., London, UK. Researchpresented in this paper has been carried out at the Bauhaus Uni-versity Weimar, Germany. Contact: me@mariorinke.de

tems. Major developments in the theory, hardware, de-sign, specification, and installation of these systems havepermitted significant applications to buildings, bridges,and industrial plants. Applications are now found in al-most all of the seismically active countries of the world,but principally in Italy, Japan, New Zealand, and theUnited States. There are, however, limitations to the useof passive systems, which deserve further study and re-search. They include the uncertainty of response in thenear field of an active fault, the non-optimal behavior ofpassive systems for both small and large earthquakes, anda lack of certainty about the ultimate limit states in un-expectedly large events. This study shall provide deeperunderstanding of the behavior of passive control devicesfor seismic excitations of different magnitude.There have been several analytical studies in the pastto demonstrate the effectiveness of seismic isolation forearthquake resistant design of bridges. Li (1989) devel-oped a procedure for optimal design of bridge isolationsystems with hysteretic dampers. He concluded that hys-teretic damper act most effectively when mounted on astiff supporting structure. Their effectiveness decreaseswith increasing flexibility of the supporting structure.Moreover is concluded that the larger the value of maxi-mum allowed isolator displacements is used the more ef-fective is the isolation system.Iemura et. al. (1998) demonstrated that when seismicisolation systems are installed, a reasonable inelastic de-sign method is required. A design procedure for isolatedbridges is proposed using the relation between seismicisolation systems and piers with respect to their energydissipation. Also parametric studies have been carriedout to investigate the optimum characteristics of seismi-cally isolated structures. The parameters mostly consid-ered include time period of the superstructure and timeperiod, damping, and yield characteristics of the isolator,and the ratio of predominant frequency of excitation tothe frequency of the isolator.Ghobarah (1988) studied the seismic response of singleand two-span highway bridges with LRB modeled as bi-linear spring. The influence of pa-rameters like the iso-lators stiffness, pier stiffness and pier eccentricity on theeffectiveness of seismic isolation was investigated. Gho-barah and Ali (1988) studied the effect of deck stiffnesson seismic responses.Reinhorn et. al. (1998) examined the effects of variation

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of the ratio of isolator and pier yield char-acteristics onthe response of isolated bridges. It has been recognizedthat, due to low redundancy and domination of the deckmode of vibration, isolated bridges are extremely sensi-tive to the characteristics of the ground motion.Kawashima and Shoji (1998) presented an analysis on theinteraction with emphasis on the yield force level of theisolator device. It was found that the post-yield stiffnessand the yield force level of the device are important topredict the nonlinear response of the pier.Koh et. al. (2000) developed a method to evaluate thecost effectiveness of seismic isolation for bridges in lowand moderate seismic regions in order to calculate theminimum life-cycle costs of seismically isolated bridgesunder specific acceleration levels. The results show thatseismic isolation is more cost effective in low and moder-ate seismic regions than in high seismic regions.

2 Method of calculation

Since the inelastic behavior of the bearings is of interestthere is a need to consider the appropriate bearing re-action to seismic load at all times of the earthquake du-ration. For the purpose of an inelastic dynamic analysisthe time history method is chosen. It provides a realis-tic measure of response because the inelastic model ac-counts for the redistribution of internal actions due to thenonlinear force displacement behavior of the components[2]. Nonlinear damping is considered as well as nonlin-ear stiffness and load deformation behavior of members.For nonlinear dynamic analysis a step-by-step integra-tion procedure is the most powerful method. The mostimportant assumption is that acceleration varies linearlywhile the properties of the system such as damping andstiffness remain constant during the time interval. In theprocedure a nonlinear system is approximated as a se-ries of linear systems and the response is calculated for aseries of small intervals of time ∆t and equilibrium is es-tablished at the beginning and end of each interval. Theaccuracy of the method highly depends on the length ofthe time increment t. It should be small enough to con-sider the change of loading p(t), nonlinear damping andstiffness properties, and the natural period of vibration.The characteristics of an SDOF system are its participat-ing forces, namely the spring and damping forces, forcesacting on mass of the system, and arbitrary applied load-ing. The force equilibrium can be shown as:

fi(t) + fd(t) + fs(t) = p(t) (1)

where fi(t) is the force acting on the mass, fs(t) is thespring force and fd(t) is the damping force. The incre-mental equations of motion for time t can be shown as:

m∆u(t) + c(t)∆u(t) + k(t)∆u(t) = ∆p(t) (2)

Current damping fd(t), elastic forces fs(t) are then com-puted using the initial velocity u(t), displacement valuesu(t), nonlinear properties of the system, damping c(t),and stiffness k(t) for that interval. At the beginning ofeach time increment new structure properties are calcu-lated based on the current deformed state. The completeresponse is then calculated by using the displacement andvelocity values computed at the end of each time step asthe initial conditions for the next time interval and re-peating until the desired time.In general terms, such formulations are described by thefollowing:

[K KR

KT”R KRR

] {UUR

}=

{FFR

}(3)

The subscript R represents the reaction forces. The tophalf of equation (3) is used to solve for {U}:

{U} = −[K]−1[KR]{UR}+ [K]−1{F} (4)

The reaction forces {FR} are computed from the bottomhalf of equation (3) as

{FR} = [KR]T”{U}+ {KRR}{UR} (5)

Equation (5) must be in equilibrium with equation (4).

3 Model development

3.1 Model configurations

To systematically analyze the effect of both regular andirregular longitudinal section geometry (i.e. symmetryand asymmetry) as well as the influence of the substruc-ture stiffness and to compare those results with noniso-lated bridges six different bridge models have been devel-oped. All bridges are simple six-span continuous deckbridges with reinforced concrete piers and prestressedconcrete box girders. The isolation concept is realized byusing isola-tion devices on the top of the pier caps. Allbridges are fixed at the pier bottoms and all movementsare restrained at the abutments. The types of bridgesare:

1. Regular Bridge. Symmetrical longitudinal sectiongeometry, harmonically varying pier lengths like theV-shape as it can be seen in figure 1 (Type 1)

2. Regular Bridge with double pier stiffness. Basicallysame properties like type 1, but all piers have doublemoment of inertia for both longitudinal and trans-verse direction (Type 2)

3. Regular Bridge non-isolated. Basically same prop-erties like type 1, but there are no isolation devicesbetween the pier cap and the bridge deck. Theseconnections are all fixed (Type 3)

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Deck Pier Mod Pier

Area (m2) 6.88 4.16 4.16Mom. of Inertia x/z (m4) 87.24 7.39 14.78Mom. of Inertia y (m4) 5.26 0.67 1.34Max. dimension (m) 14x2.3 4x2.2 4.9x2.5Mass density (kg/m3) 2500 2500 2500

Table 1: Geometrical and Physical Properties of Struc-tural Members

Figure 1: Longitudinal section of regular and irregularbridge.

4. Irregular Bridge. Asymmetrical longitudinal sec-tiongeometry, unproportionally varying pier lengths as itcan be seen in figure 1 (Type 4)

5. Irregular Bridge with double pier stiffness. Basicallysame properties like type 4, but all piers have doublemoment of inertia for both longitudinal and trans-verse direction. (Type 5)

6. Irregular Bridge non-isolated. Basically same prop-erties like type 4, but there are no isolation devicesbetween the pier cap and the bridge deck. Theseconnections are all fixed (Type 6).

The substructure of all bridges consists of rigid abutmentsand hollow reinforced concrete piers. The superstructurecomprises the reinforced concrete box girder and all in-stallations above. The main properties chosen for thestructural members are listed in tabular 1.

3.2 Force-Deformation Behavior of Bear-ings

For the present study, the lead rubber bearing consistingof alternating layers of steel shims and rubber are con-sidered as the isolation devices.The LRB is very stiff in the vertical direction and flexiblein the horizontal direction (due to the presence of steelshims in rubber). The horizontal flexibility and dampingcharacteristics of the bearing provide the desired isola-tion effects in the system (Skinner et al. 1980; Tyler andRobinson 1984; Constantinou and Tadjbakhsh 1985).For the numerical analysis the vertical stiffness of thebearings is regarded as infinitely high, i.e. there is norelative vertical deformation between the pier cap andthe deck. For the representation of the horizontal bear-ing stiffnesses a bilinear material law is chosen for each

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

Deformation (m)

Force (MN)

Lead Core Yealding

Lead Core Yealding

K1=6.5e6 N/m

K2=2e6 N/m

Figure 2: Defined material law (excl. viscous damping)

system standing for a discrete separation of the pre- andpost-yield state. The damping ratio for rubber bearingsis usually in the range of 5 to 8% and is assumed to be 7%in the analysis. The damping ratio of the global structurefor an undamped system is typically set to 5%. For thisstudy 1.5% global damping is used, because unlike typi-cal undamped structures isolated structures are designedto remain in the elastic range and it is assumed that theywill dissipate less energy within the structure during theearthquake. The lead yield force of the LRB is chosen bya set ratio yield force/deck weight of around 0.1 to be 0.5MN. This yield force level might be considered as higherthan normally used but it was chosen to ensure an elasticresponse for at least most members at lower earthquakeforces. Figure 2 shows the defined material law for bothbearing types used in the numerical simulation.

3.3 Finite Element Model

For the analysis of the six bridge types under several dy-namic loads, a simple finite element model was developedto represent all desired features. The software of choicewas ANSYS Release 10.0. For both piers and the deck,3D beam elements were used. Each node has in total 6degrees of freedom, one translation in each direction andone rotation around every axis.The bilinear isolation systems are represented by a spe-cial element that is a combination of a spring-slider anddamper in parallel. The initial stiffness is the sum of K1and K2 when both springs are still active. Once a cer-tain force in spring one is reached, no higher force can betaken and sliding occurs caused by any additional force.For higher forces to take than the limit force of springone, the remaining stiffness is hence only the stiffness ofspring two. These spring elements do not have masses

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and in their initial state they do not have a length. Bothnodes the one representing the pier cap and the one stand-ing for the deck are coincident and linked by these ele-ments. 31 Elements and 32 Nodes were used in total witha numerical extent of 143 degrees of freedom (includingthe restrains at the abutments and the pier bases). Thecalculation includes geometrical nonlinearity effects butno physical nonlinearities except the bilinear lead rubberbearings.

3.4 Ground Accelerations

Four different magnitudes of ground accelerations areconsidered to analyze the correlation of earth-quakeground motion and the response of the bridges, namely0.5g, 0.2g, 0.1g and 0.05g. These ground motions are arti-ficially generated time-history data based on accelerationspectra from Eurocode 8. With respect to the commonlyhigher natural period of isolated structures, accelerationspectra basing on ground type C were chosen. Groundtype C shifts the acceleration spectrum to higher timeperiods, which are actually closer to the natural periodof isolated structures and thus may increase the seismicresponse considerably. For each earthquake magnitudethree different earthquake excitations were generated toensure a certain maximum of the three curves with ran-dom peaks, respectively. Although all three generatedexcitations per magnitude base on the same spectrum,peaks occur with a difference of up to 40%. Figure 4shows one generated excitation of a respective magnitude.In order to simplify the load scenario and specify the ex-tent of load combina-tions, the acceleration is limited tothe horizontal direction transversal to the bridge axis.

4 Results

In the following diagrams the maximum of the three re-sponse values of the respective criteria is plotted versusthe ground acceleration. The abscissa always representsthe level of peak ground acceleration (PGA).

4.1 Modal Analysis

To obtain general information on the performance of thesix bridges, a modal analysis was carried out. Since themethod does not consider nonlinear stiffnesses, the post-yield stiffness is used in the LRB material definition inthat specific analysis. The first 10 eigenfrequencies of allbridge types are presented in figure 3.It can be observed that there is a clear shift in terms offrequency between isolated and nonisolated bridge types.The first eigenfrequency of the nonisolated regular bridgeis 2.05Hz, while the natural frequency of the isolatedbridge is, at 0.41Hz, only a fifth, which proves the de-sired effect of massive stiffness reduction. Table 2 givesan overview of the first five natural frequencies for allbridges.

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8 9 10

Eigenfrequency Number

Freq

uenc

y (1

/s)

Regular

Regular Double Pier Stiffness

Regular Nonisolated

Irregular

Irregular Double Pier Stiffness

Irregular Nonisolated

Figure 3: Distribution of eigenfrequencies

Freq No Type1 Type2 Type3 Type4 Type5 Type61 0.41 0.42 2.05 0.42 0.43 2.152 0.44 0.44 2.11 0.44 0.45 2.263 0.55 0.53 2.26 0.53 0.53 2.604 0.78 0.76 2.49 0.77 0.77 3.035 1.27 1.39 3.03 1.46 1.47 3.04

Table 2: First five natural frequencies (Hz) of all bridgetypes

4.2 Response Accelerations

Figure 4 shows the response acceleration of the applied,artificially generated earthquake ground motion for boththe isolated and nonisolated regular bridge at 0.5g groundmotion during the entire earthquake. It can be observedhow different both reactions are, namely larger ampli-tudes and higher frequencies for the nonisolated struc-ture.The peak response accelerations of both systems areshown in figure 5. While for the LRB isolated regularbridge the deck above the long pier is most acceleratedand the short and mid pier behave similarly, in the caseof irregular pier layout the second short pier gives thelargest response and the deck acceleration above the firstshort pier and the long pier is in the same range. For allbridge types, the deck above the abutments is the pointwith the maximum acceleration.Figure 5 also shows the response acceleration of the twononisolated bridge types for comparison. Due to the ab-sence of any nonlinear material, the response here is solelylinear. A disproportional increase of the response by thepier height can be observed for the regular structure.While the response acceleration increases from 0.7g to1.0g by the doubling of the pier height from 10 to 20m, apeak response of 2.2g is measured for the 40m tall pier,

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Figure 4: Deck Response Acceleration above mid pierduring earthquake (regular bridge; 0.5g ground motion)

which means a further doubling of the pier height. Thiscorrelation of response acceleration and pier height is alsofound for the irregular bridge where both first and secondshort pier respond equally. The measured acceleration ofthe long pier, however, is much lower than the long pieracceleration of the regular bridge. Comparing the peakresponses of the nonisolated and isolated bridges it canbe stated that the response acceleration is re-duced sig-nificantly by using isolation devices.

4.3 Isolator Participation in Deflection

From the performance of the isolators during the range ofground motions, another conclusion can be made regard-ing the isolator efficiency. Consequently derived from thedeflection results, the ratio of isolator and total deflectionshall be a significant representation for the effect of theapplied seismic isolation. These obtained relations canbe observed in figure 6. The isolators deflection partici-pation indicates the efficiency of a particular isolator forthe given pier configuration. A common design princi-ple for seismic isolation devices would be the adjustmentof each single isolator to obtain a similar performance interms of isolator-pier deflection ratio. However, the indi-vidual isolation behavior and thus the determination ofdiverse material laws is not regarded in this study. Thediagrams rather demonstrate the significant low partici-pation of the long pier isolator in all bridges. The isola-tor participation is almost not changing over the rangeof ground motion intensity. For lowest earthquake ac-celerations, the LRB participation is at least 62% of thetotal deflection while for higher ground motions around90% of the deflections can be contributed. The shorterthe piers and the stiffer the substructure the higher is theparticipation of the isolator in the deflection. While theisolators on the mid and short pier always range mostlyfar above 80% for all bridges, the long pier isolators par-ticipation increases to 90% (irregular with doubled pierstiffness).

5 Conclusion

The consideration of pier stiffness and pier layout re-vealed only a small influence on the resulting response.Higher substructure stiffness (i.e. double pier stiffness, ir-regular shape) leads to higher isolator efficiency through

reduction of pier deflections. The increase of pier stiff-ness, however, also causes higher bending moments atthe pier base and higher pier base shear forces. The ir-regular pier layout basically leads to a load concentrationat a single column and is therefore even more suitable forthe base-isolation concept.The response curves reveal an explicit bilinear charac-ter, which is determined by the influence of hystereticdamping and bearing stiffness reduction after lead yield-ing. There is no noteworthy reduction of response duringthe pre-yield state of the lead. Since there is hystereticdamping in post-yield state of the lead in the isolationsystem, the response is reduced significantly and the iso-lator is even more efficient (i.e. reduction is higher) forlarger magnitudes of ground motion. Apart from thesegeneral characteristics, the extent of most response val-ues is heavily dependent on the yield force level that isdefined by lead modification (i.e. geometry). The resultsshow correlation of response curves for full ground motionscale and the material law definition, because a charac-teristic change occurs mostly at the respective yield forcelevel.

References

[1] Kawashima, K. : Seismic isolation of bridges inJapan. In: 5th World Congress on Joint, Bearingsand Seismic Systems for Concrete Structures, Rome,Italy (2001)

[2] Kiureghian, A. E. ; Keshishian, P. ; Hakobian,A. : Multiple support response spectrum analysisof bridges including the site-response effect and theMSRS Code. In: Report No. UCB/EERC-97/02,University of California, Berkeley (1997)

[3] Kunde, M. C.; Jangid, R. S.: Seismic behavior ofisolated bridges: A state-of-the-art review. In: Elec-tronic Journal of Structural Engineering 3 (2003),P.140170

[4] Priestley, M. J. N. ; Calvi, G. M. ; Seible, F. : Seis-mic de-sign and retrofit of bridges. John Wiley &Sons, Inc., 1996

[5] Wilson, E. L. ; der Kiureghian, A. ; Bayom, E. P.:A replacement for SSRS method in seismic analysis.In: Journal of Earthquake Engineering and Struc-tural Dynamics 9 (1981), S. 187

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ISBN:978-988-98671-2-6 WCE 2007

(FIX)

(FIX)

Figure 5: Response acceleration LRB isolated deck

Regular Structure

0

20

40

60

80

100

0 0.2 0.4 0.6PGA (g)

Isol

ator

/ To

tal D

efle

ctio

n (%

)

Long Pier Iso/Total

Mid Pier Iso/Total

Short Pier Iso/Total

Double Pier Stiffness

0 0.2 0.4 0.6

Irregular Structure

0

20

40

60

80

100

0 0.2 0.4 0.6PGA (g)

Isol

ator

/ To

tal D

efle

ctio

n (%

)

Long Pier Iso/Total

1st Short Pier Iso/Total

2nd Short Pier Iso/Total

Double Pier Stiffness

0 0.2 0.4 0.6

Figure 6: Isolator participation on total deflection for all isolated bridges

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