experimental and analytical studies on the performance of hybrid isolation systems

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2002; 31:421–443 (DOI: 10.1002/eqe.117)

Experimental and analytical studies on the performanceof hybrid isolation systems

Shih-Po Chang1;‡, Nicos Makris2;∗;†, Andrew S. Whittaker3 andAndrew C. T. Thompson4;‡

1Arup; Los Angeles; California 90064; U.S.A.2University of California; Berkeley; 721 Davis Hall; Berkeley; CA 94720-1710; U.S.A.

3State University of New York at Bu)alo; 212 Ketter Hall; North Campus; Bu)alo; NY 14260-4300; U.S.A.4Arup, London; U.K.

SUMMARY

This paper presents experimental and analytical results on the seismic response of a rigid structuresupported on isolation systems that consist of either lead rubber or sliding bearings. Shake tabletests are conducted with various levels of isolation damping that is provided from the bearings andsupplemental viscous <uid dampers. The table motions originated from recorded strong ground motionsthat have been compressed to the extent that the mass of the model structure corresponds to the massof a typical freeway overcrossing. Experimental data are used to validate mechanical idealizations andnumerical procedures. The study concludes that supplemental damping is most e>ective in suppressingdisplacements of rigid structures with moderately long isolation periods (TI63 sec) without a>ectingbase shears. Friction damping is most e>ective in suppressing displacement ampli@cations triggered bylong duration pulses—in particular, pulses that have duration close to the isolation period. Copyright ?2001 John Wiley & Sons, Ltd.

1. INTRODUCTION

Ground motions generated from earthquakes di>er from one another in magnitude, sourcemechanism, direction from the rupture location, distance from the epicentre and local soilconditions. In view of this variability, several approaches have been adopted to enhancethe earthquake resistance of structures including sti>ening, strengthening, increasing dampingor lengthening the fundamental structural period. The latter two approaches constitute theconcept of seismic protection which during the last two decades has been accepted widely

∗ Correspondence to: Nicos Makris, Department of Civil and Environmental Engineering, University of California,Berkeley, 721 Davis Hall, Berkeley, California, 94720-1710, U.S.A.

† E-mail: [email protected]‡ Formerly graduate students at UC-Berkeley.

Contract=grant sponsor: California Department of Transportation; contract=grant number: RTA-59A169.

Published online 30 November 2001 Received 5 January 2001Copyright ? 2001 John Wiley & Sons, Ltd. Accepted 11 June 2001

422 S.-P. CHANG ET AL.

by the profession. A variety of isolation bearings and dampers have been installed in severalbuildings and bridges worldwide [1–4]. These implementations were materialized at the sametime when an increasing number of quality records from strong earthquakes demonstratedthat the dynamic characteristic of the ground near the fault have distinguishable long durationpulses which might be destructive to <exible structures.The destructive potential of near-source ground motions to <exible structures was identi@ed

from the mid-1960s [5; 6] and the need for building codes to account for these e>ects wasstressed by Anderson and Bertero [7]. Prior to the 1994 Northridge, California earthquake thecode section on base-isolated buildings required site-speci@c analysis for near-fault locationsand time-history analysis of the structural response.Following the 1994 Northridge, California and 1995 Kobe, Japan earthquakes the inter-

est of most engineers to near-source ground motions was revived and the discomfort ofsome was documented. Early post Northridge publications [8; 9] accentuated the issue oflarge base displacements partly because they used none or little isolation damping of vis-cous type only, or because response quantities were computed using arti@cially generatedground motions. More recent studies by Makris and Chang [10; 11] investigated analyticallythe eLciency of various dissipative mechanisms to protect seismic isolated structures fromrecorded near-source ground motions that contained coherent long-duration pulses in theirvelocity histories. In that study, it was found that the response of structures with relativelow isolation periods (i.e. TI62:0 sec) is substantially a>ected by the high-frequency con-tent that in many occasions overrides the long-duration pulse. Accordingly, it was concludedthat seismic isolation might be an attractive alternative even for motions that contain longvelocity and displacement pulses, provided that the appropriate energy dissipation mecha-nism is o>ered. Furthermore, it was observed that a relative low value of plastic (friction)damping (i.e. �=9 per cent) removes any resonant e>ect that a long-duration pulse has ona long-period isolation system. A recent study by Hall and Ryan [12] also con@rmed thebene@cial e>ects that seismic isolation has on a six-storey steel building. Their study in-dicated that even when the superstructure assumes 80 per cent of its design strength, theresponse quantities of the isolated building when subjected to a list of strong near-sourceground motions are within the accepted design levels. An increase of the isolation viscousdamping from �I = 10 per cent to �I = 20 per cent resulted in even more favourable responsequantities.While numerical studies indicated an appreciable sensitivity of the response of isolated

structures to the type and amount of isolation damping, the increasing need for depend-able estimates of the response of bridges motivated experimental studies to measure responsequantities and to validate mechanical idealizations and numerical schemes. A comprehensiveexperimental programme on the response of bridges equipped with modern seismic protec-tion technologies was conducted at the University of California at Berkeley [13]. Part of theaforementioned study was the investigation of the role of various damping mechanisms inassociation with the use of practical isolation bearings.This paper presents experimental and analytical @ndings on the seismic response of a

rigid block supported on two di>erent isolation systems and equipped with variouslevels of damping. The experimental data are used to validate mechanical idealizationsand numerical schemes; and to examine the dependability of the displacement expressiono>ered by the AASHTO Speci@cations when various levels of damping areconsidered.

Copyright ? 2001 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2002; 31:421–443

PERFORMANCE OF HYBRID ISOLATION SYSTEMS 423

‘ISOLATION PERIOD’ OF STRUCTURES SUPPORTED ON NON-LINEARISOLATION SYSTEMS

This paper concentrates on examining the eLciency of seismic isolation by producing basedisplacement and base shear (acceleration) spectra of a rigid block supported on a variety ofisolation systems. All response spectra, some of which are validated with few experimentaldata, are plotted as a function of the ‘isolation period’ of the structure, TI. Recognizing thatpractical isolation systems exhibit non-linear hysteretic behaviour, this section presents thetheoretical background with which one computes the isolation period, TI, which was usedto express our analytical and experimental @ndings. The expressions for the isolation period,TI, o>ered in this section are recommended in order to estimate the period needed in thedisplacement expressions o>ered by AASHTO [14] and UBC [15].While friction pendulum sliding bearings (FPS) consist of an isolation system with the

most distinct non-linearities, the resulting isolation period is rigorously de@ned as

TI = 2�√R=g (1)

where R is the radius of the curvature of the spherical disc bearings [2]. Considering thefriction pendulum slider as a bilinear system with very high pre-sliding sti>ness and a post-sliding sti>ness equal to K2, the isolation period computed as TI = 2�

√R=g=2�

√m=K2 is

directly related to the second sti>ness, K2, of the bilinear idealization. The response quantitiesof structures isolated on sliding bearings can be expressed as a function of TI given byEquation (1) for di>erent levels of the friction coeLcient, �, which prevails along the Te<on–steel interface.For elastomeric bearings, the situation is less lucid since their mechanical behaviour departs

from the linear idealization without exhibiting a single slope at all deformation levels. Severalresearchers have proposed non-linear hysteretic models to approximate the behaviour of eitherhigh damping rubber bearings (HDRB) or lead rubber bearings (LRB) [16–18]. Despite theoccasionally signi@cant non-linear behaviour, it has become a practice that the shear force,P(t), from the isolation system can be approximated with the standard two-parameter, strain-independent Kelvin model

P(t)=Kub(t) + CI(t)u̇b(t) (2)

where K and CI are, respectively the storage modulus and damping constant of the isolationsystem and ub(t) is the relative base displacement. In the case where the isolation system con-sists of elastomeric bearings only, then CI =Cb, where Cb is the damping constant originatingfrom the bearings. In the case where supplemental dampers are added, then CI =Cb + Cd,where Cd is the damping constant originating from the dampers.

Figure 1 plots a typical recorded force–displacement loop from the component testing of alead rubber bearing strained at approximately 100 per cent shear strain at a cyclic frequency!=2�f=6:28 rad=sec. Although the loops depart from the linear viscoelastic behaviour, themacroscopic storage sti>ness and damping constant are approximated with

K =

√(Pmax − Pmin

Smax −Smin

)2

− (!Cb)2 (3)



Figure 1. Recorded force displacement loop from component tests of a lead rubber bearing under76kN vertical load and 100 per cent shear strain. Forcing cyclic frequency !=2�f=6:28rad=sec.The dotted line shows the equivalent linear approximation by using the strain independent

properties shown in Figure 2.

Cb =4WD

!�(Smax −Smin)2(4)

where !=2�f is the frequency of cyclic testing and WD is the energy dissipated per cycle.The geometrical representation of the storage sti>ness K is the ratio of the force that resultsunder maximum displacement Smax over Smax. In the general case K �=Pmax=Smax.

Elastomeric bearings have nearly frequency-independent properties. Traditionally, the abilityof a bearing or any structural component to dissipate energy is expressed via the equivalentdamping coeLcient

�=!Cb

2K=

WD

4�WS(5)

a quantity that is independent of the mass of the superstructure. In Equation (5), WS is theelastic energy that is stored during a quarter cycle. Figure 2 plots the equivalent linear storagesti>ness and equivalent damping ratio extracted from a variety of cyclic component tests ontwo di>erent lead rubber bearings tested at the University of California, Berkeley [13]. On



Figure 2. Equivalent linear storage sti>ness and equivalent damping ratio extracted from a variety ofcyclic component tests on two di>erent lead rubber bearing. The heavy lines indicate the average value

of sti>ness and damping used to calibrate the isolation period and viscous damping ratio.

the same @gure, the heavy line shows the average values of K and � used to calculate theisolation period and viscous damping ratio of the isolated model. The length of the heavylines indicates the range of shear strains that the elastomeric bearings experienced during testspertinent to the study reported herein.Having established the values of the equivalent linear storage sti>ness, K , and the equivalent

damping ratio, �, the isolation period of a rigid mass supported on elastomeric bearings canbe de@ned as

TI =2�!I

= 2�√mK

(6)

Consider now that an isolated rigid block of mass, m, undergoes steady-state harmonicmotion with amplitude u0 and frequency !. In this case, the damping constant of the isolatedstructure is

CI = 2�Im!I =Cb =WD

�!u20(7)



where �I is the viscous damping ratio of the isolated structure. Equations (5) and (7) give

�I =!I

!� (8)

where !I =√K=m and ! is the frequency at which the superstructure oscillates. Equation (8)

relates the modal damping ratio of a structural system with @nite mass to the equivalentdamping coeLcient of an isolation system with virtually no mass. In many occasions duringearthquake shaking, the superstructure oscillates near its natural frequency (!≈!I) and be-cause of Equation (8), it has become a practice to assume �I ≈�. Under the equivalent linearidealization, the response quantities of the isolation structure can be expressed as a functionof TI given by Equation (6) for di>erent levels of the viscous damping ratio �I =CI=2m!I.In the case where lead rubber bearings are equipped with a substantial lead core that exhibitsa distinct yield force, Fy, at a distinct yield displacement, uy, the equivalent linear approxi-mation becomes less appropriate, yielding its place to a more appropriate bilinear model. Inthis case, the isolation period is de@ned as

TI = 2�√

mK2

(9)

where K2 is the second slope of the bilinear model (see Figure 1). Under these conditions,the response quantities of the isolated structure can be expressed as a function of TI given byEquation (9) for di>erent levels of plastic coeLcient, �=NFy=mg, where N is the number ofthe isolation bearings and mg is the weight of the superstructure. The de@nition o>ered byEquation (9) is preferred to other expressions that involve a secant sti>ness since it allowsfor a direct comparison between the isolation period resulting from sliding bearings and theisolation period resulting from lead rubber bearings. In the event that one computes theisolation period of a structure supported on lead rubber bearings by using both Equations (6)and (9), the value of TI resulting from Equation (9) will be slightly longer than the valueresulting from Equation (6). In addition to the plastic damping originating from the lead core,lead rubber bearings exhibit a small fraction of viscous damping (�b ≈ 1–2 per cent) from theelastomeric material. Sensitivity studies indicated that the e>ect of this damping mechanismis marginal, especially when larger periods are of interest [10].

CONFIGURATION OF EXPERIMENTAL MODEL

A comprehensive experimental programme on the response of seismically protected bridgeswas conducted at the University of California, Berkeley [13]. For the rigid bridge con@gu-ration, two models and several isolation bearings and viscous damping devices were tested.Figure 3 shows the simplest among the two bridge con@gurations tested—that is a rigid blockwith weight, mg=293 kN (65:87 kips) resting on four isolation bearings. This isolated blockmodel can be also equipped with <uid dampers (as shown in Figure 3). The entire system ismounted on the UC-Berkeley shaking table for testing.The study reported herein concentrates on the response of isolated structures supported on

hybrid isolation systems that consist of isolation bearings and supplemental dampers. The sup-plemental dampers used in this study are viscous <uid dampers with force proportional to the



Figure 3. Photograph of tested model on the earthquake simulator of theUniversity of California, Berkeley.

velocity. Two di>erent sizes of <uid dampers were used to achieve di>erent levels of supple-mental damping. The small damper shown on the left of Figure 3 has a stroke limitation of±4:0cm (±1:6in). This stroke limitation restricted the shear strains in the elastomeric bearingsbelow the 100 per cent level as is indicated in Figure 2. Experimental data and analyticalstudies on the response of the isolated structure where the elastomeric bearings experiencedlarge strains can be found in References [13; 18], while details on the instrumentation of themodel can be found in References [13; 19].

Scaling

During the earthquake simulation tests, the table motions had a compressed duration comparedto the original ground motions so that the time scale is consistent with the reduced scale ofthe model structure. In all experiments, accelerations and stresses were kept at full scale sothat 1 m=sec2 and 1 Pa in the real world remains the same in the laboratory. Two lengthscales, SL =6; 9, were adopted. Table I summarizes the scale transformations for selectedobservable quantities where acceleration and stresses are invariants.The relevance of the physical characteristics of the experimental model that we used in

this study can be illustrated by considering as an example the physical characteristics of the91=5 overcrossing currently under construction in Orange County, California [20]. Its deckhas an approximate weight of 5300 kips and each of its eight dampers (four dampers ateach end) has a stroke of ±8:0 in. With a length scale, SL =9, this bridge corresponds to alaboratory mass of 5300 kips=81=65:43 kips, which is approximately the weight of the model



Table I. Scale transformation of selected observable quantities.

Length [L] SL 6 9

Time [T ]√SL

√6 3

Velocity[L][T ]

√SL

√6 3

Acceleration[L][T ]2

1 1 1

Stress[M ]

[L][T ]21 1 1

Force[M ][L][T ]2

S2L 36 81

Mass [M ] S2L 36 81

used (mg=65:87 kips). Now this weight when is associated with a length scale SL =6, itcorresponds to a real-world weight of 65:87 kips× 36=2371 kips, which is approximately thesuperstructure weight of a typical four-lane freeway overcrossing.

CHARACTERIZATION OF SEISMIC PROTECTION DEVICES

Lead rubber bearings

The lead rubber bearings used in this study are equipped with a 30 mm (1:18 in) diame-ter lead core. Each bearing consists of 19, 3 mm (0:118 in)-thick, rubbers layers and 18,1:9 mm (0:075 in)-thick, steel shims with 168 mm (6:66 in) diameter. This con@guration re-sulted in a shape factor, S=25. Figure 4 (left) shows a schematic of the cross section andplan view of the lead rubber bearing. The equivalent linear properties shown in Figure 2 wereextracted from cyclic in-plane testing [21]. The yield force originating from the lead core canbe approximated with Fy = �y�d2=4, where �y ≈ 10MPa=1:5ksi is the yield stress of the lead.With d=0:03m, the calculated yield force from each bearing is Fy ≈ 7:0 kN and theoreticallythe resulting plastic coeLcient of the four lead rubber bearings is �=4Fy=mg≈ 9:7%, whileuy ≈ 0:2–0:3 cm depending on the strain level. Experimental data, however, indicate that afterthe @rst cycle, the level of yield force reduces to less than half of this value probably dueto degradation of the lead structure within the centre hole [21]. The equivalent linear proper-ties of the isolation system shown in Figure 2 yield an isolation period, TI ≈ 1:0 sec and theequivalent viscous damping ratio �I = 14 per cent.

Friction pendulum system

The friction pendulum sliding bearings used in this study have a radius of curvature R=76:2cm(30 in) and an inner diameter D=41:9 cm (16:5 in). Figure 4 (right) shows a schematic ofthe cross section and plan view of the friction pendulum sliding bearing. The coeLcient ofsliding friction reported by the manufacturer ranges from �=4 to 10 per cent depending onvelocity, contact pressure, bearing composition and sliding surface preparation. An average



Figure 4. Cross-section and plan view of a lead rubber bearing (left) anda friction pendulum bearing (right).

value of �=9 per cent was used in the analysis reported herein. The isolation period resultingfrom this bearing geometry is TI = 2�

√R=g≈ 1:75 sec.

Small viscous damper

The small damper used in this study consists of a main shock tube and a double endedpiston rod that pushes the viscous <uid through a number of stationary annular ducts. Thelarger the number of external ducts (4 maximum), the smaller the damping coeLcient of thedevice. The complex geometry of this device results from its ability to deliver controllableviscoplastic forces when used as an electrorheological damper [22]. In this study, the devicewas used in its passive con@guration as an ordinary <uid damper. Figure 5 (top) plots the forceamplitudes recorded during various cyclic tests at di>erent frequencies. The device exhibitsa linear viscous behaviour where the force is proportional to the piston velocity: Fd =Cdu̇b.The damping constant of the small damper with three bypasses is Cd = 24 kN sec=m andit becomes Cd = 35 kN sec=m with two bypasses. The supplemental viscous damping ratiodue to added dampers is �d =Cd=2m!I. In the case where the isolation system consists of



Figure 5. Recorded force amplitudes versus velocity amplitudes of small damper(top) and large damper (bottom).



Table II. Magnitude, distance and peak ground accelerations of the original earthquakemotions used in this study.

Original record Magnitude Distance PGA SAC(km) (g) name

1940 Imperial Valley Earthquake, El Centro 6.9 10.0 0.46 LA011994 Northridge Earthquake, Newhall 6.7 6.7 0.68 LA131994 Northridge Earthquake, Sylmar 6.7 6.4 0.57 LA171995 Kobe Earthquake, JMA 6.9 3.4 1.28 LA21

lead rubber bearings, !I = 2�=TI ≈ 6:28 rad=sec. For a superstructure mass, m=29:86 Mg, theresulting viscous damping ratio is �d = 6:5 per cent. In the case where the isolation systemconsists of sliding isolation bearing, !I = 2�=TI ≈ 3:6 rad=sec and �d = 11:2 per cent.

Large viscous damper

The large viscous damper used in this study is a double ended linear device with ±15:2 cm(±6 in) stroke. Figure 5 (bottom) plots the force amplitudes recorded during various cyclictests at di>erent frequencies together with the maximum forces recorded during constant ve-locity tests. Both series of tests indicate a linear viscous behaviour where the force is propor-tional to the velocity. The resulting damping constant of the large damper is approximatelyCd = 135 kN sec=m. In the case where the isolation system consists of lead rubber bearings,!I = 2�=TI ≈ 6:28 rad=sec and �d = 35 per cent. In the case where the isolation system consistsof sliding isolation bearings, !I = 2�=TI ≈ 3:6 rad=sec and �d = 60 per cent.

EARTHQUAKE SIMULATOR STUDIES

The table motions used in this study are modi@ed ground motions that were developed duringFEMA=SAC Joint Venture Steel project [23]. The motions used are the projections to a systemof axis that is at 45◦ from the fault-normal and fault-parallel direction. Table II summarizesthe magnitude, distance and peak ground acceleration of the original records that yielded thetable motions.The rotated SAC motions were compressed accordingly so that the base displacement of the

isolated block did not exceed the ±4:0 cm (±1:6 in) stroke capacity of the small damper thatwe used in our study. For a length scale SL; Table I indicates that the time is compressed by√SL. In some cases, the acceleration level of the scaled record was also reduced or ampli@ed.

All four motions selected contain either one or two distinct pulses with pulse periods that arein the vicinity of the isolation period of the test model.Figure 6 (left) shows the 100 per cent acceleration level of table motion LA13 (modi@ed

Newhall record from the 1994 Northridge earthquake) that has been scaled with a length scaleSL =6. Although the motion does not exhibit a single distinct pulse, we have combined two el-ementary pulses that can approximate some of the main kinematic characteristics of the record.The @rst pulse is a type-C1 pulse with period TC1

p = 0:38 sec (TC1p = 0:38×√

6=0:93 sec in full



Figure 6. Approximation of the 100 per cent LA13 motion (modi@ed 1994 Northridgeearthquake—Newhall record) with a succession of two trigonometric pulses (@rst column)

and response spectra for viscous and friction damping (remaining columns).

scale) and V C1p = 20:7 cm=sec. The second pulse is identi@ed as a type-B pulse with period

TBp =0:74 sec (TB

p =0:74×√6=1:81 sec in full scale) and V B

p =16:0 cm=sec. The de@nitionsof a type-A, type-B and type-C pulse are o>ered in the papers by Makris and Chang [11].The computed spectra shown in Figure 6 indicate that lengthening of the period reducesdrastically accelerations (base shears) at the expense of larger displacements. The computedspectra under various levels of viscous and friction damping have been generated with theformulation presented in Makris and Chang [11]. The second column of Figure 6 shows thecomputed spectra by assuming the equivalent linear properties of the lead rubber bearingsshown in Figure 2. The points shown with abscissa, TI = 1 sec; are data extracted fromrecorded time histories of the rigid structure supported on lead rubber bearings [19]. Theycorrelate favourably not only with the spectral values computed from the table motion, but



also with the spectral values obtained from the motion constructed with the two elementarypulses. The third column in Figure 6 shows the computed inelastic spectra by assuming that thelead rubber bearings deliver a 9 per cent plastic coeLcient and exhibit a yield displacement,uy = 0:4 cm. That is approximately 1=10 the value of the base displacement of the isolatedstructure under this input. The 9 per cent yield force is approximately the level of yield forcethat one computes by considering the shearing deformation of lead with �y ≈ 10MPa=1:5ksi.The value of the yield displacement, uy = 0:4 cm used, is beyond the 0.1–0:3 cm of yielddisplacement that one observes at the strain levels that occurred during shaking. Therefore, ananalysis with uy = 0:4 cm exaggerates the e>ects of pre-yielding elasticity which are found tobe marginal. The computed response shown in the third column indicates that a value of thecoeLcient of plastic dissipation as high as �=9 per cent entirely suppresses the displacementampli@cation due to the second pulse which is in disagreement with experimental measure-ments. Accordingly, we conclude that the level of the coeLcient of plastic dissipation is lessthan 9 per cent. Theoretical studies on the characterization of the behaviour of lead rubberbearings under unidirectional and bidirectional component testing [11; 18] indicated that theplastic coeLcient is an increasing function of strain; however, its value at �≈ 50 per centcan be as low as 4 per cent. The fourth column in Figure 6 shows the computed spectraby assuming that the superstructure was isolated with sliding bearing exhibiting a coeLcientof friction, �=9 per cent. Whereas in theory the pre-yielding sti>ness under dry friction isin@nite, when Te<on sliding bearings are used the pre-yielding sti>ness is large but @nite; andtheir behaviour can be realistically approximated with a bilinear model that exhibits a smallyield displacement, uy = 0:02 cm; [24]. The spectra shown on the right of Figure 6 are nearlyidentical to those shown in the third column indicating that a 20-fold reduction of the yielddisplacement has a marginal e>ect in the response.Figure 7 (left) plots the acceleration, velocity and displacement histories of the table motion

LA17 (modi@ed Sylmar record from the 1994 Northridge earthquake) that has been scaledwith a length scale SL =9 and subsequently its acceleration was reduced to 80 per cent.On the same graph, a type-C2 pulse with TC2

p = 0:82 sec and V C2p = 9:0 cm=sec is shown. Note

that the trigonometric pulse approximates some of the kinematic characteristics of the tabledisplacement and table velocity, however, its peak acceleration is less than 1=4 of the peaktable acceleration. The second column of Figure 7 shows the computed spectra by assumingthe equivalent linear properties of the lead rubber bearings shown in Figure 2. Again the pointsshown with abscissa, TI = 1 sec; are the data extracted from the recorded time histories of therigid structure supported on lead rubber bearings [19]. The simple type-C2 trigonometric pulsepredicts dependable estimations of the base displacement for all damping levels, however,velocities and accelerations are substantially underestimated for values of damping larger than�I = 14 per cent. It is interesting to note that for period TI¡1 sec; the acceleration spectracomputed with the table motion yield base shears that are signi@cantly larger than the baseshears computed with the trigonometric pulse. This is because the table motion, in addition tothe long duration pulse, contains high frequencies with sharp accelerations. The third columnof Figure 7 shows the computed spectra by assuming a 9 per cent plastic coeLcient and a yielddisplacement, uy = 0:4 cm. While acceleration levels are accurately predicted, displacementlevels are underestimated by a factor of approximately two. The fourth column in Figure 7shows the computed spectra by assuming that the superstructure was isolated with slidingbearings exhibiting a small yielding displacement, uy ≈ 0:02 cm and a coeLcient of friction,�=9 per cent. Under these mechanical properties, the spectra computed with the table motions



Figure 7. Approximation of the 80 per cent LA17 motion (modi@ed 1994 Northridgeearthquake—Sylmar record) with a succession of two trigonometric pulses (@rst column)


di>er drastically from the spectra computed with the trigonometric idealization shown in theleft column of Figure 7. The reason is the limited acceleration amplitude of the type-C2 pulse(aC2

g =g=0:07) marginally exceeds the coeLcient of friction, �=0:9; resulting in minimalmotion of the isolated mass. Consequently, when sliding isolation systems are of interestpulse idealizations of the earthquake excitation should be used with caution.Figure 8 (left) plots the acceleration, velocity and displacement histories of the table motion

LA21 (modi@ed JMA record from the 1995 Kobe earthquake) that was scaled with a lengthscale SL =9 and subsequently its acceleration was reduced to 50 per cent. On the same graph,a type-C1 pulse with TC1

p = 0:4 sec and V C1p = 20 cm=sec is shown. Note that in this case,

the trigonometric pulse, type-C1 approximates with @delity the main stock that is revealedin the displacement and velocity records and also captures most of the acceleration level.The second column of Figure 8 shows the computed spectra by assuming the equivalent



Figure 8. Approximation of the 50 per cent LA21 motion (modi@ed 1995 Kobe earthquake—JMArecord) with a succession of two trigonometric pulses (@rst column) and response spectra for

viscous and friction damping (remaining columns).

linear properties of the lead rubber bearings shown in Figure 2. The points shown withabscissa, TI = 1sec; are the data extracted from the recorded time histories of the rigid structuresupported on lead rubber bearings [19]. In addition, the spectral values computed from thesingle type-C1 trigonometric pulse are also dependable for most of the frequency range. Thethird and fourth columns in Figure 8 that present results from a non-linear analysis indicatedtrends opposite to those shown in Figure 7. Speci@cally, the displacement spectra computedwith the table motion are substantially smaller than the displacement computed with thetrigonometric idealization. This happens because the acceleration level of the trigonometricpulse is strong enough to initiate appreciable sliding and signi@cant o>set; yet the subsequentaccelerations of the table motion are responsible for generation of further relative motion ofthe isolated mass and enhance its partial recentring.



Figure 9. Approximation of the 70 per cent LA01 motion (modi@ed 1940 Imperial Valley Earthquake,El Centro record) with a succession of two trigonometric pulses (@rst column) and response spectra

for viscous and friction damping (remaining columns).

Figure 9 (left) plots the acceleration, velocity and displacement histories of the table motionLA01 (modi@ed El Centro record) that was scaled with a length scale SL =6 and subsequentlyits acceleration was reduced to 70 per cent. In the same graph, two elementary pulses thatcan approximate some of the kinematic characteristic of the table motion are shown. The @rstpulse is a type-B pulse with period TB

p =0:83 sec (TBp =0:83×√

6=2 sec in full scale) andV Bp =14 cm=sec (V B

p =34:3 cm=sec in full scale). The second pulse is identi@ed as a type-C1

pulse with period TC1p = 0:31sec (TC1

p = 0:31×√6=0:75sec in full scale) and V C1

p = 10cm=sec.The second column of Figure 9 shows the computed spectra by assuming the equivalent linearproperties of the lead rubber bearings shown in Figure 2. The points shown with abscissa,TI = 1sec are the data extracted from the recorded time histories of the rigid structure supportedon lead rubber bearings [19]. The third and fourth columns of Figure 9 show trends similarto those observed in Figure 7.



Table III. Damping coeLcient B.

�I ¡2% 5% 10% 20% 30% 40% 50%

B 0.8 1.0 1.2 1.5 1.7 1.9 2.0

Figure 10. Base displacements extracted from shake-table tests (points) and the corresponding values ofthe AASHTO formula after calibrating its acceleration coeLcient to match the recorded displacementwith isolation damping, �I = 20:5 per cent. The calibrated values of the A × Si coeLcient are: LA01

(A× Si =0:42), LA13 (A× Si =0:49), LA17 (A× Si =0:56) and LA21 (A× Si =0:52).

The recorded data shown in Figures 6–9 are also used to examine the validity of thedisplacement formula that is indicated by AASHTO [14].

d=250ASiTe>

B(in mm) (10)

in which A is the acceleration coeLcient given in Figures 3:2(a) and 3:2(b) of the AASHTOstandard speci@cations and Si is the site coeLcient for seismic isolation design given inTable 5-1 of the same document.The period Te> in this case is the isolation period TI and B is the damping coeLcient factor

that is applicable only to isolation systems that their dissipation resembles viscous dissipation.The damping coeLcient B is o>ered in Table 7.1-1 of Reference [14] and is repeated inTable III.For values of viscous damping ratio, �I; other than those o>ered in Table III, linear inter-

polation should be used. When �I¿30 per cent, a time-history analysis is recommended.Figure 10 shows the displacement values extracted from the shake table experiments after

being multiplied with their corresponding scaling factors, SL; to yield the full-scale dis-placements. The graph on the left shows response values for a full-scale isolation period,TI = 2:45 sec; whereas, the graph on the right shows response values for a full-scale isolation



Figure 11. Approximation of the 140 per cent LA13 motion (modi@ed 1994 Northridgeearthquake—Newhall record) with a succession of two trigonometric pulses (@rst column)


period, TI = 3:0 sec. The horizontal axis of each plot shown in Figure 10 indicates the peakrecorded table acceleration. Using Equation (10), we computed the value of the coeLcientA × Si that is needed to match the measured displacements that correspond to �I = 20 percent (B=1:5). Subsequently, we used these values of the coeLcient A × Si to compute theAASHTO predictions for �I = 14 per cent (B=1:32) and �I = 50 per cent (B=2:0). Figure10 indicates that the estimation of base displacements with the AASHTO formula is reason-able. When �I = 50 per cent (B=2:0), displacements are consistently overestimated with theAASHTO formula. However, the guide speci@cation recommends a time-history analysis.Figures 11–14 reveal several trends associated with frictional dissipation. The @rst two

columns of these @gures are the same as the @rst two columns shown in Figures 6–9; however,they are shown again for convenience. The third and fourth column of Figures 11–14 plot non-linear spectra by assuming friction dissipation with coeLcient �=6% and 9% in associationwith viscous damping �=11:2 and 60.6 per cent. These viscous damping values are the



Figure 12. Approximation of the 140 per cent LA17 motion (modi@ed 1994 Northridgeearthquake—Sylmar record) with a succession of two trigonometric pulses (@rst column)


corresponding values that result from the small and large viscous damper. The points shownwith abscissa, TI = 1:75sec are data extracted from recorded time histories of the rigid structuresupported on lead rubber bearings [19]. They correlate favourably with the spectral valuesfrom the table motions. In some case the arti@cial motions constructed with trigonometricpulse yield acceptable predictions; whereas in other cases they do not. The displacementspectra shown in the last two columns indicate that friction damping is more eLcient thanviscous damping in suppressing the displacement ampli@cation that happens at longer isolationperiods due to a longer duration pulse. Concentrating on the fourth column of Figures 11–14,it is observed that beyond TI = 1sec; all displacement, velocity and acceleration spectra assumea nearly <at shape indicating that there is no need for extremely large isolation periods inorder to enjoy the bene@ts of seismic isolation. Therefore, in prototype design, and isolationbetween TI = 1×√

6=2:4 and 1×√9=3 sec is equally e>ective as isolation periods between

TI = 1:75×√6=4:3 and 1:75×√

9=5:25 sec.



Figure 13. Approximation of the 140 per cent LA21 motion (modi@ed 1995 Kobe earthquake—JMArecord) with a succession of two trigonometric pulses (@rst column) and response spectra for viscous

and friction damping (remaining columns).

This is an important @nding since lower isolation periods require a small radius of curva-ture that reduces the possibility for permanent displacements and limits technical diLcultiesassociated with the manufacturing of large diameter friction pendulum bearings.

CONCLUSIONS AND RECOMMENDATIONS

In this paper, experimental and analytical results on the seismic response of isolated systemsare presented. The study concentrates on identifying response trends associated with di>erentenergy dissipation mechanisms.

• Supplemental viscous damping alone is bene@cial since under all four motions an increaseof the viscous damping ratio from 14 to 50 per cent reduced base displacements by half or



Figure 14. Approximation of the 90 per cent LA01 motion (modi@ed 1940 Imperial ValleyEarthquake, El Centro record) with a succession of two trigonometric pulses (@rst column)


even more without appreciably increasing base shears (accelerations). It should be noted,however, that even with a viscous damping ratio, �I = 50 per cent, the deck displacementof an isolated bridge might exceed 25 cm (10 in).

• Friction damping is more eLcient than viscous damping in suppressing the displacementampli@cation that happens at longer-isolation periods due to a longer-duration pulse.

• When sliding bearings with long-isolation periods are used (say prototype isolation period,TI = 3sec), the addition of viscous damping has marginal e>ect not only on the accelerationresponse but also on the displacement response. Similarly, at large isolation periods, thereduction of the response by increasing the coeLcient of friction from 6 to 9 per cent ismarginal. In addition, it is observed that for prototype isolation periods that exceed 3 secall displacement, velocity and acceleration spectra assume a nearly <at shape indicatingthat there is no need for extremely large-isolation periods to enjoy the bene@ts of seismicisolation.



• When lead rubber bearings are used, the level of the plastic coeLcient of dissipation thatone computes directly from the yield stress of the lead assuming a direct shear deformationof the lead core might be unrealistically large. This high value results in substantial under-estimations of spectral displacements, especially at larger-isolation periods. Nevertheless,further research is needed to examine to what extent this observation depends on the smallscale of the bearing used in this study.

ACKNOWLEDGEMENTS

Financial support for part of this study was provided by the California Department of Transportation(Caltrans) under Grant RTA-59A169. In addition to this study, the aforementioned grant supported avariety of investigations associated with the seismic protection of bridges. These were conducted byMr Eric L. Anderson, Professor Gregory L. Fenves, Mr Wei-Hsi Huang, Professor Stephen A. Mahin,Mr Troy A. Morgan and Mr Gilberto Mosqueda and others; and their contributions are reported else-where. The valuable input of Dr E. Delis is also acknowledged. The @ndings, conclusions and recom-mendations are those of the authors and do not necessarily represent those of Caltrans.

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experimental and analytical studies on the performance of hybrid isolation systems

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