Passive hybrid systems for earthquake protection of cable

Passive hybrid systems for earthquake protection of cable-stayed bridge

B.B. Soneji, R.S. Jangid∗

Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai - 400 076, India

Abstract

The performance of passive hybrid control systems for the earthquake protection of a cable-stayed bridge under real earthquake ground motionis presented. A simplified lumped mass finite-element model of the Quincy Bay-view Bridge at Illinois is used for the investigation. A viscousfluid damper (VFD) is used as a passive supplemental energy dissipation device in association with elastomeric and sliding isolation systems toform a passive hybrid control system. The effects of non-linear viscous damping of the VFD on the seismic response of an isolated cable-stayedbridge are examined by taking different values of velocity exponent of the damper. Further, the influence of a variation in viscous damping onthe response of the isolated bridge is also investigated. The seismic response of the bridge with passive hybrid systems is compared with thecorresponding response of the bridge with only isolation systems, as well as with the uncontrolled bridge. The results of the investigation showthat the addition of supplemental damping in the form of a viscous fluid damper significantly reduces the earthquake response of an isolatedcable-stayed bridge. The non-linear viscous damping is found to be more effective in controlling the peak isolator displacement of the isolatedbridge while simultaneously limiting the base shear in towers.

Keywords: Cable-stayed bridge; Isolation; Viscous fluid damper; Earthquake response; Passive hybrid systems

1. Introduction

Because of the flexibility of cable-stayed bridge, the deckexperiences a large displacement response when subjectedto dynamic loads such as an earthquake or wind. As aresult, the connections between the deck and the tower ofthe bridge become quite vulnerable under dynamic loads.A rigid connection between the tower and the deck willreduce the deck displacement but increases the base shear ofthe towers. The simplest way to overcome this situation isthrough the use of a base isolation technique by providingisolation bearings and supporting the deck at all locations. Inthe past, a very limited amount of research work had beendone on investigating the effectiveness of seismic isolation forcable-stayed bridges [1–3]. These studies had shown that theisolation in cable-stayed bridges could significantly reduce theseismically induced forces in the tower of the bridge. However,the isolation increases the displacement response of the deck,creating an uncomfortable condition for the traffic. Moreover,

because of the large displacement response of the deck, it alsobecomes difficult to provide the required seismic gap at thedeck edges along the longitudinal direction. In such a situation,supplemental damping, in addition to the isolation, can helpgreatly to reduce displacement of the deck and the tower baseshear of the cable-stayed bridge.

There are wide varieties of passive energy dissipationdevices that can be used to control the dynamic responseof the structures, such as a metallic yield damper, frictiondamper, viscous fluid damper and viscoelastic damper etc. [4].However, the most rapid growth in the application ofsupplemental damping systems to buildings and bridges hasoccurred for viscous fluid dampers, primarily because ofthe high-energy dissipation capacity of the dampers. Therehad been several analytical and experimental investigationsconducted on a seismically isolated building and bridgemodels with fluid viscous dampers [5–10]. The results ofthe investigations demonstrated a simultaneous reductionof the bearing displacement and force transmitted to thesuperstructure. Iemura and Pradono [11] investigated theeffectiveness of passive linear type dampers and semi-activevariable dampers along with elastomeric bearings for the

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58

(a) The bridge model.

(b) Finite element model of towers.

Fig. 1. Details of the semi-harp type cable-stayed bridge model.

earthquake response control of a cable-stayed bridge. Inaddition, the performance of semi-active and active hybridstrategies for the earthquake protection of building andbridge structures, including cable-stayed bridges, are alsoinvestigated [12–18]. Although there are several investigationsconducted into the application of passive hybrid systems forbuildings and multi-span bridges, studies of flexible structureslike cable-stayed bridges are meager.

In the present study, the performance of passive hybridcontrol systems for the earthquake protection of a cable-stayedbridge under real earthquake ground motion is investigated. Thepassive hybrid system is a combination of isolation bearings(elastomeric as well as sliding systems) and viscous fluiddampers (VFD) used as a supplemental energy dissipationdevice. The specific objectives of the present study aresummarized as: (i) to investigate the performance of differentpassive hybrid systems for the earthquake response control ofa cable-stayed bridge; (ii) to investigate the influence of non-linear viscous damping of the VFD on the seismic responseof isolated bridge; and (iii) to arrive at the values of designparameters of the VFD that provide optimal response controlof the isolated cable-stayed bridge.

2. The cable-stayed bridge model

The bridge model used in this study is that of theQuincy Bay-view Bridge crossing the Mississippi River atQuincy, Illinois. The bridge consists of two H-shaped concretetowers, double plane semi-harp type cables and a compositeconcrete–steel girder bridge deck. A detailed description of the

bridge can be found in Wilson and Gravelle [19]. A simplifiedlumped mass finite-element model of the bridge consideredfor seismic investigations is shown in Fig. 1(a). The bridge issymmetrical about the vertical centroidal axes. The bridge hasa central span of 274 m flanked by two side spans of 134 meach. The height of the towers above and below the deck is53.7 m and 17 m, respectively. For the purpose of analysis, thedeck is divided into 29 members, and each tower is dividedinto 11 members. Depending on the geometry, the towers aredivided into three parts. The finite-element model of the towersis shown separately in Fig. 1(b). There are 28 cable members:14 supporting the main span and 7 supporting each side span.The cable members are spaced at 2.75 m c/c at the upper partof the towers and are equally spaced at deck level on the sidespans as well as the main spans. The relevant properties of thebridge deck (for equivalent steel area) and towers are given inTable 1, while those of the cables are given in Table 2. The leftand right anchor supports are kept as roller supports. The bridgedeck is assumed to be a continuous beam, rigidly connected tothe towers such that the deck moment will not be transferred tothe tower through the deck–tower connection. The towers areconsidered to be fixed at the base. For implementing seismicisolation, the isolators are placed at each of the four supportsof the deck, replacing the conventional bearings. The VFDsare placed along the longitudinal and transverse directions atthese locations (refer to Fig. 2), so as to provide a link betweenthe deck of the bridge and the abutments and towers. Thisconfiguration is adopted to achieve effective energy dissipationat all deck-support junctions.

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Table 1Properties of the deck and towers of cable-stayed bridge

Part of thestructure

Cross-sectionalarea (m2)

Moment of inertia aboutz–z axis (m4)

Moment of inertia abouty–y axis (m4)

Moment of inertia aboutx–x axis (m4)

Young’smodulus (MPa)

Mass density(kg/m3)

Deck 0.827 0.341 19.760 0.027 205 000 7850Tower part 1 14.120 28.050 531.580 15.390 30 787 2400Tower part 2 14.120 28.050 670.970 15.390 30 787 2400Tower part 3 17.540 30.620 1239.400 19.760 30 787 2400Tower part 4 35.390 32.750 1422.420 27.640 30 787 2400

Table 2Properties for the stay cables of the cable-stayed bridge

Cable no. Cross-sectional area(m2)

Young’s modulus(MPa)

Cable weight(N/m)

1 0.0180 205 000 1765.802 0.0135 205 000 1324.353 0.0107 205 000 1049.674 0.0070 205 000 686.70

Fig. 2. Positions of the VFD and isolators.

A cable-stayed bridge, in general, behaves non-linearlywhen loaded. The degree of non-linearity will vary with thestiffness of the various members and the amount of pre-tensionin cables under self-load. However, the research on an ambientvibration survey of the cable-stayed bridge carried out byWilson and Liu [20] demonstrated that a completely linearmodel was sufficient to get reasonably accurate results for theQuincy Bay-view Bridge. As a result, no attempts are made tointroduce non-linearity into the model to study the effectivenessof passive control systems.

The deck and the tower members are modeled as space frameelements. The cables are modeled as linear elastic space trusselements. The stiffness characteristics of an inclined cable canexhibit a non-linear behavior caused by cable sag. This non-linear behavior can be taken into account by linearization of thecable stiffness using an equivalent modulus of elasticity that isless than the true material modulus [21,22]. For the analysisof the bridge under consideration, Wilson and Grevelle [19]found the value of equivalent modulus essentially equal to thetrue modulus of elasticity. Hence, the non-linearity due to cablesag is neglected and cables are treated as having a completelylinear force–deformation relationship, described by the truematerial modulus of elasticity. Moreover, cables are assumedto be capable of bearing tension as well as compression,assuming that the pre-tension in the cables will take care of thecompression induced in the dynamic analysis.

3. Seismic isolation systems

3.1. High-damping rubber bearing

The dominant features of high-damping rubber bearing(HDRB) systems are the parallel action of a linear spring andviscous damping. The restoring bearing forces Fx and Fy ,developed in two orthogonal horizontal directions (referred toas the x- and y-directions), are given by the relation{

FxFy

}=

[cb 00 cb

] {xbyb

}+

[kb 00 kb

] {xbyb

}(1)

where xb and yb are the displacements of the bearing in thex- and y-directions, respectively; xb and yb are the isolatorvelocities along the x- and y- directions, respectively; andcb and kb represent the damping and stiffness of the HDRBsystem, respectively. The stiffness and damping of the HDRBsystem are selected to provide the specific values of the twoparameters, namely the isolation time-period (Tb) and thedamping ratio (ξb), defined as

Tb = 2π

√md

6kb(2)

ξb =6cb

2mdωb(3)

where md is the mass of the deck and ωb = 2π/Tb is theisolation frequency of the bearing system. The 10% dampingin HDRB is selected for the present study.

3.2. Lead rubber bearing

Lead rubber bearings (LRB) are similar to the HDRB,but a lead plug at the center of the bearing is inserted toincrease the initial rigidity and damping capacity. For thepresent study, the model proposed by Park et al. [23] is used tocharacterize hysteretic behavior of the LRB. The experimentalverification of the model is carried out by Nagarjaiah et al. [24].The restoring forces, Fx and Fy , of the LRB system in twohorizontal directions are given by the relation{

FxFy

}=

[cb 00 cb

] {xbyb

}+ α

[kb 00 kb

] {xbyb

}+ (1 − α)F y

{ZxZ y

}(4)

where Zx and Z y are the hysteretic displacement componentsof restoring forces in the x- and y-directions, respectively; kb

60

is the initial bearing stiffness; α is an index that represents theratio of post- to pre-yield stiffness; and F y is the yield force ofthe bearing.

The hysteretic displacement components Zx and Z ysatisfy the following coupled non-linear first-order differentialequation expressed as

q

{ZxZ y

}=

[A − βsgn(xb)|Zx |Zx − τ Z2

x −βsgn(yb)|Z y |Zx − τ Zx Z y

−βsgn(xb)|Zx |Z y − τ Zx Z y A − βsgn(yb)|Z y |Z y − τ Z2y

]

×

{xbyb

}(5)

where q is the yield displacement; and β, τ and A arethe dimensionless parameters selected such that the predictedresponse from the model closely matches the experimentalresults.

The LRB system is characterized by the isolation period(Tb), damping ratio (ξb) (defined in Eq. (3)), and normalizedyield strength F0. The parameters Tb and F0 can be defined as

Tb = 2π

√md

6αkb(6)

F0 =6F y

Wd(7)

where αkb is the post-yield stiffness of the bearing; Wd = md gis the weight of the bridge deck; and F y is the yield strength ofthe bearing.

The viscous damping provided by the natural rubber of theLRB is low; hence, for the present study, the damping ratio ofthe LRB, ξb, is taken as 5%. The normalized yield strength, F0,and the yield displacement, q , of the bearing are taken to beequal to 0.05, and 0.025 m, respectively. The other parametersof the LRB system, which do not affect the peak response much,are kept constant (i.e. β = τ = 0.5, A = 1).

3.3. Friction pendulum system

The friction pendulum system (FPS) develops a lateral forceequal to the combination of the mobilized frictional forceand the restoring force that develops because of rising ofthe structure along the spherical surface. The resisting forcesprovided by the FPS can be given by{

FxFy

}=

[kb 00 kb

] {xbyb

}+

{FsxFsy

}(8)

where kb is the bearing stiffness provided by virtue of theinward gravity action at the concave surface; and Fsx and Fsyare the frictional forces in the x- and y-directions, respectively.The system is characterized by bearing isolation period (Tb),which depends on the radius of curvature of concave surfaceand the friction coefficient (µ). In the present investigation, thevalue of the friction coefficient is taken as 0.05.

The conventional model of FPS requires a track of slidingand non-sliding phases, resulting in a different set of equationsin different phases of motion. This is quite cumbersome and

complicated; as a result, the frictional forces of the FPS arerepresented by a continuous hysteretic model [25,26]. Thefrictional forces mobilized in the FPS are given by

Fsx = Fs Zx (9)

Fsy = Fs Z y (10)

where Fs is the limiting frictional force; and Zx and Z y are thedimensionless hysteretic displacement components satisfyingEq. (5). The parameter q of Eq. (5) is taken to be equal to10−4 m, keeping other parameters the same as those of theLRB.

4. Viscous fluid dampers

A VFD dissipates energy by pushing fluid through anorifice, producing a damping pressure, which creates a force.The damping constant and the velocity exponent are the twoproperties that govern the selection of VFD. In a viscousdamping model, the output of the damper (i.e. damper force)is given by [6]

Fd = sgn(v)cd |vλ| (11)

where cd = 2ξdmdωb is the damping coefficient of the damper;ξd represents the damping ratio of the damper; v is the velocityacross the damper; and λ is the velocity exponent. The value ofλ ranges between 0.3 and 2. A design with λ equal to 1 resultsin a linear viscous damper. In the present study, the influenceof linear and non-linear viscous damping on the response ofseismically isolated cable-stayed bridge is investigated.

5. Governing equations of motion

The equations of motion of the passively controlled cable-stayed bridge system subjected to earthquake ground motion isexpressed in the following matrix form [27]:

[M]{u} + [C]{u} + [K ]{u} + [D]{F} = −[M][r ]{ug} (12)

{u} = {x1, y1, z1, . . . , xN , yN , zN }T (13)

{ug} = {xg, yg, 0}T (14)

where [M], [K ] and [C] are the mass, stiffness and dampingmatrices, respectively, of the bridge structure of order 3N ×

3N (where N is the number of degrees of freedom in aparticular direction); {u}, {u}, and {u} represent structuralacceleration, structural velocity and structural displacementvectors, respectively; [D] is the location matrix for the restoringforces of isolators; {F} is the vector containing the restoringforces of isolators; [r ] is the influence coefficient matrix oforder 3N ×3; {ug} is the earthquake ground acceleration vector;xg and yg represent the earthquake ground accelerations in thelongitudinal and transverse directions, respectively; and xi , yiand zi are the displacements of the i th node of the bridge in thelongitudinal, transverse and vertical directions, respectively.

The lumped mass matrix has a diagonal form. Each elementof the matrix is the sum of half of the total mass of theadjacent segments contributing to a particular node. The

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Table 3Peak ground acceleration of various earthquake ground motions

Earthquake Recording station Applied in longitudinal direction of thebridge

Applied in transverse directionof the bridge

Component PGA (g) Component PGA (g)

Imperial Valley, 1940 El Centro N00E 0.348 N90E 0.214Kobe, 1995 Japan Meteorological Agency N00E 0.834 N90E 0.629Loma Prieta, 1989 Los Gatos Presentation Center N00E 0.570 N90E 0.607Northridge, 1994 Sylmar Converter Station N00E 0.843 N90E 0.600

element stiffness matrix for the cable members is taken to bethe space truss element stiffness matrix, whereas the spaceframe element stiffness matrix is adopted for the deck and towermembers. The global stiffness matrix of the whole structureis constructed by following the standard assembly processand static condensation is carried out to eliminate rotationaldegrees-of-freedom at each node. The assumption of classicaldamping may not be appropriate, as the level of damping in thecable-stayed bridge and the isolation systems are significantlydifferent. The non-classical damping matrix for the system isconstructed by first evaluating the classical damping matrixfor the bridge alone (without the control systems) from theassumed modal damping in each mode of vibration using modeshapes and frequencies of the bridge [27]

[C] = ([M][Φ][M−1g ])[Cg]([M−1

g ][ΦT][M]) (15)

where [Mg] is the diagonal matrix of generalized modalmasses; [Cg] is the diagonal matrix of generalized modaldamping; and [Φ] is the matrix containing mode shape vectors.The damping matrix for the complete system is constructedby directly assembling the damping matrices for the threesubsystems — structure, isolators and VFDs. The portion ofthese matrices associated with the common degrees-of-freedomincludes contributions from the subsystems.

The solution of the equations of motion of the controlledbridge system cannot be carried out using the classicalmodal superposition technique as (i) the system is non-classically damped because of the difference in the dampingin the control system compared to the damping in thestructure, and (ii) the force–deformation behaviour of LRB,FPS and VFD is non-linear. Therefore, the equations ofmotion are integrated numerically using Newmark’s step-by-step technique, considering the linear variation in accelerationover the time interval 1t . The time interval has to be kept verysmall to achieve stability of Newmark’s method. For the presentstudy, the time interval selected is 0.02 × 10−2 s.

6. Numerical study

The seismic response of the cable-stayed bridge isinvestigated under four different real earthquake groundmotions, namely (i) Imperial Valley, 1940, (ii) Kobe, 1995,(iii) Loma Prieta, 1989, and (iv) Northridge, 1994 earthquakes.The first one has been used widely by researchers in the past,and the last three represent strong earthquake motion records.Although in the present study the four seismic accelerationrecords have been taken from the database, in professional

applications, deeper attention should be devoted to the sample(and its size) of the excitation time histories. The peak groundaccelerations (PGAs) of selected earthquake ground motionsare shown in Table 3. The corresponding displacement andacceleration response spectra of the ground motions for a 2%damping ratio are shown in Fig. 3. The maximum ordinatesof the spectral acceleration of the selected earthquake motionsoccur in the range 0.3–0.6 s, implying that these groundmotions are recorded at rock or firm soil sites. These groundmotions are assumed to act uniformly at all the supports alongthe longitudinal and transverse directions of the bridge, and soilstructure interactions at the bridge supports are neglected.

The fundamental time period of the uncontrolled bridgeis found to be 1.94 s. As damping in the bridge structureis generally very low, therefore 2% damping is assumed inthe present study. To evaluate the performance of the passivehybrid control system, the response quantities selected are:relative displacement in the longitudinal (xb1) and transverse(yb1) directions of the isolators at the left abutment; relativedisplacement of the isolators in the transverse direction at theleft deck–tower junction (yb2); absolute acceleration of the deckin the longitudinal (xd ) and transverse (yd ) directions at theleft abutment; and the base shear response of the towers alongthe longitudinal (Vx ) and transverse (Vy) directions at the lefttower normalized to the weight of the deck, Wd . The responsequantities are presented only for the left half of the bridgedue to the symmetrical bridge structure. In order to assessthe performance of the passive hybrid systems, the seismicresponse of the bridge with a passive hybrid system is comparedwith the corresponding response of an isolated and uncontrolledbridge. For each isolation system, responses are obtained forisolation time periods of 2 and 2.5 s.

A parametric study is performed to investigate the effect ofvariation in damping of the VFD (considering linear viscousdamping, i.e. λ = 1) on the resultant displacement response of

the isolator, xr (i.e.√

x2b1 + y2

b1) and the resultant normalized

tower base shear Vr (i.e.√

V 2x + V 2

y /Wd ). The results of the

parametric study are presented in Figs. 4–9. The dampingratio, ξd , of VFD is varied from 5% to 40% of the criticaldamping, keeping the isolator parameters constant. Figs. 4 and5 show the peak resultant response of the bridge controlledby HDRB and VFD. It can be observed from the Fig. 4that, for all the earthquakes except Kobe, 1995, the resultantbearing displacement response increases as the isolation periodincreases. This is in agreement with the trend in displacementspectra of the earthquake ground motions (Fig. 3). Further,

62

Fig. 3. Displacement and acceleration spectra of four earthquake ground motions applied in the longitudinal and transverse directions of the bridge.

Fig. 4. Effect of variation in damping of the VFD on the peak resultant bearing displacement of the bridge with HDRB (λ = 1 and ξb = 0.1).

it can be seen from the Fig. 4 that, with increasing dampingof the VFD, the displacement response reduces reasonably.It is observed from Fig. 5 that the tower base shear reduceswith an increase in damping up to a certain level, giving anoptimum value for all earthquakes except the Northridge, 1994

earthquake, for which no optimum value of the damping of theisolators is found, up to the 40% damping considered for theinvestigation.

Figs. 6 and 7 represent the results of the parametric studyperformed for the passive hybrid system consisting of LRB with

63

Fig. 5. Effect of variation in damping of the VFD on the peak resultant tower base shear response of the bridge with HDRB (λ = 1 and ξb = 0.1).

Fig. 6. Effect of variation in damping of the VFD on the peak resultant bearing displacement of the bridge with LRB (λ = 1, ξb = 0.1 and F0 = 0.05).

VFD. It can be observed from the Fig. 6 that, with an increasein damping of the VFD, the displacement response reducessignificantly. For the tower base shear response, it is observed

from Fig. 7 that the optimal damping of VFD is found for theImperial Valley, 1940 and the Loma Prieta, 1989 earthquakes.For the Kobe, 1995 earthquake, the base shear increases with

64

Fig. 7. Effect of variation in damping of the VFD on the peak resultant tower base shear response of the bridge with LRB (λ = 1, ξb = 0.1 and F0 = 0.05).

Fig. 8. Effect of variation in damping of the VFD on the peak resultant bearing displacement of the bridge with FPS (λ = 1 and µ = 0.05).

an increase in damping of VFD, but at a slower rate. For theNorthridge, 1994 ground motion, the tower base shear reduceswith an increase in ξd for the variation range considered.

The results of the parametric study performed for the passivehybrid system consisting of FPS with VFD are presented in

Figs. 8 and 9. The trend of the results plotted in Fig. 8 indicatesthat the resultant displacement response reduces remarkablywith an increase in the damping of VFD. Further, as depictedfrom the Fig. 9, the tower base shear response increases, but ata much slower rate with increasing ξd for all the earthquakes

65

Fig. 9. Effect of variation in damping of the VFD on the peak resultant tower base shear response of the bridge with FPS (λ = 1 and µ = 0.05).

except the Northridge, 1994 earthquake, for which the resultanttower base shear goes on reducing.

Thus, the results of the parametric study performed byvarying ξd suggest that the use of VFD as a supplementaldamping device along with the isolation is beneficial for thereduction in seismic response of the cable-stayed bridge. It isobserved that passive hybrid systems are capable of controllingthe resultant displacement response of the isolators whilesimultaneously limiting the resultant base shear response of thetowers.

The results of time history analyses along the longitudinaland transverse directions are presented in Figs. 10–12 for thebridge with different passive hybrid systems for the cases withan isolation time period of 2.0 s under the Imperial Valley, 1940earthquake. The results obtained for a bridge with isolationsystems only and with a passive hybrid system are plotted in thesame graph for the purpose of comparison. Since the optimumvalue of ξd varies with the earthquake ground motions, thedamping ratio of the VFD is judiciously selected as 30% ofthe critical damping, which yields a maximum reduction in thebearing displacement of the isolated bridge without hamperingthe significant gain achieved in the base shear response withthe help of isolation. It is observed from the time variationplots that the reduction in the displacement response of theisolators is remarkable for a bridge with a passive hybridsystem. Moreover, it is observed that there is little or no increasein the absolute acceleration of the deck and the base shearresponse of the tower in both horizontal directions.

Further, to investigate the influence of non-linear viscousdamping of VFD on the seismic response of a cable-stayedbridge, the response of the bridge is obtained by taking λ tobe equal to 0.4, 0.7 and 1.0 with 30% viscous damping. The

parameters of the isolators are kept unchanged. The peak valuesof the response quantities for VFD with HDRB, LRB and FPSare presented in Tables 4, 5 and 6, respectively. The results arecompared with the responses of an uncontrolled as well as anisolated bridge.

The analytical investigation indicates that the resultsobtained with a passive hybrid system are much bettercompared to that of isolation alone. The large displacementresponses of the isolators are significantly reduced, with littleor no increase in the tower base shear by the use of a passivehybrid system. Further, the response with non-linear viscousdamping is found to be better than that with linear viscousdamping. The value of the velocity exponent, λ = 0.4, is foundto be more effective in controlling the response of the bridge.While VFD is acting with HDRB (Table 4), the maximum andminimum reductions in the tower base shear response along thelongitudinal direction are around 85% and 62%, respectively.However, along the transverse direction, the reduction observedin the tower base shear is less and in the range of 16%–55%.The displacement of the HDRB in the longitudinal direction atthe abutment is found to be reduced by up to 65%, whereaslongitudinal and transverse displacements at the deck–towerjunction are found to be reduced by up to 70%. Compared withthe results for Tb equal to 2 s, those for Tb equal to 2.5 s arenot much better, since the reduction in the tower base shearresponse is nominal and the displacement of the isolators isgreater.

Similar results are found for passive hybrid systemscomposed of VFD with LRB (Table 5) and VFD with FPS(Table 6). Numerical studies performed for all the passivehybrid systems indicate that the system with FPS is moreeffective in controlling the seismic response of the bridge. For

66

Fig. 10. Time variation of acceleration, base shear and displacement along the longitudinal and transverse directions of the bridge with HDRB and a passive hybridsystem under the Imperial Valley, 1940 earthquake motion (Tb = 2 s).

Table 4Peak responses of bridge installed with HDRB, and VFD along with HDRB

Earthquake Responsequantity

Uncontrolledresponse

HDRBTb = 2 s

HDRB + VFD HDRBTb = 2.5 s

HDRB + VFDλ = 1.0 λ = 0.7 λ = 0.4 λ = 1.0 λ = 0.7 λ = 0.4

Imperial Valley,1940

Vx /Wd 0.846 0.176 0.152 0.142 0.128 0.179 0.155 0.145 0.134Vy/Wd 0.411 0.275 0.266 0.274 0.289 0.276 0.262 0.269 0.285xb1 (mm) – 174.628 112.597 90.983 68.255 241.993 132.818 107.798 82.397yb1 (mm) – 68.749 34.346 22.354 18.949 63.733 37.097 25.012 23.358yb2 (mm) – 203.702 141.194 111.45 66.857 263.897 173.968 139.674 87.570

Kobe, 1995


Loma Prieta, 1989


Northridge, 1994


67

Fig. 11. Time variation of acceleration, base shear and displacement along the longitudinal and transverse directions of the bridge with LRB and a passive hybridsystem under the Imperial Valley, 1940 earthquake motion (Tb = 2 s).

Table 5Peak responses of bridge installed with LRB and VFD along with LRB



LRBTb = 2 s

LRB +VFD LRBTb = 2.5 s

LRB +VFDλ = 1.0 λ = 0.7 λ = 0.4 λ = 1.0 λ = 0.7 λ = 0.4



Kobe, 1995


Loma Prieta, 1989


Northridge, 1994


68

Fig. 12. Time variation of acceleration, base shear and displacement along the longitudinal and transverse directions of the bridge with FPS and a passive hybridsystem under the Imperial Valley, 1940 earthquake motion (Tb = 2 s).

Table 6Peak responses of bridge installed with FPS and VFD along with FPS



FPS Tb = 2 s FPS +VFD FPSTb = 2.5 s

FPS +VFDλ = 1.0 λ = 0.7 λ = 0.4 λ = 1.0 λ = 0.7 λ = 0.4



Kobe, 1995


Loma Prieta, 1989


Northridge, 1994


69

the combination of VFD and FPS, the displacement of theisolators at the abutment in the longitudinal direction is foundto be a minimum (50.964 mm) for the Imperial Valley, 1940earthquake and a maximum (359.759 mm) for the Northridge,1994 earthquake. Moreover, the displacement of the isolatorsat the deck–tower junction in the transverse direction is foundto be a minimum (46.262 mm) for the Imperial Valley, 1940earthquake and a maximum (135.872 mm) for the Northridge,1994 earthquake. The amount of displacement is quite smallto have any possible impact of the deck with the towers in thetransverse direction.

The results of the investigation demonstrate that the non-linear damping of VFD is capable of controlling the peak dis-placement response of the isolated bridge, and thus reducing therequired length of expansion joints. Furthermore, as the VFDgives out-of-phase response output, the peak value of the towerbase shear is also controlled effectively. Hence, the use of VFDas supplemental damping with isolation largely solves the prob-lem of superstructure displacement of an isolated bridge, alongwith controlling the seismically induced forces in the bridge.

7. Conclusions

The efficacy of passive hybrid mechanisms in protectinga cable-stayed bridge subjected to strong earthquake groundmotions has been investigated and presented. The hybridsystem consists of combinations of elastomeric and slidingisolation systems in association with a viscous fluid damper.The seismic response of a simplified model of the QuincyBay-view Bridge at Illinois is studied under two horizontalcomponents of real earthquake motion. The seismic responsesof the bridge with isolation systems alone and with passivehybrid systems have been evaluated. From the dynamicanalytical investigation of the bridge with passive hybridcontrol systems, the following conclusions may be drawn:

1. The seismic isolation in the cable-stayed bridge helps toreduce the acceleration response and the base shear responsesubstantially. However, the displacement response of thedeck increases significantly with isolation.

2. The addition of supplemental damping, in the form of aviscous fluid damper, controls the earthquake response ofthe isolated bridge significantly. Specifically, a viscous fluiddamper having non-linear viscous damping with a velocityexponent equal to 0.4 is found to be more efficient incontrolling the displacement response of the isolated bridge.

3. With passive hybrid control systems, a reduction in thedisplacement response of the isolated bridge by up to about65% in the longitudinal direction, as well as in the transversedirection, can be achieved.

4. There exists an optimum amount of damping of viscousfluid dampers for controlling the tower base shear response.Optimum values are found for all the earthquakes except theNorthridge, 1994 earthquake. However, for the displacementresponse, no such optimum values are found, as the bearingdisplacement reduces with an increase in damping of theviscous fluid damper.

5. There is very little or no increase in the tower baseshear response of the bridge with a passive hybrid system

compared to that of the isolation system alone. This isbecause of the inherent out-of-phase response output of theviscous fluid damper.

6. A passive hybrid system consisting of FPS and VFD is foundto be more effective in controlling the peak displacementresponse of the deck while simultaneously limiting the peaktower base shear response.

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Documents

Passive hybrid systems for earthquake protection of cable