SEMIACTIVE CONTROL OF SEISMICALLY ISOLATED BRIDGES

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International Journal of Structural Stability and DynamicsVol. 8, No. 4 (2008) 547–568c World Scientific Publishing Company

SEMIACTIVE CONTROL OF SEISMICALLY

ISOLATED BRIDGES

JAGADISH G. KORI∗ and R. S. JANGID†

Department of Civil Engineering

Indian Institute of Technology Bombay, Powai

Mumbai – 400 076, India †

[email protected]

Received 5 June 2007Accepted 14 March 2008

This paper describes the application of semiactive devices for controlling the earthquakeresponse of two highway bridges of different cross sections and pier heights. Each of thebridges consists of a three-span continuous deck supported on the piers and abutments.Semiactive devices such as the magnetorheological damper, the variable friction damperand the variable stiffness device are considered as the control devices. These devices areinserted between the deck and piers or abutments of the isolated bridge. The semiactivedevice changes its properties according to the structural response and adds control forcesto the system. Each pier supporting the bridge is modeled as a linear lumped masssystem. The optimum parametric values of the semiactive dampers are evaluated andconsidered in analysis of the bridge. A comparative study is performed for different semi-active devices installed on the bridges under different seismic loadings in the longitudinaldirection. The behaviors of the bridges with different semiactive isolation devices arecompared with the corresponding nonisolated ones. The semiactive dampers are observedas an effective protective device in reducing the displacements of the isolation bridgesas well as the base shear of the piers.

Keywords : Base isolation; bridge; earthquake; semiactive friction damper; variable stiff-ness device; MR damper

1. Introduction

Recent devastating earthquakes have revealed that bridges are the most vulnerable

components of the transportation system. It has been observed that the earthquake

damage is mainly due to the excessive displacement of the bridge deck or bearings.

Hence, there is a need for improved performance of highway bridges subjected to

severe earthquake ground motions. The performance of bridges during earthquakes

can be improved by introducing suitable energy dissipation devices into the bridgesystem. This can be achieved by installing suitable control devices in the bridge

∗Research Scholar.†Professor.

547



548 J. G. Kori & R. S. Jangid

to dissipate the kinetic energy, thereby reducing the deformations of the piers and

deck. The concept of structural control may be utilized to either reduce the amount

of energy transferred into the bridge structure from the ground motion or absorb

some of the energy already transmitted to the bridge structure.

Structural control systems can be classified as passive, active, semiactive and

hybrid. In a passive control system, the properties of the device cannot be modified

after installation and it does not require external power or a computer process for

operation. Active control systems utilize actuators to exert control forces on the

structure, which are determined by incorporating the actuators within a feedback

control system that employs the measured structural response or ground motions

as the input data. Semiactive systems may be viewed as passive control systems,

which have been modified to allow for adjustment of the mechanical properties

(e.g. damping, stiffness and friction level). Semiactive control systems have beenreceiving significant attention in recent years, because they provide a mediator

between the active and passive control systems. The three primary categories of

passive, active and semiactive devices can be placed in various combinations to

result in hybrid control systems.

Researchers are more concerned with the vibration control of buildings, for which

many advances have been made. In contrast, the vibration control of bridges has not

been studied to the same extent. Comparatively few studies have been conducted

in the past regarding the effectiveness of control devices for the seismic design of

bridges. Ghobarah and Ali1 investigated the response of a three-span bridge iso-lated by the lead–rubber bearings subjected to earthquake motions. Using a smart

base isolation concept, the control of bridges under seismic excitations was studied

by Yang and Yu.2 Some experimental and numerical studies of semiactive control of

highway bridges were reported by Kawashima and Unjoh3 and Symans and Kelly.4

Studies have also been carried out on application of semiactive intelligent stiffener

control devices to the Walnut Creek Bridge in the USA.5 Analytical models for

elastomeric bearings were developed by Nagarajaiah and Ferrell6 and Hwang et al .7

Application of the semiactive variable stiffness damper (SAVSD) to the cable-stayedbridge was studied by He et al .8 and Agrawal et al .9 Along the lines of semiactive

control, the seismic protection of highway bridges was investigated using the mag-

netorheological (MR) damper by Erkus et al .,10 Liu et al .11 and Sahahrabudhe and

Nagarajaiah.12 Kunde and Jangid13 reviewed the analytical and experimental stud-

ies on the effectiveness of seismic isolation and its implementation in actual bridges.

The seismic response of isolated bridges using lead–rubber bearings was studied by

Jangid.14 Some design formulas were developed and proposed for the supplemental

viscous dampers to highway bridges by Hwang and Tseng.15 The seismic response of

the simply supported base-isolated bridge with different isolators was investigatedby Matsagar and Jangid.16 Soneji and Jangid17,18 studied the effectiveness of seis-

mic isolation and semiactive MR dampers in reducing the seismic response of the

cable-stayed bridges. It is noted that all of the aforementioned studies have focused

on the performance evaluation of base-isolated bridges and little effort has been



Semiactive Control of Seismically Isolated Bridges 549

spent to evaluate the performance of semiactively controlled bridge systems. The

focus of this study is to numerically evaluate the potency and seismic performance

of semiactive control systems in the isolated bridges.

The objectives of the present study are: (i) to study the various semiactive

control devices for the reduction of seismic response of highway bridges, (ii) to

investigate the optimum parameters of semiactive control devices under different

ground motions, and (iii) to examine the suitable semiactive device with isolator

from the comparative study. Three types of semiactive devices are considered for

the isolated bridges, with the focus on the following parameters: the variation of

input command voltage in the MR damper, the variation of the gain multiplier in

variable friction devices, and the ratio of damper stiffness to isolator stiffness in

variable stiffness devices.

2. Structural Model of Controlled Bridges

The general layout of the two isolated bridges (with different cross sections and

pier heights) considered is shown in Fig. 1(a). Each of them consists of a three-span

continuous deck supported by the isolation systems. The semiactive dampers are

placed between the super- and the sub-structure at the abutment or pier locations.

(a)

(b)

Fig. 1. Isolated bridge: (a) general layout, (b) mathematical model.




The substructure of each bridge consists of rigid abutments and reinforced concrete

piers. The following assumptions are made for the analysis of the isolated bridge

model:

(1) The bridge deck is straight and is supported at discrete locations along itslongitudinal axis by cross diaphragms with a zero skew angle. The bridge deck

is idealized as a rigid body.

(2) The bridge piers are assumed to remain in the elastic state during the earth-

quake excitation. This is a reasonable assumption as the isolation can reduce

the earthquake response in such a way that the structure remains within the

elastic range.

(3) Each pier is modeled as a lumped mass system with a number of segments.

Each segment is connected by a node with one horizontal degree of freedom.The mass of each segment is lumped into the two adjacent nodes.

(4) Bridge piers are assumed to be rigidly fixed at the foundation level.

(5) The bridge is founded on firm soil or rock, and the earthquake excitations are

assumed to be synchronous at all supports.

(6) The stiffness contribution of nonstructural elements, such as curbs, parapet

walls and wearing coat, is neglected; however, their inertial effect is considered

in the simulation.

(7) Same isolators or dampers are inserted at the piers or abutments.

The above assumptions lead to the mathematical model of the isolated bridge

system [shown in Fig. 1(b)], which was also studied by Ghobarah and Ali,1 Li,19

Pagnini and Solari,20 and Kunde and Jangid.21 The bridge is subjected to the

earthquake ground motion in the longitudinal direction. The governing equations

of motion of the isolated bridge are

Mx + Cx + Kx + DF = −Mrxg (1)

where M, C and K are the mass, damping and stiffness matrices, respectively, of the bridge model system; x = {x0, x1, x2, . . . , xn}

T is the vector of displacement of

the bridge; x0 is the displacement of the bridge deck relative to the ground; xi is the

displacement of the ith node of the bridge pier relative to the ground; x and x denote

the corresponding velocity and acceleration vectors, respectively; D is the location

matrix for the forces of the isolator and damper systems; F = {F a, F p}T

is the vector

of forces produced by the control devices; F a and F p represent the forces of the

control devices at the abutment and the pier level, respectively; r = {1, 1, . . . , 1}T

is the influence coefficient vector of size n × 1; and xg represents the earthquake

ground acceleration.Equation (1) can be recast in the state space as a set of first-order equations,

as follows:

z = Az + B F + Exg, (2)




where z is the state vector, and A, B and E are the system matrices. The state

vector and the system matrices are

z = x

x , A = 0 I

−M−1K −M−1C , B = 0

−M−1D , E = 0

−r . (3)

The restoring force produced by the isolator, F bj , and the damper, F dj, at the

abutment and the pier level is given by

F j = F bj + F dj (for j = a and p). (4)

The damping matrix of the pier is not explicitly known, which is constructed

from the assumed modal damping (ξp) for each mode of vibration using its mode-

shape and frequency. The pier of the bridge is considered to be of uniform cross-

section throughout the height. The fundamental period T p of the pier that is freeat the top is

T p =2π

(1.875)2

mph4

EI , (5)

where mp is the mass per unit length of the pier, h is the height of the pier, and EI

is the flexural rigidity of the pier. Equation (5) is based on the fundamental period

of a uniform cantilever beam under transverse vibrations.

3. Control Devices

In this study, laminated rubber bearings are used as the isolators for the bridge. In

addition, the passive viscous damper and three types of semiactive control systems

are considered in the comparative study with regard to the seismic performance

of the bridge. The semiactive dampers considered include the MR damper, the

variable friction damper and the variable stiffness device. The basic characteristics

of these systems are explained in the following subsections.

3.1. Laminated rubber bearing

The laminated rubber bearing (LRB) is most commonly used in seismic isolation

systems. The basic components of the LRB are steel and rubber plates built through

the vulcanization process in alternate layers, as shown in Fig. 2(a). The restoring

force developed in the bearing, F b, is given by

F b = cbxb + kbxb, (6)

where xb and xb are the relative displacement and velocity of the LRB, respectively;

and cb and kb are the damping and stiffness constants of the LRB, respectively.

The stiffness and damping of the LRB are selected to provide the specific values

of the two parameters, namely the isolation time period (T b) and damping ratio




F b

xb

k bRubber

Steel-plates

(a)

xd

Viscous fluid

Orifice

Piston rod

Piston headF d

(b)

Fig. 2. Schematic and mathematical model of various control devices: (a) laminated rubberbearing, (b) viscous damper.

(ξb), defined as

T b = 2π md

Σkb , (7)

ξb =Σcb

2mdωb

, (8)

where Σkb is the total stiffness of the LRB, Σcb is the total effective viscous damping

of the LRB, and ωb = 2π/T b is the isolation frequency.

3.2. Viscous damper

A typical viscous damper consists of viscous material in the form of either a liquid

(silicon oil) or a solid (special rubbers or acrylics). A fluid viscous damper operates

on the principle of fluid flow through orifices. A schematic model of the viscous

damper and its force-deformation behavior are shown in Fig. 2(b). For ideally purely

viscous (Newtonian) fluids, the damper force is proportional to the relative velocity

between its two ends. The force in the damper (F d) is, as given by Ref. 22,

F d = C dxd, (9)

where C d is the damping coefficient of the damper, and xd is the velocity across

the damper. The damping value of the viscous damper is selected based on thedamper’s damping ratio (ξd) parameter, defined as

ξd =ΣC d

2mdωb

, (10)

where ΣC d is the total effective damping coefficient of the viscous damper.




3.3. Magnetorheological damper

The magnetorheological (MR) damper consists of a hydraulic cylinder containing

a solution that, in the presence of a magnetic field, can reversibly change from a

free-flowing, linear viscous fluid to a semisolid with controllable yield strength. TheMR dampers shows dynamically nonlinear force-velocity behavior. Hence a more

accurate modeling of MR dampers is necessary. The same is true for modeling of

the control devices in predicting the behavior of the isolated system. The modified

Bouc–Wen model (Spencer et al .23) is extremely versatile and can exhibit a wide

variety of hysteretic behaviors. A schematic of this model is shown in Fig. 3(a). The

governing equations of the force predicted by this model are

F d = c1yd + k1(xd − x), (11)

z = −γ |xd − yd|z|z|n−1 − β (xd − yd)|z|n + A(xd − yd). (12)

The velocity of the device, yd, is given by

yd =1

c0 + c1{α z + c0xd + k0(xd − yd)}, (13)

(a)

(b)

(c)

Fig. 3. Schematic and mathematical model of various semiactive control systems: (a) MRdamper, (b) variable friction damper, (c) variable stiffness device.




where z is an evolutionary variable that accounts for the history dependence of the

response; xd is the damper displacement; xd is the velocity across the damper; k1is the accumulator stiffness; c1 is viscous damping at lower velocity in the model

to produce the rolloff; c0 is viscous damping at larger velocity; k0 is the stiffness

at large velocity; yd is the damper piston displacement, and x is the initial dis-

placement of the spring; and α ,β,γ,n and A are the parameters called the shape

or characteristic parameters of the model, which control the linearity in unloading

and the smoothness of transition from the pre- to the post-yield region.

The model parameters α, c0 and c1 depend on the voltage to the current driver:

α = αa + αbu, c0 = c0a + c0bu, c1 = c1a + c1bu, (14)

while the filtered voltage u is determined by the applied voltage v to the control

circuit:

u = −η(u − v) (15)

where 1/η is the time constant of this first order filter. A bang–bang control strategy

based on Lyapunov stability theory was used by Spencer et al .23 for controlling MR

dampers. This control algorithm determines the current sent to the damper as

v = V maxH {−(xd + xg)T F d}, (16)

where H (·) is the Heaviside step function and V max the maximum input commandvoltage to the MR device.

3.4. Semiactive variable friction damper

A semiactive variable friction damper (SAVFD) is a displacement-dependent energy

dissipation device, because its damper force is independent of the velocity and fre-

quency content of excitations. A friction damper in general consists of two bodies,

which slide with respect to each other under a controllable clamping force N , gen-erating a dissipative force proportional to the clamping force N (≥ 0) and the coef-

ficient of friction µ between the surfaces. Figure 3(b) shows the semiactive variable

friction damper and the mechanical model. A semiactive friction damper requires

a feedback control algorithm and online measurement of the structural response

in order to determine the appropriate level of the clamping force. Here, a recently

developed predictive control24 with a direct output feedback concept is considered.

The control rule for determining the damper force (F d = µN ) of an SAVFD at the

tth time step can be evaluated by

F d[t] = Rf F c[t], (17)

where the critical force F c is evaluated using

F c[t] = Pz[t − 1] + QF d[t − 1] + Rxg[t − 1]. (18)




The factor Rf is a ratio of the damper force to the critical friction force, which is

also treated as a gain multiplier. The matrices P, Q and R are the control gains,

written as

P = kdDf (Ad − I), Q = kdDf Bd + I, R = kdDf Ed, (19)

where Df is a constant matrix composed of damper orientations, kd is the damper

stiffness, and Ad = eA∆t represents the discrete time system matrix, with ∆t as

the time interval. The constant coefficient matrices Bd and Ed are the discrete time

counterpart of the matrices B and E, written as

Bd = A−1(Ad − I)B, Ed = A−1(Ad − I)E. (20)

3.5. Semiactive variable stiffness device

A semiactive variable stiffness device (SAVSD) system is able to open or close

the control value of the device, thereby dissipating or absorbing the energy of the

structure.9 Based on the feedback information of the structural response, the control

device switches off or on the control valve for energy dissipation. When the structure

reaches the maximum displacement position and starts to move in the opposite

direction, the energy dissipation device is opened by the control system and the

stiffness of the system becomes zero. When the energy dissipation device is closed,the system provides a certain stiffness by which the seismic energy is absorbed. A

schematic model of the damper mechanism is shown in Fig. 3(c). The damper is

composed of a cylinder-piston system with a valve in the bypass pipe connecting

two sides of the cylinder filled with hydraulic oil. The total stiffness consists of the

fluid stiffness kf and the device stiffness kc. Hence, the equivalent effective stiffness

of the entire device (kh) is given by

kh =kf kc

kf + kc

. (21)

The control force (F d) can be calculated as

F d = khvsxd, (22)

where xd is the relative displacement between the deck and the pier.

For the sake of simplicity and the requirement of little computational effort, a

switching control law is considered. The control force vector (F d) can be calculated

from Eq. (22) and the vs expressed for the switching control law is

vs =

1 if xdxd ≥ 0,

0 otherwise,(23)

where vs = 1 if the SAVSD valve is closed, and vs = 0 if it is open.




Table 1. Dynamic properties of bridges.

Bridge properties Bridge I Bridge II

Span length (m) 3 @ 30 3 @ 30

Pier height (m) 8 10Pier shape

Cross-sectional area of deck (m2) 3.57 3.57

Cross-sectional area of pier (m2) 4.09 1.767

Moment of inertia of deck in longitudinal direction (m4) 2.08 2.08

Moment of inertia of pier in longitudinal direction (m4) 0.64 0.438

Fundamental period of pier in longitudinal direction(s) 0.1 0.245

Young’s modulus of elasticity (Gpa) 20.64 20.64

Mass density (kg/m3) 2.4 × 103 2.4 × 103

Fundamental period of nonisolated bridge 0.45 1.5

in longitudinal direction (s)

4. Numerical Study

In the numerical study, two bridge models of different cross sections and pier heights

with and without control devices are considered for comparison of the seismic

responses. Each of the bridges is composed of a three-span continuous deck with

reinforced concrete piers and a prestressed concrete box girder. The dynamic prop-

erties of the two bridges are given in Table 1, based on the data of the bridges

studied by Wang et al .25 and Kunde and Jangid.21 The bridge considered for thefirst example, referred to as bridge I, has hollow circular piers, and the isolators

are placed at the pier cap. The fundamental period of bridge I is 0.45 s. The bridge

considered for the second example, referred to as bridge II, is a relatively flexible

bridge with oblong piers. The fundamental period of bridge II is 1.5 s. Here, four sets

of semiactive dampers are installed between the deck and the piers or abutments

for exertion of the control forces. For comparison, the response of the bridge deck

to the base motion is computed under the following conditions: (i) bridge without

isolators; (ii) bridge controlled with the isolators, i.e. with the LRB; (iii) bridgewith the isolators and viscous dampers; (iv) bridge with the isolators and semi-

active dampers, i.e. MR damper, variable friction dampers and variable stiffness

devices.

The performance of controlled bridge systems is investigated under four real

earthquake ground motions, namely El-Centro, 1940 (PGA = 0.348 g); Kobe,

1995 (PGA = 0.834g); Loma Prieta, 1989 (PGA = 0.57g); and Northridge, 1994

(PGA = 0.843 g). The seismic response of the corresponding nonisolated bridge sys-

tem is also analyzed, for comparison purposes. The piers of the nonisolated bridges

are assumed to be connected to the superstructure by a fixed bearing, which allowsrotation but no displacement to occur. The number of nodes considered in the pier

is five (i.e. n = 5). The damping of the pier is taken as ξp = 5% of the critical damp-

ing for all modes of vibration. The bridge isolated by the LRB system is designed to

provide an isolation period of T b = 2 s and the effective damping ratio is ξb = 10%.




In order to compare the performance of semiactive dampers, a passive viscous

damper is considered in this study. Four sets of viscous dampers are installed in

the isolated bridge in place of the semiactive devices. The responses of the bridge

system desired are: the isolator displacement, the acceleration at the center of the

bridge deck, the base shear in the piers, and the damper control force. The pier

base shear and damper control force were expressed in the normalized form with

respect to the weight of the bridge deck, W d.

The performance of the MR damper is studied by varying the input command

voltage V max to the damper device in the range, 0–10 V, keeping all other parame-

ters constant. The parameters presented in Table 2 are based on the experimental

results of a 20-ton MR damper and have been linearly scaled up to have a max-

imum capacity of 1000 kN (Yang et al .26), with a maximum command voltage of

V max = 10V. The results of parametric study for the MR damper under the fourearthquake excitations are plotted in Figs. 4 and 5 for bridges I and II, respectively.

It can be observed that the displacement response of the isolator reduces with the

increase in the command voltage V . However, there exists an optimum value of volt-

age input for which the deck acceleration and pier base shear response attains the

minimum. The optimum command voltage is found to be 5 V and 3 V for bridges I

and II, respectively. Thus, for a given structural system, there exists an optimum

command voltage of the MR damper for which the deck acceleration and pier base

shear of the isolated bridges become minimum. However, the isolator displacement

goes on decreasing with the increase in the command voltage of the MR damper.In Eqs. (18) and (19), kd is an important parameter for application of the

SAVFD. As such, the optimal value of kd for achieving the minimum response of

the system is evaluated and shown in Fig. 6. The optimal value of kd for minimizing

the response of the system in bridge I ranges from 2.5 to 3.5. Thus, to study the

effect of the gain multiplier factor Rf of the SAVFD on the seismic response of

the bridges, the optimal value of kd is taken as 3. The effect of the gain multiplier

factor Rf of the SAVFD on the seismic response of bridges I and II is shown in

Figs. 7 and 8, respectively. The parameter Rf varies in the range from 0 to 0.99,implying that the variable damper friction force F d in Eq. (17) should be kept

slightly lower than the critical friction force. The lower value of Rf ensures that the

damper remains in the slip state during the entire earthquake excitation and can

Table 2. Parameters of the modified Bouc–Wen model for a 20-ton capacityMR damper.

Parameter Value Parameter Value

αa 46.2 kN/m γ 164.0 m−2

αb 41.2 kN/m/V β 164.0 m−2

k0 0.002 kN/m x 0.18 mk1 0.0097 kN/m c1a 8359.2 kN-s/mη 100s−1 c1b 7482.9 kN-s/m/Vc0a 110.0 kN-s/m A 1107.2c0b 114.3 kN-s/m/V n 2




Fig. 4. Effects of command voltage on peak displacement, deck acceleration, base shear andcontrol force for bridge I with MR damper.

Fig. 5. Effects of command voltage on peak displacement, deck acceleration, base shear andcontrol force for bridge II with MR damper.




Fig.6.

Effectsofdamperstiffnesskd

onpeakdisplacement,deckacceleration,baseshearandcon

trolforceforbridgeIwithSA

VFD.




Fig. 7. Effects of the damper stiffness ratio on peak displacement, deck acceleration, base shearand control force for bridge I with SAVFD.

Fig. 8. Effects of the damper force to critical friction force ratio on peak displacement, deckacceleration, base shear and control force for bridge II with SAVFD.




continuously dissipate the seismic energy. From the figures, it is observed that the

isolator displacement reduces mildly with the increase in the Rf value. However,

the deck acceleration and pier base shear decrease for 0.4 < Rf < 0.7, but increase

suddenly when Rf > 0.8. This indicates that the optimum gain multiplier Rf of

the variable friction damper can be considered as 0.6 for both bridges under all

earthquake ground motions. Further, the damper control force increases with the

increase in the gain multiplier Rf , as was expected.

For the SAVSD, a parametric study is conducted by varying the damper stiffness

ratio (αk = kh/kb) in the range of 0–2. The effect of αk on the seismic response under

all the earthquake excitations is plotted in Figs. 9 and 10 for bridges I and II, respec-

tively. The results show that the isolator displacement reduces with the increase

in the damper stiffness ratio. However, the decrease in the isolator displacement

is not very significant when αk is increased beyond unity. On the other hand, thedeck acceleration and pier base shear increase with the increase in the damper stiff-

ness ratio. Thus, the presence of an SAVSD can reduce the displacement of the

isolator, but increase the deck acceleration and pier base shear. For the present

bridge system and excitations considered, the optimum value of αk can be taken as

unity for minimizing the displacement in the deck or isolator with controlled deck

acceleration and pier base shear.

The performance of the passive viscous damper depends on the damper coef-

ficient. Here, the damping ratio is allowed to vary from ξd = 0 to 20%. Figure 11

shows the effect of the damping ratio of the viscous damper on the seismic response

Fig. 9. Effects of the damper stiffness ratio on peak displacement, deck acceleration, base shearand control force for bridge I with SAVSD.




Fig. 10. Effects of the damper stiffness ratio on peak displacement, deck acceleration, base shearand control force for bridge II with SAVSD.

Fig. 11. Effects of the viscous damper’s damping ratio on peak displacement, deck acceleration,base shear and control force for bridge I with passive viscous damper.




of bridge I. As expected, the isolator displacement decreases with the increase in the

damper damping ratio. On the other hand, the deck acceleration and pier base shear

first decrease and then increase with the increase in the damper damping ratio. This

implies that there exists an optimal viscous damping value for which the pier base

shear and deck acceleration attain the minimum. For the selected bridge system

and excitations, the optimum viscous damping ratio is in the vicinity of 10%.

Based on the various optimal parameter values of the control devices, the peak

values of the isolator displacements, deck accelerations, base shear V b and maximum

control force F computed for bridges I and II are tabulated in Tables 3 and 4,

respectively. These tables indicate that there is significant reduction in the isolator

displacement when the bridge is supplemented by passive or semiactive dampers.

A reduction of the order of 50% in the isolator displacement was observed for

the isolated bridges with semiactive damper systems. In some cases the presenceof the supplemental passive or semiactive dampers can slightly increase the deck

acceleration and base shear. However, this increase in the deck acceleration and base

Table 3. Peak responses of bridge I under different control conditions.

Control system (1) Isolator Deck Pier base Controldisplacement acceleration shear force

(cm) (2) (g) (3) (Vb/wd) (4) (F /wd) (5)

Earthquake motion: El-Centro, 1940 Nonisolated 0.883 0.478 Isolated 15.017 0.154 0.047 0.019VD + isolated 6.728 0.127 0.038 0.018MRD + isolated 3.222 0.114 0.035 0.042SAVFD + isolated 2.807 0.107 0.065 0.031SAVSD + isolated 5.676 0.198 0.085 0.054

Earthquake motion: Kobe, 1995

Nonisolated 2.411 1.325 Isolated 32.444 0.339 0.092 0.041VD + isolated 12.225 0.309 0.097 0.061

MRD + isolated 10.437 0.287 0.068 0.055SAVFD + isolated 12.598 0.337 0.105 0.054SAVSD + isolated 12.332 0.635 0.229 0.179

Earthquake motion: Loma-Prieta, 1989

Nonisolated 1.348 0.662 Isolated 54.074 0.553 0.132 0.068VD + isolated 20.684 0.325 0.092 0.053MRD + isolated 16.162 0.295 0.087 0.061SAVFD + isolated 15.02 0.278 0.106 0.040SAVSD + isolated 14.966 0.721 0.199 0.143

Earthquake motion: Northridge, 1994





Table 4. Peak responses of bridge II under different control conditions.

Control system (1) Isolator Deck Pier base Controldisplacement acceleration shear force

(cm) (2) (g) (3) (Vb/wd) (4) (F /wd) (5)

Earthquake motion: El-Centro, 1940


Earthquake motion: Kobe, 1995

Nonisolated 0.829 0.351 Isolated 30.239 0.296 0.075 0.038VD + isolated 13.105 0.284 0.082 0.050

MRD + isolated 12.421 0.263 0.078 0.059SAVFD + isolated 12.736 0.242 0.118 0.088SAVSD + isolated 13.312 0.536 0.168 0.162

Earthquake motion: Loma-Prieta, 1989


Earthquake motion: Northridge, 1994


shear is generally small compared with the corresponding nonisolated response. In

Figs. 11 and 12, the time variation of the deck displacements of bridge I under theEl-Centro earthquake (1940) and of bridge II under the Kobe earthquake (1995),

respectively, have been plotted. These figures show better overall performance of

the semiactive devices compared with the passive viscous damper. In Fig. 12, the

force displacement diagrams of various control devices for bridge I subjected to

the El-Centro earthquake are compared. Evidently, the force displacements of all

semiactive devices vary continuously and smoothly, as typically shown in Fig. 3.

In Figs. 13 and 14, the deck displacements and deck accelerations, respectively, of

bridge I under the El-Centro earthquake are compared. These figures show better

overall performance of the semiactive devices in peak response reduction comparedwith the passive viscous damper.

The results of the above studies indicate that semiactive systems can be benefi-

cial in reducing the seismic response of bridge structures. These semiactive isolated

bridge systems may prevent or significantly reduce structural damage during a




Fig. 12. Force displacement diagrams of bridge I controlled by different semiactive devices sub-

jected to the El-Centro earthquake.

seismic event. Such a system may be designed and used with current conventional

isolated bridge technology. Further, it was demonstrated that the MR dampers are

more capable of controlling the peak isolator displacement of the bridges, thereby

reducing the required length of expansion joints in the bridge structures.

5. Conclusions

The effectiveness and performance of various semiactive systems installed in high-

way bridges subjected to different types of earthquakes has been investigated. The

dampers considered included the semiactive MR damper variable friction dampers

and the variable stiffness devices. The performance of the seismically isolated bridge




Fig. 13. Time history displacements of the deck of bridge I controlled by semiactive systemssubjected to the El-Centro earthquake.

Fig. 14. Time history accelerations of the deck of bridge I controlled by semiactive systemssubjected to the El-Centro earthquake.




with the semiactive dampers was compared with the bridge that was not isolated,

isolated, or isolated with passive viscous damper systems. A parametric study was

conducted to find the optimal parametric values for the semiactive control devices

for minimizing the structural response. From the trends of the numerical studies

conducted for the two bridges with different control devices, the following conclu-

sions may be drawn:

(1) Passive and semiactive control devices are very effective in controlling the earth-

quake response of highway bridges. They can also be used for retrofitting of

existing bridges.

(2) The displacement responses of the isolators in a seismically isolated bridge can

be significantly reduced by the use of semiactive dampers with marginal or no

increase in the deck acceleration and pier base shear.(3) For a given isolated bridge system and excitation, there exists an optimal com-

mand voltage for the MR damper and the gain multiplier of the variable friction

damper, for which the deck acceleration and pier base shear attain the min-

imum value. However, the isolator displacement goes on decreasing with the

increase in the command voltage for the MR damper and the gain multiplier

of the variable friction damper.

(4) The performance of the semiactive control devices for the control of seismically

isolated bridges is better than that of the passive viscous damper system in

terms of peak response reduction.(5) Among the semiactive devices, the performance of the MR damper and the

variable friction damper in response control of isolated bridges is better than

that of the stiffness devices.

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SEMIACTIVE CONTROL OF SEISMICALLY ISOLATED BRIDGES

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