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Example of application of response spectrum analysis for seismically isolated

curved bridges including soil-foundation effects

Sevket Ates a,n, Michael C. Constantinou b

a Department of Civil Engineering, Karadeniz Technical University, 61080 Trabzon, Turkeyb Department of Civil, Structural and Environmental Engineering, University at Buffalo, The State University of New York, 212 Ketter Hall, Buffalo, NY 14260, USA

a r t i c l e i n f o

Article history:

Received 3 October 2010Received in revised form

26 November 2010

Accepted 1 December 2010Available online 17 December 2010

a b s t r a c t

This paper presents seismic behaviour of isolated curved bridges in the earthquake prone regions.

For the seismic isolation of bridges, double concave friction pendulum bearings are placed betweenthe deck and the piers, and the abutments as isolation devices. A curved bridge is selected to exhibit the

application for seismic isolation. The mentioned bridge is a three-span featuring cast-in-place concrete

box girder superstructure supported on reinforced concrete columns found on drilled shafts and on

integral abutments founded on steel pipe piles. Additionally, the bridge is located on site underlain by a

deepdeposit of cohesionless material. The drilled shaft-soil system is modelled by equivalent soil springs

methodandis includedin thefinite element model.The soil modelledas a seriesof springs is connectedto

the drilled shaft at even intervals.

The multi mode method of analysis is typically implemented in a computer program capable of

performing response spectrum analysis. The response spectrum specified for the analysis is the 5%-

damped spectrum modified for the effects of the higher damping. Each isolator is represented by its

effective horizontal stiffness with a linear link element.

Asseenfrom theresultsof theoutlinedanalysis, usageof theisolation devices offerssome advantages

forthe internal forceson thedeck forthe considered curvedbridge as perthe non-isolated curvedbridge.

The response spectrum analysis is substantially required to make a decision of the displacement

capacity of the double concave friction pendulum bearings used in the study.&2010 Elsevier Ltd. All rights reserved.

1. Introduction

For bridge applications,contemporaryseismic isolationsystems

provide horizontal isolation from the effects of earthquake shaking

to reduce forces. The main function of the seismic isolation system

is to increase the period of vibration by increasing the lateral

flexibility in the bridges or other structures.

Thedoubleconcave friction pendulum (DCFP)bearing is an innova-

tiveand viable isolationsystemthat is becoming a widespread applica-

tion for the earthquake protection of structures. The DCFP bearings

consistof twospherical stainlesssteel surfaces andan articulated slidercovered by a Teflon-based high bearing capacity composite material.

The concave surfaces may have the same radii of curvature. Also, the

coefficient of friction on the two concave surfaces may be the same or

not. Hyakuda et al. [1] presented the response of a seismically isolated

building in Japan where DCFP bearings are utilized. Experimental and

analytical results on thebehaviourof a systemhavingconcave surfaces

of both equal and unequal radii and both equal and unequal coefficient

of friction at the upper and lower sliding surfaces were presented by

Tsai et al. [2]. Constantinou [3] and Fenz and Constantinou [46]

described the principles of operation of the DCFP bearing and

presented the development of the forcedisplacement relationship

based on equilibrium. The theoretical forcedisplacement relationship

was verified through characterization testing of bearings with sliding

surfaces having the same and then different radii of curvature and

coefficients of friction. Finally, practical considerations for analysis and

design of DCFP bearings were presented.

Few researchers have dealt with the dynamic response of

straight and curved box girder bridges. Sennah and Kennedy [7]

highlighted the most important references related to develop-ment of current guide specifications for the design of straight and

curvedbox-girder bridges. DeSantiago et al. [8] analyzed a series of

horizontally curved bridges using simple finiteelementmodels and

reported that thebending moment in girders of a curvedbridge can

be about 23.5% higher than moments in girders of a straight bridge

of similar span and design configuration. Mwafy and Elnashai [9]

carried out a detailed seismic performance assessment of a multi-

span curved bridge including soilstructure interaction effects.

Constantinouet al.[10] manifested analysis anddesign proceduresfor

seismically isolated bridges and examples of analysis and design of

seismic isolation systems. Ates and Constantinou [11]carried out a

parametrical study associated with the effects of the earthquake

Contents lists available at ScienceDirect

journal homepage:w ww.elsevier.com/locate/soildyn

Soil Dynamics and Earthquake Engineering

0267-7261/$ - see front matter & 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.soildyn.2010.12.002

n Corresponding author.

E-mail address: [email protected] (S. Ates).

Soil Dynamics and Earthquake Engineering 31 (2011) 648661
http://-/?-http://www.elsevier.com/locate/soildynhttp://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.soildyn.2010.12.002mailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.soildyn.2010.09.002http://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.soildyn.2010.09.002mailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.soildyn.2010.12.002http://www.elsevier.com/locate/soildynhttp://-/?-

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ground motions on the seismic response of isolated curved bridges

including soilstructure interaction.

Soilstructure interaction (SSI) effect on the seismically isolated

bridges has been also studied by many researchers. Tongaonkar and

Jangid[12]observed that the soil surrounding the pier has significant

effects on the response of the isolated bridges and under certain

circumstances the bearing displacements at abutment locations may

be underestimated if the SSI effects are not considered in the response

analysis of the system. Cases in which SSI needs to be incorporated inseismically isolated bridge design are identified and ways to take

advantage of SSI in order to enhance safety level and reduce design

costs are recommended by Spyrakos and Vlassis [13]. Ucak and

Tsopelas[14]found that the results from comprehensive numerical

analyses show that soilstructure interaction causes higher isolation

system drifts as well as, in many cases, higher pier shears when

compared to the bridges without SSI. In the light of the studies, SSI can

have both beneficial and detrimental effects on the response of the

isolated bridges dependingon the characteristicsof thegroundmotion.

The main goal of this study is to set forth the dynamic response

of isolated curved bridges subjected to response spectrum. The

soilstructure interaction is also taken into account by springs

representing the soil beneath footing and drilled shaft. Displace-

ment capacities of the DCFP bearings are also evaluated.

2. Double concave friction pendulum bearings (DCFP)

Thedouble concave friction pendulum bearings aremadeof two

concave surfaces, which are called upper and lower, and is shown

inFig. 1.

Theconcave surfaces mayhavethe same radii of curvature. Also,

the coefficient of friction on the two concave surfaces may be the

same or not. The maximum displacement capacity of the bearing is

2d, where d is the maximum displacement capacity of a single

concave surface. Note that dueto rigid body andrelativerotation of

the slider, the displacement capacity is actually slightly different

from 2d. The forcedisplacement relationship for the DCFP bearing

is given by the following equation:

F W

R1h1 R2h2

Ub

Ff1R1h1 Ff2R2h2

R1h1 R2h2

1

whereWis the vertical load,R1andR2are radii of the two concave

surfaces, h1 and h2 are the part heights of the articulated slider and

Ub is thetotaldisplacement (bearing displacement), andthe sum of

the displacements on the upper and lower surfaces are given by

Ub 2d Ub1 Ub2 2

herein Ub1 and Ub2 are the displacements of the slider on the upper

and lower concave surface, respectively, and the individual dis-

placements on each sliding surfaces are

Ub1 FFf1

W

R1h1 3

Ub2 FFf2

W

R2h2 4

In Eqs. (3) and (4), Ff1 and Ff2 are the friction forces on the

concave surfaces 1 and 2, respectively. The forces are given by

Ff1 m1Wsgn_Ub1 5

Ff2 m2Wsgn_Ub2 6

where m1 andm2 are the coefficient of friction on the concave surfaces1 and 2, respectively; _Ub1 and

_Ub2 are sliding velocities at the upper

and lower surfaces, respectively; and sgn(U) denotes the signum

function. Most applications of the DCFP bearings will likely utilize

concave surfaces of equal radii, namely, R1R2. In this study, each

radius is calculated as 88 in. Parts heights of the articulated slider h1and h2 are nearlyequal in most cases. Thus, theeffective coefficient of

friction is equal to the average ofm1andm2, and is given by

me m1R1h1 m2R2h2

R1 R2h1h27

In Eq. (1), the first term is the stiffness of the pendulum

component (spring forces) and the second term is the stiffness of

the friction component. The natural period of vibration is given by

the following equation:

T 2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR1 R2h1h2

g

s 2p

ffiffiffiffiffiReg

s 8

wheregis the acceleration of gravity; and Reis the effective radius

of curvatures. Eq. (8) shows that the natural period of vibration is

independent of mass, but it is controlled by the selection of the

radius of the spherical concave surfaces. The important parameter

is employed as ReR1+R2h1h24.27 m. It is also shown in

Eq. (8) that the stiffness of the pendulum depends on the weight

carried by bearing. Thecoefficient of thefriction of thetwo concave

surfaces depends on the bearing pressure and is given by

m1,2 fmaxfmaxfminea9 _vb9 9

where fmax and fmin are the maximum and minimum mobilized

coefficients of friction, respectively; and a is a parameter that

controls the variation of the coefficient with the velocity of sliding.

Analysis of seismically isolated bridges will be performed for

each seismic loading case considered (design basis or maximum

considered earthquake) for twodistinct sets of mechanical proper-

ties of the isolation system.

Lower bound properties are defined to be the lower bound values

of characteristic strength and post-elastic stiffness that can occur

during the lifetime of the isolators. Typically, the lower bound values

describe the behaviour of fresh bearings, at normal temperature and

following the initial cycle of high speed motion. The lower bound

values of propertiesusually result in thelargest displacement demand

on the isolators. Upper bound properties are defined to be the upper

bound values of characteristic strength and post-elastic stiffness thatcan occur during the lifetime of the isolators and considering the

effects of aging, contamination, temperature and history of loading

and movement. Typically, the upper bound values describe the

behaviour of aged and contaminated bearings, following the move-

ment that is characteristic of substantial traffic loading, when

temperature is low and during the first high speed cycle of seismic

motion. The upper bound values of properties usually result in the

largest force demand on the substructure elements.

The lower and upper bound values of mechanical properties are

determined from nominal values of properties and the use of

system property modification factors. The nominal properties are

obtained either from testing of prototype bearings identical to the

actual bearings or from test data of similar bearings from previous

projects and the use of appropriate assumptions to account for

R1

R2

h1

h2

d d

1

2 The lower concave surface

The upper concave surface

ds

Fig. 1. Double concave friction pendulum (DCFP) bearings.

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uncertainty. Typically, the analysis and design of the isolated

bridge is based on the available data from past tests of similar

bearings. The assumptions made for the range of mechanical

properties of the isolators are then confirmed in the prototype

testing that follows. If the selection of the range of mechanical

properties is properly made, the prototype bearing testing will

confirm the validity of the assumptions and thereforethe validity of

the analysis and design. Accordingly, modifications of the design

would not be necessary. Such modifications often lead to delaysand additional costs.

3. Response spectrum method of analysis

The method is based on representing the behaviour of isolators

by linear elastic elements with stiffness equal to the effective or

secant stiffness of the element at the actual displacement. The

effect of energy dissipation of the isolation system is accounted for

by representing the isolators with equivalent linear viscous ele-

ments on the basis of the energy dissipated per cycle at the actual

displacement. The response is then calculated by use of response

spectra that aremodifiedfor theeffect of damping largerthan 5% of

the critical ones. Given that the actual displacement is unknown

until the analysis is performed, the methodrequires some iterationuntil the assumed and calculated values of isolator displacement

are equal.

The 5%-damped elastic response spectrum represents the usual

seismic loading specification. Spectra for higher damping need to

be constructed for the application of multi mode method. Elastic

spectra constructed for higher viscous damping are useful in the

analysis of linear elastic structures with linear viscous damping

systems. Moreover, they are used in the simplified analysis of

yielding structures or structures exhibiting hysteretic behaviour

since simplified methods of analysis are based on the premise that

these structures may be analyzed using equivalent linear and

viscous representations. The typical approach of constructing an

elastic spectrum for damping greater than 5% is to divide the 5%-

damped spectral acceleration by a damping coefficient or dampingreduction factorB:

SaT,b SaT,5%

B 10

whereSa(T,b) is the spectral acceleration at period Tfor damping

ratio b. Note that the spectral acceleration is the acceleration at

maximum displacement and is not necessarily the maximum.

Therefore, it is related directly to the spectral displacement Sdthrough

Sd T

2p

2Sa 11

The damping reduction factor B is a function of the damping

ratio and may be a function of the period. Eq. (10) is typically usedto obtain values of coefficient B for a range of values of period Tand

for selected earthquake motions. The results for the selected

earthquake motions are statistically processed to obtain average

or median values, which upon division of the value for 5% damping

to the value for dampingb results in the corresponding value ofB.

The results are affected by the selection of the earthquake motions

andthe procedures used to scale themotionsin orderto representa

particular smooth response spectrum. Furthermore, the values of

factor B used in codes and specifications are typically on the

conservative side, rounded and based on simplified expressions.

The values of factor B recommended by FEMA 440 [15] and

Eurocode 8[16]are given as follows, respectively:

B 4

5:6ln100b

12

and

B

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0:05b

0:10

r 13

The values of factor B in various codes and specifications are

nearly identical for values of damping ratio less than or equal to

30%. This is thelimitof damping ratio forwhichsimplified methods

of analysis can be used.

Consider a seismically isolated structure represented as a singledegreeof freedom systemwithmass m, weight Wand lateral force

displacement relation having bilinear hysteretic characteristics as

shown in Fig. 2. The system is characterized by characteristic

strengthQdand post-elastic stiffnessKd. For the friction pendulum

system, the characteristic properties are defined as below, corre-

spondingly:

Qd mW 14

Kd W

Re15

where m is the coefficient of friction at large velocity of sliding. Thedisplacement of the system for an earthquake, which is described

by a particular smooth response spectrum, can be identified as D.

The effective period of the system is given by[17,18]

Teff 2p

ffiffiffiffiffiffiffiffiffiffiffiW

Keffg

s 16

Keff Kd QdD

W

RemW

D 17

SubstitutingEqs. (14) and(15)) into Eq.(16),the effectiveperiod

of the system is rewritten as follows:

Teff 2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

g=Re mg=D

s 18

In addition,the effectivedampingof thesamesystem is given by

[17,18]

beff 1

2pEd

KeffD2

19

whereEd is the energy dissipated per cycle at displacement D and

period Teff. For the behaviour depicted in Fig. 2, the energy dissipated

per cycle is given by

Ed 4QdDY 20

where Yis the yield displacement of the system. Assuming Yis equal

to zero, Eqs. (14), (16) and (17) are substituted into Eq. (19) and the

effective damping of the system is easily obtained and then given in

Lateral

displacement

Lateral force

QdKd

Fig. 2. Idealized forcedisplacement relation of typical seismic isolation system.

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more useful form as

beff 2

p

m

m D=Re

21

Itshould benoted that Eq. (21) isvalidwhenYis zero as mentioned

above. The peak dynamic response of this system may be obtained

from the responsespectrumassuming that thesystem is linearelastic

with effective period Teff. Based on the value of effective dampingbeff,

the damping reduction factor B is calculated. The response of thesystem depending on spectraldisplacement and spectralacceleration

is calculated as the response obtained for 5% damping divided by

factor B. However, since the calculation is based on an assumed value

of displacement D, the process is repeated until the assumed and

calculated values of displacement are equal. This procedure repre-

sents a simplified method of analysis that is typically used for seismi-

cally isolated structures.

4. Description of example curved bridge

A curvedbridge is selected to exhibit the application for seismic

isolation. The bridge was used as an example of bridge design

without an isolationsystem in the Federal Highway Administration

(FHWA)Seismic Design Course, Design Example No. 6, prepared by

Berger/Abam Engineers Inc.[19]. The bridge is to be modelled and

analyzed in a seismic zone with an acceleration coefficient of 0.7g

defined by Caltrans[20].

Theconfiguration of thebridge is a three-span featuringcast-in-

place concrete box girder superstructure supported on reinforced

concrete columns found on drilled shafts and on integral abut-

ments founded on steel pipe piles. The bridge is located on site

underlain by a deep deposit of cohesionless material.

The alignment of roadway over the bridge is sharply curved,

horizontally (1041), but there is no vertical curve. The two inter-

mediate bents consist of rectangular columns with a cross beam on

top. The geometry of the bridge, section properties and foundation

properties are assumed to be the same as in the original bridge in

theFHWAexample. It is presumed that theoriginalbridge design issufficient to sustain the loads and displacement demands when

seismically isolated as described herein. The bridge is only used for

comparing purpose. The following assumptions are also made for

earthquake analyses of the bridges under consideration:

Bridge superstructure and piers are assumed to remain in theelastic state during the earthquake excitation. This is a reasonable

assumption as the base isolation attempts to reduce the earth-

quake response in such a way that the structure remains within

the elastic range.

The deck of the bridge is curved and is supported at discretelocations along its longitudinal axis by cross diaphragms.

Both superstructure and substructure are modelled as lumpedmass systems divided into the number of small discrete

segments. Each adjacent segment is connected by a node and

at each node three degrees of freedom are considered. The massof each segment is assumed to be distributed between the two

adjacent nodes in the form of point masses.

Stiffness contributions of non-structural elements such assidewalk and parapet are neglected.

The force-deformation behaviour of the bearing is considered tobe linear.

Thebearings provided at thepiersand abutmentshave thesamedynamic characteristics.

The drilled shaft is represented for all motions using a springmodel with frequency-independent coefficients. The modelling

of the drilled shaft on deformable soil is performed in the same

wayas that of thestructure andis coupled to perform a dynamic

SSI analysis.

Figs. 37 show, respectively, the plan and its dimensions,

developed elevation, framing plan, horizontal sections of the

substructure, section of the superstructure and section at the

center line of the pier as an intermediate bent. The bridge is

isolated with two isolators at each abutment and pier location for a

total of 8 isolators. The isolators are directly located above the cap

of the rectangular columns and the abutments. Two isolators are

intentionally used instead of more isolators due to the fact that the

distribution of load on each isolator is accurately calculated.

Additionally, the use of more than two isolators per a location

would have caused difficulties in the calculation of the axial and

increased the cost.

Diaphragms in thebox girderat theabutmentand pier locations

above the isolators are also taken into account, in view of rigidityand self weight in the finite element model of the curved bridge.

All arch lengths are as per along the center line of the bridge.

11.8

0m

33.50m

27.25m

Rc=48.77m

27.25m

88.00m

The center line

of the bridgeThe center line

of Abutment BThe center line

of Abutment A

Pier 1 Pier 2

Fig. 3. The curved bridge plan and its dimensions.

Fig. 4. Developed elevation of the curved bridge.


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5. Modelling of the drilled shaft for piers

The drilled shaft can be modelled by equivalent soil springs

method that is illustrated inFig. 8. With the use of this technique,

the drilled shaft is included in the finite element model, and the

foundation soil is modelled as a series of springs connected to the

drilled shaft at even intervals. It should be noted that spring

stiffness must be accurately selected to represent the best beha-

viour. The soil springs at each depth are calculated using acoefficient of horizontal subgrade reaction that increases linearly

with depth and is inversely proportional to the cross sectional

dimension of the drilled shaft[21].

A sufficient number of springs should be used along the length

of the drilled shaft. The springs near the surface are usually the

most important to characterize the response of the drilled shaft

surrounded by the soil; thus a closer spacing may be used in that

region. However, in general springs evenly spaced at about half the

diameter of the drilled shaft are recommended [19].

In this study, the diameter of the drilled shaft is 2.40 m and the

drilled shaft is 18 min length. Consequently, 15 springs areused on

the center along the length of the drilled shaft. The springs are

arranged at 1.20 m intervals butat theends thesegmentsare taken

as 0.60 m in such a way that all the spring constants are calculated

based on 1.20 m tributary length of the drilled shaft. The men-

tioned arrangement is implemented such as in Fig. 8. The soil

properties beneath thefoundation of thebridge aregiven in Table 1

[19]. Inthistable, g is thetotal unit weight;f is theinternalangleoffriction; cis cohesion and nhis the constant of horizontal subgrade

reaction. New fill will be required at the abutments. The fill has

similar properties to the native soil.

In order to calculate the horizontal stiffness of the equivalent soil

springs, the coefficient of horizontal subgrade is given below [19]:

kh nhz

D 22

in which z is the depth in reference to the ground surface;D is the

diameter of the drilled shaft. The horizontal stiffnessof the equivalent

soil springs based on the coefficient of horizontal subgrade is

ki khDHtrib 23

where Htrib represents the height of tributary soil spring. Substituting

Eq. (22) into Eq. (23), the horizontal stiffness of the equivalent soil

springs can be rewritten as follows:

ki nhzHtrib 24

The horizontal stiffness of the equivalent soil springs is tabu-

lated inTable 2whereHtribis 1.20 m as per Eq. (24).

RadialDirection

Chord

Direction

88.00m

33.50m

27.25m 27.25m

76cm

23cm

90cm

Y

XZ

Fig. 5. Framing plan of the curved bridge.

Drilled shaft section:Column section:

The center line of thepier1 or 2

170cm

85cm

10

0cm

The center line of thebridge

85cm

50cm

50cm

Deck section:

1180cm

290cm 280cm 290cm100cm 100cm30cm30cm 30cm 30cm

1

70cm

25cm

18cm

240cm

Fig. 6. Horizontal sections of the substructure and the deck of the curved bridge.


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As shown in Fig. 8, vertical movement of drilled shaft isrestrained by an infinitely stiff spring at the base of the shaft.

Actual vertical resistance occurs via skin friction and end bearing.

However, for this analysis, the simplification of restrainingonly the

base of the drilled shaft is felt to be reasonable. Similarly, torsional

movement of the drilled shaft would be resisted by skin friction.

However, no torsional restraint was used in the mathematical

model. Theresponse is notsensitive tothe lack of torsionalrestraint

in the drilled shaft, and this can be demonstrated by simple

bounding analyses[19].

6. Modelling of the foundation stiffness for abutments

The abutments are modelled with three dimensional frameelements.The abutment is depictedin Fig.9a. The springs represent

the piles as shown inFig. 9b. The stiffness of the springs is given in

Table 3 for the vertical, longitudinal, transverse and rotational

directions as per each connection point between the abutment and

thepiles, respectively, taking advantage of the design example [19]

for calculating the stiffness.

7. Selection and usage of the spectrum

The response spectrum specified for the analysis is the 5%-

damped spectrum modified for the effects of the higher damping.

The ordinates of the 5%-damped response spectrum for values of

period larger than 0.8Teffare divided by the damping reduction

64

0cm

18

00cm

240cm

Ground Surface

30cm

25cm

180cm

10% Slope

Rigid beam

element

Fig. 7. Section at the center line of the pier of the curved bridge.

Z

XY

kr = 0

kv = Bedrock

Medium dense, silty

sand

i

kiki

Z

Ground surface

60cm

60cm

14@120cm=1680cm

1800cm

Fig. 8. Equivalent soil spring model of the drilled shaft and its geometry and

element layout.

Table 1

Soil properties for the subsurface materials.

Stratum Depth (m) Soil description g(kN/m3) f (deg.) nh(kN/m3)

Alluvium 0 to 4100 Medium dense,

silty sand

19 34 4000

New Fill Above grade Medium dense

sand and gravel

19 34 6250

Table 2

The horizontal stiffness of the equivalent soil springs of the drilled shaft.

Depthz(m) Spring stiffness

ki (kN/m)

0.60 3021

1.80 9077

3.00 15,133

4.20 21,189

5.40 27,231

6.60 33,287

7.80 39,343

9.00 45,385

10.20 51,441

11.40 57,497

12.60 63,553

13.80 69,595

15.00 75,651

16.20 81,707

17.40 87,749

18.00 Rigid


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factor B forthe effectivedampingof theisolatedbridge.Whereas all

modes are assumed to be damped at 5%, in this approach, only the

isolated modes of the structure are allowed the reduction of

response due to increased damping. Note that the modification

of the spectrum for higher damping requires that the effective

period and effective damping in each principal direction should be

calculated. This is done using the single degrees of freedom system

of analysis.Fig. 10presents the response spectrum used in multi

mode analysis of a seismically isolated bridgesupported on thesoil

profile type C [20]. Forthe soil type, the data accelerationspectrum

is dedicated in Table 4. The effective period is Teff2.636 s, the

effective damping is beff0.30 and the damping reduction factor

B1.82. The ordinates of the 5%-damped spectrum for period

larger than 2.11 s are divided by factor 1.82.

Analysis by the multi mode method should be independently

performed in two orthogonal directions and the results be combined

using the 10030% combination rule. The two orthogonal directions

may be any two arbitrary perpendicular directions that facilitate the

Table 3

Stiffness of the equivalent soil springs standing for the pipe piles.

Stiffness Spring location name

1 and 7 2 and 6 3 and 5 4

klong (kN/m) 5356 5356 5356 5356Longitudinal translationktrans(kN/m) 4320 4 320 4320 4320Transverse translationkver(kN/m) 608,083 608,083 608,083 608,083Vertical translationkrv(kNm/rad) 152,360 67,720 16,933 0Rotation about vertical axiskrl(kNm/rad) 17,298,935 7,688,420 1,922,320 0Rotation about longitudinal axis

krt(kNm/rad) 0 0 0 0Rotation about transverse axis

Note:krv kverd2i krl klongd2i krt ktrand

2i where di is the distance between the

center lines of the abutment and the ith pipe pile. In this study, the distance is 180,

2 180and3 180 cm rangingfrom theinnermost of thepipe pileto theoutermost

one, respectively.

Sa(T,5%) Sa(T,5%)

B

0.00

Period (sec)

0.00

0.50

1.00

1.50

2.00

pectra

cceeratong

0.8Teff

2.11sec

0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.0

Fig. 10. Acceleration response spectrum curve for soil profile type C.

CL

50cm50cm

540cm 540cm

1180cm

100cm

End diaphragm

75cm

Pipe piles filled

with

concrete

100cm

ktrans

krt=0

krv

kvert

klong

krl

1 2 34

56

7

180cm180cm180cm180cm 180cm 180cm

Fig. 9. (a) The real abutment and (b) the analytical model of the abutment having the equivalent springs representing the soil.


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analysis. The most convenient is the use of the longitudinal and

transverse bridge directions. For curved bridges, the longitudinal axis

may be takenas thechord connecting thetwo abutments. The vertical

ground acceleration effect can be included, using rational methods of

analysis and combined using the 1003030% rule. The interested

reader is referred to Wilson et al.[22]. The procedure is employed in

this study.

8. Finite element model of the curved bridge

The finite elemet model of the curved bridge consists of solid

elemets having 3 degrees of freedom at each nodal point. They are

in horizontal and vertical translational directions. In this model, the

drilled shaft is also included by equivalent soil springs mentioned

above in such a waythatthe foundation soil is considered as a series

of springs connectedto thedrilled shaft at even intervals. Thethree

dimensional finite element models are represented with the

diagram in Fig. 11. The model generated in SAP2000 [23] has

9031 nodal points and 5060 solid area elements. In addition frame

elements are used representing columns, cap beam and drilled

shafts, and the springs representing soil stiffness. Additionally, the

DCFP bearings on the abutments and the cap beams of the piers are

defined using equivalent beam element as well. The super-eleva-

tion having a slope of 10% is also taken into account in the finite

element modelin order that torsionalstressesof thegirders arenot

overlooked. Thecrosssectionalpropertiesof thebridge aregiven in

Figs. 6 and 7. Additionally, the modulus of elasticity of concrete is

taken as 3.2 107

kN/m2

.

9. Modelling of double concave friction pendulumfor response

spectrum analysis

Each isolator may be modelled as a vertical three dimensional

beam element rigidly connected at its two ends of lengthh, areaA,

moment of inertia about both bending axes Iand torsional constant

J. Theelement lengthis theheight of thebearing, h0.30 m andthe

area is the contact area, which is a circle of 0.25 m diameters. Note

that the element is intentionally used with rigid connections at its

two ends so that PD effects can be properly accounted for in the

case of the double concave bearing.

To properly represent the axial stiffness of the bearing, themodulus of elasticity is specified to be related but less than the

modulus of steel, so it can be taken as 1.05 107 kN/m2. The

bearing is not exactly a solid piece of metal so that the modulus is

reduced to half to approximate the actual situation. Torsional

constant is set J0 or a number near zero since the bearing has

insignificant torsional resistance. Moreover, shear deformations in

theelementare de-activatedby specifying very large areas in shear.

The moment of inertia of each element is calculated by the

following equation:

IKeffh

3

12E 25

where Keff is the effective stiffness of the bearing. The required

values outlined above for the linear link element for the DCFPbearings are demonstrated inTable 5.

Response spectrum analysis is performed using the response

spectrum ofFig. 10for 0.7gafter division by parameterB for periods

larger or equal to 0.8TM, whereTMis the effective period andB is the

parameterthat relates the5%-damped spectrum to thespectrumat the

effective damping. Values of 0.8TMare 2.72 s for lower bound analysis

and 2.11 s for upper bound analysis. Values of spectral acceleration

used in theanalysis arepresented in Table 4. The modified values ofthe

acceleration per the above rule are in grey colour in Table 4.

Eigen modal and multi mode response spectrum analyses were

performed in SAP2000 [23]. Figs. 12 and 13 offerthe modeshapes of

thefirst three modesof vibration of the isolated bridgein the lower

Fig. 11. Three-dimensional finite element model of the curved bridge.

Table 5

The required values of friction pendulum for the response spectrum analysis.

Bearing

location

Parameter Lower bound

properties

Upper bound

properties

Abutment Keff(kN/m) 388.76 840.57

h(m) 0.30 0.30

E(kN/m2) 1.05 108 1.05 108

A(m) 0.051 0.051

I(m4) 9.177 10-9 4.374 10-9

Pier Keff(kN/m) 781.03 1190.80

h(m) 0.30 0.30

E(kN/m2) 1.05 108 1.05 108

A(m2) 0.051 0.051

I(m4) 18.436 10-9 28.109 10-9

Table 4

Spectral acceleration used in response spectrum analysis.

Period (s) Spectral acceleration (g)

Original Vertical Modified for lower

bound properties

Modified for upper

bound properties

0.05 0.70 0.49 0.70 0.70

0.05 0.70 0.49 0.70 0.70

0.10 1.29 0.90 1.29 1.29

0.24 1.77 1.24 1.77 1.77

0.30 1.80 1.26 1.80 1.80

0.50 1.72 1.20 1.72 1.72

0.75 1.44 1.01 1.44 1.44

1.00 1.19 0.83 1.19 1.19

1.25 0.95 0.67 0.95 0.95

1.50 0.78 0.55 0.78 0.78

1.75 0.64 0.45 0.64 0.64

2.00 0.55 0.39 0.55 0.552.10 0.51 0.36 0.51 0.51

2.11 0.51 0.36 0.51 0.28

2.25 0.48 0.34 0.48 0.27

2.50 0.41 0.29 0.41 0.23

2.60 0.40 0.28 0.40 0.22

2.68 0.39 0.27 0.39 0.22

2.72 0.38 0.27 0.24 0.22

2.75 0.37 0.26 0.23 0.21

3.00 0.32 0.22 0.19 0.18

3.25 0.29 0.20 0.18 0.16

3.50 0.25 0.18 0.15 0.14

3.75 0.23 0.16 0.14 0.13

4.00 0.20 0.14 0.12 0.11


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and upper boundanalyses,respectively. Analyses are performedby

separately applying the earthquake excitation in the chord, radial

and vertical bridge directions as defined in Fig. 5. The vertical

response spectrum is taken as a 70% portion of the horizontal 5%-

damped spectrum without any modification for increaseddamping

and then is given inTable 4.

10. Numerical results for the DCFP bearing

The results of these analyses are presented in Tables 6 and 7in

terms of the bearing displacements, isolation shear force and bearing

axial forces dueto earthquake. Observations to be made in theresults

of multi mode responsespectrum analysesarethat thedisplacements

Table 6

Significant response quantities for the abutments obtained by multi mode response spectrum analysis of the isolated bridge with the DCFP.

Response name Earthquake direction Properties type of

the DCFPs

Chord(100%) Radial(100%) Vertical(100%)

DM(cm) 37.30 65.50 0.46 Lower bound

41.12 47.85 0.43 Upper bound

DTM(cm) ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

65:502 0:30 37:302 0:30 0:432q

ffi66 Lower boundffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi

47:852 0:30 41:122 0:30 0:432q

ffi 50 Upper bound

Bearing shear force (kN) 159.86 186.02 1.78 Lower bound

313.85 545.73 3.87 Upper bound

Bearing axial force (kN) 153.41 865.18 1229.78 Lower bound

180,59 1081.31 1229.16 Upper bound

Bearing total axial force (kN) ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1,229:782 0:30 865:182 0:30 153:412q

ffi1260 Lower bound

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffi1,229:162 0:30 1,081:312 0:30 180:592q ffi1270 Upper bound

Mode 1: T1= 2.636 sec Mode 2: T2= 2.530 sec

Mode 3: T3= 2.087 sec

Fig. 13. The first three modes of vibration of the isolated curved bridge with upper bound properties of the DCFP.

Mode 1: T1= 3.400 sec Mode 2: T2= 3.305 sec

Mode 3: T3 = 2.951 sec

Fig. 12. The first three modes of vibration of the isolated curved bridge with lower bound properties of the DCFP.


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of the abutment and pier bearings are different due to the pier

flexibility effect and the inertia effects in the substructure. Accord-

ingly, the abutment bearings experience lesser displacement. Max-

imum axial bearing forces develop when the earthquake excitation is

in the vertical direction only. Maximum bearing displacement occurs

whenthe bridge is under the radial directional earthquake. Thisresult

for earthquake is nearlythe same as theexpected value as 70 cm.This

is in good agreement in view of selectionof thedisplacement capacity

of theDCFPbearings recommendedby Constantinouet al. [24].Onthe

other hand, maximum shear forces at the isolated level are formed in

case of the bridge isolated by the DCFP bearings is having the upper

bound properties.

Tables 6 and 7 show a comparison of significant response

quantities obtained by the multi mode response spectrum methods

of analysis. In each type of the analyses,quantity DTMis calculated as

the vector sum of bearing displacements due to chord, radial and

Lower Bound Properties

Upper Bound Properties

16000

12000

8000

4000

0

B

endingMoment(kNm)


Upper Bound Properties8000

6000

4000

2000

0

BendingMoment(kNm)



9060300 9060300

Bridge Length (m)

16000

12000

8000

4000

0

BendingMoment(kNm)

Bridge Length (m)

9060300 9060300

Bridge Length (m) Bridge Length (m)

9060300 9060300

Bridge Length (m) Bridge Length (m)

16000

12000

8000

4000

0

BendingMoment(kNm)

Non-isolated Bridge

16000

12000

8000

4000

0

B

endingMoment(kNm)

Isolated Bridge

8000

6000

4000

2000

0

BendingMoment(kNm)

Fig.14. (a) Bendingmomentaboutthe center lineaxis of theisolated andnon-isolated curved bridgessubjected to verticaldirectional earthquake.(b) Bendingmomentabout

thecenterline axisof theisolatedand non-isolatedcurvedbridges subjected to chord directional earthquake.(c) Bendingmomentaboutthe centerline axisof theisolatedand

non-isolated curved bridges subjected to radial directional earthquake.

Table 7

Significant response quantities for the piers obtained by multi mode response spectrum analysis of the isolated bridge with the DCFP.

Response name Earthquake direction Properties type of

the DCFPs

Chord (100%) Radial(100%) Vertical(100%)

DM(cm) 47.00 64.50 2.03 Lower bound

42.37 47.55 0.20 Upper bound

DTM(cm) ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

64:502 0:30 47:002 0:30 2:032q

ffi 66 Lower boundffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

47:552 0:30 42:372 0:30 0:202q

ffi 49 Upper bound

Bearing shear force (kN) 327.60 345.03 3.02 Lower bound

408.82 699.71 6.85 Upper bound

Bearing axial force (kN) 278.98 612.53 2227.11 Lower bound

297.22 849.92 2226.62 Upper boundBearing total axial force (kN)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2227:112 0:30 612:532 0:30 278:982

q ffi2236

Lower boundffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffi2226:622 0:30 849:922 0:30 297:222

q ffi2243

Upper bound


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Lower Bound PropertiesUpper Bound Properties

Bridge Length (m)

5000

4000

3000

2000

1000

0

TorsionalMoment(kNm)


Bridge Length (m)

5000

4000

3000

2000

1000

0



90300 60 90300 60

90300 60 90300 60

90300 60 90300 60

Bridge Length (m)

20000

16000

12000

8000

4000

0

TorsionalMoment(k

Nm)

Non-isolated BridgeIsolated Bridge

BridgeLength (m)

20000

16000

12000

8000

4000

0

TorsionalMoment(k

Nm)

Bridge Length (m)

5000

4000

3000

2000

1000

0


Bridge Length (m)

5000

4000

3000

2000

1000

0


Fig. 15. (a) Torsional moment about the center line axis of the isolated and non-isolated curved bridges subjected to vertical directional earthquake. (b) Torsional moment

about the center line axis of the isolated and non-isolated curved bridges subjected to chord directional earthquake. (c) Torsional moment about the center line axis of the

isolated and non-isolated curved bridges subjected to radial directional earthquake.



4000

3000

2000

1000

0

4000

3000

2000

1000

0

ShearForce(kN)



80

60

40

20

ShearForce(kN)



0

Bridge Length (m)

1200

800

400

0

ShearForce(kN)

1200

800

400

0

ShearForce(kN)


ShearForce(kN)

360

320

280

240

200

160

ShearForce(kN)

906030 0

Bridge Length (m)

906030

0

Bridge Length (m)

906030 0

Bridge Length (m)

906030

0

Bridge Length (m)

906030 0

Bridge Length (m)

906030

Fig. 16. (a) Shear forces of the isolated and non-isolated curved bridges subjected to vertical directional earthquake. (b) Shear forces of the isolated and non-isolated curved

bridges subjected to chord directional earthquake. (c) Shear forces of the isolated and non-isolated curved bridges subjected to radial directional earthquake.


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vertical earthquake components combined using the 1003030%

rule. The axial bearing forces are calculated as the sum of bearing

axial forces due to chord, radial and vertical earthquake components

combined using the 1003030% rule. Note that for the case of the

bearing axial forces the combination used is the one that corre-

sponds to 100% of vertical earthquake. This case is the worst for the

DCFP bearings since the axial load becomes the maximum and

lateral displacement is less than the maximum value. The results

demonstrate very good agreement with the pre-calculated bearing

displacement demands.

Bridge Length (m)

8000

6000

4000

2000

0

AxialForce(kN)



800

400

0

AxialForce(kN)

8000

6000

4000

2000

0

AxialForce(kN)

0

Bridge Length (m)

8000

6000

4000

2000

0

AxialForce(kN)

8000

6000

4000

2000

0

AxialForce(kN)


1200

800

400

0

AxialForce(kN)

906030 0 906030

Bridge Length (m)

0

Bridge Length (m)

906030 0 906030

Bridge Length (m)

0

Bridge Length (m)

906030 0 906030

Fig. 17. (a) Axial forces of the isolated and non-isolated curved bridges subjected to vertical directional earthquake. (b) Axial forces of the isolated and non-isolated curved

bridges subjected to chord directional earthquake. (c) Axial forces of the isolated and non-isolated curved bridges subjected to radial directional earthquake.

Table 8

Structural accelerations of the marked point of the curved bridge (PGA

0.7g686.70 cm/s2).

Earthquake

direction

Acceleration (cm/s2)

Isolated

(Lower)

Isolated

(Upper)

Non-

Isolated

Max. Max. Max.

Vertical

ax 0.18 0.30 3.78

ay 88.90 93.85 314.17

az 1084.91 1082.27 1425.02Chord

ax 160.22 239.22 1636.93

ay 1.98 3.43 5.03

az 13.36 12.32 9.88

Radial

ax 1.96 3.66 5.64

ay 185.72 420.55 1736.62

az 214.48 207.06 789.46

Table 9

Structural displacements of the marked point of the curved bridge.

Earthquake direction Displacement (cm)

Isolated (Lower) Isolated (Upper) Non-Isolated

Max. Max. Max.

Vertical

ux 0.00 0.00 0.03

Uy 0.25 0.28 2.44

uz 2.64 2.62 13.13

Chord

ux 46.43 41.73 15.98uy 0.46 0.46 0.05

uz 0.03 0.03 0.08

Radial

ux 0.46 0.53 0.03

uy 47.55 65.86 8.28

uz 0.36 0.33 4.95


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11. Numerical results of the isolated curved bridge

As per the results, internal forces for the isolated and non-

isolated curved bridges subjected to acceleration response spectra

are clarified withFigs. 1417. The graphics include the lower and

upper bound properties of the double concave friction pendulum,

and maximum and minimum values of the internal forces such as

bending andtorsional moments,and shear andaxial forces forboth

bridge configurations. The response spectra are separately appliedto theconsidered bridgein thechord, radial andvertical directions.

Fig. 14ac compares the results of the bending moments about

radial directionobtainedusing theresponse spectrum method. It is

noted that the responses obtained at the deck are compared for

isolated and non-isolated bridge models when subjected to earth-

quake ground motions. When the vertical directional earthquake is

applied to the bridge with isolation bearings, the bending moments

arenearly thesame for the lower andupper boundpropertiescasesof

the DCFP bearings. But, the differences arise in case the bridge is

subject to the two horizontal directions. The deck bending moments

obtained from the response spectrum analysis of the isolated curved

bridge decreasearound 6590% if these arecomparedwith the results

obtained for the non-isolated curved bridge. The results clearly show

that consideration of double concave friction pendulum bearings for

the isolation of the curved bridges for the response spectrum analysis

decreases the deck bending moments. Additionally, effectiveness of

theseismic isolation on the bending momentsof thecurved bridges is

about in portion as 1015% and in the trend of a decline when the

bridge is subjectedto thevertical earthquake ground motion.Hence,it

is not to ignore that the vertical direction of the earthquake is more

effective on the bridges.

The outcomes of torsional moment about chord axis of the

isolated and non-isolated curved bridges subjected to chord, radial

and vertical directional earthquakes are depicted inFig. 15ac. In

the light of the figures, it is seen thatthe seismic isolation systemis

important for reduction of the undesirable torsional effects.

The reduction of the deck shear and axial forces obtained for the

isolated curved bridgeis obvious, if theforces arecomparedwith those

obtained for the non-isolated curved bridge as seen in Figs. 16 and 17.

It can also be added that the responses by the lower bound

properties are smaller than the upper bound ones.

Tables 8 and 9 give an opportunity to compare the structural

accelerations and displacements on the bridge, which are marked

inFig. 5. It can be seen that the structural accelerations consider-

able decrease in case seismic isolation technique is used. However,

the structural displacements as expected increase compared with

these of non-isolated bridge.

12. Conclusion

This study outlines an investigation about the responses of the

isolated and non-isolated curved bridges subjected to responsespectra as per Caltrans Seismic Design Criteria, Version 1.4 (2006)

for magnitude 7.2570.25, 0.7g acceleration and soil profile C. In

order to seismically isolate the bridge, the double concave friction

pendulum bearings as isolation devices are placed between the

deck and the pier/the abutments as isolation devices. Response

history acceleration of the selected ground motions is considered as

the earthquake ground motion. The analyses are carried out for the

isolated and non-isolated bridges, separately. The soilstructure

interaction is also considered by springs representing the soil

beneath footing and the drilled shaft surrounding of soil. The

maximum and minimum response values of the isolated and non-

isolated bridges are compared with each other for different cases.

According to the response spectrum analysis, the displacements

of the abutment and pier bearings are different due to the pier

flexibilityeffect and inertia effects in the substructure. Accordingly,

the abutment bearings experience lesser displacement. Maximum

axial bearing forces develop when the earthquake excitation is in

the vertical direction of the response spectrum.

Maximum bearing displacement occurs when the bridge is under

the radial directional earthquake. Besides, the total maximum dis-

placement of each bearing is calculated as the vector sum of bearing

displacements due to vertical, chord and radial earthquake compo-

nents combined using the 1003030% rule and obtained as nearly66 cm in case the lower bound properties of the DCFP bearings are

considered. The displacement capacity is overestimated as compared

to thereference regarding response historyanalysis [11]. Similarly,the

shear forces at the DCFP bearings level, the accelerations transmitted

to structures and displacements obtained from response history

analysis are some of the larger values than those obtained from the

response spectrum analysis.

While the structural accelerations are decreased on the bridge,

spectral displacements are increased due to the usage of the DCFP

bearings as seismic protectors.

Finally, it is pointed out that the base isolation of the considered

curved bridge subject to the response spectra significantly decreases

the deck responses.

Acknowledgement

The authors acknowledge the Scientific and Technical Research

Council of Turkey (TUBITAK) for supporting the studies of Sevket

ATES at the University at Buffalo.

References

[1] Hyakuda T, Saito K, Matsushita T, Tanaka N, Yoneki S, Yasuda M, Miyazaki M,Suzuki A, Sawada T. The structural design and earthquake observation of aseismic isolation building using Friction Pendulum system. In: Proceedings ofthe 7th international seminar on seismic isolation, passive energy dissipationand active control of vibrations of structures, Assisi, Italy; 2001.

[2] Tsai CS, Chen WS, Chiang TC, Chen BJ. Component and shaking table tests forfull-scale multiple friction pendulum system. Earthquake Engineering andStructural Dynamics 2006;35:165375.

[3] Constantinou MC. Friction pendulum double concave bearing. NEES Report.Available at: /http://nees.buffalo.edu/dec304/FP-DC%20Report-DEMO.pdfS;2004.

[4] Fenz DM, Constantinou MC. Behavior of double concave friction pendulumbearing. Earthquake Engineering and Structural Dynamics 2006;35(11):140324.

[5] Fenz DM, Constantinou MC. Spherical sliding isolation bearings with adaptivebehavior: theory. Earthquake Engineering and Structural Dynamics 2008;37:16383.

[6] Fenz DM, Constantinou MC. Spherical sliding isolation bearings with adaptivebehavior: experimental verification. Earthquake Engineering and StructuralDynamics 2008;37:185205.

[7] Sennah KM, Kennedy JB. State-of-art- in design of curved box-girder bridges.Journal of Bridge Engineering 2001;6(3):15967.

[8] DeSantiago E, Mohammadi J, Albaijat HMO. Analysis of horizontally curvedbridges using simple finite-element models. The Practice Periodical onStructural Design and Construction 2005;10(1):1821.

[9] Mwafy AM, Elnashai AS. Assessment of seismic integrity of multi-span curvedbridges in mid-America.IL, USA: Mid-America Earthquake Center Civil andEnvironmental Engineering Department, University of Illinois at Urbana-Champaign; 2007.

[10] Constantinou MC, Whittaker AS, Fenz DM, Apostolakis G. Seismic isolation ofbridges.Report submittedto the State of California Department of Transporta-tion; 2007.

[11] Ates S, Constantinou MC. Example of application of response history analysisfor seismically isolated curved bridges on drilled shaft withspringsrepresent-ing soil. Soil Dynamics and Earthquake Engineering 2010, doi:10.1016/

j.soildyn.2010.09.002.[12] Tongaonkar NP, Jangid RS. Seismic response of isolated bridges with soil

structure interaction. Soil Dynamics and Earthquake Engineering 2003;23:287302.

[13] Spyrakos CC, Vlassis AG. Effect Of soilstructure interaction on seismicallyisolated bridges. Journal of Earthquake Engineering 2002;6(3):391429.

[14] Ucak A, Tsopelas P. Effect of soilstructure interaction on seismic isolated

bridge. Journal of Structural Engineering 2008;134(7):115464.

http://nees.buffalo.edu/dec304/FP-DC%20Report-DEMO.pdfhttp://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.soildyn.2010.09.002http://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.soildyn.2010.09.002http://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.soildyn.2010.09.002http://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.soildyn.2010.09.002http://nees.buffalo.edu/dec304/FP-DC%20Report-DEMO.pdf

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[15] Federal EmergencyManagement Agency. FEMA440, Improvementof NonlinearStatic Seismic Analysis Procedures. Washington DC; 2005.

[16] European Committee for Standardization. Design of Structures for EarthquakeResistance. Part 2: Bridges, Eurocode 8, EN1998-2, draft; August 2005.

[17] American Association of State Highway and Transportation OfficialsAASHTO.Guide specifications for seismic isolation design. Washington, D.C; 1999.

[18] CaliforniaBuildings StandardsCommission. CaliforniaBuilding Code, Sacramento,California; 2001.

[19] Berger/Abam Engineers, Inc. Federal Highway Administration Seismic DesignCourse, Design Example No. 6, Publication no. FHWA-SA-97-011 and Barcodeno. PB97-142111; 1996.

[20] California Department of TransportationCaltrans. Seismic Design Criteria,Version 1.4; 2006.

[21] TerzagiK. Evaluation ofcoefficientof subgradereaction.Geotechnique,London1955;5:4.

[22] Wilson E, Suharwardy I, Habibullah E. A clarification of the orthogonal effectsin a three-dimensional seismic analysis. Earthquake Spectra 1995;11:4.

[23] SAP2000.Integratedfiniteelementanalysis anddesignof structuresbasicanalysisreference manual. Berkeley, California: Computer and Structures Inc.; 2007.

[24] ConstantinouMC, WhittakerAS,Kalpakidis Y,Fenz DM,WarnGP.. Performanceof seismic isolation hardware under service and seismic loading. Technicalreport MCEER-07-0012, Buffalo, NY; 2007.


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