example of application of response history analysis for seismically isolated curved bridges on...

Soil Dynamics and Earthquake Engineering 31 (2011) 334–350

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Soil Dynamics and Earthquake Engineering

0267-72

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/soildyn

Example of application of response history analysis for seismically isolatedcurved bridges on drilled shaft with springs representing soil

Sevket Ates a, Michael C. Constantinou b,n

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 2 July 2010

Received in revised form

3 September 2010

Accepted 7 September 2010

61/$ - see front matter & 2010 Elsevier Ltd. A

016/j.soildyn.2010.09.002

esponding author.

ail address: [email protected] (M.C. C

a b s t r a c t

The main objective of this study is to perform a parametrical study associated with the effects of the

earthquake ground motions on the seismic response of isolated curved bridges including soil–structure

interaction.

For the isolated bridge system, double concave friction pendulum bearings are placed between the

deck and the piers, the abutments as isolation devices. A curved bridge is selected to exhibit the

application for seismic isolation. The bridge is to be modeled and analyzed in a seismic zone with an

acceleration coefficient of 0.7g. The configuration of the bridge is a three-span, 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. The bridge is located on site underlain by a deep deposit

of cohesionless material. The drilled shaft–soil system is modeled by equivalent soil springs method,

and is included in the finite element model. The soil is modeled as a series of springs connected to the

drilled shaft at even intervals.

The reduction of the internal forces on the deck for the isolated curved bridge is observed, if the

forces are compared with those obtained for the non-isolated curved bridge.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Curved bridges have been frequently constructed in multi-level junctions, and to cross an obstacle such as a river, a canal ora railway on which if there need a curve shape connection to jointwo of the roads. The bridge type is picked over others as anexample to show the effect of earthquake ground motions on thecurved bridges due to the fact that torsional stresses of the girdersare the most challenging and interesting part of the designprocess. In the design of curved girder bridges, the engineer isfaced with a complex stress situation, since these types of bridgesare subjected to both bending and torsional forces. In general, thetorsional forces consist of two parts such as St. Venant’s andwarping. Thus, the procedure is significantly difficult to determinethe induced stresses of a curved girder.

A curved bridge, the reason for the selection is mentionedabove, is modeled and analyzed with and without isolatorsaccording to seismic design of bridges procedures obtaining fromFederal Highway Administration Seismic Design Course, DesignExample no. 6.

ll rights reserved.

onstantinou).

The use of horizontally curved bridges has been increased tomeet the demand of highway construction. When an alignmentrequires for a horizontal curve, engineers design a series ofsimple-span straight chords. A comparison of straight-chordedsections to curved sections showed that curved members aremore economical than straight-chorded members [1,2]. Mwafyand Elnashai [3] carried out a detailed seismic performanceassessment of a multi-span curved bridge including soil–structureinteraction effects.

It has been, recently, reported in the Wenchuan earthquake ofChina in 2008 that the four curved spans of the Baihau bridge inYigxiu township collapsed, whereas the other parts of the mentionedbridge that are straight span are safely remained on foot [4].

The seismic design of bridges relies on the dissipation ofearthquake-induced energy through nonlinear response in se-lected components of the structural frame. Such response isassociated with structural damage that produces direct loss repaircost, indirect loss such as possible closure, rerouting, businessinterruption and perhaps casualties such as injuries and loss oflife. Importantly, traditional seismic analysis and design proce-dures do not permit the accurate estimation of structuraldeformations and damage, making it impossible to predict thelikelihood of direct and indirect losses and casualties.

Seismic protective systems, herein assumed to include seismicisolators and energy dissipation devices, were developed to

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https://www.researchgate.net/publication/32962326_Assessment_of_Seismic_Integrity_of_Multi-Span_Curved_Bridges_in_Mid-America?el=1_x_8&enrichId=rgreq-73568711-b828-4653-9332-af9a00e989ad&enrichSource=Y292ZXJQYWdlOzIzMjM5MDUxMDtBUzoxNDU2MTU4ODc1NDAyMjRAMTQxMTcyODk0MTY1NA==

https://www.researchgate.net/publication/242392010_Experimental_and_Analytical_Studies_of_a_Horizontally_Curved_Steel_I-Girder_Bridge_during_Erection?el=1_x_8&enrichId=rgreq-73568711-b828-4653-9332-af9a00e989ad&enrichSource=Y292ZXJQYWdlOzIzMjM5MDUxMDtBUzoxNDU2MTU4ODc1NDAyMjRAMTQxMTcyODk0MTY1NA==

https://www.researchgate.net/publication/245281453_Historical_Perspective_on_Horizontally_Curved_I_Girder_Bridge_Design_in_the_United_States?el=1_x_8&enrichId=rgreq-73568711-b828-4653-9332-af9a00e989ad&enrichSource=Y292ZXJQYWdlOzIzMjM5MDUxMDtBUzoxNDU2MTU4ODc1NDAyMjRAMTQxMTcyODk0MTY1NA==

S. Ates, M.C. Constantinou / Soil Dynamics and Earthquake Engineering 31 (2011) 334–350 335

mitigate the effects of earthquake shaking on bridges andbuildings. Seismic isolators are typically installed between thegirders and bent caps or abutments. For bridge construction, thetypical design goals associated with the use of seismic isolationare reduction of forces as accelerations in the superstructure andsubstructure, and force redistribution between the piers and theabutments.

Contemporary seismic isolation systems for bridge applica-tions provide horizontal isolation from the effects of earthquakeshaking, and an energy dissipation mechanism to reducedisplacements. Fig. 1a illustrates the effect of horizontal isolationon the inertial forces that can develop in a typical bridge. Theelongation of the fundamental period (period shift in Fig. 1a) ofthe bridge can substantially reduce, by a factor exceeding 3 inmost cases, the accelerations that can develop in a bridgesuperstructure. Such significant reductions in acceleration enablethe cost-effective construction of bridges that respond in theelastic range (no damage) in design earthquake shaking. Fig. 1billustrates the effect of isolation on the displacement response ofthe bridge. It must be noted that nearly all of the displacementwill typically occur over the height of the isolator and not in thesuperstructure, piers or abutments.

The increase in displacement response associated with the useof seismic isolators has a harmful impact on expansion joints inbridges. To control displacements, and thus reduce demands onjoints and the cost of the isolators, damping (energy dissipation)is typically introduced in the isolator. Damping in the two mostcommon bridge seismic isolators in use, the lead–rubber (LR)

0.0 0.5 1.0 1.5 2Perio

0.0

0.5

1.0

1.5

2.0

Spe

ctra

l Acc

eler

atio

n (g

)

Increasi

Period shift

50

40

30

20

10

00.0 0.5 1.0 1.5

Perio

Spe

ctra

l Dis

plac

emen

t (in

)

Fig. 1. Principles of seismic isolation: (a) reduction in spectral

bearing and the friction pendulum (FP) bearing, is achievedthrough hysteretic energy dissipation.

Soil–structure interaction (SSI) effect on the seismicallyisolated bridges has been studied by many researchers. Tongaon-kar and Jangid [5] observed that the soil surrounding the pier hassignificant effects on the response of the isolated bridges andunder certain circumstances the bearing displacements at abut-ment locations may be underestimated if the SSI effects are notconsidered in the response analysis of the system. Cases inwhich SSI needs to be incorporated in seismically isolated bridgedesign are identified and ways to take advantage of SSI in orderto enhance safety level and reduce design costs are recommendedby Spyrakos and Vlassis [6]. Ucak and Tsopelas [7] achievedthat the results from comprehensive numerical analyses showthat soil–structure interaction causes higher isolation systemdrifts as well as, in many cases, higher pier shears when comparedto the bridges without SSI. In the light of the studies, SSI can haveboth beneficial and detrimental effects on the response of theisolated bridges depending on the characteristics of the groundmotion.

Despite of the fact that isolated and non-isolated bridges havebeen analyzed so far, analysis of both curved and isolated bridgesare meager in the field of the earthquake engineering. Thus, theobjective of this study is to perform a parametrical studyassociated with the earthquake of ground motions and its effectson the response of isolated curved bridges. The soil–structureinteraction is also considered by springs representing of the soilbeneath footing and drilled shaft surrounding of soil.

.0 2.5 3.0 3.5 4.0d (sec)

ng damping

2.0 2.5 3.0 3.5 4.0d (sec)

accelerations and (b) increase in spectral displacements.

https://www.researchgate.net/publication/239391103_Effect_of_Soil-Structure_Interaction_on_Seismic_Isolated_Bridges?el=1_x_8&enrichId=rgreq-73568711-b828-4653-9332-af9a00e989ad&enrichSource=Y292ZXJQYWdlOzIzMjM5MDUxMDtBUzoxNDU2MTU4ODc1NDAyMjRAMTQxMTcyODk0MTY1NA==

https://www.researchgate.net/publication/222551653_Seismic_response_of_isolated_bridges_with_soil-structure_interaction?el=1_x_8&enrichId=rgreq-73568711-b828-4653-9332-af9a00e989ad&enrichSource=Y292ZXJQYWdlOzIzMjM5MDUxMDtBUzoxNDU2MTU4ODc1NDAyMjRAMTQxMTcyODk0MTY1NA==

https://www.researchgate.net/publication/233013287_Effect_of_soil-structure_interaction_on_seismically_isolated_beiges?el=1_x_8&enrichId=rgreq-73568711-b828-4653-9332-af9a00e989ad&enrichSource=Y292ZXJQYWdlOzIzMjM5MDUxMDtBUzoxNDU2MTU4ODc1NDAyMjRAMTQxMTcyODk0MTY1NA==

S. Ates, M.C. Constantinou / Soil Dynamics and Earthquake Engineering 31 (2011) 334–350336

2. Double concave friction pendulum (DCFP) bearings

The double concave friction pendulum bearings are made oftwo concave surfaces which are called as upper and lower, and asshown in Fig. 2 [8–10].

The concave surfaces may have the same radii of curvature.Also, the coefficient of friction on the two concave surfaces maybe the same or not. The maximum displacement capacity of thebearing is 2d, where d is the maximum displacement capacity of asingle concave surface. Note that due to rigid body and relativerotation of the slider, the displacement capacity is actuallyslightly different from 2d. The force–displacement relationshipfor the DCFP bearing is given by the following equation:

F ¼W

R1�h1þR2�h2

� �Ubþ

Ff 1ðR1�h1ÞþFf 2ðR2�h2Þ

R1�h1þR2�h2

� �ð1Þ

where W is the vertical load, R1 and R2 are radii of the two concavesurfaces, h1 and h2 are the part heights of the articulated slider, Ub

is the total displacement (bearing displacement) and the sum ofthe displacements on the upper and lower surfaces are given by

Ub ¼ 2d¼Ub1þUb2 ð2Þ

herein Ub1 and Ub2 are the displacements of the slider on theupper and lower concave surfaces, respectively, and the individualdisplacements on each sliding surfaces are

Ub1 ¼F�Ff 1

W

� �ðR1�h1Þ ð3Þ

Ub2 ¼F�Ff 2

W

� �ðR2�h2Þ ð4Þ

In Eqs. (3) and (4), Ff1 and Ff2 are the friction forces on theconcave surfaces 1 and 2, respectively. The forces are given by

Ff 1 ¼ m1W sgnð _U b1Þ ð5Þ

Ff 2 ¼ m2W sgnð _U b2Þ ð6Þ

where m1 and m2 are the coefficient of friction on the concavesurfaces 1 and 2, respectively; _U b1 and _U b2 are sliding velocities atthe upper and lower surfaces, respectively; sgn(U) denotes thesignum function. Most applications of the DCFP bearings willlikely utilize concave surfaces of equal radii, namely, R1¼R2. Partsheights of the articulated slider h1 and h2 are nearly equal in mostcases. Thus, the effective coefficient of friction is equal to the

R

R2

d

1

2

ds

Fig. 2. The double concave frictio

average of m1 and m2, and is given by

me ¼m1ðR1�h1Þþm2ðR2�h2Þ

R1þR2�h1�h2ð7Þ

In Eq. (1), the first term is the stiffness of the pendulumcomponent (spring forces) and the second term is the stiffness ofthe friction component. The natural period of vibration is given bythe following equation:

T ¼ 2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR1þR2�h1�h2

g

s¼ 2p

ffiffiffiffiffiRe

g

sð8Þ

where g is the acceleration of gravity; Re is the effective radius ofcurvatures. Eq. (8) shows that the natural period of vibration isindependent of mass, but it is controlled by the selection of theradius of the spherical concave surfaces. The important parameteris employed as Re¼R1+R2�h1�h2¼4.27 m. It is also shown inthis equation that the stiffness of the pendulum depends on theweight carried by bearing. The coefficient of the friction of the twoconcave surfaces depend on the bearing pressure and given by

m1,2 ¼ fmax�ðfmax�fminÞeða9 _vb9Þ ð9Þ

where fmax and fmin are the maximum and minimum mobilizedcoefficients of friction, respectively; and a is a parameter thatcontrols the variation of the coefficient with the velocity of sliding.

Analysis of seismically isolated bridges shall be performed foreach seismic loading case considered (design basis or maximumconsidered earthquake) for two distinct sets of mechanicalproperties of the isolation system.

Lower bound properties are defined to be the lower bound valuesof characteristic strength and post-elastic stiffness that can occurduring the lifetime of the isolators. Typically, the lower bound valuesdescribe the behavior of fresh bearings, at normal temperature andfollowing the initial cycle of high speed motion. The lower boundvalues of properties usually result in the largest displacementdemand on the isolators. Upper bound properties that are defined tobe the upper bound values of characteristic strength and post-elasticstiffness that can occur during the lifetime of the isolators andconsidering the effects of aging, contamination, temperature andhistory of loading and movement. Typically, the upper bound valuesdescribe the behavior of aged and contaminated bearings, followingmovement that is characteristic of substantial traffic loading, whentemperature is low and during the first high speed cycle of seismicmotion. The upper bound values of properties usually result in thelargest force demand on the substructure elements.

The lower and upper bound values of mechanical properties aredetermined from nominal values of properties and the use of system

1

h1

h2

d

The lower concave

The upper concave

n pendulum (DCFP) bearings.

https://www.researchgate.net/publication/244968383_Spherical_Sliding_Isolation_Bearings_with_Adaptive_Behavior_Experimental_Verification?el=1_x_8&enrichId=rgreq-73568711-b828-4653-9332-af9a00e989ad&enrichSource=Y292ZXJQYWdlOzIzMjM5MDUxMDtBUzoxNDU2MTU4ODc1NDAyMjRAMTQxMTcyODk0MTY1NA==

https://www.researchgate.net/publication/229744645_Spherical_sliding_isolation_bearings_with_adaptive_behavior_Theory?el=1_x_8&enrichId=rgreq-73568711-b828-4653-9332-af9a00e989ad&enrichSource=Y292ZXJQYWdlOzIzMjM5MDUxMDtBUzoxNDU2MTU4ODc1NDAyMjRAMTQxMTcyODk0MTY1NA==


property modification factors. The nominal properties are obtainedeither from testing of prototype bearings identical to the actualbearings or from test data of similar bearings from previous projectsand the use of appropriate assumptions to account for uncertainty.Typically, the analysis and design of the isolated bridge is based onavailable data from past tests of similar bearings. The assumptionsmade for the range of mechanical properties of the isolators is thenconfirmed in the prototype testing that follows. If the selection ofthe range of mechanical properties is properly made, the prototypebearing testing will confirm the validity of the assumptions andtherefore the validity of the analysis and design. Accordingly,modifications of the design would not be necessary. Such modifica-tions often lead to delays and additional costs.

3. Response history method of analysis

When response history analysis is performed, a suite of notfewer than three appropriate ground motions shall be used in theanalysis and the ground motions shall be selected and scaled. Themaximum displacement of the isolation system shall be calcu-lated from the vectorial sum of the two orthogonal displacementcomponents at each time step. For each ground motion analyzed,the parameters of interest shall be calculated. If at least sevenground motions are analyzed, the average value of the responseparameter of interest shall be permitted to be used for design. Iffewer than seven ground motions are analyzed, the maximumvalue of the response parameter of interest shall be used fordesign.

Ground motions shall consist of pairs of appropriate horizontalground motion acceleration components that shall be selectedand scaled from individual recorded events. Appropriate groundmotions shall be selected from events having magnitudes, faultdistance, and source mechanisms that are consistent with thosethat control the maximum considered earthquake. Where therequired number of recorded ground motion pairs is not available,appropriate simulated ground motion pairs shall be used to makeup the total number required. For each pair of horizontal groundmotion components, a SRSS spectrum shall be constructed bytaking the square root of the sum of the squares of the five-percent-damped response spectra for the scaled components inwhich an identical scale factor is applied to both components of apair. Each pair of motions shall be scaled such that for each periodbetween 0.5Teff and 1.25Teff [11] the average of the SRSS spectrafrom all horizontal component pairs does not fall below 1.3 times

All arch lengths are as per along the center line of the brid

11.8

0m

33.50m

27.25m

88.00m

The center line ofAbutment A

Pier 1

Rc = 48.77m

Fig. 3. The curved bridge pl

the corresponding ordinate of the response spectrum by morethan 10%.

Vertical ground motion histories may be included in the dynamicanalysis provided that the vertical motions are rationally selectedand scaled, the analysis method is accurate and the results areindependently verified. Consideration of the vertical ground motionmay be necessary when assessing bearing uplift or tension.

4. Description of example curved bridge

A curved bridge is selected to exhibit the application forseismic isolation. The bridge was used as an example of bridgedesign without an isolation system in the Federal HighwayAdministration Seismic Design Course, Design Example No. 6,prepared by BERGER/ABAM Engineers Inc. [12]. The bridge is to bemodeled and analyzed in a seismic zone with an accelerationcoefficient of 0.7g.

The configuration of the bridge is a three-span, cast-in-placeconcrete box girder superstructure supported on reinforcedconcrete columns found on drilled shafts and on integralabutments founded on steel pipe piles. The bridge is located onsite 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 twointermediate bents consist of rectangular columns with a crossbeam on top. The geometry of the bridge, section properties andfoundation properties are assumed to be the same in the originalbridge in the FHWA example. It is presumed (without any checks)that the original bridge design is sufficient to sustain theloads and displacement demands when seismically isolated asdescribed herein. The bridge is only used for comparing purpose.The fallowing assumptions are also made for earthquake analysesof the bridges under consideration:

�

ge.

P

an a

Bridge superstructure and piers are assumed to remain in theelastic state during the earthquake excitation. This is areasonable assumption as the base isolation attempts toreduce the earthquake response in such a way that thestructure remains within the elastic range.
� The deck of the bridge is curved and is supported at discrete
locations along its longitudinal axis by cross diaphragms.
� Both superstructure and substructure are modeled as lumped
mass systems divided into number of small discrete segments.Each adjacent segment is connected by a node and at eachnode three degrees of freedom are considered. The mass of

27.25m

The center line ofthe bridge

The center line ofAbutment B

ier 2

nd its dimensions.


each segment is assumed to be distributed between the twoadjacent nodes in the form of point masses.
� Stiffness contribution of non-structural elements such as
sidewalk and parapet is neglected.
� The force-deformation behavior of the bearing is considered to
be linear.
� The bearings provided at the piers and abutments have the
same dynamic characteristics.
� The drilled shaft is represented for all motions using a spring
model with frequency-independent coefficients. The modelingof the drilled shaft on deformable soil is performed in the sameway as that of the structure and is coupled to perform adynamic SSI analysis.

DrColumn section:

The center line of the pier1 or 2

170cm

85cm

100c

m

The center line of the bridge

85cm

50cm

50cm

Deck section:

1180

290cm 280c100cm 30cm30cm

Fig. 6. Horizontal sections of the substruct

Chord Dir

88.00

33.50

27.25m

76cm

23cm

90cm

Y

Z

Fig. 5. Framing plan of

Fig. 4. Developed elevation

Figs. 3–7 show, respectively, plan and its dimensions, devel-oped elevation, framing plan, horizontal sections of the sub-
structure, section of the superstructure, and section at the centerline of the pier as an intermediate bent. The bridge is isolated withtwo isolators at each abutment and pier location for a total ofeight isolators. The isolators are directly located above the cap ofthe rectangular columns and the abutments. Two isolators areintentionally used instead of more isolators due to the fact thatthe distribution of load on each isolator is accurately calculated.Additionally, the use of more than two isolators per a locationwould have resulted in uncertainty in the calculation of the axialload in vertically stiff FP bearings, and would have increased thecost.
illed shaft section:

cm

m 290cm 100cm30cm 30cm

170c

m

25cm

18cm

∅240cm

ure and the deck of the curved bridge.

Radial Direction

ection

m

m

27.25mX

the curved bridge.

of the curved bridge.

640c

m18

00cm

170cm

∅240cm

Ground Surface

30cm

25cm

180c

m

Slope = 10%

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@

120c

m =

168

0cm

1800

cm

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

element layout.

Table 1Soil properties for the subsurface materials.

Stratum Depth (ft) 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


Diaphragms in the box girder at the abutment and pierlocations above the isolators are also taken into account, in viewof rigidity and self-weight in the finite element model of thecurved bridge.

5. Modeling of the drilled shaft for piers

The drilled shaft can be modeled by equivalent soil springsmethod which is illustrated in Fig. 8. With the use of thistechnique, the drilled shaft is included in the finite elementmodel, and the foundation soil is modeled as a series of springsconnected to the drilled shaft at even intervals. It should be notedthat these spring stiffness must be accurately selected torepresent the best behavior. The soil springs at each depth arecalculated using a coefficient of horizontal subgrade reaction thatincreases linearly with depth and is inversely proportional to thecross sectional dimension of the drilled shaft [13].

A sufficient number of springs should be used along the lengthof the drilled shaft. The springs near the surface are usually themost important to characterize the response of the drilled shaftsurrounded by the soil; thus a closer spacing may be used in that

region. However, in generally springs spaced are recommendedthat at about half the diameter of the drilled shaft [12].

In this study, the diameter of the drilled shaft is 2.40 m and thedrilled shaft is 18 m in length. Consequently, 15 springs are usedon the center along the length of the drilled shaft to be 1.20 m.The springs are arranged at 1.20 m intervals but at the ends thesegments are taken as 0.60 m in such a way that all the springconstants based on 1.20 m tributary length of the drilled shaftis will be calculated. The mentioned arrangement is implementedsuch as in Fig. 8. The soil properties beneath the foundation ofthe bridge are given in Table 1 [12]. In this table, N is standardpenetration resistance as per blows per foot; g is total unitweight; f is internal angle of friction; c is cohesion and nh

is constant of horizontal subgrade reaction. New fill will berequired at the abutments. The fill has similar properties to thenative soil.


In order to calculate the horizontal stiffness of the equivalentsoil springs, the coefficient of horizontal subgrade is given below:

kh ¼nhz

Dð10Þ

Table 2The 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 5356

Longitudinal translation

ktrans (kN/m) 4320 4320 4320 4320

Transverse translation

kver (kN/m) 608,083 608,083 608,083 608,083

Vertical translation

krv (kNm/rad) 152,360 67,720 16,933 0

Rotation about vertical axis

krl (kN m/rad) 17,298,935 7,688,420 1,922,320 0

Rotation about longitudinal axis

krt (kNm/rad) 0 0 0 0

Rotation about transverse axis

Note:

krv ¼ kverd2i

krl ¼ klongd2i

krt ¼ ktrand2i

where di is a distance between the center lines of the abutment and the ith pipe

pile. In this study, the distance is 180 cm, 2�180 cm, and 3�180 cm ranging from

innermost of the pipe pile to outermost one, respectively.

ktrans

krt = 0

krv

kvert

klong

krl

12 3 4

CL

180cm 180cm 180cm 180cm50cm

540cm

1180cm

100cm

End diaphragm

Fig. 9. (a) Abutment and (b) the abutment wit

in which z is the depth in reference to the ground surface; D is thediameter of the drilled shaft. The horizontal stiffness of theequivalent soil springs based on the coefficient of horizontalsubgrade is

ki ¼ khDHtrib ð11Þ

where Htrib represents height of tributary soil spring. Bysubstituting Eq. (10) into Eq. (11), the horizontal stiffness of the

5 6 7

180cm 180cm 50cm

540cm

75cm

Pipe piles filled withconcrete

100cm

h equivalent soil springs used in analysis.

Table 3The horizontal stiffness of the equivalent soil springs of the drilled shaft.

Depth, z (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

2.00

(g)


equivalent soil springs can be rewritten as follows:

ki ¼ nhzHtrib ð12Þ

The horizontal stiffness of the equivalent soil springs aretabulated in Table 2 when Htrib is 1.2 m as per Eq. (12).

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 restraining onlythe base of the drilled shaft is felt to be reasonable. Similarly,torsional movement of the drilled shaft would be resisted by skinfriction. However, no torsional restraint was used in themathematical model. The response is not sensitive to lack oftorsional restraint in the drilled shaft, and this can be demon-strated by simple bounding analyses [12].

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Period (sec)

0.00

0.50

1.00

1.50

Spec

tral

Acc

eler

atio

n

0.7g

0.6g

0.2g

0.1g

Fig. 11. Acceleration response spectra for earthquake of magnitude 7.2570.25 for

6. Modeling of the foundation stiffness for abutments

The abutments are modeled with three dimensional frameelements. The abutment is depicted in Fig. 9a. The springsrepresent the piles as shown in Fig. 9b. The stiffness of thesprings is also given in Table 2 for the vertical, longitudinal,transverse and rotational directions as per each connection pointsbetween the abutment and the piles, respectively. It is taken asthe advantage of the design example [12] for calculating thestiffness.

soil profile type C [16].

Table 4The selected earthquake ground motions.

No. Earthquake name Recordingstation

MW Distance(km)

Siteclass

Scalefactor

1 1976 Gazli, USSR Karakyr 6.80 5.46 C 1.30

2 1989 Loma Prieta,

USA

LGPC 6.93 3.88 C 0.88

3 1989 Loma Prieta,

USA

Saratoga 6.93 9.31 C 1.84

4 1994 Northridge,

USA

Jensen

Filter Plant

6.69 5.43 C 1.26

5 1994 Northridge,

USA

Sylmar-

Coverter

Station East

6.69 5.19 C 1.14

6 1995 Kobe, Japan Takarazuka 6.90 3.00 D 1.43

7 1999 Duzce, Turkey Bolu 7.14 12.41 D 1.77

7. Finite element model of the curved bridge

The finite element model of the curved bridge consists of solidelements having three degrees of freedom at each nodal point.They are in horizontal and vertical translational directions. In thismodel, the drilled shaft is also included by equivalent soil springsmentioned above in such a way that the foundation soil isconsidered as a series of springs connected to the drilled shaft atbalance intervals. The soil springs at each depth are provided inTable 3. The three dimensional finite element models arerepresented with view in Fig. 10. The model has 9031 nodalpoints and 5060 solid area elements. In addition to frame elementsrepresenting columns, cap beam and drilled shafts, and the springsrepresenting soil stiffness. For the rest, friction pendulum bearingson the abutments and the cap beams of the piers are definedthrough the nonlinear link elements in SAP2000 [17] capable of

Fig. 10. Extrude view of three-dim

the properties. The super-elevation having 10% slope is also takeninto account in the finite element model in order that torsionalstresses of the girders are not overlooked. The cross sectionalproperties of the bridge are given in Figs. 6 and 7. Additionally, themodulus of elasticity of concrete is taken as E¼25,000 MPa.

8. Selection and scaling of ground motions

Response history analysis requires that ground motions areselected and scaled to represent the response spectrum as shownin Fig. 11 for magnitude 7.2570.25, acceleration of 0.7g and soil

ensional finite element model.

3.0

2.5

2.0

1.5

1.0

0.5

0.00 1 2 3 4 5

Period (sec)

Spe

ctra

l Acc

eler

atio

n (g

)

SRSS spectra of 7 groundmotion pairsMean of 7 SRSS spectra90% of 1.3 target

Fig. 12. Target spectral acceleration.

0.00 4.00 8.00 12.00 16.00 20.00Time (sec)

-2.00

-1.00

0.00

1.00

2.00

Acc

eler

atio

n (g

)

Fault-normal

Fig. 13. Acceleration time history of the Gazli earthq

0.00 5.00 10.00 15.00 20.00 25.00Time (sec)

-2.00

-1.00

0.00

1.00

2.00

Acc

eler

atio

n (g

) Fault-normal

Fig. 14. Acceleration time history of the Loma Prieta e

0.00 10.00 20.00 30.00 40.00Time (sec)

-2.00

-1.00

0.00

1.00

2.00

Acc

eler

atio

n (g

) Fault-normal

Fig. 15. Acceleration time history of the Loma Prieta ear


profile C has such large spectral values that only motions withnear-fault characteristics could be selected as raw motions asgiven in Table 4. Seven ground motions are selected for scaling inorder to use average results of dynamic analysis. Table 4 lists theseven near-fault ground motions selected for the analyses. Eachraw ground motion has been rotated to fault-normal (FN) andfault-parallel (FP) directions. The moment magnitudes for the rawmotions are range from 6.7 to 7.1; the site-to-source distances arerange from 3 to 12 km; and all the records are from Site Classes Cand D per the 2003 NEHRP Recommended Provisions [14]. Theground motion with no. 1 is from a backward-directivity regionand all other motions are from forward-directivity regions (PEER-NGA database).

The selected earthquake ground motions are scaled as follows;each pair of the raw motions no. 1 through 7 of Table 4 wasamplitude scaled by a single factor to minimize the sum of thesquared error between the target spectral values of the targetspectrum and the geometric mean of the spectral ordinates for thepair at periods of 1, 2, 3 and 4 s. The weighting factor at 1 s is 0.1

0.00 4.00 8.00 12.00 16.00 20.00Time (sec)

-2.00

-1.00

0.00

1.00

2.00A

ccel

erat

ion

(g) Fault-parallel

uake, USSR, recorded at Karakyr station in 1976.

0.00 5.00 10.00 15.00 20.00 25.00Time (sec)

-2.00

-1.00

0.00

1.00

2.00

Acc

eler

atio

n (g

) Fault-parallel

arthquake, USA, recorded at LGPC station in 1989.

0.00 10.00 20.00 30.00 40.00Time (sec)

-2.00

-1.00

0.00

1.00

2.00

Acc

eler

atio

n (g

) Fault-parallel

thquake, USA, recorded at Saratoga station in 1989.


and the factors at 2, 3 and 4 s are 0.3. This scaling procedure seeksto preserve the record-to-record dispersion of spectral ordinatesand the spectral shapes of the ground motions. The square root ofsum of squares (SRSS) of the 5%-damped spectra of the scaledmotions are calculated and the mean of the seven SRSS spectra isconstructed for periods in the range of 0–5 s. This mean of SRSSspectra is compared to the target spectrum times 1.3. The mean ofSRSS spectra is multiplied by a single scale factor so that it doesnot fall below 1.3 times the target spectrum by more than 10% inthe period range of 1–4 s. The final scale factor for each pair of raw

0.00 5.00 10.00 15.00 20.00 25.00 30.00Time (sec)

-2.00

-1.00

0.00

1.00

2.00

Acc

eler

atio

n (g

)

Fault-normal

Fig. 16. Acceleration time history of the Northridge earthqua

0.00 10.00 20.00 30.00 40.00Time (sec)

-2.00

-1.00

0.00

1.00

2.00

Acc

eler

atio

n (g

)

Fault-normal

Fig. 17. Acceleration time history of the Northridge ear

0.00 10.00 20.00 30.00 40.00 50.00Time (sec)

-2.00

-1.00

0.00

1.00

2.00

Acc

eler

atio

n (g

) Fault-normal

Fig. 18. Acceleration time history of the Kobe earthqua

0.00 10.00 20.00 30.00 40.00 50.00 60.00Time (sec)

-2.00

-1.00

0.00

1.00

2.00

Acc

eler

atio

n (g

) Fault-normal

Fig. 19. Acceleration time history of the Duzce earth

motions is calculated as the scale factor determined in the scalingdescribed that above times the single scale factor determined inpart, and the final scale factor for each motion is listed in Table 4.

Fig. 12 presents the 5%-damped SRSS spectra of the sevenscaled motions, the mean SRSS spectra and the target spectrummultiplied by 0.9�1.3 (lower bound for mean SRSS spectrum). Itmay be seen that the scaled motions have the mean SRSSspectrum above the lower acceptable bound over the entireperiod range. The scaled motions need to satisfy the lower boundacceptable criterion over the period range 0.5–1.25Teff, which for

0.00 5.00 10.00 15.00 20.00 25.00 30.00Time (sec)

-2.00

-1.00

0.00

1.00

2.00

Acc

eler

atio

n (g

) Fault-parallel

ke, USA, recorded at Jensen Filter Plant station in 1994.

0.00 10.00 20.00 30.00 40.00Time (sec)

-2.00

-1.00

0.00

1.00

2.00

Acc

eler

atio

n (g

) Fault-parallel

thquake, USA, recorded at Sylmar station in 1994.

0.00 10.00 20.00 30.00 40.00 50.00Time (sec)

-2.00

-1.00

0.00

1.00

2.00

Acc

eler

atio

n (g

) Fault-parallel

ke, Japan, recorded at Takarazuka station in 1995.

0.00 10.00 20.00 30.00 40.00 50.00 60.00Time (sec)

-2.00

-1.00

0.00

1.00

2.00

Acc

eler

atio

n (g

)

Fault-parallel

quake, Turkey, recorded at Bolu station in 1999.

Table 5Earthquake directions to be applied to the bridge.

Earthquake Earthquake direction

No. Name Recordingstation

Chord (X) Radial (Y)

01 NP 1976 Gazli, USSR Karakyr Fault-normal Fault-parallel01 PN Fault-parallel Fault-normal

02 NP 1989 LomaPrieta, USA

LGPC Fault-normal Fault-parallel

02 PN Fault-parallel Fault-normal

03 NP 1989 LomaPrieta, USA

Saratoga Fault-normal Fault-parallel


04 NP 1994Northridge, USA

Jensen FilterPlant

Fault-normal Fault-parallel


05 NP 1994Northridge, USA

Sylmar- CoverterStation East

Fault-normal Fault-parallel


06 NP 1995 Kobe,Japan

Takarazuka Fault-normal Fault-parallel


07 NP 1999 Duzce,Turkey

Bolu Fault-normal Fault-parallel


Table 7Enveloped results for double concave friction pendulums having lower bound properti

Earthquake Displacement (cm) Chord direction sh

Abutment Pier Abutment

01 NP 50.72 49.10 156.12

02 NP 70.13 71.70 193.75

03 NP 61.11 59.69 201.54

04 NP 67.01 68.07 244.51

05 NP 50.77 51.97 206.34

06 NP 42.72 40.36 115.87

07 NP 32.46 31.80 140.38

Average 53.56 53.24 179.790.147 W

01 PN 49.63 50.57 165.95

02 PN 71.25 69.93 168.13

03 PN 60.53 62.03 171.96

04 PN 67.13 66.29 94.25

05 PN 51.94 51.03 116.27

06 PN 38.25 38.66 133.88

07 PN 34.52 33.71 194.73

Average 53.32 53.17 149.310.122 W

Table 6Properties of friction pendulum bearings for response history analysis in SAP2000.

Properties Lower bound analysis Upper bound analysis

Abutment Pier Abutment Pier

W (kN) 1225 2315 1225 2315

Mass (kN s2/m) 2.3117 2.3117 2.3117 2.3117

FP element height (m) 0.30 0.30 0.30 0.30

Shear deformation

location (m)

0.15 0.15 0.15 0.15

Vertical stiffness (kN/m) 16,636,220 16,636,220 16,636,220 16,636,220

Effective stiffness (kN/m) 388.76 781.03 840.57 1190.80

Elastic stiffness (kN/m) 19,263.20 22,765.60 39,971.14 46,897.14

Friction coefficient, Slow 0.040 0.025 0.083 0.0515

Friction coefficient, Fast 0.080 0.050 0.166 0.103

Rate parameter (s/m) 49.21 49.21 49.21 49.21

Radius (m) 4.27 4.27 4.27 4.27

Torsional stiffness

(kN m/rad)

10,000 10,000 10,000 10,000

Rotational stiffness

(kN m/rad)

0 0 0 0


the FP system is 1.3 (0.5 of Teff in the upper bound analysis) to4.1 s (1.25 of Teff in the lower bound analysis). Therefore, thescaling may be viewed as slightly conservative and can be used inthe analysis of all examples presented herein with different valuesof effective period.

Figs. 13–19 show acceleration time histories of the original andscaled ground motion mentioned in Table 5. Out of the all figuresregarding time histories of the ground motions denote fault-normal(left) and fault-parallel (right) motions, respectively. The scalingfactors can be calculated to be as outlined above according to Fig. 12.

9. Modeling of double concave friction pendulum

The double concave bearing is modeled using the singleconcave friction pendulum element of SAP2000 with radius equalto the effective radius Re and the rate parameter equal to one halfthat for a single concave bearing as nonlinear elements [8]. Eachelement for the isolators is extended between two verticallyaligned end nodes at a distance of 0.30 m specified sheardeformation at mid-height.

Table 6 presents values of parameters for modeling thebearings in SAP2000. The properties of friction coefficient fast,friction coefficient slow and rate parameter are, respectively,parameters fmax, fmin and a [11,15].

fmin is set equal to one half of fmax based on experimentalresults presented by Constantinou et al. [15]. fmin and a do notaffect the results in terms of displacement demands and shearforces but may affect the computational efficiency and accuracy ofthe solution if inappropriately selected. The elastic stiffnessshould be calculated using

Kelastic ¼fminW

Yð13Þ

where Y is the yield displacement and is typically used as to be2.54 mm. This value is used in the calculation of the elasticstiffness presented in Table 6.

10. Numerical results for DCFP

Tables 7 and 8 offer the results obtained from response historyanalysis of the seismically isolated curved bridge with doubleconcave friction pendulum having lower and upper bound

es.

ear force (kN) Radial direction shear force (kN)

Pier Abutment Pier

331.46 136.91 372.96

469.98 141.36 309.22

424.92 175.34 468.60

472.60 136.82 262.61

426.56 104.57 235.52

251.58 127.52 336.22

297.84 149.32 267.77

382.13 138.83 321.840.165 W 0.113 W 0.139 W

346.54 164.75 351.53

284.23 281.25 490.35

420.51 201.36 427.45

251.22 249.44 504.36

231.96 201.05 407.48

302.29 154.97 278.89

371.27 193.31 310.92

315.43 206.59 395.850.136 W 0.169 W 0.171 W

Table 8Enveloped results for double concave friction pendulums having upper bound properties.

Earthquake Displacement (cm) Chord direction shear force (kN) Radial direction shear force (kN)

Abutment Pier Abutment Pier Abutment Pier

01 NP 28.22 27.15 198.91 353.88 203.85 396.32

02 NP 42.09 42.88 256.83 439.15 227.60 367.76

03 NP 40.39 41.45 251.98 472.91 216.48 438.80

04 NP 47.24 49.15 235.92 485.68 240.24 367.23

05 NP 38.18 39.01 264.57 489.77 215.91 358.33

06 NP 38.30 35.20 165.82 356.28 215.64 433.77

07 NP 28.07 27.71 177.79 355.97 205.23 376.08

Average 37.50 36.01 221.69 421.95 217.85 391.180.181 W 0.182 W 0.178 W 0.169 W

01 PN 25.96 26.39 215.33 341.83 208.34 360.24

02 PN 41.61 40.74 177.48 341.78 241.84 478.78

03 PN 39.14 40.46 205.81 398.10 283.78 495.11

04 PN 47.22 46.28 181.57 342.63 267.50 518.15

05 PN 36.86 36.50 189.13 346.45 281.34 478.47

06 PN 32.56 33.66 229.03 393.38 189.53 307.85

07 PN 28.73 29.74 253.49 394.40 250.47 400.41

Average 37.51 36.25 207.40 365.51 246.11 434.140.170 W 0.158 W 0.201 W 0.188 W

Fig. 20. Pier and deck connection detail with double concave friction pendulum.


properties, respectively. The outlined analysis is performed withthe fault-normal (FN) and fault-parallel (FP) components alongthe two horizontal directions, namely chord and radial, respec-tively, and then the analysis is repeated with the componentsrotated as defined in Table 5. The results presented in the tablesconsist of the resultant isolator displacements and the horizontalshear forces at the pier and abutment locations.

The results on isolator displacement represent the criticalparameter for comparing the results obtained from analysis. Thedynamic response history analysis results are enveloped,the calculated displacement (average of seven motions) in theanalysis with lower bound properties of the friction pendulum is53.56 cm for the abutment bearings and 53.24 cm for the pierbearings. This very good agreement demonstrates the validity of

the selected 66 cm-displacement capacity of the DCFP bearingsfor lower bound properties.

In the case of the analysis with upper bound properties of thefriction pendulum, the response history analysis method predictsisolator displacements of 37.51 cm for the abutments and 36.25 cmfor the piers. They are under estimate values as per comparing withthe selected displacement capacity of DCFP bearings.

Connection details of the deck and the pier cap of the curvedbridge isolated by double concave friction pendulum bearings aregiven in Fig. 20. Due the fact that the deck has super-elevationhaving slope of 10%, the connection should be different from usualconnection details. Hence, in order to make a flat bed for frictionpendulum, the pedestals are required in such a way that placeddisplacement position of the friction pendulum is prevented.


11. Numerical results of the curved bridge isolated by theDCFP bearings

In this section of the paper, the internal forces are clarifiedwith graphics for the isolated and non-isolated curved bridgessubjected to earthquake ground motions, nos. 07 NP and 07 PN,given by Figs. 13–19. The motions are applied to the consideredbridge in the chord and radial directions as a fault-normal andfault-parallel defined in Table 5. The directions are also defined inFig. 5.

Maximum and minimum envelope response quantities,namely bending and torsional moments, and shear and axialforces, are given by Figs. 21–28 for the isolated and non-isolatedcurved bridges subjected to earthquake ground motions. Thegraphics also cover the lower and upper bound properties of thedouble concave friction pendulum bearings.

The results of the maximum and minimum bending momentsabout radial direction obtained using the response history methodof analysis. When the earthquake is applied to the bridge withand without isolation bearings, the bending moments are

0 30 60 90

-20000

-10000

0

10000

20000Ben

ding

Mom

ent (

kNm

)

Lower BoundUpper Bound

Isolated Bridge

The center line length of the bridge (m)

Fig. 21. Bending moment about horizontal radial axis of the isolated

0 30 60 90The center line length of the bridge (m)

-10000

-5000

0

5000

10000Tors

iona

l Mom

ent (

kNm

)


Fig. 22. Torsional moment about horizontal chord axis of the isolated


-4000

-2000

0

2000

4000

She

ar F

orce

(kN

) Lower BoundUpper Bound

Fig. 23. Shear forces of the isolated and non-isolated

considerably different. The deck bending moments obtained fromthe response history method of analysis of the isolated curvedbridge are decreased if these are compared with the resultsobtained for the non-isolated curved bridge. The results clearlyshow that consideration of double concave friction pendulumbearings for the isolation of the curved bridges for the responsehistory analysis when the bridge is subjected to the horizontalearthquake ground motion decrease the deck bending moments.

The outcomes of torsional moment about chord axis of theisolated and non-isolated curved bridges subjected to horizontaldirectional earthquakes show that the seismic isolation system isimportant for reduction of the undesirable torsional effectsparticularly at the midspan of the considered bridge.

The reduction of the deck shear and axial forces obtained forthe isolated curved bridge is obvious, if the forces are comparedwith those obtained for the non-isolated curved bridge.

The structural accelerations results are also evaluated for themidpoint as marked in Fig. 5 of the midspan of the curved bridge.In the light of Table 9, it can be seen that the structuralaccelerations significantly reduce in case of seismic isolation


-20000

-10000

0

10000

20000Ben

ding

Mom

ent (

kNm

)Non-isolated Bridge

and non-isolated curved bridges subjected to 07 NP earthquake.


-10000

-5000

0

5000

10000Tors

iona

l Mom

ent (

kNm

)

and non-isolated curved bridges subjected to 07 NP earthquake.


-4000

-2000

0

2000

4000

She

ar F

orce

s (k

N)

curved bridges subjected to 07 NP earthquake.


-15000

-7500

0

7500

15000

Axi

al F

orce

(kN

)


-15000

-7500

0

7500

15000

Axi

al F

orce

(kN


Fig. 24. Axial forces of the isolated and non-isolated curved bridges subjected to 07 NP earthquake.


-40000

-20000

0

20000

40000Ben

ding

Mom

ent (

kNm

)0 30 60 90

The center line length of the bridge (m)

-40000

-20000

0

20000

40000Ben

ding

Mom

ent (

kNm

)


Isolated Bridge Non-isolated Bridge

Fig. 25. Bending moment about horizontal radial axis of the isolated and non-isolated curved bridges subjected to 07 PN earthquake.


-15000

-7500

0

7500

15000Tors

iona

l Mom

ent (

kNm

)

0 30 60 90The center line length of the bridge (ft)

-15000

-7500

0

7500

15000Tors

iona

l Mom

ent (

kNm

)


Fig. 26. Torsional moment about horizontal chord axis of the isolated and non-isolated curved bridges subjected to 07 PN earthquake.


-5000

-2500

0

2500

5000

She

ar F

orce

(kN

)


-5000

-2500

0

2500

5000

She

ar F

orce

(kN


Fig. 27. Shear forces of the isolated and non-isolated curved bridges subjected to 07 PN earthquake.


technique is used. For comparing purpose, the maximum andminimum acceleration values of the modified earthquake groundmotions are also given in Table 10. Structural accelerations ofthe isolated curved bridge transmitted by the earthquake groundmotions are nearly the same as the ones of the motions.However, structural accelerations of the non-isolated curved

bridge transmitted by the earthquake ground motions substan-tially increase as three times as according to the maximum andminimum values of the modified ground motions.

As seen in Table 11, in the isolated bridge, the structuraldisplacements as expected are augmented when comparing withthese of non-isolated bridge this is because of the friction


-20000

-10000

0

10000

20000

Axi

al F

orce

(kN

)


-20000

-10000

0

10000

20000

Axi

al F

orce

(kN


Fig. 28. Axial forces of the isolated and non-isolated curved bridges subjected to 07 PN earthquake.

Table 9Structural accelerations of the marked point of the curved bridge.

Earthquake no. Acceleration (m/s2)

Isolated (Lower) Isolated (Upper) Non-Isolated

Max Min Max Min Max Min

01 NP ax 7.74 �8.36 7.78 �8.10 16.20 �16.01

ay 8.56 �9.17 8.34 �9.57 19.43 �19.48

az 2.08 �2.31 2.08 �2.24 7.26 �7.35

01 PN ax 8.84 �9.41 8.44 �9.82 14.42 �15.23

ay 7.71 �8.02 7.58 �8.35 19.24 �18.22

az 3.19 �2.50 3.24 �2.56 6.01 �5.93

02 NP ax 6.46 �6.99 6.40 �4.35 20.87 �19.85

ay 3.40 �4.93 3.44 �7.64 8.91 �8.27

az 0.91 �0.91 0.77 �1.32 4.53 �4.95

02 PN ax 3.60 �4.78 3.56 �7.97 10.93 �10.72

ay 6.61 �6.96 6.14 �4.39 15.17 �15.85

az 1.25 �1.10 1.13 �0.77 9.99 �9.48

03 NP ax 4.74 �8.91 5.13 �9.05 10.66 �8.76

ay 5.94 �5.53 5.68 �5.95 9.42 �10.17

az 0.72 �0.95 0.91 �0.90 4.05 �4.35

03 PN ax 5.57 �5.41 4.83 �5.57 8.17 �10.73

ay 4.66 �9.11 5.17 �9.49 11.33 �8.30

az 0.96 �1.04 0.84 �0.87 3.66 �2.83

04 NP ax 5.08 �7.27 4.66 �6.48 11.20 �12.14

ay 14.40 �12.98 15.55 �13.46 37.49 �31.55

az 2.39 �2.19 2.29 �2.23 11.11 �10.89

04 PN ax 13.29 �12.83 13.74 �13.05 28.56 �16.43

ay 4.77 7.31 4.70 �6.47 11.88 �11.55

az 1.12 �1.10 0.80 �0.97 3.72 �3.83

05 NP ax 4.16 �10.80 4.68 �11.18 17.03 �11.34

ay 5.65 �6.03 6.33 �6.50 7.63 �11.57

az 1.33 �0.96 1.50 �1.13 3.96 �3.63

05 PN ax 5.51 �5.82 6.34 �6.02 10.09 �9.90

ay 5.18 �11.32 6.57 �11.78 22.59 �14.54

az 1.46 �2.49 1.33 �2.49 6.78 �6.55

06 NP ax 9.81 �8.11 10.07 �7.87 18.48 �19.43

ay 8.61 �11.11 8.68 �11.67 32.55 �30.01

az 1.03 �1.17 13.09 �10.16 18.10 �18.41

06 PN ax 8.86 �10.79 8.82 �11.14 19.61 �23.05

ay 10.19 �7.93 10.72 �7.46 13.36 �21.67

az 2.21 �2.16 0.88 �1.11 7.81 �7.77

07 NP ax 13.61 �9.93 14.10 �9.86 32.03 �28.93

ay 14.19 �9.60 14.10 �10.01 13.86 �23.38

az 1.15 �1.34 1.04 �1.22 6.71 �6.51

07 PN ax 14.68 �9.32 14.89 �9.72 18.73 �21.96

ay 14.35 �9.88 15.01 �10.01 31.06 �44.07

az 2.52 �2.73 2.33 �2.29 14.50 �13.26

Table 10Acceleration of the modified ground motions.

Earthquake Acceleration (m/s2)

No. Name Direction Max Min

01 1976 Gazli, USSR Fault-normal 7.64 �7.27

Fault-parallel 9.05 �8.77

02 1989 Loma Prieta, USA Fault-normal 8.07 �6.71


03 1989 Loma Prieta, USA Fault-normal 7.28 �5.26


04 1994 Northridge, USA Fault-normal 6.35 �5.45


05 1994 Northridge, USA Fault-normal 9.36 �4.95


06 1995 Kobe, Japan Fault-normal 8.10 �9.04


07 1999 Duzce, Turkey Fault-normal 9.09 �13.62



pendulums. In such a way that the when structural displacementincrease, the structural acceleration, of course, decrease trans-mitted to the bridge and the fundamental period of the bridge is

lengthened. This is the main philosophy of the theory of the baseisolation.

12. Conclusion

This study outlines an investigation about the dynamicresponses of the isolated and non-isolated curved bridgessubjected to earthquake ground motions modified as per CaltransSeismic Design Criteria, Version 1.4 for magnitude 7.2570.25,0.7g acceleration and soil profile C [16]. For the isolated bridgesystem, double concave friction pendulum bearings are placedbetween the deck and the pier/the abutments as isolation devices.Response history acceleration of the selected ground motions areconsidered as the earthquake ground motion. The analyses arecarried out for the isolated and non-isolated bridges, separately.The soil–structure interaction is also considered by springsrepresenting of the soil beneath footing and drilled shaftsurrounding of soil. The maximum and minimum response valuesof the isolated and non-isolated bridges are compared with eachother for different cases. The results obtained from this study canbe categorized as

(i)
The upper and lower bound of properties for analysis is likelyconservative. By using the properties for the DCFP bearing,important reductions are observed for the internal forces,namely bending and torsional moments, and shear and axialforces, of the isolated curved bridge.

Table 11Structural displacements of the marked point of the curved bridge.

Earthquake

no.

Displacement (cm)

Isolated (lower) Isolated (upper) Non-isolated

Max Min Max Min Max Min

01 NP Ux 37.97 �42.34 22.17 �15.6 14.33 �13.56

Uy 35.59 �48.18 18.47 �26.8 9.627 �6.883

Uz �2.54 �2.819 �2.464 �2.845 �7.061 �15.04

01 PN Ux 37.47 �50.44 21.18 �26.29 11.05 �9.423

Uy 36.09 �39.73 20.19 �14.15 7.391 �6.096

Uz �2.464 �2.87 �2.464 �2.896 �7.696 �14.83

02 NP Ux 71.53 �53.29 37.16 �42.8 17.09 �18.34

Uy 27.84 �36.07 22.02 �18.19 5.131 �4.115

Uz �2.515 �2.769 �2.565 �2.769 �7.747 �14.43

02 PN Ux 29.95 �37.69 23.62 �17.68 9.296 �9.144

Uy 69.09 �51.28 33.55 �39.73 9.271 �7.264

Uz �2.54 �2.819 �2.515 �2.87 �4.369 �18.08

03 NP Ux 54.31 �36.58 41.33 �30.53 10.11 �11

Uy 37.87 �59.16 24.64 �37.24 4.928 �3.226

Uz �2.515 �2.769 �2.54 �2.87 �8.433 �13.69

03 PN Ux 39.78 �61.82 23.65 �40.16 7.874 �8.611

Uy 52.83 �34.24 40.01 �29.49 4.75 �5.258

Uz �2.489 �2.845 �2.489 �2.845 �8.865 �13.74

04 NP Ux 61.32 �67.97 48.46 �40.01 10.01 �9.677

Uy 24.05 �23.62 21.36 �18.29 13.54 �12.01

Uz �2.286 �3.15 �2.286 �3.15 �5.41 �17.02

04 PN Ux 24.31 �25.45 23.55 �19.84 13 �14.43

Uy 59.66 �65.91 45.92 �37.13 5.105 �4.42

Uz �2.565 �2.845 �2.515 �2.819 �8.661 �13.72

05 NP Ux 47.8 �51.82 38.91 �21.01 9.703 �12.01

Uy 30.2 �20.35 23.95 �19.94 6.553 �3.327

Uz �2.54 �2.794 �2.515 �2.819 �8.763 �13.54

05 PN Ux 31.29 �20.22 27.48 �18.59 9.296 �8.458

Uy 46.1 �50.65 36.58 �20.6 7.798 �7.315

Uz �2.413 �2.946 �2.413 �2.87 �6.96 �15.09

06 NP Ux 16.84 �33.3 10.85 �26.09 18.19 �16.03

Uy 27.03 �38.96 25.7 �33.3 16.23 �17.09

Uz �2.464 �2.819 �2.438 �2.87 �0.508 �22.28

06 PN Ux 27.58 �38.58 26.06 �33.53 20.5 �20.07

Uy 17.07 �31.67 11.86 �23.01 7.645 �6.553

Uz �2.388 �2.921 �2.464 �2.972 �6.172 �16.51

07 NP Ux 31.17 �31.5 27.61 �25.17 24.08 �22.4

Uy 18.87 �31.14 21.67 �26.29 13.34 �6.096

Uz �2.515 �2.87 �2.489 �2.845 �6.756 �15.95

07 PN Ux 16.51 �33.66 18.82 �29.67 18.01 �18.75

Uy 30.15 �33.27 25.5 �26.42 17.81 �13.08

Uz �2.159 �3.124 �2.235 �3.175 �2.134 �20.45


(ii)
In case of the analyses of the isolated curved bridge with thelower bound properties of the friction pendulum beingutilized, the average bearing displacement is bigger thanthose of the upper bound properties of the friction pendulum.The results on isolator displacement in the lower boundproperties give a good agreement with the expected value as66 cm. On the contrary, shear forces obtained from the lowerbound properties at the bearing level is bigger than when theupper bound properties is preferred for DCFP bearings todesign.
(iii)
The results of bending moments obtained using the responsehistory method of analysis for the isolated curved bridge aresignificantly smaller than the responses obtained for the non-isolated bridge. The results clearly show that consideration ofdouble concave friction pendulum bearings for the isolation
of the curved bridges, when the bridge is subjected to thehorizontal earthquake ground motion, the bending momentsof the curved deck decrease.

(iv)
When the response history method of analysis is executed,the torsional moment of the isolated and non-isolated curvedbridges subjected to horizontal directional earthquakes showthat the seismic isolation system is important for reductionof the undesirable torsional effects particularly at themidspan of the considered bridge. Additionally, the reductionof the deck shear and axial forces obtained for the isolatedcurved bridge is achieved, if the forces are compared withthose obtained for the non-isolated curved bridge.
(v)
Structural accelerations of the non-isolated curved bridgetransmitted by the earthquake ground motions substantiallyincrease as per the maximum and minimum values of themodified ground motions. On the other hand, the mentionedvalues of the isolated bridge are considerably smaller thanthese of the non-isolated bridge. When the structuraldisplacements come to evaluate, they are augmentedwhen comparing with these of the non-isolated bridge thisis because of the displacement capacity of the frictionpendulums.
(vi)
Vertical ground motion significantly affects structural accel-erations and displacements at the midspan of the curvedbridge. On the other hand, in the case of the curved bridgeisolated with DCFP bearings the effects highly decrease.Therefore, the vertical ground motion can be disregarded. Inshort, the vertical ground acceleration is found to have aminor effect on the response of the isolated bridge.
Acknowledgements

The authors acknowledge the Scientific and Technical ResearchCouncil of Turkey (TUBITAK) for supporting the studies of SevketATES at the University at Buffalo.

References

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example of application of response history analysis for seismically isolated curved bridges on...

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