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Original Research Article
Seismic response characteristics of a base isolatedcable-stayed bridge under moderate and strongground motions
Ahad Javanmardi, Zainah Ibrahim *, Khaled Ghaedi, Mohammed Jameel,Hamed Khatibi, Meldi Suhatril
Civil Engineering Department, University of Malaya, Kuala Lumpur 50603, Malaysia
a r c h i v e s o f c i v i l a n d m e c h a n i c a l e n g i n e e r i n g 1 7 ( 2 0 1 7 ) 4 1 9 – 4 3 2
a r t i c l e i n f o
Article history:
Received 7 September 2016
Accepted 2 December 2016
Available online 24 December 2016
Keywords:
Cable-stayed bridge
Seismic performance
Nonlinear dynamic analysis
Isolation system
Lead-rubber bearing
a b s t r a c t
In this study, the seismic behavior of an existing steel cable-stayed bridge equipped with
lead-rubber bearing subjected to moderate and strong earthquakes is investigated. The
bridge is located at high seismic zone and experienced an earthquake in 1988 which caused
the failure of one of its anchorage plate of the support. Herein, the bridge was modeled in
three dimensions and the base isolators implemented at the abutments and deck-tower
connection. The bridge seismic responses were evaluated through nonlinear dynamic time-
history analysis. The comparative analysis confirmed that the base isolation system was an
effective tool in reducing seismic force transmit from substructure to superstructure.
Furthermore, the overall seismic performance of cable-stayed bridge significantly enhanced
in longitudinal and transverse directions. However, it is observed that the axial force of the
tower in substructure increased due to the isolation system induced torsional deformation
to the superstructure under transverse seismic loads.
© 2016 Politechnika Wrocławska. Published by Elsevier Sp. z o.o. All rights reserved.
Available online at www.sciencedirect.com
ScienceDirect
journal homepage: http://www.elsevier.com/locate/acme
1. Introduction
In recent years the application of cable-stayed bridges hasrisen significantly around the globe due to their advantages,i.e. appealing esthetics, longer span length, light weight andsmall structural members and efficient in load resistance.However, they are characterized by longer natural time periodand low structural damping which make them highly flexibleand susceptible to large amplitude oscillation under seismicloadings [1,2]. They are required to stay in service afterearthquakes for emergency cases. Several researches have
* Corresponding author.E-mail addresses: [email protected], [email protected]
[email protected] (Z. Ibrahim), [email protected] (K. Ghaedhttp://dx.doi.org/10.1016/j.acme.2016.12.0021644-9665/© 2016 Politechnika Wrocławska. Published by Elsevier Sp.
studied the static and dynamic behavior of cable-stayedbridges [3–8]. Wang and Yang [9] elaborated that the mainsources of geometric nonlinearity in cable-stayed bridges,which were the beam-column effect, the cable sag effect andthe large displacement effect (P-delta). The cable sag effect ledto substantial nonlinearity in cable-stayed bridges. Theseidentified nonlinearities were highly influenced on thedynamic performance of cable-stayed bridges. Au et al. [10]developed the constitutive model for the cables for determi-nation of natural frequencies and modes shapes of the bridgeaccurately. The deck connection between tower and piersgreatly affected the seismic performance of the cable-stayed
du.my (A. Javanmardi),i).
z o.o. All rights reserved.
List of notation
A, b, g dimensionless quantitiesBL damping coefficientd initial displacementdisol isolator displacementdsub substructure displacementdy isolator yield displacementFi force mobilized in isolators in the i directionFisol isolator shear forcefy steel tensile stressf 0c compressive strength of concreteFY yield forcekd post-yield stiffness of isolatorKisol effective stiffness of isolatorKu loading and unloading stiffness (elastic stiff-
ness)PGA peak ground accelerationQd characteristics strengthSD1 design spectral displacementTeff effective time periodU2,3 bearing displacement in the 2 and 3 directionsUX,Y,Z support translation in the X, Y and Z directionsW superstructure weightY yield displacementZ2,3 hysteretic dimensionless quantity in the 2 and 3
directionsa ratio of post-yield stiffness to pre-yield stiffnessj viscous damping
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bridges [3]. The rigid connection of deck and tower limited thehorizontal deck displacement under earthquake excitationand led to transmission of forces from superstructure tosubstructure, and hence increased the base shear of the tower[11,12]. On the other hand, the movable or floating configura-tion had higher deck flexibility and enlarged the horizontaldeck displacement under service loadings [13]. In addition,shape and height of the tower, substantially affected thedynamic response of the cable-stayed bridge [7,14,15].
Seismic control of the cable-stayed bridge has broughtseveral authors attention [16–19]. Ali and Abdel-Ghaffar [16]constructed the constitutive model for passive seismic controlof a cable-stayed bridge, in order to optimize the mechanicalproperties and location of the bearings. The passive controlsystem could be used as an alternative in retrofitting strategyfor the exiting cable-stayed bridges [19]. Wesolowsky andWilson [20] evaluated the base shear reduction of isolatedcable-stayed bridges for near-field ground motions and alsostated that the characteristics of near-field ground motionshave to be consider when the base isolators are designed.Seismic isolation is an effective tool for protection of new orretrofit of existing bridges as the isolation retrofitting is foundto be more economical than conventional retrofitting ofbridges in seismic zones [21,22]. Nonetheless, there is a lackof research on the seismic response behavior of isolated cable-stayed bridges with unique characteristics such as geometryirregularity and elevation difference of abutments [23–25].
This paper attempts to investigate the seismic behavior ofan existing steel cable-stayed bridge equipped with base
isolators under bidirectional moderate and strong earth-quakes. The bridge experienced an earthquake of ML = 6.0magnitude in 1988 with peak ground acceleration (PGA) of0.15 � g in horizontal direction. It was confirmed that one ofthe four anchorage plates which connected the steel boxgirders to the abutment failed due to high stress concentra-tions under dead load and stresses produced by seismic loads[26,27]. The bridge was closed immediately for repairing.Furthermore, this bridge is characterized by its asymmetricgeometry and 7.3 m elevation difference between the Westand the East abatements. Hereupon, the base isolation systemis utilized to protect the superstructure from seismic loads andminimized the damage to the bridge. In line with this, the lead-rubber bearings (LRB) are implemented at abutments anddeck-tower connection. The isolators are designed based onAASHTO [28,29] and with bidirectional interaction. Full scalethree-dimensional (3D) finite element (FE) model of the bridgeis developed with all source of nonlinearities and then verifiedwith the previous field experiment for consistency. Thenonlinear seismic behavior of the bridge is studied throughtime-history analysis in longitudinal and transverse direc-tions.
2. Methodology
2.1. Description of Shipshaw cable-stayed bridge
Shipshaw bridge is a non-symmetric double-plane fan-typecable-stayed bridge over Saguenay River near JonquiereQuebec. The bridge is consisted of a double leg steel towerand two parallel box girders supporting a composite deck. Thebridge has four identical spans of 45.8 m with a total length of183.2 m. Further, the bridge has 4% downward slope from theEast to the west abutment. The bridge support system isfounded on rock. The tower bearings are hinged and allowed torotate in transverse axis. The abutment bearings are rollersupported which only allow the longitudinal movement andprevent the uplifting of the deck which is generated by cableforces. Meanwhile, the deck-tower connection is considered asa rigid connection.
The deck with 11 m breadth is made of concrete deck withthickness of 165 mm and has two non-structural precastparapets at each side. Furthermore, the deck is supported byfive longitudinal stringers which placed equally at 2.4 minterval. Floor beams are spaced at 7 m interval in transversedirection. The floor beams transfer the stringer loads to boxgirders. The box girder dimension is 1.5 m � 2.4 m with weband flange thickness of 50 mm. The tower height is 43 m whichconsisted of two 1.5 m � 2.4 m steel boxes with flange and webthickness of 50 mm. Four cables are connected from top of thetower to the box girders. Each cable consists of nine strandswith cross-sectional area of 65.1 mm2. The detail of the bridgeis shown in Fig. 1.
2.2. Numerical bridge modeling
Since cable-stayed bridges are complex structures with highdegree of redundancy and have a large number of degrees offreedom [6,7,30], the simplification of the model leads to
Fig. 1 – Shipshaw cable-stayed bridge detailing.
a r c h i v e s o f c i v i l a n d m e c h a n i c a l e n g i n e e r i n g 1 7 ( 2 0 1 7 ) 4 1 9 – 4 3 2 421
significant reduction in number of degrees of freedom andhence reduces the size of stiffness matrix and decreases theanalysis time consumption. To aid the aim, the nonlineardynamic time history analysis of Shipshaw cable-stayedbridge is analyzed by SAP2000 software [31]. The numericalanalysis is conducted on a simplified 3D full scale model asshown in Fig. 2. The bridge deck is modeled as shell elementwith 0.165 m thickness. The tower and box girders which areattached to sides of the concrete slab are modeled as 3D beamelements. For structural steel material Fy = 414 MPa withelastic modulus of 200 GPa and for concrete material f 0c ¼27:5 MPa with young modulus of 24.8 GPa are used in FE Model.The Poisson's ratio for steel and concrete is considered as 0.3and 0.2, respectively. The cables with diameters of 65.1 mm2
are modeled as cable elements taking into account the cablesag effect and the pre-tensioning force to minimize the verticaldeck deflection under dead loads. The modulus of elasticity ofcables is set to be 175 GPa with yield strength of 1500 MPa andultimate strength of 1725 MPa [27]. On the basis of simplifica-tion of the model, the numerical model has a total of 36
Fig. 2 – Three dimensional finite element m
elements which involves 52 and 118 numbers of mass andstiffness degrees of freedoms, respectively. The supportcondition at the base of the tower is hinged which only allowsthe tower to rotate about longitudinal and transverse axes andthere is no translation (UX = UY = UZ = 0). The abutments of thebridge are roller which means that they can move alonglongitudinal direction while translation is restrained invertical and transverse directions (UY = UZ = 0). Moreover, thenonlinearity of materials, P-delta effect and self-weight of thebridge have been taken into account in the analysis.
Fig. 3 shows the flexural mode shapes of the bridge fromnumerical analysis. The cumulative modal mass participationpercentage for the first 4 flexural modes is 95.3%. The largestmodal mass participation percentage is from the secondflexural mode, which is 64.27%. Table 1 shows the natural timeperiods of the bridge obtained from the previous experimentalmodal analysis [26] compared to numerical modal analysis inthe present study. There is a reasonable agreement of fournatural time periods computed experimentally and numeri-cally.
odel of Shipshaw cable-stayed bridge.
Fig. 3 – Four flexural mode shapes of the cable-stayed bridge.
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2.3. Earthquake ground motions
Seismic performance of cable-stayed bridge is evaluated usingtwo components of earthquake ground motion records. Thecharacteristics of earthquake ground motions highly affect theseismic responses of the bridge. In this context, a total of fourhistorical ground motion records are used in the analysiswhere two of them are moderate earthquakes and the other
Table 2 – Ground motion records characteristics.
Earthquake Station Magnitude
Sierra Madre-1991 Altadena, Easton Canyon Park 6.7
South Napa-2014 Huichica Creek 6.0
Cook Starit-2013 Ward Fire Station 5.9
Cape Mendocino-1992 Petrolia 7.0
Table 1 – Natural time periods of Shipshaw cable-stayed bridg
Mode Mode shape Time p
Experimental
1 1st flexural 1.85
2 2nd flexural 0.85
3 3rd flexural 0.57
4 4th flexural 0.38
two are strong earthquakes. The PGA values for two moderateearthquake ground motions range from 0.179 g to 0.449 g,whereas PGA values for two strong earthquake groundmotions vary from 0.807 g to 1.497 g. Table 2 shows the groundmotions characteristics used in the analysis. The accelerationand displacement response spectra for 5% structural dampingof the four ground motions are represented in Fig. 4. Themaximum ordinates of the spectral accelerations for Sierra
Distance (km) Longitudinaldirection
Transversedirection
PGA (g) PGV (cm/s) PGA (g) PGV (cm/s)
12.5 0.447 27.2 0.179 7.812 0.403 57.66 0.293 22.515 1.035 33.75 0.807 21.0915.5 1.497 126.1 1.039 40.5
e.
eriods (s) Percentage difference (%)
Numerical
2.09 12.90.86 1.20.57 0.00.42 10.5
0.0
0.5
1.0
1.5
2.0
2.5
0 1 2 3 4 5SpectralAccelera�o
n(g)
Time Perio d (s)
Longitudinal
0
0.5
1
1.5
2
0 1 2 3 4 5
SpectralAccelera�o
n(g)
Time Perio d (s)
Tran sverse Sierra Ma dre
Sout h Napa
Ward
CapeMendocino
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 1 2 3 4 5
SpectralDisplacemen
t(m)
Time Perio d (s)
Longitudinal
0
0.05
0.1
0.15
0.2
0.25
0.3
0 1 2 3 4 5SpectralDisplacemen
t(m)
Time period (s)
Tran sverse
(a)
(b)
Fig. 4 – (a) Acceleration and (b) displacement spectra of ground motions in longitudinal and transverse directions applied tothe bridge considering 5% damping.
Step A •Bridg e and sit e dat a dete rmination.
Step B•Using Simpli fed method to analyse the bridge in longitudinal di rec� on and to ge t ini�a les�ma�on for mul�-modal sp ectral analysis.
Step C•Usin g Simplife d metho d to analys e the bridg e in tran sverse di rectio n and to getinitial estimatio n for mult i-mod al spect ral analy sis
Step D•Combine d th e obtaine d resul ts of Step s B and C and �in d th e desig n valu e fordisplacements and forces
Step E •Desig n th e Lea d rubbe r bearing.
Fig. 5 – Methodology and design flow chart of seismicallyisolated bridge.
a r c h i v e s o f c i v i l a n d m e c h a n i c a l e n g i n e e r i n g 1 7 ( 2 0 1 7 ) 4 1 9 – 4 3 2 423
Madre, South Napa, Cook Starit and Cape Mendocino are 1.513 g,0.618 g, 2.257 g and 1.759 g occurring at 0.18, 0.08, 0.13 and 0.07 s,respectively along the longitudinal direction, whereas intransverse direction the maximum ordinates of the spectralaccelerations for Sierra Madre, South Napa, Cook Starit and CapeMendocino are 0.444 g, 0.426 g, 1.812 g and 1.367 g occurring at0.23, 0.08, 0.09 and 0.17 s, respectively. The ground motions areimposed uniformly at all bridge supports. The soil–supportsinteraction is neglected in the present study.
2.4. Base isolator design
Seismic isolation is an approach which reduces the seismicforce to or near the elastic capacity of the structure member,thereby eliminating inelastic deformation. The main aim ofutilizing the isolation system is to decrease the fundamentalfrequency of structural vibration to a value lower thanpredominate energy-containing frequency of earthquake.The performance criteria of isolated bridge during earthquakedesign may be specified by the owner, i.e. (i) displacementductility demand reduction in columns to keep the bridge openfor emergency vehicles after the earthquake; (ii) to keep bridgeresponse fully elastic; (iii) for the existing bridge, there shouldnot be any impacts at abutments and also minimum or zeroductility demand in columns; (iv) reduction of substructureforces in case the bridge is located on weak soils for reductionof foundation cost. Generally, isolators should be stiff for non-seismic loads and flexible for seismic loads. In this study,isolators are implemented at the abutments and deck-towerconnection by allowing the deck to sit on the base isolators.
LRB was invented by Robinson and Tucker in New Zealand[32]. It has been widely implemented in civil engineering
structures such as buildings and bridges. The design procedureof LRB devices are based on the Guide Specifications SeismicIsolation Design (GSID)AASHTO, 2010 [28] and LRFD BridgeDesign Specifications (LRFD) AASHTO, 2012 [29]. The method-ology flowchart has five steps as shown in Fig. 5. Initially, thecable-stayed bridge is analyzed statically under its self-weight.Seismic hazard of site was determined using (i) accelerationcoefficients, (ii) site class and site factors (iii) seismic zone ofsite. Later on, these data are used to plot design responsespectrum for the bridge. Thereafter, the obtained data will beused in analyzing a single-degree-freedom-model of bridge bysimplified method in both directions, as specified in GSID [28].The simplified method is also known as direct displacementmethod which involves several iterative process to getconvergence. As shown in Fig. 6, the designed values are usedto show the bilinear hysteretic response of LRB. In this study,the bridge is analyzed for the strongest earthquake based on SI
Fig. 6 – Detail and idealized hysteresis behavior of lead rubber bearing (LRB). disol = isolator displacement; dy = isolator yielddisplacement; Fisol = isolator shear force; Fy = isolator yield force; Kd = post-yield stiffness of isolator; Kisol = effective stiffnessof isolator; Ku = loading and unloading stiffness (elastic stiffness); Qd = characteristic strength of isolator.
Fig. 7 – Schematic hysteretic property of LRB in biaxial sheardeformation.
a r c h i v e s o f c i v i l a n d m e c h a n i c a l e n g i n e e r i n g 1 7 ( 2 0 1 7 ) 4 1 9 – 4 3 2424
system at which, the initial structural displacement isassumed as [28]:
d ¼ 0:254SD1 (1)
where SD1 is design spectral displacement. The characteristicsstrength, Qd should be chosen such that the isolators do notyield under non-seismic loads but low enough to yield underseismic loads; therefore, the equation below is detected to beappropriate to achieve the goal [33]:
Qd ¼ 0:05W (2)
where W is superstructure weight on each isolators. Also, post-yield stiffness, Kd, is minimal lateral restoring force at thedesign displacement which is calculated as [28]:
Kd ¼ 0:05Wd
(3)
and the effective period, Teff of bridge and viscous dampingratio, j are computed according to Eqs. (4) and (5), respectively[28]:
Teff ¼ 2P
ffiffiffiffiffiffiffiffiWgKd
s(4)
z ¼ 2Qdðdisol�dyÞPðKisolðdisol þ dsubÞÞ2
(5)
where disol is the isolator displacement, dy is the isolator yielddisplacement, dsub is the substructure displacement and Kisol isthe effective stiffness of isolator. Therefore, total bridge dis-placement is [28]:
d ¼ 0:249SD1Teff
BL(6)
where BL is damping coefficient. The total displacementobtained from Eq. (6) and initial assumed displacement
calculated from Eq. (1) should have close agreement. Thismay be achieved through iterative process using spreadsheet.
The last parameter is the lateral force of isolation systemwhich is obtained by [33]:
Fisol ¼ Kisol�disol (7)
2.5. Biaxial model for LRBs
The forces mobilized and biaxial interaction behavior of LRBcan be obtained by [34]:
F2 ¼ aFY
YU2 þ ð1�aÞFYZ2 (8)
F3 ¼ aFY
YU3 þ ð1�aÞFYZ3 (9)
Fig. 8 – Peak response of deck displacement duringearthquake excitations in longitudinal and transversedirections.
a r c h i v e s o f c i v i l a n d m e c h a n i c a l e n g i n e e r i n g 1 7 ( 2 0 1 7 ) 4 1 9 – 4 3 2 425
where a is the ratio of post-yield stiffness to pre-yield stiffness,Y is yield displacement, FY is the yield force, U2 and U3 arebearing displacements with respect to local axes as shown inFig. 7 (2 and 3 direction) and Z2 and Z3 are unit-less hystereticquantities which represents the direction and biaxial interac-tion of hysteretic forces. Z2 and Z3 can be obtained by thecoupled differential equations [35]:
Y_Z2_Z3
� �¼ A
_U2_U3
� �Z22 gsignð _U2Z2Þ þ b� �
Z2Z3 gsignð _U3Z3Þ þ b� �
Z2Z3 gsignð _U2Z2Þ þ b� �
Z23 gsignð _U3Z3Þ þ b� �
" #
(10)
where A, b and g are dimensionless quantities. In SAP2000software, the LRB is modeled as nonlinear link element whichrepresents the orthotropic behavior of LRB with respect to a
and the yield force changes in 2 and 3 directions.
-20-15-10-505101520
0 2 4 6 8 10
Accelera�o
n(m
/Sec
2 )
Time (Sec )
Longitudinal Deck Accelera�on
Fig. 9 – Acceleration time history of the deck un
Table 3 – Peak absolute acceleration response of the bridge de
Sierra Madre Sou
Non-isolated
Isolated Non-isolate
Acceleration in X direction (m/s2) 7.90 3.38 4.03
Acceleration in Y direction (m/s2) 2.55 2.01 3.12
3. Results and discussion
3.1. Deck displacement and acceleration
The deck displacement is measured at deck-tower intersec-tion. As Fig. 8 presents, the maximum deck displacement ofthe isolated bridge is larger than the non-isolated bridge underboth moderate and strong ground motions. The maximumlongitudinal displacement of the deck is increased from 5.8 cmto 12.4 cm after implementation of the base isolation system;hence, an increment of 113.8% is observed under CapeMendocino earthquake. Similarly, in transverse direction,the maximum deck displacement is enlarged from 5.9 cm to10.2 cm under Cape Mendocino earthquake which indicates178.3% increase of deck displacement in this direction. Thedeck displacements are increased because the isolatorschanged the boundary conditions of the bridge, at which itremoved the transverse restraints of the bridge at theabutments and changed the deck-tower configuration froma rigid connection to a moveable connection. Therefore,despite the deck displacement increments in the isolatedbridge, these displacements were limited to the designdisplacements obtained by the simplified analysis of thebridge.
The acceleration of the deck is also recorded at deck-towerintersection. As Table 3 indicates, non-isolated bridge experi-enced larger deck accelerations for both moderate and strongground motions as compared to the bridge with LRBs in bothdirections. The maximum deck acceleration reductions are62.26% and 35.38% in longitudinal and transverse directions,respectively, which, was subjected to Cook Starit groundmotion. Fig. 9 shows the deck acceleration time historyresponses of the non-isolated and isolated bridge under Cape
-20-15-10-505101520
0 2 4 6 8 10
Accelera�o
n(m
/Sec
2 )
Time (Sec )
Transverse Deck Accelera�on
Non-IsolatedIsolated
der Cape Mendocino earthquake excitation.
ck under different ground accelerations.
th Napa Cook Starit Cape Mendocino
dIsolated Non-
isolatedIsolated Non-
isolatedIsolated
2.72 21.15 7.98 17.13 7.752.58 8.28 5.35 18.23 14.55
Fig. 10 – Peak response of tower's base shear duringearthquake excitations in longitudinal and transversedirections.
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Mendocino strong ground motion. Further, the peak of deckacceleration dropped from 17.13 m/s2 to �7.75 m/s2 in longi-tudinal direction, while in transverse direction the peakacceleration reduced from �18.23 m/s2 to 14.55 m/s2. This
0
5
10
15
20
25
30
35
40
45
0 1 2 3
Tower
Height
(m)
Shear Force (kN )
Thousands
Sierra MadreLongitudnial
0.0 0. 5 1. 0 1.5
Shear Force (kN )
Thousands
South NapaLongitudnial
0
0
5
10
15
20
25
30
35
40
45
0 20 0 400
Tower
Height
(m)
Shear Force (kN )
Sierra MadreTransverse
0 20 0 400
Shear Force (kN )
South NapaTransverse
0
Fig. 11 – Maximum shear force response of the tower
figure clearly shows how the isolation system reduced thepeak of deck acceleration and lengthens the accelerationresponse of the deck in both directions substantially.
3.2. Tower response
In cable-stayed bridges, the entire cable system relies on thetower, therefore, the failure or instability of the tower may leadto failure of the entire bridge. Thus, it is necessary to study theseismic behavior of the tower under seismic loading[3,12,13,36]. In this study, owing to the symmetry of bridgein transverse direction, only one side of the tower is selectedfor comparison of the results. Accordingly, an attempt is madeto investigate the tower responses in terms of moment, shearand axial force along the tower height as well as the base shearand base moment of the tower base.
3.3. Base shear and tower shear force
As Fig. 10 depicts, the base isolators reduce the base shearproduced by different ground motions excitations. Themaximum value of the base shear in longitudinal directionis 9823.2 kN due to Cape Mendocino earthquake and it is
1 2 3 4 5
Shear Force (kN)
Thousands
Cook StaritLongitudnial
0 1 2 3 4 5
Shear Force (kN)
Thousands
Cape MendocinoLongitudnial
Non-Isolated
Isolated
50 0 1,000
Shear Force (kN)
Cook StaritTransverse
0 1,00 0 2,000
Shear Force (kN)
Cape mendocinoTransverse
Non-Isolated
Isolated
along its height under different ground motions.
Fig. 12 – Maximum base moment response of the towerunder earthquake excitations in longitudinal andtransverse directions.
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dropped to 8612.7 kN when the isolation system was utilized inthe bridge. Following this, it can be seen that the maximumbase shear reduction in longitudinal direction is 49.33% underCook Starit earthquake, while the minimum reduction of baseshear in this direction is 14.05% which occurred under Cape
051015202530354045
0 2 4
Tower
Height
(m)
Bending Mome n(kN-m)
x 1000 0
Sierra MadreLongitudnial
0.0 0. 4 0. 8 1.2
Bending Moment(kN-m)
x 1000 0
South NapaLongitudnial
0
0
5
10
15
20
25
30
35
40
45
0 120 0 2400
Tower
Height
(m)
Bending Moment(kN-m)
Sierra MadreTransverse
0 200 0 4000
Bending Moment(kN-m)
South NapaTransverse
0
Fig. 13 – Bending moment distribution along the tower hei
Mendocino earthquake. Subsequently, the maximum peakresponse of the base shear of the non-isolated bridge intransverse direction is 9208.2 kN which is reduced to 3894 kNin the isolated bridge. Thereupon, in transverse direction themaximum base shear reduction is 57.71% under CapeMendocino earthquake and the minimum observed reductionis 27.39% under South Napa earthquake. It is observed that thebase shear mitigation in transverse direction is more signifi-cant as compared to longitudinal direction. This is due to thefact that, the movement of non-isolated bridge is restrained intransverse direction, while, in the isolated bridge the trans-verse movement is permitted up to the design displacement.Thus, a satisfactory base shear mitigation can be expected forthe cable-stayed bridges equipped with base isolation systemin seismic regions.
Fig. 11 illustrates the shear force of the tower as a functionof its height. According to this figure, the utilization effect ofthe LRBs on reduction of tower shear force is prominent. Theshear force reduction of the tower in the superstructure is upto 85.5% and 54.9% in longitudinal and transverse directions,respectively. Subsequently, in longitudinal and transversedirections, up to 62.9% and 37.8% decrement of shear force ofthe tower in substructure are observed. The shear force in thetower above the deck level is reduced significantly as the
1 2 3 4 5
Bending Mometnt(kN-m)
x 1000 0
Cook StaritLongitudnial
0 1 2 3 4 5
Bending Moment(kN-M)
x 1000 0
Cape MendocinoLongitudnial
Non-IsolatedIsolated
5000 10000
Bending Moment(kN-m)
Cook StaritTransverse
0 1000 0 20000
Bending Moment(kN-m)
Cape mendocinoTransverse
Non-Isolated
Isolated
ght in both directions under different ground motions.
a r c h i v e s o f c i v i l a n d m e c h a n i c a l e n g i n e e r i n g 1 7 ( 2 0 1 7 ) 4 1 9 – 4 3 2428
isolators dissipated the seismic force transmits from thesubstructure to superstructure. This reduction ultimatelyincreases the stability of the superstructure in both directions,even under the strongest earthquakes. Consequently, theshear force for the tower below the deck level also decreases assome of the forces are dissipated through the characteristics ofLRB and hence, the possibility of damage to substructure isreduced.
3.4. Base moment and tower bending moment
The value of the base moment in non-isolated bridge is quitelarge, especially in longitudinal direction as shown in Fig. 12.The maximum and minimum base moment reductions are80.53% and 52.48% under Cook Starit and Cape Mendocino inlongitudinal direction, respectively. Further, the maximummoment decrement in transverse direction is 84% under CapeMendocino earthquake, whereas, the minimum reductionpercentage is 42.06% under Sierra Madre earthquake.
Fig. 13 shows the bending moment distribution along thetower height. The bending moment of the tower in substruc-ture section is reached to its maximum value at deck level inboth directions. The tower bending moment of isolated bridgesfollowed the same trend of non-isolated bridge. As shown inthe figure, after the implementation of the base isolators, thistrend is significantly changed and caused significant decre-ment in bending moment of the tower in both superstructure
051015202530354045
0 20 0 400
Tower
Height
(m)
Axial Force (kN )
Sierra MadreLongitudnial
0 10 0 20 0 300
Axial Force (kN )
South NapaLongitudnial
051015202530354045
0 20 40
Tower
Height
(m)
Axial Force (kN )
Sierra MadreTransverse
0 25 50
Axial Force (kN )
South NapaTransverse
0
Fig. 14 – Maximum axial force of the tower along its heig
and substructure. The maximum reduction of bendingmoment in the tower is �85.4% observed in longitudinaldirection while, the minimum bending moment decrement is9.3% which lied in substructure. Thereupon, utilization of baseisolation system in the bridge results in a remarkableminimization of tower bending moment of and base momentresponses of the bridge in both directions.
3.5. Axial force
The tower axial force under different ground motions is shownin Fig. 14. As figure indicates, the axial force of the tower insubstructure is noteworthy larger than the tower axial force insuperstructure section. In longitudinal direction, the isolationsystems reduced the tower axial forces up to 82.2% in bothsubstructure and superstructure sections. Meanwhile, intransverse direction, the isolation systems slightly reducedthe axial force of the tower above the deck level, whereas theaxial force in tower below the deck is increased from 48.73% to72.22%. The reason is that, the base isolators separated thesuperstructure from substructure at the deck-tower connec-tion (from rigid configuration to movable configuration) andremoved the transverse restraints of the bridge at abutments.Therefore, a flexible plane is produced at the deck level whichled to unfavorable torsional moment when earthquakes areapplied in transverse direction. These torsional moments aretransmitted from box girders to substructure and caused a
0 30 0 60 0 90 0 1200
Axial Force (kN)
Cook StaritLongitudnial
0 40 0 80 0 1200
Axial Force (kN)
Cape MendocinoLongitudnial
Non-IsolatedIsolated
50 10 0 150
Axial Force (kN)
Cook StaritTransverse
0 10 0 20 0 300
Axial Force (kN)
Cape mendocinoTransverse
Non-IsolatedIsolated
ht under different ground motions in both directions.
a r c h i v e s o f c i v i l a n d m e c h a n i c a l e n g i n e e r i n g 1 7 ( 2 0 1 7 ) 4 1 9 – 4 3 2 429
notable increment in tower axial force in the tower section thatlied in the substructure.
3.6. Cable response
Herein, since the bridge is symmetric in transverse direction,only half side of the bridge cables are selected for thepresentation of the results. The cables are numbered as 1, 2,3 and 4 from the West to the East, respectively. Fig. 15 showsthe variation of tension forces in cables with respect to theirexisting nominal pretension force. The tension force in cables3 and 4 are higher as compared to cables 1 and 2, for the reasonthat their connected end to box girders have closer distances tothe tower. From the figure, it can also be seen that, the baseisolators caused significant reduction in all cables' forcevariation in both directions subjected to different intensityearthquakes. The cables force variation is reduced up to 81.8%
Fig. 15 – Maximum tension forces of the cables during earthqu
and 89.6% in longitudinal and transverse directions, respec-tively.
3.7. Hysteresis curves of isolators
The force–displacement hysteresis curves of LRB under twocomponents of each earthquake are investigated. Fig. 16demonstrates the hysteresis behavior of a selected LRB at theWest abutment under moderate and strong earthquakes. Asthe figure indicates, the isolator hysteresis curves reached themaximum yield force under Cook Starit and Cape Mendocinoearthquakes. This performance confirmed that the isolatorsare perfectly able to dissipate the induced seismic forces to thesuperstructure. In addition to this, the isolator dissipated theinduced energy by moderate earthquakes in linear state of itscharacteristic.
ake excitations in longitudinal and transverse directions.
-600
-400
-200
0
200
400
600
800
-0.2 -0. 1 0 0. 1 0.2
Force(kN)
Displacement (m)
Longitudinal Di rec�on
Sierra Madre South Na pa
Cook Starit Cape Mendocin o
-600
-400
-200
0
200
400
600
-0.1 -0.0 5 0 0.0 5 0. 1 0.15
Force(kN)
Displacement (m)
Transverse Di rec�on
Sierra Ma dre South Na pa
Cook Starit Cape Mendocin o
Fig. 16 – Force–displacement hysteresis curve of the selected LRB at the West abutment.
Table 4 – Summary of maximum seismic responses of the non-isolated and isolated cable-stayed bridge.
Ground motions Sierra Madre South Napa Cook Starit Cape Mendocino
Response Direction Non-isolated
Isolated Non-isolated
Isolated Non-isolated
Isolated Non-isolated
Isolated
Deck displacement of deck (cm) X 2.7 4.9 1.2 1.6 4.8 6.3 5.8 12.4Y 0.7 1.4 0.9 1.9 2.3 6.4 5.9 10.2
Acceleration of deck (m/s2) X 7.9 3.4 4.0 2.7 21.2 8.0 17.13 7.8Y 2.5 2.0 3.1 2.6 8.3 5.3 18.22 14.6
Base shear (kN) X 5359.4 3828.3 2348.2 1626.5 9206.4 4664.5 9823.2 8612.7Y 1308.6 932.4 1691 1227.6 4088.9 2779.9 9208.8 3894
Base moment (kN m) X 116,078.4 47,804 56,390 24,063.3 326,495.8 63,537.1 250,991.4 119,268.1Y 6398.9 3707 11,597.3 4476.9 25,483.3 7912.6 58,487.3 9361
Cable force 1 (kN) X 50.6 16.2 22.2 10.3 122.2 22.2 107.9 29.2Y 2.7 1.1 3.6 1.2 10.4 3 24.2 7.2
Cable force 2 (kN) X 77.7 23.3 32.8 15 201.1 38.1 186.2 42.6Y 3.7 0.8 4.3 0.8 12.6 2 30.7 3.2
Cable force 3 (kN) X 89.6 26.7 40.8 16.4 227.2 47.5 202.3 54.3Y 3.7 2.2 4.8 2.8 14.5 5.8 33.7 16.9
Cable force 4 (kN) X 125.4 40 54.9 25.3 228.3 54.6 268.2 72Y 3.9 2.3 4.5 3.2 15.3 7.5 29.3 19.3
a r c h i v e s o f c i v i l a n d m e c h a n i c a l e n g i n e e r i n g 1 7 ( 2 0 1 7 ) 4 1 9 – 4 3 2430
3.8. Overall dynamic performance
A summarized comparison of maximum seismic responses ofthe cable-stayed bridge is given in Table 4. The performancecomparison of the original configuration (non-isolated) andisolated cable-stayed bridge showed that the isolation systemis positively able to mitigate the unwanted response of thestructure under destructive seismic loads. In other words, theoverall seismic performance of the cable-stayed bridge isremarkably improved by utilizing the base isolators at thedeck-tower connections and the supports. Additionally, theisolators are able to minimize the transmission of seismicforces from substructure to superstructure, and hence,mitigate the damage to the superstructure. Following this,as the bridge is an existing structure which is located at highseismic zone and suffered damages due to earlier seismicexcitations, the base isolation system can be considered aspossible alternatives solution for seismic retrofitting strategy.
4. Conclusions
In this study, the seismic behavior of an existing steel cable-stayed bridge equipped with LRBs has been investigated. Theisolators have been designed for the strongest earthquake andimplemented at abutments and deck-tower connection of thecable-stayed bridge. The bridge seismic responses in longitu-dinal and transverse directions have been evaluated throughbi-directional moderate and strong earthquakes. In line withthis purpose, a 3D FE model of the bridge has been developedand the nonlinear dynamic time-history analysis of the bridgehas been performed. Nonlinearities sources and abutmentselevation difference of the cable-stayed bridge have beentaken into consideration in the numerical modeling. From thedetailed analysis, the implementation consequences of thebase isolation system in cable-stayed bridge led to thefollowing conclusions:
a r c h i v e s o f c i v i l a n d m e c h a n i c a l e n g i n e e r i n g 1 7 ( 2 0 1 7 ) 4 1 9 – 4 3 2 431
� Even though the deck displacement of isolated bridgeincreased up to 113.8% and 178.3% in longitudinal andtransverse directions, respectively, yet it remained in therange of the design displacement of the bridge. Meanwhile,the isolation system caused a remarkable reduction of thedeck acceleration in both directions.
� The isolation system was significantly capable to reduce thebase shear and base moment of the bridge under bothmoderate and strong ground motions.
� The reduction of bending moment and shear force in thetower proved that the isolation system is able to dissipatethe seismic forces transmitted from substructure to super-structure, and hence, reduced the occurrence of damage tothe superstructure.
� The implementation of the isolation system betweensuperstructure and substructure increased the deck flexibil-ity, especially in transverse direction and caused torsionaldeformation under transverse earthquake component. Thistorsional moment transferred to substructure through baseisolators and enlarged the axial force of the tower insubstructure.
� The cable force variation reduced substantially and enhancedthe stability of the deck under serviceability condition.
� The mitigation of maximum seismic responses might occurunder strong earthquakes, as the isolations were stiff for themoderate earthquakes. Therefore, the seismic zones are animportant parameter in design of base isolators for cable-stayed bridges.
Acknowledgements
The authors gratefully acknowledge the support given byUniversity Malaya Research Grant (UMRG – Project No. RP004A/13AET), University Malaya Postgraduate Research Fund (PPP –
Project No. PG242-2015B) and Fundamental Research GrantScheme, Ministry of Education, Malaysia (FRGS – Project No.FP028/2013A).
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