Engineering Structures 49 (2013) 396–407

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Engineering Structures

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Seismic performance assessment of highway bridges equipped withsuperelastic shape memory alloy-based laminated rubber isolationbearing

0141-0296/$ - see front matter � 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engstruct.2012.11.022

⇑ Corresponding author. Tel.: +1 250 807 9397; fax: +1 250 807 9850.E-mail address: shahria.alam@ubc.ca (M.S. Alam).

A. Rahman Bhuiyan, M. Shahria Alam ⇑School of Engineering, The University of British Columbia, Kelowna, BC, Canada V1V 1V7

a r t i c l e i n f o

Article history:Received 23 November 2011Revised 20 November 2012Accepted 20 November 2012Available online 28 December 2012

Keywords:Seismic performanceHighway bridgeStrain-rate-dependent constitutive modelNonlinear dynamic analysisLaminated rubber bearing

a b s t r a c t

Seismic performance analysis is conducted for an isolated three-span continuous highway bridge, whichis subjected to moderate to strong earthquake ground accelerations in the longitudinal direction. Twotypes of isolation bearings are used in the analysis: high damping rubber bearing (HDRB) and combinedisolation bearing consisting of shape memory alloy (SMA) wires and natural rubber bearing (NRB) enti-tled as SMA-based rubber bearing (SRB). Two types of SMA wires, such as Ni–Ti and Cu–Al–Be, are used infabricating the combined isolation bearings. In the first step of the work, analytical models for HDRB, NRBand SRB are introduced. Then, a three-span continuous highway bridge is modeled in a simplified form,using 2-DOF bridge pier-bearing system isolated by either HDRBs or SRBs. The hysteretic behavior ofHDRB is evaluated using a strain-rate dependent constitutive model (i.e. visco-elasto-plastic model),while in the case of SRBs the hysteretic behavior is modeled by a nonlinear elasto-plastic model forNRB and a simplified visco-elastic model for SMAs. A standard bilinear force–displacement relationshipis employed in the analytical model of the bridge pier to consider its nonlinear characteristic behavior.Nonlinear dynamic analysis of the bridge, based on the direct time integration approach, is conductedto evaluate the seismic responses of the bridge. This study shows that the seismic responses of the bridgeare affected by the use of different types of isolation bearings; more specifically, residual displacement ofthe deck are noticeably reduced after earthquakes in the case of SRBs compared to HDRB for moderateand strong earthquakes; however, pier displacements are smaller in the cases of SRBs for moderate earth-quakes and higher for strong earthquakes. Other response parameters of the system, such as deck dis-placement, bearing displacement and deck acceleration, are significantly larger in the cases of SRBscompared to those of HDRB. This study also depicts the effect of modeling of isolation bearings on theseismic responses of the system.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Seismic isolation has been considered as a reliable and cost-effective technology to alleviate the risks of seismic damages tohighway bridges [1–5]. In Japan and United States, more than200 bridges have been designed or retrofitted with seismic isola-tion devices in the last 20 years, for example, the 29-span continu-ous O-Hito viaduct in Japan and the 7-span continuous steel girderLake Saltonstall bridge in USA. Seismic isolation is meant to shiftthe natural period of a bridge structure in such a way that the dom-inant frequency of the earthquake ground acceleration can safelybe avoided to safeguard it against seismic damages. In addition,the inherently occupied damping property and energy dissipationmechanism prevents the bridge system from over displacement

[5]. Field data on the seismic response of isolated bridges duringrecent earthquakes [6], experimental works [7–11] and analyticalstudies [7,8,10,12–16] have indicated that isolation bearings cansubstantially improve the seismic performance of bridges and con-sequently reduce the post-disaster cost for repair and rehabilita-tion [17].

Two types of seismic isolation bearings are mainly available forthis purpose: laminated rubber bearings and sliding bearings. Thesliding bearings show reasonably good performance under a widerange of earthquake loadings and have been applied in both build-ings and bridges [18]. They are insensitive to the frequency contentof earthquake excitations as they can suppress and widen theearthquake energy over a large range of frequencies [19]. The slid-ing-type bearings have several deficiencies over laminated rubberbearings. For instance, (i) large maintenance of sliding surface isexpensive and difficult as lubrication is required while in service;(ii) difficult to mount and erect due to its large size and heavy

A. Rahman Bhuiyan, M.S. Alam / Engineering Structures 49 (2013) 396–407 397

weight; (iii) occurrence of large relative displacement betweenbridge deck and pier as it does not have re-centering capacity,and (iv) a stopper is essential. On the other hand, laminated rubberbearings have the ability to carry vertical loads in compression andaccommodate shear deformations [1]. The rubber layers reinforcedwith steel shims (Fig. 1) reduce the freedom to bulge by increasingthe vertical stiffness of the bearing. Three types of laminated rub-ber bearings are widely used as seismic isolation devices: naturalrubber bearing (NRB), lead rubber bearing (LRB), and high dampingrubber bearing (HDRB). Natural rubber bearings are inherentlyflexible (i.e. reduced stiffness) and possess small damping prop-erty. Hence, NRBs have been utilized to accommodate the thermalmovement, the effects of pre-stressing, creep, and shrinkage ofsuperstructure of highway bridges or for seismic isolation by com-bining with other energy dissipation devices such as lead, steel andviscous damper [1,5]. Other two types of bearings acquire highdamping, which are developed and widely used in various civilstructures including bridges in many countries, especially in Japanand USA [1,4,5]. Although the schematic of HDRB and NRB are thesame (Fig. 1), HDRB uses high damping rubber whereas NRB usesnatural rubber. HDRBs possess a variety of mechanical properties,which are influenced by their compounding effects [7] (i.e. thechemical composition of rubber chain, which is fully controlledby the manufacturer; for instance, in high damping rubber, a spe-cial fluid is used in the fabrication process to increase its dampingproperty), nonlinear elasto-plastic behavior [1], temperature andstrain-rate dependent viscosity property [5,20–22]. Lead rubberbearings also acquire all the mechanical properties of HDRB withreduced extent [23]. The unfortunate coincidence of the naturalperiod of a seismically isolated bridge with that of the near fieldearthquakes may enhance its seismic responses significantly. Espe-cially, laminated rubber bearings may experience large horizontaldeformation under near field earthquakes, which may cause detri-mental problems such as instability of the bearings, unseating andpounding problems of the bridge deck [14,24].

In recent years, a number of attempts have been reported, bycombining natural rubber bearing (NRB) and shape memory alloy(SMA) in seismic isolation of highway bridges, to partially solvethe problems incurred by laminated rubber bearings [14,15,24–27]. The superelasticity accompanied by hysteresis property ofthe SMA allows it to fabricate with laminated rubber bearings toreduce the residual deformation of the bridge system. Consideringthe restoration and energy dissipation capacity of SMAs, they aregaining wide interests in the research community for seismic pro-tection of highway bridges. Ozbulut and Hurlebaus [14] conducteda sensitivity analysis to examine the effectiveness of an isolationsystem consisting of SMA device and natural rubber bearing(SRB) for seismic protection of highway bridges. They utilized aneuro-fuzzy model to replicate the superelastic behavior alongwith re-centering capability of SMAs at various temperatures andloading rates, and a linear equivalent method for modeling hyster-esis behavior of natural rubber bearing, which were then applied inevaluating the seismic performance of a three-span continuousbridge. They showed that the isolation system can successfully re-duce the deck drift of highway bridges. Wilde et al. [15] used SMAbars coupled with elastomeric bearings for bridges in transverse

Fig. 1. Description of the isolation bearing (pad 1000 mm � 1000 mm with 350 mm heighshims, (b) SRB in un-deformed condition and (c) SRB in deformed condition.

direction and demonstrated that the SMA bars with elastomericbearings are effective device to control relative deck displacement.Choi et al. [24] proposed a new isolation bearing that consist ofnatural rubber bearing and pre-stressed Ni–Ti SMA wires thatwrap the bearing in the longitudinal direction. Dynamic time his-tory analyses were conducted using two earthquake ground accel-erations on multi-span continuous highway bridge to evaluate theeffectiveness of the proposed bearings where each record wasscaled up to 0.8 g. The performance of the new bearing was com-pared to that of a conventional lead rubber bearing. They showedthat the new bearing provides adequate damping properties andcentering capability, which restricts the relative displacement ofthe bridge. DesRoches and Delemont [25] utilized SMA bars asrestrainers in a multiple span simply supported isolated bridgewith elastomeric bearings and showed that the SMA bars can moreeffectively restrain the relative deck displacement compared to theconventional steel cable restrainers. Johnson et al. [26] carried outlarge-scale shake table testing to estimate the performanceimprovement of SMA restrainers fitted in an isolated multi-framebox girder bridge under seismic loading and compared their per-formance with traditional steel restrainers. Casciati et al. [27]developed an isolation system consisting of sliding system and in-clined Cu–Al–Be SMA, and conducted extensive experiments on aprototype device to illustrate the effectiveness of using the new de-vice in dissipation of energy and re-centering capability. Recently,Alam et al. [28] and Bhuiyan and Alam [29] have carried out perfor-mance evaluation of multi-span continuous highway bridge iso-lated by an isolation bearing consisting of high damping rubberbearing and Ni–Ti SMA restrainers, and demonstrated the effec-tiveness of the bearing in seismic responses of the bridge.

Several researchers have utilized SMAs for outdoor applications,for instance, Wilde et al. [15], Choi et al. [24] used superelastic Niti-nol for base isolation of bridges; however, temperature effect wasnot considered in those studies. In cold region country like Canadatemperature can range from �50 �C to +40 �C in some places. Usu-ally Nitinol’s austenite finish temperature (Af) ranges from �10 �Cto 44 �C [30], which clearly demonstrates its potential of losingsuperelasticity if the temperature goes below its Af where the sys-tem will lose its recentering capability. Therefore, SMAs having Af

below �50 �C might be a better choice for outdoor applications.For instance, Zhang et al. [16] utilized superelastic Cu–Al–Be barwith Af of �65 �C. They numerically showed the effectiveness ofsuperelastic Cu–Al–Be restrainer for bridges. Alternatively, at lowtemperatures regular SMA can also be used with the help of a con-trol system where in the case of an excitation, the SMA wires willbe automatically electrically heated above its Af to trigger its super-elasticity [31]. Considering the thermomechanical properties ofSMAs as mentioned above, previous researchers have proposedtwo different SMAs i.e. Ni–Ti and Cu–Al–Be for isolation and re-strainer applications.

In all these previous attempts, natural/lead rubber bearings(NRBs/LRBs) were mostly employed in constructing their proposedSMA based isolation bearings. Moreover, either the equivalent lin-ear model or the bilinear model [32,33] was adopted to analyticallydescribe the mechanical behaviors of the NRBs/LRBs. However, ithas been experimentally evident from the previous works

t) (a) HDRB; the rubber layers with high damping properties are vulcanized by steel

Fig. 2. Typical shear stress–strain response of HDRB as obtained by using Eqs. (1a)–(1d). These responses are obtained from a HDRB when it is subjected to a sinusoidalexcitation with 0.5 Hz and 1.75 strain. The elato-plastic response of HDRBcorresponds to Eq. (1b), the elastic response denotes by Eq. (1c) and finally therate-dependent response corresponds to Eqs. (1d) and (1e). The elasto-plastic andelastic responses of the bearing can be obtained by conducting multi-steprelaxation (MSR) tests and the rate dependent response of the bearing can beidentified using the simple relaxation (SR) test results (Bhuiyan [20]) and Bhuiyanet al. [21].

398 A. Rahman Bhuiyan, M.S. Alam / Engineering Structures 49 (2013) 396–407

[7,10,20–22] that the mechanical behavior of the NRBs/LRBs can-not be rationally replicated by using the above mentioned simplemodels, since the compounding and vulcanizing of the rubber[7,34] at its manufacturing stage significantly affect the mechani-cal behavior of the bearings. Furthermore, the use of high dampingrubber bearing (HDRB) is being widely appreciated in the seismicisolation of highway bridges and its mechanical behavior canhardly be expressed in terms of either equivalent linear or bilinearmodels that do not capture the complex mechanical behavior ofHDRB under strong earthquake ground accelerations, since it isstrongly influenced by magnitude, history and rate of displace-ments experienced [1,7,20–22]. In addition, very few or no studieswere reported to consider the nonlinear force–displacement rela-tionship of the bridge pier to include inelastic responses understrong earthquake ground accelerations. In this regard, further re-search works are required to investigate the suitability of usingSMA-based isolation bearings (SRBs) in highway bridges underseismic loads.

With this backdrop, the objective of this study is to carry outseismic performance analysis of a three-span continuous highwaybridge under moderate to strong earthquake ground accelerationsexcited in the longitudinal direction. In this regard, two types ofisolation bearings are used in the analysis: high damping rubberbearing (HDRB) and combined isolation bearing consisting ofSMA wires and natural rubber bearing entitled as (SRB) hereafter.Two types of SMA wires, such as Cu–Al–Be and Ni–Ti are used infabricating the combined isolation bearings, which are entitledhereafter as SRB-1 and SRB-2, respectively. In the first step of thework, analytical models for HDRB, NRB and SRB are briefly intro-duced. Then, a three-span continuous highway bridge is modeledin a simple form by a 2-DOF system, isolated by HDRB and SRB-1and SRB-2. The nonlinear force–displacement relationship of thebridge pier is employed in the analytical model of the bridge whichis governed by the bilinear hysteresis model. Nonlinear dynamictime history analysis of the bridge using the 4th order Runge–Kuttamethod is conducted. Finally, the variations in seismic responses ofthe bridge system due to the use of HDRB, and SRB-1 and SRB-2 areexplored.

Fig. 3. Analytical model of the HDRB showing stress and strain decompositions;shear stress represents the average stress obtained by dividing the horizontal loadby plan area of the bearing and shear strain can be obtained by dividing thehorizontal shear deformation by the height of the rubber layers. The parameterscorresponding to spring A, B, and Slider S can be identified from MSR test results[20], the parameter corresponding to spring C can be determined using the cyclicshear (CS) test results at different strain rates [20] and the parameters correspond-ing to dashpot D can be evaluated using the SR test results [20].

2. Analytical modeling of isolation bearings

Two types of isolation bearings are used in the present analysis:HDRB and SRB. SRB uses conventional NRB where SMA wires arewrapped around the bearing in the loading direction as shown ifFig. 1b and c. A brief introduction of the three components (HDRB,NRB, SMA wire) is given in the following paragraphs.

The experimental investigations conducted by several authors[1,7,20,22,34] have revealed four different fundamental propertiesof HDRBs, which together characterize its typical overall response:(i) a nonlinear elastic stress response, which is characterized bylarge elastic strains; (ii) a finite elasto-plastic response associatedwith asymptotically traced equilibrium states; (iii) a finite strain-rate dependent viscosity induced overstress, which is portrayedby relaxation tests, and finally and (iv) a damage response withinthe first few cycles which induces considerable stress softeningin the subsequent cycles. Typical stress–strain responses of HDRBare presented in Fig. 2: these responses are obtained when thebearing is subjected to a sinusoidal excitation with 0.5 Hz and1.75 strain.

Considering the first three properties, a strain-rate dependentconstitutive model for the HDRBs is developed by Bhuiyan [20]and Bhuiyan et al. [21], which is verified with sinusoidal excita-tions and subsequently implemented in a professional structuralengineering software (RESP-T) [35] for conducting seismic perfor-mance analysis of multi-span continuous highway bridges [20].

The rheology model together with the decomposition of stressesand strains are presented in Fig. 3.

Eqs. (1a)–(1e) provide the explicit expressions for the averageshear stress s and strain c of HDRB. A rigorous experimental inves-tigation was carried out by Bhuiyan [20] to identify the parametersof the model. The first branch of the model describes elasto-plasticresponse of the bearing, which is obtained from multi-step relaxa-tion test results and it corresponds to Eq. (1b). The multi-steprelaxation (MSR) test is conducted by applying a shear strain his-tory at top of the bearing where a number of relaxation periodsof 20 min, during which the applied strain is held constant, are in-serted in loading and unloading at a constant strain rate. The stres-ses obtained from each strain history are used for evaluating theelasto-plastic response of the bearing. The second branch indicatesthe elastic response of the bearing which can be obtained using thesame MSR test results and is denoted by Eq. (1c). The third branchof the model is the finite strain-rate dependent overstress, whichcan be obtained from simple relaxation (SR) test results and corre-sponds to Eqs. (1d) and (1e). The stress history obtained from theSR test results is used for determining the overstress. For furtherdetails and discussions, the interested readers are referred to theearlier efforts by Bhuiyan [20] and Bhuiyan et al. [21].

A. Rahman Bhuiyan, M.S. Alam / Engineering Structures 49 (2013) 396–407 399

s ¼ sepðcaÞ þ seeðcÞ þ soeðccÞ ð1aÞ

sep ¼ C1ca with_cs–0 for jsepj ¼ scr

_cs ¼ 0 for jsepj < scr

�ð1bÞ

see ¼ C2cþ C3jcjmsgnðcÞ ð1cÞ

soe ¼ C4cc with soe ¼ A_cd

_co

��������n

sgnð _cdÞ ð1dÞ

and

A ¼ 12ðAl expðqjcjÞ þ AuÞ þ

12ðAl expðqjcjÞ � AuÞ tan hðnsoecdÞ ð1eÞ

where Ci (i = 1–4), scr, m, Al, Au, q, n, and n are the model parametersdetermined from experiments [20] and listed in Table 1. ca, cs, cc

and , cd are the shear strains in spring A, slider S, spring C and dash-pot D, respectively as presented in Fig. 3. The parameters C1, C2, C3,scr and m are identified from MSR test results [20], C4 can be deter-mined using cyclic shear (CS) test results at different strain rates[20] and Al, Au, q and n can be known from the SR test results [20]and finally, n can be obtained from sinusoidal excitation at a partic-ular strain rate and strain level [20].

A rigorous experimental investigation [20] of different types ofNRBs has revealed that NRB exhibit significantly less strain-ratedependent viscosity induced overstress compared to that of HDRB;however, the elastic ground stress response characterized stainhardening feature of NRB at large strains becomes more dominantthan that of HDRB [20]. In order to take this fact into account, asimplified version of the rheology model suitable for NRB is pre-sented in Eq. 2, using the upper two branches of stress componentsas shown in Fig. 3. Table 1 shows the parameters of the modelsused in the study.

s ¼ sepðcaÞ þ seeðcÞ ð2aÞ

sep ¼ C1cawith_cs–0 for jsepj ¼ scr

_cs ¼ 0 for jsepj < scr

�ð2bÞ

see ¼ C2cþ C3jcjmsgnðcÞ ð2cÞ

Smart materials, such as shape memory alloys (SMAs) have greatpotentials in seismic hazard mitigation applications [15,24]. Varioustypes of SMAs (for instance, Ni–Ti, Ni–Ti–Cu, Cu–Zn–Al, Cu–Al–Be,etc.) in the form of wires and bars with different diameters havebeen experimentally investigated by a number of researchers undertensile, compressive, torsional, and shear forces where the detailscan be found in Alam et al. [30]. SMAs possess several desirableproperties to be used as dampers and restrainers in bridges [30].These properties are (i) large elastic strain range, (ii) hystereticdamping, (iii) highly reliable energy dissipation due to repeatable

Table 1Parameters for HDRB and NRB used in the analysis.

Parameters Values

HDRB NRB

C1 (MPa) 2.501 1.95C2 (MPa) 0.653 0.798C3 (MPa) 0.006 0.005C4 (MPa) 3.251 –scr (MPa) 0.247 0.15m 6.621 7.65Al (MPa) 0.354 –Au (MPa) 0.241 –n 0.223 –q 0.341 –n 1.252 –

solid state phase transformation, (iv) strain hardening, (v) excellentfatigue resistance, and (vi) excellent corrosion resistance. High costof SMA is the primary restraining factor for its wide implementationin developing smart devices. Although Cu-based SMAs are lesscostly, they exhibit poor ductility. Mechanical properties of SMAsmostly depend on the heat-treatment temperature, where smalldeviation can lead to considerable changes in their properties. Forits wider implementation, manufacturers need to produce SMAsin mass scale with proper control of its properties and transforma-tion temperatures [30].

In general, the constitutive model of SMA is very complicated ina sense that it depends upon many factors such as strain rates [36],strain magnitude and strain history [37]. Three categories of con-stitutive models are used for characterizing the superelasticityand damping properties of SMA, such as parametric, nonparamet-ric and differential equation-based models. The differential equa-tion-based constitutive models comprise two versions of models,such as phenomenological models [36,37] and thermodynamics-based models [38,39]. The thermodynamics-based models arefounded on laws of thermo dynamics and energy consideration.These models are much more complicated and computationallydemanding than the phenomenological models as they are pre-cisely derived on three dimensional constitutive laws. On the otherhand, the phenomenological models are relatively simple and easyto construct from the experimental characterization of SMAs andare readily applicable in civil engineering applications through fi-nite element software packages, such as ANSYS [40] and Seimo-Struct [41]. Considering the complexity of replicating themechanical behavior of SMAs with the use of phenomenologicalmodels, three versions of the models are used in seismic applica-tions [42] that include: a simplified model, which is constructedbased on experimentally obtained data; a thermomechanical mod-el, which considers the stress–strain–temperature relationship inSMAs; and a thermomechanical model, which takes into accountthe cyclic loading effects in SMAs. Recognizing the intricacy ofthe phenomenological models and considering the thermome-chanical behavior of SMAs, the simplified SMA model is used inthe current study. The simplified model comprises nonlinear elas-tic ground force along with the visco-elastic damping force of theSMAs, which can be idealized from the experimental characteriza-tions of SMA wires.

The simplified model of the SMAs can be written as

ss ¼ sesðcsÞ þ svsð _csÞ ð3aÞ

sesðcsÞ ¼ Escs; 0 < cs < csy ð3bÞ

sesðcsÞ ¼ ssy þ Etðcs � csyÞ; csy < cs < cst ð3cÞ

sesðcsÞ ¼ ssh þ Eshðcs � cstÞ; cst < cs ð3dÞ

svsð _csÞ ¼ cs _cs ð3eÞ

where ss is SMA stress as a function of strain cs and strain rate _cs; ses

and svs are nonlinear elastic and visco-elastic stresses of SMA,respectively; ssy and ssh are SMA stresses at beginning and end,respectively, of martensitic transformation; csy and cst are SMAstrains at beginning and end of martensitic transformation; Es, Et

and Esh are the moduli of elasticity of SMA before, during and aftermartensitic transformation, respectively and cs is damping constantof SMA, which can be realized from experimental observations[16,30]. The values of Et and Esh are usually taken, respectively,10% and 45% of Es.

Two types of SMA wires, as stated in the earlier section, are usedin the current study. Usually Nitinol’s austenite finish temperature(Af) ranges from �10 �C to 44 �C, which clearly demonstrates its

Table 2Material properties of SMA wires used in the analysis.

Dimension Specifications

Cu–Al–Be SMA (SRB-1) Ni–Ti SMA (SRB-2)

Modulus of elasticity (N/mm2) 32,040 72,000Yield strengtha (N/mm2) 235 270Length of wires (mm) 2700 2700Cross-sectional area (mm2) 600 600

a ‘Yield’ is being referred to the initiation of phase transformation of SMA.

400 A. Rahman Bhuiyan, M.S. Alam / Engineering Structures 49 (2013) 396–407

potential of losing superelasticity if the temperature goes below itsAf and thus the system will lose its recentering capability. There-fore, SMAs having Af below �50 �C might be a better choice for out-door applications, e.g. Cu–Al–Be wire. The typical stress–strainresponses of the two SMAs in the austenite phases are similar ex-cept Ni–Ti alloy has superelastic strain range up to 8% whereas therecovery strain of Cu–Al–Be is less than 4% [30]. The simplifiedstress–strain curves of SMA wire (as depicted from Eqs. (3a)–(3e)) are shown in Fig. 4. The typical properties of the two SMAsare chosen based on the experimental results provided in Alamet al. [30] and Zhang et al. [16] for Ni–Ti and Cu–Al–Be, respec-tively. Even though the same constitutive model for the two SMAsis used in the paper, their constitutive parameters are different.The material parameters of the two SMA wires are presented in Ta-ble 2, which were chosen such that they adequately simulate theirstress–strain response. It has been assumed that the SMA wiresused in this study can sustain the large deformation experiencedin the bearings without fracturing or losing their re-centeringcapabilities.

3. Analytical modeling of the bridge

A three-span continuous highway bridge (typical in seismicallyactive zone in Japan) isolated by isolation bearings is considered inthe analysis as shown in Fig. 5. The bridge consists of continuousreinforced concrete (RC) deck-steel girder isolated by isolationbearings installed below the steel girder supported on RC piers asillustrated in Fig. 5. The superstructure consists of 250 mm RC slabcovered by 75 mm of asphalt layer. The height of the continuoussteel girder is 2000 mm. The mass of a single span bridge deck is600 � 103 kg and that of a pier is 240 � 103 kg. The substructureconsists of RC piers and footings supported on shallow foundation.The reinforcement details of the bridge pier consist of D29 (diam-eter 29 mm) longitudinal reinforcement bars along the longerdirection being distributed @ 200 mm c/c (center to center) exceptat the corners where the spacing of the reinforcement bars is125 mm c/c. In the shorter direction D29 (diameter 29 mm) rein-forcement bars are distributed @ 200 mm c/c except at the cornerswhere the spacing is limited to 150 mm c/c. The hoop reinforce-ment bars in both directions are D22 (diameter 22 mm) being dis-tributed @ 125 mm c/c. As shown in Fig. 5, the bridge model issimplified in two-degree of freedom (2-DOF) system. This simplifi-cation holds true only when the bridge superstructure is particu-larly assumed to be rigid in its own plane. This does not showany significant structural effect on the seismic performance ofthe bridge system when subjected to earthquakes in longitudinaldirection [12,13]. The mass proportional damping of the bridgepier is considered in the analysis. The geometry and material

γ sy

τsy

γsh

τsh

Es

Et

Fig. 4. A typical one-dimensional superelastic model of SMA device with itscharacteristic stress and strain.

properties of the bridge piers are given in Tables 3 and 4 presentsthe geometric and material properties of isolation bearings.

For simplicity, only a single interior pier is considered and mod-eled by two degrees of freedom (2-DOF) as shown in Fig. 5. Equa-tions that govern the dynamic responses of the bridge can bederived by considering the equilibrium of all forces acting on itusing the d’Alermbert’s principle. In this case, the internal forcesare the inertia forces, the damping forces, and the restoring forces,while the external forces are the earthquake induced forces. Equa-tions of motion are given as

mp€upðtÞ þ Fpðup; tÞ � FisðtÞ ¼ �mp€ugðtÞ ð4aÞ

md€udðtÞ þ FisðtÞ ¼ �md€ugðtÞ ð4bÞ

where mp, md, up and ud are the masses and displacements of pierand deck, respectively. €up and €ud are the accelerations of pier anddeck, respectively. €ug is the ground acceleration. Fp is the internalrestoring force of the pier to be evaluated by bilinear model. Fis isthe restoring force of the isolation bearings. For HDRB, it is com-puted using Eq. (1) and it becomes Fisðup;ud; _up; _ud; _cd; tÞ whereasfor SRBs, it is evaluated by using Eq. (2), i.e. Fis(up, ud, t) and the sim-plified force of the SMAs (Eq. (3)). Incorporation of inelastic behav-ior in the nonlinear model of the bridge pier is required toadequately capture its behavior when subjected to strong earth-quakes since the bridge pier is expected to incur large displacementdue to strong seismic loadings. Particularly, in the current work theauthors have considered moderate to strong earthquake groundmotions, where the bridge piers are expected to experience inelasticdeformation. Here, the nonlinear force–displacement relationship(i.e. the bilinear model) is employed to take into account the hyster-etic behavior of the bridge pier.

4. Seismic ground acceleration histories

The nonlinear time history analyses of the 2-DOF system takeinto account the nonlinearity of the bridge pier and the isolationbearings. Moreover, the seismic responses of the bridge are depen-dent on the characteristics of earthquake ground accelerations. So,the uncertainty characteristics of the earthquake ground accelera-tions regarding ground type, intensity and frequency contents havea great effect on the nonlinear time history responses of a structureand its members. In this regard, two suits of design earthquakeground acceleration records are used in the analysis: moderateand strong. Moderate earthquake ground accelerations are definedas those ground accelerations, which are characteristically similarto the level-2 type-I earthquake ground acceleration whereas thestrong earthquake is considered to be characteristically similar tothe level-2 type-II earthquake ground acceleration. According to Ja-pan Road Association [33], Level-2 type-I earthquake is a groundacceleration corresponding to a plate boundary type earthquakewith large amplitude and long duration such as the Kanto earth-quake (Tokyo, 1923) and Level-2 type-II earthquake is one corre-sponding to an inland direct strike type earthquake with lowprobability of occurrence, strong acceleration and short duration

Fig. 5. Analytical modeling of the bridge pier.

Table 3Geometric and material properties of the bridge.

Properties Specifications

Cross-section area of the pier cap (mm2) 2000 � 12,000Cross-section area of the pier body (mm2) 2000 � 9000Height of the pier (mm) 15,000Concrete compressive strength (N/mm2) 30Young’s modulus of elasticity of steel (N/mm2) 20,0000Yield strength of steel (N/mm2) 400

Table 4Geometries and materials properties of the isolation bearings.

Dimension Specifications

HDRB NRB

Cross-section of the bearing (mm2) 1000 � 1000 1000 � 1000Total thickness of the bearing (mm) 350 350Number of rubber layers 15 15Thickness of steel layer (mm) 3.57 3.57Nominal shear modulus of rubber (MPa) 1.2 1.2

Fig. 6. Acceleration-time histories of (a) moderate and (b) strong earthquakeground accelerations.

A. Rahman Bhuiyan, M.S. Alam / Engineering Structures 49 (2013) 396–407 401

such as the Kobe earthquake (Kobe, 1995). A total of eight artificialdesign earthquake ground acceleration records of moderate andstrong earthquakes are used in the analysis. The acceleration-timehistories of the earthquakes are shown in Fig. 6a and b. The peakground acceleration (PGA) values for the suit of four moderateearthquakes vary from 0.31 g to 0.44 g (Fig. 6a) whereas the PGAvalues for the four strong earthquakes range from 0.65 g to1.07 g (Fig. 6b). The acceleration response spectra of the moderateand strong earthquake ground accelerations are shown in Fig. 7aand b, respectively. The response spectra are not calibrated in theanalysis. The different characteristic properties of moderate andstrong earthquakes in terms of duration and dominant period areevident from Figs. 6 and 7. In Fig. 7a and b, the mean responsespectrum of each set of the ground acceleration records is alsosuperimposed in the figures. The objective of presenting the re-sponse spectra of the earthquake records is to show the range ofdominant period for each earthquake. As shown in Fig. 7a and b,the dominant periods for moderate and strong earthquake groundaccelerations vary from 0 to 1.5 s and 0 to 1.0 s, respectively.

5. Numerical results and discussion

Seismic performance of the bridge system modeled by a 2-DOFsystem (Fig. 5) is evaluated for four moderate and four strongearthquake ground accelerations. For simplicity, a typical interiorbridge pier is considered in the seismic analysis of the bridge(Fig. 5). Nonlinear dynamic analysis using the 4th order Runge Kut-ta method is carried out to evaluate the seismic responses of the

(a)

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onse

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ctra

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lera

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resp

onse

spe

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Mean accelerationresponse spectrum

(b)

Mean accelerationresponse spectrum

0 1 2 3 4Period (sec)

1.4

1.2

1

0.8

0.6

0.4

0.2

0

Fig. 7. Acceleration response spectra of (a) moderate and (b) strong earthquakeground accelerations.

-4000

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0

1000

2000

3000

4000

-600 -400 -200 0 200 400 600

Shear displacement (mm)

Shear displacement (mm)

Shea

r for

ce (k

N)

Shea

r for

ce (k

N)

HDRBBe-NR

(a)

(b)Fig. 8. Shear force–displacement responses of the bearings fitted with (a) SRB-1(NRB with Cu–Al–Be alloy) and HDRB, and (b) SRB-2 (NRB with Ni–Ti alloy) andHDRB subject to a typical moderate (M-2) earthquake ground acceleration.

402 A. Rahman Bhuiyan, M.S. Alam / Engineering Structures 49 (2013) 396–407

bridge pier using three isolation bearings: HDRB, SRB-1, and SRB-2.The eigen-value analysis results have shown that the structuralperiods of the system with HDRB and SRB are 2.02 s and 1.55 s,respectively, whereas the structural period of the system withoutisolation bearing is estimated to be 0.75 s.

In comparative assessment of seismic responses of the bridge,six standard response parameters, obtained for each earthquakeground acceleration record, are addressed in the subsequent sub-sections: bearing displacement, deck displacement, pier displace-ment, deck acceleration, residual displacement of the bridge deckafter earthquake and dissipated energy of the isolation bearings.Each response parameter of the system equipped with HDRB iscompared with those of SRB-1 and SRB-2.

5.1. Bearing displacement

The bearing displacements are obtained from relative displace-ments between deck and pier. The maximum displacements ofSRB-1 for moderate earthquake ground acceleration records are107–147% of the HDRB; and the average value of the maximumdisplacement of SRB-1 is 132% of HDRB. This phenomenon maybe attributed to the fact that HDRB yields higher hysteretic re-sponses compared to that of SRB-1. It is noted that the hardeningfeature of HDRB (Figs. 8 and 9) is smaller compared to those ofSRB-1 and SRB-2. In the case of strong earthquake ground acceler-ations, the average maximum displacement of SRB-1 is almost thesame as that for moderate earthquake ground accelerations; how-ever, the maximum values of the bearing displacements vary from108% to 153% of the HDRB. In the case of SRB-2, the average of themaximum bearing displacements under moderate and strong

earthquake ground accelerations are 104% and 117% of the HDRB,respectively. The maximum bearing displacements of SRB-2 varyfrom 92% to 121% of HDRB for moderate earthquake ground accel-erations, whereas for strong earthquake ground accelerations thevalues of maximum bearing displacements have changed from93% to 132%. Moreover, the variations of bearing displacementsare clearly observed in HDRB, SRB-1 and SRB-2 for different char-acteristic properties of earthquake ground accelerations used inthe analysis. Tables 5–7 show the maximum bearing displace-ments of HDRB, SRB-1 and SRB-2, respectively. Figs. 8 and 9 pres-ent the hysteretic responses of HDRB, SRB-1 and SRB-2,respectively, for moderate and strong earthquake ground accelera-tions. The hysteretic behavior of SRB-1 and SRB-2 show some nota-ble differences (Figs. 8 and 9). The different hysteretic behavior ofthe two SMAs are attributed due to having different constitutiveparameters used in the analysis, i.e. the moduli of elasticity andyield strengths of SRB-1 are smaller than those of SRB-2. Time his-tories of the bearing displacements fitted with SRB-1 and SRB-2subject to moderate earthquake ground acceleration record (M-2)are presented in Fig. 10a and b, respectively. Fig. 11a and b demon-strate the time histories of the bearing displacements fitted withSRB-1 and SRB-2 subject to typical strong earthquake groundacceleration (S-3). In each figure, the time history of the bearingdisplacement fitted with HDRB is superimposed for comparison.The bearing displacements fitted with SRB-1 and SRB-2 are largerthan that fitted with HDRB (Fig. 10a and b). This can be attributed

Fig. 9. Shear force–displacement responses of the bearings fitted with SRB-1 (NRBwith Cu–Al–Be alloy) and HDRB, and (b) SRB-2 (NRB with Ni–Ti alloy) and HDRBsubject to a typical strong (S-3) earthquake ground acceleration.

Table 5Absolute maximum responses of the system isolated by HDRB subjected to moderate and

Earthquake/responses

Bearing displacement(mm)

Residual deformation(mm)

Deck acceler(m/s2)

M-1 144.5 36.2 5.4M-2 336.9 47.3 5.7M-3 384.3 17.1 5.0M-4 345.6 63.5 5.0

S-1 486.1 25.3 11.9S-2 389.1 7.2 6.8S-3 433.5 11.4 8.2S-4 397.4 29.5 6.9

Table 6Absolute maximum responses of the system isolated by SRB-1 (NRB-SMA (Cu–Al–Be)) sub

Earthquake/responses

Bearing displacement(mm)

Residual deformation(mm)

Deck acceler(m/s2)

M-1 155.8 32.1 5.9M-2 493.4 24.2 6.8M-3 499.6 12.7 8.6M-4 499.6 7.5 6.0

S-1 600.0 11.2 17.1S-2 597.6 16.8 13.7S-3 572.1 12.9 10.3S-4 594.1 12.1 13.1

A. Rahman Bhuiyan, M.S. Alam / Engineering Structures 49 (2013) 396–407 403

to the hysteretic behavior of the bearings (Figs. 8 and 9). The SRB-1and SRB-2 generate, in general, larger bearing displacement evenwith equal or larger hardening stiffness (Figs. 8 and 9), since thebearings with HDRB have larger damping compared to those ofSRB-1 and SRB-2.

5.2. Deck displacement

The bridges fitted with SRB-1 and SRB-2 experienced largerdeck displacements for both moderate and strong earthquakeground accelerations by 9–41% compared to that of HDRB. The ba-sis of this occurrence is identical to that of the bearing displace-ments as explained in the previous subsection. The SRB-2 deckdisplacements are lesser than the HDRB deck displacements by10% for M-3 moderate ground acceleration with PGA of 0.35 gwhich confirms the findings of Wilde et al. [15] which showed thatthe SMA isolation system provides stiff connection between pierand deck for moderate earthquake ground accelerations. In orderto prevent instability of the bearings and unseating of the bridgedeck, it is critical to restrict the relative deck displacement effec-tively [24]. The maximum deck displacements of HDRB, SRB-1and SRB-2 are presented in Tables 5–7, respectively. Time historiesof the deck displacements fitted with SRB-1 and SRB-2 subject to atypical moderate earthquake ground acceleration record (M-2) arepresented in Fig. 12a and b, respectively. In both figures, the timehistory of the deck displacement fitted with HDRB is superimposedfor comparison. It can be observed that the maximum deck dis-placements fitted with SRB-1 and SRB-2 are larger than that fittedwith HDRB; however, the deck displacement at the end of theearthquake ground acceleration record is comparatively larger inthe case of HDRB than those of SRB-1 and SRB-2. Fig. 13a and bdemonstrate the time histories of the deck displacements fittedwith SRB-1 and SRB-2 subject to typical strong earthquake groundacceleration (S-3), respectively. Similar trends of responses of thedeck are observed in the case of strong earthquake ground acceler-ation records. The results show that the characteristics of the

strong earthquake ground accelerations.

ation Pier displacement(mm)

Deck displacement(mm)

Dissipated energy(MN m)

60.2 127.9 1.36110.3 318.5 5.61121.3 452.3 5.34154.0 339.6 7.29

98.3 569.0 6.8087.2 419.2 5.8396.3 423.2 5.9591.4 437.6 5.97

jected to moderate earthquake ground accelerations.

ation Pier displacement(mm)

Deck displacement(mm)

Dissipated energy(MN m)

74.1 163.6 1.4180.1 515.0 5.1492.2 491.0 4.9372.2 540.6 7.10

129.0 682.3 7.53117.9 648.8 5.85

78.7 586.3 5.77142.0 658.1 5.87

Table 7Absolute maximum responses of the system isolated by SRB-2 (NRB-SMA (Ni–Ti)) subjected to moderate and strong earthquake ground accelerations.

Earthquake/responses

Bearing displacement(mm)

Residual deformation(mm)

Deck Acceleration(m/s2)

Pier displacement(mm)

Deck displacement(mm)

Dissipated energy(MN m)

M-1 134.2 31.3 5.9 68.7 134.9 2.49M-2 407.3 7.5 7.0 82.3 424.0 7.33M-3 371.0 18.3 6.8 99.1 408.3 6.78M-4 369.0 23.1 6.4 95.5 367.9 12.10

S-1 553.4 13.5 14.3 55.8 576.1 13.31S-2 513.4 19.3 9.4 75.9 537.2 10.61S-3 491.7 17.1 9.8 59.0 530.4 9.96S-4 525.9 28.3 9.9 75.8 548.3 10.71

(a)

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200

400

600

Bear

ing

disp

lace

men

t (m

m) HDRB

Be-NR

Fig. 10. Time history of the bearing displacement fitted with SRB-1 (NRB with Cu–Al–Be alloy) and HDRB, and (b) SRB-2 (NRB with Ni–Ti alloy) and HDRB subject to atypical moderate (M-2) earthquake ground acceleration.

HDRB

Ni-NR

HDRBBe-NR

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Bear

ing

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lace

men

t (m

m)

(a)

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(b)

0 10 20 30 40Time (sec)

Fig. 11. Time history of the bearing displacement fitted with SRB-1 (NRB with Cu–Al–Be alloy) and HDRB, and (b) SRB-2 (NRB with Ni–Ti alloy) and HDRB subject to atypical strong (S-3) earthquake ground acceleration.

404 A. Rahman Bhuiyan, M.S. Alam / Engineering Structures 49 (2013) 396–407

earthquake ground accelerations (Figs. 6 and 7) used in the analy-sis have direct effect on the responses of the bridge deck.

5.3. Pier displacement

The bridge fitted with SRB-1 experienced smaller pier displace-ments for all the moderate earthquake ground accelerations exceptfor M-1 compared to that of HDRB. The average of the maximumpier displacements with SRB-1 is 21% less than that with HDRB;however, the maximum pier displacements with SRB-1 vary from46% to 123% of HDRB. For strong earthquake ground accelerations,the average of the maximum pier displacements with SRB-1 is 26%

more than that with HDRB. The two influential factors for pier dis-placement are the energy dissipation of the bearings and the max-imum bearing force. The pier displacement decreases with theincrease of energy dissipation of the bearing but increases withthe increase of bearing force. Therefore, due to small dissipationenergy (Table 6) and large bearing force (Fig. 9) the SRB-1 produceslarger pier displacement than that equipped with HDRB understrong earthquake ground accelerations. The average pier displace-ments with SRB-2 are smaller by 17–28% compared to HDRB forboth moderate and strong earthquake ground accelerations. How-ever, the maximum pier displacements with SRB-2 vary from 62%to 114% for moderate earthquake ground accelerations, and in thecase of strong earthquake ground accelerations, the maximum pier

(a)

0 5 10 15 20 25 30 35 40Time (sec)

(b)

0 5 10 15 20 25 30 35 40Time (sec)

HDRBNi-NR

HDRBBe-NR

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200

400

600

Dec

k di

spla

cem

ent (

mm

)

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0

200

400

600

Dec

k di

spla

cem

ent (

mm

)

Fig. 12. Time history of the deck displacement fitted with SRB-1 (NRB with Cu–Al–Be alloy) and HDRB, and (b) SRB-2 (NRB with Ni–Ti alloy) and HDRB subject to atypical moderate (M-2) earthquake ground acceleration.

(a)

0 5 10 15 20 25 30 35 40Time (sec)

(b)

0 10 20 30 40Time (sec)

HDRB

Ni-NR

HDRBBe-NR

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-400

-200

0

200

400

600

Dec

k di

spla

cem

ent (

mm

)

-600

-400

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0

200

400

600

Dec

k di

spla

cem

ent (

mm

)

Fig. 13. Time history of the deck displacement fitted with SRB-1 (NRB with Cu–Al–Be alloy) and HDRB, and (b) SRB-2 (NRB with Ni–Ti alloy) and HDRB subject to atypical strong (S-3) earthquake ground acceleration.

A. Rahman Bhuiyan, M.S. Alam / Engineering Structures 49 (2013) 396–407 405

displacements vary from 57% to 83% of HDRB. The larger hystereticenergy of SRB-2 compared to that of HDRB causes smaller pier dis-placements (Tables 5–7). The yield displacement of the pier wasdetermined as 71 mm from nonlinear pushover analysis. It canbe observed from Tables 5–7 that all the piers experienced yieldingexcept for one earthquake record (M1) in the cases of HDRB andSRB-2. Time histories of the pier displacements fitted with SRB-1and SRB-2 subject to moderate earthquake ground acceleration re-cord (M-2) are presented in Fig. 14a and b along with the HDRB.The pier displacement fitted with HDRB is larger than those fittedwith SRB-1 and SRB-2. The trend of the pier displacement historiesis similar for all the bearings. Fig. 15a and b demonstrate the timehistories of the pier displacements fitted with SRB-1 and SRB-2subject to typical strong earthquake ground acceleration (S-3).Similar trends of the results are also observed for the pier displace-ments for the other strong earthquake ground accelerations.

5.4. Deck acceleration

The bridges fitted with SRB-1 and SRB-2 experienced largerdeck accelerations for both moderate and strong earthquakeground accelerations compared to the bridge with HDRB. The samereasoning as discussed in the case of bearing displacements canalso be applicable for this case, i.e., the increased damping of HDRBcompared to those of SRB-1 and SRB-2 has a direct effect on this.The average of the maximum deck accelerations with SRB-1 is30% larger than that with HDRB; however, for strong earthquake

ground acceleration, this value goes to 65% higher than with HDRB.For SRB-2, similar trend is also observed but with reduced magni-tudes. This typical trend of results can be explained by the hyster-etic responses of the bearings as shown in Figs. 8 and 9. Tables 5–7show the maximum deck accelerations of HDRB, SRB-1 and SRB-2,respectively.

5.5. Residual displacement

The residual displacement of the bearing is computed by takingthe arithmetic average of the stable absolute values of the last 10–15 s of the time history of the bearing displacements as obtainedfrom the dynamic analysis of the system for each earthquake.The presence of seismic induced residual deformation in the bear-ings makes it difficult to repair the damages on piers and else-where as it becomes difficult to place the deck to its originalposition [24]. The residual displacements of SRB-1 are smaller thanthose of HDRB for all the ground acceleration records except for S-2and S-3. Similar trend is observed in the case of SRB-2 with differ-ent magnitudes. In particular, it is observed that SRB-1 and SRB-2experience smaller residual displacements compared to that ofHDRB for the moderate ground acceleration records; however,not necessarily smaller for the strong earthquakes (Tables 5–7).This happened due to the different characteristics of the earth-quake ground accelerations (Fig. 6a and b). These earthquake re-cords were chosen by JRA [33] such that both the moderate andstrong ground motions can produce substantial amount of damage

(a)

0 5 10 15 20 25 30 35 40Time (sec)

(b)

0 5 10 15 20 25 30 35 40Time (sec)

HDRBNi-NR

HDRBBe-NR

120

70

20

-30

-80

-130

120

80

40

0

-40

-80

-120

Pier

dis

plac

emen

t (m

m)

Pier

dis

plac

emen

t (m

m)

Fig. 14. Time history of the pier displacement fitted with SRB-1 (NRB with Cu–Al–Be alloy) and HDRB, and (b) SRB-2 (NRB with Ni–Ti alloy) and HDRB subject to atypical moderate (M-2) earthquake ground acceleration.

120

70

20

-30

-80

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Pier

dis

plac

emen

t (m

m)

120

80

40

0

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Pier

dis

plac

emen

t (m

m)

(a)

0 5 10 15 20 25 30 35 40Time (sec)

(b)

0 10 20 30 40Time (sec)

HDRB

Ni-NR

HDRBBe-NR

Fig. 15. Time history of the pier displacement fitted with SRB-1 (NRB with Cu–Al–Be alloy) and HDRB, and (b) SRB-2 (NRB with Ni–Ti alloy) and HDRB subject to atypical strong (S-3) earthquake ground acceleration.

406 A. Rahman Bhuiyan, M.S. Alam / Engineering Structures 49 (2013) 396–407

to a structure. From Fig. 6a and b or Fig. 7a and b it can be observedthat although the moderate earthquake ground motions have low-er PGA compared to the strong ground motions, these records havehigher level of ground accelerations distributed over a longer per-iod of time whereas the strong ground motions are concentratedwith high PGA over a smaller period of time and after that its levelof shaking descends quickly. This is why a moderate ground mo-tion record may cause more damage to a structure compared toa strong ground motion.

5.6. Dissipated energy

The dissipated energy of HDRB, SRB-1 and SRB-2 are evaluatedfor moderate and strong earthquake ground accelerations and arepresented in Tables 5–7. From the dissipated energy as estimatedfor HDRB, SRB-1 and SRB-2, the damping ratio of each bearingcan also be determined. The damping ratio of a bearing has a directeffect on the reduction of the bearing displacement, deck accelera-tion and deck displacement, etc. Moreover, the energy dissipationhas significant effect on the reduction of pier displacement. Thepier displacement decreases with the increase of energy dissipa-tion but increases with the increase of bearing force. SRB-2 giveshigher dissipated energy compared to that of HDRB and SRB-1and its reflection is clearly displayed in the case of seismic re-sponses as presented in Tables 5–7. SRB-2 provides 96% and 82%more energy dissipation than those of HDRB and SRB-1, respec-tively (see, for example, Tables 5–7 and Figs. 8–15).

6. Concluding remarks

This study presents seismic performance assessment of high-way bridges isolated by high damping rubber and shape memoryalloy/natural rubber bearings. This study discusses a simplifiedanalytical approach for modeling isolation bearings comprised ofnatural rubber bearing (NRB) wrapped with shape memory(SMA) wire which can be used in the seismic performance analysisof isolated highway bridges. The bridge is analyzed for moderateand strong earthquake ground accelerations calibrated with designacceleration response spectra as recommended by JRA [33]. Threeversions of isolation bearings (HDRB, SRB-1 and SRB-2) are usedin the analysis. The nonlinearity of the bridge pier is consideredby employing the bilinear force–displacement relationship. Sincethe mechanical behavior of HDRB is largely dominated by strain-rate dependent overstress response and elasto-plastic stress re-sponse, a complicated strain-rate dependent constitutive modelfor the HDRB is implemented in this study. On the other hand,the mechanical behavior of NRB is mainly dominated by the elas-to-plastic stress response where the strain rate dependent stressresponse is insignificant. Therefore, a nonlinear elasto-plastic ana-lytical model for NRB is used in the analysis. A viscoelasticity-based analytical model is used for simulating the superelasticand damping properties of SMA wires. The analytical model forSRB-1 and SRB-2 are derived by combining the analytical modelsfor NRB along with Cu–Al–Be alloy and Ni–Ti alloy, respectively.

The numerical results have revealed that SMA-based isolationbearings (SRBs) satisfactorily restrain the residual displacement

A. Rahman Bhuiyan, M.S. Alam / Engineering Structures 49 (2013) 396–407 407

of the bridge deck and the displacement of the bridge pier for mod-erate earthquakes; however, for strong earthquakes the residualdisplacements and the pier displacements are not retrained byincorporation of Ni–Ti and Cu–Al–Be based SMA alloys in the iso-lation bearings. For bridge deck and bearing displacements, thebridge with HDRB has resulted in less response compared to thoseof SRB-1 and SRB-2 under both types of earthquakes. Similar trendis also observed in the case of deck accelerations. The constitutiveproperties of both types of SRBs have significant effect on the seis-mic responses of the system.

In the current study, only one interior bridge pier was consid-ered. The seismic responses of such a simplified sub-assemblagewill be different if an exterior pier is considered instead, or the to-tal assembly of the bridge is considered. This is likely to change thedynamics of the response of the entire bridge structure. It shouldbe also noted that the selection of the type and modeling approachof isolation bearings has a remarkable effect on the seismic perfor-mance evaluation of highway bridges, which has to be carefullyconsidered in the analysis and design steps of any bridge project.Further study is also needed to determine the performance of suchSMA wire based isolation bearing using an improved SMA modelby considering superelastic strain range and rate dependency.

Acknowledgement

The financial contribution of Natural Sciences and EngineeringResearch Council (NSERC) of Canada through Discovery Grant hasbeen gratefully acknowledged.

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