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First International Conference for PhD students in Civil Engineering
CEPhD 2012, 47 November 2012,ClujNapoca, Romaniawww.sensgroup.ro/ce2012
Seismic assessment of Hungarian highway bridges A case study
Jzsef Simon*1, Lszl Gergely Vigh2
1,2Budapest University of Technology and Economics, Department of Structural EngineeringH1521 Budapest, Megyetem rkp. 3., Hungary
Abstract
This paper deals with the case study of a typical Hungarian highway bridge, illustrating theseismic performance and damage evaluation method. The investigated largespan bridge consists of
continuous steel boxsection superstructure supported by reinforced concrete piers. For theanalysis, simplified beamelement numerical model is developed. Linear spectral response analysisas well as nonlinear static and cyclic analyses are invoked for the evaluation and then their resultsare compared. The model incorporates nonlinear characteristics of the critical details, such as
pier, piertosuperstructure joints, etc. Pushover and incremental dynamic analysis using severalearthquake records is applied to determine the fragility curves reflecting the probability of variousdamage occurrence. The analyses indicate that the most vulnerable component is the fixed bearing,the collapse of the whole structure is caused by the local failure of the restrained pier, and the
structure provide relatively large extra resistance against seismic loads.
Keywords: Eurocode 8 analysis methods, timehistory analysis, nonlinear analysis, pushover
analysis, seismic assessment of continuous girder bridge, incremental dynamic analysis, fragilitycurve
1. Introduction
In low or moderate seismicity regions, such as Hungary, there is no tradition of seismic design.We do not have much knowledge of the seismic behaviour of our bridges, however it is likely thatsignificant damage may be caused by an earthquake. Besides, in 2006 a new seismic hazard mapwas released with an increased seismic proneness, classifying Hungary as moderate seismic zone.
Experiences on newly erected structures in the last decade [1, 2] and parametric study on typicalcontinuous girder bridges of Hungary [3] show that seismic load may cause failure of some specificelements, such as foundations, piers, bearings, joints, etc. In order to achieve sufficient seismic
performance, these details may have to be reinforced even though they would be safe in ultimatelimit state.
The global scope of our research is to evaluate the seismic performance and the expecteddamage during the lifetime of existing Hungarian bridges on the basis of performance based designmethodology [4]. Based on the results, possible retrofit methods may be proposed.
In this paper a typical continuous girder bridge, the M0 Hros highway bridge, Hungary isexamined. A three dimensional numerical model which incorporates nonlinear characteristics ofthe critical details is developed in Open System for Earthquake Engineering Simulation FEM
software (OpenSEES) [5]. According to EC 82 [6] conventional linear spectral response analysis is*Corresponding author. Tel./ Fax.: +36 70 945 69 51Email address: [email protected]

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carried out to compute probable reaction forces and displacements, nonlinear, static pushoveranalysis is applied to determine the collapse mechanisms and nonlinear timehistory analyses aredone to capture the seismic behaviour of the bridge more precisely. Based on the results, the criticalstructural components influencing the overall seismic performance are determined. To evaluate thefeasibility of the different analysis methods, results are compared to each other on the level ofinternal forces in the critical elements. Finally, incremental dynamic analysis based stochasticassessment is used to create fragility curves of the critical components and to more preciselyevaluate the actual seismic performance of the bridge.
2. Bridge description
The case study bridge is a newly erected highway bridge over the Danube River for the M0Motorway at Hros. The structure was designed by Unitef, Inc., Ch, Inc. and PonTerv, Inc,
Hungary. The total length of the bridge is 770.42 m (3x73,5 m flood, 3x108,5 m river and 3x73,5 mflood bridges) and the total width of the deck is 21.80 m (1.9 m sidewalk + 18.0m carriageway +1.9 m sidewalk). The river bridge is a continuous three span girder with a onecell box crosssectionwith inclined webs and an orthotropic deck. The flood bridges are three span continuous composite
bridges. The steel box is identical to that of the river bridge, but the deck is a R.C. slab. The bridgeis straight in plan. In this study only the river bridge is analyzed. The river bridge shares twocommon piers with the flood bridges (pier 4 and pier 7) and is separated from the flood bridges by a+70 mm (pier 4) and a +160 mm (pier 7) expansion joint. The longitudinal view of the bridge can
be seen in Figure 1.
Figure 1. Longitudinal section of the river bridge.
Figure 2. Sideviews of pier 5. Table 1. Crosssectional data.
The steel grade of the box girder is S355, the piers are C35/45 concrete and the reinforcing steelis grade S500B. The variable crosssection parameters of the box girder and the piers are listed inTable 1. The two sideviews of pier 5 are shown in Figure 2. The crosssections are nearly the same
Girder S1 S2 S3 S4
A[m2] 0.82 0.91 1.11 1.15
Iy[m4] 3.20 4.08 5.75 5.84
Iz[m4] 2 3. 50 2 4. 50 2 5. 80 2 6. 90
It[m4] 4.83 5.77 6.52 7.05
P4 S1 S2 S3 S4
A[m2] 23 .7 27 .4 36 .4 1 08 .0
Iy[m4] 14 .1 11 .9 23 .4 3 93 .0
Iz[m4] 4 8 6. 0 4 32 .0 5 18 .0 2 43 0. 0
It
[m
4
] 34 .4 3 5. 3 8 1. 1 1 17 0. 0
P5 S1 S2 S3 S4
A[m2] 24 .2 28 .5 39 .9 1 58 .0
Iy[m4] 14 .4 12 .7 29 .4 8 12 .0
Iz[m4] 4 8 9. 0 4 35 .0 5 98 .0 5 35 0. 0
It[m4] 3 5 .7 3 9. 4 1 01 .0 2 45 0. 0
P6 S1 S2 S3 S4
A[m2] 24 .2 28 .5 39 .9 1 58 .0
Iy[m4] 14 .4 12 .7 29 .4 8 12 .0
Iz[m4] 4 8 9. 0 4 35 .0 5 98 .0 5 35 0. 0
It[m4] 3 5 .7 3 9. 4 1 01 .0 2 45 0. 0
P7 S1 S2 S3 S4
A[m2] 24 .2 27 .6 39 .9 1 72 .0
Iy[m4] 14 .4 12 .1 29 .4 9 76 .0
Iz[m4] 4 8 9. 0 4 33 .0 5 98 .0 6 23 0. 0
It[m4] 3 5 .7 3 6. 1 1 01 .0 2 93 0. 0

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at each pier, only the pier height varies. The superstructure is fixed in the longitudinal direction atpier 5, whereas one of the two bearings provides lateral restraint at each pier.
Seismic design of the structure was completed in accordance with Eurocode 8 Pt. 2, using modalspectrum analysis. The applied seismic parameters are: ground acceleration of 0.1 g, soil type C,importance class II, Type 1 spectrum. The applied mass is calculated from the dead loads and 1kN/m2 live load distributed on the carriageway. This leads to an equivalent 146 kN/m line loadalong the length of the girder. Quasielastic behaviour is considered with a behaviour factor q = 1.5.
3. Numerical model
According to the comprehensive literature overview of [7] on seismic numerical modeling ofgirder bridges, a three dimensional numerical model is developed in OpenSees [5]. A schematic
picture of the numerical model can be seen in Figure 3. The main structure is modeled by beam
elements. Elastic beam element is used for the girder and displacement based fiber section elementfor the piers because of the expected plastic deformations. The fibers have their own uniaxialstressstrain relationship. This way the crosssection is discretely modeled, confined andunconfined concrete regions and the longitudinal steel reinforcement can be taken into account. Forthe behaviour of steel the GiuffrMenegottoPinto model, and for the behaviour of concrete lineartension softening concrete material model is adopted. The beam elements are placed in the center ofgravity, the elements of the girder and the piers are joined with rigid elements. These rigid elementsare created to model the top of the pier and the rigid box section and are led to the edges of the topof the pier where the bearings are placed. The bearings on the piers and the abutments are modeled
by zerolength elements with nonlinear spring characteristics assigned to three degrees of freedom(ux, uy, uz), but rotations are free to develop. For the elastomeric bearings bilinear hysteretic
material model is used (Figure 11). This behaviour can be described by the initial stiffness (K0), thepostyield and initial stiffness ratio () and the yielding strength (Fy). Table 2 shows the propertiesof the fixed and expansion bearings. The soilstructure interaction at the foundations of the piers istaken into account with integrate linear springs, adjusted with stiffness values (Table 3) calculatedfrom foundation analysis.
The developed model is applied for the nonlinear analysis of the bridge. In the following, thedifferent seismic analysis methods available in EC82 are compared to each other. Whencompleting linear analysis (modal spectrum analysis and linear timehistory analysis), material nonlinearity is not incorporated, and elements are assigned with their initial stiffness values.
Table 2. Bearing properties.
Figure 3. Numerical model of the bridge. Table 3. Foundation stiffnesses.
PierNo. 4 5 6 7
Kx[MN/m] 4760 3850 3850 3070
Ky[MN/m] 5130 4550 4550 3220
Kx[MNm/rad] 350000 500000 500000 350000
Kx[MNm/rad] 111000 125000 125000 111000
K0[kN/mm]
Fy[kN]
[]
70
960
0.170
14
5
0.018
Fi xe d Expansi onType
Bearingcharacteristics

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4. Comparison of analysis methods
4.1. Linear response spectrum analysis (LRSA)
Linear response spectrum analysis is the most commonly used earthquake analysis methodamong designers due to its relative simplicity and effectiveness. Original seismic design of theinvestigated structure was also made by LRSA. In linear analysis, geometric and material nonlinearity is ignored. Accordingly, fixed bearings are assumed fully rigid, while expansion bearings
provide no restraint in the model. The linear dynamic analysis is carried out according to EC82 [6].The behaviour factor (q) is 1.5 for the continuous girders (superstructure) as well as for the pierwalls, and q = 1.0 should be used for the analysis and design of the bearings, abutments andfoundations. The parameters of the standard acceleration response spectrum curve are : ag= 1.0m/s2, soil type C, M > 5.5, = 0.05. The applied spectrums can be seen in Figure 4. Typical modalshapes and frequencies, obtained from the modal analysis, are illustrated in Figure 5. The reaction
forces of the bearings and the piers are summarized in Table 4. The critical components are thelongitudinally restrained pier 5 and the fixed bearings at the same place. The results are inaccordance with [3].
Figure 4. Applied standard response spectra. Figure 5. Typical modal shapes.
Table 4. Pier and bearing reaction forces from LRSA, LTHA and NLTHA.
Assuming q = 1.0, the maximal displacements are 27 mm and 36 mm in the transversal andlongitudinal direction respectively, and the maximal deflection (mostly from the dead loads) is 247mm.
Fx Fy Fz Mx My Mz
4 2558.5 4210.6 32266.3 56144.6 20787.6 1003.8
5 13414.2 18429.9 89420.5 275367.4 229907.1 13838.0
6 11631.3 17174.8 89337.8 251826.4 88429.0 10.7
7 12599.3 16290.0 87876.1 175951.2 101845.2 5152.2
Fx Fy Fz Mx My Mz
4 2362.9 4027.2 31833.4 47126.0 17728.6 876.4
5 12188.4 11864.7 84308.9 190599.2 217217.8 11393.5
6 11402.6 11632.0 84137.7 174807.9 80323.0 8.5
7 11406.4 14846.3 82225.8 141236.6 98054.1 4218.0
Fx Fy Fz Mx My Mz
4 2344.5 5636.8 31871.4 63457.8 17146.3 1261.6
5 11743.7 10142.4 84419.2 159012.1 117740.9 12587.2
6 11219.0 11065.4 84360.3 160511.9 95641.4 101.2
7 10378.4 14045.8 82327.5 149178.0 113279.7 2460.7
kNm
Linearresponsespectrumanalysisresults
kN
Pier
Pier
Pier
kN kNm
Nonlineartimehistoryanalysis results
Lineartimehistoryanalysisresults
kN kNm
Fx Fy Fz Fx Fy Fz
4 0.0 1664.0 4422.1 0.0 0.0 4410.8
5 5045. 2 7809. 3 1 3197. 5 5075. 1 0. 0 13186. 4
6 0.0 7206.5 13037.4 0.0 0.0 13028.2
7 0.0 2002.6 4513.6 0.0 0.0 4507.7
Fx Fy Fz Fx Fy Fz
4 0.0 1240.8 3795.8 0.0 0.0 3897.7
5 4910. 9 5201. 7 1 2136. 1 4916. 6 0. 0 12221. 0
6 0.0 4701.9 11873.7 0.0 0.0 11956.1
7 0.0 1656.4 4056.7 0.0 0.0 4025.1
Fx Fy Fz Fx Fy Fz
4 32.7 1026.7 3644.5 32.7 11.0 3588.8
5 1 599. 8 1329 .5 1 0396 .5 1 599. 8 18. 1 104 90. 8
6 27. 6 1371. 4 10373. 9 27. 6 18. 8 10455. 4
7 25.5 1025.8 3691.1 25.5 11.3 3709.1
Pier
Linearresponsespectrumanalysisresults
Rightbearing Leftbearing
kN kN
Rightbearing LeftbearingPier
Lineartimehistoryanalysisresults
kN kN
Pier
Nonlineartimehistoryanalysisresults
Rightbearing Leftbearing
kN kN

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4.2.Linear timehistory analysis (LTHA)
With timehistory analysis the seismic behaviour can be revealed more precisely since thestructure is analyzed in the time domain in contrast to LRSA which generally overestimates thereaction forces in a conservative manner.
A new algorithm is developed which creates synthetic acceleration records for timehistoryanalysis. The records are determined to match the given acceleration spectrum curve (see Section4.1. and Figure 6.). According to EC 8, at least 3 such records should be used. The maximum valuesof the results from the three LTHAs can be seen in Table 4. The maximum displacements are 33.9mm, 10.3 mm and 220.6 mm in the longitudinal, transversal and vertical directions.
Figure 6. The fitted three synthetic acceleration records.
4.3.Pushover analysis
As per EC82, pushover analysis (static nonlinear analysis) can be applied for design check asalternative method to LSRA, or for characterizing the failure mechanisms. The load pattern appliedin pushover analysis is basically determined by the most dominant mode shape, therefore if more
modes are relevant (e.g. in the lateral direction) the method can be used only with limitations.Generally in case of continuous girders with not too high (less than 30 m) piers one modecharacterizes the seismic behaviour in the longitudinal direction [3], so pushover analysis could be auseful tool for capacity design, and to determine the collapse mechanism. In this paper pushoveranalysis is carried out only in this direction.
Figure 7. Capacity curves for the whole structure, pier 5 and the fixed bearing.
Capacity curves (base shear force vs. top displacement) of the whole structure, the longitudinallyrestrained pier (no. 5) and the fixed bearing are shown in Figure 7. The analysis indicates that theultimate collapse of the whole structure is caused by the local failure of the longitudinally restrained
pier. However, failure/fracture of any components are not taken into consideration in thesimulation. Considering 50 mm, 100 mm and 250 mm deformations as slight, moderate and fulldamage states for the bearing, it can be realized that the fixed bearing suffers large deformations

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and bearing failure anticipates pier failure (corresponding pier curvatures are still in the linearregion). Accordingly, the most vulnerable component is the fixed bearing. This indicates that the
piers are robust, stiff, and provide relatively large extra resistance against seismic loads.
4.4.
Nonlinear time history analysis (NLTHA)
Nonlinear dynamic analysis is the most rigorous analysis type. Note that springs representingthe bearings make the structure less stiff, the dominant natural period in the longitudinal directionchanges from 0.725 s to 1.44 s. This causes a drastic response decrease according to the responsespectrum curve (Figure 4, 6.). Figure 8. shows how the natural period changes, the moments in pier5 are decreased, while displacements in the longitudinal direction increase.
The nonlinear behaviour of the fixed and expansion bearings and of the pier can be seen inFigure 9. The pier remains elastic to the applied three synthetic acceleration records (Figure 6.) Themaximum deformations of the bearings are 42 mm and 67 mm in case of the fixed and expansion
bearings respectively. These deformations are under the assumed slight damage level. Themaximum displacements of the structure are 56 mm, 49.6 mm and 212.4 mm in the longitudinal,lateral and vertical directions. Table 4 also summarizes the bearing reaction forces and pier internalforces. The calculated response can be very sensitive to the characteristics of the individual groundmotion used as seismic input, therefore a set of records should be used for higher reliability.
Figure 8. Longitudinal moment of pier 5 and longitudinal displacement of the structure with orwithout bearing elements.
Figure 9. Nonlinear behaviour of the fixed and expansion bearings and the pier.
4.5.Comparison of the results
Reaction forces from LRSA, LTHA and NLTHA are compared in Table 4. It is found that LRSAis conservative in comparison to LTHA as the latter gives lower response values especially in thelateral direction. Since in the longitudinal direction one mode characterizes the seismic behaviour,the two analyses leads to nearly the same results. In both methods, piers and fixed bearings arefound as critical elements. Nonlinear analysis methods also confirm that the most vulnerablecomponent is the fixed bearing, whereas the piers are robust and stiff. The failure of the bearinganticipates the failure of the restrained pier. The pier remains elastic at the level of bearing failure.
For the given intensity level which is determined by the standard acceleration spectrum thedisplacements are so low in the longitudinal direction that not even slight damage of the bearingsand hereby of the piers are likely to occur. The spring elements applied for the nonlinear analysis

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decrease the stiffness of the structure and thus increase the fundamental period. Thus, seismicresponses are decreased, with increasing deformation demands. The responses obtained from
NLTHA thus fundamentally differ from those of the linear analyses, they are compared in Table 4.Drastic change of the moments of the piers can be observed, the moments are lower at therestrained (pier 5) and higher at the nonrestrained (pier 4, 6, 7) piers. The horizontal forcetransmission capability of the expansion bearings results more favorable reaction force distribution.
5. Incremental dynamic analysis (IDA)
In Section 4. only deterministic analyses which are most commonly used in Europe arepresented. These analyses can highlight the most vulnerable components and details of the structureand they provide results for a given intensity level, but do not characterize the probability of failureof the structure. This probability can be expressed by creating the fragility curves of different
components or the whole structure. In this case stochastic methods are needed. The seismicperformance can be very sensitive to the characteristics of the individual acceleration record.During incremental dynamic analysis, the structure is subjected to 44 different ground motionsfollowing the instructions of FEMA P695 [8] document. The earthquake records are sampled to
provide a very diverse accelerogram set. Firstly, this set is normalized by the peak ground velocitiesso that the variance of each record is reduced to an acceptable level. The normalized set then isscaled the way that the median acceleration response spectrum of the set equals the responsespectrum used for the design at the fundamental period of the structure. This can be seen in Figure10, here the scaling is done at natural period of 1.44 s which corresponds to the dominant natural
period of the nonlinear model in the longitudinal direction. The analysis is carried out only in thelongitudinal direction.
Figure 10. Set of ground motion records scaled to a predefined spectral acceleration level atT=1.44 s.
At each scaling level the maximum longitudinal displacement of the girder is registered for eachground motion. The displacement vs. spectral intensity  defined here by the spectral acceleration relation for each record is shown in Figure 11. Plateau of the curve of a seismic record (meaningrapidly increased deformations) indicates the structural collapse for the given record. Three damagelevels (slight, moderate and full) are determined for each component. The damage is measured indeformation and in curvature ductility (=u/ y) in case of the fixed bearing and the piers,respectively. The corresponding values are 50 mm, 100 mm, 250 mm of deformation and = 1, 4and 7 curvature ductilities for slight, moderate and full damages. According to this, fragility curvesare created and shown in Figure 12. The curves confirm again that the most vulnerable componentin collapse prevention performance objective is the fixed bearing: the failure of the whole structure
is determined by the full damage of the bearing (Figure 12. thick, solid line). Piers are so robust thatthey do not even suffer slight damage when the bearing is failed.
The standard spectral acceleration at the fundamental period (1.44 s) is 1.175 m/s2. The curves

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indicate that the actual seismic performance of the structure is sufficient: relatively large extraresistance against seismic loads is provided by the preserve material and crosssection capacities,even though the structure was not designed to ductile behaviour.
Figure 11. Max. longitudinal displacementvalues from each ground motion record at
different spectral acceleration levels.
Figure 12. Fragility curves for the fixedbearing and the pier.
6. Conclusions
In this paper the M0 Hros highway bridge, Hungary is investigated. Linear and nonlinearanalyses are carried out and compared to each other. The results confirm that the most vulnerablecomponent is the fixed bearing, anticipating the failure of the restrained pier. Comparison of theanalysis results shows that the LRSA overestimates the reaction forces and displacements comparedto the LTHA, NLTHA methods. Using more sophisticated model incorporating nonlinear elements
results in more flexible structure, with decreased reaction forces and increased deformations.In addition, incremental dynamic analysis based seismic performance assessment is completed in
accordance to FEMA P695. The fragility curves created by incremental dynamic analysis indicatethat the structure provide relatively large extra resistance against seismic loads due to the increasedflexibility, and to the material and crosssection preserve capacity, even though the structure wasnot designed to ductile behaviour.
7. References
[1]
Jo A, Vigh L, Kollr L. Experiences on seismic design of structures in Hungary. MAGSZACLSZERKEZETEK, Vol. 6:(1), pp. 7281, 2009 (in Hungarian)
[2]
Vigh LG, Dunai L, Kollr L. Numerical and design considerations of earthquake resistant design of twoDanube bridges.Proc. ECEES 2006. Geneva, p. 10. Paper 1420, 2006
[3] Zsarnczay . Seismic performance analysis of common bridge types in Hungary(inHungarian). MasterThesis at Budapest University of Technology and Economics, 2010
[4]
Deierlein GG. Overview of a Comprehensive Framework for Earthquake Performance Assessment.PerformanceBased Seismic Design Concepts and Implementation. Proc. of Intl Workshop, PEERReport 2004/05, UC Berkeley, p. 1526, 2004
[5]
McKenna F, Feneves GL. Open system for earthquake engineering simulation. Pacific earthquakeengineering research center, version 2.3.2., 2012
[6] CEN: EN 19981:2008 Eurocode 8. Design of structures for earthquake resistance  Part 2: Bridges,2008
[7]
Simon J. Numerical model development for seismic assessment of continuous girder bridges.Proceedings of the Conference of Junior Researchers in Civil Engineering, pp. 216224. Budapest,Hungary, 2012
[8]
ATC: FEMA P695. Quantification of Building Seismic Performance Factors, 2009