Comparison of Highway Bridge Seismic Design in Europe and ...

Research ArticleComparison of Highway Bridge Seismic Design in Europe andChina through a Case Study

Qingguo Ben and Xiaoning Zhu

JSTI Group Nanjing Jiangsu Province 210017 China

Correspondence should be addressed to Qingguo Ben benqingguooutlookcom

Received 14 January 2022 Revised 12 March 2022 Accepted 16 March 2022 Published 27 March 2022

Academic Editor Shuang Li

Copyright copy 2022 Qingguo Ben and Xiaoning Zhu is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

With accumulated experiences of bridge damage learned from past earthquake events the highway bridge seismic designapproach is evolving from time to time It is important for both China and Europe to learn from each other to improve seismicdesign approaches A thorough comparison relating to the seismic hazard level response spectra and ductility considerationsbetween Eurocode 8 and the Chinese specification is made in this study Both of these two specifications are based on per-formance-based design philosophy However the Chinese specification is based more on deformation capacity than on strengthe design approach specified in the Chinese specification is more consistent with experiences obtained from past earthquakeevents than themethod adopted in Eurocode 8 Case study shows that bridge designed in accordance with Eurocode 8 could satisfythe force requirement under earthquake action E1 as specified in the Chinese specification but could not satisfy the displacementrequirements under earthquake action E2 It is expected that the method adopted in the Chinese specification could provideconservative seismic design in both aspects of seismic forces and displacements

1 Introduction

e first bridge design specification which includes seismicdesign provisions was published in 1925 shortly after the1923 Kanto earthquake in Japan [1 2] In China the firsthighway bridge seismic design specification was published in1977 [3 4] immediately following the July 28 1976Tangshan earthquake which is one of the most destructiveearthquakes ever happened in China In the past centuryspecifications for seismic bridge design are evolving from theforce-based designmethod to the displacement-based designmethod [2 5] e landmark earthquake events that sig-nificantly promoted the development of bridge seismicdesign philosophy in countries around the world are the1971 San Fernando earthquake (USA) the 1995 Kobeearthquake (Japan) and the 2008 Wenchuan earthquake(China) [6 7] e development of seismic bridge designspecifications was initiated primarily by the fact that theobserved representative damage types of bridge in pastearthquake events are unseating of girders longitudinal and

transverse offset of decks concrete spalling and shear failureof piers e seismic performance of bridges demonstratedthat the force-based seismic design has many shortcomingse major one is that it is not explicitly related to the seismicperformance of bridge as displacement and deformationdetermine seismic damage rather than component strength[2] It has been observed that bridges which possess ductilityand can deform inelastically to the required deformationswithout loss of strength can survive the earthquake suc-cessfully [8] In response to the bridge damage observed inpast earthquake events American Association of StateHighway and Transportation Officials (AASHTO) firstshifted its seismic design focus from the force-based R-factordesign approach [9] to the displacement-based design ap-proach in the Guide Specifications for LRFD Seismic BridgeDesign published in 2009 When designed as per currentseismic bridge design specificationscodes proper seismicdetails such as tightly spaced transverse reinforcements inthe bridge columns well performed shear keys and longseats should be provided and satisfactory bridge seismic

HindawiShock and VibrationVolume 2022 Article ID 8509752 11 pageshttpsdoiorg10115520228509752

performance can usually be achieved As reported fewerthan 015 of highway bridges which possess aforemen-tioned seismic details collapsed or were severely damaged inthe February 27 2010 Maule earthquake Chile (Mw 88)[10 11] Nowadays it is a common practice to involve a largenumber of probabilistic considerations relating to thevariability of seismic input material properties and com-ponent dimensions of bridge structures in the specificationsfor bridge seismic design Even more financial conse-quences associated with bridge damage collapse or loss ofusage following seismic attack are considered too [12ndash15]However despite the enhanced emphasis on realistic de-termination of displacement demand for bridges designphilosophy employed in current specifications could at bestbe termed as deformation-calculation-based seismic designas only the detailing of critical sections is related to thedeformation demand Greater effort should be applied todevelop a seismic design method which is more compatiblewith the concept of displacement-based design so that whenbridges are designed accordingly they can achieve a spec-ified deformation state under the design-level earthquake

It has been recognized that seismic bridge designspecifications of the USA and Japan are most influential inthe seismic design field [12 16 17] e newly publishedSpecifications for Seismic Design of Highway Bridges in Chinain 2020 make a good reference to these two specifications[14] While the Chinese design specification has relativelyfew connections with current Eurocode 8 [15] the EuropeanCommunity began its own action program in the field ofconstruction in 1975 and finished the first generation ofEuropean codes in the 1980s [15 18] e seismic bridgedesign code currently in effect in Europe is the 2005 versionDue to different originations evolution progresses anddesign philosophies there are substantial differences be-tween the Chinese seismic bridge design specification andEurocode 8 in aspects such as the seismic hazard levelresponse spectra and behavior modification factors toconsider ductility etc [19] With the development ofeconomy and close international cooperation betweenChina and European countries it is essential to differentiatethe difference existing in the design specifications In thispaper a thorough comparison between Eurocode 8 [15] andthe Specifications for Seismic Design of Highway Bridges inChina (hereafter referred to Chinese specification) [14]relating to the aforementioned aspects is made It is expectedthat this paper could be of some value to encourage Chinaand Europe to learn from each other for improving theirseismic standards in the future and that this will also pro-mote the development of highway bridge seismic designphilosophy

2 Difference and Similarity betweenEurocode 8 and Chinese Specification

21 Seismic Hazard Levels Eurocode 8 specifies a single-level seismic design of new bridges corresponding to the lifesafety limit state of the general performance-based seismicdesign framework requiring that after the seismic eventsbridges shall be designed and constructed to retain its

structural integrity and have sufficient residual resistance tobe used for emergency traffic e design seismic action forbridges of ordinary importance in Eurocode 8 has a refer-ence return period of 475 years corresponding to a 10exceedance probability in 50 years However for bridges thatare essential for public safety or that are critical for com-munications in the region the importance factor cI shouldbe applied to the design seismic action for the purpose ofachieving better bridge seismic performance It is implicit inEurocode 8 that once the life safety limit state of the bridge isachieved minimal damage of the bridge would occur underearthquake with a high probability of exceedance butlimited only to secondary bridge components e near-collapse limit state of bridge in an extreme and very rareearthquake is prevented by applying the capacity designconcept reflecting in the clauses relating to ductility andenergy dissipation [19] Single-level seismic design was alsoused in the repealed Chinese specification published in 1989(ie Specifications of Earthquake Resistant Design forHighway Engineering) [4] Currently two-level seismic de-sign for highway bridges ie one for operational perfor-mance level and the other for life safety performance level isemployed Corresponding to earthquakes with return periodof about 475 years or 10 exceedance probability in 50 years(ie earthquake action E1) and of about 2000 years or 25exceedance probability in 50 years (ie earthquake actionE2) respectively the two seismic design levels specified inthe Chinese specification are adjusted by using seismicdesign important factor Ci which is similar to the impor-tance factor cI as specified in Eurocode 8 Under operationalperformance level design earthquake highway bridges arerequired to have only minor damage and to be open to trafficimmediately after the earthquake While the life safetyperformance level is specified to protect human life duringand following a rare earthquake it corresponds to the near-collapse limit state

22 Response Spectra e basic shape of the horizontalelastic response spectra in Eurocode 8 and the Chinesespecification is illustrated in Figure 1 Obviously the re-sponse spectrum in Eurocode 8 consisted of four brancheswhile there are only three branches in the response spectrumof the Chinese specification It is important to notice thatthese two response spectra are described by the lower limit ofthe period of the constant spectral acceleration branch (TB inEurocode 8 vs 01 in the Chinese specification) the upperlimit of the period of the constant spectral accelerationbranch (TC in Eurocode 8 vs Tg in the Chinese specifica-tion) the soil factor (S in Eurocode 8 vs Cs in the Chinesespecification) and the damping correction factor (η inEurocode 8 vs Cd in the Chinese specification) e im-portance factor cI or the seismic design important factorCi isincluded in the design ground acceleration ag Values of theparameters describing both type 1 elastic response spectra inEurocode 8 and the elastic response spectra in the Chinesespecification are given in Table 1 Values of the dampingcorrection factors η and Cd are determined by (1) and (2)respectively Comparison of the damping correction factors

2 Shock and Vibration

is shown in Figure 2 It can be seen from Table 1 and Figure 2that these values vary significantly in each specification

η

10

(5 + ξ)

1113971

ge 055 (1)

Cd 1 +005 minus ξ100

008 + 16ξ100ge 055 (2)

where ξ is the damping ratio of the bridge expressed as apercentage

For the vertical elastic response spectrum in Eurocode 8the amplification factor in the constant spectral pseudo-acceleration plateau is 3 instead of 25 as in the horizontaldirection the period parameters TB TC and TD are fixed forall soil types (see Table 2) and there is no amplificationfactor due to soil type for the vertical spectrum Howeverthe soil factor and the upper limit of the period of theconstant spectral acceleration branch for the vertical elasticresponse spectrum in the Chinese specification are all dif-ferent (see Table 3) e shape of the vertical elastic responsespectrum is the same as the horizonal elastic responsespectrum in both Eurocode 8 and the Chinese specification

23 Ductility Seismic Design It is today commonplace thatthe two fundamental options for the seismic design ofbridges are seismic isolation design and ductility seismicdesign For the seismic isolation design horizontal dis-placement demand imposed by earthquake excitation isaccommodated by placing bridge deck on a system of slidingor horizontally flexible bearings at the top of the abutmentsand piers [20] while for the ductility seismic design bridge

deck is fixed or rigidly connected to at least one pier and thefixed pier is required to accommodate the horizontal dis-placement demand by developing inelastic rotations in theassigned plastic hinge regions [21] Only ductility seismicdesign is discussed in this paper Ductility seismic design inEurocode 8 is force-based as the inelastic response spectrumused is obtained from the elastic response spectrum byapplying a so-called behavior factor q e behavior factor qis the ratio of Fel (ie peak force that would have developed ifthe bridge is elastic) to Fy (ie yield force of the bridge)Equal displacement rule ie the peak displacement re-sponse of the inelastic and elastic bridges under earthquakeexcitation are about the same is adopted to determine thevalue of q e behavior factor q is expected to reflect theglobal inelastic deformations of bridge under the designseismic action and a safety factor between 15 and 2 isexpected to be achieved by properly dimensioning anddetailing the plastic hinges in the piers It should be notedthat the behavior factor q in Eurocode 8 enters in the in-elastic design response spectrum and must be determinedbeforehand therefore iterative dynamic analysis isinevitable

Force-based seismic design usually can produce safe andsatisfactory designs when combined with capacity designprinciple and careful detailing of plastic hinges However itshould be emphasized that force-based seismic design im-plicitly implies that the elastic characteristics of the bridgeare the best indicators of inelastic performance of the bridgeAdditionally the component stiffness in force-based seismicdesign is traditionally assumed to be independent of thecomponent strength and hence according to equal dis-placement principle increasing the strength of a bridgewould improve its safety But accompanying the crushing of

S ea

g

T (s)

S

25Sη

TB TC TD

(a)

S ea

g

T (s)

CS

25CSCd

01Tg

(b)

Figure 1 Basic shape of horizontal elastic response spectra (a) Eurocode 8 and (b) the Chinese specification

Table 1 Values of the parameters describing the basic shape of the horizontal elastic response spectra

Eurocode 8 Chinese specificationGround type S TB (s) TC (s) TD (s) Ground type CS (s) Tg (s)A 100 015 040 200 I0 072sim090 020sim030B 120 015 050 200 I1 080sim100 025sim035C 115 020 060 200 II 100 035sim045D 135 020 080 200 III 130sim100 045sim065E 140 015 050 200 IV 125sim090 065sim09

Shock and Vibration 3

concrete and yielding of longitudinal reinforcements in theplastic hinge regions of piers the initial bridge elasticstiffness will be irrelevant even to the subsequent elasticresponse of bridge following inelastic deformation of piersBesides the assumption of stiffness independent of strengthis proved to be invalid by detailed analysis and experimentalevidence [22] Another problem with force-based seismicdesign is the selection of appropriate member stiffness eassumed effective component stiffness used in force-basedseismic design will significantly affect the design seismicforces It is specified in Eurocode 8 that the cracked bendingand shear stiffness may be taken as one half of the uncrackedelastic stiffness of the gross section or can be estimated from(3) or (4) If inaccurate stiffness is assumed the calculateddisplacement demand will also be inaccurate and probablybe nonconservative

Ieff 008Iun + Icr (3)

where Iun is the moment of inertia of the gross section of theuncracked pier and Icr is the moment of inertia of thecracked section at the yield point of the tensilereinforcement

EcIeff ]MR d

ϕy

(4)

where v 12 MRd is the design ultimate moment and ϕy isthe curvature of pier section at first yield of the reinforcingsteel

In the Chinese specification because the aforementionedtwo-level seismic design approach is adopted calculation ofbridge responses under earthquake actions E1 and E2 shouldbe performed Different amplified important factors Ci areapplied to earthquake actions E1 and E2 Under earthquakeaction E1 bridges are required to remain essentially elasticand immediate service should be available following theearthquake erefore component forces are more impor-tant under earthquake action E1 Also elastic analysisprocedure is employed and gross section area of the piers isused to obtain a conservative assessment of the seismicdesign force Under earthquake action E2 bridge dis-placements are more critical Inelastic action of bridge pier isallowed and is intended to be restricted only to the plastichinge regions Consequently nonlinear analysis is a ne-cessity and time history analysis or equivalent elastic analysisis employed In order to obtain the realistic maximumdisplacement demand under earthquake action E2 effectivesection properties should be used when modeling ductilepiers Effective section properties as specified in the Chinesespecification should be obtained from theM-ϕ curve analysis(see (5)) of the section

Eurocode 8Chinese specification

06

08

1

12

14

16

18

η or

Cd

5 10 15 200Damping ratio ξ ()

Figure 2 Comparison of the damping correction factors in Eurocode 8 and the Chinese specification

Table 2 Parameters of the vertical elastic response spectra in Eurocode 8

Spectrum avgag TB (s) TC (s) TD (s)Type 1 090 005 015 100

Table 3 Parameters of the vertical elastic response spectra in the Chinese specification

Ground type CS (s) Tg (s)I0 060 015sim025I1 060sim070 020sim030II 060sim080 025sim040III 070sim080 030sim050IV 080sim090 055sim075


EcIeff My

ϕy

(5)

whereMy is the moment capacity of pier section at first yieldof the reinforcing steel ϕy is the curvature of pier section atfirst yield of the reinforcing steel Ec is the modulus ofelasticity of concrete and Ieff is the effective moment ofinertia of the pier section

3 Case Study

Extensive worked examples about design of highway bridgesas to Eurocode 8 have been given in reference [23] In thissection however a prototype bridge chosen from realisticproject is first designed according to Eurocode 8 and thenchecked with the Chinese specification

31 Prototype Bridge e prototype bridge is a 4-spanoverpass with spans 65 + 95+95 + 65m and total length of320m as shown in Figure 3 e deck is a post-tensionedcast in situ concrete box girder Pier heights are 14m for P138m for P2 and 30m for P3 Illustration of the pier sectionis shown in Figure 4 For pier P1H is 25m for pier P2H is502m at the bottom and is 35m at the top for pier P3 H is25m e deck is rigidly supported on P2 and P3 andsupported on P1 and the abutments through bearingsallowing free sliding and rotation in and about both hori-zontal axes e piers and abutments are founded on pilegroups e piers are made of concrete C4050 withfck 40MPa and Ec 35GPa and reinforcing steel S500 withfyk 500MPa e cover to the reinforcement center isc 40mm e piles are made of concrete C3037 withfck 30MPa and Ec 33GPa and of reinforcing steel S500with fyk 500MPa e cover to the reinforcement center isc 75mm e main elements resisting seismic forces arepiers P2 and P3 A limited ductile seismic behavior issuggested for piers P2 and P3 e value of the behaviorfactors q in the horizontal direction is 15 while that in thevertical direction is 10

32 Response Spectra e design seismic action is calculatedby using response spectrum of type 1 e ground type is Bso the characteristic periods are TB 015 s TC 05 s andTD 2 s while the soil factor is S 12 e bridge is locatedat seismic zone with a reference peak ground accelerationagR 026 g e importance factor is cI 13 and the lowerbound factor is β 020 erefore the seismic action in thehorizontal direction is ag cIagR 13times 026 g 0338 g Inthe vertical direction avgag 09 e horizontal and ver-tical design response spectra calculated according toEurocode 8 are presented in Figures 5 and 6 respectively

33 SeismicDesignResults e effective moment of inertia ofthe cracked pier calculated as per (3) is 04 times the momentof inertia of the gross section of the uncracked pier efundamental periods of the bridge estimated according to theeffective moment of inertia of the pier are 47 s 23 s and 13 s

in the transverse longitudinal and vertical directions re-spectively e combination rule of the three components ofthe seismic action in the response spectrum analysis is thelinear combination rule of the type given in (6) Summary ofthe suggested seismic reinforcements designed according toEurocode 8 is given in Tables 4 and 5 Combination of seismicdesign forces and the capacity of critical pier sections areshown in Figure 7 It can be seen from Figure 7 that the mostcritical section is of the transverse direction at the top of pier2 at which the capacity of the section is marginally larger thanthe demand of seismic design force

E

Ex

11138681113868111386811138681113868111386811138681113868 + 03 Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + 03 Ez

11138681113868111386811138681113868111386811138681113868

03 Ex

11138681113868111386811138681113868111386811138681113868 + Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + 03 Ez

11138681113868111386811138681113868111386811138681113868

03 Ex

11138681113868111386811138681113868111386811138681113868 + 03 Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + Ez

11138681113868111386811138681113868111386811138681113868

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(6)

34 Seismic Design Checking as per the ChineseSpecification Response spectra corresponding to earth-quake actions E1 and E2 in the horizontal and vertical di-rections are also shown in Figures 5 and 6 respectively Inthe horizontal direction design response spectrum ofEurocode 8 is larger than the E1 response spectrum of theChinese specification but smaller than the E2 responsespectrum of the Chinese specification However in thevertical direction design response spectrum of Eurocode 8 islarger than both of the E1 and E2 response spectra of theChinese specification in the short period range e fun-damental periods of the bridge estimated according to themoment of inertia of the gross pier sections as per theChinese specification are 42 s 16 s and 08 s in the trans-verse longitudinal and vertical directions respectively ecalculated periods according to the Chinese specification are106 304 and 385 shorter than the periods calculatedaccording to Eurocode 8

35EarthquakeActionE1 e combination rule of the threecomponents of the seismic action in the response spectrumanalysis is the square root of the sum of squares (SRSS) givenin (7) [24] ese two rules given in (6) and (7) both arebased on the assumption that the principal axes of groundmotion coincide with the structural axes and that bothhorizontal components of ground motion have the sameintensity In general these two rules usually give comparableresults Instead of using the interaction diagrams for theverification of cross sections in Eurocode 8 the verificationof cross sections in the Chinese specification is done byemploying moment-curvature analysis of the sections Alsobilinear curve with equal area under the curve to the actualmoment-curvature curve is used for simplicity and thesetwo curves intersect at the point of moment at first yieldUnder earthquake action E1 the design moment from theresponse spectrum analysis should be less than the sectionmoment at first yield Due to the smaller design responsespectra for earthquake action E1 as expected all criticalsections of the pier meet the specification requirements (seeFigure 8)


65 m 95 m 95 m 65 m

A0P1

P2

P3

A1

Figure 3 Illustration of the prototype bridge

11H05

025

025

05

1

025 02505

05

025 02505

9

Figure 4 Illustration of the pier section (unit m)

Eurocode 8E1E2

S (T

)g

0

02

04

06

08

1

12

1 2 3 4 5 60T (s)

Figure 5 Comparison of horizontal design response spectra

Eurocode 8E1E2

S (T

)g

0

02

04

06

08

1

12

1 2 3 4 5 60T (s)

Figure 6 Comparison of vertical design response spectra


Table 4 Suggested longitudinal reinforcements of piers

Location Reinforcement P1 P2 P3

BottomNumber 382 529 510Size (mm) 25 32 32Ratio () 13 23 28

TopNumber SC 437 510Size (mm) SC 32 32Ratio () SC 22 28

Note SC means reinforcement ratios should be determined based on static analysis

Table 5 Suggested transverse reinforcements of piers

Location Position Reinforcement P1 P2 P3

BottomLongitudinal Shear Not required Aswsge 1215 cm2m Aswsge 1666 cm2m

Confinement Not required Not required Not required

Transverse Shear Not required Aswsge 538 cm2m Aswsge 612 cm2mConfinement Not required Not required Not required

TopLongitudinal Shear -- Aswsge 1711 cm2m Aswsge 1533 cm2m

Confinement -- Not required Not required

Transverse Shear -- Aswsge 494 cm2m Aswsge 585 cm2mConfinement -- Not required Not required

Against buckling sle 128 cm sle 164 cm sle 164 cmNote Asw is the total cross-sectional area of hoops or ties in the one transverse direction of confinement s is spacing of tie legs on centers

Design combinations

Bottom of pier 1

0

500

1000

P (times

103 k

N)

-1000 0 1000 2000-2000Mx (times103 kNmiddotm)

(a)

Design combinations

Bottom of pier 1

0

500

1000

P (times

103 k

N)

-200 0 200 400-400My (times103 kNmiddotm)

(b)

Design combinations

Bottom of pier 2

-500

0

500

1000

1500

P (times

103 k

N)


(c)

Design combinations

Bottom of pier 2

-500

0

500

1000

1500

P (times

103 k

N)

-800 -400 0 400 800 1200-1200My (times103 kNmiddotm)

(d)

Design combinations

Top of pier 2

-400

0

400

800

1200

P (times

103 k

N)


(e)

Design combinations

Top of pier 2

-400

0

400

800

1200

P (times

103 k

N)

-600 -400 -200 0 200 400 600 800-800My (times103 kNmiddotm)

(f )

Figure 7 Continued


Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(g)

Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(h)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(i)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(j)

Figure 7 Moment-axial force interaction diagram for critical pier sections

Mx (Bottom of pier 1)Bilinearization

E1 moment demandϕy

0

50

100

150

M (times

103 k

Nm

)

2 4 6 80ϕ (times10minus3 1m)

ϕu

(a)

My (Bottom of pier 1)Bilinearization

E1 moment demand0

250

500

750

M (times

103 k

Nm

)

1 2 30ϕ (times10minus3 1m)

ϕy ϕu

(b)


E1 moment demand

0100200300400500600

M (times

103 k

Nm

)


ϕy ϕu

(c)


E1 moment demand

0250500750

100012501500

M (times

103 k

Nm

)


ϕyϕu

(d)

Mx (Top of pier 2)Bilinearization

E1 moment demand

050

100150200250300350

M (times

103 k

Nm

)


ϕyϕu

(e)

My (Top of pier 2)Bilinearization

E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕyϕu

(f )

Figure 8 Continued


E

E2x + E

2y + E

2z

1113969

(7)

36 Earthquake Action E2 As per the Chinese specificationseismic responses of the bridge under earthquake action E2can be obtained either from nonlinear time history analysisor from response spectrum analysis Nonlinear time historyanalysis is thought to be more accurate than the responsespectrum analysis However by using the nonlinear timehistory analysis response spectrum compatible artificialground motions [25 26] have to be generated first becausethe recorded ground motions are usually different in overallground motion level and spectral shape from the designspectrum Besides nonlinear frame hinge models [27 28]have to be inserted in the potential hinge regions which willunnecessarily complicate the comparison process ere-fore response spectrum analysis is chosen Deformation ofthe piers obtained from response spectrum analysis shall bemultiplied by the magnification factor specified in the fol-lowing equation

Rd 1 minus1μΔ

1113888 1113889Tlowast

T+

1μΔge 10 for

Tlowast

Tgt 10

Rd 10 forTlowast

Tle 10

(8)

where Tlowast 125Tg μΔ is the maximum pier displacementductility demand (approximately equal to 60) T is thefundamental period in the calculation direction and Tg is thecharacteristic period shown in Figure 1(b)

Displacement capacity of the pierΔu is given by (9) basedon the moment-area method for determining the pierrsquosrotation and deflection (see Figure 8) (9) is dependent onthe following three assumptions (a) the plastic rotation θu ofthe pier is concentrated at the center of the analytical plastichinge (b) the distribution of elastic curvature along the pieris linear and (c) the plastic curvature of the analytical plastichinge is constant

Δu 13H

2times ϕy + H minus

LP

21113874 1113875 times θu

LP min LP1 Lp21113872 1113873

LP1 008H + 0022fyds ge 0044fyds

Lp2 23

b

θu Lp ϕu minus ϕy1113872 1113873

Kds

(9)

where H is the height of the pier from point of maximummoment to the point of moment contraflexure ϕy is theidealized yield curvature (see Figure 8) ϕu is the ultimatecurvature (see Figure 8) Lp is the analytical plastic hingelength b is the width of the pier fy is the yield strength oflongitudinal reinforcement ds is the reinforcement diam-eter and Kds is the safety factor taken as 20

Checking of the displacement capacity of the pier underearthquake action E2 is shown in Table 6 It is clearly shownin Table 6 that longitudinal displacement capacity of pier 1


E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕy ϕu

(g)


E1 moment demand

0250500750

10001250

M (times

103 k

Nm

)


ϕy ϕu

(h)


E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕyϕu

(i)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕy ϕu

(j)

Figure 8 Moment-curvature diagram for critical pier sections


and pier 2 does not satisfy the requirements of the Chinesespecification which means pier 1 and pier 2 could notmaintain their load resistance under seismic-induceddeformations

4 Conclusions

Eurocode 8 currently in effect was published seventeen yearsago a time before the state-of-the-art highway bridgeseismic design approach was developed erefore single-level seismic design of new bridges was adopted which isdifferent from current common practice of adopting two-level seismic design For this reason response spectra de-fined in Eurocode 8 depend not only on seismic zone andsoil conditions such as that defined in the Chinese speci-fication but also on the structural system ie relating to thebehavior factor q of the bridge Ductility seismic design inEurocode 8 is force-based and structural behavior factor q isused to reflect the global inelastic deformations of bridgeunder design seismic action is approach implicitly im-plies that the elastic characteristics of the bridge are the bestindicators of inelastic performance of the bridge Howeverin the Chinese specification by employing the two-levelseismic design approach sufficient bridge strength isstressed under earthquake action E1 while sufficient dis-placement capacity of the bridge is stressed under earth-quake action E2 is design approach is more consistentwith experiences obtained from past earthquake events andit appears more straightforward and reasonable for theseismic design of bridges by employing the method specifiedin the Chinese specification Case study shows that bridgedesigned in accordance with Eurocode 8 could satisfy theforce requirement under earthquake action E1 as specified inthe Chinese specification but may not satisfy the displace-ment requirements under earthquake action E2 as specifiedin the Chinese specification It is expected that the methodadopted in the Chinese specification would provide con-servative seismic design in both aspects of seismic forces anddisplacements

Data Availability

e numerical data used to support the findings of this studyare included within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W P Yen and S Unjoh Comparison of US and JapaneseHighway Bridge Seismic Retrofitting Measures Tsukuba Ja-pan 1999

[2] M J N Priestley G M Calvi and M J Kowalsky Dis-placement-Based Seismic Design of Structures IUSS PressPavia Italy 2007

[3] Y Wancheng and F Lichu ldquoDucitlity and isolation inasseismic designs for bridges-development tendency ofChinese aseismic code for bridges from the view of Eurocode8rdquo Journal of Tongji University vol 22 no 4 pp 481ndash4851994

[4] MCPRC Specifications of Earthquake Resistant Design forHighway Engineering China Communications Press Co LtdBeijing China 1989

[5] M J N Priestley G M Calvi and M J Kowalsky ldquoDirectdisplacement-based seismic design of structuresrdquo in Pro-ceedings of the 5th New Zealand Society for Earthquake En-gineering Conference Palmerston North New Zealand March2007

[6] W H P Yen G Chen M Yashinsky Y Hashash C Holuband K Wang China Earthquake Reconnaissance ReportPerformance of Transportation Structures during the May 122008 M7 Wenchuan Earthquake US Department ofTransportation Federal Highway Administration ResearchDevelopment and Technology Turner-Fairbank HighwayResearch Center Wahington DC USA 2011

[7] S Shekhar J Ghosh and S Ghosh ldquoImpact of design codeevolution on failure mechanism and seismic fragility ofhighway bridge piersrdquo Journal of Bridge Engineering vol 25no 2 Article ID 04019140 2020

[8] S D C Hampshir S BucurZanaica S D S Lima C Bucurand S D Lima ldquoComparative study of codes for seismicdesign of structuresrdquo Mathematical Modelling in Civil En-gineering vol 9 no 1 pp 1ndash12 2013

[9] A Aashto LRFD Bridge Design Specifications AmericanAssociation of State Highway and Transportation OfficialsWashington DC USA 8th edition 2017

[10] W H P Yen G Chen I Buckle T Allen D Alzamora andJ Ger Postearthquake Reconnaissance Report on Trans-portation Infrastructure Impact of the February 27 2010Offshore Maule Earthquake in Chile US Department ofTransportation Federal Highway Administration ResearchDevelopment and Technology Turner-Fairbank HighwayResearch Center Wahington DC USA 2011

[11] C Cui and Y Xu ldquoMechanism study of vehicle-bridge dy-namic interaction under earthquake ground motionrdquoEarthquake Engineering amp Structural Dynamics vol 50 no 7pp 1931ndash1947 2021

[12] AASHTO Guide Specifications for LRFD Seismic BridgeDesign American Association of State Highway and Trans-portation Officials p 309 Washongton DC USA 2nd edi-tion 2015

[13] MOHURD Code for Seismic Design of Urban Bridges ChinaArchitecture and Building Press Beijing China 2011

[14] MCPRC Specifications for seismic design of highway bridgesChina Communications Press CoLtd Beijing China 2020

[15] European Committee for Standardization Eurocode8 Designof Structures for Earthquake Resistance-Part2 Bridges Eu-ropean Committee for Standardization Brussels Belgium2005

Table 6 Checking of displacement capacity of piers

Direction Pier Rd Δd (cm) Δu (cm) Check

Longitudinal1 10 17 608 Y2 10 193 175 N3 10 201 193 N

Transverse1 10 01 48 Y2 10 99 327 Y3 10 77 168 Y


[16] Japan Road Association Design Specifications for HighwayBridges Part V Seismic Design Japan Road AssociationTokyo Japan 2012

[17] A D E Sebai Comparisons of international seismic codeprovisions for bridges McGill University Montreal Canada2009

[18] A Ansal ldquoPerspectives on European Earthquake Engineeringand Seismology Volume 1rdquo Geotechnical Geological andEarthquake Engineering vol 34 2014

[19] B Kolias M N Fardis and A Pecker Designersrsquo Guide toEurocode 8 Design of Bridges for Earthquake Resistance ICEPublishing London UK 2012

[20] X Li and Y Shi ldquoSeismic design of bridges against near-faultground motions using combined seismic isolation andrestraining systems of LRBs and CDRsrdquo Shock and Vibrationvol 2019 Article ID 4067915 11 pages 2019

[21] Q Ben ldquoResearch on correlation of ground motion param-eters and seismic performance of bridgerdquo Northern Com-munications no 10 pp 1ndash3 2016

[22] H Li Q Ben Z Yu Y Zhang and X Lu ldquoAnalysis and ex-periment of cumulated damage of steel frame structures underearthquake actionrdquo Journal of Building Structures vol 25no 3 pp 69ndash74 2004

[23] Y Bouassida E Bouchon P Crespo P Croce L Davaineand S Denton Bridge Design to Eurocodes-Worked ExamplesPublications Office of the European Union LuxembourgEurope 2012

[24] W Smeby and A D Kiureghian ldquoModal combination rulesfor multicomponent earthquake excitationrdquo EarthquakeEngineering amp Structural Dynamics vol 13 no 1 pp 1ndash121985

[25] D A Gasparini and E H Vanmarcke SIMQKE A Programfor Artificial Motion Generation MIT Cambridge England1976

[26] F Ferreira C Moutinho A Cunha and E Caetano ldquoAnartificial accelerogram generator code written in matlabrdquoEngineering Reports vol 2 no 3 pp 1ndash17 2020

[27] S El-Tawil and G G Deierlein ldquoNonlinear analysis of mixedsteel-concrete frames I element formulationrdquo Journal ofStructural Engineering vol 127 no 6 pp 647ndash655 2001

[28] S El-Tawil and G G Deierlein ldquoNonlinear analysis of mixedsteel-concrete frames II implementation and verificationrdquoJournal of Structural Engineering vol 127 no 6 pp 656ndash6652001


performance can usually be achieved As reported fewerthan 015 of highway bridges which possess aforemen-tioned seismic details collapsed or were severely damaged inthe February 27 2010 Maule earthquake Chile (Mw 88)[10 11] Nowadays it is a common practice to involve a largenumber of probabilistic considerations relating to thevariability of seismic input material properties and com-ponent dimensions of bridge structures in the specificationsfor bridge seismic design Even more financial conse-quences associated with bridge damage collapse or loss ofusage following seismic attack are considered too [12ndash15]However despite the enhanced emphasis on realistic de-termination of displacement demand for bridges designphilosophy employed in current specifications could at bestbe termed as deformation-calculation-based seismic designas only the detailing of critical sections is related to thedeformation demand Greater effort should be applied todevelop a seismic design method which is more compatiblewith the concept of displacement-based design so that whenbridges are designed accordingly they can achieve a spec-ified deformation state under the design-level earthquake

It has been recognized that seismic bridge designspecifications of the USA and Japan are most influential inthe seismic design field [12 16 17] e newly publishedSpecifications for Seismic Design of Highway Bridges in Chinain 2020 make a good reference to these two specifications[14] While the Chinese design specification has relativelyfew connections with current Eurocode 8 [15] the EuropeanCommunity began its own action program in the field ofconstruction in 1975 and finished the first generation ofEuropean codes in the 1980s [15 18] e seismic bridgedesign code currently in effect in Europe is the 2005 versionDue to different originations evolution progresses anddesign philosophies there are substantial differences be-tween the Chinese seismic bridge design specification andEurocode 8 in aspects such as the seismic hazard levelresponse spectra and behavior modification factors toconsider ductility etc [19] With the development ofeconomy and close international cooperation betweenChina and European countries it is essential to differentiatethe difference existing in the design specifications In thispaper a thorough comparison between Eurocode 8 [15] andthe Specifications for Seismic Design of Highway Bridges inChina (hereafter referred to Chinese specification) [14]relating to the aforementioned aspects is made It is expectedthat this paper could be of some value to encourage Chinaand Europe to learn from each other for improving theirseismic standards in the future and that this will also pro-mote the development of highway bridge seismic designphilosophy

2 Difference and Similarity betweenEurocode 8 and Chinese Specification

21 Seismic Hazard Levels Eurocode 8 specifies a single-level seismic design of new bridges corresponding to the lifesafety limit state of the general performance-based seismicdesign framework requiring that after the seismic eventsbridges shall be designed and constructed to retain its

structural integrity and have sufficient residual resistance tobe used for emergency traffic e design seismic action forbridges of ordinary importance in Eurocode 8 has a refer-ence return period of 475 years corresponding to a 10exceedance probability in 50 years However for bridges thatare essential for public safety or that are critical for com-munications in the region the importance factor cI shouldbe applied to the design seismic action for the purpose ofachieving better bridge seismic performance It is implicit inEurocode 8 that once the life safety limit state of the bridge isachieved minimal damage of the bridge would occur underearthquake with a high probability of exceedance butlimited only to secondary bridge components e near-collapse limit state of bridge in an extreme and very rareearthquake is prevented by applying the capacity designconcept reflecting in the clauses relating to ductility andenergy dissipation [19] Single-level seismic design was alsoused in the repealed Chinese specification published in 1989(ie Specifications of Earthquake Resistant Design forHighway Engineering) [4] Currently two-level seismic de-sign for highway bridges ie one for operational perfor-mance level and the other for life safety performance level isemployed Corresponding to earthquakes with return periodof about 475 years or 10 exceedance probability in 50 years(ie earthquake action E1) and of about 2000 years or 25exceedance probability in 50 years (ie earthquake actionE2) respectively the two seismic design levels specified inthe Chinese specification are adjusted by using seismicdesign important factor Ci which is similar to the impor-tance factor cI as specified in Eurocode 8 Under operationalperformance level design earthquake highway bridges arerequired to have only minor damage and to be open to trafficimmediately after the earthquake While the life safetyperformance level is specified to protect human life duringand following a rare earthquake it corresponds to the near-collapse limit state

22 Response Spectra e basic shape of the horizontalelastic response spectra in Eurocode 8 and the Chinesespecification is illustrated in Figure 1 Obviously the re-sponse spectrum in Eurocode 8 consisted of four brancheswhile there are only three branches in the response spectrumof the Chinese specification It is important to notice thatthese two response spectra are described by the lower limit ofthe period of the constant spectral acceleration branch (TB inEurocode 8 vs 01 in the Chinese specification) the upperlimit of the period of the constant spectral accelerationbranch (TC in Eurocode 8 vs Tg in the Chinese specifica-tion) the soil factor (S in Eurocode 8 vs Cs in the Chinesespecification) and the damping correction factor (η inEurocode 8 vs Cd in the Chinese specification) e im-portance factor cI or the seismic design important factorCi isincluded in the design ground acceleration ag Values of theparameters describing both type 1 elastic response spectra inEurocode 8 and the elastic response spectra in the Chinesespecification are given in Table 1 Values of the dampingcorrection factors η and Cd are determined by (1) and (2)respectively Comparison of the damping correction factors



η

10

(5 + ξ)

1113971

ge 055 (1)


008 + 16ξ100ge 055 (2)






S ea

g

T (s)

S

25Sη

TB TC TD

(a)

S ea

g

T (s)

CS

25CSCd

01Tg

(b)








EcIeff ]MR d

ϕy

(4)




06

08

1

12

14

16

18

η or

Cd








EcIeff My

ϕy

(5)


3 Case Study






E

Ex

11138681113868111386811138681113868111386811138681113868 + 03 Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + 03 Ez

11138681113868111386811138681113868111386811138681113868

03 Ex

11138681113868111386811138681113868111386811138681113868 + Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + 03 Ez

11138681113868111386811138681113868111386811138681113868

03 Ex

11138681113868111386811138681113868111386811138681113868 + 03 Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + Ez

11138681113868111386811138681113868111386811138681113868

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(6)




65 m 95 m 95 m 65 m

A0P1

P2

P3

A1


11H05

025

025

05

1

025 02505

05

025 02505

9


Eurocode 8E1E2

S (T

)g

0

02

04

06

08

1

12

1 2 3 4 5 60T (s)


Eurocode 8E1E2

S (T

)g

0

02

04

06

08

1

12

1 2 3 4 5 60T (s)

















Design combinations

Bottom of pier 1

0

500

1000

P (times

103 k

N)


(a)

Design combinations

Bottom of pier 1

0

500

1000

P (times

103 k

N)


(b)

Design combinations

Bottom of pier 2

-500

0

500

1000

1500

P (times

103 k

N)


(c)

Design combinations

Bottom of pier 2

-500

0

500

1000

1500

P (times

103 k

N)


(d)

Design combinations

Top of pier 2

-400

0

400

800

1200

P (times

103 k

N)


(e)

Design combinations

Top of pier 2

-400

0

400

800

1200

P (times

103 k

N)


(f )

Figure 7 Continued


Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(g)

Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(h)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(i)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(j)



E1 moment demandϕy

0

50

100

150

M (times

103 k

Nm

)


ϕu

(a)


E1 moment demand0

250

500

750

M (times

103 k

Nm

)


ϕy ϕu

(b)


E1 moment demand

0100200300400500600

M (times

103 k

Nm

)


ϕy ϕu

(c)


E1 moment demand

0250500750

100012501500

M (times

103 k

Nm

)


ϕyϕu

(d)


E1 moment demand

050

100150200250300350

M (times

103 k

Nm

)


ϕyϕu

(e)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕyϕu

(f )

Figure 8 Continued


E

E2x + E

2y + E

2z

1113969

(7)


Rd 1 minus1μΔ

1113888 1113889Tlowast

T+

1μΔge 10 for

Tlowast

Tgt 10

Rd 10 forTlowast

Tle 10

(8)



Δu 13H


LP

21113874 1113875 times θu

LP min LP1 Lp21113872 1113873


Lp2 23

b


Kds

(9)




E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕy ϕu

(g)


E1 moment demand

0250500750

10001250

M (times

103 k

Nm

)


ϕy ϕu

(h)


E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕyϕu

(i)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕy ϕu

(j)




4 Conclusions


Data Availability




References



















Transverse1 10 01 48 Y2 10 99 327 Y3 10 77 168 Y

















η

10

(5 + ξ)

1113971

ge 055 (1)


008 + 16ξ100ge 055 (2)






S ea

g

T (s)

S

25Sη

TB TC TD

(a)

S ea

g

T (s)

CS

25CSCd

01Tg

(b)








EcIeff ]MR d

ϕy

(4)




06

08

1

12

14

16

18

η or

Cd








EcIeff My

ϕy

(5)


3 Case Study






E

Ex

11138681113868111386811138681113868111386811138681113868 + 03 Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + 03 Ez

11138681113868111386811138681113868111386811138681113868

03 Ex

11138681113868111386811138681113868111386811138681113868 + Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + 03 Ez

11138681113868111386811138681113868111386811138681113868

03 Ex

11138681113868111386811138681113868111386811138681113868 + 03 Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + Ez

11138681113868111386811138681113868111386811138681113868

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(6)




65 m 95 m 95 m 65 m

A0P1

P2

P3

A1


11H05

025

025

05

1

025 02505

05

025 02505

9


Eurocode 8E1E2

S (T

)g

0

02

04

06

08

1

12

1 2 3 4 5 60T (s)


Eurocode 8E1E2

S (T

)g

0

02

04

06

08

1

12

1 2 3 4 5 60T (s)

















Design combinations

Bottom of pier 1

0

500

1000

P (times

103 k

N)


(a)

Design combinations

Bottom of pier 1

0

500

1000

P (times

103 k

N)


(b)

Design combinations

Bottom of pier 2

-500

0

500

1000

1500

P (times

103 k

N)


(c)

Design combinations

Bottom of pier 2

-500

0

500

1000

1500

P (times

103 k

N)


(d)

Design combinations

Top of pier 2

-400

0

400

800

1200

P (times

103 k

N)


(e)

Design combinations

Top of pier 2

-400

0

400

800

1200

P (times

103 k

N)


(f )

Figure 7 Continued


Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(g)

Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(h)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(i)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(j)



E1 moment demandϕy

0

50

100

150

M (times

103 k

Nm

)


ϕu

(a)


E1 moment demand0

250

500

750

M (times

103 k

Nm

)


ϕy ϕu

(b)


E1 moment demand

0100200300400500600

M (times

103 k

Nm

)


ϕy ϕu

(c)


E1 moment demand

0250500750

100012501500

M (times

103 k

Nm

)


ϕyϕu

(d)


E1 moment demand

050

100150200250300350

M (times

103 k

Nm

)


ϕyϕu

(e)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕyϕu

(f )

Figure 8 Continued


E

E2x + E

2y + E

2z

1113969

(7)


Rd 1 minus1μΔ

1113888 1113889Tlowast

T+

1μΔge 10 for

Tlowast

Tgt 10

Rd 10 forTlowast

Tle 10

(8)



Δu 13H


LP

21113874 1113875 times θu

LP min LP1 Lp21113872 1113873


Lp2 23

b


Kds

(9)




E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕy ϕu

(g)


E1 moment demand

0250500750

10001250

M (times

103 k

Nm

)


ϕy ϕu

(h)


E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕyϕu

(i)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕy ϕu

(j)




4 Conclusions


Data Availability




References



















Transverse1 10 01 48 Y2 10 99 327 Y3 10 77 168 Y



















EcIeff ]MR d

ϕy

(4)




06

08

1

12

14

16

18

η or

Cd








EcIeff My

ϕy

(5)


3 Case Study






E

Ex

11138681113868111386811138681113868111386811138681113868 + 03 Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + 03 Ez

11138681113868111386811138681113868111386811138681113868

03 Ex

11138681113868111386811138681113868111386811138681113868 + Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + 03 Ez

11138681113868111386811138681113868111386811138681113868

03 Ex

11138681113868111386811138681113868111386811138681113868 + 03 Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + Ez

11138681113868111386811138681113868111386811138681113868

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(6)




65 m 95 m 95 m 65 m

A0P1

P2

P3

A1


11H05

025

025

05

1

025 02505

05

025 02505

9


Eurocode 8E1E2

S (T

)g

0

02

04

06

08

1

12

1 2 3 4 5 60T (s)


Eurocode 8E1E2

S (T

)g

0

02

04

06

08

1

12

1 2 3 4 5 60T (s)

















Design combinations

Bottom of pier 1

0

500

1000

P (times

103 k

N)


(a)

Design combinations

Bottom of pier 1

0

500

1000

P (times

103 k

N)


(b)

Design combinations

Bottom of pier 2

-500

0

500

1000

1500

P (times

103 k

N)


(c)

Design combinations

Bottom of pier 2

-500

0

500

1000

1500

P (times

103 k

N)


(d)

Design combinations

Top of pier 2

-400

0

400

800

1200

P (times

103 k

N)


(e)

Design combinations

Top of pier 2

-400

0

400

800

1200

P (times

103 k

N)


(f )

Figure 7 Continued


Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(g)

Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(h)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(i)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(j)



E1 moment demandϕy

0

50

100

150

M (times

103 k

Nm

)


ϕu

(a)


E1 moment demand0

250

500

750

M (times

103 k

Nm

)


ϕy ϕu

(b)


E1 moment demand

0100200300400500600

M (times

103 k

Nm

)


ϕy ϕu

(c)


E1 moment demand

0250500750

100012501500

M (times

103 k

Nm

)


ϕyϕu

(d)


E1 moment demand

050

100150200250300350

M (times

103 k

Nm

)


ϕyϕu

(e)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕyϕu

(f )

Figure 8 Continued


E

E2x + E

2y + E

2z

1113969

(7)


Rd 1 minus1μΔ

1113888 1113889Tlowast

T+

1μΔge 10 for

Tlowast

Tgt 10

Rd 10 forTlowast

Tle 10

(8)



Δu 13H


LP

21113874 1113875 times θu

LP min LP1 Lp21113872 1113873


Lp2 23

b


Kds

(9)




E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕy ϕu

(g)


E1 moment demand

0250500750

10001250

M (times

103 k

Nm

)


ϕy ϕu

(h)


E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕyϕu

(i)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕy ϕu

(j)




4 Conclusions


Data Availability




References



















Transverse1 10 01 48 Y2 10 99 327 Y3 10 77 168 Y
















EcIeff My

ϕy

(5)


3 Case Study






E

Ex

11138681113868111386811138681113868111386811138681113868 + 03 Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + 03 Ez

11138681113868111386811138681113868111386811138681113868

03 Ex

11138681113868111386811138681113868111386811138681113868 + Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + 03 Ez

11138681113868111386811138681113868111386811138681113868

03 Ex

11138681113868111386811138681113868111386811138681113868 + 03 Ey

11138681113868111386811138681113868

11138681113868111386811138681113868 + Ez

11138681113868111386811138681113868111386811138681113868

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(6)




65 m 95 m 95 m 65 m

A0P1

P2

P3

A1


11H05

025

025

05

1

025 02505

05

025 02505

9


Eurocode 8E1E2

S (T

)g

0

02

04

06

08

1

12

1 2 3 4 5 60T (s)


Eurocode 8E1E2

S (T

)g

0

02

04

06

08

1

12

1 2 3 4 5 60T (s)

















Design combinations

Bottom of pier 1

0

500

1000

P (times

103 k

N)


(a)

Design combinations

Bottom of pier 1

0

500

1000

P (times

103 k

N)


(b)

Design combinations

Bottom of pier 2

-500

0

500

1000

1500

P (times

103 k

N)


(c)

Design combinations

Bottom of pier 2

-500

0

500

1000

1500

P (times

103 k

N)


(d)

Design combinations

Top of pier 2

-400

0

400

800

1200

P (times

103 k

N)


(e)

Design combinations

Top of pier 2

-400

0

400

800

1200

P (times

103 k

N)


(f )

Figure 7 Continued


Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(g)

Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(h)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(i)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(j)



E1 moment demandϕy

0

50

100

150

M (times

103 k

Nm

)


ϕu

(a)


E1 moment demand0

250

500

750

M (times

103 k

Nm

)


ϕy ϕu

(b)


E1 moment demand

0100200300400500600

M (times

103 k

Nm

)


ϕy ϕu

(c)


E1 moment demand

0250500750

100012501500

M (times

103 k

Nm

)


ϕyϕu

(d)


E1 moment demand

050

100150200250300350

M (times

103 k

Nm

)


ϕyϕu

(e)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕyϕu

(f )

Figure 8 Continued


E

E2x + E

2y + E

2z

1113969

(7)


Rd 1 minus1μΔ

1113888 1113889Tlowast

T+

1μΔge 10 for

Tlowast

Tgt 10

Rd 10 forTlowast

Tle 10

(8)



Δu 13H


LP

21113874 1113875 times θu

LP min LP1 Lp21113872 1113873


Lp2 23

b


Kds

(9)




E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕy ϕu

(g)


E1 moment demand

0250500750

10001250

M (times

103 k

Nm

)


ϕy ϕu

(h)


E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕyϕu

(i)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕy ϕu

(j)




4 Conclusions


Data Availability




References



















Transverse1 10 01 48 Y2 10 99 327 Y3 10 77 168 Y
















65 m 95 m 95 m 65 m

A0P1

P2

P3

A1


11H05

025

025

05

1

025 02505

05

025 02505

9


Eurocode 8E1E2

S (T

)g

0

02

04

06

08

1

12

1 2 3 4 5 60T (s)


Eurocode 8E1E2

S (T

)g

0

02

04

06

08

1

12

1 2 3 4 5 60T (s)

















Design combinations

Bottom of pier 1

0

500

1000

P (times

103 k

N)


(a)

Design combinations

Bottom of pier 1

0

500

1000

P (times

103 k

N)


(b)

Design combinations

Bottom of pier 2

-500

0

500

1000

1500

P (times

103 k

N)


(c)

Design combinations

Bottom of pier 2

-500

0

500

1000

1500

P (times

103 k

N)


(d)

Design combinations

Top of pier 2

-400

0

400

800

1200

P (times

103 k

N)


(e)

Design combinations

Top of pier 2

-400

0

400

800

1200

P (times

103 k

N)


(f )

Figure 7 Continued


Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(g)

Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(h)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(i)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(j)



E1 moment demandϕy

0

50

100

150

M (times

103 k

Nm

)


ϕu

(a)


E1 moment demand0

250

500

750

M (times

103 k

Nm

)


ϕy ϕu

(b)


E1 moment demand

0100200300400500600

M (times

103 k

Nm

)


ϕy ϕu

(c)


E1 moment demand

0250500750

100012501500

M (times

103 k

Nm

)


ϕyϕu

(d)


E1 moment demand

050

100150200250300350

M (times

103 k

Nm

)


ϕyϕu

(e)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕyϕu

(f )

Figure 8 Continued


E

E2x + E

2y + E

2z

1113969

(7)


Rd 1 minus1μΔ

1113888 1113889Tlowast

T+

1μΔge 10 for

Tlowast

Tgt 10

Rd 10 forTlowast

Tle 10

(8)



Δu 13H


LP

21113874 1113875 times θu

LP min LP1 Lp21113872 1113873


Lp2 23

b


Kds

(9)




E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕy ϕu

(g)


E1 moment demand

0250500750

10001250

M (times

103 k

Nm

)


ϕy ϕu

(h)


E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕyϕu

(i)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕy ϕu

(j)




4 Conclusions


Data Availability




References



















Transverse1 10 01 48 Y2 10 99 327 Y3 10 77 168 Y






























Design combinations

Bottom of pier 1

0

500

1000

P (times

103 k

N)


(a)

Design combinations

Bottom of pier 1

0

500

1000

P (times

103 k

N)


(b)

Design combinations

Bottom of pier 2

-500

0

500

1000

1500

P (times

103 k

N)


(c)

Design combinations

Bottom of pier 2

-500

0

500

1000

1500

P (times

103 k

N)


(d)

Design combinations

Top of pier 2

-400

0

400

800

1200

P (times

103 k

N)


(e)

Design combinations

Top of pier 2

-400

0

400

800

1200

P (times

103 k

N)


(f )

Figure 7 Continued


Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(g)

Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(h)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(i)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(j)



E1 moment demandϕy

0

50

100

150

M (times

103 k

Nm

)


ϕu

(a)


E1 moment demand0

250

500

750

M (times

103 k

Nm

)


ϕy ϕu

(b)


E1 moment demand

0100200300400500600

M (times

103 k

Nm

)


ϕy ϕu

(c)


E1 moment demand

0250500750

100012501500

M (times

103 k

Nm

)


ϕyϕu

(d)


E1 moment demand

050

100150200250300350

M (times

103 k

Nm

)


ϕyϕu

(e)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕyϕu

(f )

Figure 8 Continued


E

E2x + E

2y + E

2z

1113969

(7)


Rd 1 minus1μΔ

1113888 1113889Tlowast

T+

1μΔge 10 for

Tlowast

Tgt 10

Rd 10 forTlowast

Tle 10

(8)



Δu 13H


LP

21113874 1113875 times θu

LP min LP1 Lp21113872 1113873


Lp2 23

b


Kds

(9)




E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕy ϕu

(g)


E1 moment demand

0250500750

10001250

M (times

103 k

Nm

)


ϕy ϕu

(h)


E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕyϕu

(i)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕy ϕu

(j)




4 Conclusions


Data Availability




References



















Transverse1 10 01 48 Y2 10 99 327 Y3 10 77 168 Y
















Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(g)

Design combinations

Bottom of pier 3

0

500

1000

P (times

103 k

N)


(h)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(i)

Design combinations

Top of pier 3


0

500

1000

P (times

103 k

N)

(j)



E1 moment demandϕy

0

50

100

150

M (times

103 k

Nm

)


ϕu

(a)


E1 moment demand0

250

500

750

M (times

103 k

Nm

)


ϕy ϕu

(b)


E1 moment demand

0100200300400500600

M (times

103 k

Nm

)


ϕy ϕu

(c)


E1 moment demand

0250500750

100012501500

M (times

103 k

Nm

)


ϕyϕu

(d)


E1 moment demand

050

100150200250300350

M (times

103 k

Nm

)


ϕyϕu

(e)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕyϕu

(f )

Figure 8 Continued


E

E2x + E

2y + E

2z

1113969

(7)


Rd 1 minus1μΔ

1113888 1113889Tlowast

T+

1μΔge 10 for

Tlowast

Tgt 10

Rd 10 forTlowast

Tle 10

(8)



Δu 13H


LP

21113874 1113875 times θu

LP min LP1 Lp21113872 1113873


Lp2 23

b


Kds

(9)




E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕy ϕu

(g)


E1 moment demand

0250500750

10001250

M (times

103 k

Nm

)


ϕy ϕu

(h)


E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕyϕu

(i)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕy ϕu

(j)




4 Conclusions


Data Availability




References



















Transverse1 10 01 48 Y2 10 99 327 Y3 10 77 168 Y
















E

E2x + E

2y + E

2z

1113969

(7)


Rd 1 minus1μΔ

1113888 1113889Tlowast

T+

1μΔge 10 for

Tlowast

Tgt 10

Rd 10 forTlowast

Tle 10

(8)



Δu 13H


LP

21113874 1113875 times θu

LP min LP1 Lp21113872 1113873


Lp2 23

b


Kds

(9)




E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕy ϕu

(g)


E1 moment demand

0250500750

10001250

M (times

103 k

Nm

)


ϕy ϕu

(h)


E1 moment demand

050

100150200250

M (times

103 k

Nm

)


ϕyϕu

(i)


E1 moment demand

0

300

600

900

1200

M (times

103 k

Nm

)


ϕy ϕu

(j)




4 Conclusions


Data Availability




References



















Transverse1 10 01 48 Y2 10 99 327 Y3 10 77 168 Y

















4 Conclusions


Data Availability




References



















Transverse1 10 01 48 Y2 10 99 327 Y3 10 77 168 Y
















Comparison of Highway Bridge Seismic Design in Europe and ...

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