SEISMIC RESPONSE ANALYSIS OF LONG-SPAN CONTINUOUS RIGID-FRAMED BRIDG

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1 SEISMIC RESPONSE ANALYSIS OF LONG-SPAN CONTINUOUS RIGID-FRAMED BRIDG Song Wa-li 1, Liu Gao-jun 2, Song Wen-chao 3 and Ren Wen-jie 4 1 Profeor, School of Civil Engineering, Hebei Univerity of Technology, Tianjin China 2 Engineer, Tianjin Urban Contruction Deign Intitute, Tianjin China 3 Engineer, Tianjin Urban Contruction bloc invetment Ltd, Tianjin China 4 Aociate Profeor, School of Civil Engineering, Hebei Univerity of Technology, Tianjin China ong924@126 com ABSTRACT: Highway croing mountain valley, continuou rigid-framed bridge with high pier and long pan i contructed In thi paper, for thi type of bridge, the dynamic time-hitory analyi method i ued to analyze the eimic repone of bridge under uniform excitation and traveling-wave effect The focu i on a three-pan highway bridge with unequal height pier croing a mountain valley Group pile effect and oil-tructure interaction being taken into account, the bridge and it foundation ytem, including the urrounding oil, are modeled by finite element The analye how that traveling-wave ha trong influence on repone of earthquake, and the relative diplacement of top and bottom of low pier i le enitive to traveling-wave velocity than that of high pier Due to traveling-wave effect, the maximal moment at top of low pier i much larger than that of high pier, but it variation i le than that of high pier with the change of wave velocity The effect of oil-tructure interaction being taken into account, decreae of whole tiffne of tructure reult in that the frequency of vibration reduce and relative diplacement of top and bottom of pier increae KEYWORDS: Continuou rigid-frame bridge, Time hitory analyi method, Traveling-wave effect, Soil-tructure interaction, Group pile effect 1 INTRODUCTION Highway croing mountain valley, continuou rigid-framed bridge with high pier and long pan i contructed It cale i far over the range regulated by Specification of Earthquake Reitant Deign for Highway Engineering in China [1] In eimic deign of the bridge, it i neceary to undertand dynamic repone of bridge under earthquake-induced loading, epecially the repone of bridge with high pier or long pan Becaue the difference of height of pier i great, the earthquake behavior of high pier i quite different from that of low pier, o the dynamic time-hitory analyi method i adopted to carry out the anti-eimic performance of continuou rigid-framed bridge The preence of oil play a key role in haping the dynamic repone of both aboveground and underground tructure and hould be taken into account in any realitic tructural analyi procedure [2] According to oil-tructure interaction and traveling-wave effect of earthquake wave, finite element model of a three-pan continuou rigid-frame bridge with high pier i et up 2 CONFIGURATION OF BRIDGE The particular highway bridge invetigated ha three-pan irregular configuration (110m + 200m + 110m) in length,with hollow box-like contruction, a hown in Figure 1 The deck i 10m in width (6m at the bottom) and ret on the abutment and two pier of unequal height (50 and 100 m) with two thin-walled hape, which i repreentative of pier contructed acro valley in eimic mountainou terrain Furthermore, Figure 1 how cro-ection detail of high pier(every thin wall i 600cm 100cm), a well a the deck-to-abutment upport ytem and the deck-to-pier connection, The pretreed reinforced concrete deck ha ingle room and

2 it cro-ection varie in longitudinal direction, the height of beam (35~10m) and thickne of bottom plate (30~ 120cm) change in econd-degree parabola The height of deck i 10m at top of pier and 35m at abutment a well a the middle of pan Thickne of web i 50~80cm, top plate i 28 cm The foundation of a pier conit of 9 cat-in-place pile, which are founded on medium decompoed rock The diameter of pile i 2 m The boundary condition of pier can be taken a full fixity In term of material propertie, box beam i C60, pier i C50 and bearing platform i C30 (a) View of the bridge (unit: m) (b) Cro-ection of high pier (unit: cm) Figure 1 Configuration of bridge 3 THE DYNAMIC TIME-HISTORY ANALYSIS METHOD For long pan bridge, the difference of earthquake wave at upporting point i taken into account uing large ma method and analogy tatic diplacement, in which repone of ground diplacement and internal force are truly reflected by horizontal moving effect of ground Adding a uppoitional large ma M ll to tructure ma M in excitation direction at upporting point, Repone of tructure i attained, which i called Large ma method In thi bridge, the ratio between M ll and M i equal to 10 6, o tructure ma i neglected When earthquake wave i added Movement equation [3] [6] of bridge tructure ytem at time t i a follow ( M u( + C u( + Ku( = F( (31) In the above, u i the acceleration vector of node, u i the velocity vector, M i ma matrix, C i damp matrix, K i tiffne matrix, and F( i load vector of node Every matrix and vector i integrated by repone matrix of pile, oil and upertructure unit, o Equation (31) can be rewrote in Equation (32) ( M 0 u C C b u K K b u = 0 M bb + MⅡ u Cb Cbb Kb Kbb ub Fb b ub (32) If damp function caued by moving velocity of upporting point i neglected, due to exit of large ma M ll, the firt item of left of Equation i epecially larger than other The econd and third item of left of equation

3 and the effect of M bb being neglected, Equation (32)can be predigeted in Equation (33) M Ⅱ u b = { F b } (33) Abolute diplacement of tructure i reolved into analogy tatic diplacement Y and analogy dynamic diplacement Y d Auming that damp force of tructure i direct proportion to dynamic relative velocity, u,u b T i replaced by Y d, 0, then 1 [ M ] Y + [ C ] Y + [ K ] Y = [ M ][ ][ M ] { F } d d d α (34) When excitation take place at every upporting point, lager ma i added The contraint i relaxed in excitation direction; the moving acceleration of ground ḃ u i attained under function of F b When excitation of traveling wave i only taken into account, F b i attained according to acceleration value of ame earthquake wave with certain phae ll b 4 FINITE ELEMENT MODEL FOR BRIDGE Baed on characteritic of oil and tructure, the bridge deck and the pier are modeled uing the oftware Mida/Civil2006, box beam and pier were imulated in beam element It i aumed that boundary retriction i joined elatically with node Weight of box beam and tranvere clapboard i conidered a deadweight See Figure 2 Figure 2 Beam finite element model for the bridge For earthquake wave, the dynamic time-hitory i analyzed uing El-Centro wave, earthquake intenity recorded i 7 degree, peak value of horizontal acceleration recorded i 1458 m/ 2, and that of vertical acceleration recorded i m/ 2 Soil-tructure interaction being conidered or neglected, the dynamic time-hitory i analyzed, in which the longitudinal and tranvere earthquake wave i local horizontal wave and the vertical wave i vertical local wave 5 THE EFFECT OF TRAVELING-WAVE ON RESPONSE OF EARTHQUAKE In order to analyze the effect of traveling-wave on repone of earthquake wave, two uppoition are

4 conidered in thi work [4] Firtly, earthquake wave travel in longitudinal direction In the econd option, friction between deck and liding bearing at bridge end i equal to zero The earthquake wave velocity i 200~1400 m/ in ground The value of longitudinal wave velocity i a follow: 200m/, 300m/, 400m/, 500m/, 600m/, 800m/, 1000m/, 1200m/ and 1400m/, accordingly, the difference of time when wave arrive to two pier i calculated Repone of pier include relative diplacement of top and bottom of pier, moment at top of pier and center of pan The reult are hown in Figure 3 and Table 1 Relative diplacement of top and bottom of pier(mm) The wave velocity(m/) Short pier High pier Figure 3 The relation of relative diplacement and the wave velocity Table 1 The relation of maximal moment at top of pier and the wave velocity Wave velocity (m/) Maximal moment at top of low pier (knm) Maximal moment at top of high pier(knm) Under the function of uniform excitation, relative diplacement of top and bottom of low pier and high pier i 90732mm and 91117mm, while relative diplacement i 91000mm and mm when wave velocity i 200m/, therefore, effect of traveling-wave being taken into account, relative diplacement increae by 029% and 3019%, which i becaue that the tiffne of low pier i larger than that of high pier For internal force, maximal moment at top of low pier i far larger than that of high pier, but with the change of wave velocity, the variation of maximal moment at top of high pier change a lot Furthermore, on the bai of time-hitory analyi, with the quickening of wave velocity,the moment at center of middle pan increae and that at center of ide pan reduce 6 ANALYSIS OF THE BRIDGE WITH SOIL -STRUCTURE INTERACTION For pier hown a Figure 1, group pier effect i taken into account In calculation, pier are converted into

5 tiffne in x, y and z direction on the principle of equivalent tiffne In order to imulate the pier function each other due to common vibration of ground among pier, group pier effect i imulated a pecial rigid-frame, and ground among pier i imulated a two force taff to connect pier in longitudinal and tranvere direction For eimic calculation of bridge, it i uually aumed that mechanic model i et up on abolute rigid foundation, In fact, deformation of oil around pile ha effect on vibration of pier, oil-tructure interaction will change dynamic property of tructure, damp and repone of earthquake It i aumed that oil medium i liner elatic and continuou, retriction function i decribed a double direction liner pring with damp, it equivalent element tiffne K of foundation pring i calculated uing m method [5] in Equation (61) In above, i depth of oil layer, a: σ zx = mzx z (61) σ zx i tranvere reitant tre of oil layer on pile, m i reitant tre coefficient of oil layer, z xz i tranvere diplacement, o equivalent tiffne k of foundation pring i decribed k p x Aσ x ( a bp )( m z xz ) = x zx = = = z z z ab p mz (62) In above, a i the thickne of oil layer replaced by foundation pring, b i calculating width of pile Group pier effect and oil-tructure interaction being taken into account in different mode, relative diplacement of top and bottom of pier, the moment at top of pier are hown in Table 2 Table 2 The effect of oil-tructure interaction on relative diplacement and moment Item Poition Taking no account of oil-tructure interaction Taking account of oil-tructure interaction Diplacement (mm) Low pier Diplacement (mm) High pier Axial force (kn) Center of ide pan Axial force (kn) Center of middle pan Moment (knm) Center of ide pan Moment (knm) Center of middle pan Moment (knm) Top of low pier Moment (knm) Top of high pier The effect of oil-tructure interaction being taken into account, vibration frequency of the firt mode reduce by 61%, which i becaue that whole tiffne of tructure reduce Relative diplacement of top and bottom of pier increae, while internal force increae or decreae occaionally 7 CONCLUSIONS The analye demontrate that effect of traveling-wave ha trong influence on repone of earthquake, o thi effect hould be taken into account in eimic calculation of bridge The analye how that traveling-wave ha tronger influence on relative diplacement of top and bottom of high pier than that of low pier, the lower the wave velocity i, the larger the difference i Due to traveling-wave effect, the maximal moment at top of low

6 pier i much larger than that of high pier, but it variation i le than that of high pier with the change of wave velocity Furthermore, on the bai of time-hitory analyi, with the quickening of wave velocity,the moment at center of middle pan increae and that at center of ide pan reduce The effect of oil-tructure interaction being taken into account, decreae of whole tiffne of tructure reult in that the frequency of vibration reduce and relative diplacement of top and bottom of pier increae REFERENCES [1] Minitry of Communication of the People Republic of China, (1989) Specification of Earthquake Reitant Deign for Highway Engineering (JTJ ), the People Communication Pre [2] AJ Kappo, GD Manoli, IF Mochona (2002) Seimic aement and deign of R/C bridge with irregular configuration including SSI effect Engineering Structure 24, [3] Zhang Wei, Liu Jian-xin,Zhang Qian (2005) Seimic Repone Analyi of Long-pan Continuou Rigid-framed Bridge Earthquake Reitant Engineering and Retrofitting, 27:6, [4] Shen Yong-gang, CHEN J ian-wei, XIANG Yi-qiang (2007) Seimic Analyi of Long Span Continuou Rigid-Frame Bridge with Thin-Walled High Pier, highwag 4, [5] Minitry of Communication of the People Republic of China, (2007) Code for Deign of Ground Bae and Foundation of Highway Bridge and Culvert (JTG D ), the People Communication Pre [6] Cui Yang, (2007), Seimic Repone Analyi of Long-pan Continuou Rigid-framed Bridge under Several Point Excitation and Traveling-wave Effect, Municipal Engineering and Road-bridge,