A Numerical Study on Impact Damage Assessment of PC Box Girder Bridge by Pounding Effect

Transcription

1 A Numerical Sudy on Impac Damage Assessmen of PC Box Girder Bridge by Pounding Effec H. Tamai, Y. Sonoda, K. Goou and Y.Kajia Kyushu Universiy, Japan Absrac When a large earhquake occurs, displacemen response of supersrucure exceeds expansion gap and here is a possibiliy of pounding beween a bridge girder and an abumen. Therefore, exising specificaions for highway bridges recommend ha sufficien gap beween he ends of wo adjacen girders shall be aken for prevening a collision beween a supersrucure and an abumen. Bu if expansion gap is large, a supersrucure is able o slide in he horizonal direcion under ground moion and i brings abou excess bending momen of a bridge pier. Thus, i is concerned ha damage of a bridge pier migh be significanly large and oal consrucion cos migh become higher due o he reinforcemen of a bridge pier. Recenly, some researchers have proposed a new design concep ha pounding beween girder and abumen is allowed by small expansion gap. Main objecives of his concep are o conrol displacemen response of bridge supersrucure wih considering he horizonal resisance of abumen by pounding. However his concep has no acceped as an effecive alernaive design concep of bridge. Main reason is ha damage condiions of a supersrucure and an abumen by pounding have no ever quaniaively esimaed. So in his sudy, o evaluae he damage condiion of an abumen by pounding, impac response analyses of pounding effec are conduced using 3-dimensional FEM. From hose FE analysis resuls, a simplified model of pounding by rheological concep is proposed o make use of hose resuls for seismic response analysis of bridge. Keywords: pounding effec, impac response analysis, damage assessmen, rheological model. Yoshimi Sonoda Kyushu Universiy 744 Moooka, Nishi-ku, Fukuoka Japan sonoda@doc.kyushu-u.ac.jp Tel:

2 1.0 Inroducion There were various kinds of damage of bridge srucures in Hyogo-ken nanbu earhquake by severe ground moion. Some of he repored damages were occurred by pounding beween bridge girders or beween a supersrucure and an abumen. Therefore, exising specificaions for highway bridge recommend ha sufficien gap beween he ends of wo adjacen girders shall be aken for prevening a collision beween wo adjacen supersrucures or beween a supersrucure and an abumen [1]. Thus according o he exising design of bridge, expansion gap is likely oo large compared o appropriae disance. I is expeced ha excess expansion gap allows large horizonal displacemen of a supersrucure and i brings abou excess bending momen of a bridge pier. Thus, i is concerned ha damage of a bridge pier becomes significanly large and i increases oal consrucion cos of a bridge pier. Recenly, some researchers have proposed a new design concep ha i allows he pounding beween girder and abumen [2]. Main objecives of his concep are o conrol he displacemen of supersrucure wih considering he horizonal resisance of abumen by pounding. I is poined ou ha his concep could reduce oal consrucion cos of pier design. However his concep has no acceped as an effecive alernaive design concep of bridge. Main reason is ha damage condiions of a supersrucure and an abumen by pounding have no ever quaniaively esimaed. Afer Hyogo-ken nanbu earhquake, many sudies have been made on seismic response characerisics of he bridge by considering he pounding effec. Bu mos of hem are based on nonlinear seismic analysis by frame model and pounding effec is easily assumed as a linear spring which has an unsubsaniaed consan. Thus damage condiions of a supersrucure and an abumen by pounding have no quaniaively esimaed. To evaluae hose damage condiions accuraely, i is considered ha pounding effec is no reaed as vibraion problem by frame model bu i is reaed as impac problem by FE model. So he main objecive of his sudy is o evaluae he damage condiion of an abumen by pounding phenomenon. To achieve his, impac response analyses of pounding effec are conduced using 3-dimensional FEM. From hose FE analysis resuls, a simplified model of pounding by rheological concep is proposed o make use of hose resuls for seismic response analysis of bridge. 2.0 Ouline of pounding analysis using 3-D FEM 2.1 General descripion of analyical mehod The numerical analyses are conduced using non-linear FE sofware, MSC.MARC2005 in his sudy. Single-sep Houbol algorihm is applied as he ime inegraion echnique. This mehod has second-order accuracy and uncondiionally sable. Time sep is conrolled auomaically beween minimum ime sep 1.0e-6(s) and maximum ime sep 1.0e-3(s). Pounding phenomenon is simulaed by seing iniial velociy on all nodes of a supersrucure. Main parameer in hese analyses is impac velociy and 5 cases of 1.0, 1.5, 2.0, 2.5 and 3.0(m/s) are considered. Acually i is expeced ha he pounding phenomenon beween a supersrucure and an abumen occurs repeaedly in he case of a grea earhquake, bu in his sudy only single impac is considered.

3 2.2 Analyical objec The bridge o be sudied is an exising wo-span coninuous bridge. The span lengh of his bridge is 40.0m, as shown in Figure 1. The abumens are locaed a boh ends. The bridge srucure is symmerical, wih Pier 1 as is cener. The bearing suppor srucure a Pier 1 is fixed and hose a boh abumens are movable. The supersrucure is consruced from pre-sressed concree wih pos-ensioned box-girder. The girder heigh is 1.2m, and he girder widh is 12.0m. The pier is consruced from reinforced concree and oval shaped. A ma foundaion is adoped as he foundaion ype of subsrucure. The abumen has he reverse T ype wing. The ground a he bridge sie is Ground Type 1 of Japanese specificaion of seismic design and liquefacion is assumed no o occur even hough an earhquake occurs. Figure 1. Side view of bridge (uni: mm). Y Z X Figure 2. Analyical model. 2.3 Analyical model The 3-dimensional FE mesh is shown in Figure 2. In his sudy, he abumen and 1/2 par of span lengh of bridge are precisely modeled. Firsly, wih respec o modeling of abumen composed of rebar and concree, concree and rebar are discreized by 8-node iso-parameric solid elemen and 2-node russ elemen respecively. Backfill soil is also discreized by 8-node iso-parameric solid elemen. As for he girder, hough i is acually composed of rebar and concree, all domains are modeled as homogeneous RC elemen. This reason is ha he main objecive of his sudy is o evaluae damage of abumen quaniaively. RC elemen ha modeled by 8-node iso-parameric

4 solid has inermediae siffness calculaed in volume raio of concree and rebar. Toal number of nodes and elemens are and 21571, respecively. All nodes of girder end and opposie nodes of an abumen are resrained in Y-direcion and Z-direcion. Nodes locaed in he boom of he abumen and nodes locaed in he suppor of he girder are resrained in Y-direcion. Nodes locaed in back-end of backfill soil are resrained in all direcions. In his sudy, conac model is inroduced beween bridge girder and abumen, and beween abumen and backfill soil. In his conac model, dynamic fricion and slip are no considered. Table 1: Maerial properies abumen girder rebar concree RC elemen Backfill soil Young s modulus(gpa) Poisson s raio Densiy(g/cm 3 ) Compressive srengh(mpa) Tensile srengh(mpa) Yield sress Maerial properies and consiuive models Maerial properies are shown in Table 1. Rebar elemens and concree elemens of he abumen are assumed as elaso-plasic bodies as shown in Figure 3a) and 3b). The consiuive model of rebar elemen is reaed o be ypical bi-linear elaso-plasic model wih 1/100 srain hardening coefficien in isoropic hardening rule. Unloading siffness is assumed he same as iniial siffness. For he consiuive model of concree, i is also assumed as bi-linear elaso-plasic model wih 1/100 srain hardening coefficien in compression side. In ension side, srain sofening model ha ensile sress increases linearly up o ensile srengh and decreases gradually afer ensile srengh is assumed. In he analysis, 1/10 of compressive srengh is adoped as ensile srengh. In his sofening model, ulimae ensile srain is calculaed by he following equaion. G f f ε u 5 (1) f h 2Ec Where, G f is ensile fracure energy; f is ensile srengh of concree; h is minimum lengh of elemen; and E c is young s modulus of concree. In his analysis, value of G f is assumed 0.141(N/mm) and ension sofening siffness E c (shown in Figure 3b)) is calculaed by ulimae ensile srengh. Bond-slip failure beween rebar and concree migh occur under severe impac loading, bu perfec bond condiion is applied in his model. Consiuive model of RC elemens of he girder is assumed as he same model of concree elemen as shown in Figure.3a). Backfill soil is regarded as elasic sandy soil wih N=5. Young s modulus of soil is calculaed by he following equaion (2). E = N (2)

5 Where, N ; N-value, and g ; graviy acceleraion. σ σ σ y E s 100 f E c E c ε ε u ε E s ε E c 100 f c a) Rebar elemen b) Concree elemen Figure 3. Consiuive model. 3.0 Analyical resuls 3.1 Deformaion behavior of parape Figure 4 shows he relaion beween X-direcion displacemen of crown of parape and ime. I is confirmed ha he maximum displacemen a 3.0m/s is almos 3.5 imes larger han ha of a 1.0m/s. I is noed ha every displacemen response up o 150ms is M-shaped curve. Abou his reason, he exisence of backfill soil mus have some influence on his resul. Figure 5 shows he difference beween crown and base a each impac velociy. The relaive displacemen beween crown and base is regarded as he maximum displacemen of parape. I is confirmed ha maximum displacemens a 2.5, 3.0m/s exceed 1/150 of he heigh of parape. Figure 6 shows he deformaion response of parape under he 3.0m/s pounding. From his figure, i is found ha deformaion response of parape is similar o he response of slab suppored on hree sides under impac load. 3.2 Impac force Figure 7 shows he relaion beween impac force and ime and Figure 8 shows he relaion beween he maximum impac force and impac velociy. I is confirmed ha he maximum impac force and he duraion of impac force increase wih he impac velociy. The maximum impac force a 3.0m/s is almos 2.5 imes larger han he one a 1.0m/s. I is recognized ha he maximum impac force a 1.0m/s is almos 5.0 imes larger han he dead-load reacion force (abou 4400kN) a A2 abumen. In addiion, he maximum impac force a 3.0m/s is almos 13.0 imes larger han ha of he dead-load reacion force. From his resul, hough he curren horizonal design load of he bridge resrained device is 1.5 imes large value of he dead-load reacion force, i is found ha he maximum impac force is considerably large compared wih he dead-load reacion force.

6 Displacemem (mm) m/s 1.5m/s 2.0m/s 2.5m/s 3.0m/s Time (msec) Maximum of displacemen (mm) Impac velociy (m/s) Figure 4. Displacemen-ime relaion. Figure 5. Difference beween maximum (crown of parape) displacemen of crown and base impac velociy relaion. Displacemen large small a) Before impac b) A he ime of he maximum displacemen Figure 6. Deformaion behaviour of parape. Impac force (kn) m/s 1.5m/s 2.0m/s 2.5m/s 3.0m/s Time (msec) Maximum of impac force (kn) Impac velociy (msec) Figure 7. Impac force ime relaion. Figure 8. Maximum impac force impac velociy relaion.

7 3.3 Damage of he abumen wih equivalen cracking srain To quaniaively evaluae he damage of abumen by pounding of girder, he damage of abumen is checked by equivalen cracking srain. Equivalen cracking srain corresponds o ulimae ensile srain afer ensile srengh. Figure 9 shows he color conour of he equivalen cracking srain of he abumen in each cases of impac velociy 1.0, 2.0 and 3.0m/s. If equivalen cracking srain is larger han , he elemen is displayed by black color ha means he possibiliy of macrocrack. In he case of 1.0m/s impac velociy, i is found ha he damage occurs only in he boom of parape. While, in he case of 2.0m/s impac velociy, i is found ha he damage occurs in he boom of parape and abumen. In addiion, in he case of 3.0m/s impac velociy, i is confirmed ha he severe damage spreads over he enire parape and he wing of he abumen. Thus, in he case of 3.0m/s, failure possibiliy of he abumen is concerned. a) 1.0m/s b) 2.0m/s c) 3.0m/s Figure 9. Damage disribuion of he abumen wih equivalen cracking srain. (Upper: a ime 7msec, Lower: a ime 20msec afer impac) 3.4 Damage of he abumen wih equivalen plasic srain The damage of abumen is evaluaed by oal equivalen plasic srain. Toal equivalen plasic srain corresponds o compressive srain. Figure 10 shows he oal equivalen plasic srain of he abumen under impac of girder in each cases of impac velociy. If equivalen plasic srain is larger han 0.002, he elemen is displayed by black color ha means he possibiliy of compressive failure. In he case of 1.0m/s impac velociy, i is found ha he severe damage does no occur in he abumen. On he conrary, in he case of 3.0m/s, i is found ha he compressive failure could occur in some elemens.

8 a) 1.0m/s b) 2.0m/s c) 3.0m/s Figure 10. Damage disribuion of he abumen wih oal equivalen plasic srain. (A ime 20msec afer impac) 4.0 Simplified model of pounding effec 4.1 Simplified model using rheological concep In he previous chaper, impac response analyses of pounding effec were conduced using 3- dimensional FEM, and hen he damage condiion of an abumen by pounding was invesigaed. I is difficul o direcly apply hese numerical resuls o bridge design or seismic response analysis based on frame model, so i is imporan o presen simplified model ha include damage effec under pounding. Thus, in his chaper, o reflec hese numerical resuls o bridge design, simplified model is proposed by he relaion beween impac force and displacemen obained from FE analyses in previous chaper m/sec Impac force (kn) m/sec k 1 c 1 c2 k2 oal x f Displacemen (mm) vo x da x sp x Figure 11. Impac force displacemen relaion obained from FE analysis. Figure elemen model. Unil now, impac spring model has proposed o express pounding effec in he seismic response analysis by some researchers [3]. This model assume a linear spring and i could no include damage effec under pounding. Relaions beween impac force and displacemen obained from FE analyses are complex as shown in Figure 11. As hey have characerisics which are abruply increased afer impac and i gradually decreased, hey are formed closed loop. I is difficul o

9 describe such complex behaviors by one linear spring. So we focus aenion on rheological model o describe hem. Rheological model is composed of several springs and dashpos, and i is usually used o represen he visco-elasiciy. In his sudy, 4elemen model represened by a Maxwell uni and a Voig uni conneced in series as shown in Figure 12 is applied. 4 elemen model has four consans ( k 1, c 1, k 2 and c 2 ) wih respec o mechanical characerisic. Decision procedure of hem is described below. Firsly, cerain values are se as iniial consans. Secondly, displacemen obained from FE analysis is given o 4 elemen model, and hen moion equaion of his model is solved by forward difference. So reacion force corresponding o displacemen is able o be calculaed by equaion (3). x vo and x da in equaion(3) are calculaed by equaion(4), (5). Finally, he reacion force is compared o impac force obained from FE analysis wih respec o iniial gradien, maximum impac force and impulse. If each error exceeds olerance, iniial value is changed and above calculaion is repeaed unil each error saisfies olerance. In his calculaion, olerance is applied 10%. In his way, four rheological consans are deermined. vo oal vo da ( f k1x ) f f + = k2 x+ x x (3) c1 c2 vo vo ( c1 k1 ) x + f x = (4) c1 da da c2x + f x = (5) c 2 oal vo Where, x + is displacemen obained from FE analysis a +, x is displacemen obained da from Voig model a, x is displacemen obained from dashpo a, is ime sep and f is reacion force obained from 4 elemen model a. Each error is calculaed by equaion (6). φr φ A error(%) = 100 (6) φr Where, φ R is each value calculaed by 4 elemen model and φ A is each value obained from FE analysis. Four rheological consans deermined in his way are shown in Table 2. I is found ha k 1 and c1 decrease as impac velociy increases, while c 2 increases as impac velociy increases. This resul is nohing more han one of he combinaion of rheological consans, herefore i is necessary o reconsider he appropriae rheological consans. However i is confirmed ha he simplified model proposed in his sudy will be useful for seismic design or seismic response analysis by frame model.

10 Table 2: Lis of he rheology consans deermined by our calculaion Consans Impac velociy k 1 (kn/mm) c 1 (kn s/mm) k 2 (kn/mm) c 2 (kn s/mm) 1.0 (m/s) (m/s) (m/s) (m/s) (m/s) Conclusions In his sudy, o evaluae he damage condiion of an abumen by pounding, impac response analyses of pounding effec were conduced using 3-dimensional FEM. From hese resuls, he simplified model of pounding is proposed. Following resuls are summarized as: 1) I is found ha he difference beween maximum displacemen of crown and base of parape under he 3.0m/s impac velociy exceeds 1/150 of heigh of parape. Deformaion response of parape is similar o he response of slab suppored wih hree sides under impac load. 2) I is recognized ha he maximum impac force is almos from 5.0 o 13.0 imes larger han ha of he dead-load reacion force (abou 4400kN) a A2 abumen. From his resul, i is found ha he curren design load of he bridge resrained device is underesimaed and he maximum impac force is considerably larger han i. 3) In he case of 3.0m/s impac velociy, i is confirmed ha severe damage spreads over he following regions (enire parape, he boom of abumen and he wing of abumen) from he disribuion of equivalen cracking srain. 4) We proposed he simplified model of pounding effec based on rheological concep. I is expeced o apply he seismic response analysis by frame model. 6.0 References 1. Japan Road Associaion. Specificaions for highway bridges Par V (Seismic design), Tokyo: Maruzen, [In Japanese] 2. Moriyama, T., Hamamoo, T., Nishimoo, Y., Yoda, T., Ishikawa, N., Fundamenal sudy on gap reducion beween wo girders considering he pounding of PC bridge girders, Journal of Srucural Engineering, JSCE, 2005, Vol.51A, pp [In Japanese] 3. Kawashima, K., An analyical model of conac and impac in dynamic response analysis, Journal of Srucural Mechanics and Earhquake Engineering, JSCE, April 1981, Vol.308, pp [In Japanese]