RETROFIT OF LARGE BRIDGE PIERS WITH RECTANGULAR-HOLLOW CROSS-SECTION

Transcription

1 13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada Augut 1-6, 2004 Paper o RETROFIT OF LARGE BRIDGE PIERS WITH RECTAGULAR-HOLLOW CROSS-SECTIO Georgio TSIOIS 1 and Artur V. PITO 2 SUMMARY The paper deal with the eimic retrofit of bridge pier with rectangular hollow cro-ection uing fibrereinforced polymer (FRP) acket. Finite element method (FEM) analye how that the exiting empirical law for FRP-confined concrete are not uitable for hollow pier with large dimenion. The effectively confined zone i concentrated in the corner and it extent depend on the dimenion of the acket. A fibre model of a hollow cro-ection i analyed, modifying the concrete propertie according to the aforementioned obervation. The effectivene of acketing i conditioned by the axial load, longitudinal reinforcement and acket dimenion. An empirical deign equation i formulated. ITRODUCTIO It ha become clear from field obervation and experimental data that exiting bridge pier deigned before the introduction of modern eimic code are vulnerable to earthquake and therefore appropriate retrofit olution hould be tudied. Thi need i further accentuated by the ignificant economic lo related to eriou damage or collape of a maor bridge and by the importance of bridge tructure within complex tranportation and communication ytem. Particular attention i devoted in thi work to bridge pier with hollow cro-ection. Although thi tructural type i common in highway bridge acro Europe and other eimic-prone region, it ha been the obect of reearch only recently. A ound background exit for the calculation of flexural and hear trength of reinforced concrete (RC) element retrofitted with externally applied fibre-reinforced polymer (FRP) trip. Deign equation and detailing rule have been propoed in reearch report, e.g. Seible [1], and later incorporated in informative, fib [2], and normative document, CE [3]. o reference i made in thee document to pier with rectangular hollow cro-ection. Recent experimental reult from pier with hollow cro-ection retrofitted with FRP trip, reported by Ogata [4], Cheng [5] and Peloo [6], on one hand provide confidence in the effectivene of the propoed deign equation and technique and on the other highlight the need for rational deign rule, a ome time FRP reinforcement i over-deigned. However, the mall cale of the teted pecimen doe not allow a generaliation of the obervation. 1 PhD tudent, Technical Univerity of Milan, Department of Structural Engineering, Milan, Italy (formerly at JRC) 2 Scientific officer, European Commiion, Joint Reearch Centre, IPSC, ELSA, Ipra, Italy

2 Baed on compreion tet on concrete pecimen encaed in FRP acket, a number of bilinear contitutive law, with increaing tre for the econd branch, have been propoed for FRP-confined concrete. In contrat, experimental evidence from pecimen wrapped with a few FRP layer and/or pecimen with rectangular cro-ection indicate that the tre-train curve comprie a oftening potpeak branch with enhanced ultimate train, a well a maximum and reidual trength. The bilinear empirical model cannot capture thi behaviour and the need for an alternative approach emerge. According to a theoretical model propoed by Spoeltra [7], the lateral train of concrete i related to the axial train and then an iterative procedure i followed until attainment of a given ultimate train of the FRP. Deign formulae have been propoed for the maximum trength and the ultimate train of FRPconfined concrete. Baed on thee, Monti [8] elaborated deign equation for the deign of FRP acket applied on circular RC column. A large number of contitutive law for FRP-confined concrete have been examined by De Lorenzi [9]. The value etimated by the propoed empirical formulae were compared to the experimental value of trength and ultimate train. The prediction for the ultimate train were found to overetimate the experimental data, while error ranging from 10% to 60% were oberved on the value of compreive trength, often on the unconervative ide. The dicrepancie of the contitutive law for FRP-confined concrete are reflected on the global repone of element, a highlighted in a numerical tudy of a circular RC cro-ection wrapped with ten layer of FRP, performed by Yuan [10]. The reult of momentcurvature analye indicate ignificant difference in the predicted value of trength and ultimate curvature. While moment capacity i influenced mainly by concrete trength, curvature capacity directly depend on the ultimate train of concrete. Concrete ultimate train and cro-ection curvature capacity are of great importance in eimic retrofit and hence it i unfortunate that a reliable model i not available yet. The obective of the reearch preented in thi paper i to examine the effectivene of FRP acket for the confinement of bridge pier with large hollow cro-ection. A two-level numerical approach i decribed. Analye of a acketed rectangular hollow concrete cro-ection were performed uing the Finite Element Method (FEM) with the aim of tudying the effect of confinement on the concrete propertie. The reult of thee analye were incorporated in a fibre model of a RC cro-ection and then parametric moment-curvature analye were performed in order to tudy the effect of geometric and mechanical characteritic of the cro-ection. The propoed numerical approach wa checked againt experimental evidence. Finally, empirical deign equation were derived on the bai of more than 1000 numerical analye. EFFECT OF FRP JACKETS O COCRETE PROPERTIES OF HOLLOW CROSS-SECTIOS The effect of the FRP acket on the propertie of concrete wa examined by FEM analye uing the computer code Cat3m, Millard [11]. Thi wa neceary becaue of the inconitencie of exiting contitutive law for FRP-confined concrete and becaue of the limited confidence in their applicability to rectangular hollow cro-ection with large dimenion. The width of the pier cro-ection wa b = m and the depth d = 1.5b. The thickne of both the web and the flange wa t = 0.2b. Five value were conidered for the height of the concrete acket, namely h = 0.0 (no concrete acket), h = 0.05 m, h = 0.10 m, h = 0.15 m and h = 0.20 m. The thickne of the FRP acket wa t = 1 mm, t = 3 mm and t = 5 mm. In thi way, a total number of 15 different cae were tudied. The corner of the concrete cro-ection wa rounded at a radiu of about 5 cm, a recommended for practical application. For reaon of ymmetry, only a fourth of the cro-ection wa analyed. Cubic element with 8 or 6 integration point were ued for the concrete cro-ection, while

3 hell element with 4 integration point were employed for the FRP acket. The baic cro-ection dimenion are given in Figure 1. Figure 1. Definition of baic cro-ection dimenion A platicity-baed tri-dimenional contitutive law wa ued for the concrete element ( E c = 33.5 GPa, ν = 0.2, f c = 36 MPa and ε o = for monotonic behaviour). Elatic behaviour wa conidered for the FPR acket ( E f1= 52 GPa, E f2= 5 GPa, ν = 0.2). It wa decided to tudy a GFRP acket, which i conidered more effective for the enhancement of deformation capacity, rather than a CFRP acket, which i more uitable for trength enhancement. Orthotropic behaviour wa ued to account for the preence of fibre only in the horizontal direction. The propertie in the other direction were etimated conidering the contribution of the matrix rein only. Elatic behaviour for the FRP element i a limitation, a failure due to tenile fracture of the FRP trip (and exploive collape of concrete) wa not conidered. Typical value of ultimate FRP train can be higher than 3%, when meaured through tenile tet. Experimental reult from RC element trengthened with FRP trip, though, indicate failure for maller train. To account for that, a afety factor in the order of 0.6 ha been propoed by Seible [1] and fib [2]. Thi deign value wa not urpaed in the analye. Perfect bond wa conidered between the two material. The effect of confinement within the cro-ection i dicued with reference to Figure 2 in which the area with the ame compreive trength have the ame colour. Dark blue colour correpond to the mallet increae and change to light blue, green, yellow and red for the area with the highet increae. Zone with different extent of confinement may be identified. Zone 1 comprie the corner of the croection, without the external rounded part. A moderate increae in compreive and reidual trength i oberved in thi zone. The external part of the corner, where the bigget increae i oberved, i termed Zone 2. Zone 3 coincide with the flange, where a mall increae in compreive and reidual trength i oberved. Finally, Zone 4 encompae the additional concrete for the parabolic acket. In thi zone a mall increae in trength i oberved. The web i not conidered to benefit from the retrofit. For a rectangular acket (top left in Figure 2) the effect of confinement i concentrated in the corner. For a parabolic acket, alo the area outide the corner benefit from the retrofit: the confined area extend from the corner to part of the web and the additional concrete. Thi effect i more pronounced for larger value of the acket height, h. The effect of the acket thickne i to increae the concrete trength, without

4 affecting the tre pattern. Similar obervation hold alo for the other propertie of interet, which are dicued in the following. h = 0.00 m h = 0.05 m h = 0.10 m h = 0.15 m h = 0.20 m Figure 2. Effect of acket height on the compreive trength of concrete ( t = 5 mm) Figure 3 plot indicative tre-train curve in the different zone of the cro-ection for a rectangular acket and all three value of the acket thickne. The curve for unconfined concrete i alo included for comparion. The tre i obtained a the um of the nodal reaction at each zone, divided by the area of the zone. Stree are normalied to the compreive trength of unconfined concrete. The actual behaviour (oftening after peak trength) doe not follow the empirical relation propoed for FRPconfined concrete (bilinear law with acending econd branch). In fact, the effect of confinement i to increae the compreive and reidual trength of concrete and to mooth the oftening tiffne. Thi i reminicent of the behaviour of full cro-ection confined with teel tirrup or acket. Similar behaviour wa experimentally oberved on rectangular concrete pecimen wrapped with few FRP trip, a reported by Karabini [12]: the pecimen howed oftening after maximum trength, while increaing trength in the econd branch wa oberved for higher amount of FRP. In the numerical analye, a bilinear tre-train curve with increaing trength for the econd branch wa oberved for extremely

5 high value of the acket thickne that do not have practical application and alo in a few element cloe to the rounded corner. everthele, thi wa not reflected on the global tre-train curve for each zone. ormalied axial tre t = 1 mm t = 3 mm t = 5 mm zone Axial train (%) ormalied axial tre t = 1 mm t = 3 mm t = 5 mm zone Axial train (%) ormalied axial tre t = 1 mm t = 3 mm t = 5 mm zone Axial train (%) Figure 3. umerical tre-train curve for FRP-confined concrete (rectangular acket) for uniform compreive force and definition of zone (at the cro-ection corner) The numerical reult are further dicued with focu on characteritic value of the tre-train curve. The value of interet are the compreive trength, the reidual trength and the oftening tiffne. The oftening tiffne i obtained a the difference of the maximum and reidual trength, divided by the difference of the correponding train. Thee parameter, on one hand, give a qualitative view of the improvement of the concrete propertie due to confinement. On the other hand, they are the material parameter ued for the moment-curvature analye decribed in the following ection. The effect of the acket on the concrete compreive trength i dicued in more detail with reference to Figure 4, where tree are normalied to the compreive trength of unconfined concrete. For all cae the concrete compreive trength increae with the acket thickne, t. In Zone 1 and 3 the compreive trength i increaed by 40% and 20%, repectively. In Zone 2 the compreive trength i increaed by more than 80% for t = 5 mm. The compreive trength enhancement increae until h = 0.10 m and then remain almot contant. Conidering Zone 4, it i intereting to note that the compreive trength decreae with increaing value of the acket height. The above obervation ugget that a parabolic acket of limited height i beneficial for the concrete propertie, but when the acket become relatively large, no further effect i obtained, or even a detrimental effect i oberved. The value h = 0.10 m can be conidered a an upper limit for the examined cae.

6 Compreive trength t = 1 mm t = 3 mm t = 5 mm zone 1 Compreive trength t = 1 mm t = 3 mm t = 5 mm zone 2 Compreive trength t = 1 mm t = 3 mm t = 5 mm zone 3 Compreive trength t = 1 mm t = 3 mm t = 5 mm zone 4 Figure 4. Effect of acket on the compreive trength of concrete Figure 5 plot the change of the concrete reidual trength for different value of the acket height and thickne. The reidual trength i normalied to the compreive trength of unconfined concrete. The reidual trength increae with the acket thickne. The area that benefit more i again the region near the rounded corner. Moderate improvement i oberved in Zone 1 and 4, while in Zone 3 the reidual trength remain at le that 0.6 f c. An intereting feature i that for mall amount of FRP, t = 1 mm, the improvement doe not increae with the acket height. Alo for the reidual trength, no further improvement i obtained for acket with height larger than h = 0.10 m. The oftening tiffne decreae with the acket height. The decreae i fater until h = 0.10 m and then no change, or lower decreae i oberved. EFFECT OF FRP JACKETS O CURVATURE DUCTILITY OF HOLLOW CROSS-SECTIOS Moment-curvature analye were performed uing the finite element code Cat3m, Millard [11], with the aim to tudy the effect of the acket dimenion, axial load and reinforcement ratio on the effectivene of the retrofit. on-linear behaviour wa conidered for the concrete fibre and a modified Menegotto-Pinto contitutive law for the teel fibre, both decribed by Guede [13]. The FRP acket wa not included in the model. In lieu, the cro-ection wa divided in five zone (the fifth zone i the web, which i not conidered to experience any confinement effect) with propertie modified in accordance to the reult of the FEM analye. An equivalent I cro-ection wa analyed, intead of the original rectangular hollow cro-ection. Rectangular element with four integration point and triangular element with three integration point where ued for the concrete fibre and point element with one integration point were

7 employed for the teel rebar. The teel fibre were poitioned at the external and internal face of the flange, a well a through the web: 20% of vertical reinforcement wa concentrated at the external face of the flange, 10% wa concentrated at the internal face of the flange and the remaining 70% wa ditributed along the web. Reidual trength t = 1 mm t = 3 mm t = 5 mm zone 1 Reidual trength t = 1 mm t = 3 mm t = 5 mm zone Reidual trength t = 1 mm t = 3 mm t = 5 mm zone 3 Reidual trength t = 1 mm t = 3 mm t = 5 mm zone Figure 5. Effect of acket on the reidual trength of concrete Different value of axial load (ranging from ν = 0.0 to ν = 0.3) and longitudinal reinforcement ratio ( ρ = 0.17%, ρ = 0.34%, ρ = 0.68% and ρ = 2%) were conidered. Curvature ductility i defined by way of a bilinear approximation of the actual moment-curvature diagram. The yield moment i equal to the maximum moment, M max. The yield curvature i defined at the interection of a line from the origin paing through the numerical curve at 0.8 M max and a horizontal line at M max. The ultimate curvature i conervatively defined at M, ee Figure 7a. max Selected reult are plotted in Figure 6 for a acket of height h = 0.10 m. For both the a-built and retrofitted cro-ection, increae of axial load initially increae the curvature ductility. Thi range of axial load correpond to failure of the cro-ection due to collape of teel, a indicated by rapid lo of reitance in the moment-curvature diagram. After a certain value, further increae of axial load, caue decreae of curvature ductility. Thi range of axial load correpond to failure of the cro-ection due to cruhing of concrete, a indicated by mooth decreae of reitance after the peak in the momentcurvature diagram. The limit value of axial load range from ν = 0.0 to ν = 0.1 for the a-built cro-

8 ection and from ν = 0.05 to ν = 0.2 for the acketed cro-ection, depending on the dimenion of the acket and the longitudinal reinforcement ratio. A expected, curvature ductility decreae with increaing reinforcement ratio. ormalied axial load p hor = 0.17% p hor = 0.34% p hor = 0.68% p hor = 2% ormalied axial load p hor = 0.17% p hor = 0.34% p hor = 0.68% p hor = 2% t = 1 mm Curvature ductility Curvature ductility ormalied axial load p hor = 0.17% p hor = 0.34% p hor = 0.68% p hor = 2% t = 3 mm ormalied axial load p hor = 0.17% p hor = 0.34% p hor = 0.68% p hor = 2% t = 5 mm Curvature ductility Curvature ductility Figure 6. Effect of acket, axial load and longitudinal reinforcement ratio on the curvature ductility of the cro-ection ( h = 0.10 m) The ratio of the curvature ductility of the acketed cro-ection to the curvature ductility of the a-built cro-ection can be ued a an effectivene index. The effect of axial load i to initially increae the effectivene of the retrofit and then to decreae it. The limit value of the axial load depend on the amount of longitudinal reinforcement, acket thickne and acket height. For low to medium amount of vertical reinforcement (from ρ = 0.17% to ρ = 0.68%) acketing i not effective for pier with very low value of axial load, namely ν < In thee cae, large tenion train develop in the teel before ignificant compreion on the concrete and failure i due to collape of teel. For higher amount of longitudinal reinforcement acketing i effective even for low value of axial load. The numerical reult clearly indicate that thi retrofit method i mot effective for medium to high axial load, namely in the range from ν = 0.1 to ν = 0.3. Among the examined cae, the maximum value of the effectivene index wa µ ϕ, retrofitted / µ ϕ,a built = 3.7, for a acket with height h = 0.20 m and thickne t = 5 mm. It i important at thi point to recall that ultimate curvature i conervatively defined at maximum moment, a chematically hown in Figure 7a.

9 Thi definition i adopted becaue it render it poible to derive deign-oriented empirical expreion that have relatively good correlation with the numerical value. Although thi might lead in overdimenioning at certain cae, the reult remain on the afe ide. Value of the effectivene index a high a µ ϕ, retrofitted / µ ϕ,a built = 7.0 are obtained if ultimate curvature i defined at the point of the momentcurvature diagram where there i a 20% lo of trength, a hown in Figure 7b. Thi definition i more realitic and demontrate the actual effectivene of the retrofit method. The firt definition i kept in the following for conitency. M max 0.75M max M max 0.75M max 0.2M max Moment Moment ϕy ϕu ϕ y ϕu Curvature Curvature (a) (b) Figure 7. Definition of failure criteria and curvature ductility: at maximum moment (a) and at 20% lo of trength (b) Moment (km) a-built retrofitted (h = 0.2 m) retrofitted (h = 0.0 m) Curvature (1/m) Figure 8. Cyclic moment-curvature diagram for the a-built and acketed cro-ection For the examined cae, the maximum increae of moment capacity i about 20%. When increaing the dimenion of the cro-ection, an increae of tiffne i expected. A member with increaed tiffne

10 will attract higher eimic force and thi fact ha to be taken into conideration when deigning the global retrofit. Thi increae will alo affect the dynamic propertie, which are ignificant for bridge tructure. Jacketing will decreae the uually high period of bridge pier and then mot probably will increae the pectral ordinate and accordingly the eimic demand. The above correpond to increae in hear demand that might exhaut the a-built capacity and trengthening will be required. Retrofit of the foundation might be needed. The effect of FRP acketing on the energy diipation capacity i verified in Figure 8 that plot the moment-curvature numerical curve for ν = 0.2, ρ = 2%, t = 5 mm and the two extreme value of the acket height. For the cae of rectangular acket and the ame level of impoed curvature, no ignificant difference i oberved between the a-built and the retrofitted cro-ection. everthele, the retrofitted cro-ection ha a much higher curvature ductility, which can be exploited alo under cyclic loading. For higher value of the concrete acket, both trength and ultimate curvature increae and then a more pronounced diipation capacity i evidenced by the wider hyteretic cycle. COMPARISO TO EXPERIMETAL RESULTS The experimental reult of a mall-cale pecimen of a pier retrofitted with longitudinal and tranveral GFRP trip teted at the Univerity of Pavia are compared in thi ection to the reult of the numerical procedure decribed in the previou ection. The caled pecimen had a rectangular hollow cro-ection with external dimenion 0.45x0.45 m and internal dimenion 0.35x0.35 m. The longitudinal reinforcement conited of 40 Φ 8 rebar uniformly ditributed along the internal and external face of the pier, correponding to reinforcement ratio ρ = The horizontal reinforcement conited of one rectangular tirrup for each wall of the pecimen, vertically paced at m. The compreive trength of concrete wa f c = 30.3 MPa. The yield tre of teel wa f y = 550 MPa, while the ultimate tre wa f u = 660 MPa. The a-built pecimen failed due to combination of flexure and hear at drift δ = 3.6 %. The retrofit intervention conited in applying longitudinal and tranveral GFRP trip. Two longitudinal layer of 0.1 m-wide trip were applied on both face orthogonal to the loading direction. The tranveral trip had the ame width and the pacing wa 0.2 m from centre to centre. Compared to the a-built pecimen, the retrofitted pecimen howed larger deformation capacity ( δ = 6.0 %), table repone and larger capacity of energy diipation. A detailed decription of the geometry, material and experimental behaviour i given by Peloo [6]. Following the numerical procedure decribed previouly, the concrete cro-ection wrapped with the FRP trip wa analyed under increaing compreive load. The thickne of the FRP trip wa modified in order to take into conideration the effect of partial wrapping. While continuou acket exert a contant lateral preure along the height of the element, partial wrapping i le efficient a part of the concrete remain unconfined. A confinement effectivene coefficient i ued, baed on the aumption that the unconfined zone between two conecutive trip i encloed by a parabola with 45 o lope [2]. The effect of wrapping i to increae the maximum trength and the correponding deformation. The numerical reult indicate that for the examined cae a oftening branch, with moother lope compared to unconfined concrete, follow the point of maximum compreive tre, until a reidual trength. While plain concrete i conidered to have nil reidual trength, the value for FRP-confined concrete range from 0.3 f c to 0.8 f c in the different zone of the cro-ection. Confinement reult alo in increae of the concrete peudo-ductility, a een by the deformation capacity of FRP-confined concrete, compared to unconfined concrete.

11 The effect of confinement i retricted to the corner of the cro-ection. Apart from a tre concentration at the external part of the corner, conitent with experimental obervation, the cro-ection may be divided in three region. One comprie the part outide the corner, where the maximum trength i not increaed, but the reidual trength i f r1 = 0.2fc. The econd area correpond to the external part of the corner, where the maximum trength i increaed by 10% and the reidual trength i f r 2 = 0.75fc. In thi zone an acending branch initiate at train level of about 0.7%. Thi i reminicent of the econd branch of the empirical bilinear contitutive law for FRP-confined concrete. In the following analye thi branch will be ignored and contant reidual tre, f r2, will be conidered. Finally, the third zone comprie the remaining part of the corner, where the maximum trength remain unchanged and the reidual trength i f r3 = 0.5f c. Thee value hold for the given geometry; more general conideration were dicued in the previou ection. The numerical tre-train curve were ued to define the propertie of the concrete fibre in a fibre/timohenko beam element, Guede [13], ued to model the retrofitted pier. The horizontal FRP trip were not included in the model, but their effect wa accounted for by appropriately modifying the concrete propertie in the three region of the cro-ection. The longitudinal FRP trip were modelled uing four-point quadrangular element with equivalent area, poitioned on the two face of the croection. An elatic-perfectly platic contitutive law wa conidered for the longitudinal trip in order to impoe a limit on the trength of the longitudinal trip, correponding to the nominal maximum tre. umerical imulation conidering elatic behaviour of the longitudinal trip howed that the trength contantly increaed with diplacement, even after many concrete fibre had collaped Force (k) Experimental umerical Diplacement (m) Figure 9. Experimental and numerical force-diplacement curve The complete model wa ued to imulate the cyclic tet on the retrofitted pecimen. The numerical and experimental force-diplacement curve are compared in Figure 9, where good agreement i oberved. The reitance and degradation predicted by the numerical model are cloe to the experimental value. Some difference are oberved in the reloading branche of the cycle of large amplitude. The pinching

12 repone of the teted pier can be attributed to the opening and cloing of crack in the concrete and alo to inelatic hear deformation, both of which are not fully conidered in the numerical analyi. Thee difference reult in higher energy diipation in the numerical model. ote that the difference are localied on the cycle with large diplacement, δ > 4.8%, where relatively important hear deformation and big crack opening are expected. The comparion between the numerical and experimental reult erve a a validation for the numerical tool and their combination. The numerical imulation yield rational reult, which are able to interpret the experimental behaviour of the teted pecimen. The experimental reult verify the effectivene of FRP acket for upgrading of bridge pier with hollow cro-ection. The agreement between the numerical and experimental global reult provide confidence in the numerical tool and procedure. DESIG EQUATIOS Graph imilar to thoe preented in Figure 6 may be ued to dimenion the acket for a given croection and a target value of curvature ductility. The obective of thi ection i to derive empirical deign equation for FRP acket applied on bridge pier with rectangular hollow cro-ection. The deign equation are baed on the numerical reult preented previouly. The deign of the acket i een a a tep within a global retrofit procedure. The term global refer to the conideration of all poible failure mode. Conidering RC bridge pier, the main eimic deficiencie, which have been reported from field obervation and laboratory teting, are premature termination of vertical reinforcement, lapped plice within the potential platic hinge region, inadequate confinement (mall deformation and diipation capacitie) and inadequate hear capacity. Quite often, exiting bridge pier preent a combination of the aforementioned eimic deficiencie. everthele, only the weaket of them i the main caue of failure. It i obviou that if the obective of the retrofit intervention i to provide reitance againt the weaket mechanim only, then mot probably failure will be due to the econd weaket mode. Thi i the reaon to introduce the global retrofit procedure. Jacketing i propoed a a method to increae confinement. An expreion of curvature ductility a a function of the examined geometrical and mechanical characteritic of the cro-ection (axial load, longitudinal reinforcement ratio, height and thickne of the acket) i ought. Thee characteritic are grouped in a ingle deign parameter, termed S = f ( ν, h, t, ρ) in the following, and then an expreion in the form µ ϕ = f(s) i fitted to the numerical reult. The empirical equation take the form (0.1+ ν + ρ ) (1 h ) = 52.94exp (1 + t 0. (1) ) µ ϕ,m (0.1+ ν + ρ ) (1 h ) = 42.35exp (1 + t 0. (2) ) µ ϕ, S (0.1+ ν ) (1 + h ) ρ = (3) 0.2 (1 + t ) In the previou equation ν i the normalied axial load, h i the acket height (in m), t i the acket thickne (in mm) and ρ i the longitudinal reinforcement ratio (in %). The normalied axial load,

13 ν = P / Acfc, and the ratio of longitudinal reinforcement, ρ = A /A c, are defined for the original rectangular cro-ection without the acket, A c. P i the axial force, f c i the nominal compreive trength of concrete and A i the area of teel rebar. µ ϕ, m i the mean value, while µ ϕ,0. 05 i the 5% characteritic value (95% of the empirical value are lower than the correponding numerical value). The numerical value are plotted in Figure 10, along with Equation 1 and 2. The correlation factor for 2 Equation 1 i R = Equation 1 Equation 2 Curvature ductility S = f(v, h,t,p) Figure 10. Empirical fit to the numerical value of curvature ductility The effectivene index i defined a the ratio of curvature ductility of the retrofitted cro-ection to that of the a-built one. Starting from thi definition and uing Equation 2, one obtain 0.1 µ ϕ,retrofitted, (1 + h ) I 0.05 = = 0.6 exp 8.1(0.1 + ν ) ρ (4) µ ϕ,a built,0.05 (1 + t ) Due to the relatively poor correlation, a modification i included in Equation 4 to obtain the 5% characteritic value of the effectivene index (95% of the empirical value are lower than the numerical value). The empirical and numerical value are compared in Figure 11. In Equation 1 to 4 there are two unknown deign parameter, namely acket height and thickne. Thi mean that one ha to elect one of them and then enter the deign formulae with thi value and the deired value of curvature ductility, or effectivene index, in order to calculate the other. It might be preferable to limit the acket height o a not to increae the trength and tiffne of the retrofitted member. The limit h = 0.10 m, identified in thi tudy, may be conidered. Beide, it might be deired to limit the acket thickne in order to avoid practical problem related to the uperpoition of many FRP layer. The above imply an iterative procedure and require ome engineering udgement.

14 4 Effectivene index (numerical) Effectivene index (empirical) Figure 11. Empirical (5% characteritic) and numerical value of the effectivene index The empirical deign equation derived in thi ection can be ued when the geometrical and mechanical characteritic of the pier fall within the limit examined in the preent tudy. Conidering axial load, longitudinal reinforcement ratio, acket height and thickne, it i believed that the whole range of practical interet ha been examined. For pier with dimenion maller than thoe examined in thi tudy, the acket dimenion may be caled down and conervative reult will be obtained. The deign formulae hould not be ued for pier with larger dimenion becaue it i expected that confinement will not be the ame effective and then the propoed equation might provide unafe reult. COCLUSIOS FEM analye of a concrete cro-ection wrapped with an FRP acket ugget that for the cae of hollow pier with large dimenion and for realitic dimenion of the acket, the tre-train curve after the peak trength comprie a oftening branch with a lope le teep than the one for unconfined concrete. Maximum and reidual trength are increaed with repect to unconfined concrete. Ditinct zone of the cro-ection with different effect of confinement have been identified. For rectangular acket, the effectively confined zone i limited to the corner, where peak and reidual trength are notably improved. For elliptical acket, moderate improvement i oberved alo in part of the flange and added concrete. A limit value of the acket height, after which the concrete propertie are not further improvement, wa identified. The effectivene of acket for the enhancement of the deformation capacity of RC cro-ection i conditioned by the axial load, longitudinal reinforcement and dimenion of the acket. The acket are mot effective in the range of axial load from ν = 0.1 to ν = 0.3, which, luckily, correpond to the axial load bridge pier uually carry. The moment capacity of the cro-ection i increaed by about 20%. Thi reult in higher force and then hear trengthening and upgrade of the foundation might be required. FRP acket improve the cyclic behaviour of cro-ection and therefore higher energy diipation capacity i enured.

15 On the ground of extended numerical tudie and limited experimental reult, it i concluded that, keeping in mind the aforementioned limitation, parabolic FRP acket contitute an effective method for improving the eimic repone of poorly-detailed hollow bridge pier. AKOWLEDGEMETS The greatet part of thi work wa carried out under a JRC grant (Contract o P1B20 ISP IT) to the firt author and within the SAFERR Reearch Training etwork (Contract o. HPR-CT ). The upport of the European Commiion i acknowledged. REFERECES 1. Seible F, Prietley MJ, Innamorato D. Earthquake retrofit of bridge column with continuou carbon fiber acket Volume II, Deign guideline. Report o. ACTT-95/08, San Diego: Structural Engineering, Univerity of California, San Diego, fib. Deign and ue of externally bonded FRP reinforcement for reinforced concrete tructure. Lauanne: Fédération Internationale du Béton, CE. Eurocode 8: Deign of tructure for earthquake reitance Part 3: Strengthening and repair of building (Draft o 3). Bruel: Comité Européen de ormaliation, Ogata T, Oada K. Seimic retrofitting of expreway bridge in Japan. Cement and Concrete Compoite 2000; 22(1): Cheng CT, Yang JC, Yeh YK, Chen SE. Seimic performance of repaired hollow-bridge pier. Contruction and Building Material 2003; 17(5): Peloo S. FRP eimic retrofit of quare hollow ection bridge pier. MSc diertation, Pavia: ROSE School, Univerità degli Studi di Pavia, Spoeltra MR, Monti G. FRP-confined concrete model. ASCE Journal of Compoite for Contruction 1999; 3(3): Monti G, iticò, Santini S. Deign of FRP acket for upgrade of circular bridge pier. ASCE Journal of Compoite for Contruction 2001; 5(2): De Lorenzi L. A comparative tudy of model on confinement of concrete cylinder with FRP compoite. Work o 46, Publication 01:04, Göteborg: Chalmer Univerity of Technology, Yuan XF, Lam L, Teng JG, Smith ST. FRP-confined RC column under combined bending and compreion: a comparative tudy of concrete tre-train model. Teng JG, Editor. FRP Compoite in Civil Engineering. Amterdam: Elevier Science Ltd, 2001: Millard A. Catem 2000, Guide d utiliation. Rapport CEA 93/007. Saclay: CEA, Karabini AI, Rouaki TC. Behaviour of rectangular FRP confined concrete element ubected to monotonic and cyclic compreive load. Proceeding of the fib 2003 Sympoium: Concrete Structure in Seimic Region, Athen, Greece. Paper no Athen: Technical Chamber of Greece, Guede J, Pegon P, Pinto AV. A fibre/timohenko beam element in CASTEM JRC Special publication I.94.31, Ipra: European Commiion, Joint Reearch Centre, 1994.