SEISMIC STRENGTHENING OF COLUMNS BY ADDING NEW CONCRETE. Stephanos E. Dritsos 1

Transcription

1 49 SEISMIC STRENGTHENING OF COLUMNS BY ADDING NEW CONCRETE Stephano E. Drito 1 ABSTRACT Placing reinforced concrete jacket or layer to trengthen or repair and trengthen concrete column i a normal contruction practice but there are many unreolved iue regarding the capacity of the trengthened element. In the abence of any guidance, engineering judgement i often ued. Thi paper et out to ait the engineer when conidering ome of thee unreolved iue. Revied value for factor of afety are propoed for deign. A procedure to guarantee a ufficient connection between contact urface and to determine the performance of retrofitted column i preented, conidering the trengthened column a compoite element. The parameter affecting the main mechanim for the tranfer of hear tre at the between new and old concrete are decribed and practical deign conideration are given. An approximate procedure i preented, baed on the deign of monolithic element, upplemented by the ue of pecific modification factor (monolithic factor), in order to evaluate the capacity of a trengthened element. Available experimental reult are proceed to derive appropriate value for monolithic behaviour factor and an extended analytical analyi i ued to fill in gap in the experimental work. Although thi paper ha particular relevance to eimic trengthening, it content will have a wider application to trengthening in general. The object of thi paper i to provide guidance o that the engineer i better equipped to deal with the practical deign need of today. Keyword: Column, Concrete, Earthquake, Jacket, Redeign, Repair, Retrofitting, Seimic and Strengthening. 1. INTRODUCTION It i now recognized in mot earthquake prone area that the vat majority of the exiting building tock i under a much higher eimic rik when compared to that of new building. Thi i becaue old building were contructed either before the implementation of a eimic rik Code or under the proviion of old eimic Code, which are now known to be inadequate. In Greece, the proportion of old building at rik i about 80% when conidering 1985 a the year to ditinguih between old and new building (a major reviion of the exiting eimic Code wa implemented in thi year). Therefore, eimic trengthening i a requirement in many cae. The election of the mot uitable trengthening technique for a pecific building i a difficult iue. The engineer mut decide between a number of alternative trategie and method, which may be unfamiliar or may need pecialit taff for implementation. For exiting reinforced concrete building, eimic trengthening normally focue on the vertical element (column and wall). Strengthening of beam i uually conidered a a econd priority, ince the tructural integrity i mainly affected by the capacity of the vertical element and the technique, when executed for beam, may diturb the reident of the upper level in a multi-torey building. A number of technique, in the form of jacketing, are ued in practice to trengthen deficient reinforced concrete column. Concrete, teel or fiber reinforced polymer (FRP) are normally ued for the jacket. Steel and FRP jacketing are very popular in many countrie ince they have the advantage of a minimal increae of cro ectional dimenion of the column. Moreover, they can be executed quickly with little interruption to the ue of the tructure while work i carried out. Extenive reearch reult for both the above technique have already been publihed. For teel jacketing, the pioneering experimental reearch undertaken at the Univerity of California, San Diego (Chai et al., 1991; Chai et al., 1994; Prietley et al., 1994a; Prietley et al., 1994b;) hould be mentioned while hundred of paper have been preented on FRP jacketing. A comprehenive literature review on relevant publication can be found in fib Bul. N o. 14 (2001) and fib Bul. N o. 24 (2003). The above technique are normally ued to enhance column ductility and hear capacity and are very effective in preventing bond failure in column with inadequately lapped longitudinal reinforcement. However, they offer little to the axial and flexural trength of an element and are inappropriate if a coniderable increae in tiffne i required. If thi i the cae, concrete jacketing ha the advantage. Moreover, in many countrie uch a Greece, where reinforced concrete i the mot popular contruction material for new building, engineer appear to prefer the trengthening olution of adding new concrete. Thi preference i becaue engineer are familiar with thi type of contruction, while local experienced contractor and peronnel are readily available. 1 Aociate Profeor of the Department of Civil Engineering at the Univerity of Patra, Patra, Greece (Member). BULLETIN OF THE NEW ZEALAND SOCIETY FOR EARTHQUAKE ENGINEERING, Vol. 40, No. 2, June 2007

2 50 Concrete jacketing ha been experimentally invetigated in the pat. Bett et al. (1988), Rodriguez and Park (1991), Eroy et al. (1993), Rodriguez and Park (1994), Hakuto (1995), Stoppenhagen et al. (1995) Drito et al. (1997), Gome and Appleton (1998), Rodriguez and Santiago (1998), Julio et al. (2003), Tono (2004) and Julio et al. (2005) have preented intereting reearch and it ha been proved that the bending, the hear capacity, the tiffne and the ductility of column can be improved. The method can alo improve the axial load carrying capacity of column and may alleviate problem caued by inadequate lap plice length (Bouia et al., 2004). If ite condition do not allowed the contruction of jacket, trengthening can be performed by placing an addition concrete layer on one or more ide of the element. Although placing reinforced concrete jacket or layer i a normal contruction practice and a number of paper have been preented, there are till many unreolved iue concerning the evaluation of the capacity of thee trengthened element. The cope of thi paper i to anwer ome of thee unreolved iue. A lack of knowledge often lead to an unreaonable ue of the technique, high cot and, at time, unproductive reult. Thi paper, in part, follow on from a previou work (Drito 2005a), where the practical application of trengthening or repair and trengthening of building before and after an earthquake were invetigated. Thi paper concentrate on column concrete jacketing. Strengthened or repaired and trengthened element from reinforced concrete can be conidered a, in general, multiphaed element. They conit of the initial part or component of the load bearing tructure and new element (made from imilar or other material) that are connected in order to limit hear lippage between the contact urface and to avoid detachment. Conequently, for the tructural deign of the above element, the proce of deigning compoite element hould be followed and the tranfer mechanim of the force at the between the old and the new element hould be taken into conideration. Obviouly, the evaluation of the capacity of trengthened or repaired and trengthened element doe not have the ame degree of reliability a that for monolithic element of new tructure. The reliability of calculation decreae becaue there are more uncertaintie. Thee uncertaintie are due to the following: (a) A lack of ufficient documentation and exploitable cientific knowledge in the field of contact urface mechanic with regard to the ditribution of tre in the old and the new element (thi would include exiting gravity load on the initial element, any remaining deformitie or any potential unloading), (b) The accuracy of the aement of the capacity of damaged element, a it ha uually been evaluated uing empirical or emi-empirical method. That i, ince damage cannot be meaured accurately, it aement i influenced by engineering judgement and (c) The detail of the implementation of the work and the quality control influence dratically the effectivene of the intervention and, conequently, the behaviour of the trengthened or repaired and trengthened element. The above uncertaintie hould be taken into conideration, when evaluating the reitance of a retrofitted element, by mean of pecial partial afety factor (γ Rd ). However, for critical project, analytical reult hould be confirmed with laboratory trial (GRECO, 2005). The tructural deign of trengthened or repaired and trengthened concrete element can be placed into the framework of the preently known procee of deign that are ued for new contruction, upplemented by the following (Taio, 1983; EC 8, 1995; GRECO, 2005; Drito, 2005b): (a) New revied factor of afety for old and new material are ued, (b) The between the contact urface hould be invetigated to enure that, by calculation, failure in each trengthened or repaired and trengthened element precede failure at the between the old and the new material and (c) The mechanical characteritic of each trengthened or repaired and trengthened element hould be determined by conidering the element a compoite element, by taking into account the lippage at the between the exiting and the new element. Alternatively, an approximate proce involving monolithic correction factor (monolithic behaviour coefficient) could be ued. The above three critical point for the tructural deign of trengthened or repaired and trengthened element will be decribed in detail in the following ection. 2. REVISED FACTORS OF SAFETY If in an exiting tructure, the dimenion of element have been meaured, the location and ize of the reinforcement have been determined and the individual trength of the exiting material have been etablihed, the actual trength of the element, ignoring gro contructional fault, may be greater than that of the initial deign. Therefore, under certain condition, lower partial afety factor for the material of the tructural ytem could be propoed. Partial afety factor value of γ c equal to 1.2 for concrete and γ equal to 1.05 for teel are propoed in Part 1-4 of EC 8 (1995). In the mot recent draft of GRECO (2005), value for γ c and γ depend on the reliability level of the documentation procedure that i applied to ae the mechanical characteritic of the exiting material. For the highet reliability level, the propoed value of γ c and γ are 1.35 and 1.05 repectively. For the medium reliability level, the propoed repective value of 1.50 and 1.15 are the ame a thoe for new tructure, while for the lowet reliability level they equal 1.65 and 1.25 repectively. A far a dead load partial afety factor (γ g ) are concerned, value hould alo depend on the reliability level of the procedure ued to ae the dead load of a tructure. The GRECO (2005) propoed value for γ g are 1.20, 1.35 and 1.50 for the high, medium and low reliability level repectively. Again, the propoed medium reliability level value i the ame a that for new tructure. If in deign, trength reduction factor are ued intead of partial afety factor, a i the practice in many countrie outide Europe, the above conideration could be expreed a follow: for a medium realibility level to evaluate exiting loading and material characteritic, trength reduction factor value could be conidered the ame a that for new tructure. If the documentation procedure for the evaluation of material trength and exiting load lead to a higher or lower reliability level, a repective increae or reduction of the above value by 10% hould be conidered. For new material added during an intervention, partial afety factor value are generally larger than thoe pecified for new tructure. Thi would be becaue the repair work may often

3 51 be carried out under difficult condition of acce and unknown level of quality control and uperviion and, therefore, the uncertainty of achieving the deired trength can be greater. For concrete and teel reinforcement, GRECO (2005) advie applying multiplication factor of 1.10 or 1.20 (depending on the contruction condition) to the partial afety factor of 1.50 and 1.15 for γ c and γ repectively, which are adopted for new tructure. Taking into account that the multiplication factor of 1.10 and 1.20 concern only material trength and not load, trength reduction factor, when ued, hould be divided by 1.05 and 1.10 repectively. 3. CONTROL OF A SUFFICIENT CONNECTION BETWEEN CONTACT SURFACES Load tranfer mechanim between the old and new material mut be capable of tranferring the tenile, compreive and hear tree that develop at the. A far a tenile tree are concerned, the tranfer can be guaranteed if the developed tree are lower than the tenile trength of the weaket concrete. If not, an appropriate quantity of reinforcement or anchor bar croing to the contact urface hould be provided, a pecified later in thi paper. Regarding concrete-to-concrete direct compreion, a full continuity compreion tranfer can be expected at the if adequate treatment meaure have been performed on the old concrete urface (uch a roughening). However, a lower modulu of elaticity hould be conidered for concrete adjacent the, a higher deformation develop due to the mechanical treatment of the exiting concrete and contact and compaction imperfection (CEB Bul. N o. 162, 1983). Obviouly, the compreive trength can be conidered to equal the lowet compreive trength of the contact material. In order to guarantee a ufficient connection between contact urface, the check for afety at the ultimate limit tate can be expreed ymbolically by the following equation of afety: S d R d (1) where: S d i the deign action effect and R d i the deign reitance. Thi control will include checking the hear force and the hear reitance at the between the old and the new element. That i to ay, the following relationhip mut be atified: V Sd V (2) Rd where: V i the hear force acting at the Sd and V i the hear reitance at the. Rd Obviouly, a guaranteed connection that avoid premature failure would be deirable. Thi would be becaue it repreent the critical factor for the effectivene of the intervention and would enure an acceptable degree of reliability for calculation. If failure between the contact urface precede failure of the trengthened element, the load bearing capacity of the connection will determine the load bearing capacity of the trengthened element. In addition, the load bearing capacity of the trengthened element cannot be conidered maller than that of the original untrengthened element. The control between contact urface along the whole length of the trengthening tructural element hould be baed on average value of V and V correponding to Sd Rd variou egment of length l i-j (i and j for ucceive egment) into which the element ha been divided. That i to ay: V Sd(i-j) V (3) Rd(i-j) The length of egment hould not be greater than twice the width of the cro ection of the column. Furthermore, following the ame rule adopted for the deign of compoite element (for example, EC 4, 2002), the proce can be facilitated if egment break are located at characteritic cro ection. A uch, ection dividing an element hould be placed at the following location: (a) at the larget poitive or negative bending moment, (b) at the upport, (c) at poition of point load, (d) where there are abrupt change in cro ection and (e) at the end of cantilever. 3.1 Shear force acting at the An evaluation of the hear force that develop between the contact urface ( from equation 3) can be obtained V Sd(i-j) by analying each egment auming monolithic behaviour (by approximately calculating the hear tre at the uing mechanic theory). Alternatively, the more accurate calculation method that i applied for teel and concrete compoite tructural element could be ued. Figure 1 chematically illutrate the hear force that develop between contact urface for the three cae where concrete i added a an under layer, an over layer or a ide layer. If a tructural element ha been trengthened with the new layer of concrete, the ize of the hear reitance between the contact urface, for a egment length of l i-j, can be determined by conidering the equilibrium of force in the new concrete egment ABCDA of figure 1. That i: V = V = F F (4) BC Sd(i-j) Sd AB CD A proce of ection analyi can be ued to determine the magnitude of the force F ΑΒ and F CD. That i, by taking ection through the whole element at poition i and j repectively and determining the internal tenile or compreive force correponding to layer ection AΒ or CD.

4 52 new concrete layer j FCD D C old concrete r l i-j Vd(i-j) i A FAB B Figure 1. Shear force at the 3.2 Interface hear reitance Four mechanim contribute to the hear reitance at the ( from equation 3 above). Thee are V Rd(i-j) concrete-to-concrete adheion, concrete-to-concrete friction, the connecting action from either teel bar placed acro the between the old and the new concrete or bent down bar welded between the bar of the old and the new concrete. Thee four mechanim can be ubdivided into the two group of unreinforced and reinforced, depending on whether or not additional teel i placed acro the or welded between the bar of the old and the new concrete. In general, the hear reitance developed at the depend on the amount of lippage at the Unreinforced The two mechanim acting at an unreinforced are adheion and friction. It mut be noted that maximum adheion value are achieved for low lip value (in the region of 0.02 mm), while friction become important for much higher lippage. Therefore, the maximum reitance from adheion and friction do no coincide and cannot be conidered to act together. Figure 2 (CEB Bul. N o. 162, 1983) preent hear reitance (τ) againt lip () plot for ome cae of original column urface roughne with and without adheion. Factor that affect the adheion between exiting and new concrete are the tenile trength of the contact material, the urface roughne of the original column (a demontrated by figure 2) and the urface treatment of the original column (expoing the aggregate give higher bond trength). Moreover, the method of placing the new concrete ha an effect (hotcrete i better than in-itu concrete becaue the impact force mortar into urface pore and void). In addition, monolithic behaviour can be expected when bonding agent are properly applied between the contact urface. 4 rough with adheion 3 τ (N/mm 2 ) 2 1 rough without adheion mooth with adheion (mm) Figure 2. Concrete-to-concrete adheion (CEB Bul. N o. 162, 1983).

5 53 The parameter that affect concrete-to-concrete friction are the ize and hape of the aggregate if expoed (large angular aggregate are better) and the urface roughne of the original column (rougher urface have greater area of urface contact). Additional parameter include the concrete compreive trength, the external normal compreive tre (a higher normal tre give a higher hear tiffne) and if the loading i cyclic or not (cyclic loading quickly deteriorate the contact urface giving a larger lip or a lower hear repone). Repreentation that model concrete-to-concrete friction can be found in the literature (CEB Bul. N o. 162, 1983) and figure 3 preent a model propoed by Toukanta and Taio (1989). From figure 3, it can be een that the hear reitance due to friction (τ f ) reache a maximum when the relative lip i in the region of 1.75 mm. The maximum value of the deign concrete-to-concrete hear reitance due to friction (τ fu ) can be calculated from the following equation: τ = 0.4(f σ ) (5) 2 1/3 fu c c where: f c i the compreive trength of the weaker concrete and σ c i the compreive tre. 4 3 τ τ f f τ τ fu fu = τf/τfu (mm) Figure 3. Roughened concrete-to-concrete friction (Toukanta and Taio, 1989) Reinforced When a teel bar croe the between old and new concrete, an additional action that may occur i clamping action. Thi action would take place when the urface of the old concrete ha been roughened, or hotcrete ha been placed and if the teel bar i adequately anchored. When a hear tre i applied, a lip i produced and the contact urface between the old and the new concrete mut open a one urface ride up over the other due to the roughne. Therefore, a tenile tre i activated in the teel bar, which in turn produce a correponding compreive tre, or clamping action, and a frictional reitance i mobilied. Equation 5 can be modified in order to take into account the additional frictional reitance mobilied by clamping action, a follow: τ = 0.4(f ( σ +ρ f )) (6) 2 1/3 fu c c d y where: ρ d i the total cro ectional area of the hear connector (A d ) divided by the cro ectional area between the contact urface (A cd ). Figure 4 (CEB Bul. N o. 162, 1983) preent a plot of normalied hear reitance (V) againt lip for dowel action for monotonic loading. Parameter that affect dowel action include the concrete trength of the new and the old concrete, the yield tre of the dowel (f y ), the diameter of the dowel (d b ) and the amount of dowel placed. Repreentation uch a figure 4 can only be ued if the dowel are adequately embedded in the old and the new concrete (at depth of at leat 6 time the dowel diameter). In addition, meaure hould be taken to avoid failure due to placing dowel too cloe to the edge of the concrete (at leat 3, 5 or 6 time the dowel diameter are repectively required from the edge of the original column or the top or bae of the original column or jacket if a partial jacket i placed). The maximum value of the deign hear reitance from dowel action (V u ) can be calculated from the following equation (Ramuen, 1963; Vintzeleou and Taio 1986): V = 1.3 d f f (7) 2 u b c y If earthquake action i expected, it would be conervative to remove the value of 1.3 from equation 7 (GRECO, 2005).

6 V/Vu V 4 = 4 V 3 d u V f = V f d u y b c (mm) b 1.0 Figure 4. Shear force againt lip ditribution for dowel action (CEB Bul. N o. 162, 1983). A practice that i commonly ued and ha a good reputation i to weld bent down bar between the reinforcement of the old concrete and the new concrete. When there i relative lip between the old and the new concrete, a part of the force in the old bar i tranferred to the new bar via the bent down bar. Figure 5a conervatively demontrate the mechanim (CEB Bul. N o. 162, 1983; Taio, 2004; Taio, 2005). When there i lippage at the, one of the angled leg of the bent down bar i elongated by a factor of /( 2) while the other angled leg i hortened by the ame factor. Therefore, the repective tenile or compreive train (ε b ) and tree (σ b ) are: / 2 σ =Ε f (8) ε = b 2h = 2h and b 2h yb where: h i the ditance between the centreline of the outer arm of the bent down bar, E i the modulu of elaticity for the teel bar and f yb i the characteritic value of the yield trength of the teel bar. By conidering the equilibrium of force, the following equation can be derived: and T A A E A f b b b b yb 2 = σ = 2h (9) T = A E T = 2A f b y b yb 2h (10) where T i the force that can be tranferred to the new reinforcement, expreing in other word the hear capacity of the, A b i the cro ectional area of the bent down bar and T y i the force required to yield the bar. Figure 5b preent plot of T /T y againt lip for grade S500 teel bent down bar for ditance of h of 60 mm and 120 mm, where train hardening of the teel ha been taken into conideration. It can be een from figure 5b that the mechanim i mobilied for very mall lippage and thi jutifie the well-deerved reputation of bent down bar. h 1.2 new bar T old bar T/Ty h = 60 mm h = 120 mm 0.2 T (mm) (a) Figure 5. (a) Bent down bar model and (b) normalied force againt lippage. (b)

7 Deign conideration The total hear reitance between contact urface can be found by umming the individual hear reitance that are mobilied by each individual mechanim for a common lip. Figure 6a preent a plot of the uperpoition of lippage from all the mechanim dicued above for the tranfer of hear tre at the and figure 6b preent linear implification of the longitudinal tranfer of hear tre. A can be een from figure 6a, the problem become complicated when all the mechanim are conidered to act together. When conidering the required performance level, if an acceptable value of lippage i determined, the repective V reitance can be found by calculating the reitance for each mechanim and umming the reult. Alternatively, in order to implify calculation, bilinear diagram of the type OY 0 U of figure 6b could be applied. Elatic implification, a in curve OY 1 or OU of figure 6b, could be ued to facilitate the analyi. More precie reult could be obtained by uing elato-platic diagram uch a curve OY 1 UR of figure 6b. In general, the remaining hear reitance (V re ) could be conidered a inignificant. In figure 6b, the ultimate hear reitance (V u ) i defined a being 20% le than the maximum hear reitance (V max ) and the failure lip ( u ) correpond to thi ultimate hear reitance. V V max V max V u Y 1 U V = 0.2 V max V 0 Y 0 V re R (a) max O 0 1 (b) u Figure 6. The longitudinal tranfer of hear tre (a) uperpoition of mechanim and (b) linear implification. For tructural element that reit eimic action, it may be ueful (and it would implify calculation) if the mechanim of adheion and friction were ignored and only the hear reitance from dowel or other hear connector i taken into conideration. In other element that do not reit eimic action (for example concrete lab), it could be conidered that hear connector are required only when, in ome region of the tructural element, the hear tre between the contact urface exceed the hear trength from adheion or friction. It i conervatively acceptable to ay that if failure occur between the contact urface at ome point and a crack appear, the crack will extend to the remaining region between the contact urface even if the hear force ha been calculated to be le than the correponding hear reitance. In order to prevent a brittle failure at the, a minimum amount of teel hear connector in the form of dowel or bent down bar are required for concrete-to-concrete connection. The required percentage can be calculated in a imilar way to that of determining the minimum hear reinforcement in monolithic element and the following relationhip ha been propoed (Drito, 2005b; GRECO, 2005): ρ d max (0.18 f ctm /f yk, 0.12%) (11a) where: f yk i the characteritic yield trength of the teel hear connector or bent down bar and f ctm i the average tenile trength of concrete. The average tenile trength of concrete can be evaluated through the compreive concrete trength by conidering available literature or code relationhip. In EC 2 (2004), the average tenile trength, for concrete grade le than 50 MPa, i expreed a: f ctm = 0.3 f ck 2/3 (MPa) (11b) 4. CAPACITY OF STRENGTHENED ELEMENTS 4.1 General procedure accounting for lip The connecting procedure between the contact urface would have an important effect on the capacity of a compoite element. Shear tranfer at the i the mot critical iue for an element ubjected to bending. Figure 7 chematically preent the train ditribution againt height of cro ection for three different cae where trengthening ha been carried out in the tenile region. The three different cae are a follow: a) When the connection enure no lippage between the contact urface, the behaviour of compoite element can be conidered a monolithic and the train ditribution with height of cro ection will be linear, a hown in figure 7a, b) When the connection allow free lippage between the contact urface, the behaviour of the compoite element will be determined by the behaviour of the two part of the element, a preented in figure 7b and c) In practice, with realitic connection, the relative lippage between the contact urface depend on the magnitude of the hear tre that develop between the contact urface and the

8 56 hear reitance. If there i lippage, then the train ditribution will have a dicontinuity, a hown in figure 7c. Obviouly, the ize of the dicontinuity in the linear train ditribution (figure 7c) i dependent on the relative lippage between the contact urface (Lampropoulo and Drito, 2006; Tioulou and Drito, 2006). Conequently, in order to not only etimate the trength of the compoite element but alo the amount of activated tre or developed deformation between the contact urface, a model to imulate the hear tre and the hear train that would occur at the due to lippage would be required. Thi can be achieved by uing a diagram of hear tre againt lippage and would depend on the hear tranfer mechanim mobilied between the two part of the element (a decribed in ection 3.2 above and ummaried by figure 6a). Simplified diagram, a preented in figure 6b, can ignificantly minimie computation time. exiting element new element (a) (b) (c) Figure 7. Ditribution of train with height of cro ection for different connection between contact urface: (a) complete connection, (b) abence of connection and (c) partial connection. In order to implify calculation, further aumption depending on the pecial condition of the connection between the contact urface that could be conidered, depending on the pecific tructural condition, are a follow: a) The thickne of the connection can be ignored and it can be conidered a if the old and the new element are in complete contact, b) The tranfer of force by adheion can be ignored unle epoxy rein glue ha been ued between the contact urface and c) When a glue, dowel or anchor ha been ued between the contact urface, only relative lippage at the can occur and it can be aumed that there will be no diplacement perpendicular to the. Conequently, when the element i ubjected to bending, the curvature of two element can be conidered a the ame. Thi implification cannot alway be applied. For example, when a new layer of concrete ha been added to the original concrete element without an intermediary layer of rein or without hear connection, the implification can only be conidered when the urface of the original element ha been mechanically carified, roughened with a cabbier, andblated or water blated and d) The effect of hrinkage of the new material (for example, concrete or mortar) and the influence of differential creep could be ignored. The magnitude of the lippage that reult between the contact urface hould atify limit tate control for functionalim and failure, including thoe for which the effect of lippage are neglected. The proce of deign for trengthened or repaired and trengthened element decribed in thi ection can be extremely laboriou and may involve a large calculation time. An analytical procedure ha been propoed in the pat (Drito, 1994; Drito, 1996) but any deign proce of thi type i probably unfeaible in intervention of a large cale, unle uitable oftware ha been developed. Moreover, in order to follow the above procedure, accurate and reliable model for the imulation of the contact urface behaviour are required and thee model mut take into account real on ite working practice. To implify calculation, an approximate proce could be applied by firt conidering monolithic condition in order to ue well-known tructural deign method for reinforced concrete element. Therefore, the mechanical characteritic and the capacity of a trengthened or repaired and trengthened can be aeed by auming the entire element, coniting of the old and additional element, i monolithic. The reult could then be corrected uing pecial correction factor that can be defined a monolithic behaviour factor, for ituation where reliable value are available. 4.2 Approximate procedure uing monolithic behaviour factor The tranfer of the actual characteritic of repone for the compoite element may be conidered equivalent to applying uitable corrective factor of imulation to a comparable monolithic element with the ame characteritic and cro ection. Thee monolithic correction factor for the tiffne (k k ) and the reitance (k r ) can be defined a follow: k (EI) Re = k (12) (EI) Mo k R Re = r (13) R Mo where: (EI) Re and (EI) Mo are the tiffne of the retrofitted and correponding monolithic element repectively and R Re and R Mo are the trength of the retrofitted and correponding monolithic element repectively. The reitance indicator (r) may alo individually concern bending capacity, hear capacity or axial force capacity and hould be followed by

9 57 indicator M, V or N repectively. Uually, k k i le than or equal to k r and k r i le than or equal to unity. Obviouly, under the above framework, the complexity of the ubject can be greatly implified. With the given monolithic correction factor, the tructural deign and the aement of the analyi data can be converted to the correponding field of deign for monolithic element that i familiar to the engineer. Modern eimic deign of exiting tructure i moving toward a diplacement capacity aement of the tructure. In thi cae, the yield trength or the failure trength of an element cannot be conidered to fully expre an element capacity. In order to expre the whole behaviour of an element, a capacity curve in term of action effect againt diplacement i required. Figure 8 preent typical capacity curve for monolithic and trengthened element. For monolithic element, guideline for deign and recent draft Code (FEMA 356, 2000; fib, 2003; GRECO, 2005) provide an idealized curve for any element, a hown in curve (a) of figure 8. Moreover, formula are alo provided to evaluate value for the yield and failure trength (F y,mo equal F u,mo ) and for the diplacement at both the yield tage (δ y,mo ) and at the failure tage (δ u,mo ) (fib, 2003; GRECO, 2005). However, appropriate formula have not yet been made available in the literature regarding the correponding relevant value for a trengthened element and any derived formula cannot be verified due to limited experimental data. F y,mo = F u,mo F y,re = F u,re (a) (b) Action effect δ y,mo δ y,re Deformation δ u,mo δ u,re Figure 8. Capacity curve for (a) monolithic element and (b) trengthened or repaired and trengthened element. Therefore, ince the critical characteritic of an element are not only the trength and tiffne but alo the diplacement at the yield, maximum load and failure tage, additional monolithic behaviour factor regarding diplacement capacitie can be defined a follow: and θ = k y,re δ θ y y,mo θ = k u,re δ θ u u,mo (15b) (15c) and δ y,re k δ = y (14a) δ y,mo δ u, Re k δ = (14b) u δ u, Mo where: k δy and k δu are the diplacement monolithic behaviour factor at the yield and ultimate tage repectively and δ y,re and δ u,re are the diplacement of the trengthened element at the correponding tage. If the above monolithic factor are provided (for example, by a Code), the capacity curve of the trengthened element, a in figure 8b, can be determined in term of action effect againt diplacement. Conequently, for a flexure-controlled reinforced concrete element trengthened with additional reinforced concrete, the element capacity curve could be determined in term of bending moment and chord rotation by uing the monolithic factor value k r, k δy and k δu, a follow: M = k M y,re r y,mo (15a) where: M y,re, θ y,re and θ u,re expre the capacitie of the trengthened element regarding yield moment, chord rotation at yield and chord rotation at failure, while M y,mo, θ y,mo and θ u,mo expre the repective capacitie for the monolithic element. The chord rotation (rather than platic rotation) i a well undertood mechanical characteritic ued to expre flexurecontrolled deformation and ha been adopted for European eimic deign (Panagiotako and Fardi, 2001; EC 8, 2004; fib, 2003; GRECO, 2005). The chord rotation i defined a the angle between the tangent to the axi of the element and the chord connecting the treed ection under conideration and the end of the hear pan. In eimic deign, the conidered ection are normally the end of the element and the chord rotation at the yield and ultimate tage can be calculated from emi-empirical expreion provided in many reference in the literature (for example, fib, 2003; EC 8, 2004). The bending moment at yield can be eaily calculated through either conventional deign equation (CEB/fib, 1993) or other more accurate expreion provided by fib (2003). Finally, the ecant to yield tiffne of the trengthened element can be calculated from M y,re and θ y,re without uing the tiffne monolithic factor, a follow:

10 58 (EI) M y,re = L Re (16) 3 θ y,re where: L equal M/V and i the hear pan of the trengthened element. From the above dicuion, it i obviou that the determination of reliable monolithic correction factor value, for ue by the engineer in practice, i crucial for the application of the propoed redeign framework. Extenive analytic invetigation and experimental trial are required in order to determine reliable correction factor value. In thi direction, the real characteritic of tiffne, trength and diplacement capacitie of a retrofitted element mut be evaluated. Then thee characteritic mut be compared with the characteritic of an equivalent monolithic element with the ame cro ectional and detailing characteritic. Conequently, it i obviou that reult will have an influence in practical application only if the intervention can be applied in the ame way a in the laboratory. However, it mut be tre that, until now, no reearch project ha been performed with the aim of producing monolithic factor for deign purpoe. Moreover, although there i ome experimental data in the literature regarding trengthening by the addition of new reinforced concrete, appropriate data from which monolithic factor could be obtained i minimal. It i therefore evident that, in practice, the engineer judgement will be required a, for many cae, the experimental data doe not fit the pecific application condition in practice. In any cae, for practicing engineer, a ueful guide to the etimate of monolithic correction factor value can be found in Part 1-4 of EC 8 (1995), fib Bulletin 24 (fib, 2003) and GRECO (2005). However, it mut be treed that value have been obtained in a more or le empirical way according to expert knowledge and judgement and there i a lack of cientific jutification. Experimental reult baed monolithic correction factor value for a number of connection procedure will be derived in the following ection. 5. DERIVING VALUES FOR MONOLITHIC BEHAVIOUR FACTORS For exiting concrete frame building, deigned only for vertical load or deigned under old eimic Code proviion, eimic retrofitting mainly concern trengthening the vertical element. If the technique of adding new reinforced concrete i choen, thi i mainly performed by placing reinforced concrete jacket around the old element, a hown in figure 9. Sometime, depending on the pecific ite condition, the new concrete layer may be placed on one or more ide of the element. In the following, monolithic correction factor value will be derived by proceing available experimental data. For concrete jacket, experimental reult from a number of reearch project performed at the Univerity of Patra (Bouia et al., 2004; Vandoro and Drito, 2006a; Vandoro and Drito, 2006b; Vandoro and Drito, 2006c) will be proceed and further analyed. For trengthening by the addition of new concrete layer, experimental data will be drawn from a pat reearch project performed at the National Technical Univerity of Athen (Vailiou, 1975). Figure 9. Concrete column before placing a new concrete jacket. 5.1 Concrete jacket Figure 10 preent experimentally obtained force againt diplacement envelope curve concerning eight trengthened column pecimen and a repective monolithic pecimen (Mo) teted under cyclic loading. The repective envelope curve of an initial original column pecimen (O) i alo preented in the ame figure for comparative purpoe. In order to obtain value for the trength and the deformation at the three critical tage of yield, maximum load and failure load, trilinear idealization of the experimental curve can be performed. The yield point can be determined by uing a procedure imilar thoe propoed by Pauley and Prietley (1992), ATC 40 (1996) and GRECO (2005). A hown figure 11a, the elatic branch of the trilinear curve croe the real experimental curve at the point that i 60% of the yield load. In addition, up to the point of maximum load, the area created by the real experimental curve inide the trilinear curve mut equal the area created by the real experimental curve outide the bilinear curve. The failure point i defined a the point on the decending branch of the experimental curve where the load i 20% le than the maximum lateral load. Figure 11b

11 59 preent average value for the poitive and negative quadrant of the trilinear curve. Eight original column, with an initial cro ection of 250 mm by 250 mm, were trengthened by placing a 75 mm thick hotcrete jacket. A local contractor wa ued for the work. Four 14 mm diameter grade S220 longitudinal reinforcing bar were placed at the corner of the original column. Thi wa equivalent to a reinforcement ratio of almot 1.0%, which i typical of old contruction practice ince the minimum pecified in old Greek code wa 0.8%. The tirrup conited of 8 mm diameter grade S220 bar paced at every 200 mm. The longitudinal reinforcing bar of the jacket were four 20 mm diameter grade S500 bar placed at the corner of the jacket. Stirrup of 10 mm diameter grade S500 were placed in the jacket at a pacing of 100 mm. Thu, the reinforcement ratio of the jacketed column wa 1.15%, which i within the range typically ued for new contruction. The monolithic column had exactly the ame reinforcement and final cro ectional dimenion (400 mm by 400 mm) a the jacketed column. Four different treatment procedure were ued at the between the original column and the jacket. An treatment (denoted a R) wa ued for column R1 and R2 and involved the ue of a mechanical cabbler to roughening the urface of the original column before trengthening. An treatment (denoted a D) wa ued for column D1 and D2 and involved the ue of dowel a connector at the between the original column and the jacket. A combination of the above two treatment (denoted a RD) wa ued for column RD1 and RD2. Finally, an treatment (denoted a W) wa ued for column W1 and W2 and involved welding bent down teel connector between the longitudinal bar of the original column and the jacket. 200 Load (kn) R1 R2 D1 D2 RD1 RD2 W1 W2 Mo O -200 Diplacement (mm) Figure 10. Load againt diplacement envelope curve for all teted pecimen (Bouia et al., 2004; Vandoro and Drito, 2006b; Vandoro and Drito, 2006c). The concrete trength and maximum applied axial load of the pecimen are preented in table 1. A can be een on table 1, high jacket trength were achieved in mot cae. Thi i common in practice a it atifie the reaonable demand of minimizing the jacket thickne. Moreover, high concrete trength can be eaily achieved when hotcreting. P max P y Load (kn) 0.6P y δ y δ max δ u Load (kn) 120 R1 R2 100 D1 80 D2 60 RD1 RD2 40 W1 20 W2 0 Mo Diplacement (mm) Diplacement (mm) (a) Figure 11. Trilinear idealization curve: (α) definition and (b) reult for the trengthened and monolithic pecimen. (b)

12 60 When determining the value of normalized axial load (v) for the trengthened pecimen, the following formula wa adopted: where: N i the applied axial load, and A co f co and A cj f cj are the cro ectional area multiplied by the concrete trength of original concrete and jacket repectively. N v = (A f + A f ) co co cj cj (17) Table 1. Concrete trength and applied axial load for the experimental column pecimen. Specimen Column concrete Jacket concrete Axial load Normalized axial trength (MPa) trength (MPa) (kn) load R R D D RD RD W W Mo O A it i evident from table 1, the reported value are not the ame for every pecimen. Conequently, a direct comparion between the trengthened column and the monolithic pecimen to identify the influence of the treatment at the i not poible, ince the concrete propertie and axial load ignificantly influence the reult. Therefore, the experimental force againt diplacement curve have been analytically tranformed a if hypothetical pecimen with the ame concrete trength and axial load a the monolithic pecimen were under invetigation. Vandoro and Drito (2006a) have previouly preented the converion procedure in detail. In ummary, the converion procedure conit of the following three tep: a) For pecimen Mo and for every trengthened pecimen (conidered a monolithic for thi procedure), the load and diplacement at the yield, the maximum load and the failure tage were analytically calculated uing appropriate formula (EC 2, 2004; EC 8, 2004). b) Converion coefficient were derived a the ratio of the analytical load and diplacement value of pecimen Mo at the above three critical tage to the correponding value for each trengthened pecimen and c) Tranformed value preented in figure 12 were obtained by multiplying the experimental value of figure 11 by the correponding converion coefficient. Obviouly, the concrete trength of the jacket and epecially the normalized axial load have the greatet influence on the deformation capacitie at the ultimate and failure tage. Thu, the larget difference between the initial and the tranformed trilinear curve are oberved for pecimen R1, R2, D1, RD1 and RD2. However, ince concrete trength and epecially the normalized axial load have the greatet influence on the deformation capacitie at the ultimate and failure tage, the larget difference between the initial and tranformed trilinear curve are oberved for pecimen R1, R2, D1, RD1 and RD2. The tranformed curve are preented in figure 12. By uing equation 12 and 13, reitance monolithic factor value can now be derived for the yield (k r,y ), maximum (k r,max ) and ultimate (k r,u ) tage, a preented in table 2. Table 2 alo preent the correponding diplacement monolithic factor value. The monolithic behaviour factor at the maximum load tage (k δmax ) can be defined in a imilar way to equation 14a and 14b a the diplacement correponding to the maximum load of the trengthened element (δ max,re ) divided by the diplacement correponding to the maximum load of the monolithic element(δ max,mo ).

13 61 Load (kn) R1 R2 D1 D2 RD1 RD2 W1 W2 Mo Diplacement (mm) Figure 12. Tranformed curve for the trengthened teted pecimen and the monolithic pecimen. Table 2. Experimental monolithic factor value for RC jacketed column. Specimen k r,y k δy k r,max k δmax k r,u k δu R R D D RD RD W W However, for deign application two ource of uncertaintie hould be taken into conideration. Thee are: (a) difference between experiment laboratory reult and what can be achieved by the real application in practice and (b) the model and aumption ued in the analytical work when tranforming the force againt diplacement curve. Moreover, although when conidering trength, it i conervative to accept the lowet poible value, thi i not the cae when deformation i conidered. For thi ituation, average value for deformation, at the yield and failure tage, appear to be more accurate. Following on from thee conideration, value for monolithic factor baed on experimental reult (k r,exp, k δy,exp and k δu,exp ) that can be proviionally uggeted for deign purpoe are preented in table 3. Value for k k are not provided in table 3, however the ecant of yield tiffne, for ue in conventional elatic analyi, can be obtained by ubtituting equation 15a and 15b into equation 16, a follow: therefore, and obviouly, from equation 12 above (EI) (EI) k Re k M r = k 3θ δy k y,mo y,mo L (18) r = (EI) Re Mo (19) k δ y k r = k (20) k δ y Table 3. Propoed deign monolithic factor value for column trengthened with concrete jacket under the contruction and loading condition ued in the experimental work Type of treatment k r,exp k δy,exp k δu,exp R D RD W A it can be een from table 3, the value for k r,exp are alway lower than unity and range from 0.77 to 0.85, value for k δy,exp are far higher than unity and range from 1.45 to 1.90 while value k δu,exp range from 0.75 to 1.15 and, in mot cae, are lower than unity.

14 62 Furthermore, it can be een that the type of treatment influence the deformation factor k δy,exp and k δu,exp much more than the trength factor k r,exp. In other word, the exitence of teel connector at the ha a light influence on trength but a coniderable influence on the deformation capacity of the element. When comparing the different treatment procedure, pecimen RD and W performed cloer to monolithic behaviour. By taking into account that, for the experimental program, procedure W wa performed by welding bent down bar in mooth condition, behaviour even cloer to monolithic could be expected if roughening had alo been performed. However, procedure W i not uually undertaken on ite, ince it i a time conuming technique with a number of practical problem. Thee are: (a) the exiting teel bar may be corroded and/or not weldable, (b) bend down bar mut be individually detailed for each column to fit well between the old and the new bar and (c) welding on ite can only be performed under pecific condition and only by qualified pecialit welder. Therefore, value for monolithic factor regarding the RD procedure i of pecific interet ince, in practice thi hould be the recommended procedure for connecting at the, while it not acceptable to contruct jacket without taking any pecial connecting meaure between the old element and the jacket (Drito, 2005b; GRECO, 2005; Vandoro and Drito, 2006c). Value of 0.80 for k r and 0.70 for k k are propoed in Part 1-4 of EC 8 (1995). When compared to the value for procedure RD from table 3, it could be concluded that thee value are reaonably conervative for trength and lightly high for tiffne. The relevant value propoed for deign in the recent draft verion of Part 3 of EC 8 (2004) are in the range of 0.90 to 1.00 for k ry, 1.05 to 1.25 for k δy and equal to 1.00 for k δu. By comparing thee value with the relevant one preented in table 3, it i obviou that the propoed Code value are in reaonable agreement for the cae of the trength coefficient k r. Thi i not the cae for diplacement factor a value for k δy are underetimated and value of k δu are, in mot cae, overetimated. It mut be treed that analytical reult regarding action effect in the vertical element of a tructure, when concrete jacket have been ued to trengthen ome column, are not alway on the ide of afety if the lowet poible value for tiffne i ued for the jacketed vertical element. In thi cae, it i poible that maximum action effect and tree can be underetimated in the vertical untrengthened element. In all cae, a conervative deign for the exiting element of a tructure would take into account the mot unfavourable combination of action effect that would reult from one of two analye. In the firt analyi, the lowet poible value of tiffne of the trengthened vertical element hould be conidered by uing either equation 17 or by completely ignoring the material of the original column. That i to ay, by only taking into conideration the cro ection of the jacket. In the econd analyi, the tiffne of column can be etimated by auming a complete connection between the jacket and the original column. In other word, the entire cro ection can be conidered a monolithic. It mut alo be treed that value in table 2 and the propoed value in table 3 are limited by the pecific parameter involved when obtaining the experimental data. Therefore, more experimental reult are required, baed on different element propertie, dimenion and applied axial load, before accurate value for monolithic factor can be generally propoed for deign and Code ue. Alternatively, in the framework of the preent tudy, analytical finite element imulation can be ued to bridge the gap between experimental obtained value and deign need. To thi end, the finite element program ANSYS (2002) ha been ued to perform analytical parametric tudie that imulated the relative lippage between the contact urface, uing pecial contact element depending on the treatment procedure ued at the. Economou (2004) invetigated the main parameter affecting monolithic factor value and reported that, for typical practical application, difference in the quantity of reinforcement had a minimal influence. Similarly, in the ame reearch, the influence of the jacket concrete trength wa found to have an inignificant effect. Two graph from Economou (2004) are preented in figure 13 and jutify the jacket concrete trength finding kk 0.50 kr A cj/a co 0.40 A cj/a co C20 C30 C40 Concrete trength (MPa) 0.00 C20 C30 C40 Concrete trength (MPa) Figure 13. Concrete trength influence on monolithic value (Economou, 2004). The critical parameter affecting the monolithic factor value were found to be: (a) the roughne, which can be expreed by the magnitude of the coefficient of friction (µ), (b) the value of the normalized axial load and (c) the ratio of cro ectional area of the jacket divided by the initial column cro ectional area (A cj /A co ). Therefore, thee three parameter are examined hereafter. A large number of hypothetical type R pecimen with different combination of the above parameter have been analyed. Bet-fit curve for all examined imulation are preented in figure 14, 15 and