ANALYTICAL MODELING ON DEBONDING FAILURE OF FRP-STRENGTHENED RC FLEXURAL STRUCTURES. Abstract. Introduction

Transcription

1 ANALYTICAL MODELING ON DEBONDING FAILURE OF FR-STRENGTHENED RC FLEXURAL STRUCTURES Dr. Hedong Niu, Ibaraki University, Hitahi, Japan ro. Zhishen Wu, Ibaraki University, Hitahi, Japan Abstrat Eetive appliation o FR to onrete struture is not possible until a undamental understanding o the mehanis and ailure mehanisms o the retroit system is available. This paper is mainly oused on developing a methodology or prediting the debonding ailure aused by intermediate lexural raks in FR-strengthened R/C beam. Firstly, based on the strain ompatibility, an iterative analytial method is presented to predit the strutural response o strengthened beam. Then using onept o rature mehanis, a omprehensive study is direted to lariying debonding ailure mehanisms orresponding to experimental results. Finally, a uniied energy-based model is established to predit the debonding ailure in FR-strengthened R/C beam. Introdution In the past twenty years, iber reinored plasti (FR) laminates widely and suessully applied in aerospae strutures have gradually been aepted as a highly attrative alternative in lieu o their steel ounterpart in the ield o strengthening and upgrading o ivil engineering strutures. This an be attributed to their superior harateristis suh as light weight, high tensile strength, orrosion resistane, good tailorability and ease o appliation. These FR materials an be externally bonded to the tension ae o onrete strutures with any desirable shape via a thin layer o epoxy adhesive and thus enhane stiness and strength o the strutures to be strengthened. As we know, the pivot to this bond tehnique is to ensure peret omposite ation between FR laminates, ailure o whih may invalidate the stress transer rom onrete substrate to FR reinorement and ause undesirable premature ailure prior to the theoretially expeted load. As shown in Figure, FR-strengthened onrete beams may be subjeted to unavorable ailure modes in addition to rushing o onrete and shear ailure, suh as rupture o FR laminates, delamination o FR initiated rom the ut-o point, peeling-o o FR aused by shear rak and debonding o FR aused by intermediate lexural rak. Among them, rushing o onrete, shear ailure and rupture o FR an be avoided in the strutural design and their orresponding ultimate strength o strutural member an be predited using onventional RC beam theory. So ar onsiderable researh has been direted to investigating the phenomenon o interaial shear and normal stress onentrations at the ut-o point o FR and the orresponding ailure riteria have been developed or prediting the delamination o FR initiated rom the FR ends (e.g. [-5]). Dierent rom other researhers, Zhang et al. [6] suggested a plausible mode o ailure whih is ontrolled by the harateristis o the individual teeth in between adjaent raks in the onrete over and proposed a theoretial model or prediting the premature plate peeling ailure load whih depends on the size o stabilized rak spaings. The peeling-o o FR initiated rom shear raks o onrete an be prevented by a rational design and muh researh work on FR shear strengthening has been done [7-9]. However, very limited literatures an be ound onerning the debonding o FR aused by intermediate lexural raks generally loated near the maximum moment region, whih is onsidered to be a more dominant ailure mode than the delamination o FR at urtailment zone or the strengthened

2 Mid-span FR-Strengthened RC Beam FR-Strengthened lain Beam (a) Rupture o FR Debonding ropagation Debonding ropagation (b) Delamination o FR at FR ends Mid-span FR-Strengthened RC Beam Debonding ropagation () eeling-o o FR by Shear Craks FR-Strengthened lain Beam Debonding ropagation (d) Debonding o FR Caused by Intermediate Flexural Craks Figure. Failure Modes Observed in FR-Strengthened Conrete Beams beam with thinner FR sheets. A thorough understanding o suh kind o debonding ailure mehanism is ruial to developing the orresponding predition method or ivil engineers. Reent studies [-] have demonstrated that proper understanding and modeling o FR-onrete interae-related phenomena and ailures ould be improved via the appliation o rature mehanis theories. The traditional strength-based theory an only predit the loal rature but not the ultimate ailure load o the retroitted strutures. Wu and Niu [3-4] and Niu and Wu [5] theoretially investigated the eet o lexural raks on interaial stress distribution and pointed out that it is reasonable to use rature mehanis onept or predition o debonding ailure load. Reently, Niu and Wu [6] lariied the debonding behavior and ailure mehanism due to multiple lexural raks in FR-strengthened R/C beams through perorming nonlinear rature mehanis-based inite element analysis. It is shown that debonding behavior and the ultimate load o debonding ailure are signiiantly inluened by whether rak spaing is less than the eetive transer length o FR sheets or not and interaial rature energy.

3 In this paper, partiular emphasis is plaed on developing an analytial model or prediting the debonding ailure load aused by lexural raks, whih onsists o setion analysis based on strain ompatibility, onept o rature mehanis and simpliied assumptions based on debonding mehanisms. Firstly, an iterative analytial method to analyze the strutural response o FR-strengthened RC beam is established based on strain ompatibility and equilibrium. Then debonding mehanisms are interpreted or dierent rak patterns observed in pratial experiments and the orresponding analytial predition model is proposed. Finally, some disussions are made on model parameters. Strutural Response in FR-strengthened RC Beams A doubly reinored retangular setion is illustrated in this setion to develop an iterative analytial proedure to predit the strutural response to load appliation. This analytial study is based on the strain ompatibility, equilibrium, and hoie o material onstitutive relations or onrete, reinoring steel and FR. In the analysis, the ollowing assumption are made: (a) Linear strain distribution throughout the ull depth o the setion; (b) slip between the longitudinal reinoring steel and the surrounding onrete; () slip between the external FR reinorement and the onrete substrate; (d) premature FR separation or shear ailure is aounted or; (e) The tensile strength o the adhesive is ignored; () tensile strength is onsidered ater raking. ' Stress, ' ε ε = ε ε E =tanα α ε = E ' '.38 = k k = ( ε ε ).5.38 ε Strain, ε (a) (b) Figure. Constitutive Relationships: (a) Idealized Stress-Strain Curve or Conrete in Uniaxial Compression (ater [7]); (b) Reinoring Steel and FR To provide highly aurate predition, onrete is assumed to ollow the widely-used stress-strain urve proposed by Hognestad [7], reinoring steel is modelled by elasti peretly plasti urve in tension and ompression, and FR materials are assumed to behave linear elastially until to ailure, as shown in Figure, where =ompressive strength o onrete; =stress in onrete; ε = strain in onrete orresponding to ompressive strength; ε = strain in onrete; E =initial elasti modulus o onrete; y =yield strength; E s =elasti modulus o steel; ε y = yield strain in reinoring steel; rp =tensile strength o FR; E rp =elasti modulus o FR; ε rp = ultimate tensile strain in FR. Stress rp y E s ε y E rp ε rp Strain 3

4 d b d h h n ε ε s σ σ s neutral axis C s C A s ε s t σ s t T s A rp ε rp σ rp T rp Figure 3. Strain, Stress and Fore Distribution at Setion Start Input the geometri size o the FR-strengthened beam, the material properties, the measured p osition and the external load h n=d +h/. Assuming that ε ε Consider that steels are not yielding The moment attained by the setion analysis approximates the external moment & steels are not yielding & ε ε Assuming that ε max ε > ε Consider that steels are not yielding The moment attained by the setion analysis approximates the external moment & steels are not yielding & ε max ε > ε Consider that only lower steels are yielding N o solution h n < h N o Consider that only lower steels are yielding The moment attained by the setion analysis approximates the external moment & only lower steels are yielding & ε ε The moment attained by the setion analysis approximates the external moment & only lower steels are yielding & ε max ε > ε Consider that all steels are yielding Consider that all steels are yielding The moment attained by the setion analysis approximates the external moment & all steels are yielding ε ε & The moment attained by the setion analysis approximates the external moment & all steels are yielding & ε max ε > ε h n= hn +h/. Figure 4. Flow Chart or Calulating FR Stress or a Given Load Based on the strain ompatibility and equilibrium o internal ores, FR stress or external load an be predited or a speii loading stage. Figure 3 shows the strain, stress and ore distribution along the depth o ross-setion. In view o nonlinear behavior o onrete and reinoring steel, this 4

5 analysis should be perormed by an iterative proedure. Every possible ase should be heked or a given load or FR stress at a ertain setion, suh as whether the strain in the extreme iber o onrete in ompression is larger than ε or not, ompression steel or tension steel yields or not. In the analysis, the ultimate ompressive strain o onrete ε max is assumed to be.35. With respet to alulation o external load or a given FR stress, it an be very easily perormed as ollows: irstly assume ε <ε, alulate the neutral axis h n and hek whether the assumed onditions is met, i not, then assume ε <ε and repeat the same proedure until the alulation result agrees with the assumption ondition; seondly, the loation o the resultant o ompressive ore an be easily determined on the basis o the alulated neutral axis; and inally, the external load an be determined by the equilibrium o the moment at given setion. Determination o FR stress is an inverse operation to the above stated and uses an iterative proedure ollowing Figure 4. Detailed analytial equations rom the equilibrium o internal ore an be reerred to [4] and it was ound that either external load or FR stress an be predited with high auray by ompared to experimental results [8]. This kind o setion analysis based on strain ompatibility an be used to predit the rushing o onrete and rupture o FR. It is evident that suh analysis an hardly provide a reasonable predition or debonding ailure aused by intermediate lexural rak, whih an be attributed to the at that debonded setion violates the assumption used in setion analysis and knowledge about suh debonding mehanisms is still laking. Bonding and Debonding Mehanisms As shown in Figure d, debonding o FR laminates is oten observed to be initiated rom the ends o lexural raks near the maximum moment region, with subsequent propagation out to the ends o FR. Suh debonding ollows two possible paths: along the interae between adhesive layer and onrete substrate or through the onrete substrate adjaent to the bond interae. Generally, the latter mode is enountered in FR-strengthened RC beam provided with good bond ondition. Despite where debonding ours, it an be regarded that debonding propagation resembles mode II rature more losely than mode I rature beause FR laminates are primarily loaded in tension and the adhesive is primarily in shear providing the neessary shear onnetion between onrete and FR. In pratie, suh debonding propagation may be assoiated with mode I rature within onrete surae layer [9], but the integrated eet an be similar to mode II rature behavior, whih lies in the at that only a thin layer o onrete adheres to the FR debonding surae. Simple Shear Test FR Sheet t FR Sheet t t Conrete t Conrete b b L b b L (a) ull-ush Shear Test (b) ull-ull Shear Test Figure 5. Simple Shear Test on FR-Bonded Conrete rism 5

6 τ τ τ τ O G δ δ G O δ δ δ (a) Linear Bond-Slip Curve (b) Bilinear Bond-Slip Curve Figure 6. Interaial Constitutive Relationships To investigate the bonding and debonding mehanisms or FR-bonded onrete strutures, onsiderable researh has been onduted on pure shear test on FR-bonded onrete prisms shown in Figure 5. It is worthy o being noted that Täljsten [] irstly presented the use o rature mehanis approahes or the plate bonding tehnique. The derived ormula was solved analytially or simpliied bond-slip urve without sotening behavior. However, the author pointed that nonlinear equation derived or a realisti bond-slip urve ould only be used or numerial alulations. Reently, Yuan et al. [] and Wu et al. [] introdued several interaial onstitutive laws (as shown in Figure 6) desribing preand post- raking behavior o FR-onrete interae to analytially solve the nonlinear shear transer problems o pull-push and pull-pull shear tests. It shows that rature mehanis an be used to well explain the debonding initiation, propagation and inal ailure, whih shames the strength theory-based method. Moreover, it provides a simple expression or determining the load-arrying apaity. rovided that the bond length L is larger than the eetive transer length, the maximum transerable load in pull-push or pull-pull shear test an be expressed in the same orm with respet to the hoie o dierent interaial onstitutive relationships: max b G Et = () where E, t and b are elasti modulus, thikness and width o FR, respetively; G is the interaial rature energy onsumed or debonding ailure. FR-Strengthened R/C Beams As or FR-strengthened R/C beam, generally intermediate lexural rak initiated debonding is observed to be aompanied with two dierent rak patterns: loalized rak pattern more oten than not enountered in plain onrete beam strengthened with FR laminates and distributed rak pattern in strengthened RC beam, whih is shown in Figure d. Due to the eet o moment and dierent rak patterns, it may not be taken or granted that the debonding mehanisms are same or strengthened beam and FR-bonded onrete prism and the expressions derived rom simple shear test an be kept intat to apply to strengthened beam. To this end, the authors [3][5][6] onduted a omprehensive study on stress transer, debonding propagation and ailure mehanism using theoretial and numerial method. In what ollows, the similarities and dissimilarities are addressed between debonding mehanisms in raked FR-strengthened R/C beam and simple shear test. Based on theory o elastiity, Wu and Niu [3] theoretially investigated the eet o lexural raks around the maximum moment region or several load ases: three-point bending, our-point bending and uniormly distributed bending by adopting linear bond-slip relationship without sotening 6

7 behavior (Figure 6a) or modeling interaial behavior. It was onluded that high interaial shear stresses at the ends o raks are mainly responsible or debonding o FR in raked R/C beam strengthened with FR and the gradient o the moment, or shear ore has an insigniiant eet on the interaial shear stress distribution. By ignoring the minor terms in the derived expressions or interaial shear stress the maximum shear stress τ max in all load ases onverges to ks τ max = () b E t where is the axial ore in FR at rak; k s is shear stiness o employed interaial bond-slip urve; E, t and b are elasti modulus, thikness and width o FR, respetively. Using the onept o rature energy, the above equation an be rewritten in the same orm as Equation () derived rom simple shear test: max b G Et = (3) where max is the maximum transerable ore in FR at rak in FR-strengthened beam. Load(kN) One rak 3mm 5mm Deletion(mm) Load(kN) One rak.5mm 75mm Deletion(mm) (a) Single Crak and Large Crak Spaings (b) Short Crak Spaings Figure 7. Load versus Deletion Curves FR stress (Ma) one lexural rak rak spaing=3mm rak spaing=5mm Distane rom the mid-span (mm) (a) Single Crak and Large Crak Spaings (b) Short Crak Spaings Figure 8. FR Stress Distributions FR stress (Ma) Eetive transer length one lexural rak rak spaing=.5mm rak spaing=75mm Approx. urve Eetive transer length Distane rom the mid-span (mm) 7

8 In view o the at that interaial shear transer behavior an be well represented by bilinear bond-slip relationship (Figure 6b) with onsideration o sotening behavior [3], Niu and Wu [5] presented a losed-orm analytial solution or prediting interaial shear stress and FR stress distributions aused by lexural raks in FR-strengthened R/C beam, and lariied the debonding mehanism aused by one lexural rak using bilinear interaial model. rovided that FR ore at end o lexural rak in strengthened beam is same as that at load end in pull-push shear test, it is ound that interaial shear stress distributions are almost same or both FR-strengthened beam and pull-push shear speimen [8]. For the ase o single rak or loalized one in FR-strengthened plain beam, FR stress keeps onstant and load inreases no more one debonding is initiated and propagated outwards to end o FR. Considering that theoretial study is inapable to present the debonding propagation and stress redistribution between raks, Niu and Wu [6] onduted a inite element analysis and ound that rak spaing has a signiiant eet on debonding ailure mehanism and ultimate load-arrying apaity by employing disrete rak model to model onrete rak propagation and bilinear bond-slip relationship to model interaial behavior. Large rak spaing, or rather rak spaing larger than eetive transer length, yields almost the same ultimate load as that o one rak ase, while short rak spaing auses a dierent debonding mehanism to that o one rak ase and the ultimate load is higher. With respet to short rak spaing, or rak spaing shorter than eetive transer length, debonding initiation does not mean the inal debonding ailure. Debonding propagation is resisted by the adjaent rak and muh more energy is needed to make the stress redistribution, whih to some degree orresponds to inreasing the shear transer length and thus ontributes to sustaining inrease in FR stress and external load. Figure 7 and 8 demonstrate eet o rak spaing on strutural response. It is shown that with derease o rak spaing FR an be eetively utilized and the orresponding stress distribution an be approximated to a monotonially smoothly urve similar to that o one rak ase, with an inreased eetive transer length. Analytial Model or rediting Debonding Failure In FR-strengthened R/C beam, intermediate rak indued debonding ailure is oten aompanied by two rak patterns, i.e. loalized and distributed rak patterns. Based on the above disussions, the debonding ailure mehanism or the ase o loalized rak pattern is similar to that or simple shear test and thus the orresponding debonding ailure an be predited by ombining the rature energy based Equation () or determining the ultimate transerable load in FR and strain ompatibility based predition method. The predition proedure an be simpliied in Figure 9. τ () () b G Et debonding ailure; < b G Et no debonding Figure 9. redition or Debodning Failure Aompanied by Loalized Crak attern Yoshizawa and Wu [4] investigated the rak behavior in onrete through onduting uniaxial tension tests and bending test on FR-strengthened strutures with and without reinoring steel. It is 8

9 ound that the average rak spaing is averaged rom 7 mm to mm in FR-strengthened RC strutures. In view o that interaial shear stress is mainly aused by dierene between FR stresses, or ase o debonding ailure by distributed raks, it an be regarded that raks are uniormly smeared over the whole beam and debonding ailure is result in one debonding is initiated between two lexural raks with a spaing o an eetive transer length. Figure 8b shows that this assumption is onvining. Based on suh assumption, uniied predition proedure an be established or debonding ailure in Figure, where the ase is simpliied to that o loalized rak i = or unraked setion. τ L e () L e = k E t () ) ( (3) b G Et debonding ailure; < b G Et no debonding Figure. redition or Debodning Failure Aompanied by Distributed Crak attern Aording to Equation (), the eetive transer length L e an be approximated by: L e τ b max = G E t τ E t L ( mm) = k e E t ( Ma mm) (4) where τ is loal bond strength o interae, k is a oeiient determined by experiment, other symbols are deined beore. As stated above, the key parameter in prediting inal debonding ailure or FR-strengthened R/C beams is interaial rature energy G. In this predition model, debonding mode, or rather whether debonding ours in adjaent onrete interae or adhesive, is releted by the magnitude o G. Conluding Remarks Combining the strain ompatibility method and rature energy-based debonding mehanism, a uniied analytial model is established or prediting/evaluating debonding ailure aused by intermediate lexural raks in FR-strengthened RC beams. It is ound that this model is onvining rom the theoretial and numerial investigation onduted by the authors. Further investigation, however, is required to be done, suh as investigation into the relation between eetive transer length and onrete properties, size eet, and alibration o interaial rature energy rom a large amount o experimental results. 9

10 Reerenes. Roberts, T. M. (989), Approximate Analysis o Shear and rmal Stress Conentrations in the Adhesive Layer o lated RC Beams, The Strutural Engineer, 67(), Ziraba, Y. N., Baluh, M. H., Basunbul, I. A., Shari, A. M., Azad, A. K., and Al-Sulaimani, G. J. (994), Guidelines toward the Design o Reinored Conrete Beams with External lates, ACI Strutural Journal, 9(6), Quantrill, R. J., Hollaway, L. C., and Thorne, A. M. (996), reditions o the Maximum late Stresses o FR Strengthened Beams: art II, Magazine o Conrete Researh, 48(77), Täljsten, B. (997), Strengthening o Beams by late Bonding, Journal o Materials in Civil Engineering, ASCE, 9(4), Malek, A. M., Saadatmanesh, H., and Ehsani, M. R. (998), redition o Failure Load o R/C Beams Strengthened with FR late due to Stress Conentration at the late, ACI Strutural Journal, 95(), Zhang, S., Raoo, M. and Wood, L. A. (995), redition o eeling Failure o Reinored Conrete Beams with Externally Bonded Steel lates, roeedings o the Institution o Civil Engineers, Strutures and Buildings,, Al-Sulaimani, G. J., Shari, A., Basunbul, I. A., Baluh, M. H., and Ghaleb, B. N. (994), Shear Repair or Reinored Conrete by Fiber Glass late Bonding, ACI Strutural Journal, 9(3), Khalia, A., Gold, W. J., Nanni, A., and Abdel Aziz, M. I. (998), Contribution o Externally Bonded FR to Shear Capaity o Flexural Members, Journal o Composites or Constrution, ASCE, (4), Triantaillou, T. C. and Antonopoulos, C.. (), Design o Conrete Flexural Members Strengthened in Shear with FR, Journal o Composites or Constrution, ASCE, 4(4), Wu, Z. S., Matsuzaki, T., and Tanabe, K. (997), Interae Crak ropagation in FR Strengthened Conrete Strutures, roeedings o 3rd International Symposium on FRRCS, Sapporo, Japan, Triantaillou, T. C. (998), Frature Mehanis Approahes to Conrete Strengthening Using FR Materials, Frature Mehanis o Conrete Strutures roeedings FRAMCOS-3, AEDIFICATIO ublishers, D-794 Freiburg, Germany, Niu, H. D., Wu, Z. S. and Asakura, T. (999), A Numerial Analysis on Bonding Mehanism o FR-Strengthened Conrete Strutures Using nlinear Frature Mehanis, roeedings o the Japan Conrete Institute, (3), Wu, Z. S. and Niu, H. D. (), Shear Transer along FR-Conrete Interae in Flexural Members, Journal o Material, Conrete Strutures and avements, JSCE, 49(66), Wu, Z. S. and Niu, H. D. (), Study on Debonding Failure Load o RC Beams Strengthened with FR Sheets, Journal o Strutural Engineering, JSCE, 46A, Niu, H. D. and Wu, Z. S. (), Interaial Debonding Mehanism Inluened by Flexural Craks in FR-Strengthened Beams, Journal o Strutural Engineering, JSCE, 47A, Niu, H. D. and Wu, Z. S., Debonding and Frature Mehanis o FR-Strengthened R/C Beams Inluened by Flexural Craks, Submitted to Journal o Composites or Constrution, ASCE. 7. Hognestad, E. (95), A Study o Combined Bending and Axial Load in Reinored Conrete Members, University o Illinois Engineering Experimental Station, Bulletin Series. 399, 8.

11 8. Wu, Z. S. and Niu, H. D., Load-Carrying Capaity Due to Debonding Failure o FR-Strengthened R/C Beams, Submitted to Journal o Strutural Engineering, ASCE. 9. Wu, Z. S., Niu, H. D., and Yin, J. (), On Interaial Frature in FR-Strengthened Strutures, roeedings o International Symposium o Young Sholars on Mehanis and Material Engineering or Siene and Experiments, Changsha, China, Täljsten, B. (996), Strengthening o Conrete risms Using the late-bonding Tehnique, International Journal o Frature, 8, Yuan, H., Wu, Z. S., and Yoshizawa, H. (), Theoretial Solutions on Interaial Stress Transer o Externally Bonded Steel/Composite Laminates, Journal o Strutural Mehanis and Earthquake Engineering, JSCE, 8(), Wu, Z. S., Yuan, H., and Niu, H. D. (), Stress Transer and Frature ropagation in Dierent Kinds o Adhesive Joints, Journal o Engineering Mehanis, ASCE, 8(3) (in press). 3. Yoshizawa, H., Wu, Z. S. and Yuan, H. (), Study on FR-Conrete Interae Bond erormane, Journal o Material, Conrete Strutures and avements, JSCE, 49(66), 5-9 (in Japanese). 4. Yoshizawa, H. and Wu, Z. S. (999), Craking Behavior o lain Conrete and Reinored Conrete Members Strengthened with Carbon Fiber Sheets, Fourth international symposium on iber reinored polymer reinorement or reinored onrete strutures, ACI International S-88,