SP-230 74 Finite Element Modeling of Cyli Behavior of Shear Wall Struture Retrofitted using GFRP by Z.J. Li, T. Balendra, K.H. Tan, and K.H. Kong Synopsis: In this paper, a non-linear 3-D finite element analysis (FEA) model using ABAQUS (Hibbit, Karlsson and Sorensen, In. 2003) was developed to predit the yli behavior of shear wall strutures. In this FEA model, SPRING element is used to simulate the onstraint deformation due to fiber reinfored polymer (FRP) wrapping, and improved onrete stress-strain urve is onsidered to aount for the improvement of strength and dutility of onrete under FRP onfinement. A damaged plastiity-based onrete model is used to apture the behavior of onrete under yli loading. Method to identify shear failure due to FRP debonding and FRP rupture in FEA is also proposed. The model is validated using the results from the experimental study. It is shown that the proposed model an predit the shear failure and yli hysteresis behavior of GFRP-wrapped shear wall reasonably well. Keywords: yli behavior; fiber-reinfored polymer; finite element analysis; glass fibers; retrofitting; seismi; shear strength; shear wall 1305
1306 Li et al. Z.J. Li is a researh sholar and phd andidate in the Department of Civil Engineering at National University of Singapore. He has reeived his Master degree in South China University of Tehnology. His urrent researh interests inulde seismi behavior of strutures and seismi retrofitting using FRP. T. Balendra is a professor in ivil engineering at the National University of Singapore. He reeived his phd degree from Northwestern University in USA. His urrent researh interests inlude performane and retrofitting of seismi resistant strutures. ACI member K.H. Tan is an assoiate professor in ivil engineering at National University of Singapore where he reeived his MEng degree. He reeived his phd degree from the University of Tokyo. His urrent researh interests inlude FRP systems, strutural omposites and strutural strengthening. K.H. Kong is a researh fellow in ivil engineering department at National University of Singapore, where he reeived his PHD degree. His urrent researh interests inlude: earthquake engineering, strutural analysis, strutural onrete design and high strength light weight onrete. INTRODUCTION During reent earthquakes (e.g. 1994 Northridge earthquake in the USA, 1995 Kobe earthquake in Japan, and 2003 Bam earthquake in Iran), many old buildings designed without seismi provisions suffered severe damages. As a result, seismi retrofitting of old buildings has attrated more attention. The traditional seismi retrofit methods, suh as adding new shear wall or infilled wall, steel jaketing and onrete aging, have disadvantages to some extent, for example, adding mass to the footing and labor and equipment intensive. In reent years, seismi retrofit using FRP has beome a promising alternative to the traditional seismi retrofit methods due to the exellent harateristi of FRP suh as high strength to weight ratio, immunity to orrosion, easy and fast installation. Although onsiderable researh work has been arried out on FRP for seismi appliation, most of the literature only reported experimental investigations and some
FRPRCS-7 1307 analytial analyses, but seldom disussed FEA (finite element analysis) modeling (Laursen et al. 1995; Lombard et al. 2000; Ma and Xiao 1997; Matsuzaki et al. 2000; Restrepo et al. 1998; Seisble et al. 1997; Haroun et al. 2001; Ye et al. 2001). This may be due to the diffiulties of FEA modeling, for example, in apturing the yli behavior of onrete, modeling onrete-frp interfae, identifying the failure of FRP, and simulating the behavior of FRP. Reently, for monotoni loading, FEA models of FRP retrofitted strutures have been proposed. Buyle-Bodin et al. (2002) proposed a 2D FEA model using the Frenh Code Castem2000 (developed by CEA, Frenh nulear researh enter) to analyze the flexural behavior of externally bonded CFRP (arbon FRP) RC strutures under pushover loading. In this model, the internal steel bars as well as the CFRP plates were modeled using two-node bar linear elements. The model ould simulate CFRP bonding and the results ompared well with the test results. Kong et al. (2003) proposed a 3D finite-element model using program ABAQUS to simulate shear walls wrapped with GFRP (glass FRP). In their model, FRP was modeled using SHELL element and the results of FEA mathed well with the test results. Eusebio et al (2002) used software DIANA (2000) to perform 2D FEA modeling of FRP retrofitted masonry panles. They used SPRING element to simulate the onstraint on deformation provided by FRP strips. However, they did not onsider the improvement of onrete strength due to FRP onfinement. In this paper, a 3D FEA modeling using program ABAQUS for yli behavior of FRP retrofitted shear walls is being proposed. In this FEA modeling, SPRING element is used to simulate the onstraint on deformation provided by FRP strips. The improvement in strength of onrete ore due to FRP onfinement is also onsidered. A onrete model based on damaged plastiity is used to apture the yli behavior of onrete. And a failure riterion of FRP retrofitted strutures is proposed. The modeling is validated using the experimental results (Z.J. Li et al. 2004). RESEARCH SIGNIFICANCE The nonlinear 3D FEA model using ABAQUS proposed herein provides researhers and designers with a omputational tool for design of GFRP retrofitted shear
1308 Li et al. wall strutures. Through FEA modeling, the failure mode, the failure loation, the extent of strength and dutility improvement due to the hosen number FRP layers an be obtained. Therefore, with the proposed FEA modeling, it is possible for designers to do trial and error analysis until an effetive and reasonable retrofit sheme is ahieved. FEA MODELING Overview of the physial model A 1/5 sale model of the lower 2.6 story shear wall of a 25-story building in Singapore is onsidered. This model, when wrapped with GFRP, was tested previously by Li et al. (2004) under yli loading. The wall is an I-shaped wall with two flange walls and one enter wall. The thikness of the wall is 45mm throughout. The length of the enter wall is 955mm, the length of the flange wall is 657mm, and the height of the wall is 1314mm. (as shown in Figure 1). The lateral yli load (the loading history is shown in Figure 2) was transferred from the atuator to the wall through the upper loading transfer beams. The rate of yli loading hanged twie: 0.006mm/s in the first 3 yles (maximum top displaement is 3mm,6mm and 9mm,respetively ); 0.01mm/s in the fourth yle(maximum top displaement is 12mm), and 0.05mm/s in the finial yles (maximum top displaement is 15mm twie and 30mm twie). The longitudinal reinforing bars in the enter wall and the mid portion of the flange wall are 8mm diameter smooth high yield steel bars ( f = 525 MPa). The longitudinal reinforing bars in the edge portion of the flange wall and the base blok are 10mm diameter deformed high yield steel bars ( f = 480 MPa). The horizontal bars in y y the wall are 6mm smooth mild steel bars ( f = 350 MPa). The ube ompressive strength y at the day of test was f u =27.58MPa. A layer of unidiretional Glass FRP (Mbrae EG900 glass fiber reinfored polymer) was used to wrap the speimen. GFRP bolts were used at the flange wall-web wall joints to anhor GFRP sheets and then the anhor parts were overed by GFPR sheets. Thikness of the GFRP sheets is 0.353mm, and Young's module is 69.65GPa. The ultimate tensile strength of GFRP is 1667.7MPa and the ultimate tensile strain is 0.02.
FRPRCS-7 1309 Overview of the FEA model A total of 220 elements of C3D8R type (8 node solid brik elements with one Gaussian integration point) were used to model the tested wall. The 3-D view of the meshing of the RC wall is shown in Figure 3. Steel reinfored bars in the onrete wall were modeled as one-diretional strain elements (rods) and were simulated by rebar option. In ABAQUS, when rebar option is used, the steel reinforing bars will be superposed on a mesh of standard element types, like C3D8R type element. The onrete behavior of walls will be onsidered independent of the reinforing bars. The effets assoiated with the rebar-onrete interfae, like bond slip and dowel ation, are normally modeled approximately by introduing some tension stiffening into the onrete modeling. The reinforing bars were superimposed onto the wall. SPRING element was used to model the onstraint on deformation provided by wrapping FRP. Totally 525 SPRING elements were used. The boundary ondition of the base of the wall was simulated as fixed end. In order to prevent out-of-plane displaement, roller supports were plaed at eah node of the surfae of brik elements 37, 38, 107 and 108. A vertial pressure load was applied on flange and web of the top elements to simulate the vertial load. Lateral onentrated point loads were applied on eah of the top node on the flange walls to simulate the lateral yli displaement shown in Figure 2. Laws of materials The steel reinforing bars were onsidered as elasti perfetly plasti materials in both tension and ompression. The assumed uniaxial stress-strain urve of the steel bars is shown in Figure 4. The main parameters of steel materials like yield strength, Young s modulus and ultimate strength were obtained from the experimental study. The stiffness of the SPRING element was equal to that of the GFRP material (69.65GPa). A new onrete model (Conrete Damaged Plastiity model) in ABAQUS version 6.3 was used to simulate the behavior of onrete of the walls. This model is a ontinuum plastiity-based damage model for onrete. It assumes that the two main failure mehanisms are tensile raking and ompressive rushing of the onrete material, and that the uniaxial tensile and ompressive response of onrete is haraterized by
1310 Li et al. damaged plastiity. Under uniaxial tension, the stress-strain response follows a linear elasti relationship until the failure stress σ t0, whih represents the onset of miro-raking in the onrete material. Beyond this failure stress, the formation of miro-raks is represented marosopially with a softening stress-strain response. On the other hand, under uniaxial ompression the response is linear until the value of initial yield, σ 0. In the plasti regime the response is typially haraterized by stress hardening followed by strain softening beyond the ultimate stress, σ u. When the onrete speimen is unloaded from any point on the strain softening branh of the stress-strain urves, the unloading response is weakened and the elasti stiffness of the material is damaged. The degradation of the elasti stiffness is haraterized by two damage variables, d t and d ( 0 d, 1 ). Under yli loading onditions the t d degradation mehanisms are quite omplex, involving the opening and losing of previously formed miro-raks and their interation. The stiffness reovery effet, namely some reovery of the elasti stiffness as the load hanges sign in yli test, is onsidered. The weight fators, w t and w, ontrol the reovery of the tensile and ompressive stiffness upon load reversal, respetively. w, whih results in the reovery of the ompressive stiffness, is more important beause when the load hanges from tension to ompression, tensile raks will lose. The whole model desribed above is shown in Figure 5. The stiffness reovery fators were hosen as the default values: w t = 0 and w = 1. For the tension stiffening effet, CONRETE TENSION STIFFENING TYPE=STRAIN option (more suitable for onrete with reinforement) was used and the redution of onrete tensile strength to zero is assumed to our at 10 times the strain at failure. The ompression stress-strain urve of onrete was alulated by the formula proposed by Teng (2001), onsidering the improvement of onrete strength and strain due to GFRP onfinement. The improved onrete stress-strain urve proposed by Teng(2001) is shown in Figure 6. The improved stress-strain relationship (the parameters are denoted in Figure 6) is:
FRPRCS-7 1311 σ σ ( E E2 ) = Eε 4 f o ' = f + E ε o 2 2 ε 2 (0 ε ( ε t ε ε ) t ε ) (1) where ε t E ε ε 2 o 2 f o ' = ( E E 2 ) f ' f o ' = ε = 2 + k 2 f f l o ' (For E-glass FRP, k 26. 7 ) 2 = f l = 2 f h frp 2 t frp + b 2 f f o ' fl ' = 1+ k1ks k 1 2 ' f ' = (Confinement effetiveness oeffiient) f l ' = k s f l, b Ae k s = h A o A A e 1 [( b / h)( h 2R ) = 2 + ( h / b)( b 2R ) h ] /(3A ) ρ 1 ρ s 2 g s ρ s = Reinforement bar ratio b h =Width of the retangular onrete ore =Height of the retangular onrete ore Aording to Tan (2002), the whole onrete an be divided into several regions of onrete ore separated by the internal transverse links, beause the internal links provide additional anhor points and help in restraining the onrete from bulging out. Sine the shear wall under investigation is an I shape wall, FRP bolts were used to anhor the flange wall-web wall joints (Li et al. 2004). Thus, FRP bolts an be onsidered as the internal transverse links, and the I shape wall an be divided into 4 retangular regions as shown in Figure 7. Equation (1) was used to alulate the improved strength stress-strain urve for onrete of eah region, sine different region
1312 Li et al. had different width and height. The alulated ompression stress-strain urves of these four-region onrete are shown in Figure 8. The parameters of onrete used in the FEA modeling like Young s module, ompressive strength, were obtained from the experimental study. Parameters to identify failure in FEA study The equations for shear given in ACI 318 ode (2002) were used to identify the shear failure of the RC shear wall. In ACI 318 ode, for members subjeted to additional axial ompression fore, the shear apaity of onrete is: N u f ' v = (1 + )( ) MPa (2) 14A 6 g where, N is the axial ompression fore and u A g the area of the ross setion. The shear apaity provided by the horizontal steel reinforement is: Av f yd vs = MPa (3) s2as where, A v is area of horizontal shear reinforement within a vertial distane s 2 and horizontal distane d, A s the area of shear surfae. v The equation of shear apaity of FRP wrap is derived by Triantafillou (2000) is: = 0.8 ε ρ MPa (4) f E f where, E f f f = Young s modulus of fiber ε f =effetive FRP strain at failure whih is alulated as 0.0025 (FRP rupture) and 0.002 (FRP debonding) (Kong et al., 2003). ρ f =FRP shear reinforement ratio, whih is 2t b f w for ontinuously bonded shear reinforement with thikness t f.
FRPRCS-7 1313 t f =thikness of the fiber. D =length of flange wall. b w =thikness of flange wall. Thus, the shear apaity of reinfored onrete without FRP retrofitted an be alulated using: N u f ' Av f y d v = v + vs = ( 1+ )( ) + (5) 14A 6 s A g 2 s And the shear apaity of RC shear wall retrofitted using FRP an be alulated using N u f ' Av f y d v = v + vs + v f = (1 + )( ) + + 0.8E f ε f ρ f (6) 14A 6 s A g 2 s Based on formulas (2) to (6), the shear apaity of the RC flange wall was alulated as 1.74MPa, and the shear apaity before FRP debonding and FRP rupture were 3.49MPa and 3.93MPa, respetively. COMPARISON BETWEEN TEST AND FEA Analysis of shear failure In the experimental study, yielding of the steel reinforement ourred first at the bottom of the outmost 10mm deformed bar when top displaement was 10.11mm and orresponding fore was 192.52kN (4th yle). The first FRP debonding appeared at the left flange wall orner and at the right flange wall orner, when the displaement was 15mm (5 th yle). With inrease in displaement, more debonding ourred, and the onrete orner began to spall and rush. Finally, after the first 30mm peak displaement was passed and the opposite diretion displaement of 23.5mm was reahed (7 th yle), the right flange wall onrete orner rushed abruptly and the nearby FRP debonded dramatially (as shown in Figure 9). The failure mode of the speimen was shear failure with FRP debonding followed by FRP rupture.
1314 Li et al. In FEA modeling, the 1 st flexural rak (shear stress> shear apaity of reinfored onrete=1.74mpa) ourred at 53.6kN when the top lateral displaement was 0.75mm (1 st yle). As shown in Figure 10, at this stage, the shear stress of some of the ritial regions in the flange wall started to exeed the shear apaity of reinfored onrete, and the additional shear fore will be sustained by FRP. As shown in Figure 11, the first debonding of FRP (shear stress> shear apaity due to FRP debonding 3.49MPa) ourred at the orner region of the shorter flange wall in the third yle (9mm displaement yle). However, the debonding region was very small in the third and fourth yles (9mm and 12mm displaement yles), this is why in the experiment no FRP debonding was observed until the fifth yle (15mm displaement yle). In the fifth and sixth yles (twie 15mm displaement yle), the region of debonding developed dramatially as shown in Figure 12. As an be seen from Figure 12, the regions of debonding are mainly at the orner of the flange wall and the nearby regions. This mathes well with the regions of debonding in the test. The final shear failure due to FRP rupture in the 7 th yle (30mm displaement yle) (shear stress> shear apaity due to FRP rupture 3.93MPa) is shown in Figure 13. The FRP rupture regions onentrated at the orners of flange wall and nearby regions as what had been observed in the test. Thus, FEA proposed previously an predit the shear failure of the shear wall tested quite well. Analysis on global sale In the tested shear wall speimen, miro-raks exist due to shrinkage effets of onrete. Suh miro-raks will redue the stiffness, the initial stiffness and the stiffness in the proess of loading, of the tested speimen. For the saled models, suh influene will be amplified due to size effet (Elnashai et al 1990; Kong et al 2003). In ABAQUS, suh miro-raks annot be modeled, and thus when omparing the FEA results with the test results, the influene of the miro-raks should be aounted. For this purpose, the displaement of FEA needs to be amplified by a fator of 4, whih was obtained by dividing the ultimate stiffness of test results by that of the FEA analysis. The yle by yle omparison of the top lateral fore-displaement urves between the test and FEA is shown in Figure 14. As an be seen from Figure 14, FEA modeling ould predit the shape of the hysteresis fore-displaement urves reasonably
FRPRCS-7 1315 well. It is noted that the proposed FEA modeling underestimated the lateral fore to some extent. However, onsidering the variation of materials in the test, suh error is aeptable. CONCLUSION A 3D non-linear finite element model with SPRING elements to aount for the improvement of strength and dutility of onrete under FRP onfinement is proposed. This model predits the failure mode and the overall hysteresti behavior of GFRP retrofitted shear wall strutures reasonably well. REFERENCES ACI 318, 2002, Building ode requirements for strutural onrete and ommentary. Buyle-Bodin F., David E. and Ragneau E., 2002, Finite Element Modelling of Flexural Behaviour of Externally Bonded CFRP Reinfored Conrete Strutures, Engineering Strutures V. 24, pp. 1423-1429. DIANA, 2000, User Manual-DIANA Version 7, DIANA Analysis, P.O. Box 113, 2600 AC Delft, The Netherlands. Elnashai A.S, Pilakoutas K., Ambraseys N.N.,1990, Experimental Behavior of reinfored onrete walls under earthquake loading, Earthquake Engineering and Strutural Dynamis. V. 19. pp. 389-407. Eusebio M., Palumbo. P., Lozza F. and Manfredi G., 2002, Numerial Modelling of Masonry Panels Strengthened Using FRPs, Finite Elements in Civil Engineering Appliations, Swets& Zeitlinger, Lisse, Hendriks & Rots (Ed.), pp. 295-303. Haroun M. A., Mosallam A. S., Feng M. Q. and Elsanadedy H. M., 2001, Experimental Investiation of Seismi Repair and Retrofit of Bridge Columns by Composite Jakets, Proeedings of the International Conferene on FRP Composites in Civil Engineering, De 12-15 2001, Hong Kong, China, pp. 839-848. Hibbit, Karlsson and Sorensen, In., 2003, ABAQUS/Standard user s manual (Version 6.3), Pawtuket, RI.
1316 Li et al. Kong K. H.; Tan K. H.; and Balendra, T., 2003, Retrofitting of shear walls designed to BS 8110 for seismi loads using FRP, Proeedings of the Sixth International Symposium on FRP Reinforement for Conrete Stritires(FRPRCS-6), Tan. K. H (ed.), July 8-10, 2003, Singapore, Vol. 2, pp. 1127-1136. Laursen P. T.; Seibel F.; Hegemier G. A.; and Innamorato D., 1995, Seismi Retrofit and Repair of Masonry Walls with Carbon Overlays, Non-metalli (FRP) reinforement for onrete strutures, E&FN Spon, Taerwe L. (ed.), pp. 617-623. Li, Z.J.m; K.H. Kong; T. Balendra; and K.H. Tan, 2004, Behaviour of FRP retrofitted shear walls designed aording to BS8110, Developments in Mehanis of Strutures & Materials, Australia, Andrew J. Deeks and Hong Hao (eds), pp. 133-137 Lombard J. C.; Lau D. T.; Humar J. L.; Cheung M. S.; and Foo S., 2000, Seismi Repair and strengthening of Reinfored Conrete Shear Walls for Flexure and Shear using Carbon Fibre Sheets, Advaned Composite Materials in Bridges and Strutures, Montreal, The Canadian Soiety for Civil Engineering, Humar J. and Razaqpur A. G (eds), pp. 645-652. Ma, R., and Xiao, Y., 1997, Seismi Retrofit and Repair of Cirular Bridge Columns with Advaned Composite Materials, Earthquake Spetra, V. 15, No. 4, pp. 747-764. Matsuzaki Y.; Nakano K.; Fujii S.; and Fukuyama H., 2000, Seismi Retrofit using Continuous Fiber sheets, Proeedings 12 th World Conferene on Earthquake Engineering, New Zealand, pp. 2524-2531. Restrepo J. I.; Wang Y. C.; Irwin R. W.; and Devino B., 1998, Fibreglass/epoxy Composites for the Seismi Upgrading of Reinfored Conrete Beams with Shear and Bar Curtailment Defiienies, Proeedings 8th European Conferene on Composite Materials, Naples, Italy, pp. 59-66. Seisble F.; Priestley M. J. N.; Hegemier G. A.; and Innamorato, D., 1997, Seismi Retrofit of RC Columns with ontinuous Carbon Fiber Jakets, Journal of Composites for Constrution (ASCE), V. 1, No. 2, pp. 52-62. Tan K. H., 2002, Strength Enhanement of Retangular Reinfored Conrete Columns using Fiber-Reinfored Polymer, Journal of Composites for Constrution, V. 6, No. 3, Aug. 1, pp. 175-183.
FRPRCS-7 1317 Teng J. G.; Chen J. F.; Smith S. T.; and Lam, L., 2001, FRP-strengthened RC strutures. New York : Wiley. Triantafillou and Antonopoulus., 2000, Design approah for onrete members strengthened in shear with FRP, ASCE Journal of Composites for Constrution. Ye, L. P.; Zhao, S. H.; Zhang, K.; and Feng, P., 2001, Experimental Study on Seismi Strengthening of RC Columns with Wrapped CFRP Sheets, Proeedings of the International Conferene on FRP Composites in Civil Engineering, De. 12-15, 2001, Hong Kong, China, pp. 885-892. Figure 1 Plan view and geometry of the tested model Figure 2 Cyli loading history
1318 Li et al. Figure 3 3-D view of the modeling of the reinfored onrete wall Figure 4 Stress-strain urve for steel used in ABAQUS
FRPRCS-7 1319 Figure 5 Stress-strain urve of onrete damaged plastiity model used in ABAQUS Figure 6 Stress-strain urve of improved strength of onfined onrete (Teng 2001) Figure 7 Wall divided into regions
1320 Li et al. Figure 8 Stress-strain urves for onfined onrete of different regions Figure 9 Failure mode of the speimen: FRP debonding followed by FRP rupture (Z.J. Li et al. 2004) Figure 10 Initial shear failure in reinfored onrete flange wall at 53.6kN. Shade region has shear stress > 1.74 MPa (shear apaity of reinfored onrete)
FRPRCS-7 1321 Figure 11 Initial shear failure due to FRP debonding at the 9mm displaement yle. Shade region has shear stress > 3.49 MPa (FRP debonding shear apaity) Figure 12 Shear failure due to FRP debonding at the 15mm displaement yle. Shade region has shear stress > 3.49 MPa(FRP debonding shear apaity)
1322 Li et al. Figure 13 Shear failure due to FRP rupture (At the end of 30mm displaement yle, lateral fore was 151.78kN) Shade region has shear stress > 3.93 MPa (FRP rupture shear apaity)
FRPRCS-7 1323 Figure 14 Cyle-by-yle omparison between experiment and finite element analysis (displaement of FEA amplified by a fator of 4 to onsider size effet)
1324 Li et al.