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Structural performances of short steel-fiber reinforced concrete beams with externally bonded FRP sheets
Construction and Building Materials 17 (2003) 463–470
Structural performances of short steel-fiber reinforced concrete beams with externally bonded FRP sheets J. Yin, Z.S. Wu* Department of Urban and Civil Engineering, Ibaraki University, Nakanarusawa-cho 4-12-1, Hitachi 316-8511, Japan
Abstract The application of externally bonding FRP sheets to concrete structures has become a popular strengthening procedure. However, such FRP strengthening effect sometimes could not be well achieved due to the premature interfacial debonding along FRP–concrete bond interface. In FRP-reinforced plain concrete members, the rapid propagation of localized flexural cracks in concrete is one of the primary reasons that cause the concentration of interfacial shear stress around where concrete crack happens, thus resulting in the debonding initiation. Therefore, an effective control of crack localization and propagation in concrete might be a solution to avoid or delay the debonding. This article presents an approach to improve the FRP strengthening performance to concrete beams by mixing short steel-fibers into the concrete matrix. To investigate the enhancement of FRP strengthening effect, a series of experiments are carried out, which include a standard JIS test of short four-point bending beams without FRP strengthening and a test of three-point bending FRP-strengthened concrete beams with different volume fractions of mixed short steel-fibers. The control of crack propagation and the increase of concrete toughness through mixing short steel-fibers are achieved. In the experiment of three-point bending, FRP-strengthened concrete beams increasing steel-fiber volume fraction, leads to a smeared crack distribution in the concrete. The ultimate failure mode also changes from peeling-induced debonding to FRP rupture so that the FRP sheet can exert its strengthening effect sufficiently. In addition, a finite element analysis is performed to compare the experimental results, in which the increase of concrete toughness is described by fracture energy. The simulation basically reproduces the experiments. The validity of the proposed approach is demonstrated. 䊚 2003 Elsevier Science Ltd. All rights reserved. Keywords: Fibre reinforced polymer strengthening; Interfacial debonding; Fibre reinforced polymer rupture; Steel-fiber reinforced concrete; Fracture energies; Crack distribution
1. Introduction The applications of FRP sheets as tension reinforcement have been widely used in repair and upgrading of concrete structures. However, interfacial fracture that happens along the FRP–concrete bond interface significantly limits the strengthening performance of FRP reinforcements. From the experiment of FRP-strengthened plain concrete beams by Wu et al. w1,2x, it is found that interfacial debonding in most cases initiates where a localized flexural crack formed in the concrete. Then, it develops further in forms of a pure mode II fracture within the adhesive resin or through the interfacial concrete adjacent to the bond interface. The first type of debonding can be prevented by applying advanced surface processing techniques and bonding procedures *Corresponding author. Tel.: q81-294-38-5179; fax: q81-294-385268. E-mail address: [email protected] (Z.S. Wu).
with proper adhesive agents, as addressed by Meier w3x. The second type of debonding has been commonly observed in practice. Asakura et al. w4x applied the FRP bonding technique to strengthening roadyrailway tunnel linings, which were plain concrete structures. From their experiments, the strengthening performance of FRP sheets could not be achieved sufficiently because the typical localized crack in tunnel lining easily caused the debonding along interfacial concrete though the enhancement of load-carrying capacity, to some extent, could be obtained. So, improving the interfacial bond condition does not help much since the crack in concrete to a great extent depends on the original properties of the concrete. A finite element analysis was extensively performed by Wu and Yin w5x, which studied the influences of bond interface and concrete properties on the cracking behavior of FRP-strengthened concrete beams by nonlinear fracture mechanics. It was found that when the
0950-0618/03/$ - see front matter 䊚 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0950-0618Ž03.00044-8
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J. Yin, Z.S. Wu / Construction and Building Materials 17 (2003) 463–470
ened beams with the same steel-fiber volume fractions was carried out to study how the enhanced concrete toughness affects the FRP strengthening performance. Experimental results indicated that the mixing of short steel-fibers greatly affected the cracking behavior in concrete, from localized crack to distributed crack. The failure mode also changed from the peeling-induced debonding to the rupture of FRP sheets. The loadcarrying capacity of the FRP-strengthened beam was markedly enhanced. In addition, a finite element analysis was carried out by DIANA w8x. The cracking behavior was modeled by a smeared crack model and the concrete toughness improvement by mixing short steel-fibers was described by the equivalent fracture energy. Comparison to the experimental results was provided and good agreement was shown. Fig. 1. Dimensions of two specimens and load conditions.
interfacial bond condition is well guaranteed increasing fracture energy of concrete may prevent the crack from being localized and provide better stress transfer between the FRP sheets and the concrete matrix. The concept of fracture energy employed in non-linear fracture mechanics can be considered as an indicator of the crack resistance ability of concrete, otherwise called toughness. Therefore, our motivation is to find means to increase concrete toughness. A practical and effective solution, which has been adopted to bring concrete itself better performance, is to incorporate a small amount of short fibers into the concrete. Various kinds of short fibers such as featherfibers, wood-fibers, steel-fibers and man-made polymeric-fibers could be used. Some researches have been made on short fiber reinforced concrete. Ito w6x conducted experiments on vinylon short fiber reinforced concrete beams that discussed the effects of fiber length and mixing amount on the concrete strength and toughness. In the aspect of theoretical modeling, a micromechanical model was proposed by Li et al. w7x, in which the bridging of inclined individual short fiber across a crack was modeled on the basis of fracture mechanics. These previous researches focus simply on the improvement of the concrete properties. How it contributes to the strengthening performance of externally bonded FRP sheets is the interest of this article. This article intends to discuss this issue by using short steel-fibers to reinforce concrete. An experimental program was conducted. First, a short beam based on Japanese Industrial Standards (JIS), without externally bonded FRP sheets, reinforced with different volume fractions of steel-fiber (0–1.0% by volume), was tested to verify the enhancement of concrete toughness. Then, a three-point bending test of a series of FRP-strength-
2. Experimental study 2.1. Outline of experiments Two kinds of experiments are included. Firstly, to study the concrete toughness enhancement by mixing short steel-fibers, a test of the short JIS beams without externally bonded FRP sheets was performed. The specimen dimension is illustrated in Fig. 1a, with a pre-cut notch 0.5=1.7 cm at mid-span. It was subjected to fourpoint bending load in the test. Four cases with different volume fractions of short steel-fiber, 0, 0.25, 0.5 and 1.0%, corresponding to the steel-fiber amount per volume with 0 kgym3, 19.5 kgym3, 39 kgym3, 78 kgym3, respectively, were studied. Then, an investigation of the FRP strengthening performance of steel-fiber reinforced concrete was made on a three-point bending beam whose dimensions were the same as used in Ref. w5x (Fig. 1b). Before bonding the FRP sheets, the bottom surface of the concrete beam was polished by diamond sands, and the filler putty was applied to create a smooth substrate surface. The same volume fraction of steel-fibers as mixed in the JIS short beam specimen was used. The applied short steel-fiber was 30-mm long with a diameter of 0.5 mm. The mixing procedure of short steel-fibers into concrete was as follows: (1) stirring cement, aggregates in a mixer for 2–3 min; (2) pouring in water gradually while stirring them together for 1 min; (3) mixing in short steel-fibers and continuously stirring for 1 min; and (4) putting the completely mixed concrete into the specimen mold. The test cases are listed in Table 1, where NF, SF and CS denote plain concrete, steel-fiber reinforced concrete (SFRC) and carbon FRP-strengthened specimens, respectively. The properties of SF reinforced concrete with different steel-fiber volume fractions were calibrated by a compression test of cylinder specimens. It is
J. Yin, Z.S. Wu / Construction and Building Materials 17 (2003) 463–470 Table 1 Description of test cases Specimen
Volume fraction of steel-fiber (%)
Externally bonded FRP Sheet
NF SF-0.25 SF-0.50 SF-1.00
0 0.25 0.50 1.00
No No No No
CS–NF CS–SF-0.25 CS–SF-0.50 CS–SF-1.00
0 0.25 0.50 1.00
Yes Yes Yes Yes
Table 2 Experimental results of SFRC beams Specimen
Load at crack initiation (kN)
Peak load (kN)
Deflection at Peak load (mm)
NF SF-0.25 SF-0.50 SF-1.00
8.6 7.2 8.4 8.8
8.7 7.6 9.6 10.5
0.08 0.2 0.63 0.78
Fig. 2. Load-deflection relations of SFRC beams.
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found that the different steel-fiber volume fractions do not influence some concrete properties within the tested range. The average values are Young’s modulus Ecs25 GPa, Poisson ratio ns0.2, and compressive strength f cs26 MPa. As for the FRP sheets, Young’s modulus is EFRPs230 GPa, designed thickness is 0.11 mm, and tensile strength is f FRPs3.7 GPa, according to the specifications of FRP sheets provided by the manufacturer. 2.2. Test procedures and experimental results 2.2.1. JIS SFRC beam without FRP strengthening The deflection of the concrete beams was measured at mid-span by LVDTs. Considering the softening behavior after peak load, a displacement control loading scheme would have been adopted. However, due to the limitation of the test machine whose minimum loading rate for displacement control is only 0.5 mmymin, which is too fast for the crack propagation process to be observed, the force control at the rate of 0.5 kNymin was applied up to the peak load, followed by a displacement control of 0.5 mmymin. Table 2 lists the experimental results of the SFRC beams. It can be seen that except the case of SF-0.25, the loads at crack initiation were almost at the same level even with the different volume fractions of steelfibers. Howver, the peak load and the deflection at peak load increased with the increase of steel-fiber volume fraction. From the experimental observation, cracking behaviors were similar that only one localized crack occurred at the mid-span. However, the beams of higher steel-fiber fraction, from the load-deflection relations in Fig. 2, had better deformational behavior with longer gentle softening curves. Also, at the same load level the crack propagation was effectively controlled, as seen in Fig. 3. 2.2.2. FRP-strengthened SFRC beams In this section let us look at how the enhanced concrete toughness by the mixed steel-fibers affects the
Fig. 3. Load-crack length relations of SFRC beams.
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Fig. 4. Strain gauge arrangement on the bonded FRP sheets.
FRP strengthening performance. In order to monitor the FRP strengthening effect, a series of strain gauges were bonded on the bottom of the FRP sheets, as shown in Fig. 4, to measure the strain distribution. For the loading procedure, a force control scheme was used. The loading rate was set to 1.0 kNymin firstly and slowed down to 0.5 kNymin when the structural stiffness started to decrease due to the occurrence of concrete cracks.
Fig. 5 shows the development of cracking behaviors during the loading process of each case until final failure. For all the cases, the initial crack always occurred near the mid-span. With the increase of steelfiber volume fraction, by comparing Fig. 5a–d, the newformed cracks tended to be distributed. The number of distributed cracks also increased. The ultimate failure mode changed from peeling-induced debonding, as observed in cases of CS–NF, CS–SF-0.25 and CS–SF0.50, to the FRP sheet rupture in the case of CS–SF1.00. In the beams of debonding failure, the micro concrete cracks near the bond interface occurred firstly. With further loading, a main diagonal crack formed, followed by a rapid crack propagation along the interfacial concrete which led to the ultimate delamination of FRP sheets. Table 3 lists the experimental data of FRP-strengthened SFRC beams. Similar to the SFRC
Fig. 5. Progressive crack patterns. Table 3 Experimental data of FRP-strengthened SFRC beams Specimen types
Load at crack initiation (kN)
Load at debonding initiation (kN)
Peak load (kN)
Failure mode
CS–NF CS–SF-0.25 CS–SF-0.50 CS–SF-1.00
15.0 15.0 15.3 15.8
21.3 27.0 31.2 –
28.4 31.0 33.6 46.1
Peeling debonding Peeling debonding Peeling debonding FRP rupture
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Fig. 6. Load-deflection relations of FRP-strengthened SFRC beams.
beams without FRP strengthening, the loads at crack initiation have no apparent difference in these four cases. This implies that mixing steel-fibers does not affect much the tensile strength of the reinforced concrete. But the load at debonding initiation and peak load increases with the increase of steel-fiber volume fraction (Fig. 6). In addition, the FRP stress distributions at debonding initiation and occurrence of FRP rupture are compared in Fig. 7, which are calculated from the measured FRP strain distribution with the strain gauges. It can be seen that the FRP stress in specimen CS–SF-1.00 is apparently higher than the others that eventually fail due to interfacial debonding. However, among the three debonding failure specimens, the effective FRP stress transfer length increases with the increase of steel-fiber volume fraction. All these experimental results imply that mixing short steel-fibers into concrete, significantly enhances the concrete toughness and deformational behavior. Such an improvement of concrete properties benefits the strengthening performance of FRP sheets, if applied as the external reinforcement. Specifically, the highly localized concrete crack is effectively controlled. As a consequence, the premature interfacial debonding can be avoided. The stress transfer between FRP sheets and concrete is improved. Finally, the load-carrying capacity of the FRP-strengthened concrete beam is increased.
Fig. 7. Stress distribution of FRP sheets at debonding initiation and FRP rupture.
employed in the smeared crack model. A linear softening diagram is chosen for the post-cracking behavior. The material properties to be used in the finite element simulation are based on the experimental data. The tensile strength of SFRC is approximated from the calibrated compressive strength by the equation f ts 0.23f 2y3 c s2.0 MPa, according to JSCE standard w9x. Although such an equation is usually applied to normal concrete, the following simulation results show it is also acceptable for the steel-fiber reinforced concrete. The concrete fracture energy GIf is regarded as an unknown that depends on the short steel-fiber volume fractions. The FRP sheet is assumed linear elastic until rupture. The manufacturer-provided specifications of Young’s modulus, design thickness and tensile strength are adopted. Between FRP sheets and concrete is an epoxy bond layer, whose behavior is governed by a fictitious interfacial crack model used in Ref. w10x. However, in this article, it is assumed that the bond layer is physically perfect without any non-linearity. Because of the struc-
3. Finite element simulations Based on the experiments, a Two-dimensional finite element analysis is done by DIANA w8x. Concrete cracking behavior is modeled by a rotating smeared crack model. The mesh size dependence that suffers conventional smeared crack models has been avoided by varying crack bandwidth according to the mesh dimensions. For simplicity, but without losing physical meaning, the SFRC is considered as a homogenous material before cracking. The enhancement of concrete toughness by short steel-fiber in post-cracking stage is expressed by concrete fracture energy that has been
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Fig. 8. Finite element mesh.
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3.2. FRP-strengthened SFRC Beams
Fig. 9. Fracture energy identification by fitting experimental results.
tural symmetry, only one half of the specimen was simulated. The finite element meshes of the two tests are illustrated in Fig. 8. 3.1. Simulation strengthening
of
SFRC
beams
without
FRP
Because it has been assumed that the concrete toughness is reflected uniquely by the concrete fracture energy, it is necessary to identify the values for the SFRC with different steel-fiber volume fractions. In addition, since the same volume fractions are applied to FRP-strengthened beams, the identified values can be used in the next simulation. By fixing the concrete tensile strength at f ts2.0 MPa, the fracture energy is predicted by fitting the simulation load-deflection curves to the four experimental results with steel-fiber volume fractions of 0, 0.25, 0.50 and 1.00%, as shown in Fig. 9. The corresponding fracture energies GIf of 0.35 Nymm, 2.5 Nymm, 5.0 Nymm and 8.0 Nymm, respectively, are identified. It can be seen that by mixing short steel-fibers, even by a small amount, the equivalent fracture energy GIf of SFRC can be remarkably increased. This demonstrates the short steel-fibers can significantly improve concrete toughness.
As illustrated in Fig. 8b, the FRP-strengthened SFRC beam is discretized by four-node plane stress element, interface element w8x and truss element to simulate concrete matrix, bond layer and FRP sheets, respectively. Because in the experiment no premature interfacial debonding in epoxy bond layer was observed in the adhesive layer, an interfacial bond strength f bs3.0 MPa and an interfacial fracture energy GIIf s2.0 Nymm were assumed. With these values, the epoxy bond layer was considered not to crack according to the finite element analysis by Wu and Yin w5x. The fracture energy GIf of SFRC identified in the previous simulation was used. First, let us compare the load-deflection results with the experiments. As seen in Fig. 10, similar to the experimental behaviors, the load-carrying capacity of FE simulation increases with the increase of concrete fracture energy GIf. Although in the case of CS–SF1.00, the simulation curve is lower than the experimental one, such an increasing trend is clearly presented. Fig. 11 shows the simulation result of crack pattern in each case. In the case of CS–NF, a secondary localized flexural crack is observed in a distance from the primary flexural crack at the mid-span. The debonding occurs along the interfacial concrete from the roots of two localized cracks. This reproduces the cracking behavior and failure mode in experiment well as presented in Fig. 5a. With the increase of fracture energy to 2.5, 5.0 and 8.0 Nymm in the cases of CS–SF-0.25, CS–SF-0.50 and CS–SF-1.00, no obvious debonding is found from the simulation results. The cracks are distributed and the cracking zone tends to expand. It means that increasing fracture energy GIf can effectively prevent the crack from being highly localized and propagating, so that debonding does not occur easily. The concrete cracking zones with strain localization are presented in dark color. The stress distribution in FRP sheets at final failure is given in Fig. 12. For the case of CS–SF, the FRP
Fig. 10. Comparison of load-deflection curves between simulation and experiments.
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4. Conclusions Through an experimental study and finite element simulation, it can be concluded that mixing short steelfibers into concrete can greatly improve concrete toughness, which could be measured by means of the equivalent fracture energy of reinforced concrete, so that the crack propagation in concrete can be controlled. In FRP-strengthened concrete structures, such an improvement can have FRP sheet providing better strengthening effect. It could effectively prevent the rapid propagation of localized concrete crack. Concrete cracks tend to be distributed so as to lower the probability of interfacial debonding failure. The failure mode may change from interfacial debonding to FRP rupture. Hence, FRP sheets can carry more loads in the composite concrete structures through interfacial bond. Therefore, this study suggests that if the reinforcing procedure by mixing short steel-fibers into concrete had been applied to the original concrete structures, the better strengthening performance of later externally bonded FRP sheets on these concrete structures should have been obtained nowadays. Its application is considered to be promising in the future, especially to those plain concrete structures such as tunnel lining. It is expected that the enhancement of original concrete toughness by mixing short fibers can be greatly paid off in the later structure strengthening by externally bonded FRP composites. Fig. 11. Crack patterns in concrete by FE simulation.
Acknowledgments stress does not increase after it reaches 2300 MPa, after which debonding occurs. For CS–SF-0.25 and CS–SF0.50, the maximum FRP stress increases. It approximately reaches the design rupture stress of FRP sheets in the case of CS–SF-1.00. It suggests that the higher the fracture energy the SFRC has, the higher the stress in FRP sheets can be obtained and the more FRP strengthening can be provided.
Fig. 12. FRP stress distributions along bond span.
The financial support to partial work of this article from Advanced Technology Research in China (863 National Program) under grant 2001AA336010 is gratefully acknowledged. References w1x Wu ZS, Matsuzaki T, Tanabe K. Interface crack propagation in FRP-strengthened concrete structures. Proc FRPRCS-3 1997;1:319 –26. w2x Wu ZS, Matsuzaki T, Tanabe K. Experimental study of fracture mechanism of FRP-strengthened concrete beams. JCI Symposium on FRP Reinforced Concrete Structures, JCI, 1998; 119– 126. w3x Meier U. Post strengthening by continuous fiber laminates in Europe. Proc FRPRCS-3 1997;1:41 –58. w4x Asakura T, Ando T, Kojima Y. Experiments of inner reinforced tunnel linings. Internal Report of Railway Technical Research Institute, 1998. w5x Wu ZS, Yin J. Fracturing behaviors of FRP-strengthened concrete structures. J Eng Fracture Mech, (in press). w6x Ito T. Study on vinylon short fiber reinforced concrete. Proceedings of International Conference on Fiber Reinforced Concrete, Guangzhou, 1997; 21–26.
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w7x Li VC, Wang Y, Backer S. A micromechanical model of tension-softening and bridging toughening of short random fiber reinforced brittle matrix composites. J Mech Phys Solids 1991;39(5):607 –25. w8x DIANA-7 User’s Manual—Nonlinear Analysis. The Hague: Lakerveld b.v, 1998.
w9x Standard specification for design and construction of concrete structures: part I Design. JSCE Concrete Library Special Publication, Japan Society of Civil Engineers, 1986. w10x Yin J, Wu ZS. Simulations on crack distribution in FRPstrengthened concrete beams with interfacial fictitious crack model. Proc FraMCos-4 2001;2:1079 –86 (Cachan, France).
Structural performances of short steel-fiber reinforced concrete beams with externally bonded FRP sheets J. Yin, Z.S. Wu* Department of Urban and Civil Engineering, Ibaraki University, Nakanarusawa-cho 4-12-1, Hitachi 316-8511, Japan
Abstract The application of externally bonding FRP sheets to concrete structures has become a popular strengthening procedure. However, such FRP strengthening effect sometimes could not be well achieved due to the premature interfacial debonding along FRP–concrete bond interface. In FRP-reinforced plain concrete members, the rapid propagation of localized flexural cracks in concrete is one of the primary reasons that cause the concentration of interfacial shear stress around where concrete crack happens, thus resulting in the debonding initiation. Therefore, an effective control of crack localization and propagation in concrete might be a solution to avoid or delay the debonding. This article presents an approach to improve the FRP strengthening performance to concrete beams by mixing short steel-fibers into the concrete matrix. To investigate the enhancement of FRP strengthening effect, a series of experiments are carried out, which include a standard JIS test of short four-point bending beams without FRP strengthening and a test of three-point bending FRP-strengthened concrete beams with different volume fractions of mixed short steel-fibers. The control of crack propagation and the increase of concrete toughness through mixing short steel-fibers are achieved. In the experiment of three-point bending, FRP-strengthened concrete beams increasing steel-fiber volume fraction, leads to a smeared crack distribution in the concrete. The ultimate failure mode also changes from peeling-induced debonding to FRP rupture so that the FRP sheet can exert its strengthening effect sufficiently. In addition, a finite element analysis is performed to compare the experimental results, in which the increase of concrete toughness is described by fracture energy. The simulation basically reproduces the experiments. The validity of the proposed approach is demonstrated. 䊚 2003 Elsevier Science Ltd. All rights reserved. Keywords: Fibre reinforced polymer strengthening; Interfacial debonding; Fibre reinforced polymer rupture; Steel-fiber reinforced concrete; Fracture energies; Crack distribution
1. Introduction The applications of FRP sheets as tension reinforcement have been widely used in repair and upgrading of concrete structures. However, interfacial fracture that happens along the FRP–concrete bond interface significantly limits the strengthening performance of FRP reinforcements. From the experiment of FRP-strengthened plain concrete beams by Wu et al. w1,2x, it is found that interfacial debonding in most cases initiates where a localized flexural crack formed in the concrete. Then, it develops further in forms of a pure mode II fracture within the adhesive resin or through the interfacial concrete adjacent to the bond interface. The first type of debonding can be prevented by applying advanced surface processing techniques and bonding procedures *Corresponding author. Tel.: q81-294-38-5179; fax: q81-294-385268. E-mail address: [email protected] (Z.S. Wu).
with proper adhesive agents, as addressed by Meier w3x. The second type of debonding has been commonly observed in practice. Asakura et al. w4x applied the FRP bonding technique to strengthening roadyrailway tunnel linings, which were plain concrete structures. From their experiments, the strengthening performance of FRP sheets could not be achieved sufficiently because the typical localized crack in tunnel lining easily caused the debonding along interfacial concrete though the enhancement of load-carrying capacity, to some extent, could be obtained. So, improving the interfacial bond condition does not help much since the crack in concrete to a great extent depends on the original properties of the concrete. A finite element analysis was extensively performed by Wu and Yin w5x, which studied the influences of bond interface and concrete properties on the cracking behavior of FRP-strengthened concrete beams by nonlinear fracture mechanics. It was found that when the
0950-0618/03/$ - see front matter 䊚 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0950-0618Ž03.00044-8
464
J. Yin, Z.S. Wu / Construction and Building Materials 17 (2003) 463–470
ened beams with the same steel-fiber volume fractions was carried out to study how the enhanced concrete toughness affects the FRP strengthening performance. Experimental results indicated that the mixing of short steel-fibers greatly affected the cracking behavior in concrete, from localized crack to distributed crack. The failure mode also changed from the peeling-induced debonding to the rupture of FRP sheets. The loadcarrying capacity of the FRP-strengthened beam was markedly enhanced. In addition, a finite element analysis was carried out by DIANA w8x. The cracking behavior was modeled by a smeared crack model and the concrete toughness improvement by mixing short steel-fibers was described by the equivalent fracture energy. Comparison to the experimental results was provided and good agreement was shown. Fig. 1. Dimensions of two specimens and load conditions.
interfacial bond condition is well guaranteed increasing fracture energy of concrete may prevent the crack from being localized and provide better stress transfer between the FRP sheets and the concrete matrix. The concept of fracture energy employed in non-linear fracture mechanics can be considered as an indicator of the crack resistance ability of concrete, otherwise called toughness. Therefore, our motivation is to find means to increase concrete toughness. A practical and effective solution, which has been adopted to bring concrete itself better performance, is to incorporate a small amount of short fibers into the concrete. Various kinds of short fibers such as featherfibers, wood-fibers, steel-fibers and man-made polymeric-fibers could be used. Some researches have been made on short fiber reinforced concrete. Ito w6x conducted experiments on vinylon short fiber reinforced concrete beams that discussed the effects of fiber length and mixing amount on the concrete strength and toughness. In the aspect of theoretical modeling, a micromechanical model was proposed by Li et al. w7x, in which the bridging of inclined individual short fiber across a crack was modeled on the basis of fracture mechanics. These previous researches focus simply on the improvement of the concrete properties. How it contributes to the strengthening performance of externally bonded FRP sheets is the interest of this article. This article intends to discuss this issue by using short steel-fibers to reinforce concrete. An experimental program was conducted. First, a short beam based on Japanese Industrial Standards (JIS), without externally bonded FRP sheets, reinforced with different volume fractions of steel-fiber (0–1.0% by volume), was tested to verify the enhancement of concrete toughness. Then, a three-point bending test of a series of FRP-strength-
2. Experimental study 2.1. Outline of experiments Two kinds of experiments are included. Firstly, to study the concrete toughness enhancement by mixing short steel-fibers, a test of the short JIS beams without externally bonded FRP sheets was performed. The specimen dimension is illustrated in Fig. 1a, with a pre-cut notch 0.5=1.7 cm at mid-span. It was subjected to fourpoint bending load in the test. Four cases with different volume fractions of short steel-fiber, 0, 0.25, 0.5 and 1.0%, corresponding to the steel-fiber amount per volume with 0 kgym3, 19.5 kgym3, 39 kgym3, 78 kgym3, respectively, were studied. Then, an investigation of the FRP strengthening performance of steel-fiber reinforced concrete was made on a three-point bending beam whose dimensions were the same as used in Ref. w5x (Fig. 1b). Before bonding the FRP sheets, the bottom surface of the concrete beam was polished by diamond sands, and the filler putty was applied to create a smooth substrate surface. The same volume fraction of steel-fibers as mixed in the JIS short beam specimen was used. The applied short steel-fiber was 30-mm long with a diameter of 0.5 mm. The mixing procedure of short steel-fibers into concrete was as follows: (1) stirring cement, aggregates in a mixer for 2–3 min; (2) pouring in water gradually while stirring them together for 1 min; (3) mixing in short steel-fibers and continuously stirring for 1 min; and (4) putting the completely mixed concrete into the specimen mold. The test cases are listed in Table 1, where NF, SF and CS denote plain concrete, steel-fiber reinforced concrete (SFRC) and carbon FRP-strengthened specimens, respectively. The properties of SF reinforced concrete with different steel-fiber volume fractions were calibrated by a compression test of cylinder specimens. It is
J. Yin, Z.S. Wu / Construction and Building Materials 17 (2003) 463–470 Table 1 Description of test cases Specimen
Volume fraction of steel-fiber (%)
Externally bonded FRP Sheet
NF SF-0.25 SF-0.50 SF-1.00
0 0.25 0.50 1.00
No No No No
CS–NF CS–SF-0.25 CS–SF-0.50 CS–SF-1.00
0 0.25 0.50 1.00
Yes Yes Yes Yes
Table 2 Experimental results of SFRC beams Specimen
Load at crack initiation (kN)
Peak load (kN)
Deflection at Peak load (mm)
NF SF-0.25 SF-0.50 SF-1.00
8.6 7.2 8.4 8.8
8.7 7.6 9.6 10.5
0.08 0.2 0.63 0.78
Fig. 2. Load-deflection relations of SFRC beams.
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found that the different steel-fiber volume fractions do not influence some concrete properties within the tested range. The average values are Young’s modulus Ecs25 GPa, Poisson ratio ns0.2, and compressive strength f cs26 MPa. As for the FRP sheets, Young’s modulus is EFRPs230 GPa, designed thickness is 0.11 mm, and tensile strength is f FRPs3.7 GPa, according to the specifications of FRP sheets provided by the manufacturer. 2.2. Test procedures and experimental results 2.2.1. JIS SFRC beam without FRP strengthening The deflection of the concrete beams was measured at mid-span by LVDTs. Considering the softening behavior after peak load, a displacement control loading scheme would have been adopted. However, due to the limitation of the test machine whose minimum loading rate for displacement control is only 0.5 mmymin, which is too fast for the crack propagation process to be observed, the force control at the rate of 0.5 kNymin was applied up to the peak load, followed by a displacement control of 0.5 mmymin. Table 2 lists the experimental results of the SFRC beams. It can be seen that except the case of SF-0.25, the loads at crack initiation were almost at the same level even with the different volume fractions of steelfibers. Howver, the peak load and the deflection at peak load increased with the increase of steel-fiber volume fraction. From the experimental observation, cracking behaviors were similar that only one localized crack occurred at the mid-span. However, the beams of higher steel-fiber fraction, from the load-deflection relations in Fig. 2, had better deformational behavior with longer gentle softening curves. Also, at the same load level the crack propagation was effectively controlled, as seen in Fig. 3. 2.2.2. FRP-strengthened SFRC beams In this section let us look at how the enhanced concrete toughness by the mixed steel-fibers affects the
Fig. 3. Load-crack length relations of SFRC beams.
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Fig. 4. Strain gauge arrangement on the bonded FRP sheets.
FRP strengthening performance. In order to monitor the FRP strengthening effect, a series of strain gauges were bonded on the bottom of the FRP sheets, as shown in Fig. 4, to measure the strain distribution. For the loading procedure, a force control scheme was used. The loading rate was set to 1.0 kNymin firstly and slowed down to 0.5 kNymin when the structural stiffness started to decrease due to the occurrence of concrete cracks.
Fig. 5 shows the development of cracking behaviors during the loading process of each case until final failure. For all the cases, the initial crack always occurred near the mid-span. With the increase of steelfiber volume fraction, by comparing Fig. 5a–d, the newformed cracks tended to be distributed. The number of distributed cracks also increased. The ultimate failure mode changed from peeling-induced debonding, as observed in cases of CS–NF, CS–SF-0.25 and CS–SF0.50, to the FRP sheet rupture in the case of CS–SF1.00. In the beams of debonding failure, the micro concrete cracks near the bond interface occurred firstly. With further loading, a main diagonal crack formed, followed by a rapid crack propagation along the interfacial concrete which led to the ultimate delamination of FRP sheets. Table 3 lists the experimental data of FRP-strengthened SFRC beams. Similar to the SFRC
Fig. 5. Progressive crack patterns. Table 3 Experimental data of FRP-strengthened SFRC beams Specimen types
Load at crack initiation (kN)
Load at debonding initiation (kN)
Peak load (kN)
Failure mode
CS–NF CS–SF-0.25 CS–SF-0.50 CS–SF-1.00
15.0 15.0 15.3 15.8
21.3 27.0 31.2 –
28.4 31.0 33.6 46.1
Peeling debonding Peeling debonding Peeling debonding FRP rupture
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Fig. 6. Load-deflection relations of FRP-strengthened SFRC beams.
beams without FRP strengthening, the loads at crack initiation have no apparent difference in these four cases. This implies that mixing steel-fibers does not affect much the tensile strength of the reinforced concrete. But the load at debonding initiation and peak load increases with the increase of steel-fiber volume fraction (Fig. 6). In addition, the FRP stress distributions at debonding initiation and occurrence of FRP rupture are compared in Fig. 7, which are calculated from the measured FRP strain distribution with the strain gauges. It can be seen that the FRP stress in specimen CS–SF-1.00 is apparently higher than the others that eventually fail due to interfacial debonding. However, among the three debonding failure specimens, the effective FRP stress transfer length increases with the increase of steel-fiber volume fraction. All these experimental results imply that mixing short steel-fibers into concrete, significantly enhances the concrete toughness and deformational behavior. Such an improvement of concrete properties benefits the strengthening performance of FRP sheets, if applied as the external reinforcement. Specifically, the highly localized concrete crack is effectively controlled. As a consequence, the premature interfacial debonding can be avoided. The stress transfer between FRP sheets and concrete is improved. Finally, the load-carrying capacity of the FRP-strengthened concrete beam is increased.
Fig. 7. Stress distribution of FRP sheets at debonding initiation and FRP rupture.
employed in the smeared crack model. A linear softening diagram is chosen for the post-cracking behavior. The material properties to be used in the finite element simulation are based on the experimental data. The tensile strength of SFRC is approximated from the calibrated compressive strength by the equation f ts 0.23f 2y3 c s2.0 MPa, according to JSCE standard w9x. Although such an equation is usually applied to normal concrete, the following simulation results show it is also acceptable for the steel-fiber reinforced concrete. The concrete fracture energy GIf is regarded as an unknown that depends on the short steel-fiber volume fractions. The FRP sheet is assumed linear elastic until rupture. The manufacturer-provided specifications of Young’s modulus, design thickness and tensile strength are adopted. Between FRP sheets and concrete is an epoxy bond layer, whose behavior is governed by a fictitious interfacial crack model used in Ref. w10x. However, in this article, it is assumed that the bond layer is physically perfect without any non-linearity. Because of the struc-
3. Finite element simulations Based on the experiments, a Two-dimensional finite element analysis is done by DIANA w8x. Concrete cracking behavior is modeled by a rotating smeared crack model. The mesh size dependence that suffers conventional smeared crack models has been avoided by varying crack bandwidth according to the mesh dimensions. For simplicity, but without losing physical meaning, the SFRC is considered as a homogenous material before cracking. The enhancement of concrete toughness by short steel-fiber in post-cracking stage is expressed by concrete fracture energy that has been
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Fig. 8. Finite element mesh.
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3.2. FRP-strengthened SFRC Beams
Fig. 9. Fracture energy identification by fitting experimental results.
tural symmetry, only one half of the specimen was simulated. The finite element meshes of the two tests are illustrated in Fig. 8. 3.1. Simulation strengthening
of
SFRC
beams
without
FRP
Because it has been assumed that the concrete toughness is reflected uniquely by the concrete fracture energy, it is necessary to identify the values for the SFRC with different steel-fiber volume fractions. In addition, since the same volume fractions are applied to FRP-strengthened beams, the identified values can be used in the next simulation. By fixing the concrete tensile strength at f ts2.0 MPa, the fracture energy is predicted by fitting the simulation load-deflection curves to the four experimental results with steel-fiber volume fractions of 0, 0.25, 0.50 and 1.00%, as shown in Fig. 9. The corresponding fracture energies GIf of 0.35 Nymm, 2.5 Nymm, 5.0 Nymm and 8.0 Nymm, respectively, are identified. It can be seen that by mixing short steel-fibers, even by a small amount, the equivalent fracture energy GIf of SFRC can be remarkably increased. This demonstrates the short steel-fibers can significantly improve concrete toughness.
As illustrated in Fig. 8b, the FRP-strengthened SFRC beam is discretized by four-node plane stress element, interface element w8x and truss element to simulate concrete matrix, bond layer and FRP sheets, respectively. Because in the experiment no premature interfacial debonding in epoxy bond layer was observed in the adhesive layer, an interfacial bond strength f bs3.0 MPa and an interfacial fracture energy GIIf s2.0 Nymm were assumed. With these values, the epoxy bond layer was considered not to crack according to the finite element analysis by Wu and Yin w5x. The fracture energy GIf of SFRC identified in the previous simulation was used. First, let us compare the load-deflection results with the experiments. As seen in Fig. 10, similar to the experimental behaviors, the load-carrying capacity of FE simulation increases with the increase of concrete fracture energy GIf. Although in the case of CS–SF1.00, the simulation curve is lower than the experimental one, such an increasing trend is clearly presented. Fig. 11 shows the simulation result of crack pattern in each case. In the case of CS–NF, a secondary localized flexural crack is observed in a distance from the primary flexural crack at the mid-span. The debonding occurs along the interfacial concrete from the roots of two localized cracks. This reproduces the cracking behavior and failure mode in experiment well as presented in Fig. 5a. With the increase of fracture energy to 2.5, 5.0 and 8.0 Nymm in the cases of CS–SF-0.25, CS–SF-0.50 and CS–SF-1.00, no obvious debonding is found from the simulation results. The cracks are distributed and the cracking zone tends to expand. It means that increasing fracture energy GIf can effectively prevent the crack from being highly localized and propagating, so that debonding does not occur easily. The concrete cracking zones with strain localization are presented in dark color. The stress distribution in FRP sheets at final failure is given in Fig. 12. For the case of CS–SF, the FRP
Fig. 10. Comparison of load-deflection curves between simulation and experiments.
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4. Conclusions Through an experimental study and finite element simulation, it can be concluded that mixing short steelfibers into concrete can greatly improve concrete toughness, which could be measured by means of the equivalent fracture energy of reinforced concrete, so that the crack propagation in concrete can be controlled. In FRP-strengthened concrete structures, such an improvement can have FRP sheet providing better strengthening effect. It could effectively prevent the rapid propagation of localized concrete crack. Concrete cracks tend to be distributed so as to lower the probability of interfacial debonding failure. The failure mode may change from interfacial debonding to FRP rupture. Hence, FRP sheets can carry more loads in the composite concrete structures through interfacial bond. Therefore, this study suggests that if the reinforcing procedure by mixing short steel-fibers into concrete had been applied to the original concrete structures, the better strengthening performance of later externally bonded FRP sheets on these concrete structures should have been obtained nowadays. Its application is considered to be promising in the future, especially to those plain concrete structures such as tunnel lining. It is expected that the enhancement of original concrete toughness by mixing short fibers can be greatly paid off in the later structure strengthening by externally bonded FRP composites. Fig. 11. Crack patterns in concrete by FE simulation.
Acknowledgments stress does not increase after it reaches 2300 MPa, after which debonding occurs. For CS–SF-0.25 and CS–SF0.50, the maximum FRP stress increases. It approximately reaches the design rupture stress of FRP sheets in the case of CS–SF-1.00. It suggests that the higher the fracture energy the SFRC has, the higher the stress in FRP sheets can be obtained and the more FRP strengthening can be provided.
Fig. 12. FRP stress distributions along bond span.
The financial support to partial work of this article from Advanced Technology Research in China (863 National Program) under grant 2001AA336010 is gratefully acknowledged. References w1x Wu ZS, Matsuzaki T, Tanabe K. Interface crack propagation in FRP-strengthened concrete structures. Proc FRPRCS-3 1997;1:319 –26. w2x Wu ZS, Matsuzaki T, Tanabe K. Experimental study of fracture mechanism of FRP-strengthened concrete beams. JCI Symposium on FRP Reinforced Concrete Structures, JCI, 1998; 119– 126. w3x Meier U. Post strengthening by continuous fiber laminates in Europe. Proc FRPRCS-3 1997;1:41 –58. w4x Asakura T, Ando T, Kojima Y. Experiments of inner reinforced tunnel linings. Internal Report of Railway Technical Research Institute, 1998. w5x Wu ZS, Yin J. Fracturing behaviors of FRP-strengthened concrete structures. J Eng Fracture Mech, (in press). w6x Ito T. Study on vinylon short fiber reinforced concrete. Proceedings of International Conference on Fiber Reinforced Concrete, Guangzhou, 1997; 21–26.
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w7x Li VC, Wang Y, Backer S. A micromechanical model of tension-softening and bridging toughening of short random fiber reinforced brittle matrix composites. J Mech Phys Solids 1991;39(5):607 –25. w8x DIANA-7 User’s Manual—Nonlinear Analysis. The Hague: Lakerveld b.v, 1998.
w9x Standard specification for design and construction of concrete structures: part I Design. JSCE Concrete Library Special Publication, Japan Society of Civil Engineers, 1986. w10x Yin J, Wu ZS. Simulations on crack distribution in FRPstrengthened concrete beams with interfacial fictitious crack model. Proc FraMCos-4 2001;2:1079 –86 (Cachan, France).