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Strengthening RC beams using externally bonded CFRP sheets with end self-locking
Journal Pre-proofs Strengthening RC beams using externally bonded CFRP sheets with end selflocking Chao-Yang Zhou, Ya-Nan Yu, En-Li Xie PII: DOI: Reference:
S0263-8223(19)34651-3 https://doi.org/10.1016/j.compstruct.2020.112070 COST 112070
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
8 December 2019 1 February 2020 14 February 2020
Please cite this article as: Zhou, C-Y., Yu, Y-N., Xie, E-L., Strengthening RC beams using externally bonded CFRP sheets with end self-locking, Composite Structures (2020), doi: https://doi.org/10.1016/j.compstruct. 2020.112070
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© 2020 Published by Elsevier Ltd.
Strengthening RC beams using externally bonded CFRP sheets with end self-locking Chao-Yang Zhou, Ya-Nan Yu, En-Li Xie* School of Civil Engineering, Central South University, Changsha 410075, China;
Abstract: When laminates of fiber reinforced polymer (FRP) are just bonded on the substrate of reinforced concrete (RC) members for strengthening, debonding failure often happens prematurely and suddenly on the FRP-concrete joints. It is unbeneficial to efficient employment of FRP and reliable service of the structures. This paper introduces a mixed anchoring technique for FRP sheets that combines external bonding (EB) and a novel type of end anchorage. FRP sheets are self-locked at ends by wrapping about a slotted plate in a specified way. Experiments on four concrete beams demonstrated that adding end self-locking to EB can effectively solve the serious problems of usual debonding. End debonding was simply prohibited and intermediate crack debonding was substantially restricted despite occurrence. As a result, not only ultimate strength but also failure ductility of the strengthened specimens was greatly enhanced. The final failure featured by either FRP rupture or concrete crush regardless of debonding degree. Finite element models are then established to simulate the responses of the strengthened beams with hybrid anchored FRP. The numerical results show good agreements with the test observations including debonding process and failure modes. It proves capability and accuracy of the modeling as a useful tool for further research. keywords: Fiber reinforced polymer;Concrete beams; Debonding; Mixed anchorage; Self-locking
1. Introduction High-performance laminates of Fiber reinforced polymer (FRP), especially the carbon fiber reinforced polymer (CFRP) sheets, are widely used in the strengthening of reinforced concrete (RC) structures due to high strength-to-weight ratio, excellent corrosion resistance and easy installation. External bonding (EB) as a traditional way of strengthening only relies on the adhesive layer between the sheet and the component to transfer the interfacial stresses. If the stresses in a RC flexural member strengthened approach the tensile strength of concrete or the bonding ability of the interface, the concrete substrate, the cover or the bonding interface will be very prone to peeling off [1]. Generally named as debonding failure, it is abrupt and immature to limit the efficient use of materials. As was mentioned in [2, 3], the maximum stresses of FRP sheets as final debonding approaches is often merely 10~35 percentage of its ultimate strength. Many efforts have been made to deal with premature debonding. Suitable approaches were explored to predict debonding load, which involves interfacial stress analysis and debonding failure
criterion [4-8]. In addition, helpful measures have been put forward to protect against debonding failure. The common practice is wrapping transverse U-shaped strips of FRP sheet over the longitudinal FRP laminate [9,10]. It is effective in delaying premature debonding and even avoids any bond failure when the strips are provided with adequate number, thickness and layout. But the rational design and the dependability under such harmful environment as moisture, ultraviolet and high temperature are still in question. Among later developments are covering FRP sheets with spiked fanning fiber anchors [11], shooting nails through the specially made FRP plate [12], fixing a series of plates to press the laminate [13], installing wave-shaped anchors to clamp it [14] and so on [15]. Advantages and disadvantages of those methods are discussed in detail by references [3,16]. All in all, they proved useful to control of debonding and promotion of behavior. However, some problems remain pending due to one or more of the following reasons: (1) immature design guideline for debonding prevention; (2) undue damage to the original member; (3) limited scope of engineering application; and (4) time-consuming onsite construction. Therefore，it is desirable to make further investigation or new attempts. An alternative method has been developed in our group to strengthen reinforced concrete members using mechanical anchored FRP. The first author invented an anchorage device that can implement self-locking of the FRP sheet at the end by wrapping around twin rods in parallel in a special manner[17].In the first stage, it was applied for flexural strengthening of narrow RC beams and shear strengthening of RC T-beams, and the results were encouraging [18-19].In this paper,the twin-rod anchorage has been upgraded to become a slotted plate.Such upgradation can decrease the thickness and increase the flexural stiffness of the device in the longitudinal direction of strip, making it compact, very thin and so favorable in application.The slotted plate inter-locks with the sheet end in the patented way of winding and then connects with concrete by pre-planted bolts. Such end anchorage in association with epoxy bond as usual forms hybrid or mixed anchorage (HA). Experiments on RC beams under four-point bending are carried out to verify the superiority of HA over EB in debonding prevention. The numerical analysis is carried out using finite element software package ABAQUS. Available test results were used to validate the models for parameter study in the near future.
2. MIXED ANCHORAGE WITH END SELF-LOCKING OF FRP 2.1 Anchor plate inter-locking with FRP strips The slotted plate (Fig. 1 (a)) is a simple, efficient and patented device to anchor flexible strip. As a millimeter-scale compact anchor, it can be combined with the end of a strip of FRP sheet to realize inter-locking by special winding method which is shown in Fig. 1 (b) and Fig. 2. After the slotted plate is connected with the strengthened component through 2 bolts (Fig. 3), the FRP strip will become the external unbonded reinforcement material of the component, which can be used for rapid retrofit or temporary strengthening. In general, it is recommended to bond the FRP strip along the length of the soffit with the traditional process, because it is beneficial to the coincident working and crack control.
The combination of mechanical fastening and external bonding may be called hybrid or mixed anchorage for FRP strips. In simple words ，hybrid or mixed anchorage equals to bonding plus fastening. There is of course more than one mechanical fastening device and attaching other devices to bonding (e.g. [14]) can also be classified as hybrid anchorage. The slotted plate has obvious characteristics different from others as follows. First of all, it is convenient to obtain more and more tight anchoring effect by just winding round the anchor plate and with the help of self-locking even without (also not exclusive) glue. Then, it is compact and does not need to be assembled as for the wave-shaped anchor. One hole is enough on each side of FRP strip to install the plate, which is conducive to preventing a row of holes very close together from causing local damage to the anchorage zone of the component. Besides, it is ultra-thin, the required thickness is usually a few millimeters only (Fig. 2), so it has little impact on the appearance after strengthening.
Anchor
(a) A slotted plate
FRP Sheet
(b) The winding method
Fig. 1 The slotted plate inter-locking with FRP strip Bolt
Slotted plate
FRP
Fig. 2 End anchor system of the FRP strip
(a) Bottom view
(b) Side view
Fig. 3 Combination of an anchor plate with the beam
The FRP strip is close contact with the slotted plate and may carry large tension. Therefore, the material, size and shape in detail of the slotted plate need to be determined by special research. They are generally related to the thickness, number of layers and strength of the FRP strip. It is equally important to assure high machining accuracy. It is required that sampling inspection be done by a specially devised test of plate-strip assembly for qualified products. The slotted plate used in this test is made of thin steel plate with thickness of 6mm. The test results show that the ultimate stress of CFRP strip in the assembly can reach more than 95% of its ultimate strength.
2.2 Mixed anchorage technology with end self-locking When the reinforced concrete beams are strengthened by EB FRP strips with end self-locking, the construction technology of such mixed anchorage mainly includes the following steps. 1) Detect the steel bars and mark the hole location. According to the strengthening design and the size of the anchor plate, the implantation position of anchor bolts is determined by avoiding the bars in existence. 2) Drill holes and plant bolts. Drill holes in the place of bolt implantation, clean the ash slag in the inner wall of the hole, then inject glue into the hole and quickly implant the anchor bolts, meanwhile pay attention to ensuring their perpendicularity to the substrate. 3) Treat the substrate of the beam. On the surface where the beam and the FRP strip will bond, remove the slurry and degraded concrete until the new surface of the structure is exposed, clean it and keep dry. 4) Cut the strip and let it wrap round the anchor plate (WRAP). According to the distance of anchor holes in the long direction of the beam, the cutting length of the FRP strip is calculated. After cutting, impregnating glue is applied, and the ends of the strip are wound around the slotted plate (WASP). 5) Brush glue and install anchor plate. Brush the glue on the substrate of the beam, and insert the anchor rods into the anchor plates which have been wrapped by the FRP strip, and then tighten with nuts. 6) Roll and slightly pull strip. Press the strip with a rolling brush, pull it slightly at both ends of the strip to keep it straight and add glue when necessary.
2.3 Distinctions of hybrid anchorage with end self-locking Compared with the classical way of externally bonding, it is believed that the hybrid anchorage
in this paper has the following advantages for flexural strengthening of RC beams. 1) It can directly prevent the end debonding. This is because the anchor plate can help the FRP strip undertake substantial longitudinal tension at the ends of bond line, and thus greatly alleviate the concentration of interfacial shear stresses. If necessary, inward normal stresses can be provided to resist the outward debonding. 2) It can effectively inhibit the later development of the debonding due to intermediate cracks (IC), and then improve the ductility and ultimate capacity as well. As to delay the IC debonding, it is basically harmless, though possibly less useful than to restrain the end debonding. 3) It can save a lot of solidifying time of the epoxy layer as quick drying glue can be chosen for planting bolts and curing the bond line without disturbance is unnecessary. So it is especially suitable for bridge strengthening on busy traffic trunk lines and other emergency rehabilitation. 4) It can relax the high dependence on the strength of concrete and hence break through the limitation to the applicability of EB strengthening. Points 1) and 2) mentioned above will be verified by experiments in this paper. The point 4) has been proved in engineering practice. In 2014, several cultural relic buildings in Changsha, Hunan Province, China needed to be retrofitting and a large number of floor slabs were designed to be strengthened with EB CFRP sheets. However, the normal tensile bond strength could not meet the requirements of Chinese code due to deterioration of concrete performance. After a special demonstration, it was decided to attach slotted plates at two ends of the FRP strips to ensure safety and durability. The reason is that the anchor bolt with slotted plate can transfer the forces required by the FRP strip to the deep concrete, not just the substrate and cover of concrete. In the conventional approach of EB, however, the concrete strength is almost always the dominant factor for the detachment when adhesive of high quality is used.
3. Experimental investigation 3.1 Specimens and materials In the experimental program, four beams were tested including one unstrengthened specimen as reference. Among the three beams strengthened with CFRP sheets, one was strengthened by externally bonding and the other two by mixed anchorage with one or two layers of sheets. As shown in Fig. 4, all of the specimens were simply supported and tested in four-point loading. They have the same configuration, internal reinforcement and loading pattern. Their length, width and depth of section were 3200 mm, 250 mm and 300 mm respectively. Two longitudinal steel bars with 16 mm diameter were put near the beam bottom to resist tension, which concrete cover was 25 mm thick, area percentage was 0.6%. Steel stirrups with 8 mm diameter were supplied over the whole span at a center-to-center spacing of 100 mm to avoid shear failure. The clear span, the shear span, and the effective depth of section were 3000 mm, 1200 mm, and 267 mm, respectively.
All specimens were cast from a single batch of commercial concrete. The compressive strength for concrete cubes with side length of 150 mm achieved an average value of 35.6 MPa. Plain bars were used for stirrups and in the compression zone, and deformed bars were used to bear tension. Unidirectional continuous CFRP sheets (Sigma T700SC) and epoxy resin (Good-bond JN-C3P) were used for strengthening. The geometrical parameters and material properties are given in Table 1. Table 1 Parameters of rebars and FRP Diameter Materials
D,
Elastic
Sectional area
mm2
modulus
A, mm2
Yield strength
Ultimate strength
fyt, MPa
fuk, MPa
E, GPa
Stirrups
8
50.3
210
399.05
596.51
Compression bars
10
78.5
210
401.17
587.68
Tension bars
16
201.1
200
538.16
656.12
—
230
—
3319
CFRP sheets
0.167 mm (thickness)
P/2
P/2
300
2 10
31 8@100
Tension bars
100
300 275
250 2 16
Stirrups
Compression bars
600 3200
1200
1200
2 10 8@100 2 16
100
Fig. 4 Dimensions, reinforcements and loading pattern of beams (Unit: mm)
Table 2 presented the variables in detail according to strengthening schemes of the beams. The control specimen B1 is a reinforced concrete beam. Specimens B2 and B3 were strengthened with one ply of externally-bonded (EB) or hybrid anchored (HA) FRP. One more layer of hybrid anchored FRP was added in Specimen B4 as shown in Fig. 5, and the length of the second layer is 600mm shorter than that of the first one. Table 2 Tested parameters of beam specimens (Unit: mm)
Specimen
Strengthening method
CFRP Nominal
B1
Control beam
B2
EB
CFRP Strip width
CFRP Strip length
—
—
—
0.167
100
1800
thickness
B3
HA
0.167
100
1800
B4
HA
0.167×2
100
1800/1200
1200
100
1800
Fig. 5 Strengthening schemes of the beam B4 (Unit: mm)
3.2 Test setup and instruments The test setup is shown in Fig. 6(a). A concentrated force was applied at the midspan of a steel box beam and then distributed to two loading points 600 mm apart on the specimen. The measurement instruments included one force cell to measure the applied load, a linear variable differential transformer at midspan of the specimen to measure the vertical displacement. In order to get strains, a strain gauge was bonded at the midspan of each longitudinal bar in tension. Strain gauges were also bonded on the external surface of FRP strip and the top of beam at the midspan. Furthermore, the generation and propagation of crack were carefully observed. The loading and testing instrumentations include one load cell to measure the applied load, three LVDTs (at both supports, midspan) to measure the vertical displacements, and strain gauges to measure the strains of concrete, rebars and FRP sheet, as shown in Fig. 6(b). All beams were loaded by a hydraulic jack. The strains were collected using a DH3818 data acquisition system.
(a) Test setup of specimen Load cell
Strain gauge
Strain gauge FRP
Bolt
Slotted plate
(b) Layout of strain gauges Fig. 6 Test setup and monitoring devices of specimen
3.3 Experimental phenomena and results Table 3 Comparison of test results
method
Ultimate displacement, mm
Cracking load, kN
B1
—
62.68
26
85
95
—
Concrete crush
B2
EB
25.48
28
90
104
9.47
FRP debonding
B3
HA
56.56
28
92
118
24.21
FRP rupture
B4
HA (2 plies)
51.76
28
95
138
45.26
Concrete crush
Strengthening
Yield Ultimate load Increment of Pu load, kN Pu, kN ξ, %
140 120 100
Load (kN)
Specimens
80
B1, reference beam B2, externally-bonded B3, hybrid anchorage B4, hybrid anchorage, two layers
60 40 20 0
0
10
20
30
40
50
Midspan deflection (mm)
Fig. 7 Load-defection curves of the beams
60
70
Failure mode
The main test results of the four specimens are presented in Table 3. The relationships of load versus midspan deflection are shown in Fig. 7. The behavior of these beams in the process of loading has similarity as well as difference in characteristics, which are depicted as follows and then summarized. The reference beam B1——In the initial stage of loading, the mid-span deflection of the beam increases linearly with the load. When the load was added to 26 kN, the initial crack was found in the pure bending segment, and a turning occurred to the load-deflection curve, implying that the deformation began to accelerate. As the load continued to increase, new cracks gradually emerge, and existing cracks keep extending and widening. Most of them were vertical cracks between the loading points, some were located in the shear span where the bending moment is larger, and a few cracks inclined after entering the web of the beam. When the load reached 85 kN, the tension bar at mid-span yielded with 2690 με strain, the maximum crack width was about 2.2 mm, and the loaddeflection curve showed a significant turning point. After that, the crack width, strain and deflection speedily increased, but new cracks rarely appeared. At the load of 94 kN, creasing and crushing of compressed concrete were found near a loading point within the pure bending segment, signifying the arrival of the ultimate state. The compressive strain of concrete at the mid-span reached 3389 με, the tensile strain of the steel bar was 6504 με, and the maximum crack width was about 3.7 mm. The distribution of cracks is shown in Fig. 8 (a). The EB FRP strengthened beam B2——Before the longitudinal bars yielded, the performance of this strengthened beam was similar to that of the reference beam. The loads at cracking and yielding increased to 28 kN and 90 kN respectively, and the maximum crack width decreased greatly to 0.35 mm when yielding. When it was loaded to about 92 kN, occasional crackling noise, presumably from debonding, were heard, but the naked eye could not see where it happened. The tensile strains of steel bars and CFRP sheets at the mid-span are 3344 με and 3510 με, respectively. The maximum crack width is about 0.6 mm. Since then, the sound of debonding had become more and more loud and frequent. When the load reached 100 kN, it can be seen that the local sheet had slightly detached at 350 mm from a loading point, which signed that intermediate crack debonding had begun. The tensile strains of bars and sheets were 4356 με and 4906 με, respectively. The maximum crack width was about 1.2 mm. At 102 kN, the debonding phenomenon was obvious at 400 mm outside the loading point, and the debonding length was about 200 mm. The tensile strains of bars and sheets were 5268 με and 5980 με, respectively, and the maximum crack width was about 2.1 mm. After the bar yielded, especially after the sheet began to debond, it became difficult to increase and even maintain the load. The main manifestation of the specimen was the rapid development of various deformation and damage. At 104 kN, with a brittle sound, a large area of the sheet suddenly collapsed, as shown in Fig. 8 (b). The load quickly fell back to 87 kN. The tensile strains previously recorded of bars and sheets were 6068 με and 7169 με, respectively. The maximum crack width was 4.2 mm and the length of debonding segment was over 960 mm. The HA FRP strengthened beam B3——This beam behaved like specimen B2 before the yielding of tension steel bars. The cracking load (28 kN) did not change. The load at yielding (92
kN) increased slightly, and the maximum crack width decreased to 0.3 mm. The loads when debonding was occasionally heard, slightly seen and evidently visible increased to 100 kN, 104 kN and 105 kN respectively, implying that the debonding process was delayed, But the main difference from B2 was the performance in the later stage of debonding. When the load reached 118kN, there was a sudden loud noise. At the same time, the load drops sharply to 70 kN. It was found that the sheet had broken 80% at the end of an anchor plate (Fig. 8 (c)), indicating that the peak load had passed. Before the ultimate state, the measured compressive strain of concrete at the top and midspan of the beam was only 1894 με, while the tensile strains of bar and sheet were as high as 8625 με and 12650 με, respectively. The maximum crack width was 3 mm. The sheet detached almost over whole the length. The failure of this beam was featured by sheet rupturing after debonding. Although the ultimate deflection at the midspan is less than that of the reference beam, it is larger than the corresponding value of the EB FRP strengthened beam when the sheet was fracturing. It demonstrated that both the bearing capacity and the ductility of the beam were improved even if the sheet was broken. The HA FRP strengthened beam B4——It has one layer of short strip more than B3. The two specimens behaved alike before rebar yielded. The cracking load (28 kN) was identical, the yielding load (95 kN) was slightly increased, and the loads when debonding was occasionally heard, slightly seen and evidently visible are respectively promoted to 105 kN, 108 kN and 110 kN. The debonding mainly occurred between the anchors of the second strip. When the load reached 138 kN, the concrete in the compression zone was obviously crushed (Fig. 8 (d). The compressive strain of concrete reached 3568 με, and the tensile strains of bars and sheets at the midspan were 8596 με and 11537 με respectively. The maximum crack width was about 3.2 mm. The beam also experienced much larger deflection at ultimate than B2, the EB FRP strengthened specimen. It was meant that the materials were efficiently exploited the brittleness of final failure were overcome. The results showed that the effect of adding one layer of short strip is mainly reflected in the later stage of loading by such as delayed process and shortened zone of debonding, reduced strain difference between bar and sheet, transformed failure mode and increased ultimate bearing capacity.
(a) Crack pattern in B1
(b) Debonded CFRP in B2
(c) Ruptured CFRP in B3
(d) Crushed concrete in B4 Fig. 8 Typical phenomena of damage
In summary, all of the four specimens went through three different phases during the whole process of loading. They were divided by concrete cracking and rebar yielding, corresponding to two turning points in the load-deflection curves. The difference among these beams lay in the behavior after rebar yielding, and in particular, after CFRP debonding for the strengthened beams. They finally failed in various modes, that were concrete crush, FRP debonding, FRP rupture after debonding, and concrete crush after debonding. The failure modes depended on the combining way of FRP with the beam and the amount of FRP. The superiority of hybrid anchorage over usual bonding consisted in avoiding the occurrence of end debonding failure and hindering the later spread of intermediate crack debonding. As a result, the ultimate capacity of beam and the utilization ratio of FRP strength were substantially enhanced. Moreover, the failure displayed improved ductility in spite of debonding. In other words, debonding was no more fatal to a beam bonded with FRP sheet if it was self-locked at ends as above-mentioned. 4. Numerical simulation It is uneasy for experimental observers to promptly capture the information of material damage such as concrete cracking, and especially the initiation and development of FRP debonding. In view of the limitations, numerical analysis is made to simulate failure progress, reveal reinforcement mechanism and thereafter conduct parameter study. It is carried out by using the ABAQUS Finite Element (FE) software [20]. Non-linear FE models are established for the specimens mentioned before. They are three-dimensional (3D) FE models based on the smeared crack approach. To deal with the convergence problems of the numerical solution, a dynamic approach is adopted according to references [21,22]. The test beams can be simplified as a quarter model accounting of the structural symmetry. The FE modeling is described in detail as follows. 4.1 Finite element models In the FE analyses, four parts were first modeled, such as concrete beam, steel bars, FRP sheets and the anchor system. The concrete beam was composed of 8-node reduced integral format 3D solid elements (C3D8R) with the mesh size of 10 mm; Steel bars were modeled of 3D two-node truss elements (T3D2) with the mesh size of 5 mm; the FRP sheet was modeled by using a 3D fournode membrane element M3D4R with the meshes of 2.5 mm; the anchor system, including anchor plate (simplified as a steel plate without a slit) and two anchor bolts, was modeled using C3D8R elements with the meshes of 10 mm. In hybrid-anchored models, the anchor bolts and FRP ends were embedded into the concrete beam and anchor plates, respectively. For the beam strengthened with two layers of CFRP sheet, since the bond strength between them is much stronger than that between FRP and concrete, the relationship between two layers of CFRP sheets was modeled using “Tie” constraint. In addition, symmetry constraint was applied on corresponding symmetry surface of each model. A vertical constraint with no-limited horizontal displacement was adopted on the center line of supporting block. In the loading process, the displacement method was used as the loading method, which was applied at a point coupled with the top surface of the loading block. Fig.9 gives the three-dimensional FE models of simulated strengthened-beam with hybridanchoring system.
(a) FE model of the HA FRP strengthened beam (bottom view)
(b) FE model of hybrid-anchored FRP strip Fig.9 Three-dimensional FE model (a quarter)
4.2. Constitutive relations 4.2.1 Concrete For the concrete, a plastic damage model in FE program was used, which was provided in the ABAQUS software. The model includes the stress-strain relationships and the damage factor. Herein the uniaxial compression stress-strain relationship and the uniaxial tension stress-crack width relationship adopted the universal Saenz model [23] and the Hordijk [24] model, respectively. The damage factor of concrete used the damage model proposed by Lubliner [25] , which assumed that plastic damage only occurred in the softening stage and the stiffness was proportional to cohesion. In addition, the ratio of the ultimate biaxial compressive stress to the ultimate uniaxial compressive stress was set as 1.16; The flow potential eccentricity was set as 0.1; The ratio of the second stress invariant on the tensile meridian to that on the compressive meridian was set as 0.667; and a viscosity parameter of 0.0005 was specified to improve the rate of convergence of FE models. 4.2.2 FRP and steel bars The FRP sheet was assumed to be a linear-elastic-brittle model. To simulate the rupture of FRP, the elastic type was set to be “Lamina”. Except for the longitudinal elastic modulus of the CFRP material, other parameters were quoted according to the literature of Francisco et al.[26], as shown in Table 4. When the stress of FRP elements exceeds the ultimate tensile strength, the elements will automatically fail. Table 4. Elastic properties of CFRP
Material
E1, MPa
E2, MPa
ν12
G12, MPa
G13, MPa
G23, MPa
CFRP sheets
230000
10754
0.266
3648
3648
1601
Note: Ei is the Young’s modulus in the i direction, νij is the Poisson ratio between directions i and
j, Gij is the shear modulus in the ij plane. Longitudinal tension bars were modelled as the linearly reinforced elastic-plastic material, while stirrups and longitudinal compression bars were completely elastic-plastic models. The anchor system was defined the same as steel. 4.2.3 Steel-concrete bond Considering the characteristics of interface bonding between longitudinal steel bars and concrete, the bond behavior between them was modeled by using spring element. However, because of ignoring the slippage between stirrups and concrete, the stirrups were directly embedded into the concrete beam. The elements were defined by building the relationship between interface bond strength and relative slip, which adopts the CEB-FIP (1993) model [27], as shown in Fig.10. 10000
8000
τ(pa)
6000
4000
2000
0
0
1
2
3
4
5
s(mm)
Fig. 10 Model of bond-slip relationship between concrete and steel
4.2.4 FRP-concrete interface In order to simulate the interface debonding between FRP and concrete, the interfacial bondslip was mainly described by defining contact behavior "Cohesive behavior" and "Damage". This method was similar to the zero-thickness bond element, which is insensitive to grid changes and has better convergence. The damage criterion used the “Maximum Separation” criterion and sets a small viscosity coefficient in "Damage Stabilization" to increase convergence. The constitution model of FRP bond-slip (Fig.11) was followed by the simplified Lu model [28], as presented in Eq. (1) – (4).
s (0 s s0 ) max s0 0 ( s s0 )
max 1.5w ft
(1)
(2)
s0 0.0195w ft
w
(3)
2.25 b f / bc
(4)
1.25 b f / bc
Where, s is relative slip,
max is the maximum interfacial shear stress, s0 is the slip corresponding
to the maximum shear stress,
w is the coefficient relating to the width ratio of FRP to the beam,
ft is the tensile strength of concrete, b f is the width of FRP strip, bc is the width of concrete beam. 4.0
τmax
3.5
shear stress(Mpa)
3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.00
s0 0.01
0.02
0.03
0.04
0.05
slip(mm)
Fig. 11 Model of bond-slip relationship between concrete and CFRP strips
4.3 Numerical results and comparisons Fig.
shows the results of FE analysis for the relation of load versus deflection at the mid-
span. The tests results are also shown for comparison. It is clear that the predictions (including failure modes) are in good coincidence with the test data for all the four test specimens.
③
140
④
②
120
FRP rupture
①
Load (kN)
100 FRP debonding
80 60
B1-FE B2-FE B3-FE B4-FE
40 20 0
0
10
20
30
B1-test B2-test B3-test B4-test
40
50
60
70
Midspan deflection (mm) Fig. 12 Load-defection curves from FE and test The crack patterns at respective ultimate loads from the tests and simulations of the four specimens are compared in Fig. 9. The comparisons demonstrate that the FE model provides a reasonable prediction of the crack pattern for all the beams. For beams B1, B3, and B4, it seems that there are more cracks and they have relatively sufficient propagation. Comparatively, cracking and ultimate deflection (also see Table 3 and Fig. 8) as well are under-developed in B2. What inhibits their growth is brittle debonding due to lack of reliable anchorage for FRP.
(a) Specimen B1
(b) Specimen B2
(c) Specimen B3
(d) Specimen B4 Fig. 9 Crack patterns of the specimens from test and simulation
The failure modes of FRP debonding and FRP rupture are shown in Fig. . The debonding failure of beam B2 is accurately predicted. However, the rupture failure of beam B3 in the analysis happens somewhat later than that in the test. This is probably because the FRP strain at rupture is less than 14430 με as stipulated in the simulation according to the given material properties, in spite of exceeding 12650 με. Although failure of concrete crushing cannot be observed from the loaddeflection curve, it can be roughly estimated from the simulated result of strain. Taking specimen B4 as an example, when the mid-span deflection is 52 mm, the maximum compressive strain exceeds 3500 με, which is shown as the black area near a load in Fig. 10 and corresponds to the crushed concrete within the pure bending segment.
Fig. 10 Concrete crushing failure of specimen B4
4.4 Debonding ductility analysis Both experimental and numerical results have shown that the EB FRP strengthened RC beam fails in abrupt debonding with very limited deflection. The HA technology can significantly increase the ultimate deflection of FRP strengthened beams. As can be seen from the simulated curve in Fig. , it has a long debonding process, which is consistent with the results observed in the test. Four key states of beam B3 are selected as an example, in which the debonding process has further development. These significant states are also indicated in Fig.
for reference. The mid-span
deflections of beam B3 in these states are 23.91 mm, 32.10 mm, 39.29 mm and 49.29 mm respectively. Fig. 11 is the distributions of shear stress at FRP-concrete interface. The stresses in gray and black are over 0.001 MPa and below -0.001 MPa, respectively. Those in the green area are between -0.001 MPa to 0.001 MPa, approximately representing the debonded regions. Fig. 12 shows the FRP strain distributions at these four states, in which where FRP remains constant strain can be identified as the debonded segments. Fig. 11 shows that debonding of the FRP strip initiated around the location of the loading point and propagated slowly away from it, especially toward the strip end. As seen from Fig. , the load decreases slightly at all four states, which is due to the redistribution of stress in the FRP strip during the propagation of debonding. On the whole, however, the load is on the rise. It can be seen from the analytical results that hybrid anchorage can effectively restrain
the later development of intermediate crack debonding and improve the ductility and ultimate bearing capacity. Even if the FRP is almost completely debonded from the concrete, it can undertake large tension and the beam can still work normally. Midspan
Load point
(a) State ①
(b) State ②
(c) State ③
(d) State ④ Fig. 11 FRP debonding area at four key states of beam B3 12000 10000
FRP strain (με)
8000 6000
state 1 state 2 state 3 state 4
4000 2000 0
0
100
200
300
400
500
600
700
800
900
Distance from FRP plate end (mm)
Fig. 12 FRP strain distributions at four key states of beam B3
6. Conclusions A novel method with simple device is invented to lock the end of flexible strip. The relevant hybrid anchorage technology of FRP strip is developed and investigated in this paper. The mixed system combines the externally-bonded FRP with the end anchorage. As a new type of mechanical
anchoring system, this end anchorage is simply made of a slotted plate for self-locking of strip and two bolts planted into concrete. The tests demonstrate that this innovation with end self-locking can overcome the main shortcomings in reinforced concrete beams strengthened by externally-bonded FRP. It is by means of avoiding end debonding and restraining the later development of intermediate crack debonding. Therefore, both ultimate capacity and failure ductility are promoted. The final failure mode is either FRP rupture or concrete crush no matter to what extent the detachment spreads. Finite element modeling is also implemented for the beams with hybrid anchored FRP. It is capable of simulating the overall responses of the complicated structural system containing debonding process, failure mode and ultimate strength. Its capability and accuracy are validated by comparisons between the numerical predictions and the test results. This work is a pilot study, and more comprehensive study is required to know the effects of various parameters on the behavior of the strengthened beams and to develop the design guidelines for debonding prevention at last.
Acknowledgements The authors are grateful for the financial support received from the National Natural Science Foundation of China (Grant No. 51878664) and the National Key R&D Program of China (Project No. 2017YFC0703506).
Data Availability Statement All data, models, and code generated or used during the study appear in the submitted article.
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under dowel load. Journal of Composites for Construction 2007;11:138-48. [6] Neto P, Alfaiate J, Dias-da-Costa D, et al. Mixed-mode fracture and load misalignment on the assessment of FRP-concrete bond connections. Composite Structures 2016;135: 49-60. [7] Mohammadi, Tayyebeh, et al. Bond behavior of FRP–concrete in presence of intermediate crack debonding failure. Journal of Composites for Construction 2017; 04017018. [8] He X-J, Zhou C-Y, Wang Y. Interfacial stresses in reinforced concrete cantilever members strengthened with fibre-reinforced polymer laminates. Advances in Structural Engineering 2020;23(2):277-88. [9]Kalfat, R., Al-Mahaidi, R., and Smith, S. T. Anchorage devices used to improve the performance of reinforced concrete beams retrofitted with FRP composites: State-of-the-art review. Journal of Composites for Construction 2013; 17(1):14-33. [10]Kotynia, R., Abdel Baky, H., Neale, K. W., and Ebead, U. A. Flexural strengthening of RC beams with externally bonded CFRP systems: Test results and 3D nonlinear FE analysis. Journal of Composites for Construction 2008; 12(2):190-201. [11] Zhang H, Smith ST, Kim S. Optimisation of carbon and glass FRP anchor design. Construction and Building Materials 2012;32:1-12. [12] Lamanna AJ, Bank LC, Scott DW. Flexural strengthening of reinforced concrete beams by mechanically attaching fiber-reinforced polymer strips. Journal of composites for construction 2004;8(3):203-10. [13] Wu Y-F, Huang Y. Hybrid bonding of FRP to reinforced concrete structures. Journal of Composites for Construction 2008;12(3):266-73. [14] Zhuo J, Wang F, Li T. Application of FRP strap in an innovative prestressed method. Journal of Materials in Civil Engineering 2009;21(4):176-80. [15] Kalfat R, Al-Mahaidi R. Investigation into bond behaviour of a new CFRP anchorage system for concrete utilising a mechanically strengthened substrate. Composite Structures 2010;92:2738-46. [16] Grelle SV, Sneed LH. Review of anchorage systems for externally bonded FRP laminates. International Journal of Concrete Structures and Materials 2013;7(1):17-33. [17] Zhou C-Y, Zhou A-L, Zhou X-T. Parallel rod anchor device and method for flexible sheet material. China: ZL2010105166838, 2012-01-25. (In Chinese). [18] Zhou, C. Y., Yu, Y. N., Xiong, Z., and He, X. J. Flexure tests on narrow concrete beams strengthened with CFRP sheets end-locked by winding around twin-rods. Acta Materiae Compositae Sinica 2018; 35(8), 2216-2221. (in Chinese) [19]Zhou, C. Y., Ren, D., and Cheng, X. N. Shear-strengthening of RC continuous T-beams with spliced CFRP U-strips around bars against flange top. Structural Engineering and Mechanics 2017; 64(1), 135-
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Chao-Yang Zhou performed writing - original draft and conceptualization. Ya-Nan Yu and En-Li Xie performed writing -review and editing; conceptualization.
The authors declare that they have no conflict of interest.
S0263-8223(19)34651-3 https://doi.org/10.1016/j.compstruct.2020.112070 COST 112070
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
8 December 2019 1 February 2020 14 February 2020
Please cite this article as: Zhou, C-Y., Yu, Y-N., Xie, E-L., Strengthening RC beams using externally bonded CFRP sheets with end self-locking, Composite Structures (2020), doi: https://doi.org/10.1016/j.compstruct. 2020.112070
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Strengthening RC beams using externally bonded CFRP sheets with end self-locking Chao-Yang Zhou, Ya-Nan Yu, En-Li Xie* School of Civil Engineering, Central South University, Changsha 410075, China;
Abstract: When laminates of fiber reinforced polymer (FRP) are just bonded on the substrate of reinforced concrete (RC) members for strengthening, debonding failure often happens prematurely and suddenly on the FRP-concrete joints. It is unbeneficial to efficient employment of FRP and reliable service of the structures. This paper introduces a mixed anchoring technique for FRP sheets that combines external bonding (EB) and a novel type of end anchorage. FRP sheets are self-locked at ends by wrapping about a slotted plate in a specified way. Experiments on four concrete beams demonstrated that adding end self-locking to EB can effectively solve the serious problems of usual debonding. End debonding was simply prohibited and intermediate crack debonding was substantially restricted despite occurrence. As a result, not only ultimate strength but also failure ductility of the strengthened specimens was greatly enhanced. The final failure featured by either FRP rupture or concrete crush regardless of debonding degree. Finite element models are then established to simulate the responses of the strengthened beams with hybrid anchored FRP. The numerical results show good agreements with the test observations including debonding process and failure modes. It proves capability and accuracy of the modeling as a useful tool for further research. keywords: Fiber reinforced polymer;Concrete beams; Debonding; Mixed anchorage; Self-locking
1. Introduction High-performance laminates of Fiber reinforced polymer (FRP), especially the carbon fiber reinforced polymer (CFRP) sheets, are widely used in the strengthening of reinforced concrete (RC) structures due to high strength-to-weight ratio, excellent corrosion resistance and easy installation. External bonding (EB) as a traditional way of strengthening only relies on the adhesive layer between the sheet and the component to transfer the interfacial stresses. If the stresses in a RC flexural member strengthened approach the tensile strength of concrete or the bonding ability of the interface, the concrete substrate, the cover or the bonding interface will be very prone to peeling off [1]. Generally named as debonding failure, it is abrupt and immature to limit the efficient use of materials. As was mentioned in [2, 3], the maximum stresses of FRP sheets as final debonding approaches is often merely 10~35 percentage of its ultimate strength. Many efforts have been made to deal with premature debonding. Suitable approaches were explored to predict debonding load, which involves interfacial stress analysis and debonding failure
criterion [4-8]. In addition, helpful measures have been put forward to protect against debonding failure. The common practice is wrapping transverse U-shaped strips of FRP sheet over the longitudinal FRP laminate [9,10]. It is effective in delaying premature debonding and even avoids any bond failure when the strips are provided with adequate number, thickness and layout. But the rational design and the dependability under such harmful environment as moisture, ultraviolet and high temperature are still in question. Among later developments are covering FRP sheets with spiked fanning fiber anchors [11], shooting nails through the specially made FRP plate [12], fixing a series of plates to press the laminate [13], installing wave-shaped anchors to clamp it [14] and so on [15]. Advantages and disadvantages of those methods are discussed in detail by references [3,16]. All in all, they proved useful to control of debonding and promotion of behavior. However, some problems remain pending due to one or more of the following reasons: (1) immature design guideline for debonding prevention; (2) undue damage to the original member; (3) limited scope of engineering application; and (4) time-consuming onsite construction. Therefore，it is desirable to make further investigation or new attempts. An alternative method has been developed in our group to strengthen reinforced concrete members using mechanical anchored FRP. The first author invented an anchorage device that can implement self-locking of the FRP sheet at the end by wrapping around twin rods in parallel in a special manner[17].In the first stage, it was applied for flexural strengthening of narrow RC beams and shear strengthening of RC T-beams, and the results were encouraging [18-19].In this paper,the twin-rod anchorage has been upgraded to become a slotted plate.Such upgradation can decrease the thickness and increase the flexural stiffness of the device in the longitudinal direction of strip, making it compact, very thin and so favorable in application.The slotted plate inter-locks with the sheet end in the patented way of winding and then connects with concrete by pre-planted bolts. Such end anchorage in association with epoxy bond as usual forms hybrid or mixed anchorage (HA). Experiments on RC beams under four-point bending are carried out to verify the superiority of HA over EB in debonding prevention. The numerical analysis is carried out using finite element software package ABAQUS. Available test results were used to validate the models for parameter study in the near future.
2. MIXED ANCHORAGE WITH END SELF-LOCKING OF FRP 2.1 Anchor plate inter-locking with FRP strips The slotted plate (Fig. 1 (a)) is a simple, efficient and patented device to anchor flexible strip. As a millimeter-scale compact anchor, it can be combined with the end of a strip of FRP sheet to realize inter-locking by special winding method which is shown in Fig. 1 (b) and Fig. 2. After the slotted plate is connected with the strengthened component through 2 bolts (Fig. 3), the FRP strip will become the external unbonded reinforcement material of the component, which can be used for rapid retrofit or temporary strengthening. In general, it is recommended to bond the FRP strip along the length of the soffit with the traditional process, because it is beneficial to the coincident working and crack control.
The combination of mechanical fastening and external bonding may be called hybrid or mixed anchorage for FRP strips. In simple words ，hybrid or mixed anchorage equals to bonding plus fastening. There is of course more than one mechanical fastening device and attaching other devices to bonding (e.g. [14]) can also be classified as hybrid anchorage. The slotted plate has obvious characteristics different from others as follows. First of all, it is convenient to obtain more and more tight anchoring effect by just winding round the anchor plate and with the help of self-locking even without (also not exclusive) glue. Then, it is compact and does not need to be assembled as for the wave-shaped anchor. One hole is enough on each side of FRP strip to install the plate, which is conducive to preventing a row of holes very close together from causing local damage to the anchorage zone of the component. Besides, it is ultra-thin, the required thickness is usually a few millimeters only (Fig. 2), so it has little impact on the appearance after strengthening.
Anchor
(a) A slotted plate
FRP Sheet
(b) The winding method
Fig. 1 The slotted plate inter-locking with FRP strip Bolt
Slotted plate
FRP
Fig. 2 End anchor system of the FRP strip
(a) Bottom view
(b) Side view
Fig. 3 Combination of an anchor plate with the beam
The FRP strip is close contact with the slotted plate and may carry large tension. Therefore, the material, size and shape in detail of the slotted plate need to be determined by special research. They are generally related to the thickness, number of layers and strength of the FRP strip. It is equally important to assure high machining accuracy. It is required that sampling inspection be done by a specially devised test of plate-strip assembly for qualified products. The slotted plate used in this test is made of thin steel plate with thickness of 6mm. The test results show that the ultimate stress of CFRP strip in the assembly can reach more than 95% of its ultimate strength.
2.2 Mixed anchorage technology with end self-locking When the reinforced concrete beams are strengthened by EB FRP strips with end self-locking, the construction technology of such mixed anchorage mainly includes the following steps. 1) Detect the steel bars and mark the hole location. According to the strengthening design and the size of the anchor plate, the implantation position of anchor bolts is determined by avoiding the bars in existence. 2) Drill holes and plant bolts. Drill holes in the place of bolt implantation, clean the ash slag in the inner wall of the hole, then inject glue into the hole and quickly implant the anchor bolts, meanwhile pay attention to ensuring their perpendicularity to the substrate. 3) Treat the substrate of the beam. On the surface where the beam and the FRP strip will bond, remove the slurry and degraded concrete until the new surface of the structure is exposed, clean it and keep dry. 4) Cut the strip and let it wrap round the anchor plate (WRAP). According to the distance of anchor holes in the long direction of the beam, the cutting length of the FRP strip is calculated. After cutting, impregnating glue is applied, and the ends of the strip are wound around the slotted plate (WASP). 5) Brush glue and install anchor plate. Brush the glue on the substrate of the beam, and insert the anchor rods into the anchor plates which have been wrapped by the FRP strip, and then tighten with nuts. 6) Roll and slightly pull strip. Press the strip with a rolling brush, pull it slightly at both ends of the strip to keep it straight and add glue when necessary.
2.3 Distinctions of hybrid anchorage with end self-locking Compared with the classical way of externally bonding, it is believed that the hybrid anchorage
in this paper has the following advantages for flexural strengthening of RC beams. 1) It can directly prevent the end debonding. This is because the anchor plate can help the FRP strip undertake substantial longitudinal tension at the ends of bond line, and thus greatly alleviate the concentration of interfacial shear stresses. If necessary, inward normal stresses can be provided to resist the outward debonding. 2) It can effectively inhibit the later development of the debonding due to intermediate cracks (IC), and then improve the ductility and ultimate capacity as well. As to delay the IC debonding, it is basically harmless, though possibly less useful than to restrain the end debonding. 3) It can save a lot of solidifying time of the epoxy layer as quick drying glue can be chosen for planting bolts and curing the bond line without disturbance is unnecessary. So it is especially suitable for bridge strengthening on busy traffic trunk lines and other emergency rehabilitation. 4) It can relax the high dependence on the strength of concrete and hence break through the limitation to the applicability of EB strengthening. Points 1) and 2) mentioned above will be verified by experiments in this paper. The point 4) has been proved in engineering practice. In 2014, several cultural relic buildings in Changsha, Hunan Province, China needed to be retrofitting and a large number of floor slabs were designed to be strengthened with EB CFRP sheets. However, the normal tensile bond strength could not meet the requirements of Chinese code due to deterioration of concrete performance. After a special demonstration, it was decided to attach slotted plates at two ends of the FRP strips to ensure safety and durability. The reason is that the anchor bolt with slotted plate can transfer the forces required by the FRP strip to the deep concrete, not just the substrate and cover of concrete. In the conventional approach of EB, however, the concrete strength is almost always the dominant factor for the detachment when adhesive of high quality is used.
3. Experimental investigation 3.1 Specimens and materials In the experimental program, four beams were tested including one unstrengthened specimen as reference. Among the three beams strengthened with CFRP sheets, one was strengthened by externally bonding and the other two by mixed anchorage with one or two layers of sheets. As shown in Fig. 4, all of the specimens were simply supported and tested in four-point loading. They have the same configuration, internal reinforcement and loading pattern. Their length, width and depth of section were 3200 mm, 250 mm and 300 mm respectively. Two longitudinal steel bars with 16 mm diameter were put near the beam bottom to resist tension, which concrete cover was 25 mm thick, area percentage was 0.6%. Steel stirrups with 8 mm diameter were supplied over the whole span at a center-to-center spacing of 100 mm to avoid shear failure. The clear span, the shear span, and the effective depth of section were 3000 mm, 1200 mm, and 267 mm, respectively.
All specimens were cast from a single batch of commercial concrete. The compressive strength for concrete cubes with side length of 150 mm achieved an average value of 35.6 MPa. Plain bars were used for stirrups and in the compression zone, and deformed bars were used to bear tension. Unidirectional continuous CFRP sheets (Sigma T700SC) and epoxy resin (Good-bond JN-C3P) were used for strengthening. The geometrical parameters and material properties are given in Table 1. Table 1 Parameters of rebars and FRP Diameter Materials
D,
Elastic
Sectional area
mm2
modulus
A, mm2
Yield strength
Ultimate strength
fyt, MPa
fuk, MPa
E, GPa
Stirrups
8
50.3
210
399.05
596.51
Compression bars
10
78.5
210
401.17
587.68
Tension bars
16
201.1
200
538.16
656.12
—
230
—
3319
CFRP sheets
0.167 mm (thickness)
P/2
P/2
300
2 10
31 8@100
Tension bars
100
300 275
250 2 16
Stirrups
Compression bars
600 3200
1200
1200
2 10 8@100 2 16
100
Fig. 4 Dimensions, reinforcements and loading pattern of beams (Unit: mm)
Table 2 presented the variables in detail according to strengthening schemes of the beams. The control specimen B1 is a reinforced concrete beam. Specimens B2 and B3 were strengthened with one ply of externally-bonded (EB) or hybrid anchored (HA) FRP. One more layer of hybrid anchored FRP was added in Specimen B4 as shown in Fig. 5, and the length of the second layer is 600mm shorter than that of the first one. Table 2 Tested parameters of beam specimens (Unit: mm)
Specimen
Strengthening method
CFRP Nominal
B1
Control beam
B2
EB
CFRP Strip width
CFRP Strip length
—
—
—
0.167
100
1800
thickness
B3
HA
0.167
100
1800
B4
HA
0.167×2
100
1800/1200
1200
100
1800
Fig. 5 Strengthening schemes of the beam B4 (Unit: mm)
3.2 Test setup and instruments The test setup is shown in Fig. 6(a). A concentrated force was applied at the midspan of a steel box beam and then distributed to two loading points 600 mm apart on the specimen. The measurement instruments included one force cell to measure the applied load, a linear variable differential transformer at midspan of the specimen to measure the vertical displacement. In order to get strains, a strain gauge was bonded at the midspan of each longitudinal bar in tension. Strain gauges were also bonded on the external surface of FRP strip and the top of beam at the midspan. Furthermore, the generation and propagation of crack were carefully observed. The loading and testing instrumentations include one load cell to measure the applied load, three LVDTs (at both supports, midspan) to measure the vertical displacements, and strain gauges to measure the strains of concrete, rebars and FRP sheet, as shown in Fig. 6(b). All beams were loaded by a hydraulic jack. The strains were collected using a DH3818 data acquisition system.
(a) Test setup of specimen Load cell
Strain gauge
Strain gauge FRP
Bolt
Slotted plate
(b) Layout of strain gauges Fig. 6 Test setup and monitoring devices of specimen
3.3 Experimental phenomena and results Table 3 Comparison of test results
method
Ultimate displacement, mm
Cracking load, kN
B1
—
62.68
26
85
95
—
Concrete crush
B2
EB
25.48
28
90
104
9.47
FRP debonding
B3
HA
56.56
28
92
118
24.21
FRP rupture
B4
HA (2 plies)
51.76
28
95
138
45.26
Concrete crush
Strengthening
Yield Ultimate load Increment of Pu load, kN Pu, kN ξ, %
140 120 100
Load (kN)
Specimens
80
B1, reference beam B2, externally-bonded B3, hybrid anchorage B4, hybrid anchorage, two layers
60 40 20 0
0
10
20
30
40
50
Midspan deflection (mm)
Fig. 7 Load-defection curves of the beams
60
70
Failure mode
The main test results of the four specimens are presented in Table 3. The relationships of load versus midspan deflection are shown in Fig. 7. The behavior of these beams in the process of loading has similarity as well as difference in characteristics, which are depicted as follows and then summarized. The reference beam B1——In the initial stage of loading, the mid-span deflection of the beam increases linearly with the load. When the load was added to 26 kN, the initial crack was found in the pure bending segment, and a turning occurred to the load-deflection curve, implying that the deformation began to accelerate. As the load continued to increase, new cracks gradually emerge, and existing cracks keep extending and widening. Most of them were vertical cracks between the loading points, some were located in the shear span where the bending moment is larger, and a few cracks inclined after entering the web of the beam. When the load reached 85 kN, the tension bar at mid-span yielded with 2690 με strain, the maximum crack width was about 2.2 mm, and the loaddeflection curve showed a significant turning point. After that, the crack width, strain and deflection speedily increased, but new cracks rarely appeared. At the load of 94 kN, creasing and crushing of compressed concrete were found near a loading point within the pure bending segment, signifying the arrival of the ultimate state. The compressive strain of concrete at the mid-span reached 3389 με, the tensile strain of the steel bar was 6504 με, and the maximum crack width was about 3.7 mm. The distribution of cracks is shown in Fig. 8 (a). The EB FRP strengthened beam B2——Before the longitudinal bars yielded, the performance of this strengthened beam was similar to that of the reference beam. The loads at cracking and yielding increased to 28 kN and 90 kN respectively, and the maximum crack width decreased greatly to 0.35 mm when yielding. When it was loaded to about 92 kN, occasional crackling noise, presumably from debonding, were heard, but the naked eye could not see where it happened. The tensile strains of steel bars and CFRP sheets at the mid-span are 3344 με and 3510 με, respectively. The maximum crack width is about 0.6 mm. Since then, the sound of debonding had become more and more loud and frequent. When the load reached 100 kN, it can be seen that the local sheet had slightly detached at 350 mm from a loading point, which signed that intermediate crack debonding had begun. The tensile strains of bars and sheets were 4356 με and 4906 με, respectively. The maximum crack width was about 1.2 mm. At 102 kN, the debonding phenomenon was obvious at 400 mm outside the loading point, and the debonding length was about 200 mm. The tensile strains of bars and sheets were 5268 με and 5980 με, respectively, and the maximum crack width was about 2.1 mm. After the bar yielded, especially after the sheet began to debond, it became difficult to increase and even maintain the load. The main manifestation of the specimen was the rapid development of various deformation and damage. At 104 kN, with a brittle sound, a large area of the sheet suddenly collapsed, as shown in Fig. 8 (b). The load quickly fell back to 87 kN. The tensile strains previously recorded of bars and sheets were 6068 με and 7169 με, respectively. The maximum crack width was 4.2 mm and the length of debonding segment was over 960 mm. The HA FRP strengthened beam B3——This beam behaved like specimen B2 before the yielding of tension steel bars. The cracking load (28 kN) did not change. The load at yielding (92
kN) increased slightly, and the maximum crack width decreased to 0.3 mm. The loads when debonding was occasionally heard, slightly seen and evidently visible increased to 100 kN, 104 kN and 105 kN respectively, implying that the debonding process was delayed, But the main difference from B2 was the performance in the later stage of debonding. When the load reached 118kN, there was a sudden loud noise. At the same time, the load drops sharply to 70 kN. It was found that the sheet had broken 80% at the end of an anchor plate (Fig. 8 (c)), indicating that the peak load had passed. Before the ultimate state, the measured compressive strain of concrete at the top and midspan of the beam was only 1894 με, while the tensile strains of bar and sheet were as high as 8625 με and 12650 με, respectively. The maximum crack width was 3 mm. The sheet detached almost over whole the length. The failure of this beam was featured by sheet rupturing after debonding. Although the ultimate deflection at the midspan is less than that of the reference beam, it is larger than the corresponding value of the EB FRP strengthened beam when the sheet was fracturing. It demonstrated that both the bearing capacity and the ductility of the beam were improved even if the sheet was broken. The HA FRP strengthened beam B4——It has one layer of short strip more than B3. The two specimens behaved alike before rebar yielded. The cracking load (28 kN) was identical, the yielding load (95 kN) was slightly increased, and the loads when debonding was occasionally heard, slightly seen and evidently visible are respectively promoted to 105 kN, 108 kN and 110 kN. The debonding mainly occurred between the anchors of the second strip. When the load reached 138 kN, the concrete in the compression zone was obviously crushed (Fig. 8 (d). The compressive strain of concrete reached 3568 με, and the tensile strains of bars and sheets at the midspan were 8596 με and 11537 με respectively. The maximum crack width was about 3.2 mm. The beam also experienced much larger deflection at ultimate than B2, the EB FRP strengthened specimen. It was meant that the materials were efficiently exploited the brittleness of final failure were overcome. The results showed that the effect of adding one layer of short strip is mainly reflected in the later stage of loading by such as delayed process and shortened zone of debonding, reduced strain difference between bar and sheet, transformed failure mode and increased ultimate bearing capacity.
(a) Crack pattern in B1
(b) Debonded CFRP in B2
(c) Ruptured CFRP in B3
(d) Crushed concrete in B4 Fig. 8 Typical phenomena of damage
In summary, all of the four specimens went through three different phases during the whole process of loading. They were divided by concrete cracking and rebar yielding, corresponding to two turning points in the load-deflection curves. The difference among these beams lay in the behavior after rebar yielding, and in particular, after CFRP debonding for the strengthened beams. They finally failed in various modes, that were concrete crush, FRP debonding, FRP rupture after debonding, and concrete crush after debonding. The failure modes depended on the combining way of FRP with the beam and the amount of FRP. The superiority of hybrid anchorage over usual bonding consisted in avoiding the occurrence of end debonding failure and hindering the later spread of intermediate crack debonding. As a result, the ultimate capacity of beam and the utilization ratio of FRP strength were substantially enhanced. Moreover, the failure displayed improved ductility in spite of debonding. In other words, debonding was no more fatal to a beam bonded with FRP sheet if it was self-locked at ends as above-mentioned. 4. Numerical simulation It is uneasy for experimental observers to promptly capture the information of material damage such as concrete cracking, and especially the initiation and development of FRP debonding. In view of the limitations, numerical analysis is made to simulate failure progress, reveal reinforcement mechanism and thereafter conduct parameter study. It is carried out by using the ABAQUS Finite Element (FE) software [20]. Non-linear FE models are established for the specimens mentioned before. They are three-dimensional (3D) FE models based on the smeared crack approach. To deal with the convergence problems of the numerical solution, a dynamic approach is adopted according to references [21,22]. The test beams can be simplified as a quarter model accounting of the structural symmetry. The FE modeling is described in detail as follows. 4.1 Finite element models In the FE analyses, four parts were first modeled, such as concrete beam, steel bars, FRP sheets and the anchor system. The concrete beam was composed of 8-node reduced integral format 3D solid elements (C3D8R) with the mesh size of 10 mm; Steel bars were modeled of 3D two-node truss elements (T3D2) with the mesh size of 5 mm; the FRP sheet was modeled by using a 3D fournode membrane element M3D4R with the meshes of 2.5 mm; the anchor system, including anchor plate (simplified as a steel plate without a slit) and two anchor bolts, was modeled using C3D8R elements with the meshes of 10 mm. In hybrid-anchored models, the anchor bolts and FRP ends were embedded into the concrete beam and anchor plates, respectively. For the beam strengthened with two layers of CFRP sheet, since the bond strength between them is much stronger than that between FRP and concrete, the relationship between two layers of CFRP sheets was modeled using “Tie” constraint. In addition, symmetry constraint was applied on corresponding symmetry surface of each model. A vertical constraint with no-limited horizontal displacement was adopted on the center line of supporting block. In the loading process, the displacement method was used as the loading method, which was applied at a point coupled with the top surface of the loading block. Fig.9 gives the three-dimensional FE models of simulated strengthened-beam with hybridanchoring system.
(a) FE model of the HA FRP strengthened beam (bottom view)
(b) FE model of hybrid-anchored FRP strip Fig.9 Three-dimensional FE model (a quarter)
4.2. Constitutive relations 4.2.1 Concrete For the concrete, a plastic damage model in FE program was used, which was provided in the ABAQUS software. The model includes the stress-strain relationships and the damage factor. Herein the uniaxial compression stress-strain relationship and the uniaxial tension stress-crack width relationship adopted the universal Saenz model [23] and the Hordijk [24] model, respectively. The damage factor of concrete used the damage model proposed by Lubliner [25] , which assumed that plastic damage only occurred in the softening stage and the stiffness was proportional to cohesion. In addition, the ratio of the ultimate biaxial compressive stress to the ultimate uniaxial compressive stress was set as 1.16; The flow potential eccentricity was set as 0.1; The ratio of the second stress invariant on the tensile meridian to that on the compressive meridian was set as 0.667; and a viscosity parameter of 0.0005 was specified to improve the rate of convergence of FE models. 4.2.2 FRP and steel bars The FRP sheet was assumed to be a linear-elastic-brittle model. To simulate the rupture of FRP, the elastic type was set to be “Lamina”. Except for the longitudinal elastic modulus of the CFRP material, other parameters were quoted according to the literature of Francisco et al.[26], as shown in Table 4. When the stress of FRP elements exceeds the ultimate tensile strength, the elements will automatically fail. Table 4. Elastic properties of CFRP
Material
E1, MPa
E2, MPa
ν12
G12, MPa
G13, MPa
G23, MPa
CFRP sheets
230000
10754
0.266
3648
3648
1601
Note: Ei is the Young’s modulus in the i direction, νij is the Poisson ratio between directions i and
j, Gij is the shear modulus in the ij plane. Longitudinal tension bars were modelled as the linearly reinforced elastic-plastic material, while stirrups and longitudinal compression bars were completely elastic-plastic models. The anchor system was defined the same as steel. 4.2.3 Steel-concrete bond Considering the characteristics of interface bonding between longitudinal steel bars and concrete, the bond behavior between them was modeled by using spring element. However, because of ignoring the slippage between stirrups and concrete, the stirrups were directly embedded into the concrete beam. The elements were defined by building the relationship between interface bond strength and relative slip, which adopts the CEB-FIP (1993) model [27], as shown in Fig.10. 10000
8000
τ(pa)
6000
4000
2000
0
0
1
2
3
4
5
s(mm)
Fig. 10 Model of bond-slip relationship between concrete and steel
4.2.4 FRP-concrete interface In order to simulate the interface debonding between FRP and concrete, the interfacial bondslip was mainly described by defining contact behavior "Cohesive behavior" and "Damage". This method was similar to the zero-thickness bond element, which is insensitive to grid changes and has better convergence. The damage criterion used the “Maximum Separation” criterion and sets a small viscosity coefficient in "Damage Stabilization" to increase convergence. The constitution model of FRP bond-slip (Fig.11) was followed by the simplified Lu model [28], as presented in Eq. (1) – (4).
s (0 s s0 ) max s0 0 ( s s0 )
max 1.5w ft
(1)
(2)
s0 0.0195w ft
w
(3)
2.25 b f / bc
(4)
1.25 b f / bc
Where, s is relative slip,
max is the maximum interfacial shear stress, s0 is the slip corresponding
to the maximum shear stress,
w is the coefficient relating to the width ratio of FRP to the beam,
ft is the tensile strength of concrete, b f is the width of FRP strip, bc is the width of concrete beam. 4.0
τmax
3.5
shear stress(Mpa)
3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.00
s0 0.01
0.02
0.03
0.04
0.05
slip(mm)
Fig. 11 Model of bond-slip relationship between concrete and CFRP strips
4.3 Numerical results and comparisons Fig.
shows the results of FE analysis for the relation of load versus deflection at the mid-
span. The tests results are also shown for comparison. It is clear that the predictions (including failure modes) are in good coincidence with the test data for all the four test specimens.
③
140
④
②
120
FRP rupture
①
Load (kN)
100 FRP debonding
80 60
B1-FE B2-FE B3-FE B4-FE
40 20 0
0
10
20
30
B1-test B2-test B3-test B4-test
40
50
60
70
Midspan deflection (mm) Fig. 12 Load-defection curves from FE and test The crack patterns at respective ultimate loads from the tests and simulations of the four specimens are compared in Fig. 9. The comparisons demonstrate that the FE model provides a reasonable prediction of the crack pattern for all the beams. For beams B1, B3, and B4, it seems that there are more cracks and they have relatively sufficient propagation. Comparatively, cracking and ultimate deflection (also see Table 3 and Fig. 8) as well are under-developed in B2. What inhibits their growth is brittle debonding due to lack of reliable anchorage for FRP.
(a) Specimen B1
(b) Specimen B2
(c) Specimen B3
(d) Specimen B4 Fig. 9 Crack patterns of the specimens from test and simulation
The failure modes of FRP debonding and FRP rupture are shown in Fig. . The debonding failure of beam B2 is accurately predicted. However, the rupture failure of beam B3 in the analysis happens somewhat later than that in the test. This is probably because the FRP strain at rupture is less than 14430 με as stipulated in the simulation according to the given material properties, in spite of exceeding 12650 με. Although failure of concrete crushing cannot be observed from the loaddeflection curve, it can be roughly estimated from the simulated result of strain. Taking specimen B4 as an example, when the mid-span deflection is 52 mm, the maximum compressive strain exceeds 3500 με, which is shown as the black area near a load in Fig. 10 and corresponds to the crushed concrete within the pure bending segment.
Fig. 10 Concrete crushing failure of specimen B4
4.4 Debonding ductility analysis Both experimental and numerical results have shown that the EB FRP strengthened RC beam fails in abrupt debonding with very limited deflection. The HA technology can significantly increase the ultimate deflection of FRP strengthened beams. As can be seen from the simulated curve in Fig. , it has a long debonding process, which is consistent with the results observed in the test. Four key states of beam B3 are selected as an example, in which the debonding process has further development. These significant states are also indicated in Fig.
for reference. The mid-span
deflections of beam B3 in these states are 23.91 mm, 32.10 mm, 39.29 mm and 49.29 mm respectively. Fig. 11 is the distributions of shear stress at FRP-concrete interface. The stresses in gray and black are over 0.001 MPa and below -0.001 MPa, respectively. Those in the green area are between -0.001 MPa to 0.001 MPa, approximately representing the debonded regions. Fig. 12 shows the FRP strain distributions at these four states, in which where FRP remains constant strain can be identified as the debonded segments. Fig. 11 shows that debonding of the FRP strip initiated around the location of the loading point and propagated slowly away from it, especially toward the strip end. As seen from Fig. , the load decreases slightly at all four states, which is due to the redistribution of stress in the FRP strip during the propagation of debonding. On the whole, however, the load is on the rise. It can be seen from the analytical results that hybrid anchorage can effectively restrain
the later development of intermediate crack debonding and improve the ductility and ultimate bearing capacity. Even if the FRP is almost completely debonded from the concrete, it can undertake large tension and the beam can still work normally. Midspan
Load point
(a) State ①
(b) State ②
(c) State ③
(d) State ④ Fig. 11 FRP debonding area at four key states of beam B3 12000 10000
FRP strain (με)
8000 6000
state 1 state 2 state 3 state 4
4000 2000 0
0
100
200
300
400
500
600
700
800
900
Distance from FRP plate end (mm)
Fig. 12 FRP strain distributions at four key states of beam B3
6. Conclusions A novel method with simple device is invented to lock the end of flexible strip. The relevant hybrid anchorage technology of FRP strip is developed and investigated in this paper. The mixed system combines the externally-bonded FRP with the end anchorage. As a new type of mechanical
anchoring system, this end anchorage is simply made of a slotted plate for self-locking of strip and two bolts planted into concrete. The tests demonstrate that this innovation with end self-locking can overcome the main shortcomings in reinforced concrete beams strengthened by externally-bonded FRP. It is by means of avoiding end debonding and restraining the later development of intermediate crack debonding. Therefore, both ultimate capacity and failure ductility are promoted. The final failure mode is either FRP rupture or concrete crush no matter to what extent the detachment spreads. Finite element modeling is also implemented for the beams with hybrid anchored FRP. It is capable of simulating the overall responses of the complicated structural system containing debonding process, failure mode and ultimate strength. Its capability and accuracy are validated by comparisons between the numerical predictions and the test results. This work is a pilot study, and more comprehensive study is required to know the effects of various parameters on the behavior of the strengthened beams and to develop the design guidelines for debonding prevention at last.
Acknowledgements The authors are grateful for the financial support received from the National Natural Science Foundation of China (Grant No. 51878664) and the National Key R&D Program of China (Project No. 2017YFC0703506).
Data Availability Statement All data, models, and code generated or used during the study appear in the submitted article.
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Chao-Yang Zhou performed writing - original draft and conceptualization. Ya-Nan Yu and En-Li Xie performed writing -review and editing; conceptualization.
The authors declare that they have no conflict of interest.