Construction and Building Materials 228 (2019) 116755
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Influence of strain rate on bond behavior of concrete members reinforced with basalt fiber-reinforced polymer rebars Dejian Shen a,b,c,⇑, Chengcai Li a,b, Zhizhuo Feng a,b, Chuyuan Wen a,b, Binod Ojha a,b a
College of Civil and Transportation Engineering, Hohai Univ., No. 1, Xikang Rd., Nanjing 210098, China Jiangsu Engineering Research Center of Crack Control in Concrete, No. 1, Xikang Rd., Nanjing 210098, China c Nanjing Engineering Research Center for Prefabricated Construction, No. 1, Xikang Rd., Nanjing 210098, China b
h i g h l i g h t s Dynamic bond behavior between concrete and BFRP rebars was investigated. A model for bond strength was proposed considering strain rate. A model for dynamic slip corresponding to bond strength was proposed. A model for dynamic bond stress-slip relationship was proposed.
a r t i c l e
i n f o
Article history: Received 13 July 2018 Received in revised form 29 May 2019 Accepted 17 August 2019
Keywords: Basalt fiber-reinforced polymer rebar Strain rate Bond strength Slip Prediction model Bond stress-slip relationship
a b s t r a c t Fiber-reinforced polymer (FRP) rebars are utilized extensively in reinforced concrete structures because of advantageous mechanical and physical properties. The bond behavior of concrete members reinforced with FRP rebars is essential to evaluate the load carrying capacity of concrete members. Although the bond behavior of concrete members reinforced with FRP rebars under static loading has been studied, research studies on the bond behavior of concrete members reinforced with basalt FRP (BFRP) rebars under dynamic loading are still lacking. The bond behaviors of concrete members reinforced with BFRP rebars under different strain rates were investigated. Test results and corresponding analysis showed that: (1) three bond failure modes of concrete members reinforced with BFRP rebars under dynamic loading were observed: crushing of concrete, bond failure at interface between resin and concrete, and bond failure at interface between fiber and resin; (2) the bond strength of concrete members reinforced with BFRP rebars increased as the strain rates increased and a model for bond strength was proposed considering strain rate; (3) the slip corresponding to bond strength decreased as the strain rates increased and a model for the slip corresponding to bond strength of concrete members reinforced with BFRP rebars was proposed considering strain rate; (4) a prediction model for bond stress-slip relationship of concrete members reinforced with BFRP rebars considering strain rate was proposed based on the BPE model which considers concrete cover, transverse confinement, steel rebar spacing and compressive strength of concrete, etc.. The proposed model showed good correlation with experimental results. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Dynamic loading, such as earthquake, blast, traffic loading, wind loading, machinery, etc., is inevitable for concrete structures during their service life [1–5]. The bond behavior of concrete members reinforced with fiber-reinforced polymer (FRP) rebars under dynamic loading is essential for evaluating the load carrying capac-
⇑ Corresponding author at: College of Civil and Transportation Engineering, Hohai Univ., No. 1, Xikang Rd., Nanjing 210098, China. E-mail address:
[email protected] (D. Shen). https://doi.org/10.1016/j.conbuildmat.2019.116755 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
ity of concrete members [6]. In the past few years, FRP has become a research hotspot in civil engineering structures [7–11]. As a newly developed material, Basalt FRP (BFRP) is developing as an alternative to steel rebars [12,13]. BFRP, extracted from crude lava [14], has advantageous mechanical and physical properties [15– 27], such as light weight [15,16], high elastic modulus [19], high corrosion resistance to aggressive environment [20–22], high tensile strength [25], and nonmagnetic properties compared with steel rebars [26,27]. Furthermore, BFRP has good ductility [16] and fire resistance [28] compared with carbon FRP (CFRP). Although the bond behavior of concrete members reinforced with
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D. Shen et al. / Construction and Building Materials 228 (2019) 116755
BFRP rebars under static loading has been studied [29,30], investigation on the bond behavior of concrete members reinforced with BFRP rebars under dynamic loading is still lacking. Therefore, further study is required to better understand the bond behavior of concrete members reinforced with BFRP rebars under dynamic loading. The bond strength of concrete members reinforced with BFRP rebars under static loading increases as the concrete strength increases [29]. Furthermore, the concrete strength increases as the strain rates increase [31–33]. Results in [34] also show that the stiffness of stress–strain relationship curves of concrete in direct compression and tension increases as the strain rates increase. Therefore, the strain rate is a factor that influences the bond strength of concrete members reinforced with BFRP rebars. Results in [35] show that the strain rate has a pronounced influence on the bond strength of concrete members reinforced with deformed steel rebars, and the higher the strain rate is, the greater the bond strength and the bond stiffness are. Result in [36] shows that the bond strength of glass FRP sheet-concrete interface under dynamic loading is larger than the corresponding static value. Result in [37] shows that the bond strength between cement mortar and steel rebars under dynamic loading increases roughly linear with the logarithm of the strain rate. Although the bond strength between steel rebars and concrete [35,37–41], and between FRP sheets and concrete [6,36] under dynamic loading has been studied, investigation on the influence of strain rate on the bond strength of concrete members reinforced with BFRP rebars is still lacking. The bond behavior of reinforced concrete members is also determined by the slip corresponding to bond strength. The open literatures mainly focus on the slip corresponding to bond strength under static loading. A constant value is utilized for evaluating the slip corresponding to bond strength [42], which compares reasonably well with the results reported in [32]. However, a variable value 0.04 d (diameter of steel rebar) is utilized as the slip corresponding to bond strength [43]. Results in [44–46] show that the value of the slip corresponding to bond strength is related to the clear distance between the lugs of the steel rebars. Results in [47,48] show that the slip corresponding to bond strength decreases as the compressive strength of the concrete increases. However, result in [46] shows that compressive strength of concrete has no effect on the slip. Therefore, the results for the value of the slip corresponding to bond strength under static loading are inconsistent, and investigation on the influence of strain rate on the slip corresponding to bond strength of concrete members reinforced with BFRP rebars is still lacking. Due to the significance of the interface between rebars and concrete, academic and experimental studies have been investigated by many researchers. Results in [29] show that the local bond stress-slip relationship of concrete members reinforced with BFRP rebars under static loading includes a ascending branch and a softening branch. The bond stress-slip relationship between basalt fiber concrete and BFRP rebars under static loading varies with the diameter and anchorage length of the BFRP rebars, and is insensitive to the compressive strength of concrete [49]. Also, the bond stress-slip relationship of concrete members reinforced with FRP rebars [50–55], FRP sheets [56] under static loading and BFRP sheets [6], CFRP sheets [36,57] under dynamic loading have been studied. However, experimental investigation on the bond stressslip relationship of concrete members reinforced with BFRP rebars under different strain rates is still lacking. Furthermore, a local bond stress-slip relationship model of concrete members reinforced with BFRP rebars considering strain rate is of fundamental importance to better understand the bond behavior of concrete members reinforced with BFRP rebars under dynamic loading.
Although the relationship between concrete and BFRP rebars has been studied, the bond stress-slip relationship of concrete members reinforced with BFRP rebars considering strain rate is still lacking. Therefore, bond stress-slip relationship of concrete members reinforced with BFRP rebars under different strain rates should be investigated. Pull-out tests on the effect of strain rate on the bond strength, the slip corresponding to bond strength, and the prediction model for bond stress-slip relationship of concrete members reinforced with BFRP rebars considering strain rate were conducted in present study for better understanding the bond behavior of concrete members reinforced with BFRP rebars under dynamic loading. 2. Experimental program 2.1. Mixture proportions and materials The mixture proportion of concrete is shown in Table 1. The cement utilized in the mix was ordinary Portland cement concrete of 42.5 grades. The Blaine fineness of cement utilized was 375 m2/ kg, which was in accordance with China National Standard GB/T 175-2009. The crushed limestone was utilized as coarse aggregate. The maximum particle sizes and apparent density of coarse aggregate were 30 mm, and 2660 kg/m3, respectively. The natural river sand was utilized in the mixture as fine aggregate, and the maximum size and fineness modulus of the fine aggregate were 1.5 mm, and 1.93, respectively. The workability of concrete mixtures was improved by adding liquid polycarboxylate-based superplasticizer, as reported in [58]. Cubic compressive strength was tested on three 150 mm cubic specimens at the age of 28 days after casting in accordance with China National Standard GB/T 500810 2002. The cylinder compressive strength f c could be calculated 0 according to the cubic compressive strength f cu as f c ¼ 0:79 f cu [59,60]. The cubic and cylinder compressive strength were 43.60, and 34.44 MPa, respectively. The splitting tensile strength f spl obtained from test was 3.65 MPa. The relationship between the splitting tensile strength f spl and the cylinder compressive strength 0 0:5 0 f c could be expressed as f spl ¼ 0:59 f c , as reported in [61]. The calculated value from the model proposed in [61] was 3.46 MPa. The result of the deviation from the test and model was 5.2%, which indicated that the test results of splitting tensile strength and cubic compressive strength in present study were reasonable. Fig. 1 shows the surface deformations of BFRP rebar. BFRP rebars with 10 mm nominal diameter were utilized for all specimens in present study. The stress-strain relationship of fiber utilized was linear until failure. The tested elastic modulus, tensile strength, and the ultimate strain of BFRP rebars were 5.2 104 MPa, 1200 MPa, and 2.31%, respectively. The fiber volume fraction of BFRP rebars was 75%, and BFRP rebars had a helical wrapping on the surface. 2.2. Test details All the pull-out specimens were designed with bond length 5 times the nominal diameter of BFRP rebars locating at the center of the molds. This method provides a simple way to investigate the bond behavior of different rebars [62–64]. As shown in Fig. 2, the size of all specimens was designed as 150 mm cube. The unbonded segments of the pull-out specimens were cast by placing two pieces of polyvinyl chloride (PVC) pipe, which was 4 mm larger than the diameter of BFRP rebars and utilized as a bond breaker, insulated around the BFRP rebars. The double-sided adhesive was set into the gaps between BFRP rebars and PVC tubes to prevent the concrete paste from flowing into the PVC tubes and
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D. Shen et al. / Construction and Building Materials 228 (2019) 116755 Table 1 Mixture proportions of concrete (kg/m3). Water
Cement
Fine aggregate
Coarse aggregate
Superplasticizer
168
420
673
1176
1.26
Fig. 1. Surface deformations of BFRP rebar.
the possibility of formation of voids, as reported in [48]. The concrete casting direction can be parallel [65] or perpendicular [66] to the direction of pull-out load for cylinder specimens or cube specimens, respectively. All the specimens were designed as cube in present study. Therefore, the concrete casting direction was perpendicular to the direction of pull-out load in present study and the rebars could be fixed horizontally in the center of the mold, which was in accordance with the method proposed in [66]. Concrete was cast in two layers: firstly, up to the level of BFRP rebars; secondly, the rest of the empty portion. This method could prevent the formation of voids [67]. Compaction of concrete was done by the vibrator ensuring the complete compatibility of the specimens. All the specimens were cured at 95% relative humidity and 20 °C after casting. Fig. 2 shows the detailed schematic drawing of the specimen for the pull-out test. The FRP rebars are linearly elastic and do not yield [68]. The tensile strength of BFRP rebars cannot be tested by conventional friction grips that are utilized for steel rebars to avoid the possibility of premature failures [69]. Therefore, a special anchorage system containing a steel tube filled with an epoxy resin grout was designed to create confinement pressure on the BFRP rebars, which ensured that no slip occurred during the pull-out test, as reported in [70]. The configurations of the twenty specimens are shown in Table 2. Each pull-out specimen is identified with a label ‘‘DXSYn”. D means the diameter of BFRP rebars (i.e. D = diameter of BFRP rebars), X means the diameter of BFRP rebars (i.e. 10 = diameter of BFRP rebars is 10 mm), S means the strain rate (i.e. S = strain rate), Y means the designed strain rate (i.e. 0, 1, 2, and 3 mean that the strain rates are 3.68 10–4, 3.68 10–3, 3.68 10–2, and 3.68 10–1 s1, respectively), and n means the progressive test number.
hydraulic testing machine). For all specimens, a loading rate of 3 kN/min was initially applied for one minute, as reported in [63]. After that, dynamic loading was applied on specimens D10S0, D10S1, D10S2, and D10S3 up to the bond failure at displacement rate of 7 10–5, 7 10–4, 7 10–3, and 7 10–2 m/s, respectively, as reported in [59,60]. The strain rate was calculated through dividing the displacement rate by the sum of bond length (50 mm), the length of PVC pipe (50 mm), and the length of BFRP rebars on the loading end (90 mm). The static strain rate ranges from 0.5 10–5 s1 to 5 10–5 s1 [71]. The strain rate of 3.68 10–4 s1 in present study was close to the range of static strain rate. Therefore, the strain rate of 3.68 10–4 s1 could be considered as fully-static strain rate. The load was measured with electronic load cell attached in the machine. Two linear variable differential transformers (LVDTs) were installed on the surface of concrete and the free end of BFRP rebars, as shown in Fig. 3. The data logger DH5922 was utilized to record the load and displacement for all specimens at a frequency of 50.0 kHz. Each test specimen was broken to visualize the nature of bond failure mechanism at the interface between concrete and BFRP rebars. 3. Test results and discussion The influence of strain rate on the bond behavior of concrete members reinforced with BFRP rebars was analyzed. The bond strength and the slip corresponding to bond strength at free end of BFRP rebars for all the specimens are shown in Table 2. The bond strength is calculated by assuming that the bond stress is uniformly distributed along the bond length and could be calculated from ultimate pull-out load using Eq. (1):
smax ¼
F
ð1Þ
p d la
where smax is the bond strength, MPa; F is the ultimate pull-out load, kN; d is the diameter of BFRP rebars, mm; and la is bond length, mm, and is 50 mm. The free end slip of BFRP rebars is calculated using Eq. (2):
sfree ¼ sbar scon
2.3. Testing procedure Test setup scheme and schematic diagram are shown in the Fig. 3. Pull-out tests were carried out with MTS 322 (a servo-
ð2Þ
where sfree is free end slip of BFRP rebars, mm; sbar is measured displacement on the free end of BFRP rebars, mm; and scon is measured displacement on the surface of concrete, mm.
PVC tube
10
150
Steel tube BFRP rebar Double-sided adhesive
20
50
140
150
(a)
(b)
400
Fig. 2. Details of specimens: (a) photo of mold; (b) schematic drawing of specimen (all units in millimeters).
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D. Shen et al. / Construction and Building Materials 228 (2019) 116755
Table 2 Test results of bond strength and slip corresponding to bond strength. Identification of specimens
Strain rate (s1)
Bond strength (MPa) Individual
Average
Results from Eq. (5)
Deviations (%)
Individual
Average
Results from Eq. (7)
Deviations (%)
D10S0-1 D10S0-2 D10S0-3 D10S0-4 D10S0-5 D10S1-1 D10S1-2 D10S1-3 D10S1-4 D10S1-5 D10S2-1 D10S2-2 D10S2-3 D10S2-4 D10S2-5 D10S3-1 D10S3-2 D10S3-3 D10S3-4 D10S3-5
3.68 10–4
13.87 11.51 12.74 11.69 13.17 12.79 13.71 12.45 12.24 14.45 15.12 13.45 13.84 14.30 13.36 14.01 16.05 14.65 15.88 16.09
12.60
12.60
0
3.15
3.15
0
13.13
13.09
0.3
2.89
2.93
+1.4
14.01
14.05
+0.3
2.61
2.57
1.5
15.34
15.33
0.1
3.10 3.06 3.47 3.16 2.94 3.05 3.27 2.45 2.63 3.03 2.89 2.81 2.35 2.53 2.48 2.24 1.94 2.21 2.20 1.94
2.11
2.12
+0.5
3.68 10–3
3.68 10–2
3.68 10–1
Slip corresponding to bond strength (mm)
MTS frame
Load cell Steel casing
LVDT
LVDT
PVC tube
Specimen BFRP rebar Steel tube Clamp
(a)
(b) Fig. 3. Test setup layout: (a) photo of loading device; (b) loading device.
3.1. Failure modes The bond failure modes of concrete members reinforced with BFRP rebars under different strain rates are shown in Fig. 4. Three failure modes: (1) crushing of concrete, (2) bond failure at interface between resin and concrete, and (3) bond failure at interface between fiber and resin were observed, as reported in [55]. Furthermore, the combined failure modes were mostly appeared at the bond interface between concrete and BFRP rebars. The interfacial failure modes of concrete members reinforced with BFRP rebars under different strain rates were similar. All the specimens failed due to crushing of concrete and partly accompanied by the
stripping off of the fiber surface. For each specimen, brittle failure occurred in concrete members reinforced with BFRP rebars during the pull-out test, and the brittleness was more evident as the strain rates increased. Therefore, the damages on the surface of BFRP rebars were severer for specimens D10S3 than those for specimens D10S2, D10S1 and D10S0, as shown in Fig. 4. Further examination on the failure zone indicated that damages on the BFRP rebars surface were local. In some areas, concrete was stuck on BFRP rebars leaving some undamaged parts on BFRP rebars surface, as shown in Fig. 4(c). However, in some parts the surface of BFRP rebars was peeling off prior to the crushing of concrete, as shown in Fig. 4(d).
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D. Shen et al. / Construction and Building Materials 228 (2019) 116755
Crushing of concrete
(a)
(b)
Bond failure at interface between fiber and resin
Bond failure at interface between resin and concrete
(c)
(d) Fig. 4. Failure modes for different specimens: (a) D10S0; (b) D10S1; (c) D10S2; (d) D10S3.
Fig. 5 shows the bond stress-slip relationships of concrete members reinforced with BFRP rebars under the strain rates of 3.68 10–4, 3.68 10–3, 3.68 10–2, and 3.68 10–1 s1. The comparisons of bond stress-slip relationships for specimens under different strain rates are shown in Fig. 6. The characteristics of the
16
D10S0-1 D10S0-2 D10S0-3 D10S0-4 D10S0-5
12 10 8 6 4
12 10 8 6 4 2
0
0 0
2
4
6
16
8 10 12 14 16 18 20 22 Slip (mm)
D10S2-1 D10S2-2 D10S2-3 D10S2-4 D10S2-5
14 12 10 8 6 4
(b)
8 10 12 14 16 18 20 22 Slip (mm)
6
8 10 12 14 16 18 20 22 Slip (mm)
D10S3-1 D10S3-2 D10S3-3 D10S3-4 D10S3-5
12 10 8 6 4
0 6
4
14
0 4
2
16
2
2
0
18
2
(c) 0
D10S1-1 D10S1-2 D10S1-3 D10S1-4 D10S1-5
14
2
(a)
Bond stress (MPa)
16
Bond stress (MPa)
Bond stress (MPa)
14
curves were similar regardless of strain rate and each phase of the curves was described as follows: The micro slip phase was featured by the almost linear portion of the curve. The bond stress between concrete and BFRP rebars increased rapidly with very small corresponding slip value. Similar phenomenon is also found in [72]. The micro slip phase of bond stress-slip relationship curve between high strength concrete matrix and FRP rebars is characterized by almost linear behavior,
Bond stress (MPa)
3.2. Bond stress-slip relationship of concrete members reinforced with BFRP rebars
(d)
0
2
4
6
8 10 12 14 16 18 20 22 Slip (mm)
Fig. 5. Bond stress-slip relationships for specimens under different strain rates: (a) D10S0; (b) D10S1; (c) D10S2; (d) D10S3.
D. Shen et al. / Construction and Building Materials 228 (2019) 116755
the test results in present study were reasonable. The residual curve indicated that the second peak had lower stiffness (more flat peak) than previous peak, as reported in [29].
18 D10S0-3 D10S1-2 D10S2-4 D10S3-4
Bond stress (MPa)
14 12
3.3. Effect of strain rate on bond strength
10 8 6 4 2 0 0
2
4
6
8
10 12 14 Slip (mm)
16
18
20
22
Fig. 6. Comparisons on bond stress-slip relationships for specimens under different strain rates.
where a rapid increase in the pull-out load causes almost no slip. The slip in this portion is mainly caused by the elastic deformations of materials [73]. With the increase of pull-out load, the pull-out phase occurred due to the local crushing of concrete and cracking propagation, and the bond stress increased nonlinearly with slip. Similar phenomenon is also found in [64]. After micro slip phase, the bond stress-slip relationship curve of concrete members reinforced with GFRP ribbed rebars shows a nonlinear relationship up to the bond strength because of the relative slip between GFRP ribbed rebars and surrounding concrete. During the pull-out phase, the resistance to pull-out strength included two components: the interfacial frictional bond between polymer matrix and fiber; and additional resisting force due to the mechanical deformations on the surface of fiber. Results in [74] show that the mechanical interlock between the steel rebars and surrounding concrete is the most effective component in the bond strength during the pull-out phase. Also, as shown in Fig. 6, the stiffness of this portion increased as the strain rates increased, which was in accordance with the results reported in [38]. After reaching the bond strength, the residual phase occurred, and the bond stress decreased rapidly with the significant slip. Results in [75] show that the bond stress between grout and FRP rebars decreases almost linearly after reaching the peak value of bond stress. Results in [76] also show that the bond stress between high strength concrete and steel rebars decreases with the abrupt increase in slip during the residual phase. The downtrend of bond stress stopped as it was restrained by another neck which was formed due to uneven deformations on the surface of BFRP rebars or crushed concrete along the bond length. Subsequently, the bond stress started increasing resembling the sinusoidal wave until the BFRP rebars were completely pulled out from the specimen. The sinusoidal wave resemblance of the bond stress-slip relationship curves shown in Figs. 5 and 6 were related to the surface deformation of BFRP rebars, which was in accordance with the results reported in [75]. Results in [75] show that the bond stress-slip relationship between grout and FRP rebars shows an oscillating behavior in the residual phase, and the residual load depends not only on the friction resistance but also on the mechanical interlock between grout and FRP rebars. The reoccurrence of the bond strength and its interval largely depended on the pitch of the spirally wounded fiber. Generally, the bond strength at the second peak is assumed as 50% of the first peak [72]. The bond strength at the second peak was about 30% to 60% of the first peak in present study. Therefore,
The bond strength obtained from test was 12.60, 13.13, 14.01, and 15.34 MPa when the strain rate was 3.68 10–4, 3.68 10–3, 3.68 10–2, and 3.68 10–1 s1 for specimens D10S0, D10S1, D10S2, and D10S3, respectively, as shown in Table 2. The bond strength of concrete members reinforced with BFRP rebars increased as the strain rates increased, which was in accordance with the results reported in [38]. Based on the models of bond strength of concrete members reinforced with FRP rebars proposed in [29,62], the relationship between the bond strength smax and the cylinder compressive 0 strength f c could be expressed as follows:
0:5
smax ¼ k f 0c
ð3Þ
The bond strength is a power function of the cylinder compressive strength, and the value of the parameter k varies for different types of FRP rebars. According to CEB-FIP model code 2010 [32], for a given strain rate, a model for calculating the cylinder compressive strength of concrete under dynamic loading could be expressed as follows:
0:014 e_ d ; e_ d 6 30 s1 e_ s
ð4aÞ
1=3 0d fc e_ d ¼ 0:012 ; e_ d > 30 s1 0s e_ s fc
ð4bÞ
0d
fc 0s ¼ fc
0d
0s
where f c and f c are the dynamic and quasi-static cylinder compressive strength, MPa, respectively; e_ d and e_ s are the dynamic and quasi-static strain rate, s1 , respectively; and e_ s is calculated as 30 10–6 s1. To describe the effect of strain rate on the bond strength, the dynamic increase factor (DIF), which is the ratio of the bond strength under dynamic loading to that under quasi-static loading, is derived from Eqs. (3) and (4). The value of DIF could be utilized to illustrate the rate dependence of the bond behavior. As shown in Fig. 7, for the strain rate less than and more than 3.68 10–3 s1, the result of the DIF obtained from the models developed in
1.25 Shen et al [29] and Okelo et al [62] Test data Fitting curve using Eq. (5)
1.20
d s max/τ max
16
1.15
d s = 1+ 0.039(lg(εd / εs ))1.560 τ max τ max
R2 = 0.99
1.10
τ
6
1.05 1.00 0.0
0.5
1.0
1.5 2.0 lg ( ε d / ε s )
2.5
Fig. 7. Relationship between bond strength and strain rates.
3.0
D. Shen et al. / Construction and Building Materials 228 (2019) 116755
7
[29,62] overestimated and underestimated the bond strength in present study, respectively. The deviations of the results of DIF obtained from the models in [29,62] for FRP rebars and test were large. Moreover, the previous models predicted that the DIF increased linearly as the logarithm of the ratio of e_ d to e_ s increased, which could not represent the actual bond behavior of concrete members reinforced with BFRP rebars under dynamic loading. Therefore, the models for FRP rebars could not be utilized to predict the bond strength of concrete members reinforced with BFRP rebars under different strain rates. Fig. 7 shows that the relationship between DIF and the ratio of e_ d to e_ s is nonlinear and could be expressed as follows: c
DIF ¼ sdmax =ssmax ¼ 1 þ bðlgðe_ d =e_ s ÞÞ
ð5Þ
where sdmax and ssmax are the bond strength under dynamic loading and quasi-static loading, respectively; and e_ s is calculated as 3.68 10–4 s1 in present study. Coefficient b and c were determined from the regression analysis with an R2 value of 0.99, and the results were b ¼ 0:039 and
Fig. 8. Relationship between slip corresponding to bond strength and strain rates.
obtained from Eq. (5) was 12.60, 13.09, 14.05, and 15.33 MPa when the strain rate was 3.68 10–4, 3.68 10–3, 3.68 10–2, and 3.68 10–1 s1 for specimens D10S0, D10S1, D10S2, and D10S3, respectively. The results of the deviations from Eq. (5) and the test were 0%, 0.3%, 0.3%, and 0.1%, respectively. The deviations were small. Therefore, Eq. (5) could be utilized to predict the bond strength of concrete members reinforced with BFRP rebars under different strain rates.
the strain rate was 3.68 10–4, 3.68 10–3, 3.68 10–2, and 3.68 10–1 s1 for specimens D10S0, D10S1, D10S2, and D10S3, respectively, as shown in Table 2. The results of the deviations from Eq. (7) and the test were 0%, 1.4%, 1.5%, and 0.5%, respectively. The deviations were small. Therefore, Eq. (7) could be utilized to predict the slip corresponding to bond strength of concrete members reinforced with BFRP rebars under different strain rates.
3.4. Effect of strain rate on the slip corresponding to bond strength
3.5. Prediction model for bond stress-slip relationship under dynamic loading
c ¼ 1:560. As shown in Table 2, the value of the bond strength
For steel rebars, a sophisticated slip corresponding to bond strength model considering the effect of cylinder compressive strength is developed in [47] and could be expressed as follows:
s0 ¼ 0:011dð
1:6 2 d la Þ 0 ðf c =33Þ þ 1 h d
ð6Þ
where s0 is the slip corresponding to bond strength, mm; and h is the height of specimens, mm. The DIF of the slip (DIFs ), which is the ratio of the slip corresponding to the bond strength under dynamic loading to that under quasi-static loading, is derived from experimental and theoretical models using Eqs. (4) and (6). The slip corresponding to bond strength of concrete members reinforced with BFRP rebars under strain rate of 3.68 10–1 s1 from test in present study was 2.11 mm, while the slip corresponding to bond strength obtained from the model proposed in [47] was 2.93 mm. The deviations of the results obtained from the model in [47] for steel rebars and the test were 38.9%. The deviations were large. Furthermore, the value of DIFs obtained from model proposed in [47] overestimated that in present study, as shown in Fig. 8. Therefore, the models proposed in [47] for steel rebars could not be utilized to predict the slip corresponding to the bond strength of concrete members reinforced with BFRP rebars under different strain rates. Fig. 8 shows that the relationship between DIFs and the ratio of e_ d to e_ s is nonlinear and could be expressed as follows:
DIFs ¼ sd0 =ss0 ¼ 1 mðlgðe_ d =e_ s ÞÞ
n
ð7Þ
where sd0 and ss0 are the slip corresponding to bond strength under dynamic loading and quasi-static loading, respectively. Coefficient m and n were determined from the regression analysis with an R2 value of 0.99, and the results were m ¼ 0:070 and n ¼ 1:401. The value of the slip corresponding to bond strength obtained from Eq. (7) was 3.15, 2.93, 2.57, and 2.12 mm when
The well-known BPE model was firstly developed for steel rebars and then utilized to represent the local bond stress-slip relationship of FRP rebars. Therefore, the BPE model could be utilized to analyze the bond stress-slip relationship of concrete members reinforced with BFRP rebars under dynamic loading in present study. The parameters in the BPE model were calibrated according to the test results to describe the bond behavior of BFRP rebars under different strain rates. The BPE model proposed in [42] has been utilized for describing the bond stress-slip relationship of FRP rebars effectively. The ascending branch of the BPE model could be expressed as follows:
a sd sd ¼ ; 0 6 sd 6 sd0 sdmax sd0
ð8Þ
where sd and sd are bond stress and its corresponding slip value, respectively, at any stage of loading; a is a curve-fitting parameter and the values of a must be from 0 to 1 to obtain physically meaningful results. The parameter a is evaluated by equating the areas Aa underneath the ascending branch of the experimental curve [30,77], which could be expressed as follows:
Z Aa ¼ 0
sd0
sdmax
a s sd sd ds ¼ max 0 1þa sd0
ð9Þ
Fig. 9 shows the relationship between parameter a and strain rates. The value of parameter a decreased as the strain rate increased. The value of average parameter a was 0.411, 0.307, 0.269, and 0.248 when the strain rate was 3.68 10–4, 3.68 10– 3 , 3.68 10–2, and 3.68 10–1 s1 for specimens D10S0, D10S1, D10S2, and D10S3, respectively, as shown in Table 3. The relationship between the coefficient a and the logarithm of the ratio of e_ d to e_ s was linear and could be expressed as follows:
a ¼ a0 a1 lgðe_ d =e_ s Þ
ð10Þ
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D. Shen et al. / Construction and Building Materials 228 (2019) 116755
0.50 Test data
Parameter p
0.45
P = 0.371
0.40 0.35 0.30 0.25 0.0
Fig. 9. Relationship between parameter a and strain rates.
Coefficient a0 and a1 were determined from the regression anal-
1.0
1.5 2.0 lg ( ε d / ε s )
2.5
3.0
Fig. 10. Relationship between parameter p and strain rates.
ysis with an R2 value of 0.82, and the results were a0 ¼ 0:388 and a1 ¼ 0:053. As shown in Table 3, the value of the parameter a obtained from Eq. (10) was 0.388, 0.335, 0.282, and 0.229 when the strain rate was 3.68 10–4, 3.68 10–3, 3.68 10–2, and 3.68 10–1 s1 for specimens D10S0, D10S1, D10S2, and D10S3, respectively. The results of the deviations from Eq. (10) and the test were 5.6%, 9.1%, 4.8%, and 7.7%, respectively. The deviations were small. Therefore, Eq. (10) could be utilized to predict the parameter a under different strain rates. Furthermore, the second branch proposed in the BPE model showed that the bond strength was constant as the slip increased. A linear descending branch occurred afterwards. However, experimental bond stress-slip relationship curves of FRP bars showed a lack of the second branch in the BPE model. Therefore, the modified BPE model with the same ascending branch in the BPE model and a softening branch has been developed in [77]. The linear softening branch in the modified BPE model could be expressed as follows:
sd sd ¼ 1 p d 1 ; sd > sd0 sdmax s0
0.5
ð11Þ
where p is a parameter obtained from the regression analysis on the test results, which represents the slope of the softening branch. The average parameter p was 0.488, 0.315, 0.290, and 0.390 when the strain rate was 3.68 10–4, 3.68 10–3, 3.68 10–2, and 3.68 10–1 s1 for specimens D10S0, D10S1, D10S2, and D10S3, respectively, as shown in Table 3. Fig. 10 shows the relationship between the parameter p and strain rates. The average value of parameter p for specimens under different strain rates was 0.371. The parameter p utilized in [29] ranges from 0.256 to 0.404. The result of parameter p in present study was in the range of the result in [29]. Therefore, the result of the parameter p in present study was reasonable.
Substituting Eq. (10) into Eq. (8) and combining Eqs. (5), (7), and (11), Eq. (12) was obtained as follows: 0:3880:053lgðed =es Þ sd sd ¼ ð dÞ ; 0 6 sd 6 sd0 d smax s0 _
_
ð12aÞ
sd sd ¼ 1 0:371 d 1 ; sd > sd0 sdmax s0
ð12bÞ
sdmax =ssmax ¼ 1 þ 0:039ðlgðe_ d =e_ s ÞÞ1:560
ð12cÞ
sd0 =ss0 ¼ 1 0:070ðlgðe_ d =e_ s ÞÞ
ð12dÞ
1:401
The bond stress-slip relationships for specimens D10S0-3, D10S1-1, D10S2-5, and D10S3-4 obtained from test results and Eq. (12) are shown in Fig. 11. Generally, the predicted curves obtained from Eq. (12) showed good correlation with the experimental results and the deviations of the results of the bond stress-slip relationship obtained from test results and Eq. (12) were small. The model proposed in present study could be utilized to predict bond stress-slip relationship of concrete members reinforced with BFRP rebars under dynamic loading when the diameter of BFRP rebars was 10 mm, the strain rate was less than 3.68 10– 1 1 s , and the surface of BFRP rebars had spiral indentations. Notably, the influence of strain rate on the bond stress-slip relationship of concrete members reinforced with BFRP rebars was investigated in present study. The proposed model could not be verified by other independent research studies and the strain rate of 3.68 10–4 s1 utilized in present study was not in the range of static strain rate, however, it could be utilized to evaluate the load carrying capacity of concrete members reinforced with BFRP rebars under dynamic loading. Further research with lower strain rate (in the range of static strain rate) was necessary to verify the models proposed in present study.
Table 3 Fitting results of parameters a and p. Identification of specimen
D10S0 D10S1 D10S2 D10S3
Strain rate (s1)
–4
3.68 10 3.68 10–3 3.68 10–2 3.68 10–1
Parameter a
Parameter p
Average value
Results from Eq. (10)
Deviations (%)
Average value
Results from Eq. (11)
Deviations (%)
0.411 0.307 0.269 0.248
0.388 0.335 0.282 0.229
5.6 +9.1 +4.8 7.7
0.488 0.315 0.290 0.390
0.371
24.0 +17.8 +27.9 4.9
9
D. Shen et al. / Construction and Building Materials 228 (2019) 116755
22
Test data for D10S0-3 Analytical data for D10S0-3 Test data for D10S1-1 Analytical data for D10S1-1 Test data for D10S2-5 Analytical data for D10S2-5 Test data for D10S3-4 Analytical data for D10S3-4
20 18 Bond stress (MPa)
16 14 12 10 8 6 4 2 0 0
2
4
6 8 Slip (mm)
10
12
14
Fig. 11. Comparisons on bond stress-slip relationships obtained from test data and analytical data for specimens under different strain rates.
4. Conclusions The present study presented the experimental findings on the influence of strain rate on the bond behavior of concrete members reinforced with BFRP rebars. The following conclusions were drawn from the obtained results. (1) Three bond failure modes of concrete members reinforced with BFRP rebars under dynamic loading were observed: crushing of concrete, bond failure at interface between resin and concrete, and bond failure at interface between fiber and resin. Furthermore, the combined failure modes were mostly appeared at the bond interface and the brittleness of bond failure was more evident as the strain rates increased. (2) The bond behavior of concrete members reinforced with BFRP rebars was sensitive to strain rate and the bond strength increased log-nonlinearly as the strain rates increased. A model for predicting the bond strength of concrete members reinforced with BFRP rebars was proposed considering strain rate. (3) The slip corresponding to bond strength decreased considerably as the strain rates increased. A model for predicting the slip corresponding to the bond strength of concrete members reinforced with BFRP rebars was proposed considering strain rate. (4) A model for predicting the bond stress-slip relationship of concrete members reinforced with BFRP rebars considering strain rate was proposed based on the BPE model, which could be utilized to evaluate the load carrying capacity of concrete members reinforced with BFRP rebars under dynamic loading.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The financial support of the National Natural Science Foundation of China (Grant No. 51578215) is gratefully acknowledged. This work is also sponsored by Qing Lan Project of Jiangsu Province. The support of the Fundamental Research Funds for Central
Universities (Grant acknowledged.
No
2017B41114)
is
also
gratefully
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