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Experimental study on bond properties between early-age concrete and deformed steel bars
Construction and Building Materials 236 (2020) 117593
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Experimental study on bond properties between early-age concrete and deformed steel bars Xiaopeng Hu, Gang Peng ⇑, Ditao Niu, Jing Wang School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China
h i g h l i g h t s Bond properties for deformed steel bars in early age concrete were tested. Effects of concrete age and strength grade on the bond properties were analyzed. Bond strength models for deformed steel bar in early age concrete were proposed. Bond stress-slip models for deformed steel bar in early age concrete were proposed. Agreement between proposed models and test data and existing models was achieved.
a r t i c l e
i n f o
Article history: Received 13 August 2019 Received in revised form 3 November 2019 Accepted 11 November 2019
Keywords: Early-age concrete Bond properties Deformed steel bars Bond strength model Bond stress–slip model
a b s t r a c t In this study, the bond properties of deformed steel bars in early-age concrete under monotonic loading was experimentally studied by concentric pull-out tests of specimens with six concrete ages and three concrete strength grades. The mechanisms of bond failure between concrete and deformed steel bars under monotonic loading were analyzed. Based on the mechanisms of bond failure, it was possible to determine a five-segment bond stress-slip constitutive model with folded lines. Moreover, the effects of concrete age and strength grade on the characteristic parameters of the bond stress-slip curves were discussed. The results indicated that for specimens with the same concrete strength grade, the bond stress at each characteristic point and the bond stiffness of each characteristic stage of the bond stress-slip curve present a trend of escalation, whereas the corresponding slip shows a downward trend with increasing concrete age. Moreover, with an increasing concrete strength grade, the bond stress at a characteristic point and the bond stiffness of the characteristic stage increased, whereas the slip corresponding to the bond stress decreased for specimens with the same concrete age. According to the test results, an empirical bond strength model and a five-segment bond stress–slip model of deformed steel bars in early-age concrete were proposed, in consideration of the concrete splitting tensile strength. Thereafter, the accuracy of the proposed models was verified by comparing the proposed models with the test results in this study and those of existing models. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The development of modern construction technology has shown that construction time is to be compressed as much as possible under the premise of ensuring construction quality, thereby requiring that concrete structural members can bear certain external loads at an early stage [1–2]. Loading on early concrete structures may not only cause concrete cracking [3], resulting in a deterioration of bond strength [4], but may also affect the safety of the concrete structure in the construction period [5–7]. Control⇑ Corresponding author. E-mail address: [email protected] (G. Peng). https://doi.org/10.1016/j.conbuildmat.2019.117593 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
ling the crack width of early-age concrete is of special importance for ensuring the durability of reinforced concrete structures, especially for a reinforced concrete structure in an aggressive environment [8–11]. Research shows that using a reinforcing steel bar in concrete is an effective way of preventing concrete from cracking, as the bond action between the reinforcement and concrete can restrict the cracking of the concrete to a certain extent [12]. Hence, research work on the bond behavior of early-age concrete and steel bars is pertinent to evaluating the concrete cracking tendency, and is crucial for improving the durability of concrete structures. Bond properties are the preconditions for the monolithic action in concrete and reinforcing steel bars [13]. Over the past years, several investigations on the bond behavior of deformed steel bars
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X. Hu et al. / Construction and Building Materials 236 (2020) 117593
in concrete under service periods have been conducted, and various bond strength models and bond stress-slip constitutive models have been proposed based on the test results [14–16]. As the main component of the bond resistance, the mechanical interaction between the transverse ribs of deformed steel bars and the concrete mainly depends on the surface topography of the steel bars and the mechanical properties of the surrounding concrete [17– 18]. Generally, the mechanical properties of concrete increase exponentially with increasing concrete age [19]. Thus, the bond strength models and bond stress-slip constitutive models of deformed steel bars in early-age concrete may be different than those assumed for 28-day-old concrete [20]. Accurate bond strength and bond stress-slip models of early-age concrete and reinforced steel bars can contribute to analyzing the timevarying characteristics of the bearing capacity of reinforced concrete structures, shortening the construction period scientifically, and evaluating the safety of reinforced concrete structures during the construction period. The bond behavior between early-age concrete and reinforcing steel bars has been preliminarily studied. Song et al [21] found that the bond stress-slip curves exhibited larger bond stress and had steeper descending branches, whereas the slip corresponding to the peak bond stress and the shape of the ascending branch shows no clear law of development with increasing concrete age. Chapman and Shah [20] conducted a pull-out test on deformed bars loaded at various ages, and the results of the tests were compared with the American Concrete Institute (ACI) building codesuggested equation. It was concluded that the ACI bond and development equations were conservative for older concrete, but overestimated the bond strength for very young concrete. Hughes et al. [4] found that concrete age has a profound influence on bond strength, and specifically, that the average bond strength of deformed bars increased significantly faster than the compressive strength or splitting strength of concrete with increasing concrete age. Chen et al. [22] also reported that the bond properties of the deformed steel bars and early-age concrete are significantly affected by the concrete age. This appeared as the ultimate bond stress increased with the increasing concrete age, whereas the corresponding slip was not evidently influenced by the concrete age. Investigations on the bond properties between special early-age concrete and reinforcement have been performed. Pull-out tests of fly ash specimens at an early age were conducted by Hu et al. [23], who found that with increasing concrete age, both the stress at the occurrence of free-end slippage and the maximum bond stress increased. Moreover, they observed a steeper distribution curve of the reinforcement strain along the bond length. Shen et al. [24] experimentally investigated the early-age bond behaviors between high strength concrete (HSC) and deformed steel bars using a pull-out test, and arrived at similar conclusions to those of conventional early-age concrete. Based on the test results, models of the bond strength [4,20–24] and bond stress–slip relationships [4,20,23–24] for deformed steel bars in early-age concrete have been proposed, in consideration of concrete compressive strength f cu (or f c ). However, it is well-known that the bond stress between deformed steel bars and concrete mainly depends on the mechanical interactions between the steel bars and concrete. Essentially, the failure of the bond property is the shear-splitting failure of con-
crete at the steel-concrete interface. Hence, the models of bond strength and bond stress-slip constitutive relationship based on the tensile strength of concrete are more in line with the bond failure mechanism. However, based on the author’s knowledge, models of bond strength and bond stress-slip constitutive relationships between early age concrete and steel bars based on concrete tensile strength have not been proposed. The purposes of this study are to supplement the studies on the bond properties of deformed steel bars in early-age concrete, and to establish models of bond strength and the bond stress-slip constitutive relationship between early-age concrete and steel bars based on the concrete tensile strength. The effects of concrete age and concrete strength grade on the characteristic parameters at four characteristic points of bond stress-slip curves (slip point, splitting point, peak point, and residual point) are discussed. Moreover, bond strength models and bond stress-slip constitutive models between early-age concrete and deformed steel bars are proposed, in consideration of splitting tensile strength. Thereafter, the proposed models are compared with the test results in this study and existing models in the literature [23,24].
2. Experimental programs 2.1. Materials and mix proportions Cement: The binder used in this test was a Type P.O. 42.5 Portland cement. Table 1 presents the physical and mechanical properties of cement. Aggregate: The fine aggregate was medium sand with a fineness modulus greater than 2.9, and the gradation meets the requirements of Area Ⅱ. The apparent density and bulk density of fine aggregate are 2.62 g/cm3 and 1450 kg/m3, respectively. The coarse aggregate was the continuous graded crushed stones with 5– 31.5 mm particle size, of which approximately 60% is 5–20 mm particle size crushed stone and 40% is 20–31.5 mm particle size crushed stone. Superplasticizer: The polycarboxylate based superplasticizer was adopted for the production of the concrete. The desired workability (80 mm slump value) of the concrete could be obtained by changing the addition amount of the superplasticizer, in the range of 1%–2% of the mass of the cementitious materials. The main reinforcements are ordinary hot-rolled deformed steel bars of HRB400 with a diameter of 16 mm, and the spacing between the transverse ribs of the deformed steel bars is approximately 10.40 mm. The mechanical properties test of the deformed steel bar was conducted, and the measured mechanical properties, such as, yield strength f y , ultimate tensile strength f u , modulus of elasticity Es, poisson ratio vs and elongation after breaking d are presented in Table 2. Concrete specimens were prepared with three concrete mixtures (C30, C40, and C50) in this test according to GB50010-2010 [25]. The mix proportions are presented in Table 3 [26].
2.2. Specimens preparation Six types of concrete ages (8 h, 16 h, 1 d, 3 d, 7 d, 28 d) and three types of concrete strength grade (C30, C40, and C50) were considered to investigate the bond properties between the deformed steel bars and early-age concrete. A total of 54 bond specimens were prepared in accordance with the requirements of GB/T 50081-2002 [27]. Specimens with dimensions of 150 mm 150 mm 240 mm were used for the concentric pull-out test. The effective bond length between the concrete and steel bars was five times the diameter of the steel bar (i.e., le = 80 mm), and the bond-free lengths at the loading and free ends were 80 mm and 80 mm, respectively. The bond-free lengths were formed by placing the steel bar inside polyvinyl chloride (PVC) tubes with a diameter of 25 mm, and the PVC tubes and the steel bar were filled with foam glue to prevent the leakage of paste during casting and vibration. To prevent the specimens from splitting, 2Ø 8@80 stirrups were arranged in the effective bonding section. Two linear variable differential transducers (LVDT) were attached to a 70-mm length on the free end to measure the free-
Table 1 Summary of cement physical and mechanical properties. Specific surface area (m2/kg)
351
Water content for normal consistency (%)
25
Ignition loss (%)
2.82
Stability of volume (mm)
2.5
Setting time (h)
Flexural strength (MPa)
Compressive strength (MPa)
Initial
Final
3d
28 d
3d
28 d
2.7
3.7
6.2
8.5
25.3
46.5
3
X. Hu et al. / Construction and Building Materials 236 (2020) 117593 Table 2 Mechanical properties of the main reinforcements. Diameter (mm)
f y (MPa)
f u (MPa)
Es (GPa)
vs
d (%)
16
376
568
202
0.264
16
Table 3 Mix proportions of the concrete. Concrete strength grade
Water cement ratio
C30 C40 C50
0.70 0.55 0.40
Mix proportions (kg/m3) Water
Cement
Medium sand
Crushed stone
Water-reducing admixture
178 160 158
254.3 290.9 395.3
699.2 663.0 584.1
1298.5 1346.1 1362.9
2.03 1.75 1.58
ity greater than 90%, and the molds were stripped off before the beginning of the test. For the specimens with testing ages of 3 d, 7 d, and 28 d, the specimens were cured in standard conditions for 1 d, after which the molds were stripped off, and the specimens were cured in the standard curing room continuously until the testing age. 2.3. Mechanical properties of early-age concrete
Fig. 1. Pull-out test specimen configuration (unit: mm).
end slippage between the concrete and steel bar. The steel bars were extended by 130 mm outside the concrete blocks on the opposite end, for applying the pullout force. The pull-out test specimen configurations are presented in Fig. 1. A self-made wooden mold was used to fabricate the pull-out test specimens. For the specimens with testing ages of 8 h, 16 h, and 1 d, the specimens were maintained in a standard curing room at a temperature of 20 ± 3 °C and a relative humid-
Six concrete cubes, each with a size of 100 mm 100 mm 100 mm, were fabricated from the same concrete batch for each group of pull-out specimens for the mechanical properties tests (three specimens for the cubic compressive test, and three specimens for the splitting tensile strength test). In accordance with the requirements of the China National Standard GB/T 50152-2012 [28], the cubic compressive strength and the splitting tensile strength of the concrete with different testing ages was tested after the specimens was cured under the same conditions as the bond-test specimens. A summary of the measured cubic compressive strength and splitting tensile strength are presented in Table 4. Fig. 2(a) presents the variations of relative cubic compressive strength with respect to the concrete age, and the relationships between the relative splitting tensile strength and concrete age are shown in Fig. 2(b). Besides, the test results of cubic compressive strength and splitting tensile strength of early age concrete by other scholars [24,29–31] are also shown in Fig. 2 for comparison. As shown in Fig. 2, both the cubic compressive strength and the splitting tensile strength increased rapidly in the first 7 d, then increased slowly at the age of 7 to 28 d, which was in good agreement with the results in [19,24,29–33]. Referring to the empirical models proposed in [19,32–33], the relationships between the cubic compressive strength and concrete age and splitting tensile strength and concrete age were proposed with respective correlation coefficients of 0.967 and 0.898.
f cu ðtÞ ¼ f cu ð28Þ
t ; and 2:21 þ 0:91t
f t;s ðtÞ ¼ f t;s ð28Þ
t 1:61 þ 0:96t
ð1Þ
ð2Þ
Table 4 Summary of mechanical properties for the concrete with different ages. Specimen group
C30-8 h C30-16 h C30-1 d C30-3 d C30-7 d C30-28 d C40-8 h C40-16 h C40-1 d C40-3 d C40-7 d C40-28 d C50-8 h C50-16 h C50-1 d C50-3 d C50-7 d C50-28 d
Cubic compressive strength f cu (MPa)
Splitting tensile strength f t;s (MPa)
Sample 1
Sample 2
Sample 3
Mean
S.D. (MPa)
C.V.(%)
Sample 1
Sample 2
Sample 3
Mean
S.D. (MPa)
C.V.(%)
0.58 5.50 10.51 21.06 26.59 33.66 0.65 7.91 11.67 27.15 36.03 39.02 3.08 15.99 24.11 33.42 42.84 57.73
0.54 5.99 10.50 19.89 24.67 32.21 0.81 8.39 10.32 27.78 34.37 44.35 2.81 16.70 24.41 31.55 43.70 52.44
0.54 5.43 9.37 19.53 25.21 37.90 0.68 8.25 11.60 25.87 36.91 41.20 3.20 17.24 24.25 32.25 44.51 54.81
0.55 5.65 9.93 20.16 25.21 34.59 0.71 8.18 11.70 26.77 35.34 41.52 3.03 16.64 24.26 32.97 42.84 54.99
0.02 0.31 0.66 0.80 0.99 2.96 0.09 0.25 0.76 0.98 1.29 2.68 0.20 0.63 0.15 0.95 0.84 2.65
3.87 5.42 6.61 3.98 3.95 8.55 12.32 3.02 6.50 3.65 3.66 6.45 6.51 3.77 0.62 2.87 1.95 4.82
0.09 0.59 0.94 1.85 2.41 3.19 0.14 1.21 1.32 2.26 2.41 3.22 0.35 1.34 2.04 3.12 3.02 3.71
0.13 0.72 0.78 1.72 2.35 2.67 0.21 1.03 1.49 2.52 2.38 3.66 0.42 1.52 2.56 3.26 3.66 3.66
0.12 0.81 0.68 2.03 2.06 3.21 0.18 1.12 1.26 2.41 2.65 3.47 0.45 1.56 2.32 3.31 3.21 4.11
0.11 0.71 0.80 1.87 2.27 3.02 0.18 1.12 1.36 2.40 2.48 3.45 0.41 1.47 2.31 3.23 3.30 3.83
0.02 0.11 0.13 0.16 0.19 0.31 0.04 0.09 0.12 0.13 0.15 0.22 0.05 0.12 0.26 0.10 0.33 0.25
18.37 15.65 16.39 8.34 8.23 10.13 19.88 8.04 8.79 5.45 5.97 6.40 12.62 7.95 11.28 3.05 9.97 6.45
Notes: S.D and C.V. represents the standard deviation and coefficient of variation of the test results, respectively.
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X. Hu et al. / Construction and Building Materials 236 (2020) 117593
Here, t represent the testing age, days; f cu ðtÞ and f cu ð28Þ represent the cubic compressive strength at testing age t (0 < t 28) and at 28 d, MPa; f t;s ðtÞ and f t;s ð28Þ represent the splitting tensile strength at testing age t (0 < t 28) and at 28 d, MPa. Taking the C40 specimens as an example, the test results showed that the cubic compressive strength at the ages of 8 h, 16 h, 1 d, 3 d, 7 d, and 28 d were 0.71, 8.18, 11.70, 26.77, 35.34, and 41.52 MPa, respectively. The deviations from the test and Eq. (1) were 20.9%, 16.76%, 12.08%, 5.81%, 4.15%, and 1.11%, respectively. Moreover, the test splitting tensile strength at the ages of 8 h, 16 h, 1 d, 3 d, 7 d, and 28 d were 0.18, 1.12, 1.26, 2.41, 2.65, and 3.47 MPa, respectively. The deviations from the test and Eq. (2) were 19.79%, 8.73%, 1.29%, 3.95%, 14.46%, and 1.72%, respectively. The fitting accuracy was acceptable and thus, Eq. (1) and Eq. (2) could be used to predict the cubic compressive strength and splitting tensile strength at different ages t (0 < t 28).
2.4. Procedure of concentric pull-out tests As presented in Fig. 3, a device comprising Series 647 hydraulic wedge grips was used to conduct the concentric pull-out tests. Two LVDTs with a range of ±25 mm and a precision of ±5 le were arranged at the free end, to measure the relative slippage between the steel bar and the concrete. The data were collected using a TDS-602 dynamic data-acquisition system. The external force was exerted at the loading end in a displacement control mode at a rate of 0.2 mm/min until failure. The bond stress s can be calculated as the average value over the effective bonding section based on the external force P (N), the diameter of the main steel bar d (mm), and the effective embedment length la (mm), See Eq. (3) [34,35]. The relative slippage s between the steel bar and the concrete at the free end was measured as the average of the measurements of LVDT#1 and LVDT#2.
s¼
P
pdla
ð3Þ
3. Results and discussions 3.1. Typical failure modes of specimens Stirrups in bond-test specimens can delay and restrain the development of radial-longitudinal splitting cracks, preventing the splitting failure of specimens [36]. Hence, pull-out failure was observed for all specimens in this study. As the test progressed, the relative slippage between the steel bar and concrete increased, whereas the external force gradually decreased. When the specimen failed (see Fig. 4), there were no visible cracks on the surface of the specimens. The main deformed steel bar was in the elastic stage, and was pulled out from the concrete gradually. 3.2. Bond stress-slip curves The average bond stress-slip curves of the C30, C40, and C50 specimens with concrete ages of 8 h, 16 h, 1 d, 3 d, 7 d, and 28 d
Fig. 2. Variations of (a) relative cubic compressive strength, (b) relative splitting tensile strength with concrete age.
Fig. 3. (a) Schematic and (b) photograph of the test device.
X. Hu et al. / Construction and Building Materials 236 (2020) 117593
5
bar and concrete under a complete loading cycle. As shown in Fig. 7, the bond failure mechanisms between the deformed steel bar and concrete can be analyzed in five sections, as discussed below.
Fig. 4. Failure modes of pull-out specimens.
under monotonic loading are presented in Fig. 5 and Fig. 6. Observations made on the basis of Figs. 5-6 are as follows: (1) As Fig. 5 shows, the shapes of the bond stress-slip curves appear similar for specimens with different testing ages and concrete strength grades. That is, all of the bond stress-slip curves are composed of ascending branches, descending branches, and horizontal segments, and the ascending branches consist of a micro-slip stage, slip stage, and splitting stage. (2) With regard to the specimens with the same concrete strength grade, see Fig. 5, the slip at peak bond stress shows a declining trend, whereas the peak bond stress increased with the increasing concrete age. Moreover, it can be also seen that, with the increasing concrete age, the bond stress-slip curve exhibited larger peak bond stress, and had steeper ascending and descending branches. Taking the C30 specimens as an example, the peak bond stresses were 0.25, 2.40, 6.20, 10.51, 13.19 and 16.45 MPa, whereas the corresponding slips were 3.98, 2.97, 2.13, 2.52, 2.27, and 2.42 mm, respectively. (3) In addition, with an increasing concrete strength grade from C30 to C50, see Fig. 6, the peak bond stress increased constantly, whereas the slip at peak bond stress decreased for specimens with the same concrete age. Taking the specimens with the testing age of 3 d as an example, the peak bond stresses was 10.51, 8.29, and 9.53 MPa, whereas the corresponding slips were 2.52, 2.46, and 2.35 mm, respectively. 3.3. Mechanisms of bond failure Based on the actual test results, Fig. 7 presents a schematic diagram of the bond stress-slip curves, and a schematic diagram of failure modes for interface concrete between the deformed steel
(1) OA Section: In the early loading stage, the relative slip between the reinforcement and concrete increased linearly with the increasing bond stress. The bond specimen was in the elastic stage, and the bond action between the deformed steel bar and concrete mainly depended on chemical adhesion action produced by cement gel in the concrete on the surface of steel bar. Once the relative slip between the deformed steel bar and concrete occurred (Point A in Fig. 7, and the bond stress at point A is the slip strength ss ), the chemical adhesion action was destroyed completely. The frictional action and the mechanical interaction between the transverse ribs of the deformed steel bar and concrete, constituted the bond resistance. Continuous loading resulted in a diagonal crack in the concrete near the root of the transverse rib, which was reflected in the change of the slope in the bond stress-slip curves. (2) AB section: After the diagonal cracks occurred, as the external force increased, the concrete in front of ribs was gradually extruded into powder, which was then embedded in the root of the ribs in a wedge shape, forming a new extrusion-friction surface. The radial component of the extrusion force and friction force caused circumferential tension of the peripheral concrete, leading to the generation of internal radial cracks. The circumferential tensile stress near the reinforcement was higher, and decreased rapidly with increasing distance from the reinforcing bars. Therefore, the radial splitting cracks only formed near the reinforcement at first, and then extended outward slowly with the increasing external force. Once the radial crack developed outward to a certain extent, however, it rapidly destabilized, and developed to the surface of the specimen. The upward trend of bond stress-slip curve slowed down at this time, and the bond stress reached the splitting strength scr (Point B in Fig. 7). (3) BC section: With the loading proceeding, the crushing zone of the concrete in front of the transverse rib gradually enlarged. The stress of the stirrup increased sharply once the splitting cracks extended to the stirrup position. The propagation of the splitting cracks was restrained by the stirrups. Therefore, the specimen was not split, and the pull-out force could increase continuously to a certain extent. The bond stiffness of the specimen degraded, forming the splitting stage of the bond stress-slip curve, and the bond stress quickly reached the peak strength su (Point C in Fig. 7).
Fig. 5. Bond stress-slip curves for (a) C30, (b) C40, (c) C50 specimens with different concrete ages.
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X. Hu et al. / Construction and Building Materials 236 (2020) 117593
Fig. 6. Bond stress-slip curves for the specimens with concrete age of (a) 8 h, (b) 16 h, (c) 1 d, (d) 3 d, (e) 7 d, (f) 28 d.
Fig. 7. Mechanisms of bond failure under monotonic loading.
(4) CR section: After the bond stress reached the peak value su , the concrete teeth between the transverse ribs were gradually destroyed by shear compression, and the frictional action between the steel bar and concrete gradually turned into frictional action between concrete and concrete on the shear-compression failure surface. Finally, the concrete particles on the failure surface were gradually flattened, and the concrete fragments were pulled-out, together with the reinforcing bars. The bond stress decreases gradually accompanied the rapidly increased slip between the steel bar and concrete, thereby forming the descending stage on the bond stress-slip curve, and the bond stress reached the residual strength sr (Point R in Fig. 7). (5) RR0 section: Once the bond stress was reduced to the residual strength sr , the bond stress remained basically unchanged with the further-increasing slip. The bond stress-slip curve entered the residual stage, which is reflected as the horizontal segment of a certain length on the bond stress-slip curve.
Fig. 8. (a) Characteristic bond stress-slip curve; and (b) five-segment bond stress-slip constitutive model with folded lines.
7
X. Hu et al. / Construction and Building Materials 236 (2020) 117593
3.4. Bond stress-slip models Based on the aforementioned discussion in Sections 3.2 and 3.3, and as Fig. 8(a) shows, the bond stress-slip curves can be divided into five sections by four characteristic points: the micro-slip stage, slip stage, splitting stage, declining stage, and residual stage [17,18]. Moreover, a five-stage bond-slip constitutive model was determined (see Fig. 8(b)), and a bond stress-slip constitutive relationship between the concrete and deformed steel bar was regressed, as in Eq. (4).
8 > > > > > > <
S Ss
K 1 S;
ss þ K 2 ðS Ss Þ; Ss < S Scr s ¼ scr þ K 3 ðS Scr Þ; Scr < S Su > > > su K 4 ðS Su Þ; Su < S Sr > > > : sr ; S > Sr
ð4Þ
Table 5 presents the characteristic parameters of the bond stressslip curves. These include the bond stress at the slip point (ss ), the slip corresponding to the bond stress at the slip point (Ss ), the bond stiffness of the micro-slip stage (K 1 ¼ ss =Ss ); the bond stress at the splitting point (scr ), the slip corresponding to the bond stress at the slip point (Scr ), the bond stiffness of the slip stage (K 2 ¼ ðscr ss Þ=ðScr Ss Þ); the bond stress at the peak point (su ), the slip at peak bond stress (Su ), the bond stiffness of the splitting stage (K 3 ¼ ðsu scr Þ=ðSu Scr Þ); the bond stress at the residual point (sr ), the slip corresponding to the bond stress at the slip point (Sr =10.40 mm [37]), and the bond stiffness of the descending stage
(K 4 ¼ ðsu sr Þ=ðSr Su Þ). Observations made on the basis of Table 5 are as follows: For specimens with the same concrete strength grades, the bond stress at each characteristic point of the bond stress-slip curve (ss ,scr ,su and sr ) and the bond stiffness of each characteristic stage (K 1 ,K 2 ,K 3 and K 4 ) increased, whereas the slip at characteristic points A, B, and C (Ss ,Scr , and Su ) decreased with the increasing concrete age. Similarly, for specimens with the same concrete ages, with the increasing concrete strength grade, the bond stress ss ,scr ,su , and sr and the bond stiffness K 1 ,K 2 ,K 3 , and K 4 increased, whereas the corresponding slippages Ss ,Scr , and Su decreased. The characteristic parameters of bond stress-slip curves are analyzed in detail in the following four subsections. 3.4.1. Slip point A ðss ; Ss Þ The slip point A ðss ; Ss Þ is the transition point between the micro-slip stage and slip stage. Referring to the conclusion in [16,38], the bond stress at the slip point is approximately 20% of the peak bond stress and thus, the bond stress ss can be calculated as ss ¼ 0:2su . Then, the slip Ss can be determined based on the bond stress ss and the test bond stress-slip curve. Fig. 9 presents the variations of bond stress (ss ), the slip at bond stress (Ss ) and the bond stiffness (K 1 ) of the micro-slip stage of the bond stress-slip curve, with splitting tensile strength (f t;s ). By fitting the experimental data, the bond stress (ss ) and slip values (Ss ) of the characteristic points and the bond stiffness (K 1 ) are obtained using Eqs. (5)–(7):
ss ¼ 0:86f 1:34 t;s
ð5Þ
Table 5 Characteristic parameters of the bond stress–slip curves. Specimen group
ss (MPa)
Ss (mm)
K 1 (MPamm1)
scr (MPa)
Scr (mm)
K 2 (MPamm1)
su (MPa)
Su (mm)
K3 (MPamm1)
sr (MPa)
Sr (mm)
K4 (MPamm1)
C30-8 h C30-16 h C30-1 d C30-3 d C30-7 d C30-28 d C40-8 h C40-16 h C40-1 d C40-3 d C40-7 d C40-28 d C50-8 h C50-16 h C50-1 d C50-3 d C50-7 d C50-28 d
0.05 0.51 1.29 2.13 2.65 3.29 0.14 0.69 1.66 2.61 3.48 4.44 0.18 1.36 1.87 3.43 4.82 5.51
0.51 0.42 0.36 0.29 0.22 0.12 0.38 0.27 0.22 0.19 0.15 0.12 0.42 0.23 0.17 0.14 0.14 0.08
0.11 1.24 3.69 7.36 12.22 28.57 0.37 2.62 7.46 13.71 23.67 38.22 0.45 5.94 11.40 24.74 35.35 66.80
0.20 1.92 4.95 8.40 10.53 13.13 0.52 2.79 6.72 10.64 14.06 17.71 0.73 5.34 7.67 13.67 19.13 21.88
1.96 1.69 1.41 1.23 1.21 0.99 1.83 1.49 1.44 1.43 1.03 0.99 1.41 1.41 1.39 1.20 1.12 0.88
0.07 1.10 3.48 6.84 8.09 11.37 0.26 1.75 4.19 6.54 12.12 15.23 0.56 3.45 4.81 9.95 14.84 20.68
0.25 2.40 6.20 10.51 13.19 16.45 0.64 3.44 8.29 13.15 17.37 21.88 0.91 6.64 9.53 17.01 23.79 27.21
3.98 2.97 2.13 2.52 2.27 2.42 3.48 2.86 2.46 2.52 2.50 1.73 2.71 2.44 2.35 2.44 2.26 1.98
0.03 0.37 1.01 1.77 2.52 2.38 0.08 0.49 1.23 2.40 2.32 2.86 0.14 1.34 2.16 2.44 4.40 4.89
0.16 1.02 1.75 4.15 6.01 5.16 0.47 2.01 4.02 8.39 8.45 9.34 0.58 4.82 4.35 7.36 9.65 7.19
10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40
0.02 0.20 0.63 0.90 1.04 1.52 0.03 0.24 0.67 0.67 1.26 1.79 0.04 0.27 0.75 1.23 1.93 2.52
Fig. 9. Relationships between (a) bond stress at slip point (ss ), (b) slip at slip point (Ss ), (c) bond stiffness of micro-slip stage (K 1 ) and splitting tensile strength (f t;s ).
8
X. Hu et al. / Construction and Building Materials 236 (2020) 117593
Fig. 10. Relationships between (a) bond stress at splitting point (scr ), (b) slip at splitting point (Scr ), (c) bond stiffness of slip stage (K 2 ) and splitting tensile strength (f t;s ).
Ss ¼ 0:10f t;s þ 0:43; and 3:14
K 1 ¼ 0:87f t;s
ð6Þ ð7Þ
3.4.2. Splitting point Bðscr ; Scr Þ Generally, the splitting point Bðscr ; Scr Þ is determined by the inflection point of the bond stress-slip curve. Fig. 10 presents the relationships between the bond stress at splitting point (scr ), the slip at bond stress (Scr ), the bond stiffness (K 2 ) of the slip stage of the bond stress-slip curve, and the splitting tensile strength (f t;s ). These three characteristic parameters of the bond stress-slip curve are obtained using Eqs. (8)–(10), by regression analysis with R2 values of 0.921, 0.803, and 0.881, respectively: 1:33 scr ¼ 3:43f t;s
ð8Þ
Scr ¼ 0:22f t;s þ 1:75; and
ð9Þ
1:72
K 2 ¼ 1:83f t;s
ð10Þ
1:28
K 3 ¼ 0:74f t;s
3.4.4. Residual point Rðsr ; Sr Þ When the relative slip between the steel bar and concrete is approximately equal to the spacing between adjacent transverse ribs of the deformed steel bar, it indicates that the transverse rib has reached the position of the adjacent rib. The load tends to be stable, and the bond stress reaches the residual bond stress at this time [37]. Hence, the net spacing between adjacent transverse ribs of the deformed steel bar is usually regarded as the slip value at the residual point, that is Sr ¼ 10:40 mm. Then, the corresponding bond stress can be determined based on the slip value Sr and the test bond stress-slip curve. The variations of bond stress at the residual point (sr ), and the bond stiffness of the descending stage (K 4 ) of the bond stress-slip curve with the splitting tensile strength (f t;s ) are presented in Fig. 12. By fitting the experimental data, the bond stress (sr ) and bond stiffness (K 4 ) are obtained using Eqs. (14)–(15):
sr ¼ 2:34f 0:91 t;s ; and 3.4.3. Peak point Cðsu ; Su Þ The relationships between peak bond stress (su ), the slip corresponding to peak bond stress (Su ), the bond stiffness (K 3 ) of the splitting stage of the bond stress-slip curve, and the splitting tensile strength (f t;s ) are presented in Fig. 11. The bond stress (su ) and slip values (Su ) of the peak points and the bond stiffness of the splitting stage (K 3 ) are obtained using Eqs. (11)–(13):
su ¼
1:33 4:27f t;s
Su ¼ 0:41lnðf t;s Þ þ 2:78; and
ð11Þ ð12Þ
ð13Þ
1:64
K 4 ¼ 0:24f t;s
ð14Þ ð15Þ
4. Verification of the proposed models To verify the reasonableness of the proposed models, the calculated values obtained using the proposed models and the test results in this study were compared. Moreover, the proposed models in this study were also compared with existing models in literature [23,24].
Fig. 11. Relationships between (a) bond stress at peak point (su ), (b) slip at peak point (Su ), (c) bond stiffness of splitting stage (K 3 ) and splitting tensile strength (f t;s ).
X. Hu et al. / Construction and Building Materials 236 (2020) 117593
9
Fig. 12. Relationships between (a) bond stress at residual point (sr ), (b) bond stiffness of descending stage (K 4 ) and splitting tensile strength (f t;s ).
4.1. Verification of the bond strength models 4.1.1. Comparisons between proposed models and test results in this study The results of the calculated and tested bond strength are presented in Fig. 13, wherein a data point below the diagonal line implies an underestimation of the test results. As shown in Fig. 13, the deviation between the calculated bond strength and tested bond strength is less than 25%. Thus, it can be concluded that the calculation results of bond strength essentially coincide with the test results. 4.1.2. Comparisons between proposed models and existing models As mentioned in Section 1, investigations on the bond properties between early-age concrete and steel bars were conducted in [4,20–24], and several types of calculation models of bond strength were proposed based on the test results. Relevant models for predicting the bond strength are listed below, to verify the reasonableness of the calculation models. An empirical model for calculating the bond strength of deformed steel bars in early-age fly ash concrete without transverse reinforcement was proposed in Hu [23], as follows:
qffiffiffiffiffiffiffiffiffiffiffiffi
su ¼ 1:715 f cu ðtÞ
ð16Þ
Based on the pull-out test result, a model for bond strength between deformed steel bars and early-age high strength concrete was proposed in Shen [24], as follows: 0:7
su ¼ 1:65 ðf 0c ð28ÞÞ ð1 e0:28t Þ
Fig. 13. Comparison of calculated bond strength with test results.
ð17Þ
Fig. 14 presents the variations of test bond strength in this study, the calculated bond strength from Eq. (11), and the calculated bond strength from the proposed bond strength model in [23,24] with concrete age. As shown in Fig. 14, the predicted values calculated by the models proposed in [23,24] for early-age concrete are much less than that calculated by Eq. (11). This is because transverse reinforcement in pull-out specimens can greatly improve the bond properties between the steel bars and concrete [36], while both of the pull-out specimens used in Hu [23] and Shen [24] were not confined by stirrups. Considering that the bond properties between steel bar and high strength concrete are evidently stronger than those between steel bar and ordinary concrete, the calculated bond strength from Eq. (11) is not much greater than that from the models in Shen [24]. 4.2. Verification of the bond stress-slip models 4.2.1. Comparisons between proposed models and test results in this study Based on the aforementioned formulas, the bond stress-slip curves for deformed steel bars in early age concrete were plotted. Fig. 15 presents comparisons between the calculation results of the proposed models (M) and the test results (T) in this study. It can be seen that, although there are some discrepancies between the proposed models and test data, an acceptable level of agreement was observed in their comparisons. 4.2.2. Comparisons between proposed models and existing models By experimentally investigated the early-age bond properties between high strength concrete and deformed steel bars using
Fig. 14. Comparisons on bond strength obtained from proposed models in this study and existing models.
10
X. Hu et al. / Construction and Building Materials 236 (2020) 117593
Fig. 15. Comparisons between proposed models (M) and test results (T) for (a) C30, (b) C40, (c) C50 specimens.
5. Conclusions This paper presents test results for the bond properties of deformed steel bars in early-age concrete. The effects of concrete age and concrete strength grade on bond properties between the deformed steel bars and early-age concrete are considered, and the following conclusions are drawn:
Fig. 16. Comparisons on bond stress-slip curves obtained from proposed models in this study and existing models.
not confined pull-out specimens, Shen [24] also proposed a twostage bond stress-slip constitutive models. Fig. 16 presents the comparisons on bond stress-slip curves obtained from proposed models in this study and models in Shen [24]. As shown, larger bond strengths, larger slip values corresponding to bond strength as well as gentler ascending and descending branches were observed for the bond stress-slip curves obtained from proposed models in this study, which is more consistent with the bond stress-slip curves of the well-confined pull-out specimens. These results can be explained as follows: The development of radiallongitudinal splitting cracks of pull-out specimens can be restrained, and the splitting failure of specimens can be prevented by transverse reinforcement [36]. Hence, compared with the pullout specimens without stirrups, the bond stress-slip curves of well-confined specimens exhibited larger bond strengths and larger corresponding slip values. Moreover, the bond stress between well-confined concrete and steel bars will not decrease immediately after the bond stress reaches the peak value, which reflected in the bond stress-slip curves as the well-confined specimens had a gentler ascending and descending branches. From the results of model verification, it can be concluded that the proposed models in this study are capable of reproducing the bond properties between early-age concrete and deformed steel bars with acceptable accuracy. However, it is important to note that the models proposed in this study are based on a relatively limited number of experimental tests, and are only feasible for the bond properties of a deformed steel bar of HRB400 with a diameter of 16 mm in well-confined early age concrete. Additional experimental studies are still required for enlarging the application range and improving of the accuracy of the models.
(1) For specimens with the same concrete strength grades, the bond stress at each characteristic point of the bond stressslip curve (ss ,scr ,su , and sr ) and the bond stiffness of each characteristic stage (K 1 ,K 2 ,K 3 , and K 4 ) increased, whereas the slip (Ss ,Scr , and Su ) decreased with the increasing concrete age. (2) For specimens with the same concrete ages, with an increasing concrete strength grade from C30 to C50, the bond stress (ss ,scr ,su ,sr ) and the bond stiffness (K 1 ,K 2 ,K 3 ,K 4 ) increased, whereas the corresponding slippage (Ss ,Scr and Su ) decreased. (3) Based on the analysis of the bond properties of specimens with different concrete ages and concrete strength grades, empirical models of the bond strength and bond stress–slip constitutive relationships of deformed steel bars in early-age concrete were established. The comparisons between the proposed models and test results, as well as between the proposed models and existing models, demonstrated that the proposed models in this study were acceptable.
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. Acknowledgements The authors would like to acknowledge the National Natural Science Foundation of China (Grant Nos. 51308441, 51678473, and 51590914) and Program for Changjiang Scholars and Innovative Research Team at the University of China (Grant No. IRT_17R84) for financial support. References [1] D.P. Fang, C.D. Geng, H.Y. Zhu, X.L. Liu, Floor load distribution in reinforced concrete buildings during construction, ACI Struct. J. 98 (2) (2001) 149–156. [2] Y.A. Alvarado, P.A. Calderón, I. Gasch, J.M. Adam, A numerical study into the evolution of loads on shores and slabs during construction of multistorey
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[22] C. Chen, X.B. Song, Experimental research on time-dependent bond behavior between young concrete and reinforcing steel bars, Struct. Eng. 30 (3) (2014) 160–167. [23] X.P. Hu, D.T. Niu, Y.L. Zhang, Experimental research on bond performance of reinforcement and fly ash concrete, J. Build. Struct. 34 (4) (2013) 152–157. [24] D.J. Shen, X. Shi, H. Zhang, X.F. Duan, G.Q. Jiang, Experimental study of earlyage bond behavior between high strength concrete and steel bars using a pullout test, Constr. Build. Mater. 113 (2016) 653–663. [25] MOHURD of the People’s Republic of China. Code for design of concrete structure (GB/T 50010-2010), China Architecture & Building Press, Beijing, China. [26] MOHURD of the People’s Republic of China. Standard for test method of performance on ordinary fresh concrete (GB/T 50080-2002), China Architecture & Building Press, Beijing, China. [27] MOHURD of the People’s Republic of China. Standard for test method of mechanical properties on ordinary concrete (GB/T 50081-2002), China Architecture & Building Press, Beijing, China. [28] MOHURD of the People’s Republic of China. Standard for test method of concrete structures (GB 50152-2012), China Architecture & Building Press, Beijing, China. [29] Z.Q. Xu, Experimental Research on Mechanical Properties of Early Age Concrete Materials and Structures (PhD dissertation), Beijing Jiaotong University, Beijing, China, 2016. [30] B. Chen, Y.B. Cai, J.T. Ding, W.X. Zhang, Measurement of early age concrete elastic modulus based on thermal stress test, J. Build. Mater. 19 (4) (2016) 785–790. [31] W. Jiang, Z.H. Yang, Y. Yong, Compressive creep of lightweight aggregate concrete at early age, J. Build. Mater. 19 (1) (2016) 40–44. [32] B. Sukumar, K. Nagamani, R.S. Raghavan, Evaluation of strength at early age of self-compacting concrete with high volume fly ash, Constr. Build. Mater. 22 (7) (2008) 1394–1401. [33] Committee Euro-International du Beton (CEB-FIP), CEB-FIP Model Code 1990, Thomas Telford, London, 1993. [34] P. Soroushian, K.B. Choi, Local bond of deformed bars with different diameters in confined concrete, ACI Struct. J. 86 (2) (1989) 217–222. [35] S.H. Xu, A.B. Li, H. Wang, Bond properties for deformed steel bar in frostdamaged concrete under monotonic and reversed cyclic loading, Constr. Build. Mater. 148 (2017) 344–358. [36] T.R. Robinson, Influence of transverse reinforcement on shear and bond strength, ACI 62 (3) (1965) 343–362. [37] Comite Euro-International du Beton. Bulletin D’information No. 213/214, CEBFIP Model Code 1990, Concrete structures, Lausanne, 1993. [38] J.L. Zhen, J.P. Zhuang, Experiment research on bond properties between selfcompacting concrete and reinforcement, Eng. Mech. 30 (2) (2013) 112–117.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Experimental study on bond properties between early-age concrete and deformed steel bars Xiaopeng Hu, Gang Peng ⇑, Ditao Niu, Jing Wang School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China
h i g h l i g h t s Bond properties for deformed steel bars in early age concrete were tested. Effects of concrete age and strength grade on the bond properties were analyzed. Bond strength models for deformed steel bar in early age concrete were proposed. Bond stress-slip models for deformed steel bar in early age concrete were proposed. Agreement between proposed models and test data and existing models was achieved.
a r t i c l e
i n f o
Article history: Received 13 August 2019 Received in revised form 3 November 2019 Accepted 11 November 2019
Keywords: Early-age concrete Bond properties Deformed steel bars Bond strength model Bond stress–slip model
a b s t r a c t In this study, the bond properties of deformed steel bars in early-age concrete under monotonic loading was experimentally studied by concentric pull-out tests of specimens with six concrete ages and three concrete strength grades. The mechanisms of bond failure between concrete and deformed steel bars under monotonic loading were analyzed. Based on the mechanisms of bond failure, it was possible to determine a five-segment bond stress-slip constitutive model with folded lines. Moreover, the effects of concrete age and strength grade on the characteristic parameters of the bond stress-slip curves were discussed. The results indicated that for specimens with the same concrete strength grade, the bond stress at each characteristic point and the bond stiffness of each characteristic stage of the bond stress-slip curve present a trend of escalation, whereas the corresponding slip shows a downward trend with increasing concrete age. Moreover, with an increasing concrete strength grade, the bond stress at a characteristic point and the bond stiffness of the characteristic stage increased, whereas the slip corresponding to the bond stress decreased for specimens with the same concrete age. According to the test results, an empirical bond strength model and a five-segment bond stress–slip model of deformed steel bars in early-age concrete were proposed, in consideration of the concrete splitting tensile strength. Thereafter, the accuracy of the proposed models was verified by comparing the proposed models with the test results in this study and those of existing models. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The development of modern construction technology has shown that construction time is to be compressed as much as possible under the premise of ensuring construction quality, thereby requiring that concrete structural members can bear certain external loads at an early stage [1–2]. Loading on early concrete structures may not only cause concrete cracking [3], resulting in a deterioration of bond strength [4], but may also affect the safety of the concrete structure in the construction period [5–7]. Control⇑ Corresponding author. E-mail address: [email protected] (G. Peng). https://doi.org/10.1016/j.conbuildmat.2019.117593 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
ling the crack width of early-age concrete is of special importance for ensuring the durability of reinforced concrete structures, especially for a reinforced concrete structure in an aggressive environment [8–11]. Research shows that using a reinforcing steel bar in concrete is an effective way of preventing concrete from cracking, as the bond action between the reinforcement and concrete can restrict the cracking of the concrete to a certain extent [12]. Hence, research work on the bond behavior of early-age concrete and steel bars is pertinent to evaluating the concrete cracking tendency, and is crucial for improving the durability of concrete structures. Bond properties are the preconditions for the monolithic action in concrete and reinforcing steel bars [13]. Over the past years, several investigations on the bond behavior of deformed steel bars
2
X. Hu et al. / Construction and Building Materials 236 (2020) 117593
in concrete under service periods have been conducted, and various bond strength models and bond stress-slip constitutive models have been proposed based on the test results [14–16]. As the main component of the bond resistance, the mechanical interaction between the transverse ribs of deformed steel bars and the concrete mainly depends on the surface topography of the steel bars and the mechanical properties of the surrounding concrete [17– 18]. Generally, the mechanical properties of concrete increase exponentially with increasing concrete age [19]. Thus, the bond strength models and bond stress-slip constitutive models of deformed steel bars in early-age concrete may be different than those assumed for 28-day-old concrete [20]. Accurate bond strength and bond stress-slip models of early-age concrete and reinforced steel bars can contribute to analyzing the timevarying characteristics of the bearing capacity of reinforced concrete structures, shortening the construction period scientifically, and evaluating the safety of reinforced concrete structures during the construction period. The bond behavior between early-age concrete and reinforcing steel bars has been preliminarily studied. Song et al [21] found that the bond stress-slip curves exhibited larger bond stress and had steeper descending branches, whereas the slip corresponding to the peak bond stress and the shape of the ascending branch shows no clear law of development with increasing concrete age. Chapman and Shah [20] conducted a pull-out test on deformed bars loaded at various ages, and the results of the tests were compared with the American Concrete Institute (ACI) building codesuggested equation. It was concluded that the ACI bond and development equations were conservative for older concrete, but overestimated the bond strength for very young concrete. Hughes et al. [4] found that concrete age has a profound influence on bond strength, and specifically, that the average bond strength of deformed bars increased significantly faster than the compressive strength or splitting strength of concrete with increasing concrete age. Chen et al. [22] also reported that the bond properties of the deformed steel bars and early-age concrete are significantly affected by the concrete age. This appeared as the ultimate bond stress increased with the increasing concrete age, whereas the corresponding slip was not evidently influenced by the concrete age. Investigations on the bond properties between special early-age concrete and reinforcement have been performed. Pull-out tests of fly ash specimens at an early age were conducted by Hu et al. [23], who found that with increasing concrete age, both the stress at the occurrence of free-end slippage and the maximum bond stress increased. Moreover, they observed a steeper distribution curve of the reinforcement strain along the bond length. Shen et al. [24] experimentally investigated the early-age bond behaviors between high strength concrete (HSC) and deformed steel bars using a pull-out test, and arrived at similar conclusions to those of conventional early-age concrete. Based on the test results, models of the bond strength [4,20–24] and bond stress–slip relationships [4,20,23–24] for deformed steel bars in early-age concrete have been proposed, in consideration of concrete compressive strength f cu (or f c ). However, it is well-known that the bond stress between deformed steel bars and concrete mainly depends on the mechanical interactions between the steel bars and concrete. Essentially, the failure of the bond property is the shear-splitting failure of con-
crete at the steel-concrete interface. Hence, the models of bond strength and bond stress-slip constitutive relationship based on the tensile strength of concrete are more in line with the bond failure mechanism. However, based on the author’s knowledge, models of bond strength and bond stress-slip constitutive relationships between early age concrete and steel bars based on concrete tensile strength have not been proposed. The purposes of this study are to supplement the studies on the bond properties of deformed steel bars in early-age concrete, and to establish models of bond strength and the bond stress-slip constitutive relationship between early-age concrete and steel bars based on the concrete tensile strength. The effects of concrete age and concrete strength grade on the characteristic parameters at four characteristic points of bond stress-slip curves (slip point, splitting point, peak point, and residual point) are discussed. Moreover, bond strength models and bond stress-slip constitutive models between early-age concrete and deformed steel bars are proposed, in consideration of splitting tensile strength. Thereafter, the proposed models are compared with the test results in this study and existing models in the literature [23,24].
2. Experimental programs 2.1. Materials and mix proportions Cement: The binder used in this test was a Type P.O. 42.5 Portland cement. Table 1 presents the physical and mechanical properties of cement. Aggregate: The fine aggregate was medium sand with a fineness modulus greater than 2.9, and the gradation meets the requirements of Area Ⅱ. The apparent density and bulk density of fine aggregate are 2.62 g/cm3 and 1450 kg/m3, respectively. The coarse aggregate was the continuous graded crushed stones with 5– 31.5 mm particle size, of which approximately 60% is 5–20 mm particle size crushed stone and 40% is 20–31.5 mm particle size crushed stone. Superplasticizer: The polycarboxylate based superplasticizer was adopted for the production of the concrete. The desired workability (80 mm slump value) of the concrete could be obtained by changing the addition amount of the superplasticizer, in the range of 1%–2% of the mass of the cementitious materials. The main reinforcements are ordinary hot-rolled deformed steel bars of HRB400 with a diameter of 16 mm, and the spacing between the transverse ribs of the deformed steel bars is approximately 10.40 mm. The mechanical properties test of the deformed steel bar was conducted, and the measured mechanical properties, such as, yield strength f y , ultimate tensile strength f u , modulus of elasticity Es, poisson ratio vs and elongation after breaking d are presented in Table 2. Concrete specimens were prepared with three concrete mixtures (C30, C40, and C50) in this test according to GB50010-2010 [25]. The mix proportions are presented in Table 3 [26].
2.2. Specimens preparation Six types of concrete ages (8 h, 16 h, 1 d, 3 d, 7 d, 28 d) and three types of concrete strength grade (C30, C40, and C50) were considered to investigate the bond properties between the deformed steel bars and early-age concrete. A total of 54 bond specimens were prepared in accordance with the requirements of GB/T 50081-2002 [27]. Specimens with dimensions of 150 mm 150 mm 240 mm were used for the concentric pull-out test. The effective bond length between the concrete and steel bars was five times the diameter of the steel bar (i.e., le = 80 mm), and the bond-free lengths at the loading and free ends were 80 mm and 80 mm, respectively. The bond-free lengths were formed by placing the steel bar inside polyvinyl chloride (PVC) tubes with a diameter of 25 mm, and the PVC tubes and the steel bar were filled with foam glue to prevent the leakage of paste during casting and vibration. To prevent the specimens from splitting, 2Ø 8@80 stirrups were arranged in the effective bonding section. Two linear variable differential transducers (LVDT) were attached to a 70-mm length on the free end to measure the free-
Table 1 Summary of cement physical and mechanical properties. Specific surface area (m2/kg)
351
Water content for normal consistency (%)
25
Ignition loss (%)
2.82
Stability of volume (mm)
2.5
Setting time (h)
Flexural strength (MPa)
Compressive strength (MPa)
Initial
Final
3d
28 d
3d
28 d
2.7
3.7
6.2
8.5
25.3
46.5
3
X. Hu et al. / Construction and Building Materials 236 (2020) 117593 Table 2 Mechanical properties of the main reinforcements. Diameter (mm)
f y (MPa)
f u (MPa)
Es (GPa)
vs
d (%)
16
376
568
202
0.264
16
Table 3 Mix proportions of the concrete. Concrete strength grade
Water cement ratio
C30 C40 C50
0.70 0.55 0.40
Mix proportions (kg/m3) Water
Cement
Medium sand
Crushed stone
Water-reducing admixture
178 160 158
254.3 290.9 395.3
699.2 663.0 584.1
1298.5 1346.1 1362.9
2.03 1.75 1.58
ity greater than 90%, and the molds were stripped off before the beginning of the test. For the specimens with testing ages of 3 d, 7 d, and 28 d, the specimens were cured in standard conditions for 1 d, after which the molds were stripped off, and the specimens were cured in the standard curing room continuously until the testing age. 2.3. Mechanical properties of early-age concrete
Fig. 1. Pull-out test specimen configuration (unit: mm).
end slippage between the concrete and steel bar. The steel bars were extended by 130 mm outside the concrete blocks on the opposite end, for applying the pullout force. The pull-out test specimen configurations are presented in Fig. 1. A self-made wooden mold was used to fabricate the pull-out test specimens. For the specimens with testing ages of 8 h, 16 h, and 1 d, the specimens were maintained in a standard curing room at a temperature of 20 ± 3 °C and a relative humid-
Six concrete cubes, each with a size of 100 mm 100 mm 100 mm, were fabricated from the same concrete batch for each group of pull-out specimens for the mechanical properties tests (three specimens for the cubic compressive test, and three specimens for the splitting tensile strength test). In accordance with the requirements of the China National Standard GB/T 50152-2012 [28], the cubic compressive strength and the splitting tensile strength of the concrete with different testing ages was tested after the specimens was cured under the same conditions as the bond-test specimens. A summary of the measured cubic compressive strength and splitting tensile strength are presented in Table 4. Fig. 2(a) presents the variations of relative cubic compressive strength with respect to the concrete age, and the relationships between the relative splitting tensile strength and concrete age are shown in Fig. 2(b). Besides, the test results of cubic compressive strength and splitting tensile strength of early age concrete by other scholars [24,29–31] are also shown in Fig. 2 for comparison. As shown in Fig. 2, both the cubic compressive strength and the splitting tensile strength increased rapidly in the first 7 d, then increased slowly at the age of 7 to 28 d, which was in good agreement with the results in [19,24,29–33]. Referring to the empirical models proposed in [19,32–33], the relationships between the cubic compressive strength and concrete age and splitting tensile strength and concrete age were proposed with respective correlation coefficients of 0.967 and 0.898.
f cu ðtÞ ¼ f cu ð28Þ
t ; and 2:21 þ 0:91t
f t;s ðtÞ ¼ f t;s ð28Þ
t 1:61 þ 0:96t
ð1Þ
ð2Þ
Table 4 Summary of mechanical properties for the concrete with different ages. Specimen group
C30-8 h C30-16 h C30-1 d C30-3 d C30-7 d C30-28 d C40-8 h C40-16 h C40-1 d C40-3 d C40-7 d C40-28 d C50-8 h C50-16 h C50-1 d C50-3 d C50-7 d C50-28 d
Cubic compressive strength f cu (MPa)
Splitting tensile strength f t;s (MPa)
Sample 1
Sample 2
Sample 3
Mean
S.D. (MPa)
C.V.(%)
Sample 1
Sample 2
Sample 3
Mean
S.D. (MPa)
C.V.(%)
0.58 5.50 10.51 21.06 26.59 33.66 0.65 7.91 11.67 27.15 36.03 39.02 3.08 15.99 24.11 33.42 42.84 57.73
0.54 5.99 10.50 19.89 24.67 32.21 0.81 8.39 10.32 27.78 34.37 44.35 2.81 16.70 24.41 31.55 43.70 52.44
0.54 5.43 9.37 19.53 25.21 37.90 0.68 8.25 11.60 25.87 36.91 41.20 3.20 17.24 24.25 32.25 44.51 54.81
0.55 5.65 9.93 20.16 25.21 34.59 0.71 8.18 11.70 26.77 35.34 41.52 3.03 16.64 24.26 32.97 42.84 54.99
0.02 0.31 0.66 0.80 0.99 2.96 0.09 0.25 0.76 0.98 1.29 2.68 0.20 0.63 0.15 0.95 0.84 2.65
3.87 5.42 6.61 3.98 3.95 8.55 12.32 3.02 6.50 3.65 3.66 6.45 6.51 3.77 0.62 2.87 1.95 4.82
0.09 0.59 0.94 1.85 2.41 3.19 0.14 1.21 1.32 2.26 2.41 3.22 0.35 1.34 2.04 3.12 3.02 3.71
0.13 0.72 0.78 1.72 2.35 2.67 0.21 1.03 1.49 2.52 2.38 3.66 0.42 1.52 2.56 3.26 3.66 3.66
0.12 0.81 0.68 2.03 2.06 3.21 0.18 1.12 1.26 2.41 2.65 3.47 0.45 1.56 2.32 3.31 3.21 4.11
0.11 0.71 0.80 1.87 2.27 3.02 0.18 1.12 1.36 2.40 2.48 3.45 0.41 1.47 2.31 3.23 3.30 3.83
0.02 0.11 0.13 0.16 0.19 0.31 0.04 0.09 0.12 0.13 0.15 0.22 0.05 0.12 0.26 0.10 0.33 0.25
18.37 15.65 16.39 8.34 8.23 10.13 19.88 8.04 8.79 5.45 5.97 6.40 12.62 7.95 11.28 3.05 9.97 6.45
Notes: S.D and C.V. represents the standard deviation and coefficient of variation of the test results, respectively.
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Here, t represent the testing age, days; f cu ðtÞ and f cu ð28Þ represent the cubic compressive strength at testing age t (0 < t 28) and at 28 d, MPa; f t;s ðtÞ and f t;s ð28Þ represent the splitting tensile strength at testing age t (0 < t 28) and at 28 d, MPa. Taking the C40 specimens as an example, the test results showed that the cubic compressive strength at the ages of 8 h, 16 h, 1 d, 3 d, 7 d, and 28 d were 0.71, 8.18, 11.70, 26.77, 35.34, and 41.52 MPa, respectively. The deviations from the test and Eq. (1) were 20.9%, 16.76%, 12.08%, 5.81%, 4.15%, and 1.11%, respectively. Moreover, the test splitting tensile strength at the ages of 8 h, 16 h, 1 d, 3 d, 7 d, and 28 d were 0.18, 1.12, 1.26, 2.41, 2.65, and 3.47 MPa, respectively. The deviations from the test and Eq. (2) were 19.79%, 8.73%, 1.29%, 3.95%, 14.46%, and 1.72%, respectively. The fitting accuracy was acceptable and thus, Eq. (1) and Eq. (2) could be used to predict the cubic compressive strength and splitting tensile strength at different ages t (0 < t 28).
2.4. Procedure of concentric pull-out tests As presented in Fig. 3, a device comprising Series 647 hydraulic wedge grips was used to conduct the concentric pull-out tests. Two LVDTs with a range of ±25 mm and a precision of ±5 le were arranged at the free end, to measure the relative slippage between the steel bar and the concrete. The data were collected using a TDS-602 dynamic data-acquisition system. The external force was exerted at the loading end in a displacement control mode at a rate of 0.2 mm/min until failure. The bond stress s can be calculated as the average value over the effective bonding section based on the external force P (N), the diameter of the main steel bar d (mm), and the effective embedment length la (mm), See Eq. (3) [34,35]. The relative slippage s between the steel bar and the concrete at the free end was measured as the average of the measurements of LVDT#1 and LVDT#2.
s¼
P
pdla
ð3Þ
3. Results and discussions 3.1. Typical failure modes of specimens Stirrups in bond-test specimens can delay and restrain the development of radial-longitudinal splitting cracks, preventing the splitting failure of specimens [36]. Hence, pull-out failure was observed for all specimens in this study. As the test progressed, the relative slippage between the steel bar and concrete increased, whereas the external force gradually decreased. When the specimen failed (see Fig. 4), there were no visible cracks on the surface of the specimens. The main deformed steel bar was in the elastic stage, and was pulled out from the concrete gradually. 3.2. Bond stress-slip curves The average bond stress-slip curves of the C30, C40, and C50 specimens with concrete ages of 8 h, 16 h, 1 d, 3 d, 7 d, and 28 d
Fig. 2. Variations of (a) relative cubic compressive strength, (b) relative splitting tensile strength with concrete age.
Fig. 3. (a) Schematic and (b) photograph of the test device.
X. Hu et al. / Construction and Building Materials 236 (2020) 117593
5
bar and concrete under a complete loading cycle. As shown in Fig. 7, the bond failure mechanisms between the deformed steel bar and concrete can be analyzed in five sections, as discussed below.
Fig. 4. Failure modes of pull-out specimens.
under monotonic loading are presented in Fig. 5 and Fig. 6. Observations made on the basis of Figs. 5-6 are as follows: (1) As Fig. 5 shows, the shapes of the bond stress-slip curves appear similar for specimens with different testing ages and concrete strength grades. That is, all of the bond stress-slip curves are composed of ascending branches, descending branches, and horizontal segments, and the ascending branches consist of a micro-slip stage, slip stage, and splitting stage. (2) With regard to the specimens with the same concrete strength grade, see Fig. 5, the slip at peak bond stress shows a declining trend, whereas the peak bond stress increased with the increasing concrete age. Moreover, it can be also seen that, with the increasing concrete age, the bond stress-slip curve exhibited larger peak bond stress, and had steeper ascending and descending branches. Taking the C30 specimens as an example, the peak bond stresses were 0.25, 2.40, 6.20, 10.51, 13.19 and 16.45 MPa, whereas the corresponding slips were 3.98, 2.97, 2.13, 2.52, 2.27, and 2.42 mm, respectively. (3) In addition, with an increasing concrete strength grade from C30 to C50, see Fig. 6, the peak bond stress increased constantly, whereas the slip at peak bond stress decreased for specimens with the same concrete age. Taking the specimens with the testing age of 3 d as an example, the peak bond stresses was 10.51, 8.29, and 9.53 MPa, whereas the corresponding slips were 2.52, 2.46, and 2.35 mm, respectively. 3.3. Mechanisms of bond failure Based on the actual test results, Fig. 7 presents a schematic diagram of the bond stress-slip curves, and a schematic diagram of failure modes for interface concrete between the deformed steel
(1) OA Section: In the early loading stage, the relative slip between the reinforcement and concrete increased linearly with the increasing bond stress. The bond specimen was in the elastic stage, and the bond action between the deformed steel bar and concrete mainly depended on chemical adhesion action produced by cement gel in the concrete on the surface of steel bar. Once the relative slip between the deformed steel bar and concrete occurred (Point A in Fig. 7, and the bond stress at point A is the slip strength ss ), the chemical adhesion action was destroyed completely. The frictional action and the mechanical interaction between the transverse ribs of the deformed steel bar and concrete, constituted the bond resistance. Continuous loading resulted in a diagonal crack in the concrete near the root of the transverse rib, which was reflected in the change of the slope in the bond stress-slip curves. (2) AB section: After the diagonal cracks occurred, as the external force increased, the concrete in front of ribs was gradually extruded into powder, which was then embedded in the root of the ribs in a wedge shape, forming a new extrusion-friction surface. The radial component of the extrusion force and friction force caused circumferential tension of the peripheral concrete, leading to the generation of internal radial cracks. The circumferential tensile stress near the reinforcement was higher, and decreased rapidly with increasing distance from the reinforcing bars. Therefore, the radial splitting cracks only formed near the reinforcement at first, and then extended outward slowly with the increasing external force. Once the radial crack developed outward to a certain extent, however, it rapidly destabilized, and developed to the surface of the specimen. The upward trend of bond stress-slip curve slowed down at this time, and the bond stress reached the splitting strength scr (Point B in Fig. 7). (3) BC section: With the loading proceeding, the crushing zone of the concrete in front of the transverse rib gradually enlarged. The stress of the stirrup increased sharply once the splitting cracks extended to the stirrup position. The propagation of the splitting cracks was restrained by the stirrups. Therefore, the specimen was not split, and the pull-out force could increase continuously to a certain extent. The bond stiffness of the specimen degraded, forming the splitting stage of the bond stress-slip curve, and the bond stress quickly reached the peak strength su (Point C in Fig. 7).
Fig. 5. Bond stress-slip curves for (a) C30, (b) C40, (c) C50 specimens with different concrete ages.
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Fig. 6. Bond stress-slip curves for the specimens with concrete age of (a) 8 h, (b) 16 h, (c) 1 d, (d) 3 d, (e) 7 d, (f) 28 d.
Fig. 7. Mechanisms of bond failure under monotonic loading.
(4) CR section: After the bond stress reached the peak value su , the concrete teeth between the transverse ribs were gradually destroyed by shear compression, and the frictional action between the steel bar and concrete gradually turned into frictional action between concrete and concrete on the shear-compression failure surface. Finally, the concrete particles on the failure surface were gradually flattened, and the concrete fragments were pulled-out, together with the reinforcing bars. The bond stress decreases gradually accompanied the rapidly increased slip between the steel bar and concrete, thereby forming the descending stage on the bond stress-slip curve, and the bond stress reached the residual strength sr (Point R in Fig. 7). (5) RR0 section: Once the bond stress was reduced to the residual strength sr , the bond stress remained basically unchanged with the further-increasing slip. The bond stress-slip curve entered the residual stage, which is reflected as the horizontal segment of a certain length on the bond stress-slip curve.
Fig. 8. (a) Characteristic bond stress-slip curve; and (b) five-segment bond stress-slip constitutive model with folded lines.
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3.4. Bond stress-slip models Based on the aforementioned discussion in Sections 3.2 and 3.3, and as Fig. 8(a) shows, the bond stress-slip curves can be divided into five sections by four characteristic points: the micro-slip stage, slip stage, splitting stage, declining stage, and residual stage [17,18]. Moreover, a five-stage bond-slip constitutive model was determined (see Fig. 8(b)), and a bond stress-slip constitutive relationship between the concrete and deformed steel bar was regressed, as in Eq. (4).
8 > > > > > > <
S Ss
K 1 S;
ss þ K 2 ðS Ss Þ; Ss < S Scr s ¼ scr þ K 3 ðS Scr Þ; Scr < S Su > > > su K 4 ðS Su Þ; Su < S Sr > > > : sr ; S > Sr
ð4Þ
Table 5 presents the characteristic parameters of the bond stressslip curves. These include the bond stress at the slip point (ss ), the slip corresponding to the bond stress at the slip point (Ss ), the bond stiffness of the micro-slip stage (K 1 ¼ ss =Ss ); the bond stress at the splitting point (scr ), the slip corresponding to the bond stress at the slip point (Scr ), the bond stiffness of the slip stage (K 2 ¼ ðscr ss Þ=ðScr Ss Þ); the bond stress at the peak point (su ), the slip at peak bond stress (Su ), the bond stiffness of the splitting stage (K 3 ¼ ðsu scr Þ=ðSu Scr Þ); the bond stress at the residual point (sr ), the slip corresponding to the bond stress at the slip point (Sr =10.40 mm [37]), and the bond stiffness of the descending stage
(K 4 ¼ ðsu sr Þ=ðSr Su Þ). Observations made on the basis of Table 5 are as follows: For specimens with the same concrete strength grades, the bond stress at each characteristic point of the bond stress-slip curve (ss ,scr ,su and sr ) and the bond stiffness of each characteristic stage (K 1 ,K 2 ,K 3 and K 4 ) increased, whereas the slip at characteristic points A, B, and C (Ss ,Scr , and Su ) decreased with the increasing concrete age. Similarly, for specimens with the same concrete ages, with the increasing concrete strength grade, the bond stress ss ,scr ,su , and sr and the bond stiffness K 1 ,K 2 ,K 3 , and K 4 increased, whereas the corresponding slippages Ss ,Scr , and Su decreased. The characteristic parameters of bond stress-slip curves are analyzed in detail in the following four subsections. 3.4.1. Slip point A ðss ; Ss Þ The slip point A ðss ; Ss Þ is the transition point between the micro-slip stage and slip stage. Referring to the conclusion in [16,38], the bond stress at the slip point is approximately 20% of the peak bond stress and thus, the bond stress ss can be calculated as ss ¼ 0:2su . Then, the slip Ss can be determined based on the bond stress ss and the test bond stress-slip curve. Fig. 9 presents the variations of bond stress (ss ), the slip at bond stress (Ss ) and the bond stiffness (K 1 ) of the micro-slip stage of the bond stress-slip curve, with splitting tensile strength (f t;s ). By fitting the experimental data, the bond stress (ss ) and slip values (Ss ) of the characteristic points and the bond stiffness (K 1 ) are obtained using Eqs. (5)–(7):
ss ¼ 0:86f 1:34 t;s
ð5Þ
Table 5 Characteristic parameters of the bond stress–slip curves. Specimen group
ss (MPa)
Ss (mm)
K 1 (MPamm1)
scr (MPa)
Scr (mm)
K 2 (MPamm1)
su (MPa)
Su (mm)
K3 (MPamm1)
sr (MPa)
Sr (mm)
K4 (MPamm1)
C30-8 h C30-16 h C30-1 d C30-3 d C30-7 d C30-28 d C40-8 h C40-16 h C40-1 d C40-3 d C40-7 d C40-28 d C50-8 h C50-16 h C50-1 d C50-3 d C50-7 d C50-28 d
0.05 0.51 1.29 2.13 2.65 3.29 0.14 0.69 1.66 2.61 3.48 4.44 0.18 1.36 1.87 3.43 4.82 5.51
0.51 0.42 0.36 0.29 0.22 0.12 0.38 0.27 0.22 0.19 0.15 0.12 0.42 0.23 0.17 0.14 0.14 0.08
0.11 1.24 3.69 7.36 12.22 28.57 0.37 2.62 7.46 13.71 23.67 38.22 0.45 5.94 11.40 24.74 35.35 66.80
0.20 1.92 4.95 8.40 10.53 13.13 0.52 2.79 6.72 10.64 14.06 17.71 0.73 5.34 7.67 13.67 19.13 21.88
1.96 1.69 1.41 1.23 1.21 0.99 1.83 1.49 1.44 1.43 1.03 0.99 1.41 1.41 1.39 1.20 1.12 0.88
0.07 1.10 3.48 6.84 8.09 11.37 0.26 1.75 4.19 6.54 12.12 15.23 0.56 3.45 4.81 9.95 14.84 20.68
0.25 2.40 6.20 10.51 13.19 16.45 0.64 3.44 8.29 13.15 17.37 21.88 0.91 6.64 9.53 17.01 23.79 27.21
3.98 2.97 2.13 2.52 2.27 2.42 3.48 2.86 2.46 2.52 2.50 1.73 2.71 2.44 2.35 2.44 2.26 1.98
0.03 0.37 1.01 1.77 2.52 2.38 0.08 0.49 1.23 2.40 2.32 2.86 0.14 1.34 2.16 2.44 4.40 4.89
0.16 1.02 1.75 4.15 6.01 5.16 0.47 2.01 4.02 8.39 8.45 9.34 0.58 4.82 4.35 7.36 9.65 7.19
10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40 10.40
0.02 0.20 0.63 0.90 1.04 1.52 0.03 0.24 0.67 0.67 1.26 1.79 0.04 0.27 0.75 1.23 1.93 2.52
Fig. 9. Relationships between (a) bond stress at slip point (ss ), (b) slip at slip point (Ss ), (c) bond stiffness of micro-slip stage (K 1 ) and splitting tensile strength (f t;s ).
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Fig. 10. Relationships between (a) bond stress at splitting point (scr ), (b) slip at splitting point (Scr ), (c) bond stiffness of slip stage (K 2 ) and splitting tensile strength (f t;s ).
Ss ¼ 0:10f t;s þ 0:43; and 3:14
K 1 ¼ 0:87f t;s
ð6Þ ð7Þ
3.4.2. Splitting point Bðscr ; Scr Þ Generally, the splitting point Bðscr ; Scr Þ is determined by the inflection point of the bond stress-slip curve. Fig. 10 presents the relationships between the bond stress at splitting point (scr ), the slip at bond stress (Scr ), the bond stiffness (K 2 ) of the slip stage of the bond stress-slip curve, and the splitting tensile strength (f t;s ). These three characteristic parameters of the bond stress-slip curve are obtained using Eqs. (8)–(10), by regression analysis with R2 values of 0.921, 0.803, and 0.881, respectively: 1:33 scr ¼ 3:43f t;s
ð8Þ
Scr ¼ 0:22f t;s þ 1:75; and
ð9Þ
1:72
K 2 ¼ 1:83f t;s
ð10Þ
1:28
K 3 ¼ 0:74f t;s
3.4.4. Residual point Rðsr ; Sr Þ When the relative slip between the steel bar and concrete is approximately equal to the spacing between adjacent transverse ribs of the deformed steel bar, it indicates that the transverse rib has reached the position of the adjacent rib. The load tends to be stable, and the bond stress reaches the residual bond stress at this time [37]. Hence, the net spacing between adjacent transverse ribs of the deformed steel bar is usually regarded as the slip value at the residual point, that is Sr ¼ 10:40 mm. Then, the corresponding bond stress can be determined based on the slip value Sr and the test bond stress-slip curve. The variations of bond stress at the residual point (sr ), and the bond stiffness of the descending stage (K 4 ) of the bond stress-slip curve with the splitting tensile strength (f t;s ) are presented in Fig. 12. By fitting the experimental data, the bond stress (sr ) and bond stiffness (K 4 ) are obtained using Eqs. (14)–(15):
sr ¼ 2:34f 0:91 t;s ; and 3.4.3. Peak point Cðsu ; Su Þ The relationships between peak bond stress (su ), the slip corresponding to peak bond stress (Su ), the bond stiffness (K 3 ) of the splitting stage of the bond stress-slip curve, and the splitting tensile strength (f t;s ) are presented in Fig. 11. The bond stress (su ) and slip values (Su ) of the peak points and the bond stiffness of the splitting stage (K 3 ) are obtained using Eqs. (11)–(13):
su ¼
1:33 4:27f t;s
Su ¼ 0:41lnðf t;s Þ þ 2:78; and
ð11Þ ð12Þ
ð13Þ
1:64
K 4 ¼ 0:24f t;s
ð14Þ ð15Þ
4. Verification of the proposed models To verify the reasonableness of the proposed models, the calculated values obtained using the proposed models and the test results in this study were compared. Moreover, the proposed models in this study were also compared with existing models in literature [23,24].
Fig. 11. Relationships between (a) bond stress at peak point (su ), (b) slip at peak point (Su ), (c) bond stiffness of splitting stage (K 3 ) and splitting tensile strength (f t;s ).
X. Hu et al. / Construction and Building Materials 236 (2020) 117593
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Fig. 12. Relationships between (a) bond stress at residual point (sr ), (b) bond stiffness of descending stage (K 4 ) and splitting tensile strength (f t;s ).
4.1. Verification of the bond strength models 4.1.1. Comparisons between proposed models and test results in this study The results of the calculated and tested bond strength are presented in Fig. 13, wherein a data point below the diagonal line implies an underestimation of the test results. As shown in Fig. 13, the deviation between the calculated bond strength and tested bond strength is less than 25%. Thus, it can be concluded that the calculation results of bond strength essentially coincide with the test results. 4.1.2. Comparisons between proposed models and existing models As mentioned in Section 1, investigations on the bond properties between early-age concrete and steel bars were conducted in [4,20–24], and several types of calculation models of bond strength were proposed based on the test results. Relevant models for predicting the bond strength are listed below, to verify the reasonableness of the calculation models. An empirical model for calculating the bond strength of deformed steel bars in early-age fly ash concrete without transverse reinforcement was proposed in Hu [23], as follows:
qffiffiffiffiffiffiffiffiffiffiffiffi
su ¼ 1:715 f cu ðtÞ
ð16Þ
Based on the pull-out test result, a model for bond strength between deformed steel bars and early-age high strength concrete was proposed in Shen [24], as follows: 0:7
su ¼ 1:65 ðf 0c ð28ÞÞ ð1 e0:28t Þ
Fig. 13. Comparison of calculated bond strength with test results.
ð17Þ
Fig. 14 presents the variations of test bond strength in this study, the calculated bond strength from Eq. (11), and the calculated bond strength from the proposed bond strength model in [23,24] with concrete age. As shown in Fig. 14, the predicted values calculated by the models proposed in [23,24] for early-age concrete are much less than that calculated by Eq. (11). This is because transverse reinforcement in pull-out specimens can greatly improve the bond properties between the steel bars and concrete [36], while both of the pull-out specimens used in Hu [23] and Shen [24] were not confined by stirrups. Considering that the bond properties between steel bar and high strength concrete are evidently stronger than those between steel bar and ordinary concrete, the calculated bond strength from Eq. (11) is not much greater than that from the models in Shen [24]. 4.2. Verification of the bond stress-slip models 4.2.1. Comparisons between proposed models and test results in this study Based on the aforementioned formulas, the bond stress-slip curves for deformed steel bars in early age concrete were plotted. Fig. 15 presents comparisons between the calculation results of the proposed models (M) and the test results (T) in this study. It can be seen that, although there are some discrepancies between the proposed models and test data, an acceptable level of agreement was observed in their comparisons. 4.2.2. Comparisons between proposed models and existing models By experimentally investigated the early-age bond properties between high strength concrete and deformed steel bars using
Fig. 14. Comparisons on bond strength obtained from proposed models in this study and existing models.
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Fig. 15. Comparisons between proposed models (M) and test results (T) for (a) C30, (b) C40, (c) C50 specimens.
5. Conclusions This paper presents test results for the bond properties of deformed steel bars in early-age concrete. The effects of concrete age and concrete strength grade on bond properties between the deformed steel bars and early-age concrete are considered, and the following conclusions are drawn:
Fig. 16. Comparisons on bond stress-slip curves obtained from proposed models in this study and existing models.
not confined pull-out specimens, Shen [24] also proposed a twostage bond stress-slip constitutive models. Fig. 16 presents the comparisons on bond stress-slip curves obtained from proposed models in this study and models in Shen [24]. As shown, larger bond strengths, larger slip values corresponding to bond strength as well as gentler ascending and descending branches were observed for the bond stress-slip curves obtained from proposed models in this study, which is more consistent with the bond stress-slip curves of the well-confined pull-out specimens. These results can be explained as follows: The development of radiallongitudinal splitting cracks of pull-out specimens can be restrained, and the splitting failure of specimens can be prevented by transverse reinforcement [36]. Hence, compared with the pullout specimens without stirrups, the bond stress-slip curves of well-confined specimens exhibited larger bond strengths and larger corresponding slip values. Moreover, the bond stress between well-confined concrete and steel bars will not decrease immediately after the bond stress reaches the peak value, which reflected in the bond stress-slip curves as the well-confined specimens had a gentler ascending and descending branches. From the results of model verification, it can be concluded that the proposed models in this study are capable of reproducing the bond properties between early-age concrete and deformed steel bars with acceptable accuracy. However, it is important to note that the models proposed in this study are based on a relatively limited number of experimental tests, and are only feasible for the bond properties of a deformed steel bar of HRB400 with a diameter of 16 mm in well-confined early age concrete. Additional experimental studies are still required for enlarging the application range and improving of the accuracy of the models.
(1) For specimens with the same concrete strength grades, the bond stress at each characteristic point of the bond stressslip curve (ss ,scr ,su , and sr ) and the bond stiffness of each characteristic stage (K 1 ,K 2 ,K 3 , and K 4 ) increased, whereas the slip (Ss ,Scr , and Su ) decreased with the increasing concrete age. (2) For specimens with the same concrete ages, with an increasing concrete strength grade from C30 to C50, the bond stress (ss ,scr ,su ,sr ) and the bond stiffness (K 1 ,K 2 ,K 3 ,K 4 ) increased, whereas the corresponding slippage (Ss ,Scr and Su ) decreased. (3) Based on the analysis of the bond properties of specimens with different concrete ages and concrete strength grades, empirical models of the bond strength and bond stress–slip constitutive relationships of deformed steel bars in early-age concrete were established. The comparisons between the proposed models and test results, as well as between the proposed models and existing models, demonstrated that the proposed models in this study were acceptable.
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. Acknowledgements The authors would like to acknowledge the National Natural Science Foundation of China (Grant Nos. 51308441, 51678473, and 51590914) and Program for Changjiang Scholars and Innovative Research Team at the University of China (Grant No. IRT_17R84) for financial support. References [1] D.P. Fang, C.D. Geng, H.Y. Zhu, X.L. Liu, Floor load distribution in reinforced concrete buildings during construction, ACI Struct. J. 98 (2) (2001) 149–156. [2] Y.A. Alvarado, P.A. Calderón, I. Gasch, J.M. Adam, A numerical study into the evolution of loads on shores and slabs during construction of multistorey
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