Influence of specimen dimensions and reinforcement corrosion on bond performance of steel bars in concrete

Abstract

To study the deterioration of bond performance between concrete and corroded steel bars with designed corrosion levels of 0%, 0.5%, 1.0%, 2.0%, 5.0%, 8.0%, and 10.0%, pull-out tests were performed on cube specimens with the dimensions of 10D × 10D × 10D, where D is the diameter of longitudinal rebars (D = 14, 20, and 25 mm, respectively). The experimental results indicated that with the specimen dimensions increased, the expansive cracks induced by corrosion products appeared earlier and the maximum expansive cracking width was larger at the same corrosion levels. The bond strength and the initial bond stiffness first increased and then dramatically decreased as the concrete deterioration and reinforcement corrosion levels increased for each specimen dimension, whereas the specimens with the larger diameter (D = 25 mm) were more sensitive to the corrosion than those with the smaller diameter (D = 14, 20 mm). The free-end slip and the energy dissipation for each specimen dimensions, which decreased slowly with increasing corrosion levels before the corrosion-induced cracks and then weakened rapidly when the corrosion-induced cracks appeared, was almost independent of the influence on corrosion levels after the corrosion-induced cracks appeared. Based on the experimental results, a simplified expression for the calculation of residual bond stress and an empirical model of the bond–slip constitutive equation that considers the influence of reinforcement corrosion were proposed, which can be used in finite element analysis of corroded reinforced concrete.

Keywords

bond performance concrete corroded steel bars corrosion-induced cracks specimen dimensions

Introduction

The chemical properties (high alkalinity) and physical performance (high resistivity) of the concrete cover in reinforced concrete (RC) structures are fundamental to ensure that the internal reinforcing steel bars in concrete are not affected by the external environment at short time (Shi et al., 2011). Passivation membrane on the surface of rebars is in a relatively steady state at a high alkalinity environment and destroyed when the alkalinity of concrete tends to decrease that causes the beginning of the corrosion of rebars in concrete (Lu et al., 2019). Val and Stewart (2003) pointed out that premature concrete deterioration caused by reinforcement corrosion is a major contributing factor to the loss of serviceability for existing RC structures. Generally, the environment-induced corrosion of rebars in concrete is mainly attributed to two aspects (Zhang et al., 2018a). (1) Chloride ions penetration, coming from the sea wind, seawater, deicing salt, and aggregate containing chloride in concrete, all of which may reduce their serviceability. (2) Acid mediums invasion, such as CO₂ in atmospheric environment, NO₂ and SO₂ in acid rain, which are reacted with the alkaline substance of Ca(OH)₂ and calcium silicate hydrate (C–S–H) in concrete.

Good bond performance between rebars and surrounding concrete is overwhelmingly critical to ensure that the two materials can work and deform together in RC structures (Feng et al., 2016; Tondolo, 2015; Wu et al., 2016; Yang et al., 2018). However, the formation of corrosion products would alter the bond conditions at the steel–concrete interface and thus affects the deterioration of the bond behavior or serviceability of the RC structures more directly. Previous research works have found that the reinforcement corrosion, which is quite aside from decreasing the cross-sectional area and mechanical properties of rebars (Almusallam, 2001; Coccia et al., 2016; Sanz et al., 2018; Wang et al., 2016; Zhang et al., 2019), causes cracking or spalling of the concrete cover due to the expansive pressure applied by corrosion products so that the bearing capacity and serviceability of RC members degenerate rapidly (Coronelli et al., 2013; Khan et al., 2014; Zhao et al., 2013; Zhou et al., 2017). In addition, the degradation of ultimate bond stress (bond strength) is much severe than the cross-sectional area loss of reinforcement (Li et al., 2014; Ma et al., 2017).

Over the past few years, many studies that analyzed the bond performance in the presence of reinforcement corrosion were conducted actively in RC members (Hou et al., 2018; Lin et al., 2019). Several studies have concentrated mainly on influence parameters, such as rebar diameter (D), effective bonded length (L), protective thickness of concrete (C), rebar grades, concrete grades, and transverse reinforcements (stirrups) (Fang et al., 2004), that affect the bond anchorage capacity of corroded RC structures. Wu et al. (2016) conducted an experimental test to study the deterioration of bond stress between concrete and rebars with different diameters. The results manifested that the bond strength of specimens with the smaller diameters (12, 16 mm) increased first and then decreased with increasing corrosion levels, whereas the larger diameters (20, 25 mm) weakened continuously because of smaller protective concrete thickness. Pull-out tests were applied by Coccia et al. (2016) to analyze the degradation of bond strength with various corrosion levels and an analytical model was proposed to evaluate the internal stress with the corrosion extents. Ma et al. (2017) proposed an empirical bond strength degradation model that considers the influence of corrosion levels using the pull-out test specimens, in which the reinforcements were instrumented with interior strain gauges. Choi et al. (2014) developed some analytical and empirical bond strength models through investigating the difference of bond properties in RC members, which were corroded by natural and artificial corrosion methods. The experimental investigation demonstrated that the bond strength and the bond stiffness (represented by the slope of initial bond–slip curves) between rebars and concrete increased with aggrandizing corrosion levels before the corrosion-induced cracks (approximately 2% corrosion loss), and then decreased rapidly with the corrosion levels increased continuously (Fang et al., 2004; Lan et al., 2008; Xiao and Lei, 2011). Previous investigation that analyzed the bond performance of corroded steel bars is mainly based on the lower corrosion of reinforcement. Relatively less information, nevertheless, is available on bond behavior for RC members that have highly corroded rebars (Lin et al., 2017). A higher corrosion of reinforcement can cause an increase of localized stresses in surrounding concrete and aggravate the cracking of the concrete cover, thus the deterioration law of the bond strength at different corrosion stages may be different. In addition, little research has been done to analyze the deterioration of bond behavior from the angles of corrosion-induced crack width, bond stiffness, bond energy dissipation, and residual bond stress. It is worth mentioning that for the different specimen dimensions, reinforcement corrosion has a diverse influence on the deterioration of bond performance due to different bond mechanisms and failure modes, which is extremely crucial for the accurate prediction of loading capacity and serviceability of RC structures. Therefore, further studies are required to quantify the influence of specimen size on bond performance between highly corroded rebars and concrete.

In this article, a total amount of 63 pull-out test specimens were cast to examine the effects of specimen dimensions and corrosion levels on bond behavior between rebars and concrete. The maximum expansive cracking width and bond properties, such as bond strength, bond energy dissipation, bond stiffness, and residual bond stress, were extensively discussed. Then, a simplified calculation model of residual bond stress and an empirical model of the bond–slip constitutive equation between corroded rebars and concrete were established by the regression analysis of experimental data.

Experimental program

Material properties

Ordinary Portland cement type 42.5R, medium sand, tap water, crushed limestones aggregate with a maximum size of 25 mm were used in this investigation. The concrete mix proportion for the water:sand:coarse aggregate:cement was 1:1.35:3.0:0.49. Concrete cube specimens, of 150×150×150 mm dimensions, were cured for 28 days under standard conditions and had an average compressive strength and tensile splitting strength of 43.53 and 3.32 MPa, respectively.

HRB400 deformed bars with diameters of 14, 20, and 25 mm were used in preparing pull-out tests. The detailed rebar characteristics and mechanical properties are given in Table 1.

Table 1.

Detailed rebar characteristics and properties.

Diameter, D (mm)	Rib height, R_h (mm)	Rib spacing, R_s (mm)	Yield tensile strength, f_y (MPa)	Ultimate tensile strength, f_u (MPa)	Elastic modulus, E_s (MPa)
14	1.10	9.0	438.65	585.57	2.02 × 10⁵
20	1.61	9.80	466.57	618.59	2.03 × 10⁵
25	1.82	12.30	444.66	598.33	2.10 × 10⁵

Specimen design

Pull-out test in cube specimens with three dimensions of 140, 200, and 250 mm were constructed to determine the local bond–slip behavior between concrete and corroded rebars with corrosion levels of 0%, 0.5%, 1.0%, 2.0%, 5.0%, 8.0%, and 10.0%. The geometry and dimensions of the pull-out test specimens are depicted in Figure 1. Three specimens were prepared for each corrosion level, in the light of the fact that the bond properties may be dispersed widely. Each longitudinal rebar (D = 14, 20, and 25 mm) was placed in the center of concrete cube specimens with a bond length of 2D to prevent the yielding of the rebar before bond failure under the pull-out load. The unbonded segments on both ends of specimens were obtained using polyvinyl chloride (PVC) pipe and the annular space between the rebar and the PVC tube was filled with polyurethane foam to avoid concrete flowing into it during the casting procedure. The transverse reinforcements (stirrups) with a diameter of 6 mm (see Figure 1(b)), which were square with a length of 5D from outside-to-outside surface and a spacing of 2.5D to simulate the RC structures in service, had an average yield strength and ultimate strength of 332.21 and 456.36 MPa, respectively. In addition, the stirrups and the unbonded segments of rebars were brushed with epoxy resin for anti-corrosion purposes.

Figure 1.

Test specimens: (a) pull-out specimen geometry (all in mm) and (b) photo before concrete casting.

Accelerated corrosion

The accelerated electrochemical corrosion method was impressed on the reinforcement with a low current density of 200 μA/cm², as suggested in Mancini and Tondolo (2014). It was said that if the higher corrosion ratio with current density exceeds 250 μA/cm², then it could have a negative influence by reason of some spurious bond deterioration of the RC behavior (Tondolo, 2015). The specimens were immersed in 5% NaCl solution for 7 days before the direct current was applied. The reinforcement and stainless steel plate were the anode and cathode of a constant current generator, respectively, as presented in Figure 2. Meanwhile, some concrete cubes were also immersed in 5% NaCl solution to determine the deterioration of the compressive strength of concrete. Faraday’s Law, as equation (1), was applied to estimate the designed corrosion level of the reinforcements by controlling the electric current and the time of reinforcement corrosion. The achieved corrosion level, however, was measured as the mass loss of the reinforcement, which signified an average corrosion ratio along the bond length

Δ m = \frac{55.847 \times I \times t}{2 \times 96, 487}

(1)

where $Δ m$ is the mass loss of the rebars (g), I is the average electrical current (A), and t is the corrosion duration time (s).

Figure 2.

Electrochemical accelerated corrosion system.

Loading and measuring instrumentation

After corroding and drying in ambient conditions in the laboratory for 2 months, the pull-out tests were performed using an electro-hydraulic servo universal testing machine with a capacity of 1000 kN, as shown in Figure 3. The relative slips between the rebars and concrete were measured using two linear variable differential transformers (LVDTs) with a precision of ±0.001 mm positioned on free end of the rebar, and the force sensor was installed on loading end to collect the pull-out force, which ensured that the force and slip data could be gathered simultaneously. Data from the force sensor and LVDT were collected by the NI 9215 automatic data acquisition system produced by National Instruments at a frequency of 32 Hz. The load control procedure was used with a loading ratio about 0.03D² kN/min, according to the Chinese Standard (GB/T 50152-2012).

Figure 3.

Pull-out test setup.

Corrosion-loss measurement

The achieved corrosion-loss of longitudinal rebars can be obtained as follows. (1) The corroded rebars were taken out from the specimens and the bond length was cut when the pull-out test was completed. (2) The bond segments of rebars were cleaned with 12% HCl solution and neutralized with 3% Na₂CO₃ solution. (3) The corroded rebars were weighed by electronic scales with an accuracy of 0.01 g, and the bond length of the corroded rebar was measured after it was dried by count Vernier calipers with an accuracy of 0.01 mm. Then, the linear density of reinforcement was calculated as described in ASTM G1-03 (2003). The mean corrosion ratio of reinforcement along the bond length can be expressed using the following equation

η = \frac{W_{0} - W_{1}}{W_{0}} \times 100 %

(2)

where η is the actual corrosion level of reinforcement (%), W₀ is the weight density per unit length of virgin reinforcement (g/mm), and W₁ is the weight density per unit length after the removal of corrosion products (g/mm).

To evaluate the reliability of measurement methods applied by the linear density of reinforcement, an error analysis test was carried out in our previous research (Zhang et al., 2018b, 2019). The experimental results manifested that the maximum measurement error measured by the linear density of reinforcement was only 0.549%, which was in an acceptance range compared with the mass loss induced by corrosion.

Figure 4 demonstrates the typical bond segments of longitudinal corroded rebars with a diameter of 20 mm after the cleaning procedure was performed. It was found that for slightly corroded rebar, a small amount of corrosion pitting was relatively uniform for 2.38% mass loss, while for some seriously corroded rebars with a 5.91% mass loss, deep, long, and narrow corrosion pitting was unevenly distributed along the bond length and a serious corrosion loss of longitudinal ribs was observed.

Figure 4.

Longitudinal rebars with different corrosion levels after the cleaning procedure: (a) η = 0%, (b) η = 2.38%, and (c) η = 5.91%.

Results and discussion

Tested results

The average bond stress τ is calculated assuming a uniform distribution of bond stress between rebars and surrounding concrete along the bond length (Wu et al., 2016). It is obtained from the measured load force using equation (3)

τ = \frac{F}{π DL}

(3)

where τ is bond stress (MPa), F is the pull-out force (kN), D is the diameter of longitudinal rebar (mm), and L is the bond length (mm).

The pull-out test results of specimens are summarized in Table 2, where τ_u is the bond strength and S_f is the free-end slip corresponding to bond strength. Specimens are designated DA-E, where DA is the dimension of specimens with the diameters of 14, 20, and 25 mm, and the E is an expected reinforcement corrosion levels of 0%, 0.5%, 1.0%, 2.0%, 5.0%, 8.0%, and 10.0%.

Table 2.

Test results of corroded specimens with different dimensions.

Serial number	η (%)	f_cu (MPa)	τ_u (MPa)					S_f (mm)
Serial number	η (%)	f_cu (MPa)	S1	S2	S3	Avg	SD	S1	S2	S3	Avg	SD
D14-0	0.00	49.30	19.40	21.09	22.48	20.99	1.26	1.06	0.82	1.07	0.98	0.12
D14-0.5	0.56	49.76	23.12	23.22	27.73	24.70	2.15	1.18	0.94	0.90	1.01	0.12
D14-1.0	1.18	48.48	25.13	26.60	31.10	27.61	2.54	0.83	1.27	0.71	0.94	0.24
D14-2.0	2.37	47.68	27.96	29.30	35.13	30.80	3.11	0.37	1.11	0.27	0.58	0.37
D14-5.0	4.42	47.12	26.75	27.72	30.42	28.30	1.55	0.18	0.12	0.23	0.18	0.04
D14-8.0	7.57	45.44	22.30	25.19	28.06	25.18	2.35	0.07	0.17	0.18	0.14	0.05
D14-10.0	10.38	44.50	19.85	23.68	25.01	22.85	2.19	0.09	0.13	0.16	0.13	0.03
D20-0	0.00	49.30	18.70	19.02	19.12	18.95	0.18	1.34	1.80	1.53	1.56	0.19
D20-0.5	0.52	49.76	24.09	25.49	30.64	26.47	2.83	1.48	0.62	0.39	0.83	0.47
D20-1.0	0.99	48.48	27.52	29.44	35.37	30.78	3.34	0.56	0.67	0.78	0.67	0.09
D20-2.0	2.38	47.68	28.31	31.51	34.80	31.54	2.65	0.35	0.19	1.91	0.82	0.78
D20-5.0	5.91	47.12	21.38	22.19	27.80	23.79	2.85	0.13	0.11	0.19	0.14	0.03
D20-8.0	8.29	45.44	16.80	20.80	21.15	19.58	1.97	0.20	0.12	0.14	0.15	0.03
D20-10.0	10.43	44.50	16.45	17.66	19.52	17.88	1.26	0.10	0.22	0.20	0.17	0.05
D25-0	0.00	49.30	21.50	22.93	24.74	23.06	1.33	2.04	1.64	2.54	2.07	0.37
D25-0.5	0.59	49.76	26.84	28.69	34.49	30.01	3.26	0.37	0.62	1.00	0.66	0.26
D25-1.0	0.99	48.48	33.31	39.50	40.10	37.64	3.07	1.06	0.63	1.08	0.92	0.21
D25-2.0	1.76	47.68	20.86	20.94	25.44	22.41	2.14	0.18	0.34	0.18	0.23	0.08
D25-5.0	5.42	47.12	13.37	16.06	17.08	15.50	1.56	0.84	0.21	0.62	0.56	0.26
D25-8.0	8.05	45.44	12.46	12.83	13.70	12.99	0.52	0.13	0.10	0.24	0.16	0.06
D25-10.0	12.30	44.50	8.21	8.81	−	12.30	0.51	0.02	0.04	−	0.03	0.01

η is the achieved corrosion level of reinforcement; S1, S2, and S3 are the three different specimens from small to large order of bond strength for each scenario; Avg is the average value of three identical specimens; SD is the standard deviation for each series; and the data of specimen D25-10.0-S3 are not collected due to loading eccentricity.

Corrosion-induced cracking

In this test, the corrosion crack information was recorded in detail using the fracture width gauge with an eye to corrosion-induced cracking may have an influence on the bond behavior. It was found that the cracks first appeared at the free-end when the corrosion level was up to about 2.0%, and then the corrosion-induced cracking along the longitudinal rebars developed from the free-end to load-end as the corrosion procedure continued. The crack width in the free-end was wider than in the load-end as the bond segments were located in the free-end part of specimens. The typical cracking pattern of corroded specimens is depicted in Figure 5. It is worth mentioning that the cracking pattern was discrepant for the different dimensions of specimens. As the dimension of specimens increased, the expansive cracks appeared earlier and the maximum crack width was larger (see Figure 6). After the reinforcement corrosion levels was about 5.0%, the specimens with the diameter of 14, 20, and 25 mm cracked along the longitudinal rebars with average maximum widths of 0.42, 0.61, and 1.69 mm, respectively, which became 0.75, 1.51, and 4.39 mm as the specimens continued to deteriorate for the reinforcement corrosion levels of about 10.0%. Comparing the crack widths of the diameter of 14 and 25 mm with reinforcement corrosion levels about 10.0%, the mean value of the diameter of 25 mm was approximately 5.8 times that of the diameter of 14 mm.

Figure 5.

Typical cracking patterns of specimen D25-5.0-S1.

Figure 6.

Maximum crack width versus achieved corrosion level.

Bond stress versus slip relationships

The bond stress–slip curves at various reinforcement corrosion levels for the different specimen dimensions are shown in Figure 7, where “S” is the mean value measured on the free-end slip of the longitudinal rebars by two LVDTs. It can be observed that the bond strength, the initial bond stiffness first increased and then decreased with the extent of reinforcement corrosion increased, only the influential magnitudes were changed for different specimen dimensions. This is because the friction resistance between rebars and surrounding concrete interface was increased at a lower corrosion levels (no corrosion-induced cracks), which resulted in an expansive pressure on the surrounding concrete, as other tested results have indicated (Ma et al., 2017). After the reinforcement was seriously corroded, the concrete interface eventually cracked that reduced the confinement around the reinforcement, thus the bond strength and the initial bond stiffness were gradually decreased.

Figure 7.

Bond stress–slip curves at various reinforcement corrosion levels with different specimen dimensions: (a) η = 0%, (b) η = 0.5%, (c) η = 1.0%, (d) η = 2.0%, (e) η = 5.0%, (f) η = 8.0%, and (g) η = 10.0%.

Failure mode

Two types of failure modes of the pull-out specimens are detailed in Figure 8. (1) Pull-out failure, which occurred when the concrete and stirrups were well confined, and the reinforcement was pulled out slowly. For the specimens with lower corrosion levels (no corrosion-induced cracks), the bond stress increased almost linearly up to bond strength and then decreased tardily until the bond failure. The bars were pulled out slowly from the specimens without any splitting/cracking in the concrete surface due to sufficient constraint provided by the concrete cover and stirrups. For the specimens with higher corrosion levels (corrosion-induced cracks), the corrosion-induced cracks of specimens increased gradually during the loading process. (2) Splitting failure, this occurred for specimens of D14-10.0-S1, D14-10.0-S3, and D20-5.0-S3. A sharp decrease in the bond stress and a sudden increase in corrosion-induced cracks could be obviously observed after the ultimate load (see Figure 7). This phenomenon could be attributed to the corrosion-induced cracking or spalling of concrete cover reduced the confinement provided by concrete and stirrups.

Figure 8.

Failure modes of specimens: (a) pull-out failure and (b) splitting failure.

Bond strength

The average bond strength at various corrosion levels for different specimen dimensions is illustrated in Figure 9. It can be noted that the general trend of bond strength for different specimen dimensions was similar, only the influential magnitudes were different at various corrosion levels. At lower corrosion levels (no corrosion-induced cracks), the bond strength was gradually upgraded as the concrete deterioration and reinforcement corrosion levels increased, which can be explained as the corrosion products improved the roughness of reinforcement and thus enhanced the frictional resistance at the steel–concrete interface. Furthermore, the bond strength of specimens with 25 mm diameter showed a faster increase than those of specimens with diameters of 14 and 20 mm as corrosion levels increased. This phenomenon can be attributed to the following two reasons. First, the specimens with 25 mm diameter had a longer bond length and the corrosion products spilled from the PVC pipes were more difficult than other specimens, which caused the corrosion products fully used to increase the frictional resistance. Besides, the specimens with 25 mm diameter had a larger protective concrete thickness that can effectively enhance the confinement around the reinforcement. For specimens with diameters of 14, 20, and 25 mm, there were 46.7%, 66.4%, and 63.2% increases in bond strength for 2.37%, 2.38%, and 0.99% corrosion levels, respectively, compared with those of un-corroded specimens. At higher corrosion levels (corrosion-induced cracks), a decreasing trend in the bond strength appeared with the continual increasing of corrosion products. For specimens with diameters of 14, 20, and 25 mm, the decrements were being recorded as 25.8%, 43.3%, and 77.3% for 10.38%, 10.43%, and 12.30% corrosion levels, respectively, compared with the crest of bond strength. This is because the expansive stress applied by corrosion products exceeds the tensile strength of concrete and causes the appearance of corrosion-induced cracking of the concrete cover, which, to a large extent, reduced the confinement of the concrete cover. Moreover, the corrosion products were a layer of porous oxide that provides lubrication, which weakened the frictional coefficient at the steel–concrete interface. It should be noted that the bond strength for specimens with the larger diameter (D = 25 mm) was more sensitive to corrosion than those with the smaller diameters (D = 14, 20 mm). This is because the larger diameter had more corrosion products compared with those of the smaller diameters at the same corrosion level. The appearance of expansive pressure applied by corrosion products altered the bond conditions at the steel–concrete interface and then accelerated the cracking or spalling of the concrete cover.

Figure 9.

Bond strength versus achieved corrosion level.

Free-end slips corresponding to bond strength

Figure 10 depicts the free-end slips corresponding to the bond strength versus achieved corrosion level for the different specimen dimensions. It can be concluded that a decreasing trend of free-end slip for different specimen dimensions was observed as the corrosion levels increased and the reduction in free-end slip value after the corrosion-induced cracks appeared was significantly less than before. Moreover, for the un-corroded specimens, an increment in the free-end slip value can be observed with increasing dimensions of specimens. The decrease of slip values symbolized that a significant reduction in ductility and energy absorbed the pull-out capacity before the bond failure occurred, which is discussed in the following section.

Figure 10.

Free-end slips versus achieved corrosion level.

Energy dissipation

The bond energy dissipation was obtained by calculating the area under the bond stress–slip curves before the ultimate bond stress (Garcia et al., 2016; Zhou et al., 2017), as equation (4), which represents the integration of bond stress and slip ranging from 0 to S_f

E = \int_{0}^{S_{f}} τ (S) d S

(4)

where E is the bond energy dissipation (N/mm) and $τ (S)$ is the bond stress (MPa).

The relationship between energy dissipation and corrosion levels is displayed in Figure 11. For un-corroded members, it is obvious that the energy dissipation increased gradually as the specimen dimensions increased and the mean energy dissipation was 17.54, 24.30, and 39.11 N/mm for the specimens with diameters of 14, 20, and 25 mm, respectively. Moreover, the energy dissipation for different specimen dimensions exhibited a remarkable reduction with increasing corrosion levels. The energy dissipation for the different specimen dimensions had less energy loss before the corrosion-induced cracks, and then decreased rapidly when the corrosion-induced cracks appeared. Although slight corrosion of reinforcement can improve the bond strength, the free-end slips corresponding to bond strength was low, thereby causing the degradation in bond energy dissipation. The bond energy dissipation was basically lost when the corrosion levels were up to 10.0% for each specimen dimension, which exhibited the characteristics of brittle failure. Meanwhile, the reduction in energy dissipation with the larger specimens (D = 25 mm) was more remarkable than those of smaller specimens (D = 14, 20 mm) with increasing corrosion levels, which were similar to the variation trend of free-end slip value discussed previously.

Figure 11.

Energy dissipation versus achieved corrosion level.

Bond stiffness

To research the influence of reinforcement corrosion on bond stress in the initial slip stage (S = 0.01, 0.10 mm), Figure 12 demonstrates the bond stress versus achieved corrosion level at different slips. This slop of the initial bond–slip curve actually represents the initial bond stiffness that responds to the energy of resisting pull-out failure (Zhou et al., 2017). As seen in Figure 12, the variation law in mean bond stiffness changed with the variation of specimen dimensions and initial slip stage. The initial bond stiffness value improved with increasing specimen dimensions for un-corroded specimens. For S = 0.01 mm, the initial bond stiffness gradually upgraded and then slowly decreased for specimens with 20 and 25 mm diameters with increasing corrosion levels. However, there was no obvious difference for specimens with 14 mm diameters due to the shorter bond length and complicated stress states of the micro-slip stage. For S = 0.10 mm, the initial bond stiffness gradually increased and then weakened for each specimen dimension with the increase of corrosion levels. It can be concluded that the mean bond stiffness increased to a maximum value before the appearance of corrosion-induced cracking and then gradually weakened with aggrandizing corrosion levels continually for each specimen dimension, which was the same as the variation trend on bond strength aforementioned.

Figure 12.

Bond stress versus achieved corrosion level at different slips.

Residual bond stress

The mean residual bond stress versus achieved corrosion level is illustrated in Figure 13. The mean residual bond stress was defined as the bond stress corresponding to the free-end slip equal to the rib spacing of reinforcement for different specimen dimensions (Zhang et al., 2018b). It can be clearly observed that the mean residual bond stress increased and then decreased slightly as the corrosion levels elevated continually. For the dimension of specimens with diameters of 14, 20, and 25 mm, the mean residual bond stress increased by about 25.5%, 89.3%, and 15.2% for 2.37%, 2.38%, and 0.99% corrosion levels, respectively, compared with those of un-corroded specimens. Figure 14 shows the relationship of the relative residual bond stress (the ratio of residual bond stress to bond strength) with achieved corrosion level. It can be found that the relative residual bond stress increased with the increase of specimen dimensions. According to the experimental results, the empirical model of the residual bond stress between corroded rebar and concrete can be expressive as equation (5), which can be used to preliminary evaluate the residual bond stress with different diameters of reinforcement

φ = \frac{τ_{r}}{τ_{u}} = 0.025 D - 0.20

(5)

where τ_r is the residual bond stress (MPa), τ_u is the bond strength (MPa), and D is the diameter of reinforcements (mm).

Figure 13.

Residual bond stress versus achieved corrosion level.

Figure 14.

Relative residual bond stress versus achieved corrosion level.

Empirical modeling of bond–slip relation

To meet the requirement of numerical analysis for RC elements, a simplified and practical bond–slip constitutive equation is essential. It can be observed from Figure 7 that the shape of the bond stress–slip curve was comprised of an ascending branch and a descending branch, thus it was reasonable to adopt a piecewise function to model the bond stress–slip expression. The well-known bond–slip expression at the ascending stage was proposed by Cosenza et al. (1997), as provided in equation (6), and has been used by other researchers (Prince and Singh, 2015). To establish a full bond–slip relation between un-corroded rebars and concrete, Xiao and Lei (2011) and Chen et al. (2018) proposed a combined expression, shown as equation (7), which is integrated by equation (6) and a descending stage suggested by Guo (1997). In this study, equation (7) was also adopted to simulate the bond–slip relation of corroded rebars in concrete

\frac{τ}{τ_{u}} = {(\frac{S}{S_{u}})}^{a}

(6)

{\begin{matrix} \frac{τ}{τ_{u}} = {(\frac{S}{S_{u}})}^{a} & (0 \leq S \leq S_{u}) \\ \frac{τ}{τ_{u}} = \frac{S / S_{u}}{b {(S / S_{u} - 1)}^{2} + S / S_{u}} & (S \geq S_{u}) \end{matrix}

(7)

where $τ$ is the bond stress (MPa), $τ_{u}$ is the bond strength (MPa), S is the relative slip between steel bars and concrete (mm), $S_{u}$ is the peak slip corresponding to the bond strength (mm), and the variables a and b are constants obtained by regression analysis.

According to the regression analysis of experimental data in second specimens (S2) for each scenario, it was found that there was no obvious difference for the value of parameter a, thus, the exponent value a can be uniformly adopted as 0.3 for all the tests. This parameter value is in accord with the results obtained by Xiao and Lei (2011). However, the parameter b, as presented in Figure 14, is affected by corrosion levels and specimen dimensions. The parameter b decreased rapidly except the specimens with 14 mm diameter before the appearance of corrosion-induced cracks, and then the b value was almost independent of the influence of corrosion levels after the corrosion-induced cracks appeared. It is important to note that the value of parameter b represents the area under the declining section of bond–slip curves. It can be seen in Figure 15 that the reduction in parameter b caused a decrease in curvature of the bond stress–slip curve after peak stress, hence reducing the ductility of the specimens.

Figure 15.

Parameter b versus achieved corrosion level with different specimen dimensions.

Typical comparisons between the experimental values and the calculated ones are depicted in Figure 16, in which the parameters E and C represent the experimental and calculated values. It can be found that the approximate curves obtained by equation (7) are in line with experimental ones, which demonstrated that the suggested expression (equation (7)) can be used to simulate the bond–slip relation between corroded rebars and concrete in finite element analysis of corroded RC.

Figure 16.

Comparisons of calculated curves with test results for different specimen dimensions: (a) η = 0%, (b) η = 0.5%, (c) η = 1.0%, (d) η = 2.0%, (e) η = 5.0%, (f) η = 8.0%, (g) η = 10.0%.

Conclusion

Pull-out tests were conducted to investigate the influence of reinforcement corrosion and specimen dimensions on bond performance between steel bars and concrete. Several conclusions in this research can be drawn as the following.

The expansive cracks induced by corrosion products appeared earlier and the maximum expansive cracking width was larger at the same corrosion levels with increasing specimen dimensions.

At a lower corrosion levels with no corrosion-induced cracking emerged, the bond strength and initial bond stiffness gradually improved with the concrete deterioration and reinforcement corrosion levels increased. At a higher corrosion levels with corrosion-induced cracking appeared, a decreasing trend in the bond strength and initial bond stiffness occurred with the corrosion products being increased continually. The bond strength and the initial bond stiffness of specimens with larger diameter (D = 25 mm) were more sensitive to the corrosion than those with smaller diameters (D = 14, 20 mm).

The free-end slip and the energy dissipation for different specimen dimensions, which weakened tardily with increasing corrosion levels before the corrosion-induced cracks and then decreased rapidly when the corrosion-induced cracks appeared, had no significant effects on corrosion levels after the corrosion-induced cracks appeared.

Based on the experimental results, a simplified calculation expression of residual bond stress and an empirical model of the bond–slip constitutive equation between corroded rebars and concrete were proposed, which can be used in finite element analysis of corroded RC.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors acknowledge the financial support received from the National Key Research and Development Program of China (grant no. 2017YFC073000) and the National Natural Science Foundation of China (grant no. 51578229).

ORCID iD

Bai Zhang

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