Degradation of steel-to-concrete bond due to corrosion

Degradation of steel-to-concrete bond due to corrosion

Construction and Building Materials xxx (2017) xxx–xxx Contents lists available at ScienceDirect Construction and Building Materials journal homepag...

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Construction and Building Materials xxx (2017) xxx–xxx

Contents lists available at ScienceDirect

Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Degradation of steel-to-concrete bond due to corrosion Cheng Jiang a,1, Yu-Fei Wu b,⇑, Ming-Jiang Dai c,2 a

Department of Civil & Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong Special Administrative Region School of Engineering, RMIT Univ., Melbourne, VIC 3000, Australia c Guiyang Survey, Design and Research Institute CO.LTD of CREEC, Guiyang, Guizhou 550002, China b

h i g h l i g h t s  A new bond-slip model for corroded steel bars is developed.  Change of friction, adhesion and mechanical interlocking due to corrosion is modeled.  Change of confinement is modeled in concrete cover effect.  The model shows a better performance compared with existing models.

a r t i c l e

i n f o

Article history: Received 27 July 2017 Received in revised form 7 September 2017 Accepted 21 September 2017 Available online xxxx Keywords: Steel bar Corrosion Bond-slip relationship Bond strength Degradation

a b s t r a c t Degradation of the bond between steel bars and concrete due to corrosion of steel significantly affects the durability of reinforced concrete (RC) structures. There are three mechanisms to transfer the interfacial shear (or bond) stress between steel bars and concrete, i.e., adhesion, friction and mechanical interlock (or dowel action). This paper discusses effects of corrosion on these three mechanisms. A new model for the bond-slip relationship between steel bars and concrete involving steel corrosion factor is proposed by modifying a recently developed unified bond-slip model. A rational approach is used in the modeling: the degradation of bond is caused by material degradation which can be modeled as degradation of concrete strength, and the degradation of confinement is taken into account in the concrete cover effect. A state-of-the-art database involving steel bar corrosion is built to evaluate the coefficients in the proposed bond-slip model. The calculated results using the proposed model show good agreement with experimental data. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Behavior of the bond between steel reinforcement and the surrounding concrete is a fundamental issue that affects the performance of reinforced concrete (RC) structures, such as load-carrying capacity and ductility, width and spacing of transverse cracks, and even plastic hinge length [1–7]. Corrosion of reinforcement steel is a serious problem that not only reduces the cross-sectional area of the reinforcing bar but also influences the behavior of the bond between steel and concrete. Corrosion changes interfacial material properties. In addition, the substantial expansion of volume of steel bars due to corrosion can cause ⇑ Corresponding author. E-mail address: [email protected] (Y.-F. Wu). Formerly: Department of Architecture and Civil Engineering, City Univ. of Hong Kong, Hong Kong Special Administrative Region. 2 Formerly: City University of Hong Kong Shenzhen Research Institute, Shenzhen, Guangdong 518057, China. 1

cracking and spalling of concrete cover which reduces the effective confinement of steel bars and thereby weaken the bond between concrete and corroded steel. To reasonably predict the steel-toconcrete interfacial bond of corroded RC structures, the effect of steel corrosion needs to be better understood and considered in the bond-slip model.

2. Previous works 2.1. Bond-slip models Extensive research on bond behavior of reinforced concrete has been carried out, and numerous empirical, semi-empirical, analytical and numerical bond-slip models based on experimental and/or analytical studies have been developed. The typical bond stressslip relationship widely accepted in extant literature is shown in Fig. 1 [1]. Several well-known models are introduced in this section.

https://doi.org/10.1016/j.conbuildmat.2017.09.142 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.

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Nomenclature a Ast B

experimental determined constant in Eq. (1) area of stirrups including all legs coefficient controlling the post-peak softening slope of the bond-slip curve in Wu and Zhao’s model minimum concrete cover, i.e., the smaller of side cover, bottom cover, or half the clear distance between rebars experimental determined coefficient 1 in Eq. (1) experimental determined coefficient 2 in Eq. (1) coefficient controlling the ascending slope of the bondslip curve in Wu and Zhao’s model diameter of longitudinal reinforcement experimental results concrete compressive strength combined confinement effect in Wu and Zhao’s model confinement effect of concrete in Wu and Zhao’s model confinement effect of stirrups in Wu and Zhao’s model anchorage or lap splice length of steel reinforcement

c c1 c2 D db Expe. fc K Kco Kst Lb

τ max Bond stress

Splitting

Stirrups

τf Unconfined

s1

s2

weight of steel bar after corrosion weight of steel bar before corrosion number of tensile steel bars relative bond strength relative slip initial slip in segmental bond-slip model at peak stress end slip in segmental bond-slip model at peak stress slip in segmental bond-slip model at onset of residual stress stirrup spacing theoretical results theoretical or experimental constant steel corrosion degree bond stress residual bond stress maximum bond stress

Sst Theo.

a g s sf smax

where smax and sf are the maximum and residual bond stress, respectively; s1, s2, and s3 are the slips at different turning points of the bond-slip curve (Fig. 1); and a is an index controlling the shape of the ascending part of the curve. Although this model can well describe the bond behavior of confined concrete in general, the model cannot be applied to different bond conditions. To propose a bond-slip model applicable to different confining levels and different failure modes, Harajli et al. conducted a series of investigations and developed a model with three different curves corresponding to three failure modes [11–13]. However, selection of the three curves is to be made by the users and the transitions between the three curves are not smooth, which can result in difficulties in applications, particularly in numerical simulations. To overcome the above mentioned problems, Wu and Zhao [14] proposed a unified and continuous bond stress-slip model as given by Eq. (3):

Pull-out

0

m m0 n Rs s s1 s2 s3

s3

Slip Fig. 1. Analytical bond stress-slip relationship under monotonic loading [1].



smax ½eB lnðB=DÞ=ðBDÞ  eD lnðB=DÞ=ðBDÞ 

ðeBs  eDs Þ

smax One of the earliest experimental investigations on bond behavior was carried out by Rehm [8] in 1957. Rehm [8] conducted a series of pull-out tests using specimens in which a single reinforcing steel bar was embedded with a short anchorage length, from which a simple bond stress-slip model was proposed (Eq. (1)).

s ¼ c1 s þ c2 s

where s and s are the bond stress and the relative slip between reinforcement and concrete, respectively. c1, c2 and a are experimentally identified coefficients. In 1983, Eligehausen et al. [9] investigated the bond behavior extensively, considering different parameters, such as concrete cover, transverse confinement, bar spacing and compressive strength of concrete. A four-stage bond stress-slip law was proposed and adopted by CEB design code [1,10], as shown in Fig. 1, given by:



8 > > > > <

s

2:5 pffiffiffiffi ¼ f c 1 þ 3:1e0:47K

ð3bÞ

K ¼ ðK co þ 33K st Þ

ð3cÞ

K co ¼

c db

ð3dÞ

K st ¼

Ast nSst db

ð3eÞ

ð1Þ

a

 a

s max s 1

smax

 sf > > smax  smax ðs  s2 Þ > s2 s3 > :

sf

0 6 s < s1 s1 6 s < s2 s2 6 s < s3 s3 6 s

ð2Þ

ð3aÞ



0:0254 þ K st 0:0232  8:34K st 

D ¼ 3 ln

 0:7315 þ K  0:13  3:375 5:176 þ 0:3333K

ð3fÞ ð3gÞ

where Kco and Kst denote the confinement effect of concrete cover and stirrups, respectively, and the combined confinement effect is given by K; fc and c are the strength and cover thickness of concrete, respectively; db is the diameter of the longitudinal bars; Ast is the area of stirrups including all legs; n is the number of tension bars enclosed by stirrups; and Sst is the spacing of stirrups. This model incorporates most factors considered in the literature, such as con-

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C. Jiang et al. / Construction and Building Materials xxx (2017) xxx–xxx

crete cover, transverse confinement and concrete strength. A significant advantage of the model is its unified form that covers all failure modes without the need of user interpretation or interference. In addition, the curves are mathematically smooth and continuous in the whole parameter space which facilities convenient application in numerical simulations.

3

3. Database To evaluate the existing models and develop a new model for the whole curve of the bond-slip relationship of corroded steel bars, a database of bond tests was built by collecting experimental results from the open literature. Test results that satisfy the following conditions are collected:

2.2. Consideration of steel corrosion Researchers have carried out extensive experimental and analytical investigations to study the effect of corrosion on bond. In 1990, Al-Sulaimani et al. [15] conducted a series of pull-out tests on unconfined specimens with three different bar diameters to study the influence of steel corrosion on bond behavior. The results showed that the bond strength increased with corrosion up to a certain amount, followed by an abrupt and rapid reduction as the corrosion further increased. Since then, many researches have been carried to further study this problem, and most of the works were conducted on unconfined specimens with similar conclusions [16– 24]. A few studies were conducted on confined specimens and stirrups were found to reduce the bond deterioration due to corrosion [20,25–27]. For a corroded bar, a coefficient g was generally used to quantify the steel corrosion as weight loss percentage (Eq. (4)):



m0  m  100% m0

ð4Þ

where m and m0 are the weight of the steel bar after and before corrosion, respectively. Most of the existing models on corrosion effect only focus on the maximum bond stress smax, where the maximum bond stress in a bond-slip model is revised to include steel corrosion, whereas other factors remain unchanged. The relative bond strength Rt is normally adopted to account for the corrosion effect:

Rs ¼

smax ðgÞ smax ð0Þ

ð5Þ

where smax (g) and smax (0) are the maximum bond stress with and without steel corrosion, respectively. The existing models for Rt are summarized in Table 1 and compared in Fig. 2. In the comparison, the following parameters are assumed for the models in references [27–29]: c/db = 2, Ast = 56.5 mm2, db = 20 mm, Sst = 100 mm and nd = 1. A recently proposed model [27,28] considered corrosion effect for the whole curve of the bond-slip relationship. There are certain limitations in this model, e.g., the Rt value is not allowed to be greater than 1, and the piecewise function is not mathematically smooth. These factors are improved by the model proposed in this work.

Table 1 Existing models for relative bond strength. Reference

Model 5:61g

¼e ¼ 1  5:6g ¼ 1  3:5g ¼ 1  ð10:544  1:586c=db Þg ¼ e32:51g ¼ 0:0159g1:06 6 1:0 ¼ 0:116g0:55 6 1:0  e19:8ðg1:5%Þ for flexural tests Rs ¼ e11:7ðg1:5%Þ for pull-out tests

Lee et al. [30] Cabrera [17] Stanish et al. [31] Yuan et al. [29] Auyeung et al. [19] Chung et al. [32] Chung et al. [21] Bhargava et al. [33]

Rs Rs Rs Rs Rs Rs Rs

Kivell [34] Lin and Zhao [27]

Rs ¼ e7:6ðg2:4%Þ 6 1:0  g 6 1:5% 1 Rs ¼ ; edðg1:5%Þ g > 1:5% 13:280:57c=db where d ¼ 43:54A st =d sst n þ1 b

d

R2

IAE

0.349 0.326 0.310 0.342 0.334 0.395 0.396 0.364 0.370 0.360 0.456

0.263 0.272 0.271 0.282 0.443 0.293 0.253 0.330 0.280 0.286 0.229

1. The reinforcement is deformed bars, and the rib spacing is within a normal range; 2. The embedded length of steel reinforcement Lb is short (Lb < 10 db) to ensure the local nature of test results; 3. The reinforcement was corroded after the specimens were cast; 4. The experimental tests were carried out under monotonic tension loading. The collected experimental data involve variations of all key factors, including concrete specimen size, bar diameter db, concrete cover thickness c, concrete strength fc, confinement condition, and corrosion level g. The scope of this investigation is limited to deformed bars and specimens; smooth bars are excluded from the database. Table 2 provides a summary of the database including all factors and the range of values. 4. Performance of existing Rt models The performance of the existing models listed in Table 1 is evaluated by comparing the model predictions with the test results in the collected database. Apart from R2, another index integral absolute error (IAE) that is often used for model assessment [37–40] is also calculated:

IAE ¼

X jExpe:  Theo:j P jExpe:j

ð6Þ

where Expe. and Theo. are experimental and theoretical results, respectively. A higher R2 or lower IAE indicates a more accurate theoretical model. The calculated results of R2 and IAE are listed in Table 1. It can be seen from the error analyses that the model proposed by Lin and Zhao [27] shows the best performance among the existing models (Table 1), with R2 = 0.456 and IAE = 0.229, followed by Chung et al. [21] with 0.396 and 0.253 for R2 and IAE, respectively. Detailed comparisons between predictions and test results of four selected models are shown in Fig. 3. Generally speaking, the results have a relatively large scattering (Fig. 3). Such large scattering is partly attributable to inaccuracy of the models but, nevertheless, is also due to inconsistency of the test results even for the same test design from the same research group. It is obvious in Fig. 2 that most of the existing models have monotonic decreasing relations with increasing corrosion level. The Rt model proposed by Lin and Zhao [27] has a small platform at the beginning of corrosion and then it has a monotonic reducing trend. Only the models proposed by Bhargava et al. [33] and Kivell [34] have Rt values greater than 1. It is shown in Section 5.1 that a rational relationship between Rt and corrosion level g should start from 1 when g = 0, increase slightly when g is small, and then decline monotonically afterwards. To this end, none of the existing Rt models listed in Table 1 matches such a trend. 5. The proposed model The bond-slip model in this work is developed by modifying the model of Wu and Zhao [14] (Eq. (3)) through modification of the bond mechanisms to include the corrosion effects. The effects of corrosion on bond mechanisms are analyzed in the following section.

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Fig. 2. Existing Rt models.

Table 2 Details of test database. Reference

c (mm)

fc (MPa)

Lb/db

65, 68, 70 69 63.5 20 25.5 62.5 68.5 69 25 69 8, 23, 38 30, 66 70 68 62.5

No No Yes No No Yes No No Yes No No Yes Yes

0–7.8 0–12.46 0–80.75 0–5 0–5.19 0–9 0–2.2 0–3.88 0–13.7 0–1.16 0–18.75 0–10.04 0–4.85

48 17 11 7 10 20 11 11 6 12 78 30 16

4

No

0–2.3

10

Lin and Zhao [27]

20

40

30 55 30 45 28 51.3 28.3 29 24 20, 30, 46 2351 35.3, 38.4, 41.9, 42.5 26 32 21 32 30

4 4 8.5 10 2.63 4 3 5.83, 2.5 6 5.57 3.57 5.56, 7.78 4

Choi et al. [36]

10, 14, 20 12 12 10 19 13 13 12 14 12 14 18 10 14 25

7.5

Yes

0–20.86

36

Total

10–25

20–70

20–55

2.5–10

Yes

0–80.75

323

Al-Sulaimani et al. [15] Cabrera [17] Almusalllam et al. [16] Mangat and Elgarf [18] Auyeung et al. [19] Fang et al. [20] Chung et al. [21] Imperatore and Rinaldi [22] Wang et al. [25] Abosrra et al. [23] Yalciner et al. [24] Zhao et al. [35] Mansoor and Zhang [26]

5.1. Corrosion effects on bond mechanisms The interfacial shear resistance at the interface of two contacted objects involves three mechanisms: friction, adhesion and mechanical interlock (or dowel action). The effects of corrosion on the three mechanisms are as follows: (1) Friction – Friction is related to frictional coefficient and normal pressure. The corroded product on the interface softens the contact surface and hence reduces the frictional coefficient. On the other hand, expansion of the corroded product leads to a higher pressure at the interface between steel reinforcement and the surrounding concrete before significant cracking of concrete. A higher pressure increases the friction. Therefore, it is possible that corrosion increases the bond resistance. Further increase in corrosion level may cause micro-cracking of the surrounding concrete which reduces the confinement effect and hence the frictional resistance. Therefore, the frictional resistance could first have an ascending and then descending trend when corrosion level increases. (2) Adhesion – Theoretically speaking, corrosion changes the surface material of steel reinforcement from Fe to Fe2O3 which is a weak material. The weakening of the interface

Stirrup involved

g

db (mm)

No. of specimens

(%)

material causes a reduction of the adhesive resistance. The increase in corrosion level further weakens the material and hence leads to a continuous reduction of adhesion. (3) Mechanical interlock – Expansion of the corroded product causes micro-cracks in the surrounding concrete. Microcracking in the surrounding of a steel bar causes a reduction in concrete strength in that region. As the mechanical interlocking is closely related to concrete strength [41], corrosion reduces the mechanical interlocking between steel bar and concrete. The increase of corrosion level further increases micro-cracking, and hence further weakens the mechanical interlocking.

5.2. Modeling of material weakening As discussed in the previous section, weakening of the material in the interface region causes reduction of frictional coefficient, adhesion and mechanical interlocking. Hence, degradation of these effects can be taken into account by reducing the material strength pffiffiffiffi in Wu and Zhao’s model. This can be achieved by replacing f c in pffiffiffiffi Eq. (3b) by ð f c Þg which is an equivalent concrete strength. pffiffiffiffi pffiffiffiffi Clearly, ð f c Þg ¼ f c  FðgÞ, where F(g) is a function of corrosion

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(a) Model by Lin and Zhao [27]

5

(b) Model by Chung etal. [21]

(c) Model by Kivell [34]

(d) Model by Bhargava et al.[33] (for pull-out tests)

Fig. 3. Performance of existing Rt models.

pffiffiffiffi level g. Based on the mechanism study, ð f c Þg should satisfy the following conditions: (1) when corrosion level is zero, bond is not affected; i.e., when pffiffiffiffi pffiffiffiffi g = 0, ð f c Þg ¼ f c ; (2) the bond strength is zero when a bar is fully corroded, i.e., pffiffiffiffi when g = 1, ð f c Þg ¼ 0; and pffiffiffiffi (3) ð f c Þg decreases monotonically when g increases. Based on the above conditions and through analyses of the trend of test results in the database, the following relationship is proposed:

FðgÞ ¼

qffiffiffiffi ,qffiffiffiffi fc f c ¼ 0:5 þ 0:5 cosðgk1 pÞ g

ð7Þ

Fig. 4. Eq. (7) with different k1 values.

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where k1 is a coefficient to be determined, which controls the descending slope, as shown in Fig. 4. Eq. (7) has only one coefficient k1 and yet provides sufficient versatility to address possible and reasonable trends of degradation. 5.3. Modeling of confinement weakening Apart from the material weakening discussed in the previous section, another effect of corrosion is the change of confinement. The confinement effect in Wu and Zhao’s model (Eq. (3)) is considered in two terms: (1) confinement effect of concrete cover (Kco); and (2) the confinement effect of stirrups (Kst). The test results in [27] show that the bond strength is insensitive to the corrosion level of stirrups (Fig. 5). Compared with other factors that significantly affect the bond, corrosion of stirrups can be neglected. In other words, modification of Kst due to corrosion can be neglected. Therefore, corrosion is only taken into account in Kco. Based on an argument similar to that in the previous section, Kco in Eq. (3) should be replaced by (Kco)g which should have first an increasing and then decreasing trend when g increases. Furthermore, the following two boundary conditions should be satisfied: (1) (Kco)g=0 = Kco; and (2) (Kco)g=1 = 0. Based on these conditions, the following relationship is proposed:

ðK co Þg =K co ¼

1g 1 þ k2 g þ k3 g2

ð8Þ

where k2 and k3 are two coefficients to be determined. Fig. 6 shows the trends of Eq. (8) with different coefficients. Again, versatility of the equation suits the reasonable and possible trends of the effect very well. 5.4. Determination of model coefficients

ðsmax Þg 2:5 pffiffiffiffi ¼ ð f c Þg 1 þ 3:1e0:47½ðK co Þg þ33K st 

ð9aÞ

Substituting Eqs. (9a) and (7) into Eq. (5) gives

Rs ¼

0:47ðK co þ33K st Þ

½0:5 þ 0:5 cosðg pÞ½1 þ 3:1e 1 þ 3:1e0:47½ðK co Þg þ33K st 



ðsmax Þg ½eB lnðB=DÞ=ðBDÞ

 eD lnðB=DÞ=ðBDÞ 

ðeBs  eDs Þ

Fig. 5. Effect of stirrup corrosion.

ð10bÞ

qffiffiffiffi qffiffiffiffi ¼ f c ½0:5 þ 0:5 cosðg0:514 pÞ fc

ð10cÞ

g

ðK co Þg ¼

K st ¼

c 1g db 1  27:027g þ 1099:275g2

ð10dÞ

Ast nSst db

ð10eÞ

0:0254 þ K st 0:0232  8:34K st

D ¼ 3 ln

0:7315 þ ðK co Þg þ 33K st 5:176 þ 0:3333½ðK co Þg þ 33K st 

ð10fÞ !  0:13  3:375

ð10gÞ

6. Performance of the proposed model

ð9bÞ

Using Eqs. (9b) and experimental results of Rs in the database, unknown coefficients k1, k2 and k3 are obtained by nonlinear regression analyses, to be 0.514, 27.0 and 1100, respectively. Therefore, the proposed bond-slip model involving steel corrosion is given by:

sg ¼

ðsmax Þg 2:5 pffiffiffiffi ¼ ð f c Þg 1 þ 3:1e0:47½ðK co Þg þ33K st 



Rewriting Eq. (3b) by including corrosion effect, the following equation is obtained:

k1

Fig. 6. Eq. (8) with different coefficients.

ð10aÞ

Eq. (10c) plotted in Fig. 7 shows the variation of effective concrete strength involving corrosion. Variation of the confinement effect caused by corrosion is shown in Fig. 8. The value of (Kco)g/ Kco increases to 1.185 at g = 1.20% followed by a steep descending trend afterwards. Fig. 9 shows the relative bond strength Rs calculated from Eq. (9b). It is shown from Fig. 9 that more confinement (by concrete cover or stirrups) reduces the enhancing effect of corrosion at the

Fig. 7. Degradation of equivalent concrete strength.

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Fig. 8. Variation of confinement effect.

(a) Unconfined

Fig. 9. Rs by the proposed model.

(b) Confined Fig. 10. Typical bond-slip curves from the proposed model.

beginning because the effect is relatively smaller for a bar with higher confinement. Fig. 10 depicts the bond-slip curves for both unconfined and stirrup confined cases calculated by the proposed model (Eqs. (10)). Degradation of the bond between steel bars and concrete is reasonably modeled in Fig. 10. Performance of the proposed model on Rs is shown in Fig. 11, with R2 and IAE equal to 0.410 and 0.239, respectively. Both R2 and IAE values are similar to the best performing existing model, by Lin and Zhao [27]. Furthermore, the proposed model has the following advantages: 1) the proposed model includes steel corrosion effect not only in the maximum bond stress but also in the whole bondslip curve; 2) the complicated corrosion effects on different mechanisms are accounted for by only three unknown coefficients, attributed to the inherent correlation between material properties and confinement characteristics in Wu and Zhao’s model, with the general bond behavior. By relating local concrete strength surrounding a steel bar and the concrete cover property to corrosion level, the full bond characteristics of corroded steel bar are automatically modeled; 3) the model can predict the trend of increasing bond resistance followed by a decrease when steel corrosion level increases, which has been observed in experimental tests; and 4) the model is unified for all failure modes, and is mathematically continuous which facilitates easy use for engineering applications and numerical simulations.

Fig. 11. Performance of the proposed Rs Model.

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7. Conclusions This paper presents a rational and novel approach to develop the bond-slip model for the steel bar-to-concrete interface, considering corrosion level. The corrosion effects on bond characteristics are attributed to two general factors: material weakening and confinement degradation. The general material weakening is accumulated into one factor and accounted for by the reduction of concrete strength which is linked to corrosion level through regression analysis. Degradation of the confinement is treated in a similar way by relating to the concrete cover confinement factor Kco to corrosion level. By using the modified concrete strength and confinement factor Kco in Wu and Zhao’s model [14], the degradation trend of steel bar-to-concrete bond due to corrosion is automatically and reasonably modeled. As corrosion causes expansion of steel bar, which increases the interfacial pressure before significant microcracking, bond strength may increase at low corrosion level and subsequently drop quickly after significant cracking surrounding the steel bar. Such trend can be correctly predicted by the proposed model due to the rational modeling process. Test database was built for determination of model coefficients. The model performs well compared to the test results and with other existing models. Acknowledgements The work described in this paper was fully supported by a grant from the National Natural Science Foundation of China (Grant No. 51378449). The authors would like to thank Dr. Hong-Wei Lin and Mr. Liang He for the constructive discussions during the work. References [1] CEB-FIP, Bond of reinforcement in concrete: state-of-art report, Fib Bulletin No. 10, Lausanne, Switzerland, 2000. [2] S. Hong, S.-K. Park, Uniaxial bond stress-slip relationship of reinforcing bars in concrete, Adv. Mater. Sci. Eng. 2012 (2012) 328570. [3] C. Jiang, Y.F. Wu, G. Wu, Plastic hinge length of FRP-confined square RC columns, J. Compos. Constr. 18 (4) (2014) 04014003. [4] D.S. Gu, Y.F. Wu, G. Wu, Z.S. Wu, Plastic hinge analysis of FRP confined circular concrete columns, Constr. Build. Mater. 27 (1) (2012) 223–233. [5] C. Jiang, Y.F. Wu, Discussion of ‘‘Modified plastic-hinge method for circular RC bridge columns” by Jason C. Goodnight; Mervyn J. Kowalsky; and James M. Nau, J. Struct. Eng. 143 (9) (2017) 07017003. [6] C. Jiang, F. Yuan, Y.F. Wu, Effect of interfacial bond on the plastic hinge length of FRP confined RC columns, J. Compos. Constr. (2017). under review. [7] D.Z. Guan, C. Jiang, Z.X. Guo, H.B. Ge, Development and seismic behavior of precast concrete beam-to-column connections, J. Earthquake Eng. (2016). in press. [8] G. Rehm, The fundamental law of bond, Proceedings of the Symposium on Bond and Crack Formation in Reinforced Concrete, Stockholm, pp. 491-498, 1957. [9] R. Eligehausen, E.P. Popov, V.V. Bertero, Local bond stress-slip relationships of deformed bars under generalized excitations. Report No. UCB/EERC-83/23, Earthquake Engingeering Research Center, College of Engineering, University of California, Berkeley, CA, 1983. [10] CE-Id. Béton, CEB-FIP Model Code 1990: Design Code, Thomas Telford, 1993. [11] M.H. Harajli, Effect of confinement using steel FRC, or FRP on the bond stressslip response of steel bars under cyclic loading, Mater. Struct. 39 (6) (2006) 621–634. [12] M.H. Harajli, B.S. Hamad, A.A. Rteil, Effect of confinement of bond strength between steel bars and concrete, ACI Struct. J. 101 (5) (2004) 595–603. [13] M.H. Harajli, M. Hout, W. Jalkh, Local bond stress-slip behavior of reinforcing bars embedded in plain and fiber concrete, ACI Mater. J. 92 (4) (1995) 343– 353.

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Please cite this article in press as: C. Jiang et al., Degradation of steel-to-concrete bond due to corrosion, Constr. Build. Mater. (2017), https://doi.org/ 10.1016/j.conbuildmat.2017.09.142