JSCE 令和3年度土木学会全国大会第76回年次学術講演会

第V部門

付着・定着・継手(2)2021年9月10日(金) 11:10 〜 12:30 V-7 (Room24)[V-515] Effect of Stirrups on Bond Strength Degradation in Cracked
Concrete by Expansion Agent Filled Pipes*Amadou Sakhir Syll1, Hiroki Shimokobe1, Toshiyuki KANAKUBO1 （1. UNIVERSITY OF TSUKUBA）
キーワード：Rebar corrosion, Bond test, Expansion agent, Crack width, stirrupThis study aims to cast deep sight on the bond strength of cracked concrete from the perspective ofconfinements by stirrups. To achieve this target, Concrete cracked by expansion agent-filled pipes inbond test specimens has been presented in the previous paper. Empirical formulas of the bond strength
deterioration with crack width as the main variable, have been proposed from pull-out test results.
These prediction formulas give a good correlation when compared to the available literature.

©公益社団法人土木学会

V-515

Japan Society of Civil Engineers 2021 Annual Meeting

Effect of Stirrups on Bond Strength Degradation in Cracked Concrete by Expansion Agent Filled Pipes
筑波大学
筑波大学
筑波大学
INTRODUCTION

12stirrups. To achieve this target, Concrete cracked byexpansion agent filled pipes in bond test specimens has been

S0S1S2

10Bond Stress (MPa)cracked concrete from the perspective of confinements by12Crack width: 0.15mm

This study aims to cast deep sight on the bond strength of8642

presented in the previous paper. Here, pull-out load vs slip

0864202468

100

120

24Slippage (mm)curves and relationships between the maximum pull-out load

Fig. 1 shows example of bond stress versus slippage
curves. The bond strength versus crack width relationship is8642shown in Fig. 2. It can be seen that the bond strength0864202468010024

Slippage (mm)decreases as the crack width increases for most specimens.

of the bond strength of a cracked specimen to that of the8642

uncracked specimen is evaluated to discuss the bond

0864
202468

100

120

24

Slippage (mm)degradation. The bond strength for uncracked specimens in(1)
𝑏⋅𝑝𝑤
𝑁⋅𝑑𝑏

⋅ℎ𝑙𝑤𝑒

⋅ 𝐸𝑆𝑡 ⋅ 𝜎𝐵(2)S0S1S2120

S0S1S210.4

40.2

0.5

11.5

Crack width (mm)00.5

1Fig. 3 Regression analysis result

Table 1 Regression analysis coefficient

reinforcement ratio, h: rib height, N: number of reinforcing
bar, lwe: bond effective length, Est: Elastic modulus of lateralreinforcement.
The following equation form is used to evaluate thedegradation of bond by regression analysis:

Seriespw (%)

ab

S00

1.61

-0.61

S1

1.10

0.43

-1.89

S2

1.68

0.24

-4.23

Where RB: Residual bond strength ratio, WCR: Crack(3)

width; a, b: Empirical coefficient.
Keywords

Rebar corrosion，Expansion agent，Crack width，Bond test , Stirrup.

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JSCE 令和3年度土木学会全国大会第76回年次学術講演会- V-515 -1.5

Crack width (mm)Fig. 2 Bond strength vs crack width

diameter of the tested bar, b: width of member, pw: lateral© Japan Society of Civil Engineers

100.6

6

confinement stress, θ :angle between the principal bondstress and the axis of reinforcement (= 45degrees), db: the80.882Where, τb,max: maximum bond stress, σl: lateral

𝑅𝐵 = 1 − 𝑎 (1 − (ⅇ 𝑏⋅𝑤𝑐𝑅 ))Residual bond strength ratio

Bond strength (MPa)𝜎𝑙,𝑚𝑎𝑥 = √0.018 ⋅1210𝜏𝑏,𝑚𝑎𝑥 = 𝜎𝑙 ⋅ 𝑐𝑜𝑡 𝜃

6Slippage (mm)Fig. 1 Example of bond strength vs slippage

S1and S2 is calculated by the formula reported in a previous
study [1] as follows :10S0S1S210Bond Stress (MPa)Residual bond strength ratio, which is defined as the ratio

Crack width: 0.7mm

S0S1S2103.1 Proposed empirical formulas

812Crack width: 0.6mm

BOND STRENGTH DEGRADATION

6Slippage (mm)12Bond Stress (MPa)

3.

10

S0S1
S2

Crack width: 0.5mm

10Bond stress (MPa)PULL-OUT TEST RESULT

812S0S1
S2

Crack width: 0.4mm

10Bond stress (MPa)2.

6Slippage (mm)12and surface crack width are discussed.

S0
S1
S2

Crack width: 0.2mm

10Bond stress (MPa)1.

○Syll Amadou Sakhir
下河邉大貴
金久保 利之

学生会員
学生会員
正会員

V-515seen in Table 1. Fig.3 compares the three formulas Until acrack width of 0.15mm, the influence of stirrup was not seenon the degradation of bond. This fine crack was still able toResidual bond strength ratio

The empirical coefficient by regression analysis can be.

Without stirrup

1fib model: upper limit
fib model: lower limit
S0 prediction

0.8
0.6
0.4
0.2

transmit the load from the bar to the surrounding concrete.

00.5

1

0.8
0.6
0.4
fib model: upper limit
fib model: lower limit
JCI 1998
S1 prediction
S2 prediction

0.2
00.5

11.5

Crack width (mm)Fig. 4 Formulas compared with previous models

the bond deterioration. The stirrups play an important role in

20terms of confinements after cracking. First, the concrete

1.5-1

cracking was restricted by stirrups, which led to the increase

astirrup can restrain the opening of the induced crack and limit

With stirrup

11.5

Crack width (mm)However, when the crack width is more than 0.15mm, theResidual bond strength ratio

Japan Society of Civil Engineers 2021 Annual Meeting

1of residual tensile strength of concrete. And then, once the0.5b-2-3

concrete cover cracked, the bearing forces due to ribs-40

transferred from the concrete to the stirrups, and the bond

0.5

1pw %

1.5

2-500.5

11.52pw %Fig.5 Influence of pw on coef a, b

strength was partly maintained by stirrups.
The obtained formulas are compared with the fib model [2]1Experimental RBin Fig.4. In absence of stirrup, the formula is in good
agreement with the fib model until the crack width reaches
0.8mm. Also, for specimens with stirrup good agreement isobtained from 0.6mm as crack width.

0.80.60.4
0.2

3.2 Influence of stirrup on the empirical coefficient00.2 0.4 0.6 0.8

1

Calculated RB

The bond deterioration due to corrosion is closely related

Fig. 6 Experimental and calculated results comparison

to the confinements provided by concrete cover and stirrups.
The fitted coefficient a and b are plotted against the stirrup
ratio pw in Fig. 5. With the increase of stirrup index (in %), a

But others show a slightly higher value of experimental RB.

and b decrease. Assuming an exponential decreasing, a and b

This indicates that the change in rebar shape or rustcan be evaluated by the following empirical equations:accumulation can be beneficial for bond degradation.

𝑎 = 1.6ⅇ −0.8𝑝𝑤(4)

𝑏 = 0.4ⅇ −1.3𝑝𝑤

(5)

4.

CONCLUSIONS
To investigate the effect of stirrup on bond degradation of

Substituting Eq. (4) and Eq. (5) into Eq. (3), the empiricalcracked concrete, pull-out bond test was conducted.

formulas for the bond strength of specimens with induced

Empirical formulas of the bond strength deterioration withcrack can be expressed as follows:

crack width as the main variable, have been proposed. These

𝑅𝐵 = 1 − 1.6ⅇ−0.8𝑝𝑤 (1 − (ⅇ 0.4ⅇ−1.3𝑝𝑤

prediction formulas give a good correlation when compared⋅𝑤𝑐𝑅))

6)

to the available literature.
REFERENCES

3.3 Experimental validation of the proposed formulas

To validate the effectiveness of the proposed formula, the[1] Yasojima, A., Kanakubo, T. Local Bond Splitting

predicted bond strength in cracked concrete is compared withBehavior of RC Members with Lateral Reinforcement, 14th

the experimental data available in the literature [3]. In theseWCEE, Paper ID 05-03-0033, 2008.

specimens with different pw values (0.33% to 1.33%), only the[2] fib Model Code 2010, Vol.1. International Federation for

main rebars were electrically corroded.

Structural Concrete, Lausanne, Switzerland.

Fig.6 shows the comparison between experimental and[3] Lin et al. Bond strength evaluation of corroded steel bars

calculated RB by formula (Eq.6). The predicted values show

via the surface crack width induced by reinforcement steel

a good agreement with experimental ones for some specimens.

corrosion, Engineering Structures, 152(1), 506-522, 2017.

JSCE 令和3年度土木学会全国大会第76回年次学術講演会© Japan Society of Civil Engineers- V-515 -