# Effect of Stirrup on Bond Strength Degradation in Concrete Cracked by Expansion Agent Filled Pipes
## 4 Evaluation of Bond Strength Degradation in Cracked Specim with Stirrup
### Comparison of the Proposed Formulas with Experimental Results in the Literature  
To validate the effectiveness of the proposed formula, the predicted bond strength in cracked concrete is compared with the experimental data available in the literature.  
Figure 16a shows the comparison of our prediction for specimen without stirrup (S0) with test results by [PERSON] et al. [16]. Beam end specimens which had a dimension of 200 mm \(\times\) 200 mm \(\times\) 300 mm, were used in pull-out test. Two types of rebars with a diameter of 12 mm and 16 mm were employed, and the concrete cover (3D) was 36 mm and 48 mm respectively. An example of corrosion-induced crack patterns from [PERSON] et al. can be seen in Figure 16b. The coefficient of variation of the ratio of the predicted bond strength to the tested bond strength is calculated. With a coefficient of variation equal to 12%, it can be clearly noted that the predicted curves are close to the experimental results in most cases.  
In the studies by [PERSON] et al. [13; 15; 29], pull-out tests were carried out in corroded specimens with an induced crack pattern similar to those modeled in the present study. Figure 16b shows an example of corrosion-induced crack patterns from [PERSON] et al. The test is performed on eccentric pull-out specimens with a 20 mm diameter rebar and different concrete cover. Only the main rebars were electrically corroded in these specimens without and with stirrup (stirrup ratio of 1.34%). Also, the residual bond strength and the induced crack width were reported. In Figure 17a,b, the models are compared with [PERSON] et al. In [PERSON]'s specimens with stirrups, the number of stirrups is equal or superior to two. Therefore, the S2 prediction is adopted for expressing the coefficient of variation. Our proposed formulas in this study generally agree well with the tested bond strength in the literature with a coefficient of variation equal to 14% and 17% in specimens without stirrup and with stirrup, respectively. The bond degradation trend in specimens with corrosion-induced cracks can be well approximated. Also, the beneficial influence of stirrups on the bond strength in cracked concrete can be well reflected.  
Figure 16: Comparison of the proposed formulas with study by [PERSON] et al.: (**a**) S0 prediction compared with specimen by [PERSON] et al.; (**b**) typical corrosion-induced cracks in specimen by [PERSON] et al. [16].  
Our bond degradation formulas remained primarily on the safe side compared with the fib model and previous studies. It also demonstrated that the crack induced by EAFP could express the net quantity of damage due to corrosion. Since the surface crack width is the most visible manifestation of damage due to corrosion, it is convenient to directly link with a damage indicator that can be easily measured. Despite these promising results, questions remain on the influence of the rebar section change or rust accumulation due to corrosion. In future investigations, it might be possible to evaluate the effect of corroded rebar in concrete cracked by EAFP.