# Bond Strength Assessment of Concrete-Corroded
## 3 Application of Artificial Neural Network (ANN) Model
### Application of ANN Method on the Cases with the Confined Condition  
In contrast to cases with the unconfined condition, cases with the confined condition (with stirrups) are more complicated and the bond strength loss is influenced by more parameters. The calculated results based on the proposed ANN method are shown in Figure 10. When only a single factor is considered as the input, the coefficient of determination is rather low, and this is not satisfactory. Similarly, the degree of accuracy increases as more parameters are involved. Again, it seems that crack width plays an important role in the bond strength loss, which shows good agreement with the experimental observations. Although the results show scattering, when all important factors are considered, a good agreement between the predicted and the experimental results can be obtained. There is a major difference between the cases with and without confinement. While the bond strength is dominated by corrosion level and crack width in the cases of unconfined condition, other parameters such as concrete strength, cover-to-diameter ratio and stirrups diameter-to-spacing ratio are important in the cases of the confined condition. Since all of these parameters are very important, it is necessary to perform a parametric analysis to correlate the parameters in terms of bond strength degradation.  
Figure 10: _Cont._Figure 10: Comparison of the results calculated by ANN method considering different parameters for the confined cases: (**a**) corrosion level; (**b**) crack width; (**c**) crack width and corrosion level; (**d**) corrosion level and stirrups diameter/spacing ratio; (**e**) crack width and stirrups diameter/spacing ratio; (**f**) crack width, corrosion level and stirrups diameter/spacing ratio; (**g**) crack width, corrosion level, concrete strength, cover to diameter ratio and stirrups diameter/spacing ratio.  
low (0.317). Unlike the cases under the unconfined condition, the cover-to-diameter ratio becomes more important, which shows better correlation on bond strength than the other parameters. Similar results are also listed in Table 4, which shows the results of cases that do not consider corrosion level. The second important parameter is the stirrups diameter-to-spacing ratio. It is followed by concrete strength and finally by crack width. However, as listed in Table 4, if only one parameter is considered, the crack width can achieve higher accuracy than when using only the corrosion level. For the other three parameters, the importance rank is the same. It is worth noting that, when all four parameters are considered, \(R^{2}\) is greater than 0.8 and the RMSE is approximately 0.1, which means that accuracy is acceptable. Therefore, the results indicate that parameters related to the confinement are more important than those related to the material property in the case with stirrups. The relative importance of the parameter is: crack width \(>\) corrosion level \(>\) cover-to-diameter ratio \(>\) stirrups diameter-to-spacing ratio \(>\) concrete strength.  
Compared with the cases of unconfined and confined conditions, the relative importance shows a different trend regarding the corrosion level and crack width due to the different importance role of the confinement. In the case of unconfined condition, since the confinement by concrete cover is not very strong, the corrosion level could be a more direct index. However, for the confined condition, the confinement stress from concrete cover and stirrups plays a more important role on the bond behavior, and the crack width shows a better predicted result on bond strength.