## 4 Experimental Numerical Study of Corrosion Cracks and their Reproduction
### Comparison of Experimental and Numerical Results  
The experimental results indicate that the amount of reinforcing bar corrosion is correlated significantly with the crack width. In contrast, the relationship between the corrosion expansion displacement and the crack width of the reinforcing bars obtained from the numerical results could not be validated. Therefore, a model that describes the latter relationship is required. According to previous studies [31; 32; 33], the amount of corrosion per unit of reinforcing bar length is expressed as  
\[W_{r}=\frac{C\rho U}{n-1}, \tag{16}\]  
where \(W_{r}\) [mg/cm\({}^{2}\)] is the amount of reinforcing bar corrosion, \(\rho\) [7850 mg/cm\({}^{3}\)] is the density of iron, \(U\) [cm] is the radial displacement applied to the reinforcing bar, \(n\) is the volume expansion coefficient of the corrosion products, and \(C\) accounts for the runoff of the corrosion products. Using the results of various sensitivity analyses giving the experimental results considered external runoff of corrosion products in electrolytic tests [34], we arrived at C = 0.8. This model required us to set the volume expansion coefficient of corrosion products on the reinforcing bar corrosion products. [PERSON] et al. [30] asserted that (i) this volume expansion coefficient is in the range of 1.8-4.8 and (ii) the chemical composition and volume expansion coefficient of the corrosion products can be large depending on the corrosion environment of iron. [PERSON] et al. [35] performed X-ray diffraction on corrosion products extracted from electrolytic corroded RC members and found that the precipitation of magnetite (Fe\({}_{3}\)O\({}_{4}\)) with a volume expansion coefficient of 2.1 was predominant. Because electric corrosion was also performed in the present experiment, this result was used to convert the volume expansion displacement into the amount of reinforcing bar corrosion. First, we compared the crack distribution on the bottom of the specimens after the experiment with the simulated results. Figure 19 shows the damage distribution on the bottom of Specim 3. In terms of the amount of corrosion on the reinforcing bar, step 10 corresponds to Cases 1-3 in Figure 17, step 50 to Cases 4 and 5, step 150 to Case 6 and 7, and step 200 to Case 8-10. With the increase in the amount of reinforcing bar corrosion, cracks were generated along the axial direction. Furthermore, the cracks at right angles to the axial direction were generally reproduced experimentally, as well as the increase in damage. In addition, the tendency of cracking perpendicular to the axis was mostly reproduced. Figure 18: Bottoms of specimens (Cases 1 to 10). Figure 20a compares the experimental results for cross-sections 1 and 3 in Figure 17 and the numerical results for sections 1 and 3 with respect to the amounts of corrosion. Similarly, Figure 20b compares the experimental results for 2 with the numerical results for section 4.2. We used the maximum crack widths of the mortar bottoms at positions 1 and 3. First, confirming the experimental results, the crack width tended to increase with the amount of corrosion in any cross-section, although the variation was large. The experimental and numerical values in Figure 20a,b show that for a given crack width, the amount of corrosion shown by the latter was underestimated compared with the former. This point is elaborated as follows. In each case, the electrolytic corrosion test confirmed the continuous contact of the corrosion products with salt water that flowed out of the test piece through the porous sponges. The corrosion products probably did not contribute to the damage to the concrete, thus having little effect on the crack width of the covered concrete with respect to the actual amount of  
Figure 19: Damage distribution on the bottom of the specimen (simulation). Figure 20: Crack width versus corrosion amount; (**a**) cross-sections 1 and 3; (**b**) cross-section 2.  
corrosion.