## 3 Model Validation
They carried out pull-out tests on cubic concrete specimens of 100 \(\times\) 100 \(\times\) 100 mm with a 12 mm diameter plain and deformed corroded rebar and with an embedment depth of 80 mm. The corrosion was simulated artificially, and was considered uniform all along the rebar. We can notice that the results they obtained are similar to our numerical model, especially the results with the plain rebars. As for the deformed rebars, we can highlight that the bond stress is significantly higher at very low degrees of corrosion compared to the bond stress of the plain specimens and compared to our models. This is because, with plain rebars, there is no mechanical contact between the reinforcement and the concrete cover, and at lower degrees of corrosion, the ribs of the deformed rebars are still not enough damaged. The results of [PERSON] et al. [9], where they carried out pull-out test on corroded concrete blocs with also only one deformed rebar, are also plotted in Figure 8. The top concrete cover varied between 25 mm and 35 mm and a fixed lateral concrete cover of 65 mm. The embedment depths were of 300 mm with only 200 mm of contact between the rebar and the concrete. The specimens had either two or four stirrups. They conducted artificial corrosion on the specimens before pulling-out the rebars. They noticed that stirrups were the more corroded than the rebars. The results they obtained are quite similar the ones with our numerical model; we notice the same tendency with small differences in term magnitudes for the bond stresses. This can be explained by the presence of the stirrups and also because the rebar is deformed. Figure 7: Evolution of the maximum pull-out load as a function of the corrosion degree. Finally, we also plotted in Figure 8 the results of tested naturally corroded specimens from [PERSON] et al. [26] from their report delivered to the Integrated Research Project \"Sustainable Bridges-Assessment for Future Traffic Demands and Longer Lives\", funded by the European Commission. The main objective of the report was to study the impact of corrosion on the structural strength of RC structure. They collected cubic pieces of concrete from the Ullasund Bridge in Norway to test them. The specimens were exposed to the natural environment of the area for approximately 30 years and were corroded naturally. The size of the specimens tested was about 150 mm \(\times\) 150 mm \(\times\) 150 mm with a single 25 mm diameter deformed rebar. These specimens were then cast in concrete cylinders of 320 mm diameter. They assessed the corrosion degree of the specimens after carrying out the pull-out test. Overall, we notice that the results from our numerical model and the experimental results from the literature and plotted in Figure 8 exhibit the same tendency, with some discrepancies in term of magnitudes. There is an increase in the bond stress, and after reaching a certain degree of corrosion (around 1.5% in our model), the bond stress drops significantly. As explained earlier, this is due to the damaging of the concrete at the interface and the cracking of the concrete cover. As for the corrosion degree where the drop occurs, the results in the literature are very scattered. [PERSON] et al. [3] noticed an increase of bond stress until reaching a corrosion degree of 1%, the bond stress drops after. [PERSON] et al. [4] found that the corrosion degree where a drop in the bond stress was noted was about 5%. [PERSON] et al. [6] found that the reduction of bond stress happens at a corrosion degree of approximately 0.5%. As mentioned before, there is a wide variety in term of results in the literature, and this had been outlined in [14,24]; furthermore the results show the same trend across the literature. Pull-out failure can be one of the three failure modes presented before. The second mode that our model is able to simulate is the cone failure of the concrete cover, as can  
Figure 8: Numerical results: bond stress-corrosion degree with comparison with the literature.