# Effects of Freeze-Thaw and Wet-Dry Cycles on Tension Stiffening Behavior of Reinforced RAC Elements
## 4 Freeze-Thaw and Wet-Dry Degradation-Law for Reinforced RAC  
With the experimental results obtained for the structural properties discussed above, a generalized degradation-law is proposed for reinforced RAC subjected to freeze-thaw aging or wet-dry aging: the law represents the relationships between an initial property of the isolated intact concrete, in this case, the concrete water absorption capacity, herein defined as concrete open porosity (\(w_{open}\)), and the variations obtained in the main structural properties of the steel-concrete composite after freeze-thaw or wet-dry degradation, that is, pre-cracking elastic modulus (\(E_{pre}\)), first crack load (\(F_{1 st}\)) and bond strength (\(\tau_{b}\)). The three proposed relationships are described in the following equations:  
\[\frac{E_{pre,AGING}}{E_{pre,REF}}=\frac{1}{1+a^{2}\cdot w_{open}} \tag{2}\]  
\[\frac{F_{1 st,AGING}}{F_{1 st,REF}}=\frac{1}{1+b^{2}\cdot w_{open}} \tag{3}\]  
\[\frac{\tau_{b,AGING}}{\tau_{b,REF}}=\frac{1}{1+c^{2}\cdot w_{open}} \tag{4}\]  
where a, b and c are calibrated parameters in relation to each of the structural properties: pre-cracking elastic modulus, first crack load and bond strength, respectively. Figure 6 presents the calibrated degradation-law curves proposed by Equations (2) and (3) and the experimental results after freeze-thaw or wet-dry degradation. The proposed degradation-law equations have physical significance and indicate that the degradation effect, expressed by the relation between the results obtained after each degradation scenario and the reference values, can be presented as a function of the initial open porosity of the concrete for each structural property of the composite. Hypothetically, if concrete were completely impermeable, that is, open porosity equal to zero, according to Equations (2)-(4), pre-cracking elastic modulus, first crack load and bond strength would not be affected by the aging effect. From the results plotted (Figure 6), it is possible to observe that, in each group, the point with the lowest open porosity represents the reinforced natural concrete composite, while the others correspond to reinforced RAC composites. Due to their higher total mortar volume (as consequence of the presence of AM), steel-RAC elements have higher values of open porosity compared to steel-concrete elements without RCA incorporation. Figure 6: Relation between concrete open porosity and structural properties in the freeze-thaw and wet-dry durability studies: (**a,b**) Pre-cracking elastic modulus; (**c,d**) First crack load; (**e,f**) Bond strength. It is worth mentioning that the proposed laws (see Equations (2)-(4)) state that concrete degradation is directly related to the initial open porosity of the concrete (wopen), which is directly related (see Equation (1)) to the total volume of mortar (V\({}_{\text{M,tot}}\) in Table 2) and, consequently, to the \"quality\" (considering the amount of attached mortar, V\({}_{\text{AM}}\) in Table 1, characterizing the employed recycled particles) and amount of RCAs. For both freeze-thaw and wet-dry aging, the smaller number of cycles (represented by the top points) did not cause significant reductions in the structural properties of the composites after degradation. However, the degradation effect is more evident in the lower points, which represent the samples that have undergone the greatest number of cycles. The more horizontal shape of the curves corresponding to the smaller number of cycles shows that, even by increasing the open porosity, the structural properties have been little changed. This means that, for a lower degradation level, the presence of recycled aggregates does not significantly influence the composite's degradation. On the other hand, the highest degradation level curves present a greater slope, which makes the structural properties of the composite more sensitive to the concrete open porosity increase.