# Influence of Cracking on the Durability of Reinforced Concrete with Carbon Nanotubes
## 3 Results and Discussion
### Capillary Absorption
\[\beta_{CR}=\frac{\frac{abs_{cc}\times A_{0}}{A_{0}+(2L_{c}\times D)}}{abs_{uc}} \tag{3}\]  
In addition, the coefficient of absorption in the cracked region \(C_{abs,CR}\) was estimated according to Equation (4), which provides a direct measure of the crack influence in the capillary absorption [37]. In Equation (4) the absorption in the cracked region, \(abs_{CR}\) (additional absorption rate due to cracking) may be determined from Equation (5), where \(A_{C}\) is the cracked area given by the product of the specimen diameter and the crack width. \[C_{abs,CR}=\frac{abs_{CR}}{A_{c}\times\sqrt{t}} \tag{4}\]  
\[abs_{CR}=(abs_{cc}\times A_{0})-abs_{uc}\times(A_{0}-A_{c}) \tag{5}\]  
Figure 4 shows the evolution of \(C_{abs,CR}\) over time. It can be observed that the effect of the crack is decreasing with time. Compared to the absorption coefficients of uncracked reference concrete (Table 5), the cracked area presents significantly higher absorption rates than the uncracked area, which confirms that artificial cracks of 0.05 mm offer no significant resistance to water uptake. In addition, it is also confirmed that there is less influence of the crack in concrete reinforced with CNT. During the first 60 min, the \(C_{abs,CR}\) was over 40% lower in CNTRC than in PC. Specimens with natural cracks are not comparable with any of the above, since the size and testing age were different, as well as the curing conditions. As mentioned in Section 2.4, these specimens were subjected to less drying and hence lower water absorption was expected. Moreover, due to the adopted cracking methodology (see Section 2.4), the crack went through all the specimen thickness. Therefore, only the early absorption was considered. The water abortion at 72 h, as well as the absorption coefficients up to 20 min, \(C_{abs,0-20\min}\), and between 6 and 72 h, \(C_{abs,6-72h}\), are presented in Table 5. The consideration of absorption coefficients up to only 20 min is justified by the rapid absorption and the lower drying conditions of these specimens. The \(C_{abs,6-72h}\) occurred in almost full saturated concrete, without significant differences between concrete specimens. As mentioned, the average crack width in tested specimens were higher than the target values, because natural pre  
Figure 4: Absorption coefficient in the cracked area, \(C_{abs,CR}\), over time. cracking is more difficult to control. However, induced cracks from bending tests are usually V-shaped, being narrower in depth. Moreover, the average crack width only slightly varied between reference and CNT reinforced concrete (\(\pm\)20%, Table 5). As expected, the absorption increased in concrete with wider cracks. However, the increase was low, because there was rapid water uptake through the crack and the exposed area to water absorption was not significantly altered. Therefore, the slight variation of crack width between concrete specimens (Table 5) had little influence in concrete results. Assuming similar crack width in both concrete types the positive contribution of CNT in reducing the early absorption coefficient of cracked concrete is confirmed, regardless of the crack target width. On average, this reduction was 18% and 6% for crack widths of about 0.1 and 0.2 mm, respectively. The modest water absorption reduction in CNT reinforced concrete (12%, on average) may be partly related to the lower drying degree and less available empty small pores in natural cracked concrete, where CNT may better contribute to the reduction of water absorption.