# Influence of Cracking on the Durability of Reinforced Concrete with Carbon Nanotubes
## 3 Results and Discussion
### Capillary Absorption
After this initial effect, the absorption rate gradually tends to approach that of reference concrete. As for uncracked concrete, the CNT were also effective in reducing the absorption coefficient of cracked concrete (Table 5). The reduction of C\({}_{\text{abs},0\text{-}3\text{h}}\) and C\({}_{\text{abs},6\text{-}7\text{h}}\) was about 10 and 24%, respectively. In this case, besides the filler and nucleation effect, the bridging effect should have a more effective contribution. In uncracked conditions, the bridging effect may only act when the specimens are previously loaded or subjected to dimensional variations from temperature and humidity gradients. The CNT only participate in the crack opening reduction by arresting the microcrack propagation into macrocracking. As shown in [PERSON] et al. [20], CNT are only able to bridge cracks up to about 1 \(\upmu\)m. Therefore, in existing cracks with over 0.05 mm average crack width, the water absorption thought the crack should be the same in CNTRC and PC. Indeed, the incorporation of CNT should act in the reduction of the crack influence at three levels: reduction of microcracking around macrocracks, decreasing the level of absorption in its vicinity; reduction of the crack propagation into the concrete specimen; induction of narrower crack openings, for a given load, due to microcrack retention. Regarding this last point, as concrete specimens were produced and analyzed with the same target crack opening, the possible positive contribution of CNT in this action was not assessed. Indeed, the direct comparison of the absorption coefficient in each concrete is not correct, because of the different crack depth between tested specimens. Therefore, to better understand the influence of the crack, the crack coefficient, \(\beta_{CR}\), was determined according to Equation (3) suggested by [PERSON] et al. [37], independent of the crack depth. This  
Figure 3: Capillary absorption over time for uncracked concrete specimens. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Cracking Condition**} & \multirow{2}{*}{**Mix**} & **Crack** & **Crack Depth, I\({}_{c}\)** & \multicolumn{2}{c}{**Capillary Absorption**} & \multicolumn{2}{c}{**Water Absorption**} \\ \cline{3-7}  & & **Width 1** & & **C\({}_{\text{abs},0\text{-}3\text{h}}\)** & **C\({}_{\text{abs},0\text{-}3\text{h}}\)** & **C\({}_{\text{abs},6\text{-}7\text{h}}\)** & \(\beta_{CR}\)** & **at 72 h** \\ \cline{3-7}  & & **(mm)** & **(mm)** & & **(mm/min43)** & & **(kg/m3)** \\ \hline \multirow{2}{*}{uncracked} & PC & - & - & 0.371 & 0.095 & & 11.08 \\  & CNTRC & - & - & 0.363 & 0.069 & & 9.71 \\ \hline \multirow{2}{*}{artificially cracked} & PC & 0.05 & 18 & 0.515 & 0.132 & 0.954 \\  & CNTRC & 0.05 & 18 & 0.466 & 0.107 & 0.868 \\ \hline \multirow{3}{*}{naturally cracked} & PC & 0.05 (0.1) & - & 0.264 & & 0.017 & 2.42 \\  & 0.1 (0.16) & - & 0.266 & & 0.019 & 2.64 \\ \cline{1-1} \cline{2-7}  & CNTRC & 0.05 (0.08) & - & 0.217 & & 0.018 & 2.28 \\ \cline{1-1} \cline{2-7}  & 0.1 (0.2) & - & 0.251 & & 0.016 & 2.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Capillary absorption coefficients and 72 h water abortion for concrete under different cracking conditions. coefficient relates the absorption in cracked concrete, \(abs_{cc}\), to the absorption in reference uncracked concrete, \(abs_{uc}\), of the same composition. These parameters were arbitrarily determined at 6 h [37]. In this case, the \(abs_{cc}\) is normalized in order to be independent of the crack depth. To this end, the specimen surface area in contact with water, \(A_{0}\), is increased by the area of the crack walls, where \(D\) is the diameter and \(L_{c}\) is the crack length. The average \(\beta_{CR}\) was 10% higher in PC than in CNTRC (Table 5), showing that the increase of absorption is more relevant in unreinforced concrete. This indicates the contribution of CNT to the microstructure refinement around the crack region.