# Influence of Cracking on the Durability of Reinforced Concrete with Carbon Nanotubes
## 3 Results and Discussion
### Carbonation Resistance  
The carbonation depth in the uncraked, xc, and cracked area, xCR, as well as the carbonation coefficient of the uncracked, Kc, and cracked area, Kc,CR, are presented in Table 6, involving the reference and the artificially or naturally cracked concrete specimens. The average crack characteristics (width and depth) are also presented in this table. In general, a good correlation (R2 > 0.9) with the square root of time was found, which confirms the suitability of Equation (1), based on [PERSON]'s first law. The uncracked area in non-reference concrete corresponds to the specimen region sufficiently far from the crack influence (equivalent to the carbonation depth). On average, the carbonation resistance was 18% improved with the CNT incorporation in uncracked concrete (Table 6). A slightly lower improvement, of 16%, was reported by [PERSON] et al. [24], taking into account the same type and amount of CNT reinforcement. Due to the preconditioning and dry exposure test conditions of the specimens, all mechanisms are likely involved in the reinforcement of the concrete matrix (filler, nucleation and bridging effect). Bridging can contribute to the reduction of the pore connectivity and consequently to CO2 diffusion in concrete by retaining crack propagation and reducing microcrack width. The nucleation effect should improve the carbonation resistance by densifying the microstructure of concrete and by increasing the amount of carbonated substances in the cementitious matrix. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Cracking** \\ **Condition** \\ \end{tabular} } & \multirow{2}{*}{**Mix**} & \multirow{2}{*}{\begin{tabular}{c} **Crack** \\ **Width**1 \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Crack** \\ **Depth, Lc** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Region of** \\ **Testing** \\ \end{tabular} } & \multicolumn{4}{c}{**Carbonation Depth**} & \multicolumn{2}{c}{**Carbonation Coefficient**} \\ \cline{5-10}  & & & & & & \multicolumn{2}{c}{**x\({}_{\text{s}}\) (mm)**} & \multicolumn{2}{c}{**Kc**} & \multirow{2}{*}{**R2**} \\ \cline{5-10}  & & **(mm)** & & & & \multicolumn{2}{c}{**7 Days**} & **28 Days** & **56 Days** & **90 Days** & **(mm/Year2.5)** \\ \hline \multirow{2}{*}{uncracked} & PC & - & - & & & 7 & 10.2 & 12.7 & 25.7 & 0.99 \\  & CNTRC & - & - & & 5.6 & 9.1 & 9.9 & 21.1 & 0.98 \\ \hline \multirow{3}{*}{artificially cracked} & PC & 0.05 & 18 & uncracked & & 10.2 & 12.4 & 14.5 & 31.2 & 0.97 \\  & & & & & cracked & 17.2 & 19.3 & 23.2 & 67.1 & \\ \cline{2-10}  & CNTRC & 0.05 & 18 & uncracked & & 9.9 & 11.5 & 12.4 & 28.2 & 0.93 \\  & & & & & & 16.9 & 18.4 & 19.9 & 65.8 & \\ \hline \multirow{3}{*}{
\begin{tabular}{c} **naturally cracked** \\ \end{tabular} } & PC & 0.05 (0.06) & - & uncracked & 2.9 & 7.3 & & & 25.1 & 0.98 \\  & & & & & 10.2 & 19.9 & & & 72.3 & 0.99 \\ \cline{2-10}  & & & & & uncracked & 3.8 & 7.1 & & 25.9 & 0.99 \\ \cline{2-10}  & & & & & & 13 & 21.4 & & 80.7 & 0.98 \\ \cline{2-10}  & & & & & & 2.5 & 6.9 & & 23.6 & 0.97 \\ \cline{2-10}  & & & & & & & 18.2 & & 65.6 & 1 \\ \cline{2-10}  & & & & & & 3.5 & 7.1 & & 25.5 & 0.99 \\  & & & & & & 10.2 & 20.5 & & 73.9 & 1 \\ \hline \hline \end{tabular}  
* \({}^{1}\) target crack width (measured average crack width).  
\end{table} 
Table 6: Carbonation resistance for concrete under different cracking conditions. The carbonation rate in the cracked region is influenced by the crack depth. Therefore, based on the methodology suggested in [PERSON] et al. [37], the carbonation coefficient through the crack, \(K_{c,CR}\), was determined regardless of \(L_{c}\). It was assumed that over \(L_{c}\) the carbonation depth in the cracked area, \(\kappa_{\text{CR}}\), is increased at the same rate of the \(x_{c}\) in the reference uncracked area. Then, from Equation (6), based on Equation (1), the time taken for the carbonation depth to reach Lc (\(t_{c}\)) can be estimated.