# Investigation of Crack Propagation and Healing of Asphalt Concrete Using Digital Image Correlation
## 3 Results and Discussion
### Proposed Healing Indices  
In this step, first, resilient modulus and resilient horizontal strain of the three samples are recorded during the fatigue tests, before and after the healing procedure. The resilient modulus decreases during the first fatigue test until it reaches the termination value. Then part of the mechanical properties of the specimens recover during step 2 and a second fatigue test is conducted on the specimens. Recovery indices based on these parameters are calculated using Equations (1) and (2) and are presented in Table 3.  
Next, the diagrams of P/P\({}_{\text{total}}\) are plotted for the samples during the first and second step of the experiments (Figure 9). Based on these diagrams and with the procedure explained in Section 2.3, the healing parameters of the samples based on the DIC method are calculated and presented in Table 3. In this table, it can be seen that the average of RI for this mixture is 97%, but the H% value is only 27.7%. Therefore, it could be concluded that strain recovery on the surface does not fully represent the recovery of the mechanical properties of the mixtures. This difference could be due to the fact that H% only investigates the healing of the microcracks on the specimens, but some viscoelastic responses such as non-linearity, thixotropy, and steric hardening can also generate mechanical recovery during the second step of the experiments. Furthermore, H% is based on the microcracks on the surface of the objects. However, healing occurs as well in the microcracks under the surface layer. This can explain the high standard deviation value for H%. The two more interesting calculated parameters are HT, which indicates the time in which all the strain recovery on the surface of the mixture happens, and SR, which shows the speed of this recovery. Without DIC, multiple experiments with different healing times should be conducted to estimate the required healing time for a mixture to achieve its optimum recovery level. However, in this research, the healing level of the asphalt mixture was plotted in time with only one experiment. This diagram was able to give the minimum time (29.33 min) to have the optimum healing for this asphalt concrete in an efficient procedure. This could be useful in practice to decide how much time a mixture needs to heal to an optimum level at a certain temperature. It is also possible to use this method to calculate the SR of different asphalt mixtures and compare their healing rates. However, it should be mentioned that HT and SR are not only dependent on the mixtures but also the temperature increase rate. Thus, they can only be used to compare different mixtures if the exact same healing procedure (step 2) is conducted.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**UTM**} & \multicolumn{2}{c}{**DIC**} \\ \hline  & **EI** & **RI** & **HT [min]** & **H\%** & **SR [\(\mu\varepsilon\)/min]** \\ \hline
**S1** & 0.86 & 0.99 & 31 & 42.3 & 0.0028 \\
**S2** & 0.86 & 0.92 & 23 & 18.87 & 0.0020 \\
**S3** & 0.94 & 0.99 & 34 & 21.98 & 0.0018 \\ \hline
**Average** & 0.89 & 0.97 & 29.33 & 27.72 & 0.0022 \\
**SD** & 0.05 & 0.04 & 5.69 & 12.72 & 0.0005 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Healing parameters of three identical asphalt samples using the data acquired by the UTM and DIC.