## 4 Results and Discussion
### Fracture Pattern and Load-Displacement Curves
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multirow{2}{*}{**Temperature (\({}^{\circ}\)C)**} & \multicolumn{5}{c}{**Fracture Load (N)**} \\ \cline{3-6}  & & **Repeat 1** & **Repeat 2** & **Repeat 3** & **Repeat 4** & **Average** \\ \hline \multirow{2}{*}{ENDB} & \(-25\) & 2401 & 2982 & 3014 & 3091 & 2872 \\ \cline{2-6}  & \(-5\) & 1955 & 2005 & 2165 & 2218 & 2086 \\ \hline \multirow{2}{*}{SCB} & \(-25\) & 2926 & 3249 & 3395 & 3493 & 3266 \\ \cline{2-6}  & \(-5\) & 2252 & 2340 & 2409 & 2643 & 2411 \\ \hline \multirow{2}{*}{SENB} & \(-25\) & 868 & 986 & 999 & 1044 & 974 \\ \cline{2-6}  & \(-5\) & 611 & 716 & 728 & 747 & 701 \\ \hline \multirow{2}{*}{ENDC} & \(-25\) & 6632 & 8595 & 8814 & 9158 & 8300 \\ \cline{2-6}  & \(-5\) & 5415 & 5617 & 5739 & 6638 & 5852 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fracture loads of the tested specimens at low temperature conditions. in the range between 0.71 and 0.81 MPa\(\sur\)m and 0.68 to 0.80 MPa\(\sur\)m with an average value of 0.76 MPa\(\sur\)m and 0.73 MPa\(\sur\)m, respectively. The minimum and maximum band for the mode I fracture toughness obtained from the SENB specimen varies from 0.58 to 0.71 MPa\(\sur\)m with the average value of 0.67 MPa\(\sur\)m. The corresponding average values of K\({}_{\text{lc}}\) for the ENDC specimen at \(-25\)\({}^{\circ}\)C and \(-5\)\({}^{\circ}\)C are also obtained equal to 0.70 and 0.49 MPa\(\sur\)m, respectively. The mode I fracture toughness values obtained in this investigation shows good consistency with the data reported by different researchers for similar HMA mixtures. The results in Table 5 compares and presents typical K\({}_{\text{lc}}\) values reported in the literature for low temperature fracture of asphalt concrete mixtures. Depending on the type of mixture (mix design), testing temperature and type of specimen utilized for fracture toughness experiment, the value of K\({}_{\text{lc}}\) varies in the range between 0.5 and 1 MPa m\({}^{0.5}\). The information in Figure 10 compares the corresponding values of fracture toughness obtained via four testing methods. It can be observed from Figure 10 that the results of the ENDB, SCB and SENB samples are in agreement and the K\({}_{\text{lc}}\) values obtained using these three specimens (especially ENDB and SCB) are close together for both low temperature conditions tested in this research. The difference between the highest and lowest fracture toughness value determined from these methods is about 8%. Such difference can be attributed to the geometry or shape of ENDB, SENB and SCB specimens (i.e., full disc, rectangular beam and semi-circular geometries, respectively), although the type of loading (i.e., three-point bending) is similar for all these three specimens. However, the data obtained from the ENDC specimen shows a noticeable reduction in the value of K\({}_{\text{lc}}\) compared to the other test samples. For example, while the ENDB and ENDC samples have the exact same geometry, their K\({}_{\text{lc}}\) values differ by approximately 20%. This is mainly due to the effect of loading type (three-point bend applied to the ENDB and diametral compression applied to the ENDC specimen). Indeed, a lower bound fracture toughness value is obtained by changing the type of loading from bending to diametral compression in the edge notch disc specimen. From the obtained experimental results, it can be concluded that the fracture toughness value is more sensitive to the type of loading (i.e., bending or compression) applied to the asphalt mixture than compared to the shape of the test specimen (i.e., circular disc or rectangular beam shape). Figure 9: Fracture toughness of tested specimens under different test temperatures: (**a**) \(-25\)\({}^{\circ}\)C and (**b**) \(-5\)\({}^{\circ}\)C.  
As stated earlier, the SCB test method was suggested in recent years by ASTM for measuring the fracture toughness of asphalt mixtures [55].