## 2 Test Specimens  
Some test samples including ENDB, SCB, BD, and SENB were selected for conducting the fracture experiment on the asphalt concrete and investigating the related fracture trajectory. Figure 1 shows the configurations of test samples. The ENDB specimen is a disc shape sample with radius R and height t that contains an edge crack along the disc diameter. By three-point bend loading of the disc and rotating the disc direction relative to the loading rollers, different combinations of mode I and mode III are introduced by the ENDB specimen. The SCB specimen is a semi-circular specimen with radius R and thickness t containing an edge crack of length a. The specimen is loaded by three-point bending and the state of mode I and II mixity can be altered by changing the crack inclination angle, crack location or loading roller distance relative to the crack as seen from Figure 1. The center crack Brazilian disc (BD) specimen is also a circular disc with radius and thickness R and t, respectively containing a center crack of length 2a. Mode I and mixed mode I/II are obtained using this specimen by changing the crack inclination angle relative to the direction of diametral compression load applied to the disc specimen. The edge cracked beam specimen subjected to bend loading (i.e., SENB specimen) can be used for introducing pure mode I and some limited combinations of mode I and mode II (i.e., dominantly mode I case). The stress intensity factors (K\({}_{\rm I}\), K\({}_{\rm II}\) and K\({}_{\rm III}\)) in the mentioned samples are functions of the specimen geometry and loading condition and can be written as:  
\[{\rm K_{i}(ENDB)}=\ \frac{3{\rm PS}}{2{\rm R}^{2}}\sqrt{\pi{\rm a}}{\rm Y_{i}} \left(\frac{{\rm a}}{{\rm t}},\frac{{\rm S}}{{\rm R}},\beta\right)\qquad{\rm i }\ =\ {\rm I},{\rm III} \tag{1}\]  
\[{\rm K_{i}(SCB)}=\ \frac{{\rm P}}{2{\rm R}{\rm t}}\sqrt{\pi{\rm a}}{\rm Y_{i}} \left(\frac{{\rm a}}{{\rm r}},\frac{{\rm S}}{{\rm R}},\beta\right)\qquad{\rm i }\ =\ {\rm I},{\rm II} \tag{2}\]  
\[{\rm K_{i}(BD)}=\ \frac{{\rm P}}{{\rm R}{\rm t}}\sqrt{\frac{{\rm a}}{{\rm r}}}{ \rm Y_{i}}\left(\frac{{\rm a}}{{\rm R}},\beta\right)\qquad{\rm i}\ =\ {\rm I},{\rm II} \tag{3}\]  
\[{\rm K_{i}(SENB)}=\ \frac{3{\rm PL}}{{\rm tw}^{2}}\sqrt{\pi{\rm a}}{\rm Y_{i}} \left(\frac{{\rm a}}{{\rm w}},\frac{{\rm S}}{{\rm L}},\frac{{\rm d}}{{\rm S}} \right)\qquad{\rm i}\ =\ {\rm I},{\rm II} \tag{4}\]  
where P is the applied load and Y\({}_{\rm i}\) are the geometry factors or normalized forms of the stress intensity factors that are functions of the specimen geometry and loading conditions [15, 17, 18, 29, 30, 46, 47]. The corresponding values of these geometry factors for any test specimen and mode mixity can be determined using the finite element analysis. For example, Table 1, illustrates the values of Y\({}_{\rm I}\), Y\({}_{\rm II}\) and Y\({}_{\rm III}\) for pure and mixed mode loading conditions of the ENDB, SCB, BD, and SENB for some loading modes. Figure 1: Description of test specimens employed for mode I, mixed mode I/II, and mixed mode I/III fracture; (**a**) edge notch disc bend (ENDB), (**b**) semi-circular bend (SCB), (**c**) Brazilian disc (BD) and (**d**) single edge notch beam (SENB).