## 2 Fracture Toughness Test Specimens  
Four different test specimens namely the SCB, ENDB, SENB and ENDC samples are selected for conducting the mode I fracture toughness experiments on asphalt mixture and for determining the corresponding K\({}_{\text{lc}}\) values. Test geometry, crack location and loading configurations used for the mode I fracture testing via these samples are illustrated in Figure 2. The ENDB and ENDC specimens are disc shaped samples with radius R and thickness t that contain an edge crack along the disc diameter. The depth of notch in ENDB and ENDC samples is defined by a. The SCB specimen is a semi-circular specimen with radius R and thickness t containing an edge crack of length a. The SENB specimen is a rectangular beam with the length, width and thickness of L, W and t, respectively, that contains a vertical edge crack of length a at the middle of the beam. As seen from Figure 2, the geometry and shape of the test samples varies in terms of shape, such as full circular, semi-disc and rectangular beam. In addition, while the type of loading in the SCB, ENDB and SENB samples is three-point bending, the ENDC specimen is loaded via diametral compression force. Based on the framework of Fracture mechanics, the severity of stress/strain ahead of the crack tip is explained by a well-known parameter called the stress intensity factor. This parameter, which is related to the singular term in the infinite series expansion for crack tip stress/strain field, is the most important and dominant term for describing the state of stress and determining the load bearing capacity of cracked bodies [57]. The mode-I stress intensity factor (K\({}_{\text{I}}\)) for the mentioned ENDB, SCB, SENB and ENDC samples are functions of the specimen geometry and loading condition and can be written as:  
\[\text{K}_{\text{I}}(\text{ENDB})=\frac{3\text{PS}}{2\text{R}^{2}}\sqrt{\pi \text{a}}\text{Y}_{\text{I}}\bigg{(}\frac{\text{a}}{\text{t}},\frac{\text{S}} {\text{R}}\bigg{)} \tag{1}\]  
\[\text{K}_{\text{I}}(\text{SCB})=\frac{\text{P}}{2\text{R}\text{t}}\sqrt{\pi \text{a}}\text{Y}_{\text{I}}\bigg{(}\frac{\text{a}}{\text{R}},\frac{\text{S}} {\text{R}}\bigg{)} \tag{2}\]  
\[\text{K}_{\text{I}}(\text{SENB})=\frac{3\text{PS}}{\text{tw}^{2}}\sqrt{\pi \text{a}}\text{Y}_{\text{I}}\bigg{(}\frac{\text{a}}{\text{w}},\frac{\text{S}} {\text{L}}\bigg{)} \tag{3}\]  
\[\text{K}_{\text{I}}(\text{ENDC})=\frac{\text{P}}{\text{R}\text{t}}\sqrt{\pi \text{a}}\text{Y}_{\text{I}}\bigg{(}\frac{\text{a}}{\text{t}}\bigg{)} \tag{4}\]  
where P is the applied load and Y\({}_{\text{I}}\) is the mode I geometry factor that is a function of the specimen geometry (i.e., a/R or a/t) and loading conditions (i.e., S/R or S/L) of the ENDB, SCB, SENB and ENDC specimens [31; 32; 58; 59; 60; 61; 62]. The corresponding values of these geometry factors can be determined using finite element analysis. Figure 3 shows the finite element models of the ENDB, ENDC, SENB and SCB samples created in the ABAQUS software. The radius and thickness of disc shape samples (i.e., for ENDB, SCB and ENDC) were considered equal to 50 mm and 30 mm, respectively. For the beam specimen, the corresponding values of L, W and \(t\) were considered as 400 mm, 50 mm and 50 mm, respectively. Material properties (Young modulus, \(E\) and Poisson's ratio \(\
u\)) for the models were constant and equal to 3 GPa and 0.3 GPa, respectively. These values are typical  
Figure 2: Description of the test specimens employed for mode I fracture toughness testing of asphalt mixture: (**a**) edge notch disc bend (ENDB), (**b**) semi-circular bend (SCB), (**c**) single edge notch beam (SENB) and (**d**) edge notch diametral compression (ENDC). values for such asphalt mixtures that have been reported and used in previous related works [33; 63; 64]. The finite element models (FEM) were created using solid C3D20 elements with total numbers of approximately 45,000 elements.