## 1 Introduction  
Cracking phenomena and the fracturing of pavements are common modes of failure in overlay structures, especially in cold regions [1, 2, 3, 4, 5]. At low temperature conditions, the probability of crack propagation from pre-existing flaws increases due to traffic loading or thermal fatigue loads induced by daily or seasonal temperature changes. A real asphalt mixture used in pavements is a multi-phase material made of some ingredients including coarse and fine aggregates, binder (or bitumen), air voids and sometimes additives in the shape of fibers or powders. Hence, the overall mechanical properties of these randomly distributed composites significantly depend on the mix-design and type of the ingredients [6, 7, 8]. In particular, the type of asphalt mixture can noticeably affect the load bearing capacity, fatigue life and propagation of fracture trajectory in these composites. Due to the loading type or environmental effects, the fracturing of asphalt pavements may take place in different basic modes including mode I (crack opening), mode II (crack in-plane sliding), mode III (crack out-of-plane tearing) and any combinations of these modes called mixed mode (e.g., mixed mode I/II, I/III, II/III or I/II/III) [9]. Accordingly,several researchers have investigated the fracture behavior of these composite materials using different testing methods under the mentioned loading modes [9; 10]. The fracture mechanics approach and linear elastic fracture mechanics were used in the mid-1970s for studying the fracture behavior of asphalt composite materials [10]. Afterwards, some experimental testing methods and test samples including the edge cracked rectangular beam specimen subjected to four-point bend loading and the semi-circular bend (SCB) specimen were employed by [PERSON] et al. [11; 12] for investigating the mode I fracture of the asphalt mixtures. Other test configurations such as the modified indirect tensile disc (MITD) specimen [13], disc-shape compact-tension specimen [14], single edge notch beam (SENB) subjected to three-point bend [9; 15], wedge splitting disc (WSD) [16], edge notch disc bend (ENDB) [17; 18; 19; 20; 21; 22; 23; 24], edge notch disc diametal compression (ENDC) [25; 26; 27], center cracked Brazilian disc subjected to diametral compression [28], semi-circular bend (SCB) specimen [29; 30; 31; 32; 33; 34], and hollow disc (or ring shape) specimen containing center crack and loaded diametrically [35] are some of the test configurations employed in the literature for investigating the fracture resistance of asphalt mixtures. Any of these test samples are suitable for simulating and conducting specific modes of fracture. For example, the MITD and WSD are suitable for pure mode I testing. Other test configurations such as the SCB, three-point bend, hollow disc ring and Brazilian disc samples can be utilized for both mode I and mixed mode I/II fracture testing. On the other hand, the ENDB and ENDC test samples are capable of conducting pure mode I and mixed mode I/III fracture tests on asphalt mixtures. As a randomly distributed heterogeneous composite mixture and due to the difference in the mechanical properties of the soft mastic part and tight aggregates, it is evident that the fracture behavior of asphalt mixtures depends on the location of initial crack inside the mixture. Indeed, if the pre-crack is located inside the aggregate or in the vicinity of bigger aggregates this can result in increasing the fracture resistance. Conversely, the cracking resistance of the asphalt mixture is reduced if the initial crack tip is placed inside the binder or soft mastic or fine aggregate mixture part. In addition to the influence of heterogeneity on the fracture strength of asphalt mixtures, the texture and composition of mixture can affect the path of propagating crack. Since the material is not homogenous, random distribution of aggregates inside the matrix of binder, soft mastic or fine aggregate matrix, may affect the trajectory of fracture during the crack propagation.