Comparison of Testing Method Effects on Cracking Resistance of Asphalt Concrete Mixtures

: As an inherent characteristic of materials, the fracture toughness is an important parameter to study the cracking behavior of asphalt concrete mixtures. Although material compositions and environmental conditions have a signiﬁcant effect on the fracture toughness, for a certain material and testing environment, the test condition including the specimen conﬁguration and loading type may also affect the obtained fracture toughness. In this paper, the effect of specimen conﬁguration and applied loading type on the measured pure mode-I fracture toughness (K Ic ) is investigated. In order to achieve this purpose, using a typical asphalt mixture, four different test specimens including Semi-Circular Bend (SCB), Edge Notch Disc Bend (ENDB), Single Edge Notch Beam (SENB) and Edge Notch Diametral Compression (ENDC) disc are tested under pure mode I. The mentioned specimens have different shapes (i.e., full disc, semi-disc and rectangular beam) and are loaded either with symmetric three-point bending or diametral compressive force. The tests were performed at two low temperatures ( − 5 ◦ C and − 25 ◦ C) and it was observed that the critical mode-I fracture toughness (K Ic ) was changed slightly (up to 10%) by changing the shape of the test specimen (i.e., disc and beam). This reveals that the fracture toughness is not signiﬁcantly dependent on the shape of the test specimen. However, the type of applied loading has a signiﬁcant inﬂuence on the determined mode I fracture toughness such that the fracture toughness determined by the disc shape specimen loaded by diametral compression (i.e., ENDC) is about 25% less than the K Ic value with the same geometry but loaded with the three-point bending (i.e., ENDB) specimen. In addition, the fracture toughness values of all tested samples were increased linearly by decreasing the test temperature such that the fracture toughness ratio (K Ic (@ − 25 ◦ C) /K Ic (@ − 5 ◦ C) ) was nearly constant for the ENDB, ENDC, SCB and SENB samples.


Introduction
As a composite material, asphalt is the most used material for paving the roads. The main components of asphalt are bitumen and aggregates and due to the brittleness of mastic and fine aggregate matrix and binder at low temperatures, the behavior of this material is mainly brittle or quasi-brittle especially at low-temperature conditions [1][2][3][4][5].
The simplicity of the specimen shape and test geometry is an important issue for conducting the fracture tests on asphalt materials. In addition, the specimen and its loading type should be a good representative for the actual loading conditions that is experienced by the paving materials in the field. Laboratory specimens prepared for the mechanical tests of asphalt mixtures are often extracted from cylindrical or slab specimens (using the gyratory compactor machine, Marshall compactor machine or roller compactor machine). Thus, the majority of specimens that are used for conducting the mode I fracture toughness tests on asphalt mixtures are in the form of discs and beams. Circular and semicircular specimens, such as the ENDB and SCB; and rectangular beam shape specimens, such as the SENB sample, are among the conventional fracture test configurations that can be easily prepared without requiring extra machining. Furthermore, all of the mentioned Fracture toughness (K Ic ) can be determined experimentally using suitable specimens and relevant test methods. Among the test configurations available for obtaining the K Ic value of asphalt mixtures, the following methods have received much attention by the researchers: (i) Edge cracked rectangular beam loaded with three-point or four-point bending [1,6,9,10,12]; (ii) Edge cracked circular compact tension specimen by pin loading (DCT) [1,2,13]; (iii) Edge cracked semi-circular specimen loaded with symmetric three-point bending (SCB) [4,6,7,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]; (iv) Center cracked Brazilian disc specimen loaded with diametral compression (BD) [30,31]; (v) Edge cracked disc specimen loaded with diametral compression (ENDC) [32,33]; (vi) Edge cracked disc specimen subjected to three-point bending (ENDB) [34][35][36][37][38][39][40][41][42]; (vii) Edge cracked circular disc loaded with wedge splitting fixture [43]; (viii) Indirect diametral disc test [44].
The simplicity of the specimen shape and test geometry is an important issue for conducting the fracture tests on asphalt materials. In addition, the specimen and its loading type should be a good representative for the actual loading conditions that is experienced by the paving materials in the field. Laboratory specimens prepared for the mechanical tests of asphalt mixtures are often extracted from cylindrical or slab specimens (using the gyratory compactor machine, Marshall compactor machine or roller compactor machine). Thus, the majority of specimens that are used for conducting the mode I fracture toughness tests on asphalt mixtures are in the form of discs and beams. Circular and semi-circular specimens, such as the ENDB and SCB; and rectangular beam shape specimens, such as the SENB sample, are among the conventional fracture test configurations that can be easily prepared without requiring extra machining. Furthermore, all of the mentioned specimens are loaded with the conventional three-point bend fixture and can provide good simulations for top-down cracking phenomenon in real asphalt pavements subjected to actual traffic loads.
Based on the previous studies the fracture behavior of brittle and quasi-brittle materials and the measured mode I fracture toughness value can be noticeably affected by the type of test specimen and applied loading [45]. For example, in an investigation conducted by Aliha et al. [46] the K Ic values of a typical rock material obtained using some standard test specimens and procedures differ up to 40%. Chao et al. [47] investigated the effect of specimen geometry on mode I fracture toughness and crack growth behavior of a brittle polymer called PMMA. Similarly, by testing different specimens subjected to three-point bend loading, Aliha et al. [48] demonstrated that the fracture toughness of plexiglass material depends on the type of specimen utilized for the testing. Furthermore, according to the previous fracture studies performed on rocks, it has been proven that the type of test specimen can noticeably affect the measured value of mode I fracture toughness [45][46][47][48]. Although the effect of mix design and asphalt ingredients on the mechanical properties and fracture behavior of asphalt mixtures has been investigated extensively [16,[49][50][51][52][53][54], the influence of specimen shape and testing method has received less attention by the asphalt fracture researchers. Some testing methods such as Semi-Circular Bending (SCB) and circular Disc Compact Tension (DCT) specimens have been proposed by ASTM for determining the fracture toughness or fracture resistance of asphalt mixtures as two standard testing methods [55,56]. However, it is still not clear whether these two methods or other testing techniques provide the same results for the fracture toughness (as material property) of asphalt mixtures. Since such testing methods use different test geometries with different loading setups, the possible influence of geometry and loading type on the cracking resistance behavior of asphalt mixture materials is an interesting issue and it is necessary to study this topic for the asphalt concrete mixtures. The main aim of this paper is to investigate the effect of specimen geometry and loading type on the value of mode I fracture toughness of asphalt concrete mixtures. In order to achieve this purpose, a series of mode I fracture toughness experiments was performed on the same asphalt mixture with different test specimens (i.e., SCB and ENDB; and SENB and ENDC configurations). The fracture tests are conducted at two sub-zero temperatures and it is shown that although there is a general agreement and consistency between the experimental results, some differences exist in the value of determined K Ic . This difference can be attributed to both the geometry (i.e., shape) of the specimen and the method of applying the loads to the samples during the fracture toughness test. However, the effect of the type of loading is more obvious than the geometry (or shape) of the test sample.

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 Ic 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 (KI) for the mentioned ENDB, SCB, SENB and ENDC samples are functions of the specimen geometry and loading condition and can be written as: where P is the applied load and YI 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 ν) for the models were constant and equal to 3 GPa and 0.3 GPa, respectively. These values are typical values for such asphalt mixtures that have been reported and used in previous related works 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 I ) for the mentioned ENDB, SCB, SENB and ENDC samples are functions of the specimen geometry and loading condition and can be written as: where P is the applied load and Y 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 ν) for the models were constant and equal to 3 GPa and 0.3 GPa, respectively. These values are typical 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. Singular type elements were all used around the crack tip for producing the root singularity of stress in this region as shown in Figure 3e. For the purpose of applying the boundary conditions, rigid body contact was assumed between the loading and supporting spans and surfaces of the specimens. The finite element models of these four samples were analyzed by applying a constant reference load of P = 100 N for each sample and the corresponding values of pure mode I stress intensity factor were determined directly via the J-integral method (built in ABAQUS code) for different crack depths and loading spans. Figure 4 shows the variations of geometry factor for pure mode I loading conditions of the analyzed samples for different a/R, a/t, a/W, S/R and S/L ratios. The results presented in Figure 4 for Y I values were obtained by normalizing the K I values obtained from the finite element analysis of the specimens using the ABAQUS code via employing Equations (1)-(4).
Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 18 [33,63,64]. The finite element models (FEM) were created using solid C3D20 elements with total numbers of approximately 45,000 elements. Singular type elements were all used around the crack tip for producing the root singularity of stress in this region as shown in Figure 3e. For the purpose of applying the boundary conditions, rigid body contact was assumed between the loading and supporting spans and surfaces of the specimens. The finite element models of these four samples were analyzed by applying a constant reference load of P = 100 N for each sample and the corresponding values of pure mode I stress intensity factor were determined directly via the J-integral method (built in ABAQUS code) for different crack depths and loading spans. Figure 4 shows the variations of geometry factor for pure mode I loading conditions of the analyzed samples for different a/R, a/t, a/W, S/R and S/L ratios. The results presented in Figure 4 for YI values were obtained by normalizing the KI values obtained from the finite element analysis of the specimens using the ABAQUS code via employing Equations (1)-(4).

Asphalt Mix Design
The Hot Mix Asphalt (HMA) used in this research is composed of 60/70 binder with performance grade PG  and siliceous aggregates with the nominal maximum aggregate size of 12.5 mm. This aggregate gradation is a common sieve size for manufacturing the HMA mixture for overlaying the roads in real pavement construction projects and laboratory investigation of asphalt mixtures [35,65]. The physical properties of the used aggregates are mentioned in Table 1 and their gradations are illustrated in Figure 5.

Asphalt Mix Design
The Hot Mix Asphalt (HMA) used in this research is composed of 60/70 binder with performance grade PG  and siliceous aggregates with the nominal maximum aggregate size of 12.5 mm. This aggregate gradation is a common sieve size for manufacturing the HMA mixture for overlaying the roads in real pavement construction projects and laboratory investigation of asphalt mixtures [35,65]. The physical properties of the used aggregates are mentioned in Table 1 and their gradations are illustrated in Figure 5. To specify the optimal percentage of bitumen, different asphalt mixtures with 4%, 5%, 6% and 7% of bitumen content were prepared. After mixing the bitumen and aggregates, the mixtures were poured into a standard Marshall cylinder with a diameter of 100 mm and further compacted with a Marshall compactor (75 strokes on each side of the sample). This compaction level is often used for simulating heavy traffic conditions and the resultant Appl. Sci. 2021, 11, 5094 7 of 17 air void content for such compacted mixture was approximately 5%. Based on some key mechanical and physical parameters such as specific density, compressive strength, flow and the air void percentage, the optimum percentage of bitumen required for manufacturing the asphalt mixture used in this investigation was determined. Table 2 shows the mechanical and physical characteristics of the HMA material utilized for the preparation of the test specimens. To specify the optimal percentage of bitumen, different asphalt mixtures with 4%, 5%, 6% and 7% of bitumen content were prepared. After mixing the bitumen and aggregates, the mixtures were poured into a standard Marshall cylinder with a diameter of 100 mm and further compacted with a Marshall compactor (75 strokes on each side of the sample). This compaction level is often used for simulating heavy traffic conditions and the resultant air void content for such compacted mixture was approximately 5%. Based on some key mechanical and physical parameters such as specific density, compressive strength, flow and the air void percentage, the optimum percentage of bitumen required for manufacturing the asphalt mixture used in this investigation was determined. Table 2 shows the mechanical and physical characteristics of the HMA material utilized for the preparation of the test specimens. Using the optimum bitumen percentage, the binder and aggregates were heated to 140 °C and then blended by a mixer. In order to prepare the disc shape samples (including the ENDB, ENDC and SCB specimens), the mixture was compacted by a compactor machine to produce cylindrical asphalt specimens with a diameter of 100 mm. Although in most of the previous studies disc shape samples with a diameter of 150 mm obtained from the gyratory compacted asphalt cylinders have been used for manufacturing the fracture toughness test specimens, the smaller size samples (i.e., disc with a diameter of 100 mm) may have some advantages, such as requiring a smaller amount of material for specimen preparation. Therefore, in some research papers disc shape specimens with a diameter of 100 mm were employed for conducting the fracture toughness testing of asphalt mixtures and it has been concluded that the small size test samples (i.e., 100 mm in diameter) can also provide valid test results for asphalt mixtures. The cylindrical samples were then sliced using a high-speed rotary diamond saw blade to obtain circular discs with the height of 30 mm. For manufacturing the SCB sample each disc was cut along the diameter   Using the optimum bitumen percentage, the binder and aggregates were heated to 140 • C and then blended by a mixer. In order to prepare the disc shape samples (including the ENDB, ENDC and SCB specimens), the mixture was compacted by a compactor machine to produce cylindrical asphalt specimens with a diameter of 100 mm. Although in most of the previous studies disc shape samples with a diameter of 150 mm obtained from the gyratory compacted asphalt cylinders have been used for manufacturing the fracture toughness test specimens, the smaller size samples (i.e., disc with a diameter of 100 mm) may have some advantages, such as requiring a smaller amount of material for specimen preparation. Therefore, in some research papers disc shape specimens with a diameter of 100 mm were employed for conducting the fracture toughness testing of asphalt mixtures and it has been concluded that the small size test samples (i.e., 100 mm in diameter) can also provide valid test results for asphalt mixtures. The cylindrical samples were then sliced using a high-speed rotary diamond saw blade to obtain circular discs with the height of 30 mm. For manufacturing the SCB sample each disc was cut along the diameter to create two semi-discs. In addition, the beam samples were manufactured by casting the mixture inside a slab mold with dimensions of 400 × 400 × 50 mm 3 . Finally, the manufactured slabs were sliced using a rotary diamond saw blade to obtain some SENB specimens with dimensions of 400 × 50 × 50 mm 3 .
Since the air void content has noticeable influence on the mechanical and strength properties of the asphalt mixtures [6], the void percentage in all prepared asphalt samples was considered constant and equal to 4.7% for the sake of comparison of the experimental results. A thin rotary diamond saw blade with a thickness of 0.5 mm was used to intro-duce an initial artificial straight edge crack in the ENDB, ENDC, SCB and SENB samples. For each specimen, eight duplicates were prepared and half of them were tested at −5 • C and the rest of them were tested at −25 • C. These two test temperatures (that both of them were below the lower performance grade of the utilized bitumen) were selected to investigate the effect of temperature on the low temperature fracture resistance of the HMA mixture. The difference between the temperatures was also considered high enough to ensure that the obtained results are dominantly related to the influence of test specimen and not due to the effect of other factors such as the scatter of test results and heterogeneity of asphalt samples. The prepared test samples were tested using a universal test machine at the mentioned test temperatures. The loading rate in all experiments was constant and equal to 1 mm/min. This loading rate, which has also been used in other research work [63], provides nearly static loading condition for the asphalt mixtures at low temperatures such that the HMA mixture behaves as brittle and elastic material. Figure 6 displays the sample testing setup for the tested mode I specimens.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 18 mixture inside a slab mold with dimensions of 400 × 400 × 50 mm 3 . Finally, the manufactured slabs were sliced using a rotary diamond saw blade to obtain some SENB specimens with dimensions of 400 × 50 × 50 mm 3 . Since the air void content has noticeable influence on the mechanical and strength properties of the asphalt mixtures [6], the void percentage in all prepared asphalt samples was considered constant and equal to 4.7% for the sake of comparison of the experimental results. A thin rotary diamond saw blade with a thickness of 0.5 mm was used to introduce an initial artificial straight edge crack in the ENDB, ENDC, SCB and SENB samples. For each specimen, eight duplicates were prepared and half of them were tested at −5 °C and the rest of them were tested at −25 °C. These two test temperatures (that both of them were below the lower performance grade of the utilized bitumen) were selected to investigate the effect of temperature on the low temperature fracture resistance of the HMA mixture. The difference between the temperatures was also considered high enough to ensure that the obtained results are dominantly related to the influence of test specimen and not due to the effect of other factors such as the scatter of test results and heterogeneity of asphalt samples. The prepared test samples were tested using a universal test machine at the mentioned test temperatures. The loading rate in all experiments was constant and equal to 1 mm/min. This loading rate, which has also been used in other research work [63], provides nearly static loading condition for the asphalt mixtures at low temperatures such that the HMA mixture behaves as brittle and elastic material. Figure 6 displays the sample testing setup for the tested mode I specimens.

ENDB SCB
Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 18 SENB ENDC Figure 6. Test setup (before and after failure) for conducting the fracture experiments using different test configurations. Figure 7 shows the samples of broken ENDB, SCB, SENB and ENDC specimens fracture under mode I. It is seen that in all samples the fracture trajectory is straight without significant kinking, which extends throughout both aggregates and mastic or fine aggregate mastic. This reveals that all investigated test samples are symmetrically broken into  Figure 7 shows the samples of broken ENDB, SCB, SENB and ENDC specimens fracture under mode I. It is seen that in all samples the fracture trajectory is straight without significant kinking, which extends throughout both aggregates and mastic or fine aggregate mastic. This reveals that all investigated test samples are symmetrically broken into two halves after fracturing. Comparison of the fracture trajectories of ENDB and ENDC samples that have the exact same geometry (or shape) but loaded in two different manners (i.e., bending and compression) showed that the fracturing of both samples is similar and the loading type has no effect on the fracture trajectory. Figure 6. Test setup (before and after failure) for conducting the fracture experiments using different test configurations. Figure 7 shows the samples of broken ENDB, SCB, SENB and ENDC specimens fracture under mode I. It is seen that in all samples the fracture trajectory is straight without significant kinking, which extends throughout both aggregates and mastic or fine aggregate mastic. This reveals that all investigated test samples are symmetrically broken into two halves after fracturing. Comparison of the fracture trajectories of ENDB and ENDC samples that have the exact same geometry (or shape) but loaded in two different manners (i.e., bending and compression) showed that the fracturing of both samples is similar and the loading type has no effect on the fracture trajectory. However, the load bearing capacity and fracture load of the tested samples were different and this shows the effect of geometry and loading type on the fracture behavior of the asphalt mixtures. Some typical load-displacement curves obtained for the tested specimens are shown in Figure 8. From these curves it can be concluded that the low temperature fracture behavior of the tested asphalt mixture is linear and brittle and, after the peak load, a sudden drop in the loading curve is observed. The ENDC and SENB samples presented the highest and lowest fracture loads, respectively. In Table 3, the fracture loads (i.e., the maximum load values) obtained from different replicates are presented for the tested ENDB, SCB, SENB and ENDC samples at two low temperatures.  However, the load bearing capacity and fracture load of the tested samples were different and this shows the effect of geometry and loading type on the fracture behavior of the asphalt mixtures. Some typical load-displacement curves obtained for the tested specimens are shown in Figure 8. From these curves it can be concluded that the low temperature fracture behavior of the tested asphalt mixture is linear and brittle and, after the peak load, a sudden drop in the loading curve is observed. The ENDC and SENB samples presented the highest and lowest fracture loads, respectively. In Table 3, the fracture loads (i.e., the maximum load values) obtained from different replicates are presented for the tested ENDB, SCB, SENB and ENDC samples at two low temperatures.

Fracture Resistance Values of Tested Samples
By considering the framework of Linear Elastic Fracture Mechanics (LEFM), the peak load of each sample was used for determining the fracture toughness value for the tested specimens. By replacing the corresponding values of critical fracture loads obtained from the experiments into Equations (1)-(4), the corresponding values of K Ic were determined. The required geometry factors (Y I ) for using these equations are also presented in Table 4 for the tested conditions (determined from numerical analyses). Figure 9 presents the mode I fracture resistance (or K Ic ) value of the tested HMA material at −25 • C and −5 • C. However, the load bearing capacity and fracture load of the tested samples were different and this shows the effect of geometry and loading type on the fracture behavior of the asphalt mixtures. Some typical load-displacement curves obtained for the tested specimens are shown in Figure 8. From these curves it can be concluded that the low temperature fracture behavior of the tested asphalt mixture is linear and brittle and, after the peak load, a sudden drop in the loading curve is observed. The ENDC and SENB samples presented the highest and lowest fracture loads, respectively. In Table 3, the fracture loads (i.e., the maximum load values) obtained from different replicates are presented for the tested ENDB, SCB, SENB and ENDC samples at two low temperatures.     Table 4. Corresponding values of geometry factor (Y I ) for the investigated test specimens. 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 KIc 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 KIc varies in the range between 0.5 and 1 MPa m 0.5 .  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 Ic 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 Ic varies in the range between 0.5 and 1 MPa m 0.5 .

Specimen Dimentions Test Condition Mode I Geometry Factor
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 Ic 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 Ic compared to the other test samples. For example, while the ENDB and ENDC samples have the exact same geometry, their K Ic 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). 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 KIc 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 KIc compared to the other test samples. For example, while the ENDB and ENDC samples have the exact same geometry, their KIc 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).
As stated earlier, the SCB test method was suggested in recent years by ASTM for measuring the fracture toughness of asphalt mixtures [55]. The information in Figure 11 shows the normalized fracture toughness ratio (KIc/KIc (SCB)) for the tested samples. This figure reveals that the ENDB and SENB test samples can also provide nearly the same fracture toughness results as obtained by the standard SCB testing method. However, the ENDC test shows an underestimated evaluation for the resistance of asphalt mixture materials against cracking compared to the standard SCB mode I test method.  As stated earlier, the SCB test method was suggested in recent years by ASTM for measuring the fracture toughness of asphalt mixtures [55]. The information in Figure 11 shows the normalized fracture toughness ratio (K Ic /K Ic (SCB) ) for the tested samples. This figure reveals that the ENDB and SENB test samples can also provide nearly the same fracture toughness results as obtained by the standard SCB testing method. However, the ENDC test shows an underestimated evaluation for the resistance of asphalt mixture materials against cracking compared to the standard SCB mode I test method.
The influence of test temperature on the measured K Ic value is illustrated and compared in Figure 12a. According to this figure, which shows the variations of K Ic versus temperature, the mode I fracture toughness value is enhanced by reducing the test temperature. By decreasing the test temperature from −5 • C to −25 • C, in all specimens the K Ic values increases by approximately 40%. As a viscoelastic material, the asphalt binder becomes stiffer by reducing the temperature. The stiffness of a bituminous material increases due to the reduction of temperature up to the lower performance grade temperature of bitumen. According to the literature, the stress intensity factor increases by increasing the stiffness or elastic modulus of bitumen [27,28,68] and consequently such behavior can result in the increase of stiffness of the HMA mixture as well. Hence, due to the stiffer HMA mixture at −25 • C compared to −5 • C, the enhancement of the low-temperature crack growth resistance for asphalt mixtures is expected. Such trends observed for the variations of fracture toughness with the temperature are also reported in other published papers [6,15,38]. The fracture toughness ratio at two testing temperatures (i.e., (K Ic (@−25 • C) /K Ic (@−5 • C) )) are also shown in Figure 12b. This figure demonstrates that a simple shift occurs in the low temperature cracking resistance of the asphalt mixtures by changing the temperature. Indeed, the (K Ic (@−25 • C) /K Ic (@−5 • C) ) ratio changes in a narrow range for the tested geometries and specimens and it can be concluded that the (K Ic (@−25 • C) /K Ic (@−5 • C) ) ratio is approximately equal to 1.4 as shown in Figure 12b. The influence of test temperature on the measured KIc value is illustrated and compared in Figure 12a. According to this figure, which shows the variations of KIc versus temperature, the mode I fracture toughness value is enhanced by reducing the test temperature. By decreasing the test temperature from −5 °C to −25 °C, in all specimens the KIc values increases by approximately 40%. As a viscoelastic material, the asphalt binder becomes stiffer by reducing the temperature. The stiffness of a bituminous material increases due to the reduction of temperature up to the lower performance grade temperature of bitumen. According to the literature, the stress intensity factor increases by increasing the stiffness or elastic modulus of bitumen [27,28,68] and consequently such behavior can result in the increase of stiffness of the HMA mixture as well. Hence, due to the stiffer HMA mixture at −25 °C compared to −5 °C, the enhancement of the low-temperature crack growth resistance for asphalt mixtures is expected. Such trends observed for the variations of fracture toughness with the temperature are also reported in other published papers [6,15,38]. The fracture toughness ratio at two testing temperatures (i.e., (KIc (@−25 °C)/KIc (@−5 °C))) are also shown in Figure 12b. This figure demonstrates that a simple shift occurs in the low temperature cracking resistance of the asphalt mixtures by changing the temperature. Indeed, the (KIc (@−25 °C)/KIc (@−5 °C)) ratio changes in a narrow range for the tested geometries and specimens and it can be concluded that the (KIc (@−25 °C)/KIc (@−5 °C)) ratio is approximately equal to 1.4 as shown in Figure 12b.