## 4 Results and Discussion
### Results and Discussion of Low-Temperature Three-Point Bending Test  
The bending test was applied to assess the effects of lignin and glass fiber on the low-temperature cracking resistance of the bituminous mix. The bending stress and bending strain were computed as listed in Table 7 and the results plotted in Figure 7a,b. The results demonstrate that the lignin fiber and glass fiber additives improve the ultimate bending tensile strength and the failure strain of modified asphalt mixtures, as shown in Figure 7a,b, respectively. From the results, it can be concluded that the bending tensile strength and maximum tensile strain of asphalt mixtures improved by 19.1% and 24.7%, respectively, with the addition of lignin fiber, and by 18.3% and 19.1%, respectively, with the addition of glass fiber as compared to control. Moreover, the composite additive improved the ultimate bending tensile strength and failure strain by 26.5% and 48.8%, respectively. The low-temperature stability of the bituminous mixes was enhanced by adding lignin and glass fiber.  
The composite admixture used in this study showed better improvement in the bending stress as well as bending strain. Both lignin fiber and glass fiber showed improvements in low-temperature stability. However, the lignin fiber showed better improvement in flexural stress and strain.  
The reasons for these can be clarified as follows. When temperatures begin to drop, the asphalt binder can withstand low-temperature tensile stress by filling between aggregates, which leads to increased bonding. However, it can only resist until a certain low temperature, after which the asphalt binder cannot resist the extreme tensile stress and thermal cracks begin to emerge.  
Adding lignin and glass fibers can enhance the cracking resistance of asphalt mixes, as it has a large specific surface area. The viscosity of asphalt was increased due to the absorption of fiber that led to the enhancement of the interface adhesion strengths. Simultaneously, the OAC was increased after using fibers (as indicated in Table 6), which resulted in an improvement in the flexibility of the bituminous mix. Asphal mixture modified with lignin fiber had higher anti-cracking resistance than that with the glass fiber, though the bituminous mix modified with a composite mixture had the best low-temperature performance. The main reason is that lignin fiber has a larger specific surface area for asphalt absorption and asphalt stabilization, as well as the highest OAC asphalt contents to improve the cracking resistance and flexibility, as extra asphalt films are formed to improve the function of filling and healing in the micro-cracks between aggregates. In addition, the shear strength of the asphalt mix can be enhanced by lignin fiber, as it can improve the friction angle and cohesive force of bitumen [19]. At the same time, glass fiber can disperse the tensile stress of asphalt mortar and prevent micro-cracks in asphalt mortar failure strain, so it can also enhance the deformation of the bituminous mix. Thus, using fibers is very beneficial as an anti-cracking measure, as it can improve the strength of asphalt mixtures at low temperatures. Additionally, it can increase the toughness of the asphalt mixtures. It can enhance the resistance of stress and deformation by load transmitting and bridging phenomenon since fibers act as a bridge to delay increasing the cracks in the asphalt mixtures by spreading through both sides of the micro-cracks [53]. Thus, the composite action of lignin and glass fibers had the greatest effect on low-temperature performance of the asphalt mixture.