## 4 Results and Discussion
### Results of Water Stability Tests
#### 4.2.2 Freeze-Thaw Splitting Test  
The freeze-thaw splitting test was also selected to assess the moisture susceptibility of the asphalt mixture. The average tensile strengths (\(R_{T1}\) and \(R_{T2}\)) and average \(TSR\) of the different modified and unmodified asphalt mixtures are listed in Table 7 and presented in Figure 6. It was found that the \(TSR\) values of the mixture of lignin fiber, glass fiber, and composite mixture increased by 3.07, 7.31, and 8.71%, respectively, in comparison with the control.  
2.3 Discussion of Moisture Susceptibility Tests Results (Marshall Immersion and Freeze-Thaw Splitting)  
Both tests results revealed that the water stability performance of the bituminous mixes improved. The bituminous mix modified by a composite admixture was more effective than the bituminous mix that was only modified with glass fiber or lignin fiber. Furthermore, the bituminous mix modified with glass fiber was better than that modified with lignin fiber.  
There are several possible explanations for this result. For example, the water stability performance of the bituminous mix can be determined by many factors such as air voids in the asphalt mixture, mineral aggregate and its interaction with asphalt, and the thickness of asphalt film. Undoubtedly, water can penetrate the aggregate, which reduces the adhesion between asphalt and aggregate, resulting in water damage to the bituminous mix.  
The relationship between \(MSR\) and \(TSR\) with different types of asphalt mixtures is shown in Figures 5 and 6, respectively. The results indicated that the residual stability ratio (\(MSR\)) was higher than the indirect tensile strength ratio (\(TSR\)). This variance in the results between the Marshall immersion test and freeze-thaw splitting test is due to the fact that the samples were compacted 75 times for each side, reducing its porosity to 3%-5% in the Marshall immersion test, and thus making the process of water penetration between aggregate and asphalt film more difficult. On the other hand, samples were compacted only 50 times for each side, with porosity of 7% in the freeze-thaw splitting test.  
Figure 6: Results of the freeze–thaw splitting test.  
The parameter values of the modified asphalt mixes with glass and lignin fibers were better than those of the control asphalt mixture, as these fibers have a high ability for asphalt absorption, increasing the thickness of the asphalt film on mineral aggregates, reducing the space between mixtures, and reducing the quantity of free asphalt. Due to the rise in the content of the asphalt internal structure with the addition of glass and lignin fibers, the adhesion force between the bitumen binder and aggregates increased, hence improving the resistance of shear and stability of mixtures and enhancing the water-resistance of the modified bituminous mix. Moreover, the _MSR_ and _TSR_ of bituminous mixes modified with glass fiber were better than those modified with lignin fiber, as the mixture modified with lignin fiber was more difficult to compact than the mixture modified with glass fiber. In addition, the lignin fiber increased the air voids of the mixture compared to glass fiber.