## 2 Materials and Methods
### Measurement
#### 3.1.5 LAS Test  
LAS tests were conducted on pre-cut SBS-modified asphalt samples mixed for different amounts of time. The stress-strain curves are presented in Figure 7.  
Figure 6: MSCR test of pre-cut SBS-modified asphalt mixed for different amounts of time. (**a**) Recovery rate, (**b**) Jnr. The critical strain is defined at the point at which the stress starts to decrease. Beyond this point, a material's behavior changes, entering the failure stage. It was observed that the critical strain points of the pre-cut SBS-modified asphalt samples were all greater than those of the conventional-process asphalt samples, indicating that pre-cut SBS-modified asphalt can withstand larger strains before fatigue failure. The width of the peak is related to pressure sensitivity, with a wider peak indicating lower pressure sensitivity. It can be seen that the peaks of pre-cut SBS-modified asphalt were wider than those of the conventional-process asphalt. The stress peak values were ordered as follows: conventional process \(>\) 15 min \(>\) 120 min \(>\) 30 min \(>\) 60 min. The stress peak represents the hardness of asphalt. The stress peaks of the pre-cut SBS-modified asphalt were lower than those of the conventional-process asphalt. This is because pre-cutting increased the surface area of the SBS, resulting in larger contact area with the base asphalt. This increased contact area facilitated swelling, leading to reduced hardness and enhanced flexibility of the modified asphalt. Within the mixing time range of 15 to 60 min, longer mixing times resulted in smaller stress peaks and greater flexibility of the modified asphalt, indicating that a 60 min mixing time yielded the best swelling effect of the pre-cut SBS modifier. However, after mixing for 120 min, the stress peak increased, which may be attributable to prolonged mixing causing changes in the asphalt components. A steeper slope of the stress peak decrease during the failure stage indicates greater brittleness and susceptibility to damage of the specimen. Similarly, the slopes of peak decrease for pre-cut SBS-modified asphalt were gentler than those of the conventional-process asphalt, indicating that the strain limit during the failure stage was larger for the pre-cut modified asphalt. The steeper slope of the peak decrease for the 60 min mixing group indicates that faster deformation occurred during failure, which was attributed to the narrower filament width and granular diameter. From the stress-strain curve characteristics, it can be deduced that the fatigue failure characteristics of the pre-cut SBS-modified asphalt were superior to those of the conventional-process asphalt. Furthermore, the calculated fatigue life N\({}_{\text{f}}\) values for pre-cut SBS-modified asphalt samples prepared with different mixing times are shown in Figure 8.  
Figure 7: Stress–strain curves of pre-cut SBS-modified asphalt mixed for different amounts of time. At both 5% and 15% strain levels, the fatigue life (Nf) values of the pre-cut SBS-modified asphalt were greater than those of the conventional-process asphalt. Under both 5% and 15% strain levels, the fatigue life of the pre-cut SBS-modified asphalt initially increased and then decreased with increasing mixing time. This suggests that when the SBS structure is filamentous and granular, the fatigue life is greater compared to when the SBS structure is particulate or atomized. This is due to the stronger interlocking effect and higher strength of the network structure when SBS is in a filamentous and granular state. At a 5% strain level, the pre-cut SBS-modified asphalt mixed for 60 min exhibited the maximum fatigue life. This implies that when the strain level is much lower than the critical strain, the fatigue life is related to the characteristics of the asphalt's stress-strain curve in the first half. In this scenario, greater asphalt ductility corresponds to a longer fatigue life. At a 15% strain level, the pre-cut SBS-modified asphalt mixed for 30 min showed the highest fatigue life.