## 4 Results and Discussion  
Figure 6 displays the volumetric properties of the asphalt mixtures containing SF and OPC. As expected, increasing the filler percentage resulted in lower air voids for both SF and OPC mixtures at each bitumen content. The use of SF as a replacement for OPC slightly decreased air voids in the asphalt mixtures. This could be attributed to the finer particle size of SF compared to OPC (Table 4), making it more effective in reducing air voids for each combination of filler and bitumen content. Air voids in both OPC and SF mixtures remained within the acceptable range of 3-5%, as per the Indian standard. The VMA of a compacted asphalt mixture is determined by calculating the volume of the intergranular voids between aggregate particles as well as the air voids and the volume of bitumen that is not absorbed by the aggregates. Normally, an inverse bell-shaped curve should be observed for VMA, but the results obtained in this study (Figure 6) only show  
Figure 5: Query points (red cross marker) of the data augmentation procedure and experimental grid points (black plus sign marker). an increasing trend. This could be due to the fact that the decreasing trend is typically associated with lower bitumen content values than those examined in this study. A similar trend was observed in a study by [PERSON] et al. at a binder percentage greater than 4.5% [63]. According to Figure 6, the VMA values for OPC mixtures were slightly higher than those for SF mixtures, with a difference ranging from 0.18% to 1.20%. The VFB, which represents the percentage of VMA filled with bitumen, was slightly higher in the SF mixtures than in the OPC mixtures due to the previously determined air voids and VMA values (Figure 6). However, the differences were small, ranging from 0.18% to 1.19%. All  
Figure 6: Vv, VMA, and VFB of OPC and SF asphalt mixtures. the asphalt mixtures investigated in this study had VFB values within the 65-85% range prescribed by Indian regulations [34]. Experimental results for MS, MQ, and MMSR are shown in Figure 7, and all three Marshall parameters exhibited a bell-shaped curve for all mixtures studied, consistent with relevant literature for both SF and OPC mixes [64]. Increasing filler content resulted in higher values for all three Marshall parameters regardless of the bitumen content, in line with previous studies [59; 65; 66]. The highest MS values for both SF and OPC mixes were achieved at 5% bitumen and 8% filler, with the SF mix showing a 2.90% higher Marshall stability than the corresponding OPC mix. This suggests that SF can be a viable replacement for OPC in asphalt mixes, which  
Figure 7: Marshall stability, Marshall quotient, and MMSR of OPC and SF asphalt mixtures. can help reduce the disposal problem of SF waste. AMs with 4% filler and 5% bitumen content meet the MoRTH requirement for conventional bitumen mixes (MS > 10 kN) [34], while filler content raised to 6% or 8% satisfies the acceptance requisite for modified bitumen mixes (MS > 13 kN), highlighting the significant improvement in mechanical response provided by the filler. Table S1 (Supplementary Materials) indicates that the Marshall flow of all the asphalt mixes examined falls within the MoRTH-specified range of 2 mm to 4 mm, with the lowest flow values being observed at 6% and 8% of SF and OPC. The combination of higher stability and lower flow serves as an empirical indicator of the resistance of asphalt mixtures against permanent deformations at high temperatures, such as the rutting phenomenon. Figure 7 reveals that the Marshall quotient (MQ) values of SF mixes are higher than those of OPC mixtures, ranging from 2.73% to 8.55%, depending on the filler content. Nevertheless, for all the mixtures investigated, MQ results fall within the acceptance range (2-6 kN/mm) specified by the Indian regulation [34]. Therefore, the addition of silica fume industrial wastes is unlikely to produce a highly plastic mechanical response.