# Effect of Gradation Segregation on Mechanical Properties of an Asphalt Mixture
## 3 Results
### Effect of Gradation Segregation on the Asphalt Mixture
#### 3.2.4 Lateral Stress Diffusion  
In this study, the internal contact force and contact point distribution of the 30 \(\times\) 6 cm asphalt skeleton models of the HC, D, and HF are analyzed as examples. As shown in Figure 11, the HC-type mixture can uniformly diffuse the upper load through the skeleton to the bottom wall, while the upper load is more diffused in the middle part of the D-type and HF-type mixture skeletons and finally it mainly acts on the middle part of the bottom wall. In order to further analyze the lateral stress diffusion performance (LSDP) of mixture skeletons at different segregation levels, after the finishing load, the stress on the middle 1/3 section of the bottom wall and the stress on the total bottom wall and the corresponding ratio \(\lambda\) were calculated. The result is shown in Figure 12.  
Figure 12 shows that when segregation of coarse aggregates occurs in mixture, the \(\lambda\) value is lower than that of the standard gradation mixture, but there was no obvious correlation between the \(\lambda\) value and the degree of segregation; when segregation of fine aggregates occurs in mixture, the \(\lambda\) value is higher than that of the standard gradation mixture, and the value of \(\lambda\) gradually increases as the degree of segregation of fine aggregate intensifies. This further indicates that the mixture skeletons at a coarse aggregate segregation level can more evenly diffuse the stress to the bottom wall, and its LSDP  
Figure 10: VSTP of asphalt mixtures at different segregation levels. is better. Further, the LSDP has no obvious correlation with the degree of segregation, while the stress concentration phenomenon is more likely to occur in the process of stress diffusion of the mixture skeletons at fine aggregate segregation level, and its LSDP is worse. As the degree of segregation of fine aggregates intensifies, the LSDP gradually gets worse. From the above analysis, it is known that because the fine aggregate segregation mixture has worse VSTP and LSDP, stress concentration occurs easily in a local area below the load range in mixture, and thus it is more likely to cause permanent deformation and form nutting. At the same time, it also can be seen from Figure 12 that there is no obvious correlation between the LSDP and the height of model. Figure 11: Distribution of contact force and contact points in mixture skeletons. Figure 12: \(\lambda\) value of asphalt mixtures. In addition, to further explore the contribution rate of aggregate with different diameters under load, the average contact forces around the aggregates were calculated. The contribution rate was then calculated using Equations (4) and (5). The result is shown in Figure 13.  
\[\widetilde{F}=\frac{\sum\limits_{j=1}^{N_{i}}F_{i,j}}{N_{i}} \tag{4}\]  
\[\eta_{i}=\frac{\widetilde{F}_{i}}{\sum\limits_{i=1}^{S}\widetilde{F}_{i}}\times 1 00\% \tag{5}\]  
where,  
\(\widetilde{F}_{i}\) = average contact force of the \(i\)-th group of aggregate;  
\(F_{ij}\) = normal contact force at the \(j\)-th contact point of the \(i\)-th group of aggregate;  
\(N_{i}\) = number of all contact points of the \(i\)-th group of aggregate;  
\(\eta_{i}\) = contribution rate to resist load of the \(i\)-th group of aggregate, and  
\(S\) = number of group divided by particle size in mixture. As shown in Figure 13, the contribution rate to resist compressive load of the skeletal structure composed of aggregates whose particle size are above 2.36 mm is more than 70%. In addition, the gradation segregation will affect the contribution rate of aggregates with different particle sizes. With the gradation from coarse to fine, the contribution rate of the \(>\)13.2 mm grade aggregate gradually decreases, while that of the \(<\)2.36 mm grade aggregate gradually increases.