# Compaction Characteristics and Minimum Void Ratio Prediction Model for Gap-Graded Soil-Rock Mixture
## 2 Vibrating Compaction Test
### Results and Discussion
#### 2.2.2 Influence of basic gradations  
Figure 5 gives the changes of the void ratios of the SRMs with gap intervals under the basic gradations with different fractal dimension \(D\). It can be seen that the changing trend of the curves is similar when \(D=2.3\), 2.5 and 2.7 (as shown in Figure 3), but it is different from that of \(D=1.9\) and 2.1. From the definition of \(D\) in Equation (1), the particle size in an assembly increases with the decreasing \(D\). When \(D=1.9\) and 2.1, the particles within 5-20 mm may act as filling components in SRMs. The absence of these particles leads to insufficient filling of the voids among the skeleton particles, resulting in the bigger void ratios of the SRMs than those of the basic gradations when \(D\) = 1.9 and 2.1. Figure 5 also demonstrates that there are the vital grain size groups acting as filling components in SRMs. The vital grain size group is 0.5-2 mm when \(D\) = 2.3, 2.5, 2.7 and it is 2-5 mm when \(D\) = 1.9, 2.1. The absence of the vital grain size group will significantly increase the void ratio of the SRM, which should be taken seriously in engineering practice.  
Figure 4: Changes of non-uniform coefficients \(C_{u}\) and coefficients of curvature \(C_{c}\) after vibrating compaction.  
Figure 3: Void ratios of the soil-rock mixture (SRM) with basic gradation \(D=2.3\) at different gap intervals.  
At the same gap interval, the void ratio \(e\) of the SRM decreases with the increasing \(D\) of the basic gradation. For example, at the gap interval of 5-20 mm, \(e\) decreases from 0.36 to 0.11 when \(D\) increases from 1.9 to 2.7. [PERSON] [26] found that the mixture of two grain size groups would have less void ratio when the mean particle size difference between the two groups is coarse. We use the ratio of \(d^{\prime}5_{0}/d5_{0}\) to represent the degree of particle size difference between the fine-grained group and coarse-grained group, where \(d5_{0}\) and \(d^{\prime}5_{0}\) are the mean diameters of the fine-grained group and coarse-grained group, respectively. The values of \(d^{\prime}5_{0}/d5_{0}\) at different gap intervals are plotted against \(D\) in Figure 6. It can be seen that the ratios of \(d^{\prime}5_{0}/d5_{0}\) increase with \(D\) irrespective of gap intervals. According to [PERSON]'s finding, it is understandable that the void ratio \(e\) of the SRM decreases with the increasing \(D\) of the basic gradation.  
As aforementioned, particle breakage will inevitably happen during the vibrating compaction on SRMs. Commonly, the degree of particle breakage is quantitatively evaluated using three indices: \(B_{15}\)[27], \(B_{g}\)[28] and \(B_{r}\)[29], where \(B_{15}\) is the ratio of the diameter before test and after test corresponding to 15% finer passing in the gradation curve; \(B_{g}\) is the maximum distance between the original gradation curve and gradation curve after test; \(B_{r}\) is the ratio of \(B_{t}\) to \(B_{p}\), where \(B_{t}\) is the area between original gradation curves and gradation curve after test, \(B_{p}\) is area between original gradation curve and the line \(d\) = 0.074 mm. Figure 7 shows the particle breakage of SRMs with gap intervals under the basic gradations with different fractal dimension \(D\). The test results demonstrate that the particle breakage of  
Figure 5: Void ratios of the SRMs with gap intervals under different basic gradations.  
Figure 6: Changes of \(d^{\prime}5_{0}/d5_{0}\) with fractal dimension \(D\) at different gap intervals.  
gap-graded SRMs is more prominent than the SRM with continuous gradation on the whole, especially at the gap interval of 5-20 mm. The degree of particle breakage decreases gradually with the increasing fractal dimension \(D\) of the basic gradation. This is because the particle sizes in SRM decrease with the increasing \(D\), and consequently less particle breakage will happen during the vibrating compaction.