## 2 Laboratory Testing Program
### Specim Preparation and Testing Program  
The only way to characterize the grading of granular materials is to use the grading curve. The grading curve contains a large amount of data; however, it lacks quantitative indicators. Hence, it is difficult to make the comparison of the particle size distribution with different gradings of granular materials. In order to completely express the grading of particles and quantitatively analyze the relationship between grading and relevant mechanical indexes, the grading of granular materials is quantified by establishing the grading equations with mathematical formulas, which has great significance for engineering practice and academic research. In this test, the method of artificial sample preparation according to FMGE was used, and the FMGE is defined as [22; 23; 24]  
\[P_{i}=\left(\frac{d_{i}}{d_{max}}\right)^{3-D_{f}}\times 100\% \tag{1}\]  
where \(D_{f}\) represents the fractal dimension, \(d_{i}\) presents the particle size (mm), \(P_{i}\) denotes the cumulative mass percentage with particle size less than \(d_{i}\) (%), and \(d_{max}\) indicates the maximum particle size (mm). The control parameters of well grading for CGSF are the coefficient of uniformity (\(C_{U}\)) and the coefficient of curvature (\(C_{C}\)), and the calculation formulas are as follows [25; 26]:  
\[C_{u}=\frac{d_{60}}{d_{10}} \tag{2}\]  
\[C_{c}=\frac{\left(d_{30}\right)^{2}}{d_{10}d_{60}} \tag{3}\]  
where \(d_{60}\), \(d_{30}\), and \(d_{10}\) refer to the particle size corresponding to the passing percentage of 60%, 30%, and 10% in the grading curve, respectively (mm). CGSF with well grading satisfies \(C_{u}\geq 5\) and \(1\leq C_{c}\leq 3\). Furthermore, combining Equations (1)-(3), the range of well grading can be captured based on the FMGE:  
\[1.89=3-\frac{\text{lg}6}{\text{lg}5}\leq D_{f}\leq 3-\frac{\text{lg}\left( \frac{3}{2}\right)}{\text{lg}3}=2.63 \tag{4}\]  
Figure 3: The large-scale dynamic and static triaxial instrument. According to Equation (4), 4 groups of tests with different fractal dimensions, i.e., \(D_{f}=1.89\), 2.13, 2.37, and 2.61, were designed to carry out the experimental research, and the test design grading curve is shown in Figure 4. A cylindrical specimen with \(D=300\) mm and \(H=600\) mm was utilized in this test; \(D\) and \(H\) are the diameter and height of the specimen, respectively. According to the Chinese Standard of Soils for Highway Engineering [18], the maximum dry density of the specimen can be obtained. Compaction degree, which was widely used for the triaxial test and situ construction [27; 28], is calculated as follows:  
\[D_{c}=\frac{\rho}{\rho_{max}}\times 100 \tag{5}\]  
where \(\rho_{max}\) denotes the maximum dry density (g/cm\({}^{3}\)), \(\rho\) is the dry density of the specimen (g/cm\({}^{3}\)), and \(D_{c}\) represents the compaction degree (%). In this test, the compaction degree was used to control the preparation of specimens and \(D_{c}=90\%\), 93%, and 96% were adopted. In addition, the compaction degree meets the requirements of the road base and subbase materials [18]. Figure 5 shows the process of the large triaxial tests. First, the above drying CGSF (as displayed in Figure 2) should be well mixed according to the designed grading curve (as shown in Figure 4). The specimen prepared in this test was too large and heavy at the laboratory. Therefore, the specimen was compacted with a compaction hammer in a mold in five layers (as shown in Figure 5a). Before placing CGSF on the next layer, the surface of the previously compacted layer was scraped to a depth of about 20 mm to guarantee well-interlocking vertically adjacent layers, just as in other studies [20; 29; 30]. The target compaction degree of the CGSF specimen was reached by controlling the thickness of each individual layer and the mass of added CGSF. After compaction, a rubber membrane was used to enclose the specimen, and the top and bottom of the specimen were tied with rubber ropes. Figure 5b displays the prepared sample.