# Particle Packing Optimization for CCR-GGBS-FA Binder Stone Waste pavement Base Material
## 2 Materials and Methods
### Test Methodology and Programme
#### 2.2.1 Maximum Dry Density Test  
Under the condition that \(D_{\text{max}}\) and \(D_{\text{min}}\) are unchanged, by adjusting the distribution ratio of each component of stone waste, a fitting curve with good correlation with the target gradation can be formulated. Therefore, based on the MAA model, this paper proposes to adjust the content of each component in the stone waste to form the fitted gradation without considering the method of cementitious materials, and establish the relationship with the target gradation by calculation; this is named the MAA-SW model (Modified Andreasen and Andersen-Stone Waste, MAA-SW), as shown in Equation (5), which has a good correlation with the target gradation. \[P(D)\ =\frac{D^{\lambda}-D_{\text{min}}^{\lambda}}{D_{\text{max}}^{\lambda}-D_{ \text{min}}^{\lambda}}. \tag{5}\]  
where \(P(D)\) is the percentage of stone waste smaller than a certain particle size \(D\), in %; \(D\) is the particle size of stone waste, in mm; \(D_{\text{max}}\) is the maximum particle size of stone waste, in mm; \(D_{\text{min}}\) is the minimum particle size of stone waste; \(\lambda\) is the distribution modulus, and the larger the value of \(\lambda\), the larger the curvature of the curve of the target gradation. Based on the MAA-SW model, it can be determined that when the fitted gradation is closer to the target gradation, the better the correlation is proved, i.e., the closer the particles' stacking state. In soil mechanics, close packed refers to the degree of close-packed arrangement of solid particles in soil with a single-grain structure and is an important indicator of the state of coarse-grained soils. In this study, the physical index of density \(\gamma_{d(\text{max})}\) (corresponding to the minimum pore ratio \(e_{\text{min}}\)) in the tightest packing state with relatively stable measured values was used as an evaluation index for the advantages and disadvantages of the particle gradation of similar stone waste, i.e., the maximum density of the stone waste particles was measured by compacting only the stone waste particles without the addition of water and cementing materials. The greater the density \(\gamma_{d(\text{max})}\) in the densest state, the more the grading particles are closely arranged, and, thus, the more the stone waste is structurally stable, with high strength, and not easily compressed. On the contrary, if the particles are loosely arranged and the structure is in an unstable state, the grading of the stone waste is poor. This test refers to the \"standard of geotechnical test methods (GB/T50123-2019)\" in the \"vibration hammering method\" to determine the density \(\gamma_{d(\text{max})}\) of the stone waste in the most compact state. The specific steps are as follows:  
(1) Process the raw stone waste for drying using two sieves of 0.075 and 0.005 mm. Sieve out the stone chips (particle size 0.075-4.75 mm), fine stone powder (particle size 0.005-0.075 mm), and ultrafine stone powder (particle size \(\leq\) 0.005 mm) to obtain the raw material for the test, as shown in Figure 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Stone Waste** & **Type of Binder** & **Gradation Group** & **Curing Time** & **Tests** & **Number of Test** \\  & & & **(Days)** & & **Groups** \\ \hline Raw stone waste & & 1 & & & \\ Stone waste & & 17 & 7, 28 & Maximum density & \\  & & 17 & & test, UCST & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test scheme of solidified stone waste. (2) Prepare a vibrating hammermill with an inner diameter of 5 cm and a height of 12.7 cm, as shown in Figure 6, and weigh its mass. (3) After mixing, pour the stone waste into a container for vibration processing. This process should be repeated three times according to the different stone waste particle sizes. The amount of material poured into the container for each treatment should produce a final volume that is slightly larger than one-third of the container after vibration.