# Research on the Compactness of Lunar Soil Simulant Based on Static Cone Penetration Test
## 3 Results and Analysis  
### The Compactness of Lunar Soil Simulant with Penetration Depth  
Figure 3 shows the variations in the single-layer lunar soil simulant under the four different overall compactness levels measured in the experiment. The four groups of lunar soil simulant were split into three categories: low, medium, and high compactness. The classification details are presented in Table 3.  
The lower the overall compactness, the greater the difference in compactness between the bottom and top barrels. That is to say, the looser the lunar soil simulant, the poorer the overall uniformity of the sample. Conversely, when the overall compactness is higher, there is a smaller difference in compactness between the bottom and top barrels. That is to say, the denser the lunar soil simulant, the better the overall uniformity of the sample. The density of lunar soil is an important indicator that characterizes its physical and mechanical properties. Analyses of the Apollo lunar soil samples have shown that the density increases with the increase in sampling depth at the same sampling point. Based on the analyses of the existing lunar soil samples, two simplified functions, namely the hyperbolic function and the power function, are employed to describe the variation in the lunar soil density with depth [19]. Figure 3: The variation curves of the compactness of the lunar soil simulant with depth under different overall compactness states. \begin{table}
\begin{tabular}{c c c} \hline
**Low Compactness** & **Medium Compactness** & **High Compactness** \\ \hline
58\% & 68\% & 78\% & 86\% \\ \hline \end{tabular}
\end{table} 
Table 3: Categories according to different compactness levels. Based on the analyses of the drilling samples from Apollo 11 and 12, the power function between the density of lunar soil and the depth is obtained as follows [19]:  
\[\rho=1.39z^{0.056} \tag{1}\]  
where \(\rho\) represents the density of the lunar soil at a certain depth(g/cm\({}^{3}\)) and \(z\) represents the depth of the lunar soil at that point (cm). When the depth is 0, its density is also 0, which is inconsistent with the actual density of the lunar soil at the surface layer. At depths exceeding 50 cm, the density increases infinitely, which does not conform to the actual situation where the density of the lunar soil tends to be stable. Therefore, the power function that describes the relationship between the density of the lunar soil and its depth is not applicable to either the surface layer or the deep layer. Instead, it is only suitable for quickly estimating the density of the shallow lunar soil. Based on the analysis of the drilling samples from the Apollo 15, 16, and 17 missions, the hyperbolic relationship between the density of the lunar soil and its depth is obtained as follows [19]:  
\[\rho=1.92\frac{z+12.2}{z+18} \tag{2}\]  
When the depth is 0, its density is 1.3 g/cm\({}^{3}\), which falls within the density range of the real surface layer lunar soil. As the depth increases, its density approaches 1.92 g/cm\({}^{3}\), consistent with the density of lunar soil at depths greater than 60 cm as studied by [PERSON] et al. [20]. Compactness is also an important indicator in characterizing the physical and mechanical properties of lunar soil. Compactness can be evaluated based on porosity. For a lunar soil simulant with the same grading, there is a conversion relationship between porosity and density. Conversions between compactness and density can be implemented under this condition [21]. Curves showing the variation in the density of simulated and real lunar soil with depth based on the compactness values are shown in Figure 4. As the depth increases, the densities of both the lunar soil simulant and real lunar soil increase. The growth rate of the density following a hyperbolic relationship is greater than that following a power function, and the density span of the lunar soil described by the hyperbolic relationship is larger than that described by the power function.