# Research on the Compactness of Lunar Soil Simulant Based on Static Cone Penetration Test
## 3 Results and Analysis
### Model of the Relationship Between Cone Tip Resistance and Compactness  
The curve depicting the variation in the cone tip resistance with penetration depth is divided into segments with intervals of 10 cm, which is the height of the single-layer \begin{table}
\begin{tabular}{c c c} \hline \hline
**Overall** & **Maximum Value of The Cone** & **Maximum Value of The Normalized** \\
**Compactness/\%** & **Tip Resistance/MPa** & **Cone Tip Resistance** \\ \hline
58 & 0.599 & 66 \\
68 & 3.262 & 339 \\
78 & 11.044 & 1082 \\
86 & 27.231 & 3037 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum values of the cone tip resistance and the normalized cone tip resistance of the lunar soil simulant under different compactness conditions. Figure 6: The variation curve of the normalized cone tip resistance with the penetration depth. Figure 7a-d show the variations in the curves of the cone tip resistance of the lunar soil simulant with compactness for different overall compaction barrels. As can be seen in the figures, the cone tip resistances of the four groups of lunar soil simulant all gradually increase with the increase in compactness, showing an overall exponential growth. For the three lunar soil simulant groups with overall compactness levels of 58%, 68%, and 78%, the growth rate of the cone tip resistance gradually accelerates. When the overall compactness is 86%, the growth rate of the cone tip resistance in the upper barrel is extremely slow. While the single-layer compactness exceeds 87.9%, the growth rate rises sharply. By comparing the variations in the curves of the cone tip resistance of the four groups of lunar soil simulant with compactness, it is found that as the overall compactness increases, the growth rate of the cone tip resistance also gradually increases. When the overall compactness is at a low or medium level, the growth rate of the cone tip resistance increases gradually with the increase in the single-layer compactness. When the overall compactness of the lunar soil simulant reaches a high level, a slight change in compactness can cause a rapid increase in the cone tip resistance. As shown in Figure 7d, the cone tip resistance starts to increase rapidly from the compactness of 87.9%. By comparing the average cone tip resistance data in Table 5, it can be found that in the layered lunar soil simulant compaction barrel with an overall compactness of 78%, the average cone tip resistance increases by approximately 2 MPa when the compactness increases by 1%. In the barrel with an overall compactness of 86%, when the compactness of the lunar soil simulant exceeds 87.9%, the average cone tip resistance increases by approximately 7 MP when the compactness increases by 1%. This shows that at overall compactness levels exceeding 86%, the growth in compactness has a significant impact on the cone tip resistance, verifying the rationality of the classification method mentioned earlier, which defines a lunar soil simulant with a compactness greater than 86% as high-compactness soil. Taking all the data points from the curves of the cone tip resistance varying with compactness under the four overall compactness levels and fitting them into one single curve can represent the more general relationship between the cone tip resistance and compactness, as shown in Figure 7e. The fitting equation of the curve is as follows:  
\[q_{c}=279.24+279.8\times\left(\frac{e^{x_{q}}+e^{-x_{q}}}{e^{x_{q}}-e^{-x_{q} }}-\frac{1}{x_{q}}\right),R^{2}=0.95 \tag{5}\]  
\[x_{q}=\frac{D-90.92}{0.16} \tag{6}\]  
The correlation coefficient R\({}^{2}\) of the fitted curve is 0.95. This fitted curve incorporates the cone tip resistance corresponding to the compactness of each single layer measured within the range from 46.5% to 89.8%. The cone tip resistance gradually increases as the compactness increases, and the curve shows exponential growth in the cone tip resistance. When the compactness is between 46.5% and 70%, the change in the cone tip resistance is relatively small, and the growth is rather gentle.