# Research on the Compactness of Lunar Soil Simulant Based on Static Cone Penetration Test
## 3 Results and Analysis
### Model of the Relationship Between Normalized Cone Tip Resistance and Compactness  
The curves of the normalized cone tip resistance of the lunar soil simulant varying with compactness under four overall compactness levels are shown in Figure 8a-d. The normalized cone tip resistance increases with the increase in compactness.  
Figure 8: The variation curves of the normalized cone tip resistance of the lunar soil simulant with compactness: (**a**) D\({}_{1}\) = 58%; (**b**) D\({}_{2}\) = 68%; (**c**) D\({}_{3}\) = 78%; (**d**) D\({}_{4}\) = 86%; (**e**) fitting of all points.  
By comparing the variation trends of the four curves, it is found that the growth rates of the normalized cone tip resistance of the lunar soil simulant with overall compactness levels of 58% and 86% are greater than those with 68% and 78%. The uniformity is also higher at the medium compactness level than the low compactness level. The growth rate of the normalized cone tip resistance of the lunar soil simulant increases slowly with the increase in compactness.  
All data points from the four curves in Figure 8a-d are fitted into one curve showing the variation in the normalized cone tip resistance of the lunar soil simulant with compactness, as depicted in Figure 8e. The following is the fitting equation of the curve:  
\[Q=28332.73+28521.38\times\left(\frac{\mathrm{e}^{x_{Q}}+\mathrm{e}^{-x_{Q}}}{ \mathrm{e}^{x_{Q}}-\mathrm{e}^{-x_{Q}}}-\frac{1}{x_{Q}}\right),R^{2}=0.97 \tag{7}\]  
\[x_{Q}=\frac{D-92.35}{0.34} \tag{8}\]  
The correlation coefficient R\({}^{2}\) of the fitted curve is 0.97. As the compactness increases, the normalized cone tip resistance also gradually increases. When the compactness is less than 70%, the normalized cone tip resistance grows slowly with a relatively small growth rate. When it is greater than 70%, the growth rate of the normalized cone tip resistance gradually increases and continues to rise. When the compactness reaches 90%, both the growth rate and the normalized cone tip resistance reach their maximum. The higher the compactness, the greater the resistance when the cone tip penetrates the lunar soil simulant, and the faster the growth rate of the normalized cone tip resistance.  
Table 6 presents the correlation coefficients of the fitted curves of the cone tip resistance of the lunar soil simulant varying with compactness. By comparing the correlation coefficients before and after the normalization of the cone tip resistance, it is found that the correlation coefficient of the fitted curve for a single overall compaction level before normalization is greater than or equal to that after normalization. When the data points for all overall compaction levels are used to fit the curve, the correlation coefficient after normalization is greater than that before normalization. This indicates that when there are sufficient experimental data, the influence of the overlying pressure on the cone tip resistance under different compactness levels can be eliminated, and the variation law of the cone tip resistance with compactness can be reflected more accurately.