# Numerical Study of Cone Penetration Tests in Lunar Regolith for Strength Index
## 2 Numerical Model
### Contact Model Parameter Calibration  
The parameters of the discrete element triaxial simulation model were calibrated using a simulated lunar regolith triaxial test under low confining pressure, accounting for the influence of low gravity on the lunar surface. The selected model parameters ensured that the discrete element sample exhibited an internal friction angle and cohesion comparable to those of the simulated lunar regolith. Four main parameters required calibration: the contact stiffness ratio (\(\kappa\)); the contact effective modulus (\(E_{\text{eff}}\)); the particle shape coefficient (\(\xi\)); and the contact friction coefficient (\(\mu\)). Sensitivity analysis was carried out for the four parameters. The analysis scheme of the parameters is shown in Table 1:  
A sensitivity analysis of the main parameters was carried out by means of control variables, and the analysis results are shown in Figure 2.  
According to Figure 2a, the initial stiffness gradually increases with the increase of effective modulus (\(E_{\text{eff}}\)), the slope after the curve peak slows down with the increase of effective modulus (\(E_{\text{eff}}\)), and the residual deviating stress increases accordingly. When the effective modulus (\(E_{\text{eff}}\)) is lower than 50 MPa, the peak deviator stress is sensitive to the change of the effective modulus (\(E_{\text{eff}}\)). Figure 2b shows that the initial slope and peak deviator stress of the stress-strain curve decrease gradually with the increase of the stiffness ratio (\(\kappa\)). The stiffness ratio (\(\kappa\)) has little effect on the stress-strain curve of the triaxial simulation. Figure 2c shows that the friction coefficient (\(\mu\)) has a significant effect on the stress-strain curve. When the friction coefficient (\(\mu\)) is lower than 0.8, the curve shows a hardening type, otherwise it shows a softening type. In addition, with the increase of the friction coefficient (\(\mu\)), the initial slope and peak deviator stress of the curve increased rapidly, and the strain softening degree increased. Figure 2d shows that, compared with the other three parameters of the linear group, the shape factor (\(\xi\)) has the most significant effect on the stress-strain curve. When it is lower than 0.3, the stress-strain curve shows a hardening type, otherwise it shows a softening type. With the increase of the shape factor (\(\xi\)), the slope of the initial stage, the peak deviator stress and the slope (absolute value) of the post-peak stage of the curve increased rapidly, the strain softening degree gradually strengthened, and the strain in the residual stable stage also increased gradually. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Group**} & **Contact Effective** & \multirow{2}{*}{**Contact Stiffness**} & **Contact Friction** & **Particle Shape** \\  & **Modulus (MPa)** & & **Ratio \(\kappa\)** & **Coefficient \(\tau\)** & **Factor \(\times\)** \\ \hline \(E_{\text{eff}}\) & \(10,50,500,1000\) & 1.0 & 1.0 & 0.5 \\ \(\kappa\) & 100 & 0.5, 2.0, 4.0, 8.0 & 1.0 & 0.5 \\ \(\mu\) & 100 & 1.0 & 0.5, 0.8, 1.2, 1.5 & 0.5 \\ \(\xi\) & 100 & 1.0 & 1.0 & 0.1, 0.3, 0.8, 1.3 \\ Control & 100 & 1.0 & 1.0 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The main parameters analysis scheme of the lunar soil particle contact model. According to the results of the sensitivity analysis, the parameter calibration will be carried out according to the following ideas: firstly, the peak deviator stress of the stress-strain curve is calibrated by the contact friction coefficient (\(\mu\)) and the particle shape coefficient (\(\xi\)); then, the slope of the initial stage of the stress-strain curve is adjusted by the contact effective modulus (\(E_{\text{eff}}\)). Finally, by fine-tuning the contact stiffness ratio (\(\kappa\)) and particle shape coefficient (\(\xi\)), the slope, peak deviator stress, and residual deviator stress of the initial stage of the stress-strain curve are adjusted more accurately.