## 3 Mechanisms of Macro- and Micro-Parameter Influence and Construction of Multiple Regression Models  
### Analysis of Major Influencing Factors on Macroscopic Mechanical Properties  
Based on the experimental parameters in Table 1, a seven-factor, four-level orthogonal experimental design was developed. Macroscopic mechanical properties, including uniaxial compressive strength (\(UCS\)), elastic modulus (\(E\)), and Poisson's ratio (\(v\)), were obtained from numerical simulations. The orthogonal experimental scheme and corresponding simulation results are summarized in Table 2. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \begin{tabular}{c} **Parameter** \\ **Levels** \\ \end{tabular} & \(R_{max}\)/\(R_{min}\) & \begin{tabular}{c} \(\overline{E}\) \\ **(GPa)** \\ \end{tabular} & \(k\) & \
\begin{tabular}{c} \(\overline{c}\) \\ **(MPa)** \\ \end{tabular} &
\begin{tabular}{c} \(\overline{\sigma}_{c}\) \\ **(MPa)** \\ \end{tabular} & \(\overline{\varphi}\) & \(\mu\) \\ \hline
1 & 1 & 3 & 1 & 5 & 10 & 15 & 0.3 \\
2 & 1.5 & 5 & 2 & 10 & 15 & 30 & 0.4 \\
3 & 2 & 7 & 3 & 15 & 20 & 45 & 0.5 \\
4 & 2.5 & 9 & 4 & 20 & 25 & 60 & 0.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Levels of micromechanical parameters. Based on the orthogonal experimental results, a multifactor analysis of variance was employed to systematically evaluate the effects of micromechanical parameters on uniaxial compressive strength (_UCS_), elastic modulus (\(E\)), and Poisson's ratio (\(v\)). As an effective statistical method, a multifactor analysis of variance allows for the quantification of the contributions of multiple independent variables (micromechanical parameters) to dependent variables (macroscopic mechanical properties), while accounting for the potential interaction effects among factors. The F-statistic was used to assess the magnitude of each factor's effect; higher F-values indicate more pronounced influences. Statistical significance was determined based on the Sig. value as follows: _Sig._ < 0.01, highly significant; 0.01 \(<\)_Sig._ \(\leq\) 0.05, significant; and _Sig._ \(>\) 0.05, not significant. The analysis results are shown in Figure 2.  
According to the results presented in Figure 2a, the factors affecting the elastic modulus (\(E\)) are ranked in the following order: effective modulus \(\overline{E}\) > stiffness ratio \(k\) > particle size ratio \(R_{max}\)/\(R_{min}\) > friction coefficient \(\mu\) > cohesion \(\overline{c}\) > tensile strength \(\overline{\sigma}_{c}\) > friction angle \(\overline{\varphi}\). These results indicate that the effective modulus has the strongest influence on the macroscopic elastic modulus, displaying an extremely significant effect. Significance analysis (_Sig._ values) further confirms that the effective modulus, stiffness ratio, and particle size ratio exhibit highly significant effects on the elastic modulus (with significance  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \multirow{2}{*}{**Number**} & \multirow{2}{*}{\(R_{max}\)/\(R_{min}\)} & \multirow{2}{*}{\(\overline{E}\)} & \multirow{2}{*}{\(\overline{c}\)} & \multirow{2}{*}{\(\overline{\sigma}_{c}\)} & \multirow{2}{*}{\(\overline{\overline{\varphi}}\)} & \multirow{2}{*}{\(\mu\)} & _UCS_ & \(\overline{E}\) & \multirow{2}{*}{\(\upsilon\)} \\  & & & (GPa) & &  
levels of zero), while the impact of the remaining parameters is relatively minor. The friction coefficient has a certain effect on the macroscopic elastic modulus, but its effect is not significant. Cohesion, tensile strength, and friction angle have almost no effect on the macroscopic elastic modulus. According to the results presented in Figure 2b, the factors affecting uniaxial compressive strength (\(UCS\)) are ranked as follows: cohesion \(\overline{c}>\) tensile strength \(\overline{\sigma}_{c}>\) effective modulus > friction coefficient \(\mu>\) friction angle \(\overline{\varphi}>\) particle size ratio \(R_{max}\)/\(R_{min}>\) stiffness ratio \(k\).