## 3 Mechanisms of Macro- and Micro-Parameter Influence and Construction of Multiple Regression Models
### Analysis of the Influence Mechanism of Significant Micromechanical Parameters Interaction
#### 3.2.2 The Effects of \(\overline{\sigma}_{c}\) and \(\overline{c}\) on the _UCS_  
The primary influencing factors for uniaxial compressive strength (_UCS_) are cohesion and tensile strength. As shown in Figure 5(a), when cohesion is held constant, _UCS_ exhibits a significant increasing trend with the increase in tensile strength. The higher the cohesion level, the more pronounced the enhancing effect of tensile strength on _UCS_. In contrast, when cohesion is low, the influence of tensile strength on _UCS_ becomes negligible. As depicted in Figure 5(b), with tensile strength held constant, _UCS_ increases with increasing cohesion. The combination of high tensile strength and high cohesion generates a stronger  
Figure 4: The effects of \(R_{max}\)/\(R_{min}\) and \(k\) on the \(E\). Figure 5: The effects of \(\overline{E}\) and \(k\) on the \(E\). synergistic effect, where their combined contribution exceeds the independent effects of individual parameters. Regression Analysis of Macroscopic and Micromechanical Parameters Based on an Intelligent Dynamic Regression Selection Mechanism  
Based on the results of orthogonal experiments and interaction tests, this study identifies key parameter combinations that significantly influence macroscopic mechanical response parameters to model their complex relationships, and an intelligent dynamic regression selection mechanism is adopted, which is capable of automatically selecting the optimal functional form from multiple candidates, including linear, quadratic, exponential, and logarithmic models. The selection is performed adaptively based on the coefficient of determination (\(R^{2}\)), ensuring that the most suitable model is chosen in a data-driven manner. An illustrative framework of this intelligent dynamic selection process is shown in Figure 7, highlighting the automatic evaluation and comparison of multiple functional forms. The significant influencing factors for the elastic modulus are \(R_{max}\)/\(R_{min}\), \(\overline{E}\), and \(k\). Intelligent dynamic regression analysis is then performed to explore their functional relationships, and the corresponding regression models are established accordingly. \[\text{Linear}:\qquad E=4.76+1.67\overline{E}-1.19\frac{R_{max}}{R_{min}}-0.84K \left(R^{2}\ =\ 0.96\right) \tag{2}\]  
\[\text{Polynomial:}\quad E=5.29+3.02\times\overline{E}\cdot\frac{R_{max}}{R_{min }}-5.50\cdot\frac{R_{max}}{R_{min}}-1.41k-0.02\left(\overline{E}\right)^{2}-0.34 \cdot\frac{R_{max}}{R_{min}}\cdot\overline{E}-0.20\overline{E}k+\]  
\[\text{$1.73\left(\frac{R_{max}}{R_{min}}\right)^{2}-0.13\cdot\frac{R_{max}}{R _{min}}+0.34k^{2}\left(R^{2}\ =\ 0.85\right)$} \tag{3}\]  
\[\text{Exponential:}\qquad E=e^{1.75+0.18\overline{E}-0.16\frac{R_{max}}{R_{min }}-0.10k}\left(R^{2}\ =\ 0.89\right) \tag{4}\]  
Figure 6: The effects of \(\overline{v}_{c}\) and \(\overline{c}\) on the _UCS_. Figure 7: Intelligent dynamic selection process. \[\text{Logarithmic}:\qquad E=-2.27+8.99\text{log}(\overline{E})-2.06\text{log}\left( \frac{R_{max}}{R_{min}}\right)-1.91\text{log}(k)\ (R^{2}\ =\ 0.88) \tag{5}\]  
By comparing the coefficients of determination, R\({}^{2}\), Formula (2) was selected to model the effects of \(R_{max}/R_{min}\), \(\overline{E}\), and \(k\) on the \(E\). The resulting model exhibits a high goodness of fit, with a coefficient of determination of \(R^{2}\) = 0.96, indicating a satisfactory fitting performance. The significant influencing factors for the uniaxial compressive strength are \(\overline{\sigma}_{c}\) and \(\overline{c}\). Dynamic regression analysis was conducted for the two factors, and their functional relationships are as follows. \[\text{Linear}:\qquad UCS=-3.32+1.78\overline{c}+0.62\overline{\sigma}_{c}\ (R^{2}\ =\ 0. 86) \tag{6}\]  
Figure 5:0  
Figure 5:1  
Figure 5:2  
By comparing the coefficients of determination \(R^{2}\), Formula (7) was selected to fit the effects of \(\overline{\sigma}_{c}\) and \(\overline{c}\) on the uniaxial compressive strength.