## 4 The Results of Micro-Parameters on Mechanical Properties of Rock  
### The Influence of Micro-Parameters on UCS  
1.1 Combined Effects of \(\overline{\sigma}_{n}/\overline{\tau}_{n}\) and \(\overrightarrow{k}\) on UCS  
The relationships between UCS and \(\overline{\sigma}_{n}/\overline{\tau}_{n}\) and \(\overrightarrow{k}\) are shown in Figure 2. It could be seen from Figure 2a that when \(\overline{\sigma}_{n}/\overline{\tau}_{n}\) \(<\) 0.8, the UCS of the model decreased continuously with increasing \(\overrightarrow{k}\). The rate of the decrease declined with increasing \(\overrightarrow{k}\), whereas the extent of the decrease grew with increasing \(\overline{\sigma}_{n}/\overline{\tau}_{n}\). When 0.8 \(\leq\overline{\sigma}_{n}/\overline{\tau}_{n}\)\(<\) 4, the UCS initially increased and then decreased with increasing \(\overrightarrow{k}\). The extent of the increase grew consistently with increasing \(\overrightarrow{k}\), and the curve maximum continuously shifted toward the right. As shown in Figure 2b, when \(\overline{\sigma}_{n}/\overline{\tau}_{n}\)\(\geq\) 4, the UCS initially increased with increasing \(\overrightarrow{k}\)  and then leveled off. Additionally, as \(\overline{\sigma}_{n}/\overline{\tau}_{n}\) increased, the change in UCS with \(\overrightarrow{k}\) became consistently larger.  
The results indicated that when \(\overrightarrow{k}\) was constant, the UCS increased with increasing \(\overline{\sigma}_{n}/\overline{\tau}_{n}\). When \(\overrightarrow{k}\) was relatively low, there was a minor increase in the UCS with increasing \(\overline{\sigma}_{n}/\overline{\tau}_{n}\). For \(\overrightarrow{k}\) = 1.11, when \(\overline{\sigma}_{n}/\overline{\tau}_{n}\)\(<\) 0.8, the UCS increased by 1.77-fold. When 0.8 \(\leq\overline{\sigma}_{n}/\overline{\tau}_{n}\)\(<\) 1, the increase in the UCS was 20.58%, and when \(\overline{\sigma}_{n}/\overline{\tau}_{n}\)\(\geq\) 1, there was an increase of 8.94%. With increasing \(\overrightarrow{k}\), the increase in UCS with \(\overline{\sigma}_{n}/\overline{\tau}_{n}\) became gradually larger. For \(\overrightarrow{k}\) = 10.11, when \(\overline{\sigma}_{n}/\overline{\tau}_{n}\)\(<\) 1, the UCS increased by 6.24-fold; when \(\overline{\sigma}_{n}/\overline{\tau}_{n}\)\(\geq\) 1, the increase in UCS was 3.22-fold.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Test Method** & \begin{tabular}{c} **Uniaxial Compression Strength** \\ (\(\sigma_{n}\)/MPa) \\ \end{tabular} & \begin{tabular}{c} **Young’s Modulus** \\ **(E/GPa)** \\ \end{tabular} & \
\begin{tabular}{c} **Poisson’s Ratio** \\ **(v)** \\ \end{tabular} &
\begin{tabular}{c} **Sample Size** \\ **(R \(\times\) H/mm)** \\ \end{tabular} \\ \hline Laboratory test & 31.91 & 4.61 & 0.241 & \(25\times 100\) \\ PFC simulation & 33.07 & 4.57 & 0.248 & \(25\times 100\) \\ \hline \end{tabular}
\end{table}
Table 3: Experimental data and simulation results.  
The response surface plots of UCS are shown in Figure 3. When \(\overline{\sigma}_{n}/\overline{\tau}_{n}<0.8\), the UCS exhibited a negative response to \(\overline{k}\) that became more evident with increasing \(\overline{\sigma}_{n}/\overline{\tau}_{n}\). When \(\overline{\sigma}_{n}/\overline{\tau}_{n}\geq 0.8\), the response of UCS to \(\overline{k}\) shifted from negative to positive. This positive response also became more evident with increasing \(\overline{\sigma}_{n}/\overline{\tau}_{n}\), and UCS exhibited a positive response to \(\overline{\sigma}_{n}/\overline{\tau}_{n}\). When \(\overline{\sigma}_{n}/\overline{\tau}_{n}<1\), the positive response of UCS was attenuated with increasing \(\overline{k}\); when \(\overline{\sigma}_{n}/\overline{\tau}_{n}>1\), the positive response was enhanced by increased \(\overline{k}\).