## 3 Creation of a Numerical Model of Basalt
### Generation of an SRM Model of Basalt Blocks
Taking uniaxial compression as an example, 10 numerical samples were selected, including three intact samples and seven cracked samples, and the crack distribution characteristics, such as the number, size, location, and angle, in each sample were different, as shown in Figure 8. Based on the above-determined initial mesoscopic parameters of the basalt with hidden cracks, FDEM simulations were conducted on the 10 numerical samples, and the corresponding mechanical parameters were obtained and compared with the laboratory test results. An iterative calibration procedure was used in this study, involving running an array of numerical mechanical tests, such as the Brazilian disc splitting, uniaxial compression, and triaxial compression, on standard-sized samples to obtain a set of meso-parameters, based on which the macro-mechanical properties obtained by FDEM modeling can match those obtained from the laboratory test, as shown in Table 1.  
Table 2 presents the macro-mechanical parameters of the standard-sized basalt determined by laboratory experiments and FDEM simulations [31,32]. On the one hand, the macro-mechanical properties obtained through FDEM modeling have a good consistency with the laboratory test results overall, indicating that the selected FDEM model and the used meso-parameters are reasonable. On the other hand, the mechanical parameters of small-sized basalt samples show significant discreteness, variability, and randomness both in the laboratory tests and numerical simulations. For example, the UCS varies from tens of MPa to hundreds of MPa, with an average of approximately 200 MPa. Evidently, it is difficult to accurately obtain the mechanical properties of basalt by simply performing indoor tests on standard-sized samples. Therefore, it is necessary to use numerical methods to study the mechanical properties of basalt with hidden cracks. In particular, the size effect analysis of the mechanical properties is more meaningful to obtain the real mechanical properties. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mechanical Parameters** & **Matrix** & **Hidden Crack** & **Rock Block** \\ \hline Bulk density, \(\rho\) (kg/m\({}^{3}\)) & 2900.00 & & 2800.00 \\ Poisson’s ratio, \(\
u\) & 0.15 & & 0.25 \\ Young’s modulus, \(E\) (GPa) & 50.00 & & 30.00 \\ Internal friction angle, \(\varphi\) (\({}^{\circ}\)) & 40.00 & 25.00 & 47.50 \\ Cohesive strength, \(c\) (MPa) & 75.00 & 15.00 & 12.50 \\ Tensile strength, \(f_{\text{f}}\) (MPa) & 18.50 & 4.00 & 7.15 \\ Mode-I fracture energy, \(G_{\text{f1}}\) (N/m) & 100.00 & 20.00 & 20.00 \\ Mode-II fracture energy, \(G_{\text{f2}}\) (N/m) & 1000.00 & 200.00 & 200.00 \\ Normal contact penalty, \(P_{\text{n}}\) (GPa-m) & 500.00 & 10.00 & 300.00 \\ Tangential contact penalty, \(P_{\text{t}}\) (GPa/m) & 500.00 & 10.00 & 300.00 \\ Fracture penalty, \(P_{\text{f}}\) (GPa) & 500.00 & 10.00 & 300.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical parameters of a basalt block used in the FDEM model. Figure 8: Numerical basalt samples with a standard size for meso-parameter calibration. **(a)** DFN models under uniaxial and triaxial compression; **(b)** DFN models under Brazilian disc splitting; **(c)** SRM models under uniaxial and triaxial compression **(left)** and Brazilian disc splitting **(right)**.