## 3 Creation of a Numerical Model of Basalt
### Generation of an SRM Model of Basalt Blocks  
To investigate the effects of sample size on the mechanical properties of basalt blocks with hidden cracks, first, a sufficiently large DFN model (i.e., 5000 mm \(\times\) 5000 mm) was generated using the Monte Carlo method based on the statistical distribution characteristics of the geometric parameters of hidden cracks obtained above. Subsequently, a series of random samplings of different positions and sizes was performed, generating many DFN sub-models of small sizes. Taking uniaxial compression simulation as an example, the widths were 25, 50, 100, 150, 200, 300, 400, 500, and 600 mm, with an aspect ratio of 2, as shown in Figure 7a. The above-generated DFN sub-models representing hidden cracks were embedded into the FDEM code Irazu representing the intact matrix to establish multiple SRM models of different sizes that characterize the real structural characteristics of basalt, i.e., a hybrid DFN-FDEM model, as shown in Figure 7b. Finally, these SRM models were subjected to a series of numerical tests, such as Brazilian basic splitting, uniaxial compression, and triaxial compression, using the calibrated meso-parameters, as shown in Table 1, based on which the size effects of the mechanical behaviors of basalt with hidden cracks, such as the mechanical parameters, stress-strain curves, strength failure criterion, and failure modes, were analyzed. To eliminate and circumvent this potential variability, uncertainty, and randomness, and considering the calculation time constraints, 10 SRM models were created under each size level in this study, and the average value of the sample calculation results was adopted under this working condition. The meso-parameters used in the FDEM models are classified as elastic parameters of triangular elements (Poisson's ratio \(\
u\), elastic modulus \(E\), and bulk density \(\rho\)), strength parameters of crack elements (fracture energy \(G_{\rm f}\), internal friction angle \(\varphi\), cohesion \(c\), and tensile strength \(f_{\rm t}\)), and penalty values (\(P_{\rm n}\), \(P_{\rm t}\), and \(P_{\rm f}\)). Generally, the fracture energy \(G_{\rm f1}\) for tensile cracks is determined according to the fracture toughness \(K_{\rm fc}\) obtained through three-point bending tests or estimated based on the tensile strength from a direct or indirect  
Figure 7: SRM (DFN–FDEM) models of a basalt block of different sizes with hidden cracks. (**a**) DFN models of different sizes; (**b**) SRM model with dimensions of 300 mm \(\times\) 600 mm. tensile test. In addition, the fracture energy \(G_{\text{f2}}\) for shear cracks is approximately set to 10 \(\times\)\(G_{\text{f1}}\), the penalty values (\(P_{\text{n}}\), \(P_{\text{t}}\), and \(P_{\text{f}}\)) are typically set to 10-100 times the elastic modulus, and the other parameters can be determined by referring to the test results [42]. In this study, the basalt is composed of a matrix and hidden cracks, where the matrix parameter values (i.e., intact basalt) can be determined by referring to the test results of cryptocrystalline basalt, and the parameter values of hidden joints, which are difficult to obtain by testing, i.e., a cohesive crack element model, can be determined by rationally reducing the parameter values of the matrix. Finally, the parameters of the upper and lower platens can be obtained from the properties of steel. The meso-parameter calibration is mainly aimed at a large number of numerical samples subjected to Brazilian disc splitting, uniaxial compression, and triaxial compression, with a standard size obtained from the above random sampling.