## 4 Analysis of Results  
### Size Effect of the Mechanical Properties of Basalt Blocks  
#### 4.1.1 Size Effects of Mechanical Parameters  
To grasp the size effects of the mechanical parameters of basalt blocks with hidden cracks, the mechanical parameters and the coefficients of variation (CoV) of multiple SRM models of various sizes were calculated. Based on the variation trends in each mechanical parameter with increasing sample size, the mechanical REV and corresponding equivalent mechanical parameters were determined, as shown in Figure 10, where the scatter points represent the discrete data of the mechanical parameters of different samples with the same size; the blue broken-line points denote the average value, and the red broken-line points represent the CoV, which is defined as the ratio of the standard deviation to the average value. In this study, an acceptable CoV was less than 10%. As shown in Figure 10, the UCS average value of basalt blocks with hidden cracks decreases gradually with the increase in the sample size, with a more evident decreasing trend for small sizes, and it remains roughly constant after exceeding a certain size. With the increase in the sample size, the UCS fluctuation range and dispersion degree of different samples with the same size decrease, and the CoV exhibits a trend that first fluctuates and then nonlinearly decreases; in particular, this decreasing trend is more evident at small  
Figure 10: Effects of the sample size on the mechanical parameters of basalt with hidden cracks. (**a**) Uniaxial compression strength, UCS; (**b**) tensile strength, BDS; (**c**) cohesive strength, \(c\); (**d**) internal friction angle, \(\varphi\). sizes. Specifically, when the sample size is less than 200 mm, the variation range of the UCS values of the various samples with the same size is wide, and the decrease trend in the CoV is the most evident, with a value greater than 20%, meaning that the model under this size cannot represent the structural characteristics of basalt. For a sample size range of 300-400 mm, the CoV is in the range of 10-20%, where the CoV of the samples with a size of 400 mm is slightly greater than 20%, and the UCS fluctuation range is significantly reduced at this time. The CoV is below 10% when the sample size is \(\geq\)500 mm, and the UCS tends to an asymptotic value, indicating that the model at this size can represent the entire rock block. Therefore, the basalt REV size characterized on the basis of the UCS fluctuation range and dispersion degree of the samples of various sizes is 500 mm, at which the UCS is 52.53 MPa, which is approximately 20% of that of a standard-sized basalt sample (i.e., 100 mm in height and 50 mm in diameter). Similarly, the entire variation trends in the tensile strength (BDS) and cohesive strength \(c\) are the same as those of the UCS, as shown in Figure 10b,c. Therefore, the REV size determined based on the property variation degree is 500 mm, at which BDS = 7.14 MPa and \(c\) = 12.50 MPa, which are approximately 30% of the corresponding mechanical parameters of the standard-sized basalt sample. In addition, the overall change trend in the internal friction angle \(\varphi\) is not evident, and the CoV of the basalt samples under each size is less than 10%. When the sample size \(\geq\) 150 mm, \(\varphi\) tends to stabilize, with a value of approximately 47.5\({}^{\circ}\), which is slightly higher than the corresponding mechanical parameter of basalt samples with a standard size, as shown in Figure 10d. In summary, the mechanical REV size of the basalt block containing hidden cracks determined based on the variation trends in the mechanical parameters of the samples with different sizes is 500 mm, at which UCS = 52.53 MPa, BDS = 7.14 MPa, \(c\) = 12.50 MPa, \(\varphi\) = 47.5\({}^{\circ}\), and \(E\) = 30.00 GPa.