## 4 REV Size of Broken Rock Mass
### Determination of _rev_  
The numerical uniaxial compression tests provide stress-strain curves of the cylindrical rock specimens with different scales. To illustrate the stress-strain curves, Figure 12 shows the results from the uniaxial compression tests on the group of 3 m \(\times\) 6 m cylindrical specimens, from which it can be seen that the peak axial stresses for the five specimens are 3.16 MPa, 4.46 MPa, 6.78 MPa, 3.43 MPa, and 3.84 MPa, respectively, and the elastic moduli are 7.91 GPa, 9.17 GPa, 9.67 GPa, 6.94 GPa, and 7.21 GPa, respectively. Although the parameters are not precisely identical, their close approximation to each other validates, to a certain extent, the efficacy of the proposed method for modeling fractured rock masses. The average peak compressive strength and the average elastic modulus of this group of models are 4.33 MPa and 8.18 GPa, respectively. Figure 12: Uniaxial compression test results of cylindrical rock samples (3 m \(\times\) 6 m): (**A**) the first Monte Carlo trial; (**B**) the second Monte Carlo trial; (**C**) the third Monte Carlo trial; (**D**) the fourth Monte Carlo trial; (**E**) the fifth Monte Carlo trial. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Density/g-cm\({}^{-3}\)** & **Bulk Modulus/GPa** & **Shear Modulus/GPa** \\ \hline
7800 & 300 & 250 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mechanical parameters of rigid bearing plate. From this example, it is evident that the equivalent rock masses and their mechanical parameters generated for the same model size and structural plane geometric parameters are not identical, which can be attributed to the fact that the distributions of the simulated structural planes are only statistically similar. The variations in peak compressive strength and elastic modulus of the rock model groups with specimen diameter of the groups are shown in Figure 13. The figure demonstrates evident size effects on the uniaxial compressive strength and elastic modulus of the broken rock masses. When the size of the equivalent rock mass is small (cylinder diameter less than 5 m), the average uniaxial compressive strength and average elastic modulus decrease rapidly with the increasing diameter of the specimens; when the diameter of the equivalent rock mass is more than 5 m, the evaluated mechanical parameters exhibit insignificant changes with increasing diameter. Therefore, the cylinder model size of 5 m \(\times\) 10 m is approximately the REV size of the investigated broken rock masses. To verify the correctness of the numerical results, a REV measurement scale index (RMSI) proposed by [PERSON] [39] is adopted to establish the relationships between these indices and the size length of numerical cubic rock specimens for the same rock masses at the Liyang pumped storage power station. The RMSI is defined as the projected area on a section per unit volume of the rock mass, which can be expressed as the following equation:  
\[RMSI=\frac{\sum\limits_{i=1}^{m}S_{i}\left(\overset{\rightarrow}{N_{i}} \bullet\overset{\rightarrow}{N_{p}}\right)}{V} \tag{18}\]  
where \(S_{i}\) is the area of the \(i\)-th structural plane, \(N_{i}\) is the unit normal vector of the structural plane, \(N_{p}\) is the defined unit normal vector, and \(V\) is the volume of rock mass. Figure 14 shows the numerical cube-model for the equivalent rock masses and the relationships between the examined RMSIs and the side length of cubic models. It can be seen from the figure that, initially, when the side length is small, the REV measurement scale indices of the rock masses increase rapidly with increasing side length of the models. When the side length exceeds 10 m, the RMSIs stabilize to specific values, which indicates a side length of 10 m of the numerical cubic rock model to be the correct size for measuring the REV size of the target rock masses. This size agrees with that determined from the cylindrical rock model, which verifies the correctness of the numerical results from the proposed method.