# Estimating RQD for Rock Masses Based on a Comprehensive Approach
## 5 Discussion  
The uncertainty of the RQD(\(D\)) for the small model sizes is stronger than that for the large ones, as shown in Figure 10. Other researchers [33; 56] have drawn similar conclusions, which have been explained in terms of virtual borehole length, suggesting that longer virtual boreholes obtain more stable RQD values and necessitate sufficiently long virtual boreholes to reflect the overall RQD of the rock mass. As revealed in Figure 10, the mean value of the RQD first decreases with the model size; then, the fluctuation rises and finally remains stable. This result differs from previous results [35; 57; 58] that suggest that, as the model size increases, the value of the RQD increases and eventually stabilizes. For each selected size, several models were employed to calculate the representative RQD, which indicates that the incorrect acquisition of the RQD for a portion of the model has no significant effect on the final computation results. This difference may be explained by the fact that the discreteness of the simulation results is taken into account for each size and that the sample size is sufficient to make the results more realistic.  
Furthermore, assuming that a model is the \(j\)th generated model with size \(D\), the mean of the RQD samples of its number threshold is denoted as \(A_{D}(j)\). Then, the formula for calculating the range R of \(A_{D}(j)\) of different models of the same size is as follows:  
\[R=(A_{D}(j))_{max}-(A_{D}(j))_{min} \tag{22}\]  
the range \(R\) decreases as the model size increases, as shown in Figure 14. This implies that, as the model size increases, the \(A_{D}(j)\) between the models of the same size becomes increasingly similar. This means that, as the model size increases, the randomness of the Monte Carlo method has less and less influence on the RQD estimation.  
Within the same structural statistically homogeneous rock mass, for small investigated rock sizes, the fracture distribution in different regions has a large difference, so the RQD calculation results exhibit discreteness. As the rock size increases, this difference gradually diminishes, and when the rock size surpasses a certain critical size, the rock characteristics do not change appreciably as the rock size increases. This critical size is known as the representative elementary volume (REV) [59; 60], and the rock mass can be treated as an equivalent continuum material. When estimating the representative RQD of the rock mass, the required error range, in this paper, fulfilled the convergence criterion of an REV change rate of 5%, which means that the REV of the slope that was researched may be considered to be 13 m. As shown in Figure 14, when the study size is smaller than the REV, the \(A_{D}(j)\) between different models of the same size varies substantially. However, the  
Figure 14: Relationship between the range R and model size.  
difference shrinks significantly after the size exceeds the REV, all less than 2.78%, indicating that the number of large-sized models created can be appropriately reduced to improve computational efficiency.  
The primary focus of this article is the quantitative selection of virtual borehole numbers for a specific-sized model using fracture network simulation technology and the subsequent evaluation of the RQD for the rock mass. This process entails conducting a comprehensive on-site investigation of the structural planes in the study area, organizing the collected geometric information of these planes and utilizing them as input parameters for a fracture network simulation. Subsequently, simulations are performed to obtain the RQD under varying conditions.  
The simulation results enable the calculation of the spacing between boreholes based on the quantitative selection outcomes of the virtual boreholes. This information is instrumental in guiding and optimizing the layout of actual boreholes to accurately measure the real RQD value.