## 4 A DFN Approach to Analyze Scale Effects in RQD Measurement
### Room-and-Pillar DFN Model  
The analysis was repeated using a DFN model from [PERSON] [32] using data collected at the Middleton mine (Derbyshire, UK). The mine is a classic square room-and-pillar mining operation with drift access, working mostly under a cover of about 100 m. Pillars are planned for a nominal 16 m \(\times\) 16 m dimensions in a plan with rooms 14 m wide. However, completed pillars are usually smaller due to over-break. Because the rock mass quality for the Middleton mine is generally good to excellent (75 \(\leq\) RQD \(\leq\) 100), the original DFN model was modified by increasing the mapped intensity (the same increment was applied to all sets). All other parameters were unchanged. The objective was to simulate a poor to good rock mass (45 \(\leq\) RQD \(\leq\) 85) using real field data regarding fracture orientation, fracture length, and fracture terminations. The final FracMan input parameters for the DFN model in this research (see Table 5) were derived from the input used in [PERSON]'s thesis in 2006.  
A 2.5-fold increase in the K value of orientation distribution (decrease dispersity) and a 5-fold increase in volumetric intensity were used. DFN fracture realization is given in Figure 17.  
Figure 16: RQD relative difference (Max RQD–Min RQD) versus measured length and P\({}_{10}\): (**a**) orthogonal boreholes; (**b**) inclined boreholes.  
Modeling Results (Room-and-Pillar Mine)  
RQD values were measured along three orthogonal boreholes and four inclined boreholes. Figures 18 and 19 show the average RQD for orthogonal and inclined boreholes, respectively.  
The results confirm the key observations made for the conceptual model. They also clearly show the existence of a representative elementary length (REL) above which RQD values assume a constant value for the rock mass. Like the previous case, the room-and-pillar DFN model represented a single homogeneous geotechnical domain without shear or fault zones. For both models, the REL was approximately 15 m (independent of the orientation of the core run). However, the definition of REL would also depend on the orientation of the core run, i.e., an REL of 10 m could be defined for the room-and-pillar DFN model concerning the orthogonal boreholes (Figure 18 vs. Figure 19).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Set** & **Orientation Distribution** & **Terminations** & **Radius Distribution** & **Volumetric Intensity** \\ \hline \multirow{4}{*}{1a} & \multirow{4}{*}{Fisher Dip/Dip direction 89/308} & \multirow{4}{*}{0\%} & \multicolumn{2}{c}{Lognormal} \\  & & K = 103.75 & & \(y_{\sigma}\) = 9.0 & 4 \\  & & & Min. 2 m & \\  & & &ognormal & \\  & & & \(\overline{y}\) = 3.3 & \\  & & & \(y_{\sigma}\) = 0.6 & 4 \\  & & & Min. 0.25 m & \\  & & & Max. 2.5 m & \\  & & & Lognormal & \\
2a & \multirow{2}{*}{Fisher Dip/Dip direction 86/219} & \multirow{2}{*}{50\%} & \(\overline{y}\) = 3.2 & \\  & & & \(y_{\sigma}\) = 1.2 & \\  & & & Min. 0.25 m & \\  & & & Lognormal & \\
2b & \multirow{2}{*}{Fisher Dip/Dip direction 89/269} & \multirow{2}{*}{31\%} & \(\overline{y}\) = 3.2 & \\  & & & \(y_{\sigma}\) = 1.2 & \\  & & & Min. 0.25 m & \\  & & & Lognormal & \\
3a & \multirow{2}{*}{Fisher Dip/Dip direction 46/193} & \multirow{2}{*}{29\%} & \(\overline{y}\) = 3.7 & \\  & & & \(y_{\sigma}\) = 1.5 & \\  & & & Min. 0.25 m & \\
3b & \multirow{2}{*}{Fisher Dip/Dip direction 44/016} & \multirow{2}{*}{0\%} & \(\overline{y}\) = 3.7 & \\  & & & \(y_{\sigma}\) = 1.5 & \\  & & & Min. 0.25 m & \\ \hline \hline \end{tabular}
\end{table}
Table 5: FracMan input parameters for the Middleton DFN model (modified from [32]).  
Figure 17: (**a**) Example of DFN realization for Middleton mine (modified intensity); (**b**) corresponding stereonet of the fracture sets (modified from [32]).