## 5 Correlation Between Fracture Frequency (\(\lambda\)) and RQD  
The discontinuity frequency, or fracture frequency (FF), is defined as the number of natural fractures per unit length of core recovered (it is equivalent to the Fracture Index-FI, or discontinuity frequency--\(\lambda\)):  
\[\lambda=\mathrm{FF}=\frac{\mathrm{number\ of\ natural\ fractures}}{\mathrm{total\ length\ of\ core\ recovered}} \tag{13}\]  
One can find the fracture frequency for a core run's whole length or for a smaller core segment. When determining the fracture frequency, artificial fractures produced during core handling or drilling should be disregarded, much like in RQD. Figure 12: (**a**) An example of a DFN (discrete fracture network) realization created using the parameters outlined in Table 8; (**b**) a stereographic projection displaying the fracture sets, with each dot representing an individual fracture [26]. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Fracture Data** & **Source** & **DFN Input Data** \\ \hline Orientation & Boreholes, outcrops, tunnels & Orientation of fractures for every fracture set \\ Length & Tunnels, outcrops, lineaments & Fracture radius distribution \\ Terminations & Tunnels, outcrops, lineaments & Choice of the model hierarchy of the sets \\ Intensity & Boreholes, scanlines (P\({}_{10}\)), outcrops (P\({}_{21}\)) & Fracture intensity (P\({}_{10}\) or P\({}_{32}\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Fracture data and input parameters for a DFN model are obtained from both digitally mapped and traditionally collected data sources [26]. The discontinuity frequency that is acquired through scanline sampling can also be used to calculate RQD. An exponential distribution with a negative value was proposed by [PERSON] and [PERSON] [27]. Their calculation shows that there is the following link between RQD and a linear discontinuity frequency, \(\lambda\):  
\[\text{RQD*}=100\text{e}^{-\lambda t}(\lambda t+1), \tag{14}\]  
where t is the length barrier in this case. As with the conventionally defined RQD, Equation (14) can be written as follows for t = 0.1 m [27]:  
\[\text{RQD*}=100\text{e}^{-0.1\lambda}(0.1\lambda+1), \tag{15}\]  
For values of \(\lambda\) in the range of 6-16 m\({}^{-1}\), the following linear equation can be used:  
\[\text{RQD*}=110.4-3.68\lambda \tag{16}\]  
Figure 13 displays the relationships found by [27] between the observed values of RQD and \(\lambda\) and the values determined by Equation (15). Based on Equation (14) and several threshold values t, the theoretical RQD* curves against values of \(\lambda\) (0-50) are depicted in Figure 14. The image demonstrates the shortcomings of both the threshold value concept and the RQD* additive technique. As a function of k, the RQD's decline becomes steeper the bigger the threshold value t, as indicated by the curves. The reason for this is the disrespect for smaller core parts. Nonetheless, the RQD* decline becomes flatter as the threshold value drops. This is due to the fact that all shorter cores are now considered, despite the fact that their quantity, and thus the number of fractures, are not. One could argue that these drawbacks are offset by choosing a threshold value that falls somewhere in the middle, such as 0.1 m, or by choosing a threshold value that is acceptable for a particular rock mass [29]. Figure 13: Relationship between RQD and discontinuity frequency, \(\lambda\)[28]. Theoretically, RQD and \(\lambda\) have a loosely linear connection; [27] proved that RQD tends to drop with an increase in \(\lambda\) in a roughly narrow diagonal band. [PERSON] and [PERSON] [30] verified this by gathering more than 30,000 data points from several rock masses (Figure 15).