## 6 A Discussion of the Qualitative Aspects (Joint Conditions) of Existing GSI Charts
In terms of size of the fractures of the different sets, [PERSON] used the methods developed by [PERSON], 1993 [30] and 2004 [31], to establish the distribution form and the mean size of the discontinuity planes per set, assumed as circular discs, from trace lengths obtained by scanline sampling. Mapped semi-trace lengths produced by their intersection with a scanline were corrected for sampling biases, including \"trimming\" or \"truncation\" (i.e., traces below a minimum length not observed or measured during surveys) and \"curtailment\" or \"censoring\". The sampled REV considered by [PERSON] was around 8000 m\({}^{3}\) ([PERSON], pers comms). Using these data summarized in Table 2, ref. [29] estimated the P32\({}_{\rm REV}\) parameter with his new analytic-stochastic methodology. His method uses the true spacings and a persistence factor  
Figure 10: An example of a bivariate histogram of sidewall separation and conditions on joint surfaces modified according to the authors of [3] used to determine the most common joint conditions for the parameters shown. Vertical axis: frequency count. Abbreviations: clean, C; clean to stained, Cst; clean to stained to chlorite, Cstcl; clean to zeolite, Cz; slightly weather rock, Słwr; stained St; stained to tuff and weathered laminated rock, Stttwlr; stained to weathered laminated rock, Stwlr; stained to zeolite, Stz; weathered laminated rock, Wlr; zeolite to weathered laminated rock, Zwlr; zeolite and chlorite, Zcl. per set to estimate the P32\({}_{\text{REV}}\) for non-persistent discontinuities. DFN modelling was also undertaken by [PERSON] using the data in Table 2 to validate his new method, resulting in a P32\({}_{\text{DFN}}\) estimate. It is not the intention to repeat the details of [PERSON]'s new method of estimating P32\({}_{\text{REV}}\), rather his results are used here to check if the quantification method used as a scaled parameter on the vertical axis of the V-GSI chart provides comparable P30\({}_{\text{UNIT VOLUME}}\) and therefore P32\({}_{\text{UNIT VOLUME}}\) estimates compared to the results of his detailed analysis and DFN modelling of the example rock mass on a real project. In summary, [PERSON] provided an average estimate for P32\({}_{\text{REV}}\) of 2.46 m\({}^{-1}\) for the given rock mass in his project using his new method (Table 2). [PERSON] used that same data (Table 2) to undertake DFN modelling (using a generation box with an assumed REV of 8000 m\({}^{3}\)), and this provided an estimated P32\({}_{\text{DFN}}\) of 2.65 m\({}^{-1}\). As [PERSON] states--this shows a good fit between the results obtained by DFN modelling and the new method using field measured data. [PERSON] also quantified P32 using [PERSON]'s methodology ([PERSON] et al., 2008 [32]), and this showed a significantly higher mean P32 of 8.87 m\({}^{-1}\). Figure 11 below shows these results plotted on the scaled vertical axis of the V-GSI chart (red arrows and dashed lines for [PERSON]'s results and a blue arrow and dashed line for the [PERSON] method). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Set** & **Avg. Dip (deg)** & **Avg. Dipolar (deg)** & **k-Fisher** & **True Spacing (m)** &
\begin{tabular}{c} **Size/dia.** \\ **(m)** \\ \end{tabular} \\ \hline S1 & 41 & 028 & 23.7 & LogNorm (0.93; 3.46) & Neg Exp (0.87) \\ S2 & 67 & 322 & 30.2 & LogNorm (2.71; 8.72) & Neg Exp (0.73) \\ S3 & 48 & 230 & 19.3 & LogNorm (1.03; 1.83) & Neg Exp (0.64) \\ S4 & 76 & 115 & 56.3 & Neg Exp (4.98) & Neg Exp (0.45) \\ \hline \end{tabular}
\end{table} 
Table 2: Summary discontinuity data modified from [PERSON], 2024 [29]. Figure 11: Plots of [PERSON]’s P32\({}_{\text{REV}}\) and P32\({}_{\text{DEN}}\) for comparison with VFC and P32\({}_{\text{UNIT VOLUME}}\) estimates plotted on the vertical axis of the V-GSI chart (see Figure 6). CL—confidence limit.