## 6 A Discussion of the Qualitative Aspects (Joint Conditions) of Existing GSI Charts
### Consideration of a Persistence Correction Factor (Pi) in P32 Estimates for V-GSI
The REV dimension shown in Figure 14 (LHS) is an approximate (horizontal) distance from the foundation surface (black line) to the red dashed line, which is the approximate location beyond weathering, and valley-side stress relief fracturing (Jsr) is no longer present further into the valley side rock mass, noting that the other sets present in this domain are shown in Table 6.  
Figure 14: Minimum REV dimension of RF Structural Domain III (LHS). RHS provides a comparison of deformation moduli (E\({}^{\prime}\)) estimates for domains for the right flank of the Katese Dam foundation keyway rock mass determined with V-GSI ratings and H-B equations with results from large in situ deformability testing undertaken prior to and during the construction of the Katese Dam [3]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Set** & **Mean Sti** & \begin{tabular}{c} **Mean Size** \\ **(m)** \\ \end{tabular} & \begin{tabular}{c} **Disc Area (m\({}^{2}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Disc Area (m\({}^{2}\))** \\ \end{tabular} &
\begin{tabular}{c} **Disc Area (m\({}^{2}\))** \\ \end{tabular} \\  & & & & **Joint Set** \\ \hline Fc & 3.3 & 15 & 176.70 & 803.25 \\ Jh & 1.7 & 13 & 132.70 & 1171.17 \\ Jv1 & 5.2 & 5 & 19.63 & 56.64 \\ Jv3 & 5.4 & 13 & 132.73 & 368.70 \\ Jsr & 2 & 13 & 132.73 & 995.49 \\  & & & **\(\Sigma\)Disc area (m\({}^{2}\))** & **3395.44** \\  & & & **\(\mathbf{P32_{REV}}\)** & **1.92** \\ \hline \hline \end{tabular}  
* LL and UL are the lower and upper limit 95% confidence limits for P32 and are calculated to be 1.7 and 2.1 respectively.  
\end{table} 
Table 6: Summary P32\({}_{\text{REV}}\) statistics for RF Domin III, Katese Dam Foundation rock mass. The field-fitted REV shown in Figure 14 (red circle LHS enlargement) is considered to be a sphere with an approximate diameter of 15 m and therefore has a radius of approximately 7.5 m. The REV sphere volume of RF Domain III is therefore around 1767 m\({}^{3}\). Other than set Jv1, the mean size of the trace lengths per set is on average close to the diameter of the REV and a single-disc area intersecting the REV sphere can be estimated using the assumed mean disc size (Table 6) per set as follows:  
\[\textit{Single Disc Area}_{i}=\pi.\left(\left(\frac{\textit{Mean Disc Size}_{i}}{2}\right)^{2}\right) \tag{10}\]  
Then the fracture area contribution in the REV for the _ith_ set can be estimated as  
\[\textit{Area}_{\textit{Contribution i}}=\frac{\textit{REV Diameter}}{\textit{St}_{i}}. \textit{Single Disc Area}_{i} \tag{11}\]  
where \(\frac{\textit{REV Diameter}}{\textit{St}_{i}}\) gives the number fractures for the ith set in the REV and the REV diameter (field assessed) is assumed to be a vector orientated perpendicular to the orientation of the _ith_ set (vectors since REV diameters have magnitude and direction per set). Then P32\({}_{\text{REV}}\) can be estimated as  
\[P32_{\text{REV}}=\sum\frac{\textit{Area}_{\textit{Contribution i}}}{\textit{ Volume}_{\text{REV}}} \tag{12}\]  
Then using Equations (10) through (12), P32\({}_{\text{REV}}\) for RF Domain III can be approximated as 1.92 m\({}^{-1}\), as shown in Table 6.  
Obviously, the areas of fractures away from the centre of the REV sphere are theoretically smaller than the full diameter of the sphere but, since the assumed average persistence for the joint sets present are close (other than Jv1) to the diameter of the sphere, it is considered reasonable to use a constant disc area (133 m\({}^{2}\)) to estimate the area contribution for the sets. Alternatively, a cube with sides equal to 15 m could have been considered for the REV and this would have yielded a slightly larger surface area per set fracture, but in both cases the average persistence for sets FC, Jh, Jv3, and Jsr is close to the maximum REV disc area and, since the exact surface area per joint cannot be determined, it is reasonable to assume that the surface area per fracture (133 m\({}^{2}\) in this case) is a constant for the given REV.