## 6 A Discussion of the Qualitative Aspects (Joint Conditions) of Existing GSI Charts
### P32\({}_{\text{DFN}}\) Estimates for the Foundation Keyway of the Kates Dam Using DFN Modelling  
As additional validation, a simple DFN was prepared for Kates RF Domain III using the mean parameters shown in Table 7. Rather than using statistical variation in joint orientation and size, these parameters were kept constant in the DFN model to illustrate a direct comparison for the field-assessed REV and the unit volume approach (Tables 5 and 6). Table 7 also shows the linear fracture frequency (P10--Figure 5) which is the number of fractures per unit length of a scanline. The mean P10 is taken as the inverse of the mean fracture spacing Sti for each joint set for a scanline or \"well\" drilled perpendicular to the mean orientation of the joint set (c.f. Mean Sti in Tables 5 and 6). The \"well\" plunge and bearing are shown in Table 7 for completeness.  
Even with constant fracture lengths and orientations, a variation in P32 can be observed across a sample rock mass. A 120 m \(\times\) 120 m \(\times\) 120 m total volume sample box is shown as Figure 15, with the colours in this figure showing the variation in the calculated P32\({}_{\text{DFN}}\) values for the discrete fractures that fall within each sample grid block. Each grid block is 12 m \(\times\) 12 m \(\times\) 12 m in size (i.e., the overall rock mass sample is divided into further sample boxes), and is intended to represent an equivalent REV sphere volume of approximately 1767 m\({}^{3}\). For each 120 m \(\times\) 120 m \(\times\) 120 m volume with smaller sample boxes, 10 realizations or randomly generated fracture networks were developed to assess variability in P32\({}_{\text{DFN}}\) in the DFN model. Realization 8 is shown in Figure 15.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Set** & **Dip** & \begin{tabular}{c} **Dip** \\ **Direction** \\ \end{tabular} & \begin{tabular}{c} **Fracture** \\ **Radius (m)** \\ \end{tabular} & \begin{tabular}{c} **Spacing (m)** \\ **(1/m)** \\ \end{tabular} & \
\begin{tabular}{c} **P10** \\ **Well Plunge** \\ \end{tabular} &
\begin{tabular}{c} **P10** \\ **Well Bearing** \\ \end{tabular} \\ \hline Fc & 2.4 & 86.3 & 7.5 & 3.3 & 0.30 & 87.6 & 266.3 \\ Jh & 2.4 & 86.3 & 6.5 & 1.7 & 0.59 & 87.6 & 266.3 \\ Jv1 & 86.8 & 31.4 & 2.5 & 5.2 & 0.19 & 3.2 & 211.4 \\ Jv3 & 76.7 & 67.7 & 6.5 & 5.4 & 0.19 & 13.3 & 247.7 \\ Jsr & 47.6 & 70.3 & 6.5 & 2.0 & 0.50 & 42.5 & 250.3 \\ \hline \hline \end{tabular}
\end{table}
Table 7: RF Domain III input value for simple DFN development.  
Figure 15: The 120 m \(\times\) 120 m \(\times\) 120 m sample of DFN Realization 8 for a rock mass developed using the parameters shown in Table 6. Variation in the P32 range is shown in the contours for each REV 12 m \(\times\) 12 m \(\times\) 12 m grid box.  
The variation in the P32\({}_{\text{DFN}}\) shown in Figures 15 and 16 can be considered analogous to variation in the natural rock mass. However, in this DFN model the variation in P32\({}_{\text{DFN}}\) occurs only as a result of the discrete location of the fractures generated for each joint set.  
Figure 16 illustrates that assuming a log normal distribution for P32, the mean P32\({}_{\text{DFN}}\) calculated for this rock mass is 1.81 m\({}^{-1}\) for realization 8. When compared to the results from Tables 5 and 6 above, the range in P32\({}_{\text{DFN}}\) is from 1.2 m\({}^{-1}\) to 2.5 m\({}^{-1}\) (shown Figure 16) and the mean P32\({}_{\text{DFN}}\) = 1.81 m\({}^{-1}\), it is evident that the results are comparable to the Unit Volume and REV approaches for RF Domain III. It is noted that introducing statistical variation in joint lengths and orientations in the DFN model using distribution-applied input parameters will introduce additional variation over and above that shown in Figure 16. Constant parameters were used to simplify the analysis.