## 9 Conclusions  
The above research and analysis and discussion provide evidence and validation that scale can and should be considered on the vertical axis of GSI charts. In this discussion the V-GSI chart is predominantly discussed, but similar conclusions can be drawn with other GSI charts with scaled vertical axes. Scale and scale effects are an inherent part of rock mechanics and rock engineering, and as demonstrated above, the inclusion of scale is feasible and a necessary progression for the GSI system. In conclusion, research in this paper shows that:  
* P30 and P32 parameters estimated via DFN modelling, a field-defined REV approach, or the unit volume approach used on the scaled vertical axis of the V-GSI, provide comparable results even though the methods of calculation are different. This is an  
Figure 18: V-GSI E* estimate vs. in situ testing E* estimates for rock mass unaffected by weathering or stress relief fracturing from Katse Arch Dam’s right flank foundation keyway (see Figures 13 and 14 for location). important finding because it provides validation that VFC (P30) and P32 parameters included on the vertical axis of the V-GSI chart, which is based on measured data, are in fact quantifiable. * Provided the size of the fractures is considered, then the inclusion of VFC (P30) and P32 as measures of increasing fracture intensity on the V-GSI chart can provide reliable first estimates of strength and deformability for use in engineering design. * The quantification of the vertical axis of the V-GSI chart provides a rational basis for comparing the ratio of the scale of a project or the scale of interest (a structure to be built on or in rock) to the scale or intensity of fracturing in a rock mass, a necessary requirement for the use of GSI. This is not to say that DFN modelling should not be undertaken as a means of checking or calibrating the quantification of P30 and P32 on the V- GSI chart. It is also not to say that the V-GSI cannot be improved on. It is an empirical system. Parameters comparable to those used in DFN modelling are also being used on the vertical axis in the V-GSI chart. It is recommended that future research in this regard should answer the following questions:  
* Why is it acceptable to use joint orientation, joint set spacing, joint set fracture frequency, and joint set persistence or size estimates to undertake DFN modelling that includes scale, but it is claimed that the same parameters cannot and should not be used to quantify GSI charts? * Why is it acceptable to quantify P30 or P32 from the same measured data using DFN methods for use in coupled DFN-mechanical models but it is not acceptable to quantify the vertical axis of GSI charts using the same parameters? Is it because P30 or P32 values are in turn related to GSI ratings on the vertical axis (a necessity to link to the H-B equations that need to be calibrated) or is it because a DFN model is visual? Where data from in situ strength and large-scale deformability testing exists for real-world rock engineering projects, it is also recommended that additional back analyses be undertaken to determine if the associated rating scales (vertical and horizontal axes) on the V-GSI or other quantified charts can be better calibrated that may in turn lead to more reliable strength and deformability estimates. It is also recommended that research be undertaken that compares results using coupled DFN-mechanical models with results from finite element continuum models or geo-mechanical models that use V-GSI ratings. It is also recommended that additional research should be undertaken to ascertain the limitation of the V-GSI system for highly anisotropic rock masses. As a final note, the use of quantified GSI charts does not exonerate a designer from understanding the geology and the variability of a given rock mass or from understanding potential failure mechanisms that cannot be captured by GSI and the H-B equations alone [33]. Conceptualization, P.S. and J.C.; Software, B.P.