## 2 Scale and Scale Effects in Rock Engineering and the Use of GSI
While there is no explicit scale provided in the original graphical GSI chart ([PERSON] and [PERSON], 2000 [13]), the use of the chart was predicated on the understanding of Figure 2.  
Figure 1: Representative elemental volume (REV) concept and scale effect reproduced from [PERSON] et al., 2025 [6]. In simplistic terms it is clear from Figure 2 that if joint spacing and consequently block sizes are near or larger than the dimension of interest (e.g., tunnel span, cut slope height, or foundation dimension) then GSI should not be used or should be used with caution. If, on the other hand, the block sizes are predominantly smaller than the dimension of interest, then it is reasonable to use GSI and the H-B equations with some caveats. Along the same theme [PERSON], 1992 [8], discussed the limitations of the use of the H-B criterion and GSI, recommending in summary that if the span or width of an excavation is only 3\(\times\) the spacing of the discontinuities in the rock mass--then another failure criterion should be used. It is implicit in Figure 2 and from [PERSON]'s 3\(\times\) factor that in design work and in construction in or on rock, in addition to the number joint sets, the controlling engineering scale (e.g., tunnel span, cut slope height, or foundation dimension) should be compared to the characteristic degree of rock fracturing present. This requires some knowledge of the spacing and persistence of the joint sets present, which in turn should provide some indication of block sizes. The problem with the scale criteria discussed above with respect to the original graphical GSI chart (Figure 3) is that there is no scale on the vertical structure caricatures, and it is not always intuitive to judge or understand the structure caricatures relative to engineering scale of interest. There is also no definitive process to guide this process. It is left to the user to use engineering judgement on the scale of caricatures in geological terms and the relative scale of a project. This has the potential to introduce errors and uncertainty into strength and deformability estimates. Understanding the above concerns and understanding the impact of scale and scale effects as summarized above provided the motivation for many authors to attempt quantifying, in particular, the vertical axis of the GSI chart. Figure 4 below provides a summary of some of the efforts up to 2013, remembering that the GSI system provides the most direct link to the H-B equations. Figure 2: Scale control on validity of Hoek–Brown relationships with GSI modified from [PERSON] and [PERSON], 1997 [11]. Figure 4: Summary chart modified from [PERSON] (2016) [14] with various scaled addition by [PERSON] and [PERSON], 1999 [15] and 2002 [16]; [PERSON] et al., 2004 [17]; [PERSON], 2005 [18]; [PERSON], 2007 [19] and 2009 [20]; and [PERSON] et al., 2013 [21]. These are not the only attempts at quantification but are considered the most relevant to this paper. Ref. [1] provides a more comprehensive list. Figure 3: Original graphical GSI chart. [PERSON] and [PERSON] [13]. This research contends that if measurement of parameters like joint spacing and joint persistence are measured and used to estimate volumetric fracture counts then it is possible to include scale-based parameters on the vertical axis of the chart. Research efforts (aiming at so-called quantification on the vertical axis) to date are not intended to improve the accuracy of GSI ratings but rather simply to have a better handle on scale when using GSI and the H-B equations.