## 2 A Hypothetical Example Application of the V-GSI Chart in a Tunnel  
### Measurement of Apparent Joint Spacings (Sa)  
The hypothetical example provided in Section 2 (Figures 2 and 3) demonstrates the process of quantifying the _VFC_ parameter for use on the vertical axis of the V-GSI chart (Figure 1) in a tunnel. Figures 2 and 3 are hypothetical in the sense that the tunnel map with fracture traces are not from a real location in the tunnel, but represent a synthesis of typical fracturing seen in many locations in the tunnel, primarily to show the method of _VFC_ quantification. Little explanation is required for the quantification process of the horizontal axis of the V-GSI chart since JCond89, which forms part of [PERSON]'s rock mass rating (RMR) system, has been widely used for more than 30 years [18]. For this example, Figure 2 is presented as a simplified and stylized fracture trace map from an assumed, hypothetical working face in a tunnel heading excavated for the WestConnex M8 Motorway twin tunnel project in Sydney, Australia, as explained above. The tunnel profile shown in Figure 2 shows the typical dimensions of the tunnel face and the spatial location of hypothetical fracture traces (perpendicular to tunnel drive orientation), along with the projected left wall, projected right wall and projected tunnel crown appearing to the left, right and above the tunnel face, respectively, for an assumed westbound tunnel heading (two vehicle lane width). More details on the project are provided in Section 3. In Figure 2, the mapped fracture traces of two discontinuity sets are shown: a sub-vertical tectonic joint set (green traces annotated as J1; with a mean dip and dip direction of \(70^{\circ}/312^{\circ}\)), and a sub-horizontal bedding set (red traces B; with a mean dip and dip direction of \(20^{\circ}/195^{\circ}\)). All orientation measurements are relative to true north. For this example, the focus is only on the joints exposed in the working face, but it should be evident that the same sets are present in the sidewalls and crown of the tunnel, and a similar analysis presented below (Sections 2.1 and 2.2) to calculate the rock mass _VFC_ can be undertaken for these exposures and used in the overall analysis. In this example, the tunnel is assumed to being driven at an orientation of \(061^{\circ}\) from true north. Figure 3 shows the concept of vector measurements of apparent spacings (Sa) for each of the two hypothetical discontinuity sets present in the rock mass for this tunnel heading. Since the working face is fully spatially defined in terms of orientation and dimensions (as are the crown and sidewalls), scaled virtual Sa vectors (colored arrows) for discontinuity sets J1 and bedding (B) can be measured between adjacent joints of the same sets because the vectors fall within the plane of the tunnel working face, with known orientation and dimensions, and therefore have both orientation and magnitude. The vectors in this case replace conversional scanline-type measurements. Sa measurements for set J1 are scaled off the map using inserted horizontal virtual vectors that lie within the plane of the tunnel working face and are perpendicular to the direction of tunnel advance (Figure 3). Sa measurements for set B are also scaled from the map using inserted vertical virtual vectors on the tunnel face (Figure 3). Each Sa  
Figure 3: Apparent spacing vectors for discontinuity sets J1 and B for the example tunnel fracture trace map shown in Figure 2. Green vectors for set J1 and red vectors for bedding (B). measurement falls within the plane of the tunnel working face, and as such are fully orientated in 3-D space. Figure 3 also shows conceptually that the spacing vectors for each set do not need to be measured strictly on a scanline or sequentially, as with conventional scanline surveys, provided that individual measurements are taken in the same direction for each set.