## 2 A Hypothetical Example Application of the V-GSI Chart in a Tunnel
### Finite Element Analysis of Example Tunnel Heading  
Using the software RS3 by Roccience (Version 4.024, 2022 Roccience Inc.), 3-D Finite Element Analysis was conducted to model tunnel convergence or deformation in the tunnel around the location of the example LHS M120 map presented in Figure 4. Table 6 below presents the material properties using the generalized Hoek-Brown failure criterion [22] that were selected for use in the software to represent the Hawkesbury Sandstone in the vicinity of the selected example tunnel heading. Strength and deformability estimates and associated H-B material properties are summarized in Table 7 (the data provided in Table 7 are automatically calculated in RS3 using the input from Table 6). Figure 5: Photographs of the left-hand side tunnel heading and crown for the same location shown in Figure 4 for the M120 mainline tunnel excavated in the Hawkesbury Sandstone. (**a**) Photograph of the tunnel face and partially obstructed crown; (**b**) photograph of the tunnel crown with laminated siltstone bed exposed (c.f. the map shown in Figure 4). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Comments** \\ \hline Unit weight & 0.024 MN/m3 & Typical value for Hawkesbury Sandstone \\ \hline Poisson’s Ratio & 0.2 & Typical value for Hawkesbury Sandstone \\ \hline \multirow{2}{*}{Intact Rock UCS} & \multirow{2}{*}{18.2 MPa} & Estimated UCS based on project-specific conversion of point load testing near \\  & & example heading (within typical range for weaker Hawkesbury Sandstone) and \\  & & calibrated with UCS testing data \\ \hline \multirow{4}{*}{V-GSI} & \multirow{4}{*}{80.2} & Refer to V-GSI calculation method in Section 2. _VFC_ rating from mapping is based on 1.4 m average true spacing from face maps from both left- and right-hand-side \\  & & headings (only the LHS map is shown in Figure 4), resulting in a _VFC_ of 0.71 (Equation (6)) and a rating of 51.7. 1.5 \(\times\)_J_[_Cond89_ is around 28.5 based on average \\  & & discontinuity condition of planar, slightly rough, \textless{1 mm coating of silt.} \\  & & V-GSI = 51.7 + 28.5 = 80.2. (Equation (10)) \\ \hline mi & 13 & Typical value for Hawkesbury Sandstone \\ \hline D & 0 & Mechanical (roadheader) excavation and therefore no damage assumed \\ \hline \multirow{2}{*}{Ei} & \multirow{2}{*}{4 GPa} & Typical value for the Hawkesbury Sandstone corresponding to the intact rock UCS \\  & & noted above \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Material property input parameters used for finite element analysis. Figure 6: Stages of 3-D finite element analysis model corresponding to the selected example tunnel heading presented in Section 3.6 (screen captures from software RS3 by Roccience Version 4.024, © 2022 Roscience Inc.). (**a**) Excavation of the mainline twinned tunnel (M110) adjacent to the selected example map, and installation of ground support in this initial twinned tunnel. (**b**) Excavation of the leading heading of the example tunnel (M120—the heading adjacent to the example map presented in Figure 4, and installation of ground support in this leading heading. (**c**) Excavation of the trailing heading (M120—the heading shown in the example map presented in Figure 4), and installation of ground support in this trailing heading. (**d**) Bolts and shotcrete shown within the fully excavated M120 tunnel of the model. The objective of this exercise was to compare the measured convergence from monitoring prisms in the crown of the tunnel in this location against predicted deformation from of the 3-D modelling. The tunnel geometry used to build this model is described in Section 3.4. The tunnel in this location was approximately 63 m below ground surface (measured to the tunnel invert) and this depth of cover was used to estimate the overburden stress. No groundwater was applied for modelling purposes, even though the map describes the rock mass as \"dry to damp\" as the tunnels were designed as draining structures.