## 2 A Hypothetical Example Application of the V-GSI Chart in a Tunnel
### Finite Element Analysis of Example Tunnel Heading
It is assumed that the groundwater table had already been drawn down in this location by excavation of the adjacent parallel tunnel (which was excavated in advance of the selected example heading presented). Based on project experience, a stress field in the model was defined based on Equations (11) and (12):  
\[\sigma_{H}=2.0\times\sigma_{v}+2.5\ (\mathrm{MPa}) \tag{11}\]  
\[\sigma_{h}=1.6\times\sigma_{v}\ (\mathrm{MPa}) \tag{12}\]  
where \(\sigma_{v}\) is the vertical (lithostatic) stress, \(\sigma_{H}\) is the primary horizontal stress, trending 90\({}^{\circ}\) in model space (i.e., perpendicular to the direction of tunnel drive), and \(\sigma_{h}\) is the secondary horizontal stress, trending 0\({}^{\circ}\) in model space (i.e., parallel to the direction of tunnel drive), all expressed in MPa. Note that the addition of 2.5 MPa in Equation (11) represents an assumed \"locked-in\" stress based on experience working in the Hawkesbury Sandstone. Of specific interest in Table 6 is the V-GSI rating, which was calculated using representative values for both the left-hand-side and right-hand-side maps of the example heading, not just that assessed for the map shown in Figure 4. There is only one discontinuity set (bedding-parallel discontinuities) with an average true spacing (St) of around 1.4 m in both the M120 and M110 in this location with an associated _VFC_ of 0.7 features/m\({}^{3}\) (1/1.4), and therefore a V-GSI rating of around 80.2 using the method described in Section 2 above. Using the parameters for the Hawkesbury Sandstone presented in Table 6, and the ground support discussed in Section 3.4, 3-D finite element analysis was conducted with three excavation stages (in chronological order based on mapping records). These stages are presented in Figure 6 below:  
1. Excavation of the mainline M110 (eastbound) tunnel and installation of ground support in this tunnel;
2. Excavation of the leading right-hand-side heading of the M120 (westbound) tunnel and installation of ground support in this leading heading;
3. Excavation of the left-hand-side M120 trailing heading (the heading shown in the example map presented in Figure 4), and installation of ground support in this heading. \begin{table}
\begin{tabular}{c c} \hline
**Hoek–Brown Parameter** & **Mean** \\ \hline mb & 6.41 \\ \hline s & 0.111 \\ \hline a & 0.501 \\ \hline Rock mass tensile strength (MPa) & \(-\)0.315 \\ \hline Rock mass uniaxial strength (MPa) & 6.051 \\ \hline Rock mass global strength (MPa) & 7.6 \\ \hline Rock mass modulus (GPa) & 3.53 \\ \hline Equivalent cohesion c (MPa) & 0.927 \\ \hline Equivalent friction angle (Phi-degrees) & 53.6 \\ \hline \end{tabular} Parameters calculated using software RSData Version 1.0.0.3 (© 2020 Roscience Inc.). Input parameters to RSData provided in Table 6. The same parameters are calculated automatically in RS3.  
\end{table} 
Table 7: Summary of strength and deformability estimates for the tunnel rock mass shown in Figures 4–6. Figure 6 shows the \"vertical displacement (the \"z displacement\"--displacement in the z axis of the model) around the excavation perimeter for each stage. Note that tunnel support is hidden from view for better viewing of the excavation geometry, but in Figure 6d, bolts and shotcrete are shown within one tunnel of the model (for the final stage, when excavation and support have been added for all sections of the tunnel). While excavation/ground support in this section of the tunnel was carried out typically in split headings of around 5 m length, the model was simplified to reduce excavation stages such that an advance of 50 m (the entire longitudinal span of the model in 3-D space) was excavated at once. Ground support (bolts and SFRS) were installed within the same excavation stage within the model. Moreover, as the M110 tunnel was not the subject of modelling efforts, it was simplified to be excavated in one stage (the first stage), although in reality would also have been excavated as a split heading. The effects of these simplifications are discussed further in Section 4.