## 3 General Characteristics of the Terrain and Excavations
### Front Stability  
To study the stability of the model under the influence of the excavation procedure and the different support systems, the finite difference program we used has a calculation tool called Resistance Reduction Method. This tool reduces the resistance parameters in small steps until the model collapses, while the relationship between the decreased resistance and the original resistance is calculated, thus defining the concept of safety factor:  
\[F_{\mathrm{S}}\frac{Available\ Resistance}{Resistance\ required\ for\ balance} \tag{4}\]  
The relationship between true strength and the minimum calculated strength required for equilibrium is a very useful type of safety factor in geotechnics. To define the factor of safety in terms of the Mohr-Coulomb law of resistance we used:  
\[F_{\mathrm{S}}=\frac{c+\sigma_{\mathrm{N}}\ \mathrm{tan}\ \phi}{c_{\mathrm{r}}+\sigma_{ \mathrm{N}}\ \mathrm{tan}\ \phi_{\mathrm{r}}} \tag{5}\]  
Table 4 shows basic parameters for the front stability analysis and Table 5 shows the results of the front stability calculations for the nine cases studied. In all cases, the state of stresses and deformations produced by the construction process were considered. In addition, all the elements of support are taken into account, including the different stiffness and strengths of concrete according to its age. Figures 34-38 show the potential failure mechanisms of the cases to, b and c, with the minimum parameters. Figure 34: Contours of major principal stress \(\sigma\)1 (in N/m\({}^{2}\)) in concrete elements. Minimum parameters. Figure 35: Evolution of the displacements in code (Uz) and gable (Ux) from excavation face. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{5}{c}{**GEOTECHNICAL PARAMETERS FOR FRONT STABILITY ANALYSIS**} \\ \hline \hline
**UNIT** & **CASES** & \begin{tabular}{c} **Modulus of** \\ **Elasticity AND (MPa)** \\ \end{tabular} & \begin{tabular}{c} **Cohesion \(c\)** \\ **(kN/m2)** \\ \end{tabular} & \begin{tabular}{c} **Friction** \\ **Angle (\({}^{\circ}\))** \\ \end{tabular} & \begin{tabular}{c} **Angle of** \\ **Dilitation** \\ **(\({}^{\circ}\))** \\ \end{tabular} \\ \hline \hline \begin{tabular}{c} Pumitic Series Bases \\ \end{tabular} & \(b\) and \(c\) & 150 & 40 & 27 & 5 \\ \hline \begin{tabular}{c} Pumitic Media Series \\ \end{tabular} & \(b\) and \(c\) & 275 & 50 & 31 & 6 \\ \hline \begin{tabular}{c} High pumice series \\ \end{tabular} & \(b\) and \(c\) & 400 & 60 & 35 & 7 \\ \hline \begin{tabular}{c} Lower tuff Low \\ \end{tabular} & \(b\) and \(c\) & 200 & 50 & 30 & 6 \\ \hline \begin{tabular}{c} Lower tuff Medium \\ \end{tabular} & \(b\) and \(c\) & 350 & 70 & 34 & 7 \\ \hline \begin{tabular}{c} Lower tuff High \\ \end{tabular} & \(b\) and \(c\) & 500 & 90 & 38 & 8 \\ \hline \begin{tabular}{c} Low Fills \\ \end{tabular} & \(to\) & fifty & 30 & 25 & 4 \\ \hline \
\begin{tabular}{c} Medium Fillers \\ \end{tabular} & \(to\) & 62 & 35 & 27 & 5 \\ \hline
\begin{tabular}{c} High Fillings \\ \end{tabular} & \(to\) & 75 & 40 & 30 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Basic parameters for the front stability analysis. \begin{table}
\begin{tabular}{c c c} \hline \hline
**CASE** & **Parameters** & **Security Factor** \\ \hline _to_ & Low Parameters & 1.61 \\ \hline _to_ & Average Parameters & 1.87 \\ \hline _to_ & High Parameters & 2.01 \\ \hline \(b\) & Low Parameters & 2.04 \\ \hline \(b\) & Average Parameters & 2.49 \\ \hline \(b\) & High Parameters & 2.96 \\ \hline \(c\) & Low Parameters & 1.89 \\ \hline \(c\) & Average Parameters & 2.29 \\ \hline \(c\) & High Parameters & 2.70 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the front stability analysis. Figure 37: Potential mechanism of instability for case (b): shallow excavation in the South Portal area (Tobas and Pomez) with minimal parameters. Definition: Caso (b) (case b), Factor de Seguridad (safety factor). Figure 36: Potential mechanism of instability for case (a): shallow excavation in fill area with minimal parameters.