## 2 Materials and Methods
### Hydrogeological Study
#### 2.3.2 Numerical model  
The hydrogeological study included a numerical modeling of the behavior of groundwater in the massif crossed by the Urdinbide tunnel, which aimed to predict its response to the construction of the work. The Visual MODFLOW 6 software [28] was used to carry out the numerical model of the flow in the study area. This software was used because it is based on finite differences and can represent well the physical processes related to groundwater flow. The geometric scope of the modeled area can be seen in Figure 8. The aquifer was divided into discrete elements of a maximum width of 25 meters, achieving a mesh in which each cell represents a prism whose hydrogeological characteristics are constant throughout its volume.  
The spatial discretization of the model is shown in Figure 9.  
The simplification of using a single value for each of the hydrogeological parameters corresponding to the set of geological materials that make up the modeled aquifer has been considered. By carrying out pumping tests in wells B2 and B3, representative values for the entire Autzagane aquifer were established, but during the model calibration phase, these  
Figure 8: Model scope and surface discretization of the model in cells. Mesh with a maximum width of 25 m.  
Figure 9: Three-dimensional view of the model showing the discretization in layers, using the Visual MODFLOW software.  
values were slightly adjusted as it was considered that these corrections had a favorable impact on the model's fit to the known real functioning. Thus, the final adjusted hydraulic parameters are shown in Table 1.  
Once the scope of the modeling had been established, the following actions on the system were considered: precipitation infiltration, discharges at the head of the Ategorri stream, discharges from other springs, and drainage from the existing tunnel of the Amorebieta-Etxano railway line. The model was adjusted in steady state, with the following water balance, which was consistent with the measured discharge in the entire Ategorri stream (Table 2).  
The calibrated model was used to establish the long-term response between two opposite scenarios: the scenario before the tunneling works and the limit scenario in a completely drained hypothesis. Figure 10 shows the isopiezometric lines of the model for the situation prior to the impact of the works in a section perpendicular to the Ategorri stream.  
Table 3 illustrates a comparison of flows between the natural situation (shown in Table 2) and the hypothesis of total draining tunnel. It should be noted that under this working hypothesis, the tunnel would be working as a scour outlet, with a flow rate of 6.6 L/s, leaving the Ategorri stream and its associated springs without flow.  
Figure 11 shows the isopiezometric lines of the model for the situation considering a draining tunnel.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Hydrostratigraphic Unit**} & **Horizontal Permeability** & **Vertical Permeability** & **Storage Coefficient** & **Efficient Porosity (\%)** \\ \hline Autzagane Aquifer & \(2.5\times 10^{-6}\) & \(2.5\times 10^{-6}\) & \(1\times 10^{-5}\) & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Adjusted hydraulic parameters.  
Figure 11: Isopiezometric lines for the hypothesis of draining tunnel, using the Visual MODFLOW software.  
Figure 10: Isopiezometric lines for the situation before tunnel construction, using the Visual MODFLOW software.  
Finally, the hydrogeological model was used to obtain the limit flows that could be evacuated through the Urdinbide tunnels, guaranteeing the necessary flow in the Ategorri stream to supply the neighborhoods of Amorebieta-Etxano under normal conditions (1.4 L/s). The waterproofing solution for the tunnels, both during their construction and in service, had to be sufficient to guarantee a water discharge in the tunnel of less than these values (4.7 L/s).