## 2 Materials and Methods  
### Problem Statement  
The groundwater model was based on the characteristics of an abandoned mine located in Martelange in south-east Belgium (Figure 1). This abandoned mine could be used for the construction of a UPSH plant. The mine of Martelange was developed to extract metamorphic slates from lower Devonian formations in the Ardenne anticlinorium. Specifically, from the \"Formation de La Roche\". The formation of these fractured slates started at the Lower Devonian, when the transgressive seas of the lower Devonian were at their maximum and clays and silts were deposited. Afterward, the clays and silt deposits were affected by different stages of deformation and metamorphism to become a dark fractured slate containing a thin bed of quartzites. The main slate cleavage (schistosity) was induced orthogonally to the main  
Figure 1: General view of Europe with Belgium highlighted with a red line (on the left) and a detailed view of Belgium (on the right) indicating the location of the considered mine (Martelange). stress conditions during metamorphism phases but was not actually parallel to the bedding plane. The exploitable layers had a dip between 55\({}^{\circ}\) and 66\({}^{\circ}\)[35]. Concerning the hydrogeological characteristics of the site, reference data was derived from previous works since, unfortunately, we did not have the opportunity to carry out hydraulic tests. According to previous works, these slates have a low global \(K\) (\(\approx\)10\({}^{-7}\) m/s [36]), and groundwater flows through preferential flow channels in multiple fractures. Thus, the hydrogeological behavior of the formation depends strongly on the aperture, density, and connectivity of the fractures. The specific storage coefficient was 10\({}^{-4}\) m\({}^{-1}\), the saturated water content was 0.05, and the residual water content was 0.01. These parameters are typical of slate mines [22; 37]. When the mining activities ceased, the piezometric head recovered, flooding the mine because its natural position is near the top of the mined cavities. The terms \"hydraulic head\" and \"piezometric head\" are used from this point forward to refer the water head inside the underground reservoir and the groundwater head, respectively. The underground cavity roughly consists of nine adjacent and vertical chambers (CH) that are connected through galleries. The volume of the chambers varies as they have different heights. Their width and length are, approximately, 15 and 45 m, respectively, while their heights vary from 70 to 110 m. The top of all chambers is located at the same depth (40 m below the surface), whilst their base depth decreases progressively from CH1 to CH9, with a decrement of about 5 m (Figure 2). Thus, the bases of chambers CH1, CH2, CH3, CH4, CH5, CH6, CH7, CH8, and CH9 are 150, 145, 140, 135, 130, 125, 120, 115, and 110 m deep, respectively. Figure 2: Schematic plan view (**a**) and cross section (**b**) of the mine in Martelange that is considered in this study. The black and red dashed lines in (**b**) indicate the natural position of the piezometric head considered in the two simulated scenarios. The black line indicates the scenarios called TOP, whilst the red line indicates the scenarios denoted as MIDDLE. The pictures taken inside the chambers can be checked at [[http://tchorski.morkitu.org/2/martelange-02.htm](http://tchorski.morkitu.org/2/martelange-02.htm)]([http://tchorski.morkitu.org/2/martelange-02.htm](http://tchorski.morkitu.org/2/martelange-02.htm)). A vertical 170-m-deep extraction shaft connects the base of CH1 with the surface [38]. Approximately, we calculated that a volume of 400,000 m\({}^{3}\) could be potentially used for UPSH. This value was obtained by considering that (1) the top of the chambers is not exceeded by the hydraulic head, and (2) 10% of the maximum available volume is not used (i.e., pumped) to avoid total emptying of the reservoir (the underground reservoir is not totally emptied to avoid the pumps and turbines being out of the water).