## 2 Materials and Methods  
### Materials  
#### 2.1.1 Soils  
_Medium-grained sand._ A 2 t bulk sample of medium-grained sand was provided by the Rheinische Baustoffwerke GmbH, which represents a sand and gravel operation located 16 km northeast of Aachen, Germany. The bulk sample is representative of overburden material that is extracted during lignite open-pit mining in the region. The material was air-dried at room temperature and homogenised by coning and quartering. Relevant soil properties (i.e., pH, specific gravity, and soil colour) and grain size distributionswere determined at RWTH Aachen University. The particle-size distribution was determined according to DIN EN ISO 17892-4 [29] (Table 1 and Figure 1) and based on the unified soil classification system (USCS); the material can be classified as medium-grained, poorly graded sand (SP). The sample's geochemistry was determined at ALS Geochemistry (Loughrea, Ireland), which performed whole-rock analysis by X-ray fluorescence spectroscopy (XRF) and inductively coupled plasma mass spectrometry (ICP-MS) with four-acid digestion. Its mineralogy was established by semi-quantitative X-ray diffraction (XRD) using an X\({}^{\prime}\)Pert Pro (PANalytical) instrument with a data collector and an X\({}^{\prime}\)Pert High Score system equipped with a Co-LFF (Empyrian) tube and an automated divergence slit (Clausthal University of Technology, Germany). The sand primarily consists of quartz with plagioclase, ankerite, and rutile as accessories.  
_Fine-grained silica sand._ A 1.5 t bulk sample of fine-grained silica sand was obtained from the Quarzwerke Frechen open-pit mine, which represents a silica sand operation located 8 km west of Cologne, Germany. The sand can be classified as medium- to fine-grained, poorly graded sand (SP) and its properties, as well as its geochemistry, are listed in Table 1. Semi-quantitative XRD showed that the sand primarily consists of quartz with ankerite and clinochlore as accessories.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Unit** & \begin{tabular}{c} **Medium-Grained** \\ **Sand** \\ \end{tabular} & \begin{tabular}{c} **Fine-Grained** \\ **Silica Sand** \\ \end{tabular} & **Test Method** \\ \hline \hline \multicolumn{5}{c}{Soil properties} \\ \hline D\({}_{60}\) & mm & 0.75 & 0.24 & DIN EN ISO 17892-4 [29] \\ D\({}_{50}\) & mm & 0.63 & 0.22 & DIN EN ISO 17892-4 [29] \\ D\({}_{30}\) & mm & 0.43 & 0.18 & DIN EN ISO 17892-4 [29] \\ D\({}_{10}\) & mm & 0.28 & 0.14 & DIN EN ISO 17892-4 [29] \\ C\({}_{\text{u}}\) & - & 2.73 & 1.78 & DIN EN ISO 17892-4 [29] \\ C\({}_{\text{c}}\) & - & 0.91 & 0.95 & DIN EN ISO 17892-4 [29] \\ USCS & - & SP & SP & ASTM D-2487 [30] \\ classification & - & \multirow{2}{*}{\begin{tabular}{c} \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} \end{tabular} } \\ Specific gravity & g/cm\({}^{3}\) & & 2.59 & 2.63 & DIN EN ISO 11508:2018-04 \\ pH value & & 7.53 & 6.48 & DIN EN 15933:2012-11 [32] \\ Soil colour & Munsell & 9.7 YR 6.0/2.8 & 0.9 Y 7.1/1.3 & \\ \hline \hline \multicolumn{5}{c}{Geochemistry (oxides)} \\ \hline SiO\({}_{2}\) & wt\% & 94.58 & 98.65 & \\ Al\({}_{2}\)O\({}_{3}\) & wt\% & 2.35 & 0.55 & \\ K\({}_{2}\)O & wt\% & 1.15 & 0.04 & \\ Fe\({}_{2}\)O\({}_{3}\) & wt\% & 0.74 & 0.05 & \\ Na\({}_{2}\)O & wt\% & 0.22 & 0.01 & \\ CaO & wt\% & 0.05 & 0.01 & \\ MgO & wt\% & 0.10 & 0.01 & \\ TiO\({}_{2}\) & wt\% & 0.06 & 0.07 & \\ P\({}_{2}\)O\({}_{5}\) & wt\% & 0.02 & \textless{}0.01 & \\ MnO & wt\% & 0.01 & \textless{}0.01 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical and chemical properties of mine soils used by this study.