# A Simple Water Retention Model Based on Grain Size Distribution
## 4 Materials and Methods  
### Materials  
The materials used in this study are tailings and toposils collected from three coal mines in the Permian coalfields of eastern Australia and some materials from the literature [13; 58; 59; 60; 61; 62; 63]. The tailings initially had a high water content and required drying in an oven before use. The toposils were cleared of particles larger than 2.36 mm and discrete organic matter (e.g., roots). For each tailings and toposil, the Atterberg limits were measured (according to AS 1289.3.9.1 and AS 1289.3.2.1) and the specific gravity (G\({}_{\rm s}\)) was measured (using a Micromeritics Accupyc II). Then, macroal particles (coal) and mineral particles for each tailings were separated on the basis of particle density, in order to measure the contact angle of macroal and mineral particles. Such measurement is necessary to assess the variability in contact angle with particle size (see discussion of Equation (14)). Density separation was achieved using a centrifuge and a \"heavy liquid\" (lithium heteropolytungstate solution) that can have its \(\mathrm{G_{s}}\) adjusted to any value below 2.85. After centrifugation, the floating material and supernatant were carefully decanted from the settled material, and both parts of the material were then washed with deionized water and the floating and settled masses were measured. Two separation procedures were conducted, with heavy liquids with \(\mathrm{G_{s}}\) of 1.4 and 2.2. The floating material collected from the heavy liquid with a \(\mathrm{G_{s}}\) of 1.4 was considered representative of the coal particles in the tailings, as coal macroals usually have a \(\mathrm{G_{s}}\) between 1.1-1.5 [64]. The settled material collected from the heavy liquid with a \(\mathrm{G_{s}}\) of 2.2 was considered representative of the mineral particles in the tailings. Particles with intermediate \(\mathrm{G_{s}}\) comprised mixed mineral and macroal grains. The contact angle for each material was measured using an approach based upon a sessile drop technique [65] and a sample preparation procedure specific to soils [66]; the same approach was used in previous research and the reader is directed to [37] for a detailed description. Note, only the receding contact angle was necessary for this study, as this angle is relevant for the drying path of the WRC. The \(\mathrm{G_{s}}\), Afterberg limits, and receding contact angle measured for each material are shown in Table 1.  
The GSD of each material listed in Table 1 was measured using laser diffraction and wet sieving. A standard sieve stack from 2360 \(\upmu\)m to 75 \(\upmu\)m was used to establish the GSD for particles larger than 75 \(\upmu\)m. Material passing the 75 \(\upmu\)m sieve was prepared to a loose dry powder and dispersed in deionized water with an ultrasonic probe, then analyzed using a Malvern Mastersizer 2000 (Malvern Panalytical, Malvern, UK). Several laser diffraction measurements were obtained to check variability, with no significant differences among different measurements observed. The GSD created for each material by combining the sieve and laser diffraction data is shown in Figure 11. Note that irregularities may be seen around 75 \(\upmu\)m particle size indicating the transition between sizing methods. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & \(\mathrm{G_{s}}\) & **Liquid Limit** & **Plastic Limit** & **Receding CA (*)** \\ \hline BT2 topsoil & 2.63 & 0.462 & 0.372 & 3 \\ M1 tailings & 1.96 & 0.497 & 0.353 & 25 \\ M1 topsoil & 2.66 & 0.274 & 0.191 & 6 \\ PD tailings & 2.22 & 0.482 & 0.208 & 21 \\ \hline M1 coal particles & -* & -* & -* & 47 \\ M1 mineral particles & -* & -* & -* & 4 \\ PD coal particles & -* & -* & -* & 44 \\ PD mineral particles & -* & -* & -* & 15 \\ \hline \hline \end{tabular}  
* Test not required for separated mineral or macroal fraction.  
\end{table}