# A Simple Water Retention Model Based on Grain Size Distribution
## 5 Results and Discussion  
### Retention Curves of the Mine Materials  
The drying path WRCs measured for each material (as described in Section 4.2) are shown in Figure 12, expressed in terms of volumetric water content. Figure 12 shows that most of the measured WRCs are relatively similar, except for BT2 topsoil that retains more water than the other materials at particular values of suction in the range measured. These WRCS are consistent with the large proportion of fines in the materials (see Figure 11). The predictions of the WRCs in Figure 12 are shown in Figure 13. The proposed model predictions, shown as black lines, agree very well for both mine tailings and reasonably well for both topsoils, although the model struggles to fit the WRC data at higher auctions. In contrast, the predictions obtained from all of the models found in the literature are relatively inaccurate, to greater and lesser degrees, for all of the studied mine materials. The inaccuracy of the proposed model generally becomes significant at auctions around 1-2 MPa or larger, which coincides with the range when adsorptive suction becomes dominant [18; 19]. Thus, it is likely the inaccuracy of the proposed model at high auctions, for the mine materials, is due to water adsorption being ignored. The performance of the proposed model is further tested against existing models by comparing predictions of WRCs using published GSD and WRC data taken from a range of published studies. The comparisons for three fine grained soils (including a tailings), and for two sands and two loans, are shown in Figures 14 and 15, respectively. Figure 12: Drying path of the water retention curves measured for each tailings and topsoil, expressed in volumetric water content vs. suction. Figure 14 and 15 show that the proposed model can adequately capture the shape of many different WRCs, and that it performs relatively consistently for both coarse- and fine-grained soil materials. In some cases, it does not give the most accurate prediction of the WRC, however, it is more consistently accurate than the other models. This superior predictive ability is demonstrated quantitively by comparing the sum of the squared errors between the experimental value of volumetric water content at a given suction and its predicted counterpart for each model in Figure 16.  
Figure 14: Water retention curve predictions for clays and a tailings from the literature. Predictions from the proposed model and various models from the literature are shown, with water retention curves expressed in terms of volumetric water content vs. suction. Appendix A provides each material’s relevant properties and GSD, and Appendix B states the model parameters used. Figure 13: Water retention curve predictions for the materials presented in Figure 12 from the proposed model and various models from the literature. Refer to Figure 11 for the GSD of each material, and Appendix B for the model parameters used. To assess the significance of the superior predictive ability of the proposed model compared to the other similarly performing models (IMP, CCQ, and MK from Figure 16), the sum of the squared errors was found for each model when predicting the plant available water, as seen in Figure 17. Note that plant available water was defined as the difference in volumetric water content between a suction of 30 kPa and 1500 kPa. Figure 16: Sum of the squared errors, for each model, from the prediction of volumetric water content for each material in Figures 13-15. Figure 15: Water retention curve predictions for sand and loam materials from the literature. Predictions from the proposed model and various models from the literature are shown, with water retention curves expressed in terms of volumetric water content vs. suction. Appendix A provides each material’s relevant properties and GSD, and Appendix B states the model parameters used. The proposed model has the lowest sum of squared errors for predicting both volumetric water content and PAW.