# A Simple Water Retention Model Based on Grain Size Distribution
## 6 Conclusions  
A scenario was introduced in this paper where toposoil improvement by coal tailings addition was suggested, with the focus on improving the plant-available water for the toposoil-tailings mixture. Determining the water retention properties of toposoil-tailings mixtures is required in order to identify the mixture proportions that result in a plant-available water range that is most favorable to plant growth. For this identification to be an efficient process, it is proposed to use a soil water retention curve prediction model instead of conducting extensive experimental testing. Many water retention models have been proposed in the literature, but it was found that these models could not adequately predict the retention properties of toposils and tailings from Australian coal measures. Consequently, a new predictive water retention model was created and this model was proposed in the research herein. The proposed model uses the grain size distribution as the main input parameter and requires no laboratory calibration. Compared to similar models from the literature, the proposed model's main improvement is achieved by filling the pores existing between particles with smaller particles according to an Apollonian gasket, but with the filling occurring only under certain criteria, which considers the size ratio and fraction of smaller particles.  
The model validation against local materials and data from the literature showed a good predictive ability of the model against other existing models, in terms of volumetric water content and plant available water. This accuracy indicates the proposed model may be useful for predicting the water retention curve of a material, when calibration to existing data is not feasible. Additionally, the proposed model may enable efficient prediction of toposoil-tailings mixtures at mine sites, allowing identification of mixtures with improved plant available water and potentially improved plant growth. Thus, this  
Figure 17: Sum of the squared errors, for each model, from the prediction of plant available water content for each material in Figures 13–15.  
model may allow easier implementation of topsoil-tailings mixtures in mine rehabilitation and the repurposing of post mining land.  
In this study, the topsoil and tailings measured had little organic matter. However, if materials of higher organic matter contents are of interest, it is possible the accuracy of the proposed model may be improved by adding a regression parameter for organic matter content. Future research may involve further validation of the model for: other materials or mixtures, materials under different boundary and stress conditions, or materials with soil structures replicating in-situ states.  
Conceptualization, A.V., O.B. and S.F.; methodology, A.V., O.B. and S.F.; validation, A.V., O.B. and S.F.; writing--original draft preparation, A.V.; writing--review and editing, A.V., O.B. and S.F.; supervision, O.B. and S.F. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.