# A Simple Water Retention Model Based on Grain Size Distribution
## 1 Introduction  
Resource mining is required to sustain the current demands of society. For example, coal mining is necessary to sustain steel and electricity production for much of the world. However, the transition from coal-fired power to renewable energy sources will likely cause a significant reduction in coal demand, which will inevitably lead to the closure of many coal mines. Mine closure leads to economic stresses for regions where a large coal mining industry is present; the Hunter Valley region in NSW, Australia, could be considered as one of these regions, where, as at the time of writing, around 40 coal mines operate. Various options to alleviate future economic stresses in this region are being proposed and investigated; one such option is to convert the vast areas occupied by coal mines to farmland, which could provide an economic benefit to the region. Implementing this option will require significant topsoil improvement, due to generally poor quality topsoil for plant growth in the Hunter Valley [1, 2], and the further degradation in topsoil quality that occurs when land is mined and then rehabilitated [3, 4, 5, 6]. Soil improvement at the large scales of mine sites has a high cost, leading to some research on use of waste materials, such as municipal wastes (compost and swaperage wastes), as more cost-effective topsoil improvements [7]. This study investigates an alternative option to mix a locally-derived mine waste material, coal mine tailings, with the available site topsoil to achieve improved plant growth potential of the soil mixture compared to the unaltered topsoil. Coal tailings are produced during the beneficiation process of coal, which, importantly, do not typically contain chemical species that are toxic to plants. These tailings are a fine grained waste product of high initial water content comprising mineralsoil particles and coal, with the coal content up to 40% or greater [8; 9]. Indeed, the fine particle size and high initial water content of these tailings materials make them problematic for conventional disposal in tailings impoundments, making the soil improvement disposal option all the more advantageous. The research presented herein is one component of broader research that focuses on improving a soil mixture's water retention properties in the context of plant growth. Water retention properties of a soil are significant for plant growth as they govern the plant available water (PAW) [10], one of many important factors for plant growth. PAW can be estimated from the difference in volumetric water content between two critical soil water suction values: the field capacity (around 30 kPa) and the wilting point (around 1500 kPa) [10]. However, measuring a soil's water retention curve (WRC) is a time-consuming laboratory process, especially when considering how many different materials must be managed in a coal mine; there may be several different toposils across a mine site, and the nature of the coal tailings produced is continually changing, as the produced tailings properties vary depending on which coal seam is being mined and processed. The number of materials to evaluate is compounded when mixtures of materials need to be tested. Thus, it is more efficient to employ an accurate model in order to predict the resultingWRC of proposed soil-tailings mixtures. Further, for such a prediction model to be efficient, it should only use easily measurable soil properties and not rely on a calibration to the mixture'sWRC. Two tailings and two toposils from coal mines in Australia were gathered for the purpose of measuring their drying path WRCs and assessing the predictive ability of a range of existing models that are published in the literature. It was concluded none of the tested models were suitably accurate (as shown in Section 4), which prompted the development of a simple but more accurate model.