Evaluating the efficiency of fractal models in estimating soil hydraulic parameters and the relationship between moisture curvature fractal dimension with these parameters

Soil and water relations are so complex that the most advanced mathematical models can hardly be able to simulate them accurately. Retention curve and unsaturated hydraulic conductivity are among the most important factors in the study of water flow in the soil. Because the high variability and soil complexity, obtaining soil hydraulic properties directly is difficult, time consuming and costly and therefore it is necessary to estimate indirect methods. The purpose of this study was to determine the fractal dimension of soil moisture curve using fractal models and to investigate the relationship between the moisture curvature fractal dimension with hydraulic parameters, clay, silt and sandy percent in a wide area. For this purpose, some soil samples collected from different tissues from the regions of the country were collected and the variables of particle size, bulk density, organic carbon, salinity, pH and moisture content were measured in different suction. Finally, the parameters of the van Genuchten model as well as models Tyler-Wheatcraft and Rieu-Sposito fractals were calculated for soil particle size distribution. The results showed that van Genuchten model parameters have fractal behavior and can be quantified by using fractal models. The results also showed that the higher the amount of sand in the soil, the fractal decreases, but the clay content has a direct linear relationship with the Tyler-Wheatcraft fractal dimension. This means that by increasing the amount of clay in the studied soils, the fractional dimension of the Tyler-Wheatcraft (Dm) model also increases and with the increase in the amount of sand, the fractal dimension of the Tyler-Wheatcraft (Dm) model decreases.