Estimation of Hydraulic Characteristics of Unsaturated Loess with SEM Images Based on Fractal Theory

The accurate determination of the soil-water characteristic curve (SWCC) and unsaturated hydraulic conductivity is vital across multiple disciplines, including hydrogeology, soil science and geotechnical engineering. Nevertheless, conventional techniques for measuring these unsaturated soil parameters are often laborious and time-consuming, posing significant practical challenges. This research presents a new technique for estimating SWCC and unsaturated hydraulic conductivity by employing fractal theory and utilizing a three-dimensional fractal dimension (Ds). The results revealed that all three soils exhibited fractal characteristics in their particle surfaces, with Ds values of 2.611 for Malan loess, 2.688 for paleosol, and 2.771 for remolded loess. The complexity of the pore structure was in the order of remolded loess > paleosol > Malan loess. The test results of the soil-water characteristic curve indicate that the water storage capacity of the three soils was in the order of paleosol > remolded loess > Malan loess. Compared with the Brooks-Correy fitting curve, the fractal model is feasible in predicting the soil-water characteristic curve. Two models were used to predict the unsaturated hydraulic conductivities of three types of soil, and the results were compared with the measured values. By comparing the R2 and RMSE values of the fractal model and the Brooks-Corey model, it was found that the fractal model proposed in this paper can effectively predict the unsaturated hydraulic properties of these three types of soil. This study provides a simple and effective alternative for predicting the SWCC and unsaturated hydraulic conductivity of unsaturated soils, with potential applications in various earth science fields.