A Particle-Size Fractal Model for Soil Water Characteristic Curve Considering Capillarity and Adsorption

Soil-water characteristic curve (SWCC) provide a fundamental description of water retention in unsaturated soils. However, conventional empirical models generally lack an explicit connection between water retention behavior and the multiscale characteristics of soil particle and pore structures. In this study, a full range SWCC model was developed based on particle-size fractal characteristics. The particle-size fractal dimension was used to describe the self-similar characteristics of the particle-size distribution, and a particle-to-pore relationship was established by incorporating the void ratio and the fractal dimension of pore tortuosity. Based on the resulting pore-size distribution, capillary and adsorptive water retention mechanisms were incorporated into a unified fractal framework. The concept of the effective specific thickness of the adsorbed water was introduced to characterize the contribution of particle surface adsorption to water retention at high matric suctions. The proposed model provides a continuous transition from capillary dominated water retention at low suctions to adsorption dominated water retention at high suctions. Its performance was evaluated using six experimental datasets covering clayey soils, silty soils, and sands over a broad range of matric suctions. Compared with the van Genuchten (VG) and Kosugi models, the proposed model achieved the lowest root mean square error (RMSE) for four of the six datasets, while its performance for the other two datasets was broadly comparable to that of the benchmark models. For Arizona silty soil #14, the RMSE was 0.0146, compared with 0.0351 for the VG model and 0.0602 for the Kosugi model, representing reductions of 58.4% and 75.7%, respectively. These comparisons indicate improved fitting performance for several soil types, particularly the silty soils and loess examined in this study. Overall, the proposed fractal framework provides a physically based link between particle-size distribution, pore structure, and soil water retention across a broad suction range.