A Particle-Size Fractal Model for Soil Water Characteristic Curve Considering Capillarity and Adsorption
- 1College of Highway Engineering, Xinjiang Communications Polytechnic University, Urumqi 831400, China
- 2College of Civil Engineering and Architecture, Xinjiang University, Urumqi 830017, China
- 3Department of Architecture and Urban Planning, Xi’an University of Technology, Xi’an 710048, China
Abstract
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.
Related
- A novel soil-water characteristic curve prediction model for unsaturated soil considering pore structure characteristics
- Wetting theorems in capillarity theory
- Bore wave solutions to the viscous Saint-Venant system with capillarity
- Generalized minimizers for the capillarity energy outside convex obstacles
- Sharp Planar Anisotropic Capillarity Outside Convex Obstacles and Two-Point Rigidity of Transported Boundary Images
BibTeX
@article{zhang2026particlesize,
title = {{A Particle-Size Fractal Model for Soil Water Characteristic Curve Considering Capillarity and Adsorption}},
author = {Shaoying Zhang and Wei Mao and Shuai Shao and Yongpeng Cao and Qingqing Ma and Kai Zhao},
journal = {Fractal and Fractional},
year = {2026},
month = oct,
doi = {10.3390/fractalfract10110738},
url = {https://www.mdpi.com/2504-3110/10/11/738},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Particle-Size Fractal Model for Soil Water Characteristic Curve Considering Capillarity and Adsorption
AU - Shaoying Zhang
AU - Wei Mao
AU - Shuai Shao
AU - Yongpeng Cao
AU - Qingqing Ma
AU - Kai Zhao
PY - 2026
DA - 2026/10/23
JO - Fractal and Fractional
DO - 10.3390/fractalfract10110738
UR - https://www.mdpi.com/2504-3110/10/11/738
AB - 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.
SN - 2504-3110
ER -