Evaluation of soil water retention curve with the pore-solid fractal model

Empirical models have been developed to describe the soil water retention curve (SWRC). Applications of the fractal theory may provide a useful tool to fill the gap between the use of empirical models and physical interpretation of their parameters. Especially a more generalized model for the SWRC has been developed based on the pore-solid fractal (PSF) distribution. The PSF model covers several existing models as its special cases and theoretically provides a direct way to estimate the SWRC fractal dimension from particle size distributions (PSDs). The first objective of this study was to evaluate the SWRC with the PSF distribution using more than 400 data sets of PSD and SWRC. The second objective was to establish a relationship between the fractal dimension and soil texture. Analyses of the data sets showed that the fractal dimension values estimated using the PSD data were consistently smaller than those estimated using the SWRC data. Therefore, using the fractal dimension from PSD to predict the SWRC will result in underestimation. To resolve the problem, the soil data sets of PSD and SWRC were used to establish relationships between the fractal dimensions in the PSF model of SWRC and soil clay content as well as soil texture class. Independent SWRC data sets were used to test the methods. Predicted results using the PSF model of SWRC with the fractal dimension estimated using clay content or soil texture class were compared with the measured soil water retention data. Linear regressions of the predicted and measured SWRC showed good agreement for relatively fine texture soils with the coefficients of determination (r2) of 0.940.