Unsaturated hydraulic conductivity modeling for porous media with two fractal regimes

- We theoretically developed 2-segment functions to model SWRC and K(θ) of soils.
- 8 soil samples showing bimodality were well fit by the SWRC and K(θ) models.
- D values from SWRC and K(θ) were almost but not quite identical.
- We discussed reasons for the discrepancy between predicted and measured K(θ) curves.

A reliable means to predict the saturation-dependence of the hydraulic conductivity would have important applications and implications across soil science. In our efforts to improve predictive capabilities we apply a bimodal pore size distribution to generate simultaneously the soil water retention curve (SWRC) and the unsaturated hydraulic conductivity K in porous media. Our specific pore size model incorporates two fractal regimes, which we treat within the pore-solid fractal approach. The calculation of the hydraulic conductivity employs critical path analysis from percolation theory, which has already been shown to perform the best overall among models commonly employed. To evaluate the developed piecewise functions, 8 soil samples with different textures, e.g., loam, silt loam, sandy loam and clay are selected. All soils show almost the same cross-over point on both water retention and hydraulic conductivity curves on semi-log plots. We find that the piecewise water retention and unsaturated hydraulic conductivity models fit well the measured data. However, the hydraulic conductivity curves predicted from the water retention data agree relatively well with the measured one just for the first regime and tend to underestimate K in the second. We also compare our results with those obtained from unimodal pore-size distribution reported by Ghanbarian-Alavijeh and Hunt (2012). Comparing the measured data with the unimodal and bimodal models indicates that the bimodal distribution provide somewhat more realistic predictions than the unimodal one. If prediction is sacrificed and we simply try to model K using our results, we find that we can generate a very accurate phenomenological description of K with only a slight change in the values of the fractal dimensionality. Reasons for this discrepancy are discussed.