Improving unsaturated hydraulic conductivity estimation in soils via percolation theory

- Surface roughness effect on K(Sw) estimations is assessed using 124 soil samples.
- Incorporating roughness improves estimations over the entire saturation range.
- Non-equilibrium conditions affect K(Sw) estimations at low water saturations.
- Uncertainties in β and D and their effects on K(Sw) estimations are discussed.
- Our model should be valid in viscous-dominated regimes (high capillary numbers).

Accurate estimation of unsaturated hydraulic conductivity K(Sw) in soils has been of great interest to soil physicists and hydrologists in the past several decades. Although various methods such as a “bundle of capillary tubes” conceptual approach were applied in the literature to theoretically model hydraulic conductivity in term of water saturation, in this study we invoke percolation theory, which quantifies the effect of the interconnectivity of pores on the macroscopic fluid flow. We incorporate the pore-solid interface roughness effect in the hydraulic conductance-pore radius (g-r) relationship, evaluate our K(Sw) model using 104 soil samples from the UNSODA database as well as another 20 soil samples from the Rijtema database, and compare it to the Ghanbarian-Alavijeh and Hunt (2012) model. Generally speaking, we experimentally demonstrate that K(Sw) estimations were improved over the entire range of water saturation when the surface roughness effect was incorporated. However, our model still underestimates the unsaturated hydraulic conductivity at low water saturations (corresponding to K(Sw) < 10− 4 cm/day). We show that after eliminating the effect of non-equilibrium conditions in the measurements K(Sw) estimations were improved substantially. Other plausible sources for K(Sw) underestimation are also discussed.