Embedding Probabilistic Pore Occupancy into Soil Hydraulic Models

Conventional soil hydraulic models describe unsaturated water retention and conductivity by assuming that water occupies the smallest pores, i.e., lower-energy pores. The author introduces a statistical pore occupancy framework to quantify the pore states by a pore distribution, retrieved from the retention function, allowing statistical inference of pore state conditions. The framework introduces a parameter b, which represents the water pore occupancy distribution, impacting the behavior of the retention and conductivity functions. The approach uses an effective energy formulation to facilitate the calculations, allowing direct integration into traditional soil-water dynamic simulators. As a second step, a back transformation is introduced for a direct physical interpretation of the pore-filling condition, leading to the probability of pores being filled or not filled with water. The framework introduces a modified closed-form formulation of the Van Genuchten-Mualem model. The new model can quantify hysteretic behavior of the retention function and simultaneously predict the hydraulic conductivity behavior. Root mean square differences (RMSD) ranged from 0.007 to 0.021 m3 m-3, for the retention data, predicting both drying and wetting experiment scenarios; and from 0.117 to 0.216 for the conductivity, expressed as log10⁡(K). The embedded statistical mechanic can also assist in quantifying the solute transport. The respective shapes of the solute breakthrough curves (BTC) were reproduced, leading to a calibration RMSD of 0.018 and 0.016 [–]. A discussion regarding the back-transformation showed how the framework can be used to infer the configuration of pores filled with water in the soil, considering the model assumptions.