Analytical models for soil pore-size distribution after tillage

Tillage causes soil fragmentation thereby increasing the proportion of interaggregate (structural) pore space. The resulting tilled layer tends to be structurally unstable as manifested by a gradual decrease in interaggregate porosity until a new equilibrium has been reached between external loads and internal capillary forces at a rate governed by the soil rheological properties. The soil pore-size distribution (PSD) will change accordingly with time. We have previously applied the Fokker-Planck equation (FPE) to describe the evolution of the PSD as the result of drift, dispersion, and degradation processes that affect the pore space in unstable soils. In this study, we provide closed-form solutions for PSD evolution, which can be used to predict temporal behavior of unsaturated soil hydraulic properties. Solutions and moments of the PSD were obtained in case: (i) drift and degradation coefficients depend on time and the dispersivity is constant and (ii) drift and dispersivity are also linearly related to pore size. Both solutions can model the reduction in pore size during the growing season awhile the second solution can account for a reduction in the dispersion of the PSD. The solutions for PSD were plotted for a mathematically convenient expression for the drift and degradation coefficients and for an expression derived from a model for soil aggregate coalescence. Experimental data on the settlement of a Millville (coarse-silty, carbonatic, mesic Typic Haploxeroll) silt loam during wetting and drying cycles were used to determine time-dependent drift and degradation coefficients according to this coalescence model. The solution for the PSD was used to independently predict the water retention curve, which exhibited a satisfactory agreement with experimental retention data at the end of two drying cycles.