Continuum percolation theory for pressure–saturation characteristics of fractal soils: extension to non-equilibrium

Abstract

Systematic experimental deviations from theoretical predictions derived for water retention characteristics of fractal porous media have previously been interpreted in terms of continuum percolation theory (at low moisture contents, below the critical volume fraction of water, α c capillary flow ceases). In other work, continuum percolation theory was applied to find the hydraulic conductivity as a function of saturation for saturations high enough to guarantee percolation of capillary flow. Now these two problems are further linked, using percolation theory to estimate non-equilibrium water retention at matric potential values such that the equilibrium water content is too low for percolation of capillary flow paths. In particular, a procedure for developing a time-dependent moisture content is developed for experimental time scales long enough that film flow can provide an alternate mechanism for equilibrating when continuous capillary flow is not possible. The time scales are defined in terms of moisture-dependent length scales and film flow and capillary flow hydraulic conductivities. Imbibition is treated in the extreme case of no film-flow contribution to equilibration. In another application at higher matric potentials, recursive relations are derived for the water content of porous media during drying when external pressures are changed at rates too rapid for equilibrium to be attained by capillary flow.