Fully Analytical Solution for Hydraulic Conductivity of Soils Based on a Probabilistic Porous Model

This paper establishes a fully analytical equation for the relative hydraulic conductivity of soils through a probabilistic porous network model. Under this approach, a parameter, accounting for the proportion of pores of a certain maximum size forming continuous paths of saturated elements between the boundaries, is obtained and used to compute the hydraulic conductivity of soils. This method avoids the necessity of the pore-scale model approach required by computational networks to obtain the hydraulic conductivity of soils at different water contents. Additionally, constraints related to computing time, memory size, and the effect of the size of the network on the results are avoided. Furthermore, the network can consider single-, double-, or triple-structured soil. The theoretical and experimental comparisons indicate that the capillary flow regime can account for the hydraulic conductivity of sandy soils for suctions below 0.1 MPa without the need for a different flow regime as the film flow. Finally, all parameters required in the relative conductivity equation can be obtained directly from the pore-size distribution or by fitting the numerical with the experimental soil water retention curves of the material. The determination of the hydraulic conductivity function of soils is required for a number of geotechnical problems: the flow of contaminants, the flow of water in slopes and cuts to define the variations in the factor of safety against the infiltration of water, the flow of water in expansive soils for the design of optimal foundations, and the behavior of buffers of bentonite pellets around the radioactive repositories of nuclear waste during wetting-drying cycles. With the present development, it is possible to define the relative permeability function from the retention curves of soils and the use of a probabilistic porous model. When the retention curves are fitted, the proportion of continuous paths of saturated pores of certain maximum size connecting the flow boundaries can be extracted. This procedure results in a fully analytical solution and a more expeditious method for the determination of the hydraulic conductivity of soils subjected to different suctions.