Influence of Relative Permeability Formulations on Hysteretic Seepage in Infinite Slopes

The paper investigates the impact of two classical relative permeability formulations, one expressed in terms of pore water pressure and the other in terms of degree of saturation, on the predicted seepage in an infinite slope subjected to surface pore pressure variations. A hysteretic retention law is employed, inducing irreversible changes in hydraulic conductivity during wetting–drying cycles. Two soils with different gradings are analysed and, for each of them, the two relative permeability formulations are matched at a reference point so as to represent the same material. Despite this calibration, the corresponding permeability fields differ significantly over the hysteretic domain, by as much as five orders of magnitude. These discrepancies are mostly the consequence of retention hysteresis and are substantially reduced if a unique, non-hysteretic retention curve is selected. For reference, a slope model with constant permeability, equal to the maximum saturated value, is also evaluated. The magnitude and rate of the slope response to surface perturbations, the number of cycles to restore equilibrium and the characteristics of the steady state regime all depend on the chosen permeability formulation. Slopes with a constant permeability react rapidly and uniformly, whereas slopes with permeability depending on pore water pressure or degree of saturation display slower, more complex and depth-attenuated responses, particularly for the finer soil. Overall, the results highlight the need for consistent calibration of both relative permeability and retention hysteresis, while underscoring the limitations of constant permeability models in capturing unsaturated seepage, even when appropriate hysteretic retention laws are adopted.