A relative permeability model for deformable soils and its impact on coupled unsaturated flow and elasto-plastic deformation processes

Relative permeability is an indispensable property for characterizing the unsaturated flow and induced deformation in soils. The widely used Mualem model is inadequate for deformable soils because of its assumption of a rigid pore structure and the resultant unique dependence of the tortuosity factor on the volumetric water content. In this study, a unified relationship between the relative permeability and the effective degree of saturation was proposed for deformable soils by incorporating our newly developed water retention curve model into the original Mualem model, in which a new tortuosity factor was defined using the fractal dimension of flow paths and the mean radius of water-filled pores for representing the effect of pore structure variation. The modified deformation-dependent relative permeability model was verified using test data on five types of soils; the verification revealed a much better performance of the proposed model than the original model, which commonly overestimates the relative permeability of deformable soils. Finally, the proposed model was implemented in a coupled numerical model for examining the unsaturated flow and elastoplastic deformation processes in a soil slope induced by rain infiltration. The numerical results showed that the deformation-dependent nature of relative permeability has a remarkable effect on the elastoplastic deformation in the slope and that neglect of the deformation-dependent behavior of relative permeability causes overestimation of the depth of failure.