Stochastic Modeling of Relative Permeability for Vegetated Covers

Vegetation induces heterogeneity in the soil porous structure and, hence, relative permeability ($k_r)$ as well. The main objective of this study is to address the uncertainties associated with relative permeability using probabilistic analysis for vegetated covers (i.e., grass and tree species). Bare cover is used as control. For this purpose, the dependence structure of suction, $\psi$, and volumetric water content,${\theta }_w$, is established via copula theory, and the $k_r$ curves are predicted with respect to varying levels of suction–volumetric water content correlation. It is found that the $k_r$ of vegetated covers is substantially lower than that in bare covers. The reduction in $k_r$ (with drying) is more in treed cover than grassed cover, since tree roots induce higher levels of suction. Moreover, the air entry value (AEV) of the soil depends on the magnitude of suction–volumetric water content correlation, which, in turn, is influenced by the type of vegetation in the soil. The $k_r$ is highly uncertain in the desaturation zone of the relative permeability curve, which is likely due to inaccuracy of suction measurements beyond 100 kPa. The stochastic behavior of $k_r$ is found to be most significant in treed covers. Finally, a simplified case study is also presented in order to demonstrate the impact of the uncertainty in relative permeability on the stability of vegetates slopes. The factor of safety (FS) is found to vary around 4 to 5% for both bare and vegetated slopes.