Stochastic modelling of relative water permeability in vegetative soils with implications on stability of bioengineered slope

Vegetation is known to influence the hydrological state variables, suction \( \left( \psi \right) \) and volumetric water content (\( \theta_{w} \)) of soil. In addition, vegetation induces heterogeneity in the soil porous structure and consequently the relative permeability (\( k_{r} \)) of water under unsaturated conditions. The indirect method of utilising the soil water characteristic curve (SWCC) is commonly adopted for the determination of \( k_{r} \). In such cases, it is essential to address the stochastic behaviour of SWCC, in order to conduct a robust analysis on the \( k_{r} \) of vegetative cover. The main aim of this study is to address the uncertainties associated with \( k_{r} \), using probabilistic analysis, for vegetative covers (i.e., grass and tree species) with bare cover as control treatment. We propose two approaches to accomplish the aforesaid objective. The univariate suction approach predicts the probability distribution functions of \( {\text{k}}_{\text{r}} \), on the basis of identified best probability distribution of suction. The bivariate suction and water content approach deals with the bivariate modelling of the water content and suction (SWCC), in order to capture the randomness in the permeability curves, due to presence of vegetation. For this purpose, the dependence structure of \( \psi \) and \( \theta_{w} \) is established via copula theory, and the \( k_{r} \) curves are predicted with respect to varying levels of \( \psi - \theta_{w} \) correlation. The results showed that the \( k_{r} \) of vegetative covers is substantially lower than that in bare covers. The reduction in \( k_{r} \) with drying is more in tree cover than grassed cover, since tree roots induce higher levels of suction. Moreover, the air entry value of the soil depends on the magnitude of \( \psi - \theta_{w} \) correlation, which in turn, is influenced by the type of vegetation in the soil. \( k_{r} \) is found to be highly uncertain in the desaturation zone of the relative permeability curve. The stochastic behaviour of \( k_{r} \) is found to be most significant in tree covers. Finally, a simplified case study is also presented in order to demonstrate the impact of the uncertainty in \( k_{r} \), on the stability of vegetates slopes. With an increment in the parameter \( \alpha \), factor of safety (FS) is found to decrease. The trend of FS is reverse of this with parameter \( n \). Overall FS is found to vary around 4–5%, for both bare and vegetative slopes.