Physically-based reduction function to model unsaturated flow associated with plant transpiration

Vegetation plays an important 'hydrological' role in stabilising geostructures. Soil water is extracted by the roots due to transpiration, this increases soil suction and, hence, soil shear strength. Transpiration occurs in two different regimes, energy-limited and the water-limited regimes respectively. These two regimes are reflected in the two branches of the transpiration reduction function used to model the hydraulic boundary conditions for vegetated ground. The water-limited branch accounts for the reduced transmissivity of the soil-root system when the degree of saturation and, hence, the hydraulic conductivity declines. The water-limited branch of existing reduction functions (e.g., Feddes function) is defined in purely phenomenological fashion with parameters that have no clear link with the complex interaction between soil hydraulic properties and root architecture. A paradigm shift can be achieved through physically-based reduction functions. These require analytical closed-form solutions of radial water flow at the soil-root interface that, in turn require introducing simplifying assumptions, i.e., steady-state flow and a simplified hydraulic conductivity function. This paper explores the implications of these assumptions by i) benchmarking the water-limited branch of the reduction function derived analytically against the one derived numerically for more realistic hydraulic behaviour and ii) assessing the steady-state assumption.