Analysis of coupled axial and lateral deformation of roots in soil

Plant roots can help to stabilise slopes. Existing analytical models to predict their mechanical contribution are however limited: they typically focus on the ultimate limit state, employ various empirical factors, and ignore much of the underlying root-soil interaction. A new model was developed based on large deflection Euler-Bernoulli elastic beam theory that can be used to study the mobilisation of root strength under various loading conditions (direct shear and pull-out). Both lateral and axial loading of the root by the soil were incorporated, based on existing methodologies for foundation piles (p-y and t-z curves). The model is able to take the key parameters into account (root biomechanical properties, root architectural properties, and soil properties) while remaining quick to solve using a numerical boundary value problem solver. The model was compared with experimental direct shear test data using various root analogues (rubber, plastic, and wood) in dry sand with various densities and effective stress levels and was able to accurately predict the measured shear force-displacement behaviour. Comparison with experimentally measured pull-out force-displacement curves using rubber and wooden root analogues with various architectures in dry and partially saturated sands was also satisfactory. In the future, this model can aid with addressing long-standing problems in the root-reinforcement community: quantifying the effect of (sequential) mobilisation of root strength in direct shear, the effect of the angle at which the root crosses a shear plane, the effect of root topology on root-reinforcement or the effect of root bending, and root shear shear forces on root-reinforcement.