A computationally-efficient finite-element model for solving root–soil mechanical interaction of complex root system architectures

Understanding root anchorage and reinforcement to soil is crucial to evaluate the stability of vegetated slopes. Existing numerical models to solve the root–soil interaction have several limitations: these models typically assumed soil to be a perfectly elastic-perfectly plastic material without considering the effect of soil dilatancy and strain-softening behaviour on the root–soil interaction. Additionally, they did not account for the debonding phenomenon at the root–soil interface, thus failing to capture the interfacial shearing and root pull-out failure. This study derived and implemented an enhanced Mohr–Coulomb constitutive (EMC–CS) model based on the critical-state theory, with due consideration of the phenomena of strain-hardening/softening and dilatancy. A new stress correction algorithm was proposed to improve the computational efficiency of stress integration. An improved root–soil interaction (RSI) model was formulated to capture load transfer between roots and soil, as well as shear-induced softening at the interfaces for complex root systems. Validation against laboratory triaxial tests demonstrated the capability of EMC–CS model to capture the key soil mechanical behaviour. A three-dimensional finite-element model that have integrated the RSI and EMC–CS models were then developed for modelling root anchorage and reinforcement. Comparisons with measured data from pull-out tests, direct-shear tests and centrifuge push-over tests demonstrated that the model can effectively capture the root–soil interaction mechanisms, including interfacial shearing behaviour, root reinforcement, root overturing resistance and the position of root breakages.