A tensile-strength model for root-soil composites considering nonlinear interfacial transfer and progressive root-group failure

During the evolution of shallow slope instability， soil tensile deformation and local crack propagation are key mechanical processes affecting slope stability. Vegetation roots can provide additional tensile restraint during this process. However， existing models still have difficulty characterizing the tensile strength of root-soil composites (RSC)， especially when nonlinear interfacial transfer and progressive root-group failure are involved.To address this issue， a hyperbolic function was adopted to describe the nonlinear response of the root-soil interface (RSI).A calculation method for the tensile response of a single root was established based on shear-lag equilibrium together with failure-mode identification. On this basis， a stiffness-based tensile-force redistribution mechanism was developed to characterize progressive root-group failure， and a root-interaction reduction coefficient was introduced to develop a tensile-strength model for RSC. Tensile tests showed that the proposed model can reproduce the force-displacement response and failure modes under different growth stages and water contents.By further coupling a logistic growth function for root architecture， a predictive model was established to describe the spatiotemporal evolution of root number， length， diameter， and inclination， and to predict the tensile strength of the RSC. This study provides a theoretical basis for evaluating and predicting root reinforcement effects in ecological slope protection.