DRAM: A three-dimensional analytical model for the mobilisation of root reinforcement in direct shear conditions

Roots can stabilise slopes against shallow landslides by mobilising their mechanical strength. Existing analytical models are highly simplified and typically focus on the ultimate limit state only, thus providing little insight into the underlying mechanism of reinforcement mobilisation. A new analytical model (‘DRAM’) was therefore developed to predict mechanical root reinforcement as a function of direct shear displacements. This model accounts for elasto-plastic root behaviour, three-dimensional root orientations, root failure through breakage or slippage, and a dynamically changing shear zone thickness. Comparison to two independent experimental direct shear data sets showed that the model was able to accurately predict the gradual mobilisation of root strength, the magnitude of peak root reinforcement, as well as the presence of significant root reinforcement at large shear displacements, associated with a relatively large quantity of roots slipping out of the surrounding soil. Because the newly developed model more closely resembles the underlying physics of the mobilisation of root reinforcement in direct shear while still being easy to use, it will be a useful tool for the engineering industry, in terms of quantifying root reinforcement distribution for limit analyses at the ultimate limit state, as well as for directing future research into the drivers of mechanical root reinforcement.