Purpose: The mechanical contribution of plant roots to the soil shear strength is commonly modelled using fibre bundle models (FBM), accounting for sequential breakage of roots. This study provides a generic framework, able to includes the many different existing approaches, to quantify the effect of various model assumptions. Methods: The framework uses (1) a single model parameter determining how load is shared between all roots, (2) a continuous power-law distribution of root area ratio over a range of root diameters, and (3) power-law relationships between root diameters and biomechanical properties. A new load sharing parameter, closely resembling how roots mobilise strength under landslide conditions, is proposed. Exact analytical solutions were found for the peak root reinforcement, thus eliminating the current need for iterative algorithms. Model assumptions and results were validated against existing biomechanical and root reinforcement data. Results: Root reinforcements proved very sensitive to the user-defined load sharing parameter. It is shown that the current method of discretising all roots in discrete diameter classes prior to reinforcement calculations leads to significant overestimations of reinforcement. Addition of a probabilistic distribution of root failure by means of Weibull survival functions, thus adding a second source of sequential mobilisation, further reduced predicted reinforcements, but only when the reduction due to load sharing was limited. Conclusion: The presented solutions greatly simplify root reinforcement calculations while maintaining analytical exactness as well as clarity in the assumptions made. The proposed standardisation of fibre bundle-type models will greatly aid comparison and exchange of data.

Mechanical root reinforcement is an important parameter to evaluate for stability analysis of rooted slopes. The contribution of roots is however difficult to quantify in situ without time-consuming methods or heavy equipment. Here we report field testing using the newly developed “corkscrew” method at two different sites with plantings of conifers and blackcurrant. In both sites we found positive correlations between root quantity and root reinforcement in surface layers where many roots were found. Below 125 mm depth, no correlations could be found, probably due to variability in soil stress and gravel content. Roots were shown not only to increase the soil peak strength, but also to add ductility to the soil, i.e., adding strength over much larger displacement ranges. Measured reinforcement, although similar to other experimental studies, was smaller than predicted using existing models. This may be attributed to the distinct difference in shear displacement required to mobilize the strength of rooted soil as compared with fallow soil. At displacements sufficient to mobilize root strength, the soil strength component has reduced from peak to a much smaller residual strength. The corkscrew method proved a promising tool to quantify root reinforcement in field conditions due to its ease of use and short test duration.

Mechanical root reinforcement is one of the mechanisms by which vegetation enhances slope stability. Common approaches to quantify this effect include either in situ shear box testing or destructive root sampling combined with a theoretical model to estimate reinforcement parameters. Both approaches, however, are time consuming. Here four new in situ techniques are evaluated to quantify mechanical root reinforcement and then compared under laboratory conditions. All four methods yield distinct results in soils reinforced with woody root analogues (acrylonitrile butadiene styrene rods), fine root analogues (polypropylene fibres) or stones. Two methods (adaptations of penetrometer testing, dubbed ‘blade penetrometer’ and ‘pull-up’) are suitable for spatially locating rooted zones and individual roots, while the other two (‘pin vane’ and ‘corkscrew’ extraction) demonstrate potential for directly quantifying the rooted soil stress–strain behaviour. These simple methods are suitable for use on difficult-to-access terrain where many measurements are needed to quantify spatial and temporal variability of root-zone properties for geotechnical calculations. The techniques are quicker to use than conventional methods and so should improve the reliability of slope stability predictions.

Summary: 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.

The mechanical contribution of plant roots to soil strength has typically been studied at the ultimate limit state only. Since many geotechnical problems are related to serviceability, such as deformation of infrastructure, a new constitutive modelling framework is introduced. The rooted soil is treated as a composite material with separate constitutive relationships for soil and roots, and a comprehensive stress–strain relationship for the root constituent is presented. The model is compared to direct shear experiments on field soil reinforced with gorse, grass and willow roots, as well as an existing root reinforcement model based on the Winkler-spring supported beam theory. The results show that both the newly developed model and the beam-type model yield good predictions for the evolution of root-reinforced shear strength as a function of increasing shear displacements. Both successfully capture the large deformations required to reach peak reinforcement, the reduction in reinforcement due to root breakage and the presence of significant reinforcement even after very large deformations, associated with root slippage. Since both fibre and beam models only require physically meaningful input parameters, they can be useful tools to study the mobilisation of rooted soil strength and simulate the response of rooted soil in continuum-based numerical simulations.