Root-soil mechanical interactions during pullout and failure of root bundles

Roots play a major role in reinforcing and stabilizing steep hillslopes. Most studies in slope stability implement root reinforcement as an apparent cohesion by upscaling the behavior of static individual roots. Recent studies, however, have shown that much better predictions of slope stability can be made if the progressive failure of bundles of roots are considered. The characteristics of progressive failure depend on interactions between soil deformation and root bundle geometric and mechanical properties. We present a detailed model for the quantitative description of the mechanical behavior of a bundle of roots under strain-controlled mechanical forcing. The Root Bundle Model explicitly considers typical values of root-size spatial distribution (number and dimension of roots), geometric factors (diameter-length proportion, tortuosity, and branching characteristics), and mechanical characteristics (tensile strength and Young's modulus) and interactions under various soil conditions (soil type, confining pressure, and soil moisture). We provide systematic analyses of the roles of these factors on the mechanical response of the bundle and explore the relative importance of various parameters to the macroscopic root-soil mechanical response. We distinguish between increased strength imparted by small roots at small deformations and the resilience imparted by larger roots to the growth of large tensile cracks, showing that the maximal reinforcement of fine roots is reached within the first 5 cm of displacement whereas a root of 20 mm diameter may reach its maximal pullout force after 10 cm displacement. The model reproduces the gradual straining and ultimate residual failure behavior of root systems often observed in hillslopes, with progressive growth of tension cracks improving estimations of root reinforcement when considering the effects of root distribution and the variation of the pullout force as a function of displacement. These results enhance understanding of root reinforcement mechanisms and enable more realistic implementation of root reinforcement modeling for stability calculations of vegetated slopes and for guiding ongoing experimental efforts to gather critical root-soil mechanical information.