Modeling root reinforcement using a root-failure Weibull survival function

Root networks contribute to slope stability through complex interactions with soil that include mechanical compression and tension. Due to the spatial heterogeneity of root distribution and the dynamics of root turnover, the quantification of root reinforcement on steep slopes is challenging and consequently the calculation of slope stability also. Although considerable progress has been made, some important aspects of root mechanics remain neglected. In this study we address specifically the role of root-strength variability on the mechanical behavior of a root bundle. Many factors contribute to the variability of root mechanical properties even within a single class of diameter. This work presents a new approach for quantifying root reinforcement that considers the variability of mechanical properties of each root diameter class. Using the data of laboratory tensile tests and field pullout tests, we calibrate the parameters of the Weibull survival function to implement the variability of root strength in a numerical model for the calculation of root reinforcement (RBMw). The results show that, for both laboratory and field data sets, the parameters of the Weibull distribution may be considered constant with the exponent equal to 2 and the normalized failure displacement equal to 1. Moreover, the results show that the variability of root strength in each root diameter class has a major influence on the behavior of a root bundle with important implications when considering different approaches in slope stability calculation. Sensitivity analysis shows that the calibration of the equations of the tensile force, the elasticity of the roots, and the root distribution are the most important steps. The new model allows the characterization of root reinforcement in terms of maximum pullout force, stiffness, and energy. Moreover, it simplifies the implementation of root reinforcement in slope stability models. The realistic quantification of root reinforcement for tensile, shear and compression behavior allows for the consideration of the stabilization effects of root networks on steep slopes and the influence that this has on the triggering of shallow landslides.