Modeling of root reinforcement of European hornbeam considering the use different fiber bundle models

This study comprises measurements of root systems of European hornbeam in forests located near Winiary, in the vicinity of Gdów (Wiśnickie Foothills, Poland) and near the town of Kanice (Moravia, Czech Republic). Field research included root measurements using the trench wall method conducted at a distance of approximately 1 m from the tree trunks. Tensile strength of the roots collected from both study sites and the geotechnical properties of the soil were determined in the laboratory. Based on the results of field measurements and laboratory tests, the root reinforcement was calculated using selected fibre bundle models. This study was aimed to compare root systems and mechanical properties of roots of the European hornbeam from the two sites and to compare the root reinforcement results obtained using different bundle models, taking into account different approaches to load distribution. The paper also discusses the impact of the tensile strength-strain characteristics of roots and their orientation relative to the direction of slip plane (zone) on the root reinforcement. The results of laboratory tests showed that tensile strength and elasticity of roots collected from both sites are very similar. Calculations showed that the values of root reinforcement computed using fiber bundle models are even 2.5 times smaller than those obtained from the classic Wu–Waldron model. On the other hand, the calculation results between fiber bundle models can differ by more than 2 times. It was also shown that the force-strain relationship used for calculation of root reinforcement has a significant impact on the results of the analyses, and the use of a bilinear force-strain relationship provides the results higher by approximately 10–13%.