An analytical model for ground support by bolting

Abstract

Bolts have been used under various geological conditions as reinforcement to support underground openings. However, quantitative evaluations of the impacts of reinforcement bolts remain controversial. When a bolt is modeled explicitly, one challenge is determining the parameter that represents the interaction between the bolt and surrounding medium. This study aims to derive a simplified Winkler model for the ground support provided by a bolt, with the mutual interaction between the bolt and the surrounding ground analytically evaluated. Theoretical solutions are derived that rigorously consider the mutual interaction between a bolt and the surrounding ground based on two-dimensional axisymmetric elasticity. The obtained solutions are compared with those from the simplified model, in which the bolt is assumed as a rod and the surrounding ground is assumed to have a constant stiffness. The numerical results show that the simplified model can evaluate the ground-bolt interaction when the ground deformation follows the bolt. However, the model cannot accurately model pullout tests as the free surface strongly influences the result, and it is difficult to define a constant representing the surrounding ground.