Estimating the support effect of energy-absorbing rock bolts based on the mechanical work transfer ability

An interaction model is proposed to describe the interaction between the energy-absorbing rock bolt and the rock mass. Based on the plane-strain axial symmetry assumption and the incremental theory of plasticity, the equilibrium equations and compatibility equations of rock mass, as well as the response of the energy-absorbing rock bolt are deduced theoretically. The proposed method was programmed in a Visual Basic environment, and a semi-analytical solution for the coupling model was achieved. The reinforcement mechanism of the energy-absorbing rock bolt in conventional tunneling is clearly demonstrated through an illustrative case study. The reinforcement effect of the energy-absorbing rock bolt under different conditions was estimated quantitatively, and its mechanical work transfer ability is presented. In addition, the validity of the proposed method was verified through numerical simulations. Finally, a number of derivative cases were investigated to reveal the influence of the bolt and rock properties on the reinforcement effect and the bolt work transferred on the rock mass. In the case of higher in-situ stress or low-strength rock mass, the support effect of the energy-absorbing rock bolt is significantly improved, and the bolt absorbs more energy. Increasing the bolt installation density could always be helpful for the stabilization of the surrounding rock mass. However, additional rock-bolt length could hardly affect ground reinforcement because the bolt section embedded in the elastic region of the rock mass could barely help to constrain the elastic displacement release. The bolt should be installed no later than the stage of critical inner pressure, namely when the plastic region occurs.