Coupling model and calculation method of yielding bolt and rockmass

Yielding bolt has been widely used for rock reinforcement in mining and civil engineering in high stress conditions. However, the interaction mechanism of the yielding bolt and the rockmass is still not clear at present; and no model is available to predict its reinforcement effect quantitatively. According to the mechanical and deformation characteristics of yielding bolt, an interaction model is proposed to account for the coupling action between the bolt and rockmass. Based on the plane strain axial symmetry assumption and the incremental theory of plasticity, equilibrium equations and compatibility equations of rockmass, and also the response of yielding rock bolt are deduced theoretically. The proposed method has been programmed in the Visual Basic development environment; and a semi-analytical solution for the coupling model is achieved using Runge-Kutta method. The reinforcement mechanism of yielding bolt is demonstrated through an illustrative case study. The distribution of shear stress and axial force along the bolt are presented; and the reinforcement effect of yielding bolt is estimated quantitatively. In addition, the validity of the proposed method is verified by numerical simulations. The reinforced ground reaction curve and the yielding bolt reaction curve can also be constructed systematically by the proposed method, which could help the support system design in conventional tunnelling.