An analytical model for estimating the force and displacement of fully grouted rock bolts

Previously proposed models for estimating the force and displacement of fully grouted rock bolts rarely describe the variations in shear stress and axial force in response to a changing load. In this work, an analytical model considering this variation pattern is developed. The model makes two assumptions: (I) failure occurs at the bolt-grout interface, and (II) the shear stiffness is constant along this interface. First, according to the variation in interfacial stress, the complete rock bolt deformation process is divided into three stages: (1) the elastic stage, (2) the softening stage, and (3) the debonding stage. Equations for axial force and displacement during each stage are derived under the two assumptions. Using these equations, the developed model accommodates the three stages. The model estimates of force and displacement show good agreement with pull-out test observations, indicating that the model effectively describes the complete rock bolt deformation process during a pull-out test. However, one limitation of the proposed model is that, for simplification, as in most related models, the radial stress along the bolt is not considered.