Analytical solution to the full-range behaviour of grouted rockbolts based on a tri-linear bond-slip model

This paper presents an analytical solution for predicting the full-range mechanical behaviour of grouted rockbolts in tension based on a realistic tri-linear bond-slip model with residual bond strength at the grout–bolt interface. The full-range behaviour consists of five consecutive stages: elastic stage, elastic–softening stage, elastic–softening–debonding stage, softening–debonding stage and debonding stage. For each stage, closed-form solutions for the load–displacement relationship, interfacial shear stress distribution and bolt axial stress distribution along the bond length were derived. The ultimate load and the effective anchor length were also obtained. The analytical model was calibrated and validated against two pullout experimental studies. The predicted load–displacement curves as well as the distributions of the interfacial shear stress and the bolt axial stress are in close agreement with test results. A parametric study is also presented, providing insights into the behaviour of the rockbolts.