Analytical model for rock bolts reaching free end slip

• An analytical model is proposed for fully grouted rock bolts under tension.
• The model takes into account free end slip of fully grouted rock bolts.
• The load displacements, the strain and shear stress distribution have been derived.
• The proposed model is in good agreement with the laboratory data.

This paper presents the difference of behaviour between fully grouted bolts with and without free end slip when loaded in tension. An analytical approach is proposed for fully encapsulated bolts when the free end of the bolt slips. This model is based on the existing bond–slip relationship of bolt–grout interface with no free end slip. The derived analytical solutions of load–slip relationship, slip distribution, the shear stress and strain distributions presented in this paper are all connected with free end slip. The analytical approach is validated by experimental results. Free end slip has a significant influence on rock bolt behaviour and should not be ignored.