An analytical model of fully grouted rock bolts subjected to tensile load

•An analytical model is proposed for fully grouted rock bolts under tension.•The model consists of the residual shear stress and the decoupling mechanisms.•The axial bolt load, shear stress and load displacements have been derived.•The proposed model agrees well with the laboratory and in situ data. An analytical model for fully encapsulated rock bolts subjected to tensile load in pull-out tests is presented. This model is based on the bond–slip relationship describing the mechanical interaction at the bolt–grout interface. The model takes into account the residual shear stress in addition to the complete decoupling mechanisms. Formulations are also derived for the load–displacement curve, shear stress distribution at the bolt–joint interface and axial load distribution in the bolt. The model was validated with experimental results from both the laboratory experiments and in situ studies.