Theoretical analysis of pullout deformation and stiffness of grouted rockbolts

The deformation calculation of rockbolts is one of key factors in anchor engineering design. In the segment of the shear deformation compatibility between the rockblots and the surrounding rockmass, the linear shear deformation stiffness is assumed. In the segment of the deformation incompatibility, the power function model of the shear stress distribution along the rockblots is presented. By means of the loading transfer differential equation, the pullout deformation and stiffness on the fully grouted and the grouted rockbolts with free end are analyzed. And the shear stress distribution function, the axial force distribution function and the displacement distribution function along the rockbolt are derived. Thus the maximum pullout force and pullout load-displacement curve on the grouted rockbolts can be obtained. Based on the shear-lag theory, from the equilibrium differential equation on an infinitesimal element of the rockmass around rockbolts, the calculation formulae for elastic deformation stiffness on the interface between the rockbolts and the rockmass are deduced. The comparison between the present results and other theoretical estimates shows that the proposed method is reasonable and feasible and has reference value for the design of deformation, stiffness and strength of grouted rockbolts.