Analytical model of fully grouted bolts in pull-out tests and in situ rock masses

The dynamic evolution characteristic of the bond strength at the interface of a bolt and a rock mass under an axial tensile load and the mechanical behavior of fully grouted bolts in situ were investigated considering the non-uniform stress of the surrounding rock along the bolts. A new dynamic bond-slip model was first proposed to describe the dynamic evolution characteristic of the bond strength at bolt-rock interfaces. Based on the proposed dynamic bond-slip model, analytical solutions of the shear stress distribution along the bolts, load-displacement relationship, and relative displacement considering the slip of the free end were developed. Then, incorporating the non-uniform normal stress of the surrounding rock along the bolts, the shear stress distribution and load-displacement behavior of the fully grouted bolts were presented. Moreover, analytical approaches were also proposed for determining the stress distribution along the bolt and rock deformation in cases of in situ prestressed and non-prestressed bolts. The proposed model and analytical solution were validated by published results from laboratory model tests and in situ tests, respectively. The new analytical solution completes the theoretical framework for addressing the fundamental problem of fully grouted bolts in pull-out tests and in situ rock masses and provides a useful theoretical tool that can potentially be applied to bolt design and laboratory and in situ testing.