Analytical relations for the mechanical properties of full-length bonded rock bolts when subjected to freeze–thaw processes

Slope failure often occurs during the spring thawing period in seasonally frozen areas, and it was concluded that the bolts did not perform as well as designed. Such failure disasters introduce an urgent need for the effective prediction of bolt performance for bolt design. Although many experiments exist to investigate the performance of bolts after exposure to freeze–thaw cycles, predictions of bolt performance under such environments are lacking. In this paper, the analytical relations for predicting the axial forces and shear stresses distributed along full-length bonded rock bolts when subjected to freeze–thaw processes were reported. The reported relations take advantage of Mindlin's displacement solution and consider the influence of crack development in rock on the elastic modulus during freeze–thaw processes. A freeze–thaw cycling factor, with proper consideration of the impact of freeze–thaw processes, is introduced and incorporated into Mindlin's displacement solution. A comparison between the predictions and experimental observations demonstrates the ability of the reported relations to accurately predict the performance (i.e., force and stress distributions) of full-length bonded rock bolts. The reported relations provide a simple, practical tool for accurately estimating the bolt performance under freeze–thaw processes. The weaknesses of the reported relations are also discussed.