Analytical model for reinforcement effect and load transfer of pre-stressed anchor cable with bore deviation

•Derived the mathematical expression of the bending anchor cable.•The bigger curvature corresponds to the smaller rock deformation and larger pull-out force.•Anchor cables with 00-0.50 curvature have better reinforcement effect by improving the wall stress.•Anchor cables with larger curvature cause the effective length decrease and uneven stress. Anchors have been widely used in slope engineering, mining engineering and foundation pit engineering, but their stabilities are significantly affected by anchor cable bending which could be contributed by complicated geological conditions and technical limitations. Theoretical analysis in this paper leads to the establishment of the stress model for the bending anchor cable, and the mathematical expression of the relationship between the ultimate pull-out force and the curvature of the bending anchor cable. Numerical simulation is used to evaluate the effect of the anchor cable curvature on the reinforcement effect. The results suggest that the stress distribution and reinforcement effect are affected by different curvatures, the bigger curvature corresponds to the smaller deformation and the larger pull-out force. The rate of decrease in the anchor cable displacement with the burial depth is linearly related to the pull-out force. In addition, the anchor cable curvature affects the response of the surrounding rock mass to stress and strain: The greater the curvature, the larger the area of the responsive rock mass and the higher mobilization of the strength of the rock mass itself. The anchor cable curvature also influences the reinforcement effect of multiple anchor cables. The results are applied to foundation pit engineering, and it is found as follows: The appropriately bending anchor cable (00-0.50 of curvature) with the same length can make wall stress and deformation more reasonable, and better control foundation deformation; however, with the increase in curvature, the effective anchoring length and the anchor cable depth decrease, and the reinforcement effect declines. The study results can provide reference for anchorage engineering.