An analytical solution for the time-dependent anchoring force in prestressed cables due to rock creep

The unloading effects induced by rock excavation on high slopes are significant, and a prestressed anchor cable is an effective reinforcement method for high-slope safety. In this work, we consider the interaction between rock creep in high slopes and the changing anchoring force of prestressed cables. We then derive theoretical solutions for the unloading rock creep and anchoring force of prestressed cables considering the coupling effect, and verify the solutions using numerical simulation. First, based on the Boussinesq problem in elastic mechanics, we simplify the problem of slope reinforcement with a single prestressed anchor cable to the problem of a concentrated force acting on a boundary of a semiinfinite medium. The concentrated force is affected by the excavation unloading effect from the slope and the anchoring forces from the anchor cables. Based on this simplification, we derive elastic solutions for the slope unloading displacement after excavation and for the anchoring force of prestressed cables. Secondly, considering rock-creep behavior and varying anchoring force, the Burgers model is used for rock masses and the elastic model is used for anchor cables. According to the coordinated deformation between rock masses and anchor cables, we obtain the analytical solutions for the rock displacement and for the anchoring force of the cables under the coupling action in the Laplace space, based on which the viscoelastic solutions for the rock displacement and for the anchoring force considering the coupling effect are solved by the Laplace inverse transform. Finally, we validate the analytical solutions by comparing against numerical simulation results with FLAC 3D . A good agreement is achieved, suggesting the fidelity of the analytical solutions. The theoretical model provides a reference for studying slope reinforcement, analyzing slope rock-creep behavior and the long-term prestress of the reinforcement structure.