Numerical simulation of fully grouted rock bolts with or without faceplates based on the tri-linear bond-slip model

Abstract

A difference scheme of the governing equation of the bolt-grout interface of the fully grouted rock bolt was derived based on the tri-linear bond-slip model, local equilibrium condition, and finite difference method. The corresponding solution formats of the fully grouted rock bolts with or without faceplates were proposed according to their different boundary conditions. Consequently, a numerical model of the fully grouted rock bolts with or without faceplates was established. This model is able to simulate the bonding, softening, and decoupling characteristics of the bolt-grout interface of the fully grouted rock bolts with or without faceplates subjected to the pullout load or rock deformation. The prediction results of this model agree well with the pullout test results, the calculation results of related scholars, and the analytical solutions, which proves its correctness. Then, the formulas of the support reaction force of the rock bolts with or without faceplates were derived according to their support mechanisms, and the support reaction force was applied during the iteration to simulate the bolt-rock interaction. This method is convenient for engineering applications owing to that it does not need to add additional degrees of freedom for rock bolts. The abovementioned model and method were incorporated into a self-developed FEM program and the effect of the initial deformation of the surrounding rock before bolt installation was considered, resulting in a numerical simulation program for fully grouted rock bolts with or without faceplates in underground caverns. Finally, this program was applied in a circular tunnel and the influences of the faceplate, bolt installation timing, bolt length, and bolt radius on the support performance of rock bolts were investigated. The following conclusions were obtained. 1) The faceplate can greatly improve the support effect. 2) The main failure mode of the rock bolts without faceplates is the shear damage at the bolt-grout interface, while the bolt pull-off is the dominant failure mode of the rock bolts with faceplates. 3) There is a critical value of bolt length. Increasing the bolt length within the critical value can significantly enhance the support effect, whereas increasing the bolt length beyond the critical value has little effect on the support effect. 4) Increasing the bolt radius can effectively enhance the support effect.