A Constitutive Solution of Full-Encapsulated Rock Bolts Based on the Continuous Yielding Equation

To study the supporting performance of rock bolts subjected to tensile loading, this paper analyzed supporting performance and failure modes of threaded rock bolts under constant normal stress conditions. This paper treated grout/bolt interface as the research object. Based on the continuous yielding equation of rock joints, this paper developed a constitutive solution to describe the supporting performance of rock bolts, incorporating constant normal stress and rock bolt rib geometry. Based on this constitutive solution, supporting performance curves of rock bolts were plotted. Moreover, experimental tests were conducted to confirm the accuracy of the proposed constitutive solution. Calculated results agreed well with experimental results. Based on the variable controlling method, a comprehensive sensitivity analysis was conducted on the supporting performance of rock bolts. The influence of different parameters was studied, including initial bond stiffness of grout/bolt interface, cohesive strength of grout/bolt interface, influencing factor of cohesive strength and shrinkage coefficient of cohesive strength. This analysis showed that initial bond stiffness and cohesive strength apparently influenced the supporting performance of rock bolts. Increasing initial bond stiffness gradually increased the maximum anchorage force. By contrast, residual anchorage force decreased slightly. Increasing cohesive strength increased the maximum and residual anchorage force. The influencing factor and shrinkage coefficient of cohesive strength mainly influenced the residual anchorage force. In the post-peak stage, increasing the influencing factor led to growth of anchorage force. However, increasing the shrinkage coefficient led to the opposite effect. The proposed constitutive solution can provide a theoretical foundation for designing rock bolt reinforcement in underground engineering.