Analytical assessment of coupled influences of surrounding rock reinforcement and deformation release on tunnel response

Attempt has been proved to be effective that surrounding rock reinforcement is emphasized simultaneously considering displacement release in weak rock tunnels. In this study, the calculation formulas for mechanical parameters of bolt-reinforced rocks are provided using the homogenization method and the supporting characteristic curve is divided into three stages with proposing the corresponding stiffness equations. The mechanical model for bolted-reinforced rock-yielding supports interaction is then established and coupled solutions for displacements and stresses around tunnels considering bolt reinforcement and yielding effects are provided. Furthermore, parametric investigations on the influences of rockbolts and yielding supports are carried out. Results show that (1) rock displacement gradually decreases as the rockbolt length increases. However, when rockbolt length becomes large enough, the further improvement of rock displacement will not be obvious by still increasing their length. (2) Both rock displacement and plastic zone of tunnel decrease with the increase of rockbolt radius. There exists the highest utilization of rockbolts corresponding to a certain rockbolt radius. (3) Also, the rock displacement and plastic zone of tunnel decrease as installation density of rockbolts including circumferential space and longitudinal space increases. Under the condition prescribed, this decreasing trend becomes sharper and the improvement is more evident. (4) Larger yielding displacement or stiffness parameter leads to smaller support pressure, but greater plastic radius of tunnel. The optimal yielding displacement and stiffness parameters need to be determined through a comprehensive investigation combining rock properties, support characteristics and tunnel design requirements.