Investigation of the failure mechanism and theoretical model of bolt-reinforced shallow tunnel faces with different bolt lengths

Using fiberglass bolts to reinforce a tunnel face is a practical auxiliary technology for ensuring tunnel face stability in soft ground.The reinforcing effect and the economics of this technology are significantly affected by bolt length.However,to date,the failure mechanism of bolt-reinforced tunnel faces with different bolt lengths has rarely been investigated.To reveal the failure mechanism of bolt-reinforced shallow tunnel faces,in this study,the stability of bolt-reinforced tunnel faces with different bolt lengths was investigated by using laboratory tests and numerical simulations,and a simplified theoretical model for practical engineering was proposed.The face support pressure and failure pattern for different bolt lengths during the face collapse process were obtained,and the influence of bolt length on face stability was clearly revealed.More specifically,the results show that face stability increases with increasing bolt length,and the reinforcing effect of face bolts is governed by the shear failure at the soil-grout interface first in the stable zone of the tunnel face and then in the failure zone.Once the bolt length in the stable zone is larger than that in the failure zone,face stability will not be improved with increasing bolt length;thus,this bolt length is referred to as the optimal bolt length L_(opt).The L_(opt)value is slightly larger than the initial failure range(in the unreinforced condition)and can be approximately calculated by L_(opt)=(1-0.0133u)D(u is the friction angle of the soil,and D is the tunnel diameter)in practical engineering.Finally,a simplified theoretical model was established to analyse the stability of reinforced tunnel faces,and the results are in good agreement with both laboratory tests and numerical simulations.The proposed model can be used as an efficient tool for the design of face bolts.