Reasonable pre-tightening force of bolt based on the theory of stress gradient

The stability of roadway surrounding rock is not only related to the strength of rock mass,but also closely re- lated to the stress field gradient of surrounding rock. In order to study the determination method of reasonable support strength of bolt in roadway surrounding rock support,a reasonable pre-tightening force is put forward in some specific geological conditions. This paper is based on the continuum damage mechanics model and introduces the stress gradi- ent theory in the field of material mechanics. The equilibrium equation and boundary conditions of the interface be- tween the plastic zone and the elastic zone of the surrounding rock are derived,and the stress gradient solution model of surrounding rock is established based on Mohr-Coulomb criterion,Drucker-Prager criterion and Hoek-Brown criterion. Taking the Mohr-Coulomb criterion as an example,using the FLAC3D numerical software,the simulation results are compared with the theoretical values,which are 93 percent consistent with the change trend,which verifies the applica- bility of the stress gradient solution method proposed in this paper. It is found that the stress gradient in the plastic area of roadway surrounding rock increases correspondingly with the increase of the pre-tightening force of bolt,the stress gradient in the elastic area decreases continuously,and the degradation degree of rock mass decreases. The authors put forward the stress compensation coefficient. The stress gradient distribution law and supporting effect of roadway sur- rounding rock under different bolt preloads are calculated by simulation. It’ s found that the change of pre-tightening force is positively correlated with the bolting effect of roadway surrounding rock,and the range of plastic zone decreases with the increase of pre-tightening force,and the stability of sur-rounding rock increases with the increase of stress gra- dient. Based on these conclusions,the corresponding compensation relation between the bolt’s pretension force and the stress gradient of surrounding rock is obtained and the optimal compensation ratio is proposed. In the field practice,the control effect of roadway deformation is improved by more than 40% ,and the stress gradient compensation coefficient is higher than 0. 65,which is higher than the safety control requirements of surrounding rock deformation,and provides a research idea for determining the reasonable support strength of the bolt.