Abstract: To avoid insufficient bolting or excess bolting and to quickly and accurately evaluate the stability of the surrounding rock stability of anchored tunnel, firstly, considering the complex of rock and bolt into the reinforcement body with homogeneous material, the physical and mechanical parameter expression of the reinforcement body is derived based on the elastic theory. Then, the coordinated deformation mechanical model of surrounding rock and the reinforcement body is established, the model is analyzed by mechanics, and the evaluation method of surrounding rock stability is put forward. Finally, this theory is compared with existing theories and numerical simulation; and the influence of different bolting strengths on the stability coefficient of surrounding rock is studied. The results indicate that the radius of plastic circle of tunnel surrounding rock and the radial displacement of tunnel wall obtained by this theory are different from the calculated results of the existing theory by 0.8% and 2.1% respectively; and the theoretical calculations are in good agreement with the results of numerical simulations, which verifies the rationality of the theory of this article. The length of the bolt and the spacing between the bolts have a great influence on the stability of the surrounding rock; and the bolt support design follow the principle of long and sparse, short and dense. The optimum bolt length is reduced when the distance between the bolts is reduced or the pretension is increased. This theory can provide a relatively simple and fast quantitative calculation method for the stability study of tunnel surrounding rock under bolt support.

Key words: tunnel engineering, homogenization method, wholly grouted bolt, elastoplastic analysis, surrounding rock stability