The stability of surrounding rock with bolt support depends on the stability within the reinforcement range. To understand the reinforcing mechanism of a rectangular roadway bolt fully and accurately, a quantitative method for evaluating the stability of the surrounding rock of a rectangular roadway must be developed. First, a roof beam model of a rectangular tunnel is established according to the deformation law of surrounding rock. Based on the elastic–plastic theory, the deflection calculation formula can be derived, and the ultimate load of the roof beam can be obtained under the plastic state without support. Second, based on the reinforcement effect of bolts, a model of a surrounding rock reinforcement body is established, the physical and mechanical properties of this body are deduced, and a method for evaluating the stability of surrounding rock is derived. Finally, by considering actual engineering cases, the theoretical calculation results of surrounding rock deformation are compared with the numerical simulation and field monitoring results. Moreover, the influence of different parameters of the bolt support on the mechanical characteristics and stability of reinforcement is investigated. The results show that the theoretical calculations approximate the numerical simulation and field monitoring values, thus verifying the rationality of the theory. The physical and mechanical properties and stability of the surrounding rock reinforcement body are considerably affected by changes in bolt length and spacing. The anchor design must apply the following principle: the bolt must either be long and sparsely spaced or short and densely spaced. The theory presented in this paper provides a relatively simple and fast quantitative calculation method for the study of the surrounding rock stability of bolt-supported rectangular roadways.

The stability of surrounding rock with bolt support depends on the stability within the reinforcement range. To understand the reinforcing mechanism of a rectangular roadway bolt fully and accurately, a quantitative method for evaluating the stability of the surrounding rock of a rectangular roadway must be developed. First, a roof beam model of a rectangular tunnel is established according to the deformation law of surrounding rock. Based on the elastic–plastic theory, the deflection calculation formula can be derived, and the ultimate load of the roof beam can be obtained under the plastic state without support. Second, based on the reinforcement effect of bolts, a model of a surrounding rock reinforcement body is established, the physical and mechanical properties of this body are deduced, and a method for evaluating the stability of surrounding rock is derived. Finally, by considering actual engineering cases, the theoretical calculation results of surrounding rock deformation are compared with the numerical simulation and field monitoring results. Moreover, the influence of different parameters of the bolt support on the mechanical characteristics and stability of reinforcement is investigated. The results show that the theoretical calculations approximate the numerical simulation and field monitoring values, thus verifying the rationality of the theory. The physical and mechanical properties and stability of the surrounding rock reinforcement body are considerably affected by changes in bolt length and spacing. The anchor design must apply the following principle: the bolt must either be long and sparsely spaced or short and densely spaced. The theory presented in this paper provides a relatively simple and fast quantitative calculation method for the study of the surrounding rock stability of bolt-supported rectangular roadways.