## 1 Introduction
This method simulates the stress release and wall displacement of rock excavation through the ground response curve (GRC) and determines the optimal support timing and strength based on the support characteristic curve (SCC) [20]. [PERSON] derived analytical solutions for the stress, strain, and displacement of tunnel surrounding rock based on the Hoek-Brown strength criterion and strain-softening model and obtained the GRC considering the plastic volume strain of the rock mass [21]. [PERSON] derived a one-dimensional numerical solution for the GRC curve of tunnels in strain-softening rock masses, which can also be degenerated into the GRC of the Tresca, Mohr-Coulomb, and Hoek-Brown strength criteria [22]. The above analytical method considers the effect of the lining on surrounding rock, but in order to facilitate the solution, the lining is regarded as a single material that is only concrete, and the supporting effect of bolts, steel arch frames, and shotcrete cannot be accurately solved. Figure 1: A tunnel supported by bolts, a steel arch frame, and shotcrete. [PERSON] et al. (2015) used the Mohr-Coulomb strength criterion to derive the expressions of the stress, displacement, and radius of the plastic zone of a circular tunnel before and after bolt support. This is of great significance for solving the interaction between the surrounding rock and the support structure [23]. [PERSON] et al. deduced the bearing capacity of surrounding rock after applying bolts. This method only considers the function of bolts to improve the mechanical properties of rock masses [24]. [PERSON] et al. (2021) deduced and analyzed the support load of bolts and secondary lining in rheological rock mass [25]. [PERSON] et al. (2021) studied the interaction process of grouting bolts and the tunnel surrounding rock and solved the radius of the plastic zone, the displacement, and the stress field of the tunnel [26]. It can be seen that the analytical method has a good effect on the analysis of the supporting effect and bearing capacity of bolts. In order to make up for the shortcomings of previous studies in considering tunnel displacement and primary support bearing capacity, this paper derives tunnel wall displacement and primary support bearing capacity based on elastic-plastic theory. A semianalytical solution is proposed to calculate the displacement of the tunnel wall and the bearing capacity of the primary support of a tunnel. Compared with previous studies, this paper considers the displacement of the tunnel wall more carefully, deduces the displacement of the tunnel wall solution after the application of bolts and the tunnel wall displacement solution after the application of a steel arch frame and shotcrete, and finally gives the calculation method of the bearing capacity of the primary support. The Xiabeishan No. 2 Tunnel was selected as a verification calculation example, and the accuracy of the calculation method proposed in this paper is verified through comparison with the numerical simulation results. Compared with the previous studies, the method proposed in this paper can directly reflect the displacement of the tunnel wall at different stages of primary support and the impact of different support methods on the bearing capacity of the primary support.