## 2 Materials and Methods
### Model Building  
In this study, the roadway in the 945 m deep buried area of Sanshandao gold mine is taken as the background [37]. The cross-section shape of this roadway is a straight wall arch with a span width of 4.4 m, wall height of 2.75 m, and arch height of 1.15 m. The roadway support scheme is constructed from shotcrete combined with rock bolt support structure. The rock bolts are resin bolts, 2.2 m in length, and spaced 1 m apart in rows. According to the results of in situ measurements, the in situ stress at the roadway depth of 945 m is 31.0 MPa\(\sim\)44.1 MPa, and in this study, the vertical stress of the model is 40 MPa, and the lateral stress coefficient is taken to be 1.0. The model has a specification of 50 m \(\times\) 50 m \(\times\) 6 m (W \(\times\) H \(\times\) L), and there are a total of 34,884 zones and 26,793 gridpoints in the model. Additionally, the mesh elements of the roadway attachments are encrypted. After the model is established, displacement and velocity constraints are applied to the front, back, left, and right surfaces and lower surfaces of the model, and the top of the model is a free surface. In the model used in this study, the value of gravitational acceleration has a minor impact on the results. The primary focus of the simulation is to investigate the influence of anchor rod parameters and shotcrete layer parameters on the energy evolution characteristics of the surrounding rock. Therefore, in this study, numerical simulations were conducted based on the deep-buried area of the Sanshandao gold mine at a depth of 945 m, utilizing in situ measured data to construct a mechanical model of the surrounding rock. The selected geotechnical parameters include a bulk modulus of 21.08 GPa, a shear modulus of 9.73 GPa, cohesion of 4 MPa, a Poisson's ratio of 0.3, and an internal friction angle of 30\({}^{\circ}\). These parameters, derived from field measurements or relevant literature, are representative and reliable. The model dimensions are 50 m \(\times\) 50 m \(\times\) 6 m, and boundary conditions were applied with displacement and velocity constraints on the front, back, left, right, and bottom surfaces, while the top surface was set as a free boundary. This configuration ensures the completeness of stress distribution and energy evolution characteristics within the study area. Furthermore, to enhance computational accuracy, the mesh around the support structures was refined to more precisely capture the energy variation in stress concentration zones. The gravitational acceleration was set to 10 m/s2, considering its minor impact in deep rock environments, allowing the study to focus on the influence of support parameters on the energy evolution of surrounding rock. A vertical stress of 40 MPa was selected, reflecting a representative value within the in situ measured range of 31.0 MPa to 44.1 MPa at a depth of 945 m. A lateral pressure coefficient of 1.0 was used to simplify the complexity of horizontal stress distribution for analytical purposes. The Mohr-Coulomb model [38], widely utilized in geomechanical analysis, was adopted to describe the elastic-plastic behavior and failure characteristics of the rock mass. The assumptions of the Mohr-Coulomb model make it particularly relevant for this study. While the model simplifies the complex behavior of real rock masses by assuming homogeneity and isotropy, these assumptions are appropriate for analyzing the large-scale energy evolution characteristics of surrounding rock in deep mining conditions. The model effectively captures the transition from elastic energy accumulation to plastic energy dissipation, which aligns with the primary focus of this research. The simulation process and specific design scheme are shown in Figures 4 and 5.