## 3 Establishment of Numerical Model for Surrounding Rock of Roadway Excavation
### Construction of Numerical Models
A support model is established in the 3 DEC software as depicted in Figure 9. Due to constraints in the numerical modeling of the support system, only the framework structure of the supports is retained, and transitional devices that do not impact the roof are removed. Considering the absence of crushing or similar occurrences in the normal operating condition of the support, as well as the metal being in the elastic phase, the support is presumed to be rigid, while the surrounding rock is considered a deformable body that has not yet met the Mohr-Coulomb criterion. Consequently, elastic contact is established between the support and the surrounding rock. The excavation process in the numerical simulation involves stepwise excavation of the roadway and stepwise support, with each step being 1.6 m. Following each step of roadway excavation, the original rock stress is applied to the surrounding rock of the excavation face and gradually reduced to mimic the process of stress release in the field after excavation. The stress release is represented by a power exponential equation, with  
Figure 8: Numerical model of the roadway surrounding rock. a rapid initial release followed by a slower release in later stages. Temporary bracing is implemented when the released stress reaches 70% of the original rock stress after each excavation step, to provide support to the surrounding rock. For the first six excavation steps, a monolithic brace is added at each step. Upon completion of these initial six steps, the numerical model forms a complete temporary support area for the roadway. The coupled model of the first six excavation steps and the temporary support is depicted in Figure 10.  
In the subsequent excavation sequence, a sequential movement of six monolithic braces in the excavation direction is employed for each excavation step, simulating a stepping repetitive support process for the roof slab. This results in the formation of an empty roof zone after the forward movement of the 6 th brace. Once the stress in the hollow roof area is released to 30% of the original rock stress, the permanent support of anchor rods and anchor cables begins. The anchor rods and anchor cables were simulated using the Cable structural unit integrated in 3 DEC software. The anchor rod has a diameter of 22 mm and a length of 2.4 m, while the anchor cable has a diameter of 17.8 mm and a length of 6 m. The spacing between the roof anchor rods is 1 m, with six rods per row and a spacing of 0.9 m. All anchor rods are arranged vertically against the roof. The spacing between the two wall anchor rods is 1 m, with four rods per row and a spacing of 1.1 m. They are all arranged vertically against the walls. The spacing between the roof anchor cables is 1.8 m, with a row spacing of 2 m. All of them are arranged vertically against the roof of the roadway. The numerical simulation process involved digging a total of 12 excavation steps, resulting in a roadway length of 19.2 m. This created a temporary support area of 9.6 m, an  
Figure 10: Coupled modeling of the first six steps of excavation and temporary support. Figure 9: Numerical modeling of temporary supports. anchored area of 6.4 m, and a permanent support area of 6.4 m. Several displacement and stress monitoring points were strategically placed on the roadway roof at 1 m intervals to observe the numerical variations in roof plate stresses and displacements. Once the excavation was completed, the coupled numerical model of temporary support and permanent support was illustrated in Figure 11.  
The 3 DEC model constructed in this paper utilizes the Moore-Cullen tensile damage criterion.