## 2 Methodology
### Simulation of the Soft Rock Tunnel Supported by Bol  
As shown in Figure 7, a model of 100 m \(\times\) 100 m (X \(\times\) Z) was established, with the Y axis representing unit length. The excavation of the tunnel was circular with a diameter of 10 m. The tunnel axis corresponded to the Y axis, with the vertical upward direction defined as the positive Z axis. The mesh utilized 8-node hexahedral elements, resulting in a total of 1584 elements and 3170 nodes. The model is a two-dimensional model. The boundary conditions of the model were as follows: the top face was a free boundary, the two sides were subject to normal constraints, and the bottom face was fully fixed. The vertical stress was set at 10.75 MPa and the horizontal stress along the tunnel axis and the horizontal stress perpendicular to the tunnel axis were 12.90 MPa, with a lateral pressure coefficient of 1.2. Considering the focus on soft rock as the main research subject, the surrounding rock parameters were selected from the fourth category of surrounding rocks based on the standard for engineering classification of rock masses [38], as detailed in Table 1. The constitutive model and yielding criteria for the surrounding rock adopted the Mohr-Coulomb model. In this study, the term \"yielding bolt\" refers to the bolt used for anchoring purposes.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & **Length** & **Cross** & **Elasticity** & **Poisson** & **Tensile** \\  & **(m)** & **Sectional Area (m\({}^{3}\))** & **Modulus (GPa)** & **Ratio** & **Failure Strain** \\ \hline Conventional bolt & 6 & 5 \(\times\) 10\({}^{-4}\) & 200 & 0.25 & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The physical and mechanical parameters of the conventional bolt.  
Figure 6: Stretch bending model. The red line refers to the bolt.  
To investigate the support effects of the two bolt types in soft rock tunnel excavation, a planar strain model of a tunnel was established. The rock mass was first brought to the initial equilibrium under the original rock stress state, with initial displacements set to zero. The excavated portion was replaced by a null model, and the support was then implemented. For comparison, simulations were conducted using three approaches: Approach One involved no bolt application, Approach Two involved the use of standard bolts, and Approach Three involved the use of yielding bolts. (Refer to Tables 2 and 3 for the parameters.).  
To more intuitively and precisely reflect the influence of the bolts on the deformation distribution of the surrounding rock, reinforcement using bolts alone was implemented after partial stress release following tunnel excavation, and this was conducted without other combined support methods. The bolt support following tunnel excavation was radially and uniformly arranged, with radial spacing along the tunnel wall approximately 1 m apart, as illustrated in Figure 8. To provide a more intuitive representation of the surrounding rock deformation within the tunnel, 16 monitoring points were evenly distributed at positions such as the arch crown, arch shoulder, sidewalls, arch foot, and arch base during simulation, as depicted in Figure 9 and Table 4.  
Figure 8: Diagram of bolt support. The red lines refer to the bolts.  
Figure 7: Chart of the plane strain model. The two red lines refer to X axis and Z axis, respectively.