# Influence Law of Foundation Pit Excavation on Stress of Surrounding Tunnel Bolt
## 2 Numerical Calculation Model  
The study in this paper was mainly implemented by FLAC3D, developed by ITASCA [30]. Based on the finite difference method, it can describe the three-dimensional constitutive  
Figure 1: Tunnel support structure cracking caused by surrounding foundation pit excavation. model of the soil and engineering materials. According to the mechanical characteristics of the simulation and calculation analysis, the material elastic-plastic change or flow process is accurately simulated in FLAC3D, which is widely used in the calculation and analysis of tunnel, slope, mine, chamber, and other geotechnical engineering [31]. Specific solution flow and modeling steps were presented in detail by [PERSON] and [PERSON] [32]. By taking the excavation of a certain foundation pit as an example, the original geomorphic unit of the site is an alluvial river terrace, and the soil calculation parameters can be obtained according to the site survey report [3,33], which is presented in Table 1. It should be pointed out that, in the excavation problem, soil deformation is also affected by soil water content or soil suction [34]; however, it was ignored in this paper. The interaction between the tunnel and the foundation pit was the focus of this paper. Along the length direction of the site, a 6 m inner diameter tunnel passes through the whole site. A bolt is currently widely used in tunnel engineering; when the tunnel deforms, the bolt also deforms and produces support stress [35]. Therefore, the deformation stability of the tunnel can be reflected by monitoring the stress change in the bolt [36,37]. The numerical calculation model was established, as shown in Figure 2a, and the Mohr-Coulomb criterion was assigned to the model [38]. In modeling, the mesh around the tunnel was encrypted because the tunnel was the focus of the investigation. The model contains 8056 grids with 16,486 nodes. The left and right sides of the model are constrained by the normal boundary conditions, and the bottom of the model is constrained by the displacements in three directions. The diameter of the tunnel is 6 m, and the depth is 6 m.  
Due to the existence of a tunnel next to the foundation pit, the soil surrounding the foundation pit deforms into the foundation pit due to the excavation unloading during the process of foundation pit excavation, which causes the deformation of the tunnel. The supporting structure of the tunnel can ensure the deformation stability of the tunnel, so it is necessary to study the stress of the tunnel bolt supporting structure caused by the excavation of the foundation pit. Concrete spraying is carried out after the bolt layout. The calculation parameters of tunnel bolt, mortar, and shotcrete are shown in Tables 2 and 3[3,33]. The bolt used seven nodes and six elements, which are numbered from 1 to 6. The no. 1 element is closest to the edge of the tunnel, and the No. 6 element is furthest away from the edge of the tunnel [3,33], as shown in Figure 2. \begin{table}
\begin{tabular}{c c c c c} \hline
**Cohesion (kPa)** & **Internal Friction Angle (\({}^{\circ}\))** & **Unit Weight (kN/m\({}^{3}\))** & **Deformation Modulus (MPa)** & **Poisson Ratio** \\ \hline
300.0 & 25.0 & 20.0 & 50.0 & 0.35 \\ \hline \end{tabular}
\end{table} 
Table 1: Calculation parameters of site soil. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Bolt Diameter** & **Bolt Area** & **Slurry Diameter** & **Slurry Perimeter** & **Tensile Strength of Bolt** & **Prestressing of Bolt** \\ \hline
22 mm & 3.50 cm\({}^{2}\) & 100 mm & 0.314 m & 250 kN & 60 kN \\ \hline Bolt length & Slurry cohesion & Slurry friction & Slurry rigidity & Bolt number & Angle between bolts \\ \hline
3 m & 20 kPa & 25\({}^{\circ}\) & 22.33 MN/m\({}^{2}\) & 21 & 9\({}^{\circ}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of bolt.