## 5 Numerical Analysis of the Supporting Performance of the Spatial Reticulated Shell  
### Numerical Calculation Model  
The plastic damage model of ABAQUS can be used to analyze the plastic damage range of concrete and the stress state of the supporting arch in the primary supporting structure of the tunnel [25], and then obtain the numerical solution of the supporting performance of the SRS arch and grid arch. The calculation model simulates the surrounding rock range of 80 m \(\times\) 60 m \(\times\) 60 m. According to the site geology and actual construction conditions, the stress and strain state of the primary support under the surrounding rock load is simulated.  
The mesh generation of the overall and detailed models is shown in Figure 18. The upper boundary of the model is established to the surface, the bottom constrains the displacement in the X, Y, and Z directions, the two sides constrain the displacement in the X direction, and the front and rear constrain the displacement in the Z direction. Different colors indicate different formation conditions, which are divided into five types of formations, from top to bottom are miscellaneous fill, mucky soil, silty medium-coarse sand, sandy clay, and moderately weathered granite. The three-dimensional models of the SRS arch and grid arch are made with the help of relevant software, and then imported into ABAQUS for parameter assignment and calculation. In the model, the three-node quadratic space beam element (B32) is used for the steel tube and steel bar, the eight-node linear hexahedron nonconforming element (C3 DBI) is used for the concrete spray layer, and the eight-node reduced integration element (C3D8R) is used for the surrounding rock. The steel skeleton and shotcrete are modeled separately, and the embedded function is used to establish the connection between them to achieve the effect of common deformation.  
Figure 17: Bending moment-steel tube strain relationship curves of the \(1/8\) section of the jointless component.  
The geotechnical parameters of the formation are shown in Table 3, which are from the engineering geological survey report. The Mohr-Coulomb elastic-plastic model is adopted for the stratum, and the bilinear follow-up strengthening model is selected for the constitutive relationship of steel tubes and steel bars, which conforms to the [PERSON] criterion [26].  
The specific types of steel material in numerical simulation are shown in Table 4, and the mechanical properties of the steel materials are shown in Table 5. In addition, the elastic modulus of the mortar bolt is 200 GPa, the bulk density is 78.5 kN/m\({}^{3}\), and the Poisson's ratio is 0.3. The elastic modulus of C25 shotcrete is 23 GPa, the bulk density is 24  
\[x=\varepsilon/\varepsilon_{\rm t} \tag{2}\] \[y=\sigma/f_{\rm t} \tag{3}\]  
where \(\varepsilon_{\rm t}\) denotes the peak strain of the uniaxial tensile stress-strain curve; \(\alpha_{\rm t}\) is the parameter value of the falling section of the uniaxial tensile stress-strain curve; and \(f_{\rm t}\) is the uniaxial tensile strength of the concrete. The concrete tensile stress-strain curve is shown in Figure 19a.
2. Compressive stress-strain relationship of the concrete \[y=\left\{\begin{array}{l}\frac{nx}{n-1+(x)^{\rm r}},x\leq 1\\ \frac{x}{\alpha_{\rm c}(x-1)^{\rm 2}+x^{\rm r}},x>1\end{array}\right\}\] (4) \[n=\frac{E_{\rm c}\varepsilon_{\rm c}}{E_{\rm c}\varepsilon_{\rm c}-f_{\rm c}}\] (5) \[x=\varepsilon/\varepsilon_{\rm c}\] (6) \[y=\sigma/f_{\rm c}\] (7)  
where \(\varepsilon_{\rm c}\) denotes the peak strain of the uniaxial compressive stress-strain curve; \(\alpha_{\rm c}\) is the parameter value of the falling section of the uniaxial compressive stress-strain curve; and \(f_{\rm c}\) is the uniaxial compressive strength of the concrete. The concrete compressive stress-strain curve is shown in Figure 19b.