## 4 Experiments and Analyses
### Forward Verification
#### 4.2.2 Developing the Tunnel Model  
To address the issue of crown uplift deformation observed in the Lianhua Tunnel, the excavation interval from YK37 + 330 to YK37 + 370 was chosen for analysis. Utilizing information from geological exploration reports among other sources, a 3D numerical model in Midas GTS NX 2024 (New eXperience of Geo-Technical analysis System) for excavating this section of the tunnel was developed, illustrated in Figure 7. The model measures 100 m along the \(X\)-axis, 40 m along the \(Y\)-axis, and 70 m along the \(Z\)-axis, with each model boundary being at least five times the tunnel's diameter away from the tunnel boundary itself, thereby satisfying numerical computation standards. The preliminary support structure is composed of steel arches, anchor bolts, and shotcrete, with anchor bolts represented by rod elements, shotcrete by plate elements, and steel arches by beam elements. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Test Number**} & \multicolumn{3}{c}{**Output Vector**} & \multicolumn{2}{c}{**Input Vector**} \\  & **c/kPa** & **\(\varphi\)/(\({}^{\circ}\))** & **E/GPa** & **\(\mu\)** & **Crown Settlement** & **Peripheral Convergence** \\ \hline
1 & 80 & 20 & 200 & 0.32 & 17.82 & 8.44 \\
2 & 80 & 22 & 250 & 0.34 & 14.28 & 6.74 \\
3 & 80 & 24 & 300 & 0.36 & 11.78 & 5.58 \\
4 & 80 & 26 & 350 &  
Model Layer Division: The geological construction and rock types mentioned in the project data led to a division of the model into two layers, the first being strongly weathered sandy shale and the second moderately weathered sandy shale. Material Characteristics of the Model: For the rock and soil, the Mohr-Coulomb model dictates the material parameters, while anchor bolts and shotcrete are modeled using an elastic framework. Shotcrete is applied in the model to a thickness of 30 cm, and the benching method is chosen for excavation. Boundary Conditions: The model's bottom is constrained in all directions, ensuring stability; the sides are restricted horizontally, promoting lateral support; the top remains an unrestricted boundary, allowing for natural adjustment. Mechanical Properties of Surrounding Rock and Tunnel Support Materials: Table 4 details the mechanical parameters used in this simulation for both the surrounding rock and the tunnel's support materials. In an effort to accurately model the unloading of rock pressure post-excavation, a construction scenario was implemented where initial support is applied at intervals of 2 m, closely aligned with the benching excavation method. Load release coefficients of 0.4, 0.3, and 0.3 were established to mimic the gradual release of the surrounding rock's load following excavation. To evaluate the validity and credibility of the parameters obtained from inversion, forward verification was conducted. Using the mechanical parameter combinations derived from the inversion results at section YK37 + 330, a corresponding forward simulation model was developed with Midas GTS NX 2024 software. The mechanical parameters of surrounding rock, as determined by the inversion model, were inputted into the forward model. This approach enabled the calculation of vault settlement and peripheral convergence displacement values for section YK37 + 330. The results, depicted in a displacement cloud diagram, are presented in Figure 8. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & **E/GPa** & \(\mu\) & **c/kPa** & \(\mathbf{\varphi}\)/(\({}^{\circ}\)) & **Unit Weight/kN/m\({}^{3}\)** \\ \hline First Soil Layer & 0.4 & 0.35 & 50 & 20 & 20 \\ Second Soil Layer & & & * & & 20 \\ Anchor Bolts/ & 210 & 0.3 & - & - & 78.5 \\ Steel Arches & 28 & 0.2 & - & - & 24 \\ Shotcrete & 28 & 0.2 & - & - & 24 \\ \hline \hline \end{tabular}  
*: To be inverted.  
\end{table} 
Table 4: Table of mechanical parameters of surrounding rock and support. Figure 7: Three-dimensional model diagram. The displacement from the numerical simulation's forward verification was compared with the actual measured displacement.