## 4 Creep Deformation Calculations and Predictions for Jinping Diversion Tunnels at Different Depths
### The Numerical Calculations and Results  
Based on the geological conditions along the Jinping diversion tunnel, a two-dimensional finite element model was established with the circular tunnel center as the origin. The model domain spans 100 m \(\times\) 100 m, employing coupled plane stress-pore pressure elements (CPE4P). To account for damage to the rock mass and large localized deformations during excavation, as well as the development of secondary fractures during the stress redistribution, fractured rock mass equivalent elements were used to simulate the mechanical behavior of the surrounding rock in the engineering disturbance zone, while intact rock elements were applied outside of this zone. The transient elastic parameters and the delineation of the engineering disturbance zone were referenced from existing studies [26]. The engineering disturbance zone was defined as 30 m \(\times\) 30 m. For the undisturbed rock mass, the elastic modulus was set to 28 GPa, Poisson's ratio was set to 0.2, and the permeability coefficient was set to 3.456 \(\times\) 10\({}^{-4}\) m/d (Table 2). For the disturbed rock mass, based on the findings in Section 3, the elastic modulus was reduced to 24 GPa (reflecting post-disturbance microcracking and damage), with Poisson's ratio maintained at 0.2 and the permeability coefficient increased to 3.456 \(\times\) 10\({}^{-3}\) m/d (Table 2). The creep parameters were calibrated using strain monitoring data (2012-2021) from Tunnel 1# of the Yalong River Hydropower Development Company. The simulation covered a 20-year creep period, with the strain states recorded every three months. The numerical calculation workflow included  
Step 1: Fixing the horizontal displacements at the lateral sides and the vertical displacements at the base. Applying the in situ stress, gravity, and seepage pressure to achieve ab initial stress equilibrium. Step 2: Computing the rock mass's equilibrium state under in situ stress conditions. Step 3: Simulating tunnel excavation to obtain instantaneous mechanical responses. Step 4: Calculating the creep behavior over 20 years after excavation. The stress distribution characteristics after excavation at different depths are shown in Figure 8. The results indicate that engineering disturbances disrupt the original stress state of the rock mass, forming distinct zones around the tunnel: a stress relief zone near the excavation, a stress concentration zone, and an undisturbed stress zone [34]. As the overburden depth increases, both the spatial extent and the magnitude of the stress concentration intensify. At a 1400 m depth, the minimum and maximum principal stresses near the tunnel are approximately 13 MPa and 76 MPa, respectively. At a 2400 m depth, these values increase to 22 MPa (minimum) and 130 MPa (maximum), with the maximum principal stress concentration at 2400 m being 1.71 times that at 1400 m. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **E/GPa** & \(\mathbf{v}\) & **k/m\(\cdot\)d\({}^{-1}\)** \\ \hline Undisturbed Rock Mass (Intact Marble) & 28 & 0.2 & 3.456 \(\times\) 10\({}^{-4}\) \\ \hline Disturbed Rock Mass & & & \\ (Fractured Marble) & 24 & 0.2 & 3.456 \(\times\) 10\({}^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters for numerical simulation of Jinping diversion tunnel. The strain states of the rock mass in the engineering disturbance zone after the excavation of the Jinping diversion tunnels are shown in Figure 9. The tunnel sections at different depths exhibit instantaneous compressive deformation on both sides due to in situ stress effects, minor tensile deformation at the tunnel crown, and localized shear strain once the tunnel is excavated. The total vertical strain in the 2400 m depth rock mass after an engineering disturbance is 1.46 times that at 1400 m, while the lateral expansion at the tunnel wall is 1.65 times higher at 2400 m compared to that at 1400 m, indicating that the impacts of engineering disturbances intensify with an increasing overburden depth.