# Study on the Damage Process and Numerical Simulation of Tunnel Excavation in Water-Rich Soft Rock
## 5 Validation of the Simulation Method Based on Dual Softening Effect
### Model Building  
Considering the convenience of modeling and computational efficiency, our model only simulates the 20 m surface loose body and 100 m buried rock stratum, and 5670 kPa vertical load is applied at the junction of the loose body and surrounding rock stratum to replace the unmodeled 170 m surrounding rock stratum. The model size and geometric arrangement are shown in Figure 15. The left and right boundaries of the model constrain the horizontal displacement, the bottom boundary constrains the vertical displacement, and the top is the free surface. The tunnel cross-section is in the form of a three-centered circle with a supine arch, with a span of 12.5 m and a height of 10.2 m. The distance between the left, right and bottom boundaries and tunnel is greater than six times the size of the tunnel, so the boundary effect can be ignored.  
The steel arch of initial support is modelled utilizing the equivalent elastic modulus. The load release coefficient of the surrounding rock is used to allocate the proportion of the load borne by the initial support and secondary lining. According to the recommended value of load sharing ratio for the two-lane tunnel in the Highway Tunnel Design Specification (JTG3370.1-2018) [67] and the comprehensive consideration of engineering experience, it is determined that surrounding rock, initial support, and secondary lining bear 10, 30, and 60% of the ground load, separately. The lateral pressure coefficient is taken as 0.8 due to the poor integrity of the weak surrounding rock. In combination with the recommended values in the engineering geological survey report and the Highway Tunnel Design Specification, the material mechanical parameters in the simulation are determined as shown in Table 1.  
Figure 14: Softening and collapse area of surrounding rock behind the arch.  
In the simulation, the permeability coefficient \(k_{D}\) of surrounding rock after tunnel excavation is adopted according to Equations (32) and (33). Referring to the physical and mechanical parameters of the site limestone statistics in Sections 2.3 and 2.4, the parameters required for calculating the damage field in the simulation are given in Table 2. Due to the extremely developed fractures, large groundwater influx, and the obvious disintegration of the surrounding rock at the site, the damage deterioration of each parameter is taken as the larger value in the range.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \begin{tabular}{c} **Weight** \\ **\(\gamma\) (kN/m3)** \\ \end{tabular} & \begin{tabular}{c} **Deformation** \\ **Modulus E** \\ **(GPa)** \\ \end{tabular} & \begin{tabular}{c} **Poisson’s** \\ **Ratio \(\mu\)** \\ \end{tabular} & \begin{tabular}{c} **Internal** \\ **Friction** \\ **Angle \(\varphi\)** (\({}^{\circ}\)) \\ \end{tabular} & \begin{tabular}{c} **Adhesion** \\ **c (kPa)** \\ \end{tabular} & \begin{tabular}{c} **Initial** \\ **Permability** \\ **Coefficient** \\ **\(k_{0}\)(cm/s)** \\ \end{tabular} & \
\begin{tabular}{c} **Height/** \\ **Thickness** \\ **(m)** \\ \end{tabular} \\ \hline
\begin{tabular}{c} Overlaying \\ Loose Body \\ Surrounding Rock \\ Initial Support \\ \end{tabular} & 17.5 & 0.04 & 0.45 & 25 & 10 & \(1\times 10^{-4}\) & 20 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical and mechanical parameters of materials in simulation.  
Figure 15: Calculation model of the typical section of the Xujiadi tunnel.