## 4 Numerical Simulation
### Parametric Study of Controls
#### 4.4.3 Overall Analysis  
The comparative analysis of horizontal acceleration and maximum reduction amplitude of principal stress of the tunnel under different grouting thickness of surrounding rock and shock absorbing layer thickness conditions is presented in Table 5.  
The comparative analysis showed that grouting in the surrounding rock significantly reduced the principal stress and acceleration of the tunnel structure, while the installation of a shock absorbing layer notably reduced the stress of the tunnel, albeit with an increase  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Parameters**} & \multicolumn{3}{c}{**Grouting Thickness of Surrounding Rock**} & \multicolumn{3}{c}{**Shock Absorbing Layer Thickness**} \\ \cline{3-10} \multicolumn{2}{c}{} & **2 m** & **4 m** & **6 m** & **10 cm** & **15 cm** & **20 cm** & **30 cm** \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Horizontal \\ acceleration \\ \end{tabular} } & Maximum & \multirow{4}{*}{\(-20\%\)} & \multirow{4}{*}{\(-24\%\)} & \multirow{4}{*}{\(-31\%\)} & \multirow{4}{*}{\(17\%\)} & \multirow{4}{*}{\(21\%\)} & \multirow{4}{*}{\(23\%\)} & \multirow{4}{*}{\(46\%\)} \\  & reduction & & & & & & & \\ \cline{1-1} \cline{6-10}  & ratio/\% & & & & & & & \\ \cline{1-1} \cline{6-10}  & Appearance & \multirow{4}{*}{Arch foot} & \multirow{4}{*}{Arch foot} & \multirow{4}{*}{Arch foot} & \multirow{4}{*}{Inverted arch} & \multirow{4}{*}{Arch foot} & \multirow{4}{*}{Inverted arch} & \multirow{4}{*}{Arch foot} & \multirow{4}{*}{Inverted arch} \\  & position & & & & & & & \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Principal \\ stress \\ \end{tabular} } & Maximum & \multirow{4}{*}{\(-68\%\)} & \multirow{4}{*}{\(-65\%\)} & \multirow{4}{*}{\(-73\%\)} & \multirow{4}{*}{\(-60\%\)} & \multirow{4}{*}{\(-61\%\)} & \multirow{4}{*}{\(-62\%\)} & \multirow{4}{*}{\(-65\%\)} \\  & reduction & & & & & & \\ \cline{1-1} \cline{6-10}  & ratio/\% & & & & & & \\ \cline{1-1} \cline{6-10}  & Appearance & \multirow{4}{*}{Inverted arch} & \multirow{4}{*}{Inverted arch} & \multirow{4}{*}{Inverted arch} & \multirow{4}{*}{Inverted arch} & \multirow{4}{*}{Inverted arch} & \multirow{4}{*}{Inverted arch} \\  & position & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Analysis of numerical results.  
in acceleration. The existence of a damping layer may lead to a decrease in the impedance of the medium in the outer extension region of the tunnel lining, consequently amplifying the acceleration response. Nonetheless, the stress response of the lining is mitigated due to the diminished deformation modulus in this zone. Both grouting in the surrounding rock and the installation of a shock absorbing layer had a stronger control effect on principal stress than on acceleration, with the maximum reduction amplitudes being 73% and 65%, respectively. The maximum amplitude of principal stress was located at the inverted arch, whereas the maximum amplitude of acceleration was situated at the arch foot and inverted arch. These findings warranted increase attention in practical applications.  
Through comparing and analyzing the distribution of peak principal stress and acceleration in tunnel structures under varying operational parameters, it is observed that as the thickness of the damping layer increases, there is a decrease in the peak value of the first principal stress. Meanwhile, the reduction amplitude of the third principal stress peak initially decreases and then increases with thickness. Opting for a 20 cm thick shock absorber layer provides superior shock absorption benefits. A thicker grouting layer results in a greater reduction in peak principal stress. Notably, the seismic resistance effect is more pronounced for grouting thicknesses ranging from 4-6 m, with a recommended thickness of 6 m for optimal application.