# Behavior of Sedimentary Rock Tunnel against Rigid Projectile Impact
## 4 Results and Discussion  
Commercial software based on the finite element method, i.e., Abaqus/Explicit, has been used for modelling and analysis. Four different sandstone rocks, Jhingurda, Singrauli, Jamrani, and Kota, were considered. A generally used design specification for metro tunnels has been used based on Delhi Metro Rail Corporation designs. A missile having a 5 Mach velocity and weighing 100 kg has been considered. The simulation has been run for 30 milliseconds, which is the time required by a missile to hit the rock ground from 100 m away. Figure 5 has been plotted to compare the deformation variation with time when a missile hits the ground surface for all the sandstone rocks considered in the present study. It has been observed that the amplitude of deformation for Jhingurda sandstone is the maximum, having a magnitude of 2.45 m. Maximum deformations of 1.35 m, 1.03 m, and 0.76 m have been observed for Singrauli, Jamrani, and Kota rocks prospectively at the ground surface. Therefore, Kota sandstone has shown maximum resistance to missile penetration, while Jhingurda sandstone has the least resistance to missile penetration. The deformation profile is one of the important output results for understanding the internal behavior of a tunnel. Figure 6 shows the comparison of the deformation profiles of four sandstone rocks. The deformation profile for Jhingurda sandstone follows a smooth curvature, while the curvature becomes distorted and non-uniform for other types of sandstone. It has also been observed that as the strength of sandstone increases, the peak deformation gets decreased, while the length of tunnel under disturbance increases with the increase in the strength of sandstone. Moreover, a slight bulging has been observed in all the sandstones except for Jhingurda sandstone. Therefore, it may be concluded that weaker sandstone requires strengthening for a smaller area after an impact loading event, while high-strength sandstone will require repair for a longer portion of the tunnel. Figure 5: Variation in deformation with time to compare the ground surface behavior under impact loading of 100 kg missile. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Slab No.**} & \multirow{2}{*}{**Height (m)**} & \multicolumn{3}{c}{**Deformation (mm)**} & \multirow{2}{*}{**\% Cent Error**} \\ \cline{3-3} \cline{5-5}  & & **Experimental Study** & & & \\ \hline S4 & 1.0 & 46 & 44.39 & 3.5 \\ S5 & 1.5 & 63 & 61.74 & 2.0 \\ S6 & 1.5 & 50 & 47.00 & 6.0 \\ S8 & 1.0 & 60 & 57.00 & 5.0 \\ S9 & 1.2 & 61 & 59.17 & 3.0 \\ S10 & 2.0 & 77 & 73.15 & 5.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of results of properties of reinforced steel. Particle velocity is one of the significant output results in the dynamic loading analysis of rock tunnels. Therefore, the peak velocity at the ground surface of different sandstone rocks is shown in Figure 7 for comparison. The peak of the particle velocity graph has been observed at 20.41 milliseconds in each case of sandstone rock. However, the variation of particle velocity follows a separate path for different rocks, but the pattern of the particle velocity plot remains similar in all the cases. Figure 8 represents the peak acceleration at the ground surface when a missile hits the different sandstone rocks. In the case of Jhingurda sandstone, the magnitude of peak velocity and acceleration is greatest. Moreover, the pattern of variation in acceleration and velocity remains similar, and therefore, it is independent of the type of sandstone. Figure 8: Comparison of particle acceleration at ground surface under present impact loading condition. Figure 6: Comparison of deformation profile generated under the response of impact load. Figure 7: Comparison of particle velocity at ground surface under present impact loading condition. Figure 9 shows the deformation contours of Jhingurda, Singrauli, Jamrani, and Kota sandstone when a 100 kg missile moving at the velocity of 5 Mach hits the ground surface of the rock-containing tunnel.