# Behavior of Sedimentary Rock Tunnel against Rigid Projectile Impact
## 2 Impact Loading Simulation
### Input Properties of Materials  
The rock mass surrounding the tunnel has been considered as a nonlinear elastoplastic material. The Mohr-Coulomb failure model has been used to incorporate the nonlinearity of four different types of sandstones. The four sandstone rocks considered in the present paper are Jhingurda, Singrauli, Jannrani, and Kota. The input parameters are taken from [PERSON] et al. [27]. Table 1 represents the different physical and mechanical properties of rocks used in the present simulation.  
Figure 1: Geometry of finite element model for impact loading simulation. (**a**) Abaqus model of Missile, 0.7637 m in length and a mass of 100 kg with 5 Mach velocity (**b**) Tunnel with an opening of 7 m in diameter and supported by a reinforced concrete(M30) liner of 0.35 m in thickness. (**c**) The rock surrounding the tunnels of 50 m \(\times\) 50 m \(\times\) 50 m and 12.5 m of overburden depth.  
Similarly, the nonlinear behavior has been considered for steel bars by providing the elastoplastic properties of steel. Table 2 and Figure 2 show the properties of steel reinforcement used in this study. The interaction between the steel bars and concrete of the liner is achieved by embedding the circular and longitudinal reinforcement. The embedment constraint in the interaction module applied the proper bond between the steel and concrete, creating a reinforced concrete liner for the rock tunnel. The Johnson-Cook model [28] has been used for modelling the steel bars and properties are taken from [PERSON] et al. [29]. [PERSON] et al. [29] had performed a series of experiments on the steel under different strain rate and at varying temperature range.  
Moreover, the concrete liner has been considered as M30 grade and its nonlinear elastoplastic behavior has been simulated through the Concrete Damage Plasticity model. It also incorporated the damage characteristic of the concrete and, therefore, proved to be useful in studying the overall failure of the internal lining.  
The M30 grade of concrete has a mass density of 2500 kg/m\({}^{3}\) and a Young's modulus of 26.6 GPa, with a 0.20 Poisson's ratio. Moreover, the dilation angle and eccentricity of 31 degrees and 0.1, respectively, have been considered. The variation in stress and damage corresponding to strain for the M30 grade of concrete are shown in Figures 3 and 4, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Rock** & **Mass Density (kg/m\({}^{3}\))** & **Young’s Modulus (GPa)** & **Poisson’s Ratio** & **Friction Angle (Degree)** & **Cohesion (MPa)** \\ \hline Jhingurda & 1670 & 2.84 & 0.25 & 21.34 & 3.68 \\ Singrauli & 2310 & 4.31 & 0.29 & 27.11 & 10.47 \\ Jamrani & 2480 & 5.29 & 0.22 & 37.79 & 11.17 \\ Kota & 2310 & 14.02 & 0.21 & 43.42 & 20.93 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Four different sandstone rock surrounding the tunnel opening.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**(\(\varrho\)) (kg/m\({}^{3}\))** & **(E) (GPa)** & **(v)** & **A (MPa)** & **B (MPa)** & **n** & **C** & **Rate (s\({}^{-1}\))** \\ \hline
7850 & 200 & 0.33 & 490 & 807 & 0.73 & 0.0114 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Elastoplastic properties of reinforced steel with Weldox 460 E grade.  
Figure 2: Plastic behavior of steel reinforcement material.