# Analysis and Application of Lining Resistance to Water Pressure in Tunnel through Karst Cave
## 2 Failure Mode of Grouting in Tunnels Crossing High-Pressure Karst Caves
### Failure Characteristics of Grouting in Tunnel Crossing the High-Pressure Karst Cave
#### 2.1.2 Results of Numerical Calculations  
According to the numerical simulation calculation results, the damage pattern results of typical steps were extracted, as shown in Figure 2, corresponding to steps 1-1, 2-1, 10-1, 19-1, 26-1, 26-5, 26-8, and 26-9, with water pressures of 0.1 MPa, 0.11 MPa, 0.19 MPa, 0.28 MPa, and 0.35 MPa, respectively. It can be observed in Figure 2 that, because the initial state of the cavity had 0.1 MPa water pressure, a circular stress zone was distributed around the cavity before the excavation of the existing parallel heading, and no structural damage occurred in the grouted stone body between the cavity and the parallel heading at this time. After the excavation of the existing parallel heading, the original stress balance was broken, and stresses were redistributed around the tunnel, on both sides of the tunnel, as well as at the top and bottom of the arch. In addition, at this time, a very obvious stress concentration appeared in the grouted stone body, and a new stress equilibrium state was finally reached under the influence of the mutual coupling of force and flow fields. Then, with the increase in water pressure inside the cavity, microcracks began to be generated  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Materials**} & **Elastic Modulus (GPa)** & \multirow{2}{*}{**Poisson’s Ratio**} & **Angle of Internal** & \multirow{2}{*}{**Permeability**} & **Cohesion** & **Gravity** \\  & & & & **Friction (\({}^{\circ}\))** & **Coefficient (m/Day)** & **(MPa)** & **(kN/m\({}^{3}\))** \\ \hline Rock & 0.48 & 0.3 & 35 & 0.044 & 0.05 & 20 \\ Grouting & 2.0 & 0.35 & 35 & 0.00443 & 0.065 & 24 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Calculation parameters of the RFPA model.  
Figure 1: Diagram of the numerical calculation model for the damage of the grouted body.  
on one side of the grouted stone body inside the tunnel, and, as the stress concentration on both sides of the grouted stone body further increased, coupled with the minimum restraint on both sides of the grouted stone body, a macroscopic main crack connecting the bottom of the tunnel arch and the interior of the cavity was gradually extended through, and another main crack extending from the interior of the cavity to the right arch of the tunnel was also gradually extended. Eventually, the grouted stone body collapsed to the interior of the tunnel as a whole with the two main cracks as the slipping surface, and the stone body was completely destroyed.  
When the surrounding rock unit underwent brittle damage, the elastic energy released from the rock body was released externally in the form of acoustic emission; hence, the acoustic emission characteristics of the rock could reflect the process of rock rupture. The calculated acoustic emission at a typical loading step is shown in Figure 3. A light color in the acoustic emission diagram indicates that the compression damage occurred in the rock unit, and a dark color indicates that the tensile damage occurred in the rock unit. From Figure 3, it can be seen that, after the parallel heading initially expanded the tunnel, as the water pressure in the cavity continued to rise, the grouted rock unit first appeared as a compression shear damage unit; then, as the water pressure in the cavity gradually increased, the compression shear damage unit gradually decreased. When the water pressure in the cavity rose to 0.35 MPa, the grouted rock unit presented cracks, which were mainly caused by tensile shear damage.  
Figure 3: Acoustic emission diagram of the model shown in Figure 1 at different steps: (**a**–**h**).  
Figure 2: Numerical calculation results of the damage model of the grouted body under the influence of a water-rich cave: (**a**–**h**).