## 5 Conclusions  
Aiming at the typical engineering weak link of the cross tunnels of HSRs, this paper analyses the initial stress state of the intersection and the dynamic response characteristics of a structure under train load through numerical calculation and indoor fatigue test. This paper subsequently presents a method to determine the influence zoning of vibration. The following main conclusions are obtained through the aforementioned analysis:  
(1) The initial stress state and dynamic response at the cross point are substantially larger than that of an ordinary high-speed tunnel structure, especially the local position of the lining structure in the 20 m range near the intersection point. The initial stress state and dynamic response reach the level of the heavy-duty railway substrate. (2) The invert for the upper tunnel and arch for the lower tunnel have a higher stress level, either due to the just stratum load or the stratum load and the train load. Regardless of initial stress or dynamic stress, the lining concrete in the invert of upper tunnel shows a typical tensile status, and the lining concrete in the arch of the lower tunnel exhibits an evident compressive condition. (3) The increase in the initial stress state and tensile stress shows a coupling effect. A high initial stress state and tensile stress increment may greatly reduce the durability of the lining structure. (4) When the height of the rock pillar between the upper and the lower tunnels is less than that of the 3 m and the Grade IV surrounding rock, the tunnel lining may have a considerably strong influence \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Rock Level**} & \multirow{2}{*}{**Angle/\({}^{\circ}\)**} & \multicolumn{2}{c}{**Rock Thickness**} \\ \cline{3-4}  & & **Strong** & **Weak** & **None** \\ \hline \multirow{2}{*}{III} & 0–60 & - & \(H\leq 0.2D\) & \(H>0.2D\) \\  & 60–90 & - & \(H\leq 0.5D\) & \(H>0.5D\) \\ \hline \multirow{2}{*}{IV} & 0–60 & - & \(H\leq 0.4D\) & \(H>0.4D\) \\  & 60–90 & - & \(H\leq 0.7D\) & \(H>0.7D\) \\ \hline \multirow{2}{*}{V} & 0–60 & - & \(H\leq 0.8D\) & \(H>0.8D\) \\  & 60–90 & - & \(H\leq 1.1D\) & \(H>1.1D\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Influence zoning of high-speed railway (HSR) cross tunnels for train speed = 250 km/h. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Rock Level**} & \multirow{2}{*}{**Angle/\({}^{\circ}\)**} & \multicolumn{2}{c}{**Rock Thickness**} \\ \cline{3-4}  & & **Strong** & **Weak** & **None** \\ \hline \multirow{2}{*}{III} & 0–60 & - & \(H\leq 0.2D\) & \(H>0.2D\) \\  & 60–90 & - & \(H\leq 0.5D\) & \(H>0.5D\) \\ \hline \multirow{2}{*}{IV} & 0–60 & - & \(H\leq 0.4D\) & \(H>0.4D\) \\  & 60–90 & - & \(H\leq 0.7D\) & \(H>0.7D\) \\ \hline \multirow{2}{*}{V} & 0–60 & - & \(H\leq 0.8D\) & \(H>0.8D\) \\  & 60–90 & - & \(H\leq 1.1D\) & \(H>1.1D\) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Influence zoning of HSR cross tunnels for train speed = 300 km/h. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Rock Level**} & \multirow{2}{*}{**Angle/\({}^{\circ}\)**} & \multicolumn{2}{c}{**Rock Thickness**} \\ \cline{3-4}  & & **Strong** & **Weak** & **None** \\ \hline \multirow{2}{*}{III} & 0–60 & \(H\leq 0.5D\) & \(0.5D<H\leq 1.6D\) & \(H>1.6D\) \\  & 60–90 & \(H\leq 0.7D\) & \(0.7D<H\leq 1.8D\) & \(H>1.8D\) \\ \hline \multirow{2}{*}{IV} & 0–60 & \(H\leq 0.7D\) & \(0.7D<H\leq 1.8D\) & \(H>1.8D\) \\  & 60–90 & \(H\leq 1D\) & \(1D<H\leq 2D\) & \(H>2D\) \\ \hline \multirow{2}{*}{V} & 0–60 & \(H\leq 1.1D\) & \(1.1D<H\leq 2.2D\) & \(H>2.2D\) \\  & 60–90 & \(H\leq 1.4D\) & \(1.4D<H\leq 2.4D\) & \(H>2.4D\) \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Influence zoning of HSR cross tunnels for train speed = 350 km/h. area--that is, the service life of the invert of the upper tunnel under the train load may be lower than the design requirements. In this paper, a method is proposed to determine zoning based on numerical simulation and indoor model test.