## 4 Analysis of Results  
### Vibration Velocity of the Existing Lining  
The vibration velocity is usually selected to evaluate the performance of the tunnel in a dynamic analysis [26; 27; 28]. Compared with the internal forces of the tunnel, the vibration velocity is more easily monitored in both numerical analysis and practice. Additionally, the threshold value of this indicator has been specifically stipulated in a related technical code. As a consequence, the blasting-induced vibration velocity of the tunnel is first analyzed herein. Figure 7 displays the distribution cloud diagram of the existing tunnel's lining vibration velocity at various times when the excavation face is situated 10 m away from it. The figure provides evidence that tunnel blasting generates shock waves. These shock waves travel towards the tunnel wall near the blasting face, resulting in vibration in that particular area. The vibration of the tunnel wall at that location gradually increases with the continuous blasting until it reaches its maximum value and gradually propagates along the tunnel axis, as observed over time. Over time, the vibration waves progressively spread towards both ends of the tunnel. However, it is worth noting that the peak value of the synthesized vibration, after superimposition, becomes weaker compared to the initial time. During blasting operations, the vibration response is more prominent on the side where the blasting is executed, while the perpendicular side experiences a less intense vibration response. Thus, the side perpendicular to the blasting location is a potentially dangerous zone, and it requires special attention to maintain safety in this area. The most unfavorable section of the existing tunnel depicts the vibration velocity distributions as presented in Figure 8. As shown in the figure, the transverse tunnel blasting has a noticeable impact on the bending area on the right side of the tunnel. Consequently, the peak vibration velocity of the lining at this specific position can be utilized as a control index. This index helps guide the blasting construction of the new transverse passage and ensures its proper management. In the latter phase of the blasting load, the tunnel floor also exhibits a certain degree of vibration response. When \(t\) = 6 ms, the maximum vibration velocity of the lining in the right arch waist area due to blasting was 2.63 cm/s. Figure 6: Equivalent blasting load curve of satellite holes at the upper bench. However, this value is lower than the standard control value of 8-10 cm/s as recommended in reference [29]. The velocity-time curves of characteristic points at the most vulnerable section are illustrated in Figure 9. As observed from the figure, the vibration response during blasting is the most severe at the lower arch position of the tunnel, owing to its proximity to the blasting source. According to the calculation result, in the whole process of the blasting load, the vibration at points C and D on the right side of the tunnel is the strongest. The maximum vibration velocity of 2.96 cm/s was observed at point D around 10.5 milliseconds after blasting. Subsequently, the vibration inside the tunnel reduced significantly after 80 milliseconds of blasting. Figure 10 shows the velocity-time curves of characteristic point D in all directions. As can be seen from the figure, the value of the vibration velocity at the most unfavorable position of the blasting side lining is \(Vx>Vz>Vy\). The blasting vibration velocity along  
Figure 8: Vibration velocity distributions at the most unfavorable section of the existing tunnel. Figure 7: The contour of the resultant vibration velocity distribution of the existing tunnel (units: m/s). Figure 9: Velocity–time curves of characteristic points at the most unfavorable section. the y direction is almost negligible, while the x direction exhibits the highest vibration velocity. Hence, it is crucial to enhance the monitoring of radial vibration velocity during tunnel construction.