# Safety Evaluation of Crossing Tunnel Engineering: A Case Study
## 3 Analysis of Highway Tunnel Safety
### Dynamic Response Analysis  
#### 3.4.1 Parameter Selection  
In dynamic analysis, several factors have an impact on the calculation results, including elastic modulus, damping parameters, spatial dimensions, blasting vibration intensity, and loading time. Accurate values of these parameters are essential to ensure that the calculated results closely reflect the real situation. Here are some considerations regarding two of these factors:  
(1) Elastic modulus: The elastic modulus significantly affects the calculation results. A higher elastic modulus of the rock mass leads to smaller vibration velocities at protected particles. Some researchers propose the concept of dynamic elastic modulus, suggesting that materials may exhibit an increased elastic modulus under the influence of blasting vibrations. However, many researchers do not consider dynamic elastic modulus in dynamic analysis. For safety reasons, this study adopts the static elastic modulus instead of the dynamic one. (2) Damping parameters: Damping parameters in the model are related to the rate of vibration velocity attenuation and have a significant impact on the calculation results. To ensure consistency between numerical calculations and actual measurements, damping parameters often require dynamic adjustment based on on-site monitoring data. There are two main approaches to input damping parameters in numerical calculations. One is to directly input the coefficients of Rayleigh damping, including the mass damping coefficient \(\alpha\) and the stiffness damping coefficient \(\beta\). The other approach involves conducting an eigenvalue analysis on the model to determine the inherent frequency of the structure and calculate the damping parameters based on the inherent frequency and damping ratio. Since there is no available on-site monitoring data on vibration velocity in this case, directly inputting damping parameters \(\alpha\) and \(\beta\) lacks a basis for value determination. Therefore, this study adopts the approach of inputting damping ratio and inherent period of the structure to generate damping parameters. The inherent period can be obtained through an eigenvalue analysis. Previous literature suggests that the damping ratio in this model can be set within the range of 0.02-0.05. For safety considerations, a damping ratio of 0.02 is chosen for this calculation. It is worth noting that the other factors mentioned, such as spatial dimensions, blasting vibration intensity, and loading time, should also be carefully considered and accurately valued to ensure the reliability of the dynamic analysis results. (3) blasting load intensity: According to the different effects of blasting on rock mass, the blasting action range can be divided into near field, middle field, and far field. The near field is the area where rocks are crushed by blasting, while the middle field often produces fracture damage to the rock mass. In the far field, the rock mass only undergoes elastic vibration due to blasting. According to the requirements of tunnel construction, the surrounding rock of the tunnel should not be damaged during blasting, and the surrounding rock is in an elastic vibration state when establishing the vibration model of the tunnel excavation blasting, with the following simplified assumptions: 1 the blasting vibration load acts on the tunnel perimeter wall in the form of uniformly distributed pressure load in the normal direction; and 2 the tunnel perimeter wall is in the far field of blasting action, and the blasting vibration load on the tunnel perimeter wall will not cause surrounding rock damage. blasting load has a significant impact on the calculation results,with larger blasting peak loads applied to the tunnel wall resulting in greater vibration velocities at protected particles. For concentrated charge or single-hole cylindrical charge, wave theory can be used to accurately calculate the initial peak stress of blasting on the borehole wall and thus calculate the blasting vibration.