# Dynamically Triggered Damage Around Rock Tunnels: An Experimental and Theoretical Investigation
## 3 Experimental Results and Analysis
### Damage Around the Arched Hole Under Impact  
In the previous analysis, the sandstone specimen with an arched hole was considered a unified entity, focusing on the overall damage caused by dynamic impact. The mechanical properties of the flawed rock formation can be assessed using one-dimensional stress wave theory, such as the three-wave method, to obtain its stress-strain curve. This approach has been adopted by many researchers to determine the influence of cracks, holes, and other defects on the overall load-bearing capacity and damage mode of the specimen. While this is valuable for evaluating the strength of the rock formation, it may not provide a clear assessment of the dynamic stability of underground spaces. Therefore, in addition to analyzing the overall dynamic response of the specimen, our focus extends to examining the deformation and destabilization characteristics of the arched hole under dynamic impact. This is approached as a two-dimensional problem, considering the stress wave scattering and dynamic stress concentration in the surrounding rock of the tunnel. The surrounding rock damage characteristics of the arched hole, determined through indoor experiments, provide further insights into the deformation and damage patterns of rock tunnels with arch-shaped sections exposed to dynamic perturbations. This understanding is crucial for revealing the dynamic damage mechanism of rock tunnels in underground spaces. Figure 7 illustrates the captured damage process at the edge of the hole. In Figure 7, the observed rock damage at the edge of the hole is categorized into the following types:  
1. [label=()]
2. Heaving, which is manifested when the top and bottom of the specimen experience significant compressive stress at a 0\({}^{\circ}\) incident angle. Under this condition, the bottom is compressed and protrudes toward the center free surface, resulting in the formation of a heave. 3. Rock ejection, which is observed in almost all cases, primarily at the top of the arch, the arch shoulder, and the foot of the arch. This rock ejection is a result of the progressive accumulation and subsequent release of strain energy around the circumference of  
Figure 6: Final fracture pattern of the samples (the red arrows represent tension, while the yellow arrows represent shear, and the direction of the arrow indicates the direction of the force). the arched hole during dynamic impacts. A portion of this energy is converted into kinetic energy, resulting in the ejection of rock debris [30]. * Spalling, which occurs in the side walls, is induced by the same mechanism as (I). This is a consequence of an elevation in the circumferential compressive stress [31] during dynamic disturbances. A stress gradient is formed within a localized area, causing deviations in the direction of principal stresses. This ultimately leads to the spalling of surrounding rock from areas experiencing higher stress levels. The five different cases are classified into three major categories based on the incident direction of the dynamic disturbances: horizontal incident, inclined incident, and vertical incident. In these three scenarios, severe compressive-shear failure always occurs perpendicular to the incident direction in the arched hole. Radial tensile strain is evident in the early stages of loading on the incident side, and macroscopic tensile cracks only form in the 90\({}^{\circ}\) incident case. Due to the small ratio between the specimen size and the incident wavelength used in the experiments, radial tensile stress concentrations are not generated in such cases, and radial tensile stresses tend to occur at wavelengths 3-5 times the radius of the hole [3; 32]. In the vast majority of cases, the ejection of rock debris occurs during the initial stages of loading. As the loading progresses, these areas of rock debris ejection further evolve and contribute to the formation of the macroscopic damage pattern described earlier.