# Dynamically Triggered Damage Around Rock Tunnels: An Experimental and Theoretical Investigation
## 3 Experimental Results and Analysis
### Fracture Process of the Sample  
The photographs of the specimens captured by a high-speed camera were processed by the DIC technique to obtain the evolution of the surface deformation of the specimens during the dynamic loading process [13; 29]. The damage to the specimen at different times under dynamic loading and the final damage pattern are given in Figure 5. The figures clearly show that the deformation of the specimen starts at the edge of the hole, forming a strain concentration, due to the concentration of dynamic stresses. When the incident wave reaches the edge of the hole, scattering and refraction occurs at the edge of the hole, resulting in an increase and decrease in the local stress. Damage occurs first in the region of increased stress because the stress distribution at the edge of the hole is affected by the inclination angle, so the deformation distribution of the specimen is not the same under the same incident stress. Combining the deformation of the specimen, the stress-strain curve and the loading time curve, it is possible to obtain the deformation characteristics of the specimen under different dynamic stress states.  
Figure 4: (**a**) Dynamic strain–stress curve of the samples; (**b**) stress time curve during dynamic impact; and (**c**) variation of the specimens’ strength and modulus of elasticity with the hole inclination angle.  
It is visible in Figure 5 that a pronounced strain concentration occurs at the hole's edge at t = 62.5 us, and the corresponding stresses are determined in combination with the loading time curve to be 31.5 MPa, 27.5 MPa, 27.1 MPa, 27.3 MPa, and 23.4 MPa for the inclination angles of \(0^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), and \(90^{\circ}\), respectively. These values are much smaller than the static compressive strength of the specimen, but as a result of the dynamic stress concentration, the incident stresses are amplified and reach the strength limit of the rock, so that the initial fracture of the specimen is formed at the edge of the hole. The inclination of the hole in the specimen corresponds to different incident angles, which directly affects the stress distribution around the holes.  
The early failure of the hole edge is dominated by the stress concentration, and as loading continues, the specimen cracks penetrate to form an X-shaped fracture zone, which follows the same damage pattern as specimens containing a circular hole and crack defects [6; 16]. At the inclination of \(0^{\circ}\), the initial strain concentrations are formed at the top and bottom of the arch, and at inclinations of \(30^{\circ}\) to \(60^{\circ}\), the strain development followed a similar pattern at the side walls of the holes, with the tensile strain concentrations in the incidence direction, followed by the strain concentrations at the left foot of the arch and at the top of the arch. In the case of \(90^{\circ}\), the two side walls of the hole first experienced strain concentrations and then the crack initiated to penetrate the whole sample at this location.  
As can be observed in Figure 5, the strain concentrations are initially generated in the incident direction at the edge of the hole and in the proximal perpendicular incident direction before overall damage to the specimen occurs. The strain concentration in the incident direction can be identified as tensile strain. However, it is only at an inclination angle of \(90^{\circ}\) that the tensile strain develops into macroscopic tensile cracks. The final fracture pattern of the specimens is plotted in Figure 6.  
Figure 5: Major principal strain evolution of the holed samples.  
It is noticed that almost all the specimens are damaged due to crack initiation in the region of the strain concentration, and then the cracks develop and connect, eventually penetrating the whole specimen. In addition, the damage to the specimen is dominated by compressive shear, initially forming a localized shear region around the hole accompanied by debris ejection.