# Dynamically Triggered Damage Around Rock Tunnels: An Experimental and Theoretical Investigation
## 1 Introduction  
Arched tunnels are commonly encountered section layout formations in various engineering projects, such as underground tunnels, mining operations, and hydraulic engineering [1]. When artificial and natural dynamic disturbances are encountered in these facilities, stress wave scattering occurs in the surrounding area and causes the migration and aggregation of stress and energy [2, 3], which, in severe cases, induces failures that threaten the safety of personnel and the stability of the tunnel, resulting in economic and property losses [4, 5]. Therefore, understanding the failure characteristics and dynamic stress distribution around these tunnels is crucial for ensuring their stability and the safety of surrounding structures. The failure of arched tunnels under dynamic impacts has been a subject of great interest and importance in the field of geotechnical engineering. Dynamic impacts can result from various sources, including earthquakes, blasting operations, and sudden loads during construction activities [6, 7]. The behavior of arched tunnels under such dynamic loadingconditions is significantly different from their response under static loading. It is generally known that dynamic loading is typically time-dependent, whereas static loading is considered time-independent [3]. In addition, the strain rate dependence of rock materials and the multiple sources of dynamic disturbances make it more challenging to estimate the dynamic failure around tunnels [8]. Nevertheless, numerous studies have been conducted to investigate the dynamic failure characteristics of arched tunnels and provided valuable insights into the failure mechanisms, energy dissipation, and stress redistribution around tunnels. The complex function method has been extensively applied to address the scattering and dynamic response problems around a hole or tunnel. Theoretical calculations of the dynamic stress distribution around the hole concentrate on the steady-state conditions. A limited number of scholars have reported on the transient dynamical response of tunnels, with a majority of studies focusing on a circular hole, and the results pointed out that the maximum stress concentration achieved around a circular hole under the action of transient P-waves is approximately 2.85-3, depending on the Poisson's ratio, which is about 10% higher than that in a steady-state condition [9; 10]. Theoretical studies revealed the scattering of stress waves and the stress distribution around the tunnels, whereas experiments are able to visualize the damage evolution under dynamic impacts, especially with the improvement of experimental techniques, high-speed photography and DIC technology, which help to capture and visualize the strain and damage evolution during the loading process [11; 12; 13]. [PERSON] et al. [14] conducted an evaluation of the dynamic rupture of circular and square holes. They utilized the SHPB test system and further examined the impact of prestressing on the damage to the specimens, with the results showing that as the prestress increased from 0 to 20 MPa, the failure mode around the hole transitioned from tensile to shear, with significant shear failure occurring at 20 MPa. [PERSON] et al. [15] conducted both experimental and numerical simulations to explore the dynamic damage characteristics of granite specimens containing arched holes and unexposed joints subjected to dynamic impact. The findings revealed that the inclination angle of the joints markedly influenced the rockburst of arched rock tunnels and the joint angles of 56\({}^{\circ}\) and 134\({}^{\circ}\) have a more severe impact on the failure of the specimens. Previous studies have shown that under dynamic impact, pronounced tensile strain concentrations and even macroscopic tensile cracks occur on the incident side of the hole, while compressive shear failure occurs in the perpendicular incidence direction [14; 15; 16; 17].