# Stress Analysis and Spalling Failure Simulation on Surrounding Rock of Deep Arch Tunnel
###### Abstract  
To study the stress distribution characteristics of surrounding rock and the spalling mechanism of deep hard rock tunnels with different arch heights, the complex variable function and angle-preserving transformation method in elasticity theory were applied to the analytic solution of tangential stress distribution of arch tunnels during stress adjustment. In addition, true triaxial tests were conducted on granite cube specimens (100 mm \(\times\) 100 mm \(\times\) 100 mm) containing holes with three arch heights (including the 25 mm semi-circular arch, 16.7 mm three-centered arch, 12.5 mm three-centered arch) to simulate the spalling process under different initial ground stresses. The stress distribution solution and experimental results show that the initial failure stress of arch holes is 0.39-0.48 times the uniaxial compressive strength (UCS) of the rock. The initial failure location occurs at the arch foot, where tangential stress maximizes. When the lateral pressure coefficient is in the range of 0.38-0.50, the tangential stress is 3.2-3.5 times the UCS. The rock debris of the hole wall are in thin flake shapes. Symmetrical V-shaped or curved failure zones occurred on hole sidewalls. The stress distribution resolution of the surrounding rock of tunnels with different arch heights shows that with the increasing burial depth, the bearing performance of the semi-circular arch tunnel is optimal. In addition, the maximum tangential stress increases as the height of the arch decreases or the lateral stress increases, making it easier for the initial failure to occur at the foot of the arch. surrounding rock stress; different arch heights; deep hard rock; tunnel; spalling; true triaxial test +
Footnote †: journal: Medical  
reported that spalling failure mostly occurs in the direction parallel to the maximum principal stress [20; 21; 22], by analyzing the surrounding rock stress when the tunnel spalling or rockburst occurs, these underground disasters can be further guided and controlled. Stress analysis of the surrounding rock of tunnels containing holes has been systematically studied by scholars [24; 25; 26; 27; 28; 29; 30]. For example, in terms of arch tunnels, [PERSON] et al. [31] analyzed the shape and size effect caused by the variation of geometric parameters of straight-walled three-centered arch tunnels on the surrounding rock stresses based on the analytical solutions obtained from the conformal mapping. [PERSON] et al. [32; 33] revealed the crack evolution mechanism of the inverted \"U-shaped\" cavity under uniaxial stress and investigated the mechanical response behavior of horseshoe openings in a cylindrical rock model under biaxial compression through stress distribution analysis. [PERSON] et al. [34] used the complex variable theory to study the stress distribution in rock bodies containing complex-shaped holes and found that the hole shape affects the stability of rock containing holes mainly by influencing the degree of stress concentration around the hole. In addition, a large number of indoor simulation experiments have been carried out on specimens containing prefabricated circular, elliptical, and rectangular holes [35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45]. For rocks containing arched holes under uniaxial compression, [PERSON] et al. [46] performed rockburst tests on straight-walled semi-circular arch tunnels and observed that the specimens showed an obvious splitting rockburst phenomena as a whole. They also obtained the range of stress-intensity ratios for splitting rockburst. As the stress-intensity ratios increased, the main failure developed into a shear failure. For the biaxial compression test, [PERSON] et al. [47] conducted a physical model test to investigate the deep hard rock spalling in horseshoe tunnels and observed that micro-cracks and swelling first appeared on the surface of sidewalls. Then, cracks continued to expand and combine to produce thin rock sheets and spalling in a laminar fashion from shallow to deep.