# Stress Analysis and Spalling Failure Simulation on Surrounding Rock of Deep Arch Tunnel
## 5 Conclusions  
In this paper, stress analysis of surrounding rock and the true triaxial simulation tests were carried out on hard rock tunnels with different arch heights (or rise-span ratios). The following conclusions are obtained:  
1. The stress distributions of the surrounding rock of the tunnel with three arch heights are consistent. With the adjustment of vertical stress, when \(\sigma_{Z}>30\) MPa, the tensile stress appears on rise-span ratios of \(f/B=1/4,f/B=1/3,f/B=1/2\) arch tunnel in order at the floor middle, while tensile stress appears at the arch top after \(\sigma_{Z}\) rises about 20 MPa. As \(\sigma_{Y}\) doubles, the \(\sigma_{Z}\) value of tensile stress at the arch top and the floor middle increases by 20 MPa correspondingly. With the increase in \(\sigma_{Z}\) or \(\sigma_{Y}\), the same maximum tangential stress value is first reached at the foot of the straight wall, which is \(f/B=1/4\) first, \(f/B=1/3\) second, \(f/B=1/2\) last, and all of them are compressive stress;
2. Indoor tests were performed to simulate the spalling process of deep hard rock tunnels with different arch heights using a true triaxial test machine. The initial failure stress of the holes with different arch heights is 0.39-0.48 times the UCS of the rock. The initial failure occurs at the arch foot, where the tangential stress is the maximum. 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. By comparison, it was found that the semi-circular arch tunnel has a better pressure-bearing capacity than the three-centered arch tunnel. The maximum tangential stress increases as the arch height decreases or the burial depth increases;
3. The four spalling periods of surrounding rock of hard rock tunnels with different arch heights were clarified. In the calm period of internal crack expansion, the internal pores were compressed, and microfractures were initiated in the rock sample. The ejection period of fine particles at the foot or shoulder of the arch represents a stage of crack expansion along the arch foot and sidewalls after an initial failure of the arch or shoulder. In the macrocrack penetration and spalling stage, macrocracks expanded after the internal microfractures. In the V- or arc-shaped groove formation  
Figure 19: Diagram of spalling process in arch tunnels:(**a**) calm period of internal crack expansion; (**b**) ejection period of fine particles at the foot or shoulder of the arch; (**c**) macroscopic fracture penetration and spalling period; (**d**) V- or arc-shaped groove formation period. period, macro cracks developed deeper in rock spalling parallel to the sidewalls continuously occurred. In this study, only the tentative experiments of three kinds of arch height specimens are considered, and the stress distribution function is solved by using the theory of elastic mechanics combined with the complex variable function. The influence of axial stress (\(\sigma_{X}\) in this paper) on the experimental results is not considered. In future work, the biaxial and true triaxial control experiments will be further carried out to make the results more universal. Resources, K.P. ; formal analysis, G.Y. ; writing--original draft, G.Y. ; supervision, K.P. ; writing--review and editing, G.Y. and S.L. ; methodology, X.S. and S.L. ; validation, G.Y. and S.L. ; funding acquisition, K.P. ; conceptualization, S.L. ; investigation, X.S. All authors have read and agreed to the published version of the manuscript. This work was funded by the National Natural Science Foundation of China (No. 51974043), and the Hunan Provincial Natural Science Foundation for Distinguished Young Scholars (2023J)[10072]; the Science and Technology Innovation Program of Hunan Province (2022 RC1173); supported by the Fundamental Research Funds for the Central Universities of Central South University. Not applicable. All the data, models, and code generated or used during the study appear in the submitted article.