# Stress Analysis and Spalling Failure Simulation on Surrounding Rock of Deep Arch Tunnel
## 3 Simulation of Spalling Failure
### Characteristics of Sidewall Fragments  
Figure 11 shows the characteristics of the rock flakes from the specimens tested. Most rock flakes are in thin shapes. Some rock flakes are also in the form of thick in the middle and thin on both sides. Fine powders were observed on the rock flakes, which were mainly produced by the tension-shear failure between rock particles during spalling. This phenomenon is similar to that observed in actual engineering. The mass of individual rock flakes from specimen A12-42.22-27.12 is in the range of 0.17-2.75 g. A spalling of small flakes first occurred in the central part of the hole sidewalls. Then a spalling of a large piece of thin wedge-shaped rock flake occurred. As the spalling developed along the axial direction of the hole, the mass of spalling rock flakes from both sidewalls decreased. There are still flexural rock pieces hanging on the sidewalls after testing. The mass of individual rock flakes from specimen A13-22.2-22.2 varies from 0.38 to 8.04 g. The mass of a single rock flake from specimen A14-17.3-28.9 varies from 0.45 to 5.12 g, with the morphology varying from flake to thin wedge shape. It was reported that after the excavation of branch tunnels, the main failure modes of the surrounding rock included the spalling failure, the thin slab  
failure, and the wedge-shaped slab failure. The thickness of rock flakes ranged from 2 mm to 2 cm. The thickness of rock flakes was relatively uniform, and the shape was irregular. These flakes were broken into several pieces after falling from the sidewalls, and the surface of the rock flakes was rough, as shown in Figure 12a. In addition, the wedge-shaped rock slabs are like a \"stone knife\", which are thick in the middle and thin at the edges, with a maximum thickness ranging from 3 cm to 0.1 m, as shown in Figure 12c. It was also revealed that both the first and third failure modes considered the splitting and stretching as the main mechanism of rock flakes. In the first mode, the surrounding rock failed with a lesser depth, whereas the third failure mode resulted in a greater spalling depth. The main failure mode of specimen A13-22.2-22.2 is flake failure, the specimen A12-42.22-27.12 underwent a wedge-shaped slab failure, and the failure of specimen A13-22.2-22.2 is a combination of them. The flake failure mechanism was influenced by the horizontal stress conditions of the surrounding rock. It can be seen from Figure 11 that the shape of the rock fragments produced in our simulated tests is comparable to that of rock fragments in actual rock engineering.  
Figure 11: Flaking debris of arch hole walls.  
Figure 10: Comparison of the hole wall failure between engineering practice and simulation test: (**a**) flaking fragments of specimen A13-22.2-22.2; (**b**) sidewall spalling of specimen A14-17.3-28.9; (**c**) sidewall spalling of specimen A12-42.2-27.1; (**d**) collapse of specimen A13-22.2-22.2 tunnel; (**e**) Songxian Gold Mine haul tunnel; (**f**) 500 m haul tunnel at Linglong Gold Mine [49]; (**g**) surface spalling at rock junction [2]; (**h**) fracture failure in 2500 m quartzite tunnel [67].