# Stress Analysis and Spalling Failure Simulation on Surrounding Rock of Deep Arch Tunnel
## 3 Simulation of Spalling Failure
### Test Results  
In this test, the Z-directional stress of specimen A12-42.2-27.1 was increased to 81.6 MPa after 18 steps starting at 68.6 MPa; the Z-directional stress of specimen A13-22.2-22.2 was increased to 64.0 MPa after 13 steps starting at 58.5 MPa; the Z-directional stress of specimen A14-17.3-28.9 was increased to 69.5 MPa after 5 steps starting at 59.5 MPa, as shown in Figure 6. Under the \"high stress + stress adjustment\" conditions, the complete failure process of the arched hole sidewall was monitored in real-time using a miniature camera. The failure states of the sidewall at different moments were obtained in combination with the video monitoring. The failure process of the hole sidewall is shown in Figures 7-9. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Depth (m)** & \(\sigma_{\rm{Hmax}}\) **(MPa)** & \(\sigma_{\rm{Hmin}}\) **(MPa)** & \(\sigma_{v}\) **(MPa)** \\ \hline
500 & 28.90 & 17.25 & 13.50 \\
650 & 35.56 & 22.19 & 17.55 \\
800 & 42.22 & 27.12 & 21.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The initial crustal stresses at different burial depths. Figure 5: Initial stress state of specimens: (**a**) specimen A12-42.2-27.1; (**b**) specimen A13-22.2-22.2; (**c**) specimen A14-17.3-28.9. Figure 6: Actual loading stress path of true triaxial test: (**a**) A12-42.2-27.1; (**b**) A13-22.2-22.2; (**c**) A14-17.3-28.9. Figure 7: Spalling process of specimen A12-42.2-27.1. The complete failure process of the arched hole sidewall of specimen A12-42.2-27.1 is shown in Figure 7. At 788 s, the vertical stress \(\sigma_{Z}\) was increased to 68.6 MPa. The test was in the load-holding phase of the loading process at this moment, resulting in a small particle ejection from the right wall, as shown in Figure 7a. The vertical stress \(\sigma_{Z}\) was increased to 70.6 MPa at 951 s, and cracks appeared at the arch foot and extended from the middle towards the wall foot. Rock flakes spalled from the arch shoulder of the left sidewall and the corner of the right wall, as shown in Figure 7b. Subsequently, \(\sigma_{Z}\) was increased to 73.6 MPa after 215 s. The middle arch foot of the right wall buckled and opened towards the arch shoulder. With further increasing vertical stress, the buckling and opening intensified, and the sidewall bulged, as shown in Figure 7c. Then, the vertical stress continued to be increased in steps of 1.0 MPa. During the load-holding stage, rock flaking occurred successively at both sidewalls, with flaking on the right side first, followed by flaking on the left side, as shown in Figure 7d. At 1714 s, a large spalling occurred at the middle of the right sidewall and developed from the middle to 1/2 length of the sidewall under a high vertical stress \(\sigma_{Z}\) of 78.6 MPa (Figure 7f). When the sidewall failure is no longer extended, the vertical stress \(\sigma_{Z}\) and horizontal stresses \(\sigma_{X}\) and \(\sigma_{Y}\) are released to 0 MPa. Figure 8: Spalling process of specimen A13-22.2-22. Figure 9: Spalling process of specimen A14-17.3-28.9. The complete failure process of the arched hole sidewall of specimen A13-22.2-22.2 is shown in Figure 8. From Figure 8a, it can be seen that the vertical stress at the initial sidewall failure was 55.9 MPa and occurred at 489 s. A small particle ejection was observed at the bottom of the left sidewall close to the loading block. For a longer period, no obvious failure was noted. At 1080 s, \(\sigma_{\mathrm{Z}}\) = 64.6 MPa, and small particles were ejected from the middle bottom of the right sidewall. This indicates that the energy accumulated due to stress concentration was released at this location. After 43 s, the vertical stress was increased to 65.6 MPa. As shown in Figure 8b, at this moment, the rock specimen is in the load-retaining phase, and the previously flexed rock fragments spalled from the middle of the left wall. At 1183 s, \(\sigma_{\mathrm{Z}}\) = 66.6 MPa (Figure 8c), the rock specimen was undergoing the stepped loading stage of vertical stress.