# Stress Analysis and Spalling Failure Simulation on Surrounding Rock of Deep Arch Tunnel
## 4 Discussion
### Stress Distribution Analysis of Surrounding Rock under Different Working Conditions
Under the low vertical stresses of the initial burial depth state, \(f/B=1/2\) semi-circular arch tangential stresses in region 1 show a decreasing trend, while the \(f/B=1/3\) three-centered arch and the \(f/B=1/4\) three-centered arch show an increasing trend, the growth rate of the tangential stress is as follows: \(f/B=1/4\) three-centered arch \(>\)\(f/B=1/3\) three-centered arch. The tangential stresses in the arch section for the three rise-span ratios show a decreasing trend in the region 2 and region 4, but an increasing trend in the region 3, the growth rate of the tangential stresses all show the following: \(f/B=1/4\) three-centered arch \(>\)\(f/B=1/3\) three-centered arch \(>\)\(f/B=1/2\) semi-circular arch. With the adjustment of the vertical stresses, the tangential stresses where the \(f/B=1/2\) semi-circular arch in the region 1 change from a negative growth rate to a positive growth rate, while the growth rates of the tangential stresses in the \(f/B=1/3\) three-centered arch and the \(f/B=1/4\) three-centered arch at this point increase continuously, the growth rate of the tangential stress values as follows: \(f/B=1/4\) three-centered arch \(>\)\(f/B=1/3\) three-centered arch, the trend of which is the same as under the initial burial depth stress, with the difference that the larger the vertical stress value, the faster the growth rate; The growth rates for the three rise-span ratios of arch sections at high vertical stresses are similar in the region 2 and region 3, while the growth rates in region 2, region 3, and region 4 show the following: \(f/B=1/4\) three-centered arch \(>\)\(f/B=1/3\) three-centered arch \(>\)\(f/B=1/2\) semi-circular arch. The effects of horizontal stress arrangement on the tangential stress of the arch tunnels with the three rise-span ratios are as follows: Under the initial stress conditions, when the minimum horizontal stress was transformed into the maximum horizontal stress, the tangential stress at point 2 and point 3 decreased. The maximum tangential stress at point 4 and the tangential stress at point 1 and point 5 increased. With the adjustment of vertical stress, when the minimum horizontal stress was laid on the hole sides, the growth rate of the tangential stress in region 1 and region 2 is greater than that of the maximum horizontal stress laid on the hole side. However, the growth rate of tangential stress in region 3 and region 4 under the minimum horizontal stress is less than that under the maximum horizontal stress. Figure 14: Tangential stress distribution in a semi-circular tunnel (\(f/B=1/2\)) under stress adjustment. Figure 15: Tangential stress distribution in a three-centered arch tunnel (\(f/B=1/3\)) under stress adjustment. the onset of rock chips spalling from the hole sidewalls (rock chips fall onto the floor). The initial vertical stress at which particle ejection occurred follows a sequence of \(f/B=1/2\) semi-circular arch \(>\)\(f/B=1/4\) three-centered arch \(>\)\(f/B=1/3\) three-centered arch. The initial vertical stress at which spalling occurred is as follows: \(f/B=1/2\) semi-circular arch \(>\)\(f/B=1/3\) three-centered arch \(>\)\(f/B=1/4\) three-centered arch. The initial stresses of the specimens were determined according to [PERSON], [PERSON] [65], and [PERSON] et al. [66]. The tunnel stresses induced by different excavation directions were simulated. The following preliminary conclusions can be drawn: The initial stress for particle ejection and rock flake initiation of \(f/B=1/2\) semi-circular arch tunnel is the highest, which is in line with the fact that a semi-circular arch tunnel has a stronger pressure-bearing capacity. The pressure-bearing capacity of \(f/B=1/3\) and \(f/B=1/4\) three-centered arch tunnels is similar. The spalling becomes more violent as the arch height of the three-centered arch tunnels decreases.