## 2 Discussion on Water Pressure Reduction Coefficient of Sub-Sea Tunnel Lining
### Bearing Capacity of Secondary Lining under Different Water Pressure Reduction Coefficients
When the water pressure reduction coefficient is 0, 0.1, 0.2, 0.4, 0.6, 0.8, and 1.0, respectively, the variation of axial force and bending moment at each part with the water pressure reduction coefficient is shown in Figures 9 and 10. As shown in Figure 9, the bending moment of all parts except the vault increases with the increase of the water pressure reduction coefficient. Among them, the growth rate of the arch foot and arch waist increases gradually, and the growth rate of the inverted arch decreases gradually. With the increase of reduction coefficient, the lining structure at the vault is transformed from inner tension to outer tension, and then the bending moment increases gradually. When the reduction coefficient increases from 0 to 1, the bending moment at the vault changes from 154.4 kN\(\cdot\)m to \(-\)338.2 kN\(\cdot\)m. The arch waist increased from 47.7 kN\(\cdot\)m to 646.8 kN\(\cdot\)m, increasing 12.6 times. The arch foot increased from \(-\)169.5 kN\(\cdot\)m to \(-\)1009.9 kN\(\cdot\)m, increasing about 5 times. The inverted arch increased from 128.3 kN\(\cdot\)m to 349.3 kN\(\cdot\)m, increasing 1.7 times. It can be seen that the change of reduction coefficient has the greatest impact on the bending moment at the arch waist, followed by the arch foot. Under the same reduction coefficient, the bending moment at the arch foot may be significantly greater than that at other parts. As shown from Figure 10, with the increase of the reduction coefficient, the axial force at each part increases linearly. Among them, the growth rate of the arch crown, arch foot and inverted arch is high, and the growth rate of the arch waist is lower than the others. The axial force at the vault increases from 555.1 kN to 3305.0 kN when the reduction coefficient increases from 0 to 1. The arch waist increased from 1002.2 kN to 3409.8 kN, increasing 2.4 times. The axial force value of the arch foot and the inverted arch is almost the same, increasing from about 1140 kN to about 4500 kN, an increase of nearly three times. Under  
Figure 10: The relationship between axial force and water pressure reduction coefficient. Figure 9: The relationship between bending moment and water pressure reduction coefficient. the same reduction coefficient, the axial force at the arch foot and the inverted arch is larger, the axial force at the arch crown is the smallest, and the axial force distribution is positively correlated with the depth. According to the relevant design documents of the tunnel, the existing reinforcement scheme of the lining is symmetrical reinforcement, and the strength grade of the main reinforcement is HRB400, which is generally based on \(\Phi\)25@150 mm configuration, the arch foot is arranged according to 2 \(\times\)\(\Phi\)25@150 mm + \(\Phi\)25@150 mm configuration. The structural safety factor calculation method refers to the Code for Design of Concrete Structures [28]. The safety factor of the tunnel structure is calculated based on the above reinforcement scheme, combined with the environment and purpose of the tunnel, and the specification stipulates that the safety factor of the tunnel structure shall be not less than 2.0. The calculation results of the safety factor of the lining structure are shown in Figure 11. The safety factor is defined in the Chinese tunnel design code [23]. It is mainly controlled by the axial force and a bending moment of the structure, which belongs to the category of the concrete structure. The tunnel lining is safe when the calculated safety factor is greater than 2.0. It can be seen from Figure 11 that under the existing reinforcement scheme, with the increase of reduction coefficient, except for the temporary increase at the vault, the safety coefficient at other parts gradually decreases, and the decline rate gradually decreases. The overall safety of the lining is controlled from the inverted arch to the arch waist.