## 5 Conclusions  
In this paper, through the numerical calculation of seepage field in sub-sea tunnels and combined with the field monitoring data, the external water pressure and its reduction coefficient of tunnel structure are studied, and the following conclusions are obtained:  
1. The height of the water level and the permeability coefficient of the surrounding rock have significant effects on the external water pressure of the initial support, but the height of the water level has little effect on the reduction coefficient of water pressure. When selecting the route of sub-sea tunnels, the buried depth of the tunnels shall be minimized, and the unfavorable geological layer shall be avoided as far as possible under the condition of meeting the minimum overburden thickness. 2. With the increase of initial support thickness, the initial support external water pressure and its reduction coefficient may gradually increase, but the effect is small. The decrease of the initial support permeability coefficient may lead to a significant increase of initial support external water pressure and its reduction coefficient. When the water inflow in the initial support is within a reasonable range, the permeability coefficient of the initial support can be appropriately increased, and the water pressure behind it can be reduced. 3. The parameters of the grouting circle have a significant effect on the external water pressure and its reduction coefficient. However, after the grouting reaches a certain degree, the improvement effect of surrounding rock anti-seepage may no longer be obvious. Reasonable grouting circle parameters shall be selected for tunnel grouting, and attention shall be paid to the construction quality of the grouting circle. 4. With the increase of water pressure, the axial force of the key sections of the tunnel increases approximately linearly, and the bending moment of each section increases; Based on the research objects defined in this paper (such as horseshoe section, water level, grouting ring), the reduction coefficient is between 0.4 and 0.6, and the tensile area of the vault is transformed from the inner side to the outer side. 5. With the increase of water pressure reduction coefficient, the overall safety factor of lining decreases continuously; based on the research objects defined in this paper (such as horseshoe section, water level, grouting ring), when the water pressure reduction coefficient is less than 0.4, the existing scheme can meet the structural safety requirements. Therefore, the water pressure reduction coefficient has to be selected according to the ground properties, mainly permeability, and the grout properties, as defined in Tables 5-7. Moreover, the water level and the support properties may have some influence. 6. The field test monitoring data of lining structure stress show that the stratum conditions greatly impact the stress of lining structure. The secondary lining of the grade IV surrounding rock section bears a small load, and the secondary lining of the grade V surrounding rock section bears a large load. However, there is still a large strength reserve even in the latter case. 7. The method of designing tunnel lining based on the water pressure reduction coefficient proposed in this paper is more in line with the actual engineering situation, reduces the project's investment, and decreases the unreasonable strengthening of the lining. Conceptualization, J.Z. ; methodology, Z.T. ; writing--review and editing, J.Z. and N.M.; funding acquisition, Z.T. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China, grant number 51978041. The participant's personal identification information used in the study did not include personal information. Ethical review and approval were not required for the study. Data Availability Statement: Data sharing is not applicable.