# Durability of Subsea Tunnels under the Coupled Action of Stress and Chloride Ions
## 1 Introduction  
Subsea tunnels are widely recognized as the preferred means of cross-channel transportation [1; 2; 3; 4] and are becoming increasingly important for the development of national life and economics. Subsea tunnels across rock strata experience the long-term effects of the rock confining pressure and water pressure, the leakage of corrosive groundwater, the erosion of noxious gas in caves (e.g., salt spray), and defects in the structure itself, which all pose serious durability problems. Therefore, it is economically important and theoretically necessary to comprehensively consider environmental factors in the structural damage analysis during service processes, predicting the service life and guiding the durability design of subsea tunnels. Chloride ion concentration is an important factor that affects the durability of subsea tunnels [5; 6; 7]. The chloride ion transmission model is one of the key problems in the subsea tunnel durability research. The traditional approach only considers the diffusion of chloride ions. [PERSON] et al. [8], [PERSON] et al. [9], and [PERSON] et al. [10] predicted the service life of Jiaozhou Bay subsea tunnel based on the life prediction model introduced by [PERSON] [11]. The transmission of chloride ions is a combined effect of diffusion andconvection [12]. The dispersion of chloride ions on the outside of the lining is affected by both the pressure of the surrounding rock and the penetration (convection) of the seawater; the inside of the lining is exposed to salt fog, which induce capillary absorption [9]. Therefore, besides the diffusion of chloride ions, the influence of convection and stress should also be considered. [PERSON] et al. [13] studied the effects of pressure penetration and capillary pressure on chloride ion transmission in subsea tunnels. Their experimental results showed that higher water pressure is linked to higher chloride ion concentrations in linings. [PERSON] [14] established a numerical model of chloride ion erosion and transport in segment joints, considering the coupling of pressure permeation and chloride ion concentration. They concluded that the external water pressure of a tunnel has a significant impact on the velocity and depth of chloride ion transmission. [PERSON] et al. [15] predicted a subsea tunnel's service life based on the proposed diffusion model, which considered the influence of troposphere thickness. [PERSON] [16] established a durability evaluation model and a calculation method for the segment structure under the action of erosion and structural load combined with stress level. The convection zone depth was considered during the analysis of the convection effect. [PERSON] et al. [17] developed a test system for accelerated corrosion degradation, focusing on shield tunnel segments under compression and bending and loading conditions. The experimental results were used to analyze the corrosion degradation regularity of shield tunnel segments under different working conditions. [PERSON] [18] calculated the service life of a subsea shield tunnel using the reliability method, considering the effect of structural stress state on the diffusion velocity of chloride ions. [PERSON] [19] studied the service life probability of existing subsea tunnels using reliability theory. [PERSON] [20] conducted a series of research on the durability of shield tunnel linings under coupled influencing factors. In conclusion, most of the studies on the durability of subsea tunnels applied a chlorine ion transmission model that is inconsistent with conditions in reality. Also, few service life prediction approaches consider random parameters or the reliability theory. To solve this problem, we introduce a theoretical method for predicting the service lives of subsea tunnels. The proposed method considers the impact of convection velocity's space-time effect and the influence of stress on chlorine ion transmission.