Sealing performance analysis of flexible joints in immersed tunnels: Integrating percolation theory with a magnification-based contact model

The leakage characteristics of flexible joints are critical to the safety of immersed tunnels. The two sealing contact surfaces are the rubber surface of the waterstop and the concrete surface of the tunnel segments. As an effective waterproof barrier in immersed tunnels, the sealing performance of the waterstop is largely determined by the contact state and surface roughness of these surfaces. However, the current design of waterstops mainly relies on engineering experience and lacks a theoretical basis for targeted design. Existing studies on the sealing of immersed tunnel joints are mostly limited to macroscopic qualitative analysis and empirical judgment. Relevant research on the accurate quantitative prediction of waterstop leakage rates remains limited. In this study, the hydraulic connection process in immersed tunnels is analyzed, and the contact pressure distribution of the rubber waterstop seal is investigated. By integrating percolation theory with a magnification-based contact model, a calculation method for joint leakage is proposed, and the modeling approach is validated using a test rig. Furthermore, the relationship between the joint deformation extent ( x ) and the leakage rate ( Q ), expressed as the x – Q curve, is obtained. The effects of joint deformation and concrete surface roughness on leakage are also discussed. The results indicate that when the compression amount of the waterstop reaches 70 mm, maintaining the root mean square (RMS) surface roughness at approximately 0.6 mm is sufficient to ensure effective joint sealing. However, when the surface roughness of the concrete tunnel segment exceeds 1.4 mm, the leakage rate begins to increase rapidly.