Analytical solution for estimating groundwater inflow into lined tunnels considering waterproofing and drainage systems

When estimating groundwater inflow into lined tunnels in water-rich regions, waterproofing and drainage systems (WDS) are usually ignored or not fully considered in existing analytical solutions. In this study, a water drainage seepage model considering drainage pipes, waterproof membranes, and geotextiles was developed. An analytical solution was then derived to predict groundwater inflow into composite-lined tunnels. The proposed analytical solution can be reduced to Goodman’s solution for an unlined tunnel. When only the initial lining was considered, the difference between the proposed analytical solution and Wang’s solution (Tunn Undergr Sp Tech 23(5):552–560, 2008) was less than 0.5%. Subsequently, the proposed analytical solution was further verified using a numerical model and good agreement between both models was observed. Finally, the relationships between groundwater inflow and the parameters of composite linings were investigated. The results of this study suggest the following: (1) groundwater inflow significantly decreases with an increase in the distance between two circular drainage pipes; (2) the higher the rock permeability, the more significant the WDS effect on groundwater inflow; and (3) when the rock permeability exceeds 1 × 10−6 m/s, WDS effects should be considered in the design of WDS. The results of this study are helpful for the optimal design of WDS for tunnels, such as the estimation of the initial lining permeability and thickness, distance between circular drainage pipes, and geotextile hydraulic conductivity. Additionally, the application of the proposed solution could provide a basis for analyzing potential adverse environmental impacts caused by tunnel drainage.