Steady-state groundwater inflow into a circular tunnel

The prediction of groundwater inflow into a tunnel is important for designing the tunnel drainage system and to minimize environmental impacts and the risk of tunnel instabilities and subsidence damage. Analytical solutions exist to calculate tunnel inflow, and, increasingly, numerical groundwater models are used to this end. In order to represent different types of tunnel support structures, this study reviews different boundary conditions that can be set at the tunnel perimeter to calculate tunnel inflow and recognizes different ways to account for the tunnel lining. Analytical solutions and numerical models to calculate tunnel inflow are compared and factors influencing the accuracy of numerical solutions are highlighted. The study suggests that numerical models provide estimates of tunnel inflows with sufficient accuracy for practical purposes if the tunnel is lined and has no drainage layer surrounding the lining, and if the hydraulic conductivity of the lining is several orders of magnitude lower than the hydraulic conductivity of the aquifer, or if the lining is thick. Otherwise, the extent of the model domain must be large with respect to the extent of the tunnel to provide accurate results. It was shown that inflows are higher for lined tunnels with a drainage layer than for unlined tunnels, if the head in the drainage layer corresponds to the level of the tunnel center or invert. If the head in the drainage layer corresponds to the level of the tunnel crown, inflows are higher for unlined tunnels. The study further suggests that for unlined tunnels, inflows are higher at the invert than at the crown. For lined tunnels with a drainage layer, the reverse is true. Differences between inflows at the crown and invert decrease with increasing depth of the tunnel under the groundwater table. The numerical solution for flow into lined tunnels without drainage layer using a transfer (Cauchy type, or 3rd-kind) boundary condition produces lower inflows compared to using a specified head (Dirichlet type, or 1st-kind) boundary condition. Using a transfer boundary condition is especially inaccurate if the lining is thick.

► Numerical and analytical solutions to calculate tunnel inflow are compared.
► Influence of boundary conditions at tunnel perimeter on calculated flow is tested.
► Impact of different tunnel support structures on tunnel inflow is analyzed.
► The use of a transfer boundary condition to represent the lining is evaluated.