Approximate analytical solution for seepage field of drained tunnel in vertically stratified phreatic aquifer

To explore the water table and water inflow after tunnel excavation in a vertically stratified phreatic aquifer, approximate analytical solutions for the steady-state water table and water inflow of a drained tunnel in a vertically stratified phreatic aquifer were obtained based on the Dupuit assumptions and the integral method. By comparing the approximate analytical solutions with numerical solutions, it was found that the relative error of the approximate analytical solution for the water table elevation is less than 10%, and the relative error of the approximate analytical solution for the water inflow is approximately 25%. The sources of the above errors are as follows: ① At the lateral boundary of water replenishment, the water surface should be tangent to the horizontal line, but the water surface for the approximate analytical solutions has a gradient. ② At the vertical boundaries near the tunnel, the total head is variable, but the total head for the approximate analytical solutions is assumed to be constant. ③ The Dupuit assumptions are applied in the flow domain near the tunnel. Although the relative errors of the approximate analytical solutions for the water table elevation and water inflow are evident, the lowered water table is reflected in the approximate analytical solutions.