Circular tunnel in a semi-infinite aquifer

The steady gravity flow that is generated by a circular tunnel disturbing the hydrostatic state of a semi-infinite, homogeneous and isotropic aquifer is solved exactly. Many aspects of the flow are found in closed analytical forms such as the water inflow, pressure, leakage and recharging infiltration, which give a complete view of the aquifer in the drained steady state. It is found that the maximum value of the recharging infiltration does not exceed the hydraulic conductivity allowing stating a criteria for recharge intervention to ensure the stability of the aquifer. In addition to the main results, two aspects of the water inflow are treated. These are the necessary modifications that are to be considered in the case of an inclined water table and in the case of a lined tunnel that develops a constant internal pressure. It is also found that under an inclined water table a tunnel may cease to drain on its complete circumferential edge and a limiting condition is stated. Furthermore, the Muskat–Goodman and other water inflow predictions are compared to the exact gravity water inflow.