Groundwater ingress to tunnels – The exact analytical solution

An analytical expression for the estimation of the steady state groundwater ingress into a drained tunnel of circular cross section is derived on the basis of conformal mapping. In contrast to the widespread approximative solution of Goodman, the derived equation is equally valid for deep and shallow tunnels and is more general than the solution by Rat and Lei since it allows variable waterheads at the tunnel circumference and at the ground surface. The implications of drainage upon the related seepage force are pointed out.