Analytical Solution for the Steady-State Karst Water Inflow into a Tunnel

An analytical solution for the karst water inflow into a lined tunnel in an infinite plane is derived based on conformal mapping. The new solution considers the center distance between the tunnel and the cavern, the radii of the tunnel and the cavern, and the property of the lining, such as the permeability coefficient as well as the lining radius. Numerical models are established and calculated using the finite difference software FLAC3D to compare with the analytical solution of inversion transformation, and a good agreement is found. Then, the parameters of effect are discussed in detail. The results indicate that the karst water inflow shows a curve relationship as the radius of tunnel increase and increases as the lining becomes thinner or the permeability coefficient of the lining increases. Moreover, the pressure head decreases as the tunnel radius and the center distance between the tunnel and the cavern increase.