Analytical Solution of Seepage Field in Karst Tunnel

Abstract

An analytical solution for the seepage field in water-filled karst tunnel is derived based on the inversion of complex function and groundwater hydraulics theory. The solution considers the distance between the tunnel and the cavern, the size of the cavern, and the properties of the lining structure, such as the permeability coefficient as well as the radius of the grouting ring. This paper also performed numerical simulations for two cases: the application of gravity and the absence of gravity. The numerical solution was obtained to verify the analytical solution, and a good agreement was found. Then, the effect of parameters is discussed in detail, including the distance between the tunnel and the cavern, the radius of the cavern, the grouting ring, and the initial support. The results show that when the radius of the cavern is constant, the pressure head and seepage flow decrease as the distance between the tunnel and the cavern increases. When the distance is constant, the pressure head and seepage flow increase with the increase of the radius of the cavern. In addition, the pressure head and the seepage flow decrease with the increase of the thickness of the grouting ring and decrease with the decrease of the permeability coefficient. As the thickness of the initial support increases, the pressure head gradually increases and the percolation decreases. Furthermore, due to the great influence of the grouting ring and initial support on the pressure head and seepage flow, the thickness and permeability coefficient of the grouting ring and initial support should be taken into account carefully during construction.