Analytical study of steady state seepage in a circular tunnel considering the outer boundary of the grouting ring as a non-constant head boundary

Abstract

The influence of groundwater seepage on tunnel is not negligible, so it is very important to calculate the distribution of pore water pressure and the seepage volume accurately. The current analytical studies of seepage field in tunnels with grouting ring assume the head outside the grouting ring to be constant, which is accurate when there is a large difference between the permeability of the grouting ring and the soil body, but less accurate when there is a small difference in permeability. Accordingly, this paper combines a new conformal transformation method and the separated variable method to overcome the current problem of not being able to obtain an analytical solution after assuming the head at the outer boundary of the grouting circle as a non-constant head. And according to the obtained analytical solution and the existing analytical solutions and numerical simulation results for comparison, comparison results show that: when 1 ≤ kr/kg ≤ 100, the absolute value of the maximum relative error between the calculation results of the external pore water pressure of the grouting circle of the CVM solution and those of the numerical solution is more than 1.5 times of that of the analytical solution of this paper, and the maximum value is nearly 3 times of that of the analytical solution of this paper. Therefore, the analytical solution obtained in this paper by assuming that the outer boundary of the grout ring is a non-constant head is more accurate and has some applicability in the case where the permeability of the soil and the grout ring do not differ much. Finally, extensive parametric analyses of the permeability and thickness of the grouting ring and the depth of the tunnel are also performed to demonstrate the capability of the proposed analytical solution. In addition, the proposed analytical solution is much less computationally demanding compared to numerical software, but the accuracy is comparable.