Three-dimensional theoretical analysis of seepage field in front of shield tunnel face

To evaluate hydraulic head distribution in front of a shield tunnel in a saturated soil layer,theoretical analysis and numerical simulations are carried out in this study.Based on the partial differential equilibrium equation of seepage flow,a three-dimensional(3D)theoretical analytical model of the shield tunnel face and the seepage field in front of it is established using the eigenfunction and the Fourier series expansion methods,and the hydraulic head calculation formula is derived.Combined with engineering cases,the theoretical analysis results and the 3D numerical simulation results are compared and analyzed.The effect of the water pressure of the tunnel face on the hydraulic head distribution is also analyzed.The results of the proposed analytical solution are in agreement with those of the numerical simulation solutions;moreover,the proposed analytical solution requires less time to calculate the seepage hydraulic head than the numerical simulation.The ratio of the initial water table to the diameter(D)of tunnel face has a more significant impact on the hydraulic head distribution at a position 0.5D above the tunnel vault.When the water pressure on the tunnel face is not considered,the values of the hydraulic head are significantly underestimated.