基于地下水动力学，将隧道注浆过程与地下水向完整井运动类比，并建立层状地质条件下渗流模型；通过保角变换法，将求解问题由平面径向流转换为平面均匀流，求解了层状地质条件渗流场解析解。在此基础上，将隧道注浆模型简化为三层地层，求解了隧道渗流量、注浆圈外水压力、衬砌外水压力解析解。为验证解的有效性，以团结隧道为背景，采用等效面积法进行数值模拟。结果显示：在注浆圈厚度增加、注浆圈渗透系数与衬砌渗透系数减小的情况下，隧道的涌水量及衬砌外水压力会减小，堵水率和注浆圈外水压力将增加。通过误差分析发现，与解析解相比较，同心圆断面误差随着注浆圈厚度误差增加，六心圆断面误差减小，模拟解两断面涌水量结果接近59%；随着注浆圈渗透系数的减小，模拟解与解析解涌水量相对误差均较大；随着衬砌渗透系数的减小，涌水量与衬砌外水压力的模拟解均大于解析解。

Based on groundwater dynamics, the tunnel grouting process was analogized with the movement of groundwater towards a complete well, and a seepage model was established under layered geological conditions. By using the conformal transformation method, the problem was transformed from a planar radial flow to a planar uniform flow, and the analytical solution of the seepage field under layered geological conditions was solved. On this basis, the tunnel grouting model was simplified into three layers of strata, and analytical solutions were obtained for the tunnel seepage flow rate, external water pressure of the grouting ring, and external water pressure of the lining. To verify the effectiveness of the solution, the equivalent area method was used and numerical simulations were conducted against the background of the unity tunnel. The results show that with an increase in the thickness of the grouting circle and a decrease in the permeability coefficient of the grouting circle and lining, the water inflow and external water pressure of the tunnel will decrease, while the water blocking rate and external water pressure of the grouting circle will increase. Through error analysis, it was found that compared with the analytical solution, the error of the concentric circular section decreases with the increase of the thickness error of the grouting ring, while the error of the six centered circular section decreases. The simulation solution show that the water inflow of the two sections is close to 59%. As the permeability coefficient of the grouting ring decreases, the relative error between the simulated and analytical solutions for water inflow is relatively large. As the permeability coefficient of the lining decreases, the simulated solutions for water inflow and external water pressure of the lining are greater than the analytical solutions.