A Review and Evaluation of Analytical Solutions for Steady-state Tunnel Inflow Using Numerical Modeling

Predicting tunnel water inflow is important regarding the safety of tunnel construction and impacts on natural environment, such as the drawdown of the water table. Accurate prediction of tunnel water inflow can scientifically guide the design and construction of tunnels. Correct selection and application of forecasting methods is a prerequisite for accurate prediction of tunnel water inflow. Analytical solutions based on groundwater dynamics such as Goodman's equation are usually applied to preliminary estimation on water inflow in mountain tunnels, and are commonly used in the geological survey for highway tunnel engineering. We evaluated the existing analytical solutions against numerical modeling using MODFLOW. There are parameters in the analytical solutions that can significantly influence the tunnel inflow estimation. These parameters are normally presumed as constants due to the generalization in inflow conditions. For example, the hydraulic conductivity is set to be constant because the analytical solutions assume porous media permeability is homogeneous and isotropic. Such simplification could impede the accuracy of the tunnel inflow estimation in practical applications. Our research investigated the effectiveness, limitations and drawbacks of the analytical solutions by comparing with outcomes from numerical models under empirical conditions. Furthermore, we examined hydrological and geological parameters that can be utilized to improve analytical solutions' accuracy in real-world tunneling projects. This testing includes the use of bounds of effective hydraulic conductivity in calculations of tunnel inflow in a heterogeneous field. This study aims at exploring the limitations of the analytical solutions for the prediction of tunnel water inflow, and identifying the applicability of the analytical solutions in real-life situation.