Semi-empirical models for predicting stable water inflow and influence radius of a tunnel considering non-Darcian effect

How to accurately predict water inflow and relevant groundwater influence of a tunnel are classical scientific issues in the field of hydrogeology, which are also of great significance to the construction and operation of underground engineering. This issue is usually investigated based on the assumption of the linear Darcy's law. However, the tunnel inflow is usually featured by high velocities or high pressures, especially in karst regions, which allows the flow regime to easily develop into non-Darcian flow regime. The impact of the non-Darcian effect on predicting water inflow and influence radius of a tunnel has not yet been systematically examined. Here, we numerically investigated the prediction of stable water inflow and influence radius under non-Darcian flow regime. By numerically solving the continuity equation of seepage flow incorporating the nonlinear Forchheimer law, a series of numerical simulations were conducted for stable water inflow into a tunnel by varying key controlling parameters. The quantitative dependencies of stable water inflow on these parameters were figured out, based on which a semi-empirical stable water inflow model was developed considering the nonDarcian effect. Meanwhile, the magnitude of the influence radius was investigated by statistical analysis of 59 actual engineering cases and estimated using existing empirical formulas. Based on these preliminary explorations, a semi-empirical model for estimating influence radius was concluded from massive simulations. The validities of our proposed semi-empirical models for stable water inflow and influence radius were further numerically verified. Comparative study and application in a real engineering case showed that compared with our proposed models, most existing empirical methods predicted a larger stable water inflow and a smaller influence range of groundwater. Besides, comparative results of proposed models with omitting non-Darcian term indicated that neglecting non-Darcian effect would overestimate both the stable water inflow and influence radius. These findings and established models would be useful for assessing stable water inflow and influence radius of a tunnel under non-Darcian flow regime.