39 / 2021-11-11 10:53:53

A semi-empirical model for water inflow into the tunnel in fractured-rock aquifers considering non-Darcian flow

Fractured rock,Water inflow,Tunnel,Non-Darcian flow,Semi-empirical equation

  Water inflow into the tunnel is usually estimated by assuming the flow in here follows the linear Darcy’s law. However, fluid flow in fractured-rock aquifers is prone to deviate from the Darcy’s law and arise to nonlinear flow phenomena due to significant inertial losses. Such a non-Darcian effect is seldom considered when evaluating water inflow into the tunnel in fractured-rock aquifers. In this study, we investigated the analytical method for predicting water inflow into the tunnel considering non-Darcian effect. A series of numerical simulations for water inflow into the tunnel were conducted with varying key parameters, in framework of non-Dacian flow characterized by the Forchheimer law. Based on these numerical results and an ingenious parameter integration method, a semi-empirical model was proposed to predict the water inflow into the tunnel involving with non-Darcian effect. The semi-empirical model has incorporated the classic theoretical formula for predicting water inflow and the Forchheimer equation for describing the non-Darcian flow. This model has a concise expression satisfying the dimensional consistency, and can be successfully reduced to the classic formula under Darcy flow regime. The validity of this semi-empirical model has been confirmed by the numerical results, showing a high fidelity for predicting water inflow into the tunnel. By means of this proposed model, the necessity of considering non-Darcian effect during calculating water inflow was finally proved in a large number of real engineering cases, including a karst tunnel project with detailed engineering geological data. The proposed model and the method used in this study can provide a guidance for accurately predicting water inflow into the tunnel under a complex non-Darcian flow regime.