Predicting Water Inflow in Tunnel Construction: A Fracture Network Model with Non-Darcy Flow Considerations

Abstract

Fractures are widely distributed in karst areas, and when flow rates are high, they exhibit complex nonlinear behavior that cannot be accurately described by Darcy’s law. In this work, a hydro-mechanical coupling model based on a discrete fracture network is proposed to predict tunnel water inflow, accounting for the impact of non-Darcy flow. The model’s feasibility has been validated by comparing it with experimental results and the field measurements of flow rates at the Bodaoling Tunnel in Guizhou, China. The results show that Darcy flow tends to overestimate water inflow by approximately 25% compared to non-Darcy flow. The non-Darcy effect grows with the increase in initial fracture width and empirical constant q. When q exceeds 8.77 × 10−6, the growth rate of the Forchheimer number along the fracture width slowed down, and the inhibitory effect of non-Darcy flow on flow became gentle. Additionally, in a complex fracture network, the inflow rate limited by non-Darcy flow at one point drives the water flow through a connect fracture to another point, which increases the difficulty in water inflow prediction. This work highlights the importance of non-Darcy flow and fracture networks when accurately predicting water inflow in tunnels.