Investigating the Problems of Unconfined Non-Darcy Flows through Embankment Dams using a Depth-Averaged Model

Fully-developed turbulent flow-through coarse-grained porous media cannot be treated with the Dupuit approach based on Darcy’s law unless Forchheimer’s resistance equation is considered to account for non-linear effects arising from drag forces. By combining this equation with the Reynolds-averaged Navier-Stokes equations, a higher-order, depth-averaged model applicable to the flow of curvilinear seepage in a non-linear turbulent regime was developed. The governing equations were numerically solved with a hybrid scheme that adopts the finite-difference and finite-volume methods. The model’s validity was then examined by carrying out numerical tests involving unconfined non-Darcy flows. The numerical results for such flows through rockfill structures with various geometric shapes were compared with the experimental data and produced a satisfactory agreement. The results of the study demonstrated that a depth-averaged model of this type is mostly preferred for accurately predicting the phreatic surface curvature and the exit height of the seepage line. Furthermore, the overall results confirmed the model’s capability for adequately capturing the dynamic behavior of the turbulent seepage flow. The present model is therefore a useful tool for practicing engineers to evaluate the conceptual design of rockfill dams.