Seepage flow is one of the most practical problems in the field of civil, geology, hydrology and agricultural engineering. Nonlinear flow through permeable deposits takes place when the mean size of the aggregates is coarse. In this paper, an analytical solution is presented for unconfined fully developed turbulent flow under "extended Dupuit-Forchheimer (D-F)" assumptions. A dimensionless form of the solution is therefore presented, and then to show the accuracy of the solution, its results are compared with new experimental data and a Darcy-based solution. According to the results of the present study, it may be concluded that the proposed analytical solution could be used to analyze satisfactorily water surface profiles and normal depth in such sloping permeable porous media under fully developed turbulent flow condition.