Commingling of 2-D Darcian seepage with pipe flow: the Polubarinova-Kochina –Chanson problem revisited

Toe drains in earth dams intercept seepage and convey water through a perpendicular pipe. This study investigates commingled flow at contrasting Reynolds numbers using sand tank (ST) experiments and HYDRUS2D modeling. In ST, the flow rate, Q, through a bottom outlet (orifice) connected to a valved-pipe is discharged into a measuring burette. In coupled flow, Darcian heads and flow rates depend on soil compartment size, hydraulic conductivity, and pipe characteristics. The ST experiment found Q from ST orifice (STO) higher than from connected pipe by 63%. Q increases with shorter pipe length. STO is analytically modeled as a Zhukovsky “slot drain.” HYDRUS2D simulations show similar flow rates for an impermeable-lateral-boundary ST rather than equipotential. An analytical 2D solution for an infinitely long ST gives nearly the same flow rate as the HYDRUS2D model. These findings enhance the understanding of commingled Darcian-pipe flows and aid efficient drainage design in earth dams.