Boundary Condition of Groundwater Flow through Sloping Seepage Face

This study has experimentally and theoretically investigated the downstream boundary condition of unconfined groundwater flow through the trapezoidal aquifers of which upstream end is vertical and downstream seepage face is sloping. Flow through the trapezoidal aquifers is experimentally simulated by a Hele-Shaw model. The upstream end is impermeable and the downstream boundary forms a drawdown flow on a sloping seepage face. The drawdown flow is formed on a seepage face when hydraulic gradient at a seepage point is less than the seepage face slope. Discharge through the sloping seepage face is found to be proportional to fluid depth (thickness of the fluid layer) at the seepage point, where a phreatic surface crosses the seepage face. When the angle of the seepage face to the horizontal is between 45 and 90°, the hydraulic gradient at the seepage point is found to be 1/2. This is independent of the seepage face slope. When the angle of the seepage face to the horizontal is less than 45°, the phreatic surface crosses the seepage face in the hydraulic gradient of $\text{tan}\left(\beta +\theta \right)/\left[1+\text{tan}\left(\beta +\theta \right)\right]$ , in which $\beta$ is the angle of the seepage face to the channel bottom and $\theta$ is the angle of the bottom slope. The theoretical result of the downstream boundary condition is found to be in good agreement with the experimental data. The phreatic surface slope or the hydraulic gradient at the seepage point forms the downstream boundary condition for the Boussinesq equation when the downstream seepage face is sloping between 0 and 90°.