Analytical and HYDRUS solutions for exfiltration through inclined seepage faces

Steady, phreatic flows in wedge-shaped aquifers subtended by a tilted bedrock and discharged through a hillslope seepage face are studied by 2-D and 1-D analytical models for fully saturated and a FEM numerical model for saturated-unsaturated flows. The curvilinear triangle in the hodograph domain is conformally mapped onto a reference half-plane where the Hilbert problem is solved for two holomorphic functions. Free boundaries and sizes of seepage face segments are found for given flow rates of the incident flows seeping downhills. The approximate (Dupuit-Forchheimer) water table is conjugated with a saturated triangle where the exact 1-D solution gives a constant Darcian velocity as a function of the angles of the soil wedge. HYDRUS-2D model gives the distributions of the pressure head, volumetric moisture content, isotachs, vector-fields of velocity and other characteristics of seepage described by the Richards-Richardson equation. Applications to stability of exfiltrating zones near tailwaters of earth dams are discussed.