Steady seepage near an impermeable obstacle

The problem of an obstacle with maximum cross-sectional area has been analytically solved in terms of a model for 2-D seepage flow with a capillary fringe. The boundary of the obstacle appears to show a 'blunt configuration', that is, the pressure reaches its maximum value at the vertex and decreases monotonically downstream. With a sufficiently large size of obstacle, a positive pressure domain in the form of a 'bubble' is formed in the vicinity of its vertex. This result has been verified by computations for saturated-unsaturated flows in terms of the finite element method for the Richards equation. It has also been shown that an obstacle can transform the initial fully saturated flow into unsaturated flow inside the 'dry shadow' domain. The shape of an obstacle in a confined aquifer that provides a minimum water head drop has been determined within the scope of the Dupuit model. A 'critical cavity shape' has been found, i.e. a cavity for which the boundary is simultaneously an isobar and a stream line.