Seepage flow through homogeneous soil into a row of drain pipes

Abstract

The effect of gap width on flow through homogeneous porous soil into a row of drain pipes is considered, by solving Darcy's law in a model configuration with axial symmetry. The resulting mixed boundary value problem of potential theory is reduced to a Fredholm integral equation of the first kind, which may be solved numerically. In practice, however, the gap width between pipes is small enough to justify an asymptotic expression for the relative flow found by the method of matched asymptotic expansions. To lowest order, it appears that the flow is sensitive to the gap parameters, not on the geometry far away from the gap. In the limit of large pipe radius and shallow depth, earlier two-dimensional results are recovered.