A mapping technique for steady‐state unconfined seepage analysis

An approach is presented for the analysis of the unconfined steady‐state seepage through homogeneous trapezoidal dams based on a bijective mapping between the flow domain, having an unknown shape, and a fixed triangular domain. It is shown that the geometrically non‐linear unconfined analysis is equivalent to the problem of determining the unknown distribution of permeability, within a triangular domain with known shape, that satisfies the set of transformed boundary conditions. The flow problem in the triangular domain is solved through a finite‐element technique analogous to that adopted for confined analyses and, on the basis of this solution, the shape of the free surface in the physical space is evaluated. The proposed approach is applied to the determination of the influence of the water levels in the upper and lower reservoirs on the elevation of the free surface seepage point.