Some general results on the seepage exclusion problem

Asymptotic roof boundary layer solutions are obtained for the quasilinear seepage exclusion problem for ellipsoidal cavities of arbitrary aspect ratio χ and arbitrary horizontal axial index k . The maximum dimensionless potential at the cavity wall, υ max , is given (χ > 0) by the equation υ max (σ, χ, k ) ∼ 2σ + f 0 (χ, k ) + f 1 (χ, k )/σ + f 2 (χ, k )/σ 2 + …, where σ = ½ακ −1/2 (α, sorptive number; κ, apical curvature) and the f n are polynomials in χ −2 and k −2 of degree ( n + 1). There is thus a hierarchy in importance of the geometrical parameters determining υ max . σ is dominant, χ is next in importance, and the effect of k is relatively minor. The above equation includes as special cases previous results for circular, elliptic, and parabolic cylinders and for spheres, spheroids, and paraboloids. For elliptic discs (χ = 0), υ max (σ 1 , k ) ∼ 4σ 1 2 + f 0 ( k ) + f 1 ( k )/σ 1 2 + f 2 ( k )/σ 1 4 + ⋯, where σ 1 = ½α −1 γ (γ, characteristic horizontal length) and the f n are polynomials in k −2 of degree ( n + 1). This equation includes as special cases previous results for strips and circular discs. The various results are relevant also to cavities with ellipsoidal and flat elliptic roofs but otherwise of arbitrary (though not too irregular) configuration. The corresponding nonlinear analysis is straightforward.