Analysis of unsaturated seepage in infinite slopes by means of horizontal ground infiltration models

Abstract

This paper describes a simple methodology to calculate the two-dimensional seepage across an infinite unsaturated slope using models of one-dimensional infiltration through horizontal ground. The methodology decomposes the seepage across the infinite slope into antisymmetric and symmetric parts, whose respective solutions are combined to calculate the actual flow regime. The antisymmetric solution is trivial and does not even require integration of the governing continuity equation, while the symmetric solution, albeit non-trivial, reduces to the case of one-dimensional flow through horizontal ground, for which solutions already exist. The methodology is generally applicable to the calculation of distinct seepage regimes across unsaturated slopes with different hydraulic properties under both stationary and transient conditions. The paper also defines the gradient of the piezometric head parallel to the slope, which is the Neumann boundary condition to be imposed on slope sections perpendicular to the ground surface. The rigorous definition of this gradient overcomes the need of imposing arbitrary boundary conditions in finite-element models. Finally, the paper demonstrates that all infiltrated water crosses the slope along the shortest path – namely, the path normal to the surface – while the flow parallel to the slope is entirely fed by an upstream source at infinite distance.