Three-Dimensional Analytical Solutions for Unsaturated Seepage Problem

Transient, three-dimensional flux equations are solved by neglecting capillary forces in the first half of the paper, and in the second the steady-state seepage, where the capillary forces are significant, is treated. The following conclusions can be drawn by analysis of solutions for the cases of no capillary effects in unsaturated, anisotropic, layered slopes: (1) The seepage flow for these cases depends on the anisotropy of the soil. It further depends on the slope of the principal axis of the conductivity tensor. The seepage flow is completely independent of the slope of the soil surface. These findings make possible a new description of lateral flow mechanisms in slopes. Thus, the surprising result is that soil can possess a kind of “hydrological memory.” This is because the conductivity tensor can stay unchanged while the soil surface is altered. (2) Based on these findings, when a land fill cover is being designed, it is possible to obtain an optimal angle to minimize infiltration. Solutions for the three-dimensional seepage problem with axisymmetric boundary fluxes and significant capillary effects are obtained by the power-series method. An important group of solutions with noncontinuous (steplike) boundary fluxes is obtained by superposition of those solutions with constant boundary fluxes for semi-infinite and finite mediums.