Solution of two-dimensional problems of unsteady heavy-fluid seepage into unsaturated porous soil on the basis of an instantaneous saturation model

Abstract

Two-dimensional problems of the unsteady seepage of a heavy fluid into a uniform unsaturated porous soil from a single channel and from an infinite periodic system of identical channels are solved. The fluid level in the channel is a known function of timet, which simulates the propagation of the fluid along a furrow normal to the plane of the problem. Seepage into the soil, which occupies the space outside (mainly below) the channel, takes place under the influence of the force of gravity and begins at the momentt=0 after it is instantaneously filled with fluid. On the interval 0 <t < t₁ the height of the fluid in the channel is constant, and whent=t ₁ it falls instantaneously to some other level, also constant. This may be the zero level, which coincides with the bottom of the channel. The problem in which the fluid level in the channel rises is also considered.