Critical tunnel cavities for water exclusion in "Green and Ampt" and "Gardner" soils

The limiting case of the analytical solution for the downward flow of water in a Green and Ampt soil around a tunnel cavity of critical shape resting on a permeable substratum at infinite depth gives the shape of the cavity and also the shape of the fringe surface of the surrounding tension-saturated region as parabolas. The cavity shape is compared with the parabolic shape obtained analytically for the water exclusion from a critical tunnel cavity in a Gardner soil of infinite extent where parabolic isobaric surfaces surround the cavity. The results are used to relate the parameters in the two models. They also add confidence for their use in soil hydrology.