Water exclusion from tunnel cavities in the saturated capillary fringe

The problem of water flow around a tunnel cavity located in the saturated capillary fringe on top of a very permeable, freely-draining substratum is considered for the critical non-leakage condition when there is uniform vertical downward flow through the upper surface of the saturated region. In this critical condition the soil-water pressure is equal to zero everywhere on the cavity wall that is also a streamline. The conditions at the upper fringe boundary are that the soil-water pressure is equal to the air-entry value of the soil and the flux through this surface is the uniform infiltration rate. The cavity surface and the fringe boundary which is elevated above the cavity position, are found through conformal mapping and the use of integral representations of nonstandard mixed boundary-value problems. They are calculated for a range of infiltration rates and compared with those obtained by assuming the upper fringe boundary to be horizontal. The exact analysis given here gives larger tunnel cavities than those given by the approximate treatment of the problem. The results have application in the design of underground repositories against entry of seepage water, the construction of protective capillary barriers and in the design of interceptor drainage systems.