Citation:
E. G. Youngs , A. R. Kacimov and Yu. V. Obnosov, Water exclusion from tunnel cavities in the saturated capillary fringe, Advances in Water Resources, Volume 27, Issue 3, March 2004, Pages 237-243
Abstract:
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.