Unsaturated seepage and subterranean holes: Conspectus, and exclusion problem for circular cylindrical cavities

This paper introduces the general theory of water exclusion from, or entry into, subterranean holes from steady uniform downward unsaturated seepage. Buried holes serve as obstacles to the flow and so increase water pressure at parts of the hole surface. When downward seepage is fast enough and/or the hole is large enough, water pressure increases to the point where a seepage surface forms and water enters the hole. Contrary to the conventional picture drawn from capillary statics, hydrodynamics shows that the larger the hole the more vulnerable it is to water entry. Cavity shape is important also. Applications include optimal design of configurations of tunnels and underground repositories (e.g., for nuclear wastes) against entry of seepage water. The theory also embraces the disturbance of seepage flows by buried impermeable obstacles such as stones and structures. The quasi‐linear exclusion problem for circular cylindrical cavities is solved. Both exact solutions and simple asymptotic results are found, and graphs and tables presented. The moisture field about the cavity exhibits upstream and downstream stagnation points and retarded regions: “roof‐drip lobes” in which the moisture content and downward flow velocity are augmented by water essentially deflected from the cavity roof, and the “dry shadow” region of reduced moisture content and flow velocity, essentially sheltered by the cavity. A practical consequence is that we can establish, for any given combination of downward seepage velocity, cavity radius, saturated hydraulic conductivity K 1 , and sorptive number α, whether or not seepage water will enter a cylindrical cavity.