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

Abstract

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 K1, and sorptive number α, whether or not seepage water will enter a cylindrical cavity.

Water film flow along fracture surfaces of porous rock

“…This concept might be applicable to a wide range of natural surfaces. These include flows along individual sides of fracture pathways through rock, surfaces of soil aggregates, seepage faces, and surfaces of caves and excavations [Philip et al, 1989]. The wetting characteristics of a natural rough surface have previously been approximated by simple corrugated surfaces [Philip, 1978].…”

Seepage into drifts with mechanical degradation

“…The amount of water flowing into a drift controls the corrosion rates of waste packages, the waste mobilization rates, and transport rates of radionuclides leaving the drift. Philip et al (1989) presented the general theory of water entry into subterranean openings from steady, uniform downward flow, and developed an analytical solution to the exclusion problem for circular cylindrical cavities acting as capillary barriers. At the stagnation point at the crown of a cylindrical opening or a drift, water accumulated, reaching locally saturated conditions, and eventually seeps into the drift.…”

“…From the analytical solution of Philip et al (1989), we can establish whether or not water enters the drift for a given combination of percolation flux, characteristic drift length, saturated hydraulic conductivity and a', where a' is a fitting parameter controlling the rate of relative permeability decrease with increasing capillary pressure in the Gardner model (1958). A January 2002 threshold percolation flux is defined as the critical value above which water will enter the drift.…”

Field investigation into unsaturated flow and transport in a fault: model analyses

“…Matrix imbibition occurred at interfaces between fractures and the matrix and between the fault and the matrix. When water arrived at the intersection between the fault and the niche, it could not immediately seep into the niche until the capillary pressure became zero because of capillary barrier effects (Philip et al, 1989;Birkholzer et al, 1999). The capillary barrier can divert flow away from the opening, resulting in that only a portion of water arriving at the niche ceiling actually seeps into the niche.…”