Seepage shedding by parabolic capillary barriers and cavities

Abstract

Abstract. The 1989 analysis of seepage exclusion from underground cavities established the parabolic and paraboloidal geometries as the most efficient. That work is extended here to an analysis of seepage into the cavity. The cavity results carry over to maximal capillary barriers of macroscopically coarse material such as smooth gravel. The analysis is extended further to the conventional submaximal capillary barrier of a coarser soil underlying finer soil. The shedding efficiency of the submaximal barrier is always less than that of the maximal barrier, and in worst case scenarios, poorly designed submaximal barriers actually concentrate seepage into the region they are supposed to protect. The 1989 work, supplemented by the present study, provides a detailed physical basis for the recent proposal that the most efficient geometry for capillary barriers is parabolic. In some (but not all) circumstances barriers are ineffective if their horizontal dimensions exceed a few sorptive lengths. IntroductionAs customarily envisaged, a capillary barrier consists of an interface, usually artificially constructed, between an upper fine-textured soil and a lower coarse-textured one. The purpose of the barrier is to divert downward unsaturated seepage laterally and around a repository or structure from which it is desired to exclude water. If, on the other hand, the layer below the barrier is extremely coarse, consisting for example of rounded coarse gravel, that layer will operate like an air-filled cavity. Evidently, fines from the upper layer must be prevented from clogging the lower layer, for instance, by a fabric membrane at the interface. Note that convexity of the coarse particles minimizes the possibility of capillary condensation [Philip, 1964[Philip, , 1977[Philip, , 1978 and resulting film flow in the lower layer.Water will then move across the barrier only when two conditions are met: (1) the interface moisture potential is nonnegative; that is, the water pressure there equals or exceeds the air pressure and (2) the gradient of total potential at the interface is downward. We shall call such barriers maximal. Importance of Parabolic and Paraboloidal GeometriesAn important element in the work of Philip et al. [1989b] was the discovery of the central role of parabolic and paraboloidal geometries in studies of the exclusion and shedding of unsaturated seepage. They found that for parabolic-cylindrical and paraboloidal cavities (and maximal capillary barriers of these shapes), ß at the cavity wall is constant, independent of position. In the regimes of total shedding the wall is thus not only a stream surface but also an equipotential surface for •. Such cavities (barriers) either exclude or partially admit seepage uniformly everywhere, and it is readily shown that these geometries are therefore the most efficient in excluding or minimizing downward seepage.Philip et al. [1989b] found that the special properties of parabolic geometries held not only for the quasilinear analysis but also for the full nonlinear an...

Oblique Porous Composite as Evaporating “Cap”: Do Desert Dunes Preserve Moisture by Capillary Barriers and Tilt of Their Slopes?

“…There are several daunting questions relevant to dune hydrology: How can the known models of “single‐tilt” capillary barriers (Philip, ; Ross, ), used by engineers for protection of landfills against infiltration, be adopted to dunes where a natural inter‐cross‐bedding of these barriers induces a complex path of infiltrated water and ultimate detention of wet pockets, which do not descend further to the regional water table? Why do the topographically oblique slopes of dunes (hillocks, nabkhas) evaporate less from the subjacent sandy subsurface massifs as compared with flatlands? Does stratification of the dunes act as a capillary barrier and contribute to reducing evaporation? …”

Boundary layer analysis of unsaturated seepage into cylindrical cavities

“…Seepage into cavities of other shapes has been analyzed by Selker [1997] and Philip [1998], but these studies also address cavities with smooth walls. An extension of the quasi-linear analysis of Philip et al [1989] to irregularly shaped cavities is provided, however, by Hughson and Dodge [2000].…”

Unsaturated Flow Through Spherical Inclusions with Contrasting Sorptive Numbers

“…This expanded the earlier work of Philip et al (1989) and Knight et al (1989) dealing with fully impervious inclusions relevant to descriptions of flow in regions proximate to macropores, tunnels, and cavities and around underground obstacles such as stones or structures. This relates to a series of solutions to the refraction (and reflection) problem, originally addressed in other fields by Maxwell and by Rayleigh (e.g., Strutt, 1871; Maxwell, 1873), and later by Philip (1998) for open parabolic shapes. Also, contributions are by Bear (1972), Kacimov (2004)(personal communication, August 2004), Frenkel (1949), Bystrov (1959), and Irmay (1964) These new papers demonstrated the use of the AEM to an unsaturated flow domain.…”