The seepage exclusion problem for spherical cavities

Knight, J. H.; Philip, J. R.; Waechter, R. T.

doi:10.1029/wr025i001p00029

Cited by 37 publications

(43 citation statements)

References 6 publications

(3 reference statements)

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“…Detailed studies of the effects of the downward seepage rate, soil hydraulic properties, and the geometrical effects of cavity (and by implication, barrier) shape and size have been made. Philip et al [1989a] gave the analysis for circular cylinders, Knight et al [1989] gave the analysis for spheres, Philip et al [1989b] gave the analysis for parabolic cylinders and paraboloids, and Philip [1989a] gave the analysis for sloping cylinders of arbitrary cross section. Philip [1989b] gave asymptotic solutions for elliptic cylinders, spheroids, strips, and discs, and Philip [1990a] gave asymptotic solutions for ellipsoids with arbitrary axial ratios, the results depending primarily on curvature at the upstream stagnation point.…”

Section: Seepage Exclusion Analyses Relevant To Maximal Capillary Barmentioning

confidence: 99%

Seepage shedding by parabolic capillary barriers and cavities

Philip¹

1998

Water Resources Research

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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...

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Section: Seepage Exclusion Analyses Relevant To Maximal Capillary Barmentioning

confidence: 99%

Seepage shedding by parabolic capillary barriers and cavities

Philip¹

1998

Water Resources Research

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“…Philip and his colleagues (Knight et al, 1989;Philip, 1989a,b;Philip 1990;Philip et al, 1989a,b) reported analytical studies on the perturbation of vertical downward flow of water around cavities in unsaturated soils. Their work was concerned with the flow in 'Gardner' soils in which the hydraulic conductivity of unsaturated soils is described by an exponential function of the soil-water pressure.…”

Section: Introductionmentioning

confidence: 94%

Water exclusion from tunnel cavities spanning a water table

Youngs

Kacimov

2005

Journal of Hydrology

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The vertical downward flow of water in unsaturated soils is perturbed by the presence of cavities. Analysis of the flow problem has shown that there is for a given situation a critical shape of a cavity for it to exclude water entry when the soil-water pressure at the cavity wall is everywhere the air-entry value for the soil and the cavity wall is a streamline. In this note cavities spanning a water table are considered when the water table is caused by artesian pressure in a water-bearing substratum. Building on previous analysis, critical shapes for such cavities are obtained for particular circumstances, thus showing that situations can exist for cavities not to fill with water although protruding below the water table. It is noted that the analysis used to obtain a solution to this problem is the same as that for the groundwater seepage problem of water movement to a waterbearing substratum under pressure from infinite ponded-water regions separated by a long island strip. q

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“…Or and Gheuehei [ 19991 concluded that dripping is sensitive to the ambient water vapor pressure in an open cavity and is likely to occur only under very high vapor pressures close to saturation. Philip et al [1989aPhilip et al [ , 1989b, Knight et al [1989] and Philip [1989aPhilip [ , 1989bPhilip [ , 1990 were the first to address the capillary barrier problem as it directly relates to seepage into buried cavities. They developed several steady-state analytical solutions for various-shaped cavities buried in a homogeneous unsaturated porous medium and subject to a uniform, constantdownward percolation flux (&).…”

Section: Capillary Barriersmentioning

confidence: 99%

Seepage into an Underground Opening Constructed in Unsaturated Fractured Rock Under Evaporative Conditions

Trautz¹,

Wang²

2001

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The seepage exclusion problem for spherical cavities

Cited by 37 publications

References 6 publications

Seepage shedding by parabolic capillary barriers and cavities

Seepage shedding by parabolic capillary barriers and cavities

Water exclusion from tunnel cavities spanning a water table

Seepage into an Underground Opening Constructed in Unsaturated Fractured Rock Under Evaporative Conditions

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