HGC Gradient Masthead


by: A. Michael Geddis

Covers made of earthen materials are used for closure of many different substrates, such as spent ore heaps, waste rock dumps, tailings impoundments, landfills, contaminated industrial complexes, and mixed waste sites.

The most common cover performance criteria are: reducing infiltration through the cover and minimizing leaching of hazardous substances from the substrate. The three most important determinants of cover performance are thickness, moisture status, and capillary break strength. In many applications, thickness is controlled by cost. A moist cover will transmit more water than a dry cover due to decreased storage capacity and increased permeability. Earthen covers minimize infiltration by promoting runoff of incident precipitation, and/or storing precipitation in the cover material that later evaporates. These are termed store-and-release covers. The moisture is stored above a capillary break engineered at the interface between fine-grained and coarse-grained materials.

The Capillary Break

The capillary break forms because the larger average pore diameter in the underlying coarse material cannot extract water by capillarity from the smaller pore diameters in the fine material, even when most pores in the fine material at the interface are saturated. Unsaturated flow occurs across the interface at locations where materials with similar pore sizes meet and can transmit water at the ambient interfacial pore pressure. Unfortunately we cannot directly measure the strength of a capillary break because our methods are too invasive. The question is then, what is the best information to collect to estimate the strength of the capillary break over time with variable (realistic) climatic conditions?

Designing covers to create a strong capillary break reduces uncertainty in estimating cover thickness. Depending on cover area, location of the borrow source, and amount of material handling, a 10% decrease in cover thickness could result in considerable cost savings.

Figure 1: Moisture Regimes Within Two Typical Soil CoversSome Theoretical Considerations

Two typical covers are shown schematically in Figure 1. Covers usually consist of a fine-grained layer over a coarse-grained substrate (Cover A) or a composite cover including a fine-grained layer (Cover B). In Cover B the fine-grained layer at the surface is designed to prevent infiltration from entering the coarse-grained intermediate layer, and the capillary break occurs at the interface between these two engineered materials. Water can only enter an underlying coarse layer when water pressure in the fine-grained layer exceeds the ability of its dominant pore size class to hold the water against gravity. When this pressure is exceeded, unsaturated flow occurs into the pores that can transmit the water at the ambient interfacial pore pressure. The main component of this pore pressure is termed soil suction (h) in centimeters (cm) or the height of water which may be drawn upward against gravity.


where: s is the surface tension
  r is the water density
  g is the gravitational acceleration
  r is the capillary radius (mm)

Equation (1) is used to estimate the thickness of the capillary fringe above water table aquifers.1 Equation (1) also tells us that only smaller diameter pores will be filled with water as we move upward through the fringe. This moisture regime is similar to that found above a capillary break.

When suction is applied to a laboratory soil sample, water is removed from pores that are too large to resist by capillarity. Every soil has a characteristic way of releasing pore water, depending on its distribution of pore sizes. A moisture characteristic curve describes the relationship between the applied suction and the water content (q) of the soil. Experimental relationships between q and h have been determined for many types of soil. The selection of these parameters for very coarse or stony soils is fraught with uncertainty and is a current research topic. Recently, databases of unsaturated hydraulic parameters based on soil textural characteristics, such as UNSODA2, have become popular.

A widely used theoretical relationship between q and h is a closed-form equation by van Genuchten3:

Equation 2(2)

where: a is a curve fitting parameter [1/cm]
  m equals 1-1/n is also a curve fitting parameter [unitless]
  qs is the saturated volumetric water content [cm3/cm3]
  qr is the residual volumetric water content [cm3/cm3]

Figure 2 shows curves based on (2) for two typical soils, a fine-grained cover, and a coarse-grained substrate. Because the soil suction must be continuous throughout a profile regardless of layering, we see a discontinuity in water content in Figure 2 where a single soil suction results in different moisture contents in the cover and substrate. This discontinuity is termed a capillary break, an interface where most infiltrating water is impeded from draining downward.

With van Genuchtenís solution, the unsaturated hydraulic conductivity may be determined using Maulemís4 equation:


where: is the unsaturated hydraulic conductivity [cm/sec]
  Ks is the saturated hydraulic conductivity [cm/sec]

Figure 3: Hydraulic Conductivity versus Soil SuctionFigure 3 shows curves of versus soil suction using (3) for the same two materials. These curves allow calcuation of the rate of moisture movement through the cover/substrate system.

What Information Is Needed?

Two pieces of information permit estimation of capillary break strength: 1) the unsaturated hydraulic parameters of the cover and substrate, and 2) the moisture regime of the cover. The moisture regime identifies pores transmitting water to the capillary break, and is best predicted using numerical methods with realistic atmospheric boundary conditions.

is the variable that determines the quantity of unsaturated flow, and therefore will determine the distribution of infiltrated precipitation in the cover. Measurement of this variable is ideally performed on a pilot-scale cover, and on the substrate, using a tension infiltrometer. This will yield paired values of h and for each location. Each measure-ment should be accompanied by a measurement using a disc permeameter. A tension infiltrometer is not useful on coarse-grained material, and either a disc permeameter or sealed, double-ring infiltrometer could be used to obtain Ks. The remaining parameters (a, n, qr, and qs) may be based on literature estimates of similarly textured material. This technique is considered valid for several reasons:

  • Because the shape of the unsaturated hydraulic conductivity curves are maintained for a given moisture characteristic curve, the largest uncertainty in will result from the selection of Ks. The unsaturated hydraulic conduc-tivity curve is pinned to Ks at h = 0, and is shifted vertically (see Figure 3) depending on the selection of Ks. This makes understanding the range of Ks at the surface crucial.

  • With sufficient computing power, numerous combinations of the assumed hydraulic parameters could be evaluated, within the range of in-situ measured Ks. Commercially available unsaturated flow models now include parameter estimating routines. The results of a numerical simulation can be evaluated inversely to determine the validity of initial parameter selection.
  • The spatial variability of in-situ unsaturated hydraulic parameters may be larger than the variability of these parameters when estimated from laboratory measurements.
  • Laboratory measurements are destructive and may result in parameters that are not representative of in-situ conditions. For covers of 12- to 18-inch thickness, a tension infiltrometer measurement may test most of the cover thickness. A disc permeameter test may penetrate a pilot-scale cover, and inverse methods can then help describe the change in flow rate with time as the zone of saturation encounters the interface between cover and substrate.

Two future Gradient articles will compare and contrast laboratory and in-situ measure-ment of the moisture characteristic parameters and outline a defensible investigation of store-and-release covers, particularly in dry climates, using field measurements and numerical modeling.


1Hillel, D. 1998. Environmental Soil Physics. Academic Press, New York.

2Leij, F.J., W.J. Alves, and M. Th. Van Genuchten. 1996. The UNSODA Unsaturated Soil Hydraulic Database. US Salinity Laboratory, USDA-ARS, EPA/600/R-96/095.

3Van Genuchten, M. Th., 1980. A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Sci. Soc. Amer. Jour., 44:892-898.

4Maulem, Y. 1976. A New Model for Predicting the Unsaturated Hydraulic Conductivity of Unsaturated Porous Media. Wat. Resour. Res., 12:513-522.

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