## Water Flow in Saturated Soil

When the pore system is completely filled with water, and hence pressure potential h is positive throughout the system, the coefficient of proportionality in Darcy's law (5.105) is called the saturated hydraulic conductivity Ks. The value of Ks is practically a constant, chiefly because the soil pores are always filled with water, and it depends not only on soil physical properties (e.g., bulk density, soil texture), but also on fluid properties (e.g., viscosity).

When water is incompressible and the solid matrix is rigid (or, of course, when the flow is steady), the flux equation (5.105) and the continuity equation (5.106) reduce to

Laplace's equation for H:

Values of saturated hydraulic conductivity Ks are obtained in the laboratory using a constant-head permeameter (basically, a facility reproducing the original experiment carried out by Darcy to demonstrate the validity of his flux law) or a falling-head per-meameter [2]. Field measurements of hydraulic conductivity of a saturated soil are commonly made by the augerhole method [17].

One alternative to direct measurements is to use theoretical equations that relate the saturated hydraulic conductivity to other soil properties. By assuming an equivalent uniform medium made up of spherical particles and employing the Hagen-Poiseuille equation for liquid flow in a capillary tube, the following Kozeny-Carman relation holds between saturated hydraulic conductivity Ks and soil porosity p:

where p is defined as the dimensionless ratio of the pore volume to the total soil volume, A is the specific surface area of the porous medium per unit volume of solid (m2/m3), and c is a constant (m3s-1) [18]. Mishra and Parker [19] used van Genuchten's water retention curve [VG retention curve, Eq. (5.104)] to derive the following expression:

where 6s,9r, and a are parameters as defined by Eq. (5.104), and d is equal to 108 cm3 s-1 if Ks is expressed in cm s-1 and a in 1/cm.

In layered soils, it is relatively simple to determine the equivalent saturated hydraulic conductivity of the whole porous system by analogy with the evaluation of the equivalent resistance of electrical circuits arranged in series or parallel. For soil layers arranged in series to the flow direction (the more common case), the flow rate is the same in all layers, and the total potential gradient equals the sum of the potential gradient in each layer. Conversely, in the parallel-flow case, the potential gradient is the same in each layer, and the total flow is the sum of the individual flow rates.

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