6.3.2 Hydraulic Conductivity

Hydraulic conductivity of soil is a measure of the its ability to transmit water when submitted to a hydraulic gradient. The coefficient of permeability (k) represents the soil’s ability to transmit and drain water. This, in turn, indicates the ability of the soil to change matric suction as a result of environmental changes (Fredlund and Rahardjo, 1993).Water coefficient of permeability of saturated soil is a function of void ratio (e) only. For unsaturated soil, the water coefficient of permeability is a function of void ratio (e) and volumetric water content (θ). This relationship is commonly expressed by a suction-dependent hydraulic conductivity function, illustrated in figure 4.

 Figure 4: Typical suction dependent hydraulic conductivity function

The hydraulic conductivity function of unsaturated soil can be obtained through direct or indirect measurement. It depends on the intrinsic permeability and the degree of saturation of the material. Saturated hydraulic conductivity Ksat, describes water movement through saturated media. There are two broad categories of determining hydraulic conductivity:

Empirical approach by which hydraulic conductivity is correlated to soil properties like pore size, particle size distributions, and soil texture.

Experimental approach in which hydraulic conductivity is determined from hydraulic experiments using Darcy's law

The experimental approach is broadly classified into:

Laboratory tests using soil samples subjected to hydraulic experiments

Field tests that are differentiated into:

small scale field tests using observations of water level in soil cavities

large scale field tests, like pump tests in wells or by observing the functioning of existing horizontal drainage systems.

Hydraulic conductivity is defined by Darcy's law, which can be written as follows for one-dimensional vertical flow:

where U is Darcy's velocity (the average velocity of the fluid through a geometric cross-sectional area within the soil), h is hydraulic head, and z is vertical distance in the soil. The coefficient of permeability K, is also sometimes used as a synonym for hydraulic conductivity. Hydraulic conductivity is defined as ratio of Darcy's velocity to applied hydraulic gradient.

Hydraulic gradient is measured as the ratio of vertical distance between the point of intake to the point of discharge (a distance called head) to the length of flow from the two points.  Hydraulic conductivity depends on grain size, structure of the soil matrix, type of soil fluid, and saturation of the soil matrix. Important properties relevant to the solid matrix of the soil include pore size distribution, pore shape, tortuosity, specific surface, and porosity.

Flow through an unsaturated soil is more complicated than flow through continuously saturated pore spaces. in this case, macropores are filled with air, leaving only finer pores to accommodate water movement. Movement of water in unsaturated soil is dictated by differences in matric potential but not the gravity. The matric potential gradient is the difference in the matric potential of the moist soil areas (high matric potential) and nearby drier areas (low matric potential) into which the water is moving (Brady and Weil, 1999).