Hydraulic conductivity

In science and engineering, hydraulic conductivity (K, in SI units of meters per second), is a property of porous materials, soils and rocks, that describes the ease with which a fluid (usually water) can move through the pore space, or fracture network.

[1] It depends on the intrinsic permeability (k, unit: m2) of the material, the degree of saturation, and on the density and viscosity of the fluid.

There are two broad approaches for determining hydraulic conductivity: The experimental approach is broadly classified into: The small-scale field tests are further subdivided into: The methods of determining hydraulic conductivity and other hydraulic properties are investigated by numerous researchers and include additional empirical approaches.

[2] Allen Hazen derived an empirical formula for approximating hydraulic conductivity from grain-size analyses: where A pedotransfer function (PTF) is a specialized empirical estimation method, used primarily in the soil sciences, but increasingly used in hydrogeology.

This procedure allows water to move through the soil under a steady state head condition while the volume of water flowing through the soil specimen is measured over a period of time.

By knowing the volume ΔV of water measured in a time Δt, over a specimen of length L and cross-sectional area A, as well as the head h, the hydraulic conductivity (K) can be derived by simply rearranging Darcy's law: Proof: Darcy's law states that the volumetric flow depends on the pressure differential ΔP between the two sides of the sample, the permeability k and the dynamic viscosity μ as: [4] In a constant head experiment, the head (difference between two heights) defines an excess water mass, ρAh, where ρ is the density of water.

This mass weighs down on the side it is on, creating a pressure differential of ΔP = ρgh, where g is the gravitational acceleration.

In the falling-head method, the soil sample is first saturated under a specific head condition.

[5] If the head drops from hi to hf in a time Δt, then the hydraulic conductivity is equal to Proof: As above, Darcy's law reads The decrease in volume is related to the falling head by ΔV = ΔhA.

In laboratory methods, the degree of disturbances affect the reliability of value of permeability of the soil.

Pumping test is the most reliable method to calculate the coefficient of permeability of a soil.

The method was developed by Hooghoudt (1934)[6] in The Netherlands and introduced in the US by Van Bavel en Kirkham (1948).

The cumulative frequency distribution is lognormal and was made with the CumFreq program.

Expressing Ki in m/day and di in m, the transmissivity Ti is found in units m2/day.

In a semi-confined aquifer, the water table is found within a soil layer with a negligibly small transmissivity, so that changes of the total transmissivity (Dt) resulting from changes in the level of the water table are negligibly small.

The resistance to vertical flow (Ri) of the ith soil layer with a saturated thickness di and vertical hydraulic conductivity Kvi is: Expressing Kvi in m/day and di in m, the resistance (Ri) is expressed in days.

) differ considerably, the aquifer is said to be anisotropic with respect to hydraulic conductivity.

The resistance of a semi-confining top layer of an aquifer can be determined from pumping tests.

[10] When calculating flow to drains[11] or to a well field[12] in an aquifer with the aim to control the water table, the anisotropy is to be taken into account, otherwise the result may be erroneous.