..................................................................................(3.6)
where C is the dimensionless constant related to the geometry of the soil pores, H is the total head, and ∇H is the hydraulic head.
The Eq. (3.6) is in the form of Darcy's equation. Therefore, the hydraulic conductivity is the proportionality constant in the Darcy's equation which can be expressed as
..........................................................................................(3.7)
where Cd2 is termed as the intrinsic permeability or permeability, denoted by K , often used to differentiate the material properties from the fluid properties against the pore geometry. Permeability has the units of m2 and is dependent only on the pore size, pore geometry, and the pore size distribution. The permeability varies from 10-7 m2 for the gravel to 10-20 m2 for the fine clay. It can be easily verified using the above equations that the conductivity of water is several times higher than the air under the same applied gradient and for the same pore geometry. It can readily be recalled from the earlier discussion on the influence of the state variables on the density and viscosity of the fluid. One can easily verify the influence of such state variables on the hydraulic conductivity of air and water through unsaturated soils. Other than these material constants, chemical and electrical pore fluid characteristics also strongly influence the flow behavior in unsaturated clay soils. Such characteristics can also alter the fabric of the clay. The aforementioned discussion on the hydraulic conductivity is applicable to both saturated and unsaturated soil system. However, the constant related to the geometry of the soil pores will be strongly influenced by the tortuous paths formed due to the occluded/entrapped air in the pore space of the unsaturated soils. The foregoing discussion signifies that the ratio of flux ( q ) to the hydraulic gradient ( ∇H ) is non-linear under unsaturated conditions. Therefore, the hydraulic conductivity depends on the volumetric water content or the soil matric suction. The plot of flux versus hydraulic gradient is obtained as shown in Fig. 3.13. It results a family of straight lines passing through the origin. Each line represents a straight line having a slope equal to the hydraulic conductivity at the indicated moisture content, θI , as shown in the figure. The hydraulic conductivity is no longer constant and is dependent on the volumetric water content.