Fig. 4.28 Conceptual profiles (after Lu and Likos, 2004)

The slope of the suction head profiles at any time instant and spatial location is the suction head gradient and is given by

Semi-infinite boundary condition can be invoked in the analysis, if the test is terminated before water flow reaches the right boundary of the soil column. The water flux at any given cross-sectional area and time increment is equal to the change in volume of water between the cross-section under consideration and right boundary of the column. Thus, the change in volume of water at any given time instant between the cross-section under consideration and right boundary is

...........................................................(4.9)

where A is the cross-sectional area of the column; t₁ and t₂ are two different time instants; ΔV_w is the change in volume of water. This can be easily computed using the shaded area between t₁ and t₂ of the temporal water content profile. Hydraulic conductivity can be calculated using Darcy's law described as a ratio of apparent velocity to hydraulic gradient, when the apparent flow velocity is computed using the following expression

...............................................................................................(4.10)