The hydraulic conductivity of unsaturated anisotropic soils has recently been described with a tensorial connectivity–tortuosity (TCT) concept. We present a mathematical formalization of the connectivity–tortuosity tensor, assuming that its principal axes coincide with those of the hydraulic conductivity tensor at saturation. The hydraulic conductivity tensor of such unsaturated anisotropic soils is given as the product of a scalar variable, the symmetric connectivity–tortuosity tensor, and the hydraulic conductivity tensor at saturation. The influence of the degree of saturation on hydraulic conductivity is illustrated for four well-defined synthetic soils through radial plots of the hydraulic conductivity scalar and of the reciprocal hydraulic resistivity scalar, both as a function of saturation. The resulting curves are ellipses. The eccentricity of these ellipses is a measure of the degree of anisotropy of the soil at a given saturation.

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