2.8 Drawing a Flow Net for a System with Anisotropic Hydraulic Conductivity
In an anisotropic system, hydraulic conductivity differs with direction. This is especially the case in groundwater basins comprised of layered sedimentary rocks of differing hydraulic conductivity. In such layered materials, groundwater flow that is roughly parallel to the layers preferentially flows through the higher hydraulic conductivity layers and thus meets less overall resistance than flow in the vertical direction, which must move through both the high and low hydraulic conductivity layers. In layered materials of differing hydraulic conductivity, the equivalent hydraulic conductivity perpendicular to the layers is lower than the hydraulic conductivity parallel to the layers. This is discussed in another Groundwater Project book (Woessner and Poeter, 2020) where the procedure for calculating one equivalent hydraulic conductivity for the parallel and perpendicular directions is provided.
Graphical construction of a flow net needs to be undertaken in an isotropic material. However, a flow net can be obtained for an anisotropic material by taking the following steps: 1) transform the geometry of the system to an equivalent isotropic system; 2) draw the flow net for the isotropic system; and, 3) transform the flow net back to the anisotropic system geometry. For an anisotropic system resulting from horizontal layering, the geometric transformation consists of either scaling the vertical z-axis by a factor of the square root of Kx/Kz, as shown in Figure 18a and b, or scaling the horizontal x-axis by a factor of the square root of Kz/Kx. The step-by-step procedure for drawing a flow net in a system with anisotropic hydraulic conductivity can be accessed through the link to Box 5 that is provided in Figure 18. The transformation can be used for both cross-sectional and plan-view flow nets. In an anisotropic system, flow lines and equipotential lines are not at right angles to one another as shown in Figure 18c.
Figure 18 – Click to view Box 5 for the step-by-step process of drawing groundwater flow nets in anisotropic systems. Drawing an anisotropic flow net: a) Flow system geometry; b) Flow system transformed with flow net drawn for isotropic conditions; c) Flow system returned to untransformed geometry with flow net for anisotropic conditions.