Layered Heterogeneity Problem
At regional scales, sedimentary rocks and unconsolidated lacustrine and marine deposits often exhibit a vertically-layered heterogeneity, with each individual bed (or layer) in the formation having a homogenous conductivity value K1, K2, etc (see Figure 1). Such layered heterogeneity can result in significant contrast in hydraulic conductivity within a layer sequence (i.e., several orders of magnitude).
These type of groundwater environments are known to act like a single homogenous, anisotropic aquifer with an effective vertical conductivity that is much smaller than the effective horizontal conductivity. Within a mathematical framework, explain why this is the case. Consider flow perpendicular to the layering and parallel to the layering. Also explain why effective anisotropy increases as aquifer thickness increases.
To make the analysis more concrete, you may use the following information from a hypothetical borehole profile:
- Layer 1:K1 = 85.0 ft/d; b1 = 2.5 ft
- Layer 2: K2 = 2.8 ft/d; b2 = 6.1 ft
- Layer 3: K3 = 22.1 ft/d; b3 = 4.4 ft
- Layer 4: K4 = 0.7 ft/d; b4 = 1.9 ft
- Layer 5: K5 = 15.5 ft/d; b5 = 2.2 ft
Figure: Outcropping of coarse-grained elements or inclusions (gravel, pebbles, stones, etc.) within a fine soil matrix (sand, clays, lime, etc.). K values represent different hydraulic conductivites; b values represent thicknesses of the layers. Adapted from Traduis Toncv: https://traduis-toncv.com/matrix-coarse-grained-soils-bibliography-01/