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Physical hydrogeology 23

Fig. 2.5 Macroscopic (Darcian) approach to the analysis of groundwater flow contrasted with the true, microscopic behaviour of
tortuous flowpaths.

tions require the use of more advanced techniques It is widely accepted that the statistical distribution
such as flow net analysis (Box 2.3) and groundwater of hydraulic conductivity for a geological formation
modelling (see Further reading and Section 5.9). is described by a log-normal probability density func-
tion with the average hydraulic conductivity calcu-
lated as a geometric mean. Trending heterogeneity
2.4 Isotropy and homogeneity within a geological formation can be regarded as
a trend in the mean hydraulic conductivity value.
Aquifer properties, such as hydraulic conductivity, An isotropic geological formation is one where the
are unlikely to conform to the idealized, uniform hydraulic conductivity is independent of the direc-
porous material whether viewed at the microscopic tion of measurement at a point in the formation.
or regional scale. The terms isotropy, anisotropy, If the hydraulic conductivity varies with the direc-
homogeneity and heterogeneity are used to describe tion of measurement at a point, the formation is
the spatial variation and directional trends in aquifer anisotropic at that point. The principal directions of
property values. anisotropy correspond to the maximum and mini-
If the hydraulic conductivity, K, is independent of mum values of hydraulic conductivity and are usually
position within a geological formation, the formation at right angles to each other. The primary cause of
is homogeneous. If the hydraulic conductivity varies anisotropy on a small scale is the orientation of clay
from place to place, then the formation is heterogene- minerals in sedimentary rocks and unconsolidated
ous. The type of heterogeneity will depend on the sediments. In consolidated rocks, the direction of
geological environment that gave rise to the deposit jointing or fracturing can impart strong anisotropy at
or rock type. As shown in Fig. 2.6, layered hetero- various scales, from the local to regional.
geneity is common in sedimentary rocks where each Combining the above definitions, and as shown
bed comprising the formation has its own hydraulic in Fig. 2.7, it is possible to recognize four possible
conductivity value. Strong, layered heterogeneity combinations of heterogeneity and anisotropy when
will be present in interbedded deposits of clay and describing the nature of the hydraulic conductivity of
sand. Similarly large contrasts can arise in cases of dis- a formation.
continuous heterogeneity caused by the presence of As a result of introducing anisotropy, it is also
faults or large-scale stratigraphic features. Trending necessary to recognize that in a three-dimensional
heterogeneity exists in formations such as deltas, allu- flow system the specific discharge or darcy velocity
vial fans and glacial outwash plains where there is (eq. 2.9) as defined by Darcy’s law, is a vector quantity
sorting and grading of the material deposits. Vertical with components q , q and q given by:
x y z
trends in hydraulic conductivity are also present in
consolidated rocks where permeability is dependent q =− K ∂ h , q =− K h ∂ , q =− K h ∂
on joint and fracture density. x x x ∂ y y y ∂ z z z ∂