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HYDC02 12/5/05 5:37 PM Page 20

20 Chapter Two

Fig. 2.2 Relation between median grain
size and water storage properties of typical
alluvial sediments. After Davis and De
Wiest (1966).

against the force of gravity is termed the specific reten- pressure closes any remaining openings such that
tion, S . As shown in Fig. 2.2, the sum of the specific the effective porosity of these formations substan-
r
yield and specific retention (S + S ) is equal to the total tially declines.
y r
porosity, n. It is useful to distinguish the total porosity
from the effective porosity, n , of a porous material.
e
The total porosity relates to the storage capability of 2.3 Darcy’s law and hydraulic conductivity
the material whereas the effective porosity relates
to the transmissive capability of the material. Water contained within the interconnected voids of
In coarse-grained rocks with large pores, the capil- soils and rocks is capable of moving, and the ability
lary films that surround the solid particles occupy of a rock to store and transmit water constitutes its
only a small proportion of the pore space such that S hydraulic properties. At the centre of the laws that
y
and n will almost equal n. In fine-grained rocks and govern the behaviour of groundwater flow in satur-
e
clay, capillary forces dominate such that S will almost ated material is that formulated empirically by the
r
equal n, but n will be much less than n. These vari- French municipal engineer for Dijon, Henry Darcy,
e
ations can be described by the term specific surface in 1856. Using the type of experimental apparatus
area, S , defined as the ratio of total surface area of the shown in Fig. 2.3, Darcy studied the flow of water
sp
interstitial voids to total volume of the porous mater- through porous material contained in a column and
4
ial. In sands, S will be of the order of 1.5 × 10 m −1 found that the total flow, Q, is proportional to both
sp
9
but in montmorillonite clay it is about 1.5 × 10 m −1 the difference in water level, h − h , measured in
2
1
(Marsily 1986). These properties are important in the manometer tubes at either end of the column and the
adsorption of water molecules and dissolved ions on cross-sectional area of flow, A, and inversely propor-
mineral surfaces, especially on clay. tional to the column length, L. When combined with
In the case of a fissured or fractured aquifer, such the constant of proportionality, K, Darcy obtained:
as weathered limestone and crystalline rocks, water
contained in the solid matrix is typically immobile h ( − h 2 )
=
1
Q KA eq. 2.4
and the only effective porosity is associated with the L
mobile water contained in the fissures and fractures.
With increasing depth, the frequency of fissures and In general terms, Darcy’s law, as it is known, can be
fractures decreases and the increasing overburden written as: