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Figure 4.2 The soil system contains three phases.
pore scale, the three phases - solid, liquid and gas - form the soil system ( Figure 4.2 ),
and the atoms, molecules and ions are the invisible elements of the system. Because
of the exceedingly large number of these elements, it is usually more convenient to
choose a volume containing a suficiently large number of atoms, molecules or ions
so that their mean statistical behaviour is relevant (Scott, 2000 ). A volume enclosing
such a continuum molecular mixture is called a representative elementary volume
(REV). The REV must be large compared to the mean free path of molecules caused
by Brownian motion. The concept of REV was developed because of the need to
describe or lump the physical properties at a geometrical point. We say that we give to
one point in space and time the value of the property of a certain volume surrounding
this point. The REV is used to deine and sometimes to measure the mean properties
of the volume in question. Consequently this concept involves an integration in space.
According to De Marsily ( 1986 ) the size of the REV is determined by two points:
1. The REV should be suficiently large to contain a soil volume that allows the deinition
of a mean global property while ensuring that the effects of the luctuations from one
pore to another are negligible.
2. The REV should be suficiently small that the parameter variations from one domain to
the next may be approximated by continuous functions, in order that we can use differ-
entiation calculus.
Figure 4.3 illustrates how to choose the size of the REV. The size of the REV is
generally linked to the existence of a lattening of the curve that connects the physical
properties with the spatial dimension. It is an averaging of the soil physical properties
within the volume. Obviously, the size of the REV varies widely with soil physical
properties, location and time and is somewhat arbitrary (Scott, 2000 ). The REV con-
cept can be used to integrate from the Navier-Stokes equations of luid low at pore
scale to the less complicated Darcy's law at the macroscopic scale. In this chapter
we start after this integration step and focus on the macroscopic scale with the Darcy
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