Page 99 - Analysis and Design of Energy Geostructures

Heat and mass transfers in the context of energy geostructures 71

in such a way: (1) it assumes evenly distributed material constituents in space; (2) it
representatively describes the material characteristics via homogeneous effective properties
associated with all points of the medium; and (3) it neglects heterogeneity at smaller
scales. Typically, the linear scale characterising the REV needs to be much smaller
than the scale of the global problem considered and much greater than the scale of the
motion of the particles that compose the material. The previous requirements ensure
that the size selected for the REV removes the effect of inhomogeneity at smaller
scales (e.g. microscopic) without eliminating the potential inhomogeneity at greater
scales (e.g. macroscopic) (see, e.g. Vulliet et al., 2016). This fact includes that as far as
the REV is independent of time and location within the medium, the different equa-
tions established are independent of the geometry of the REV. In the following, the
REV concept is employed to describe materials in their solid, liquid, or gaseous state.
When dealing with the analysis of geomaterials, the REV concept is often applied
in conjunction with the concept of volume fraction, which represents the essence of
the theory of porous media expanded by Bedford and Drumheller (1983) and De
Boer and Ehlers (1988). In this context, the REV is composed of the sum of the
volumes of any different subregions constituting it according to their volume fraction.
In the following the volume fraction concept is employed to describe geomaterials.
Based on the above, reference is made in the following to continuous and homo-
geneous materials that are characterised by at least one phase. Soil, rock and concrete
are assumed as multiphase materials characterised by one solid phase constituted by the
material particles and one fluid phase constituted by water or air (cf. Fig. 3.1); in other
words, partially saturated geomaterials are not considered, while materials fully satu-
rated with a fluid are accounted for. Steel and plastic are assumed to be materials char-
acterised by a unique solid phase. The fluid circulating in the pipes of energy
geostructures is assumed in the simplest case to be characterised by a unique liquid
phase constituted by water, but more generally by a liquid mixture constituted by
water and an antifreeze liquid. The fluid flowing in built environments adjacent to
energy geostructures is characterised by one gaseous phase constituted of air.

Figure 3.1 (A) Typical multiphase representation of a coarse-grained matrix of geomaterial and (B)
equivalent continuum homogenisation.